Abstract: An account of my interactions with Prof. Theodore Yao-tsu Wu of the California Institute of Technology.

Publication: Journal of Hydrodynamics Vol.: 31 No.: 6 ISSN: 1001-6058

ID: CaltechAUTHORS:20191218-152901688

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Abstract: This is a contribution to the special issue honoring the late John R. Blake of the University of Birmingham. All three authors had the pleasure of extensive technical interactions with John Blake during his career in the UK, USA and Australia and benefited both professionally and personally from his friendship. John’s work in developing fundamental mathematical solutions for Stokes’ flows and his application of those mathematical tools to analyses of microorganism locomotion led to special new insights into the world of small-scale swimming. This special issue devoted to John’s memory seems an appropriate occasion to present another fluid mechanical challenge associated with microorganisms, namely the dynamics of algal blooms. Though it is a special reduced-order model that is of limited practical value, John would have particularly enjoyed the analytical solution to the dynamics of algae that was presented by Rutherford Aris (1997, Reflections on Keats’ equation. Chem. Eng. Sci., 52, 2447–2455) in a somewhat eccentric paper. We revisit that solution in this paper and present an extension to Aris’ solution that includes sedimentation of the algae. We think that John would have enjoyed this solution and would, in all likelihood, have been able to expand upon it to include other features such as microorganism buoyancy variations (see, e.g. Kromkamp & Walsby 1990; Belov & Giles, 1997, Dynamical model of buoyant cyanobacteria. Hydrobiologia, 349, 87–97; Brookes & Ganf, 2001, Variations in the buoyancy response of Microcystis aeruginosa to nitrogen, phosphorus and light. J. Plankton Res., 23, 1399–1411), the death of algae (see, e.g. Serizawa et al., 2008a, Computer simulations of seasonal outbreak and diurnal vertical migration of cyanobacteria. Limnology, 9, 185–194; Reynolds, 1984, The Ecology of Freshwater Phytoplankton. Cambridge University Press), the swimming of algae (see, e.g. Pedley, 2016, Spherical squirmers: models for swimming micro-organisms. IMA J. Appl. Math., 81, 488–521) and other relevant hydrodynamic matters.

Publication: IMA Journal of Applied Mathematics Vol.: 83 No.: 4 ISSN: 0272-4960

ID: CaltechAUTHORS:20180725-162110263

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Abstract: All three authors had the pleasure of extensive technical interactions with John Blake during his career in the UK, USA and Australia and benefited both professionally and personally from his friendship. John’s work in developing fundamental mathematical solutions for Stokes’ flows and his application of those mathematical tools to analyses of micro-organism locomotion led to special new insights into that world of small-scale swimming. This special issue devoted to John’s memory seems an appropriate occasion to present another fluid mechanical challenge associated with micro-organisms, namely the dynamics of algae blooms. Though it is a special reduced-order model that is of limited practical value, John would have particularly enjoyed the analytical solution to the dynamics of algae that was presented by Rutherford Aris (1997) in a somewhat eccentric paper. We revisit that solution in this paper and present an extension to Aris’ solution that includes sedimentation of the algae. We think that John would have enjoyed this solution and would, in all likelihood, have been able to expand upon it to include other features such as micro-organism buoyancy variations (see, for example, Kromkamp et al. 1990, Belov and Giles 1997, Brookes and Ganf 2001), the death of algae (see, for example, Serizawa et al. 2008a, Reynolds 1984), the swimming of algae (see, for example, Pedley 2016), and other relevant hydrodynamic matters.

Publication: IMA Journal of Applied MathematicsISSN: 0272-4960

ID: CaltechAUTHORS:20170630-110356943

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Abstract: This paper presents a review of some of the recent developments in our understanding of the dynamics and instabilities caused by cavitation in pumps. Focus is placed on presently available data for the transfer functions for cavitating pumps and inducers, particularly on the compliance and mass flow gain factor which are so critical for pump and system stability. The resonant frequency for cavitating pumps is introduced and contexted. Finally emphasis is placed on the paucity of our understanding of pump dynamics when the device or system is subjected to global oscillation.

Publication: IOP Conference Series: Earth and Environmental Science Vol.: 49ISSN: 1755-1307

ID: CaltechAUTHORS:20161214-100327072

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Abstract: Extreme sports such as canyoneering have expanded greatly since the turn of the century yet little scientific attention has been paid to the analyses of the dangers of those activities. The author was much involved in promoting one such sport, namely canyoneering, and presents this paper as an example of the kind of fluids engineering analyses that are needed in order to objectively quantify those dangers and properly advise the participants. In canyoneering, the primary fluid-related sources of danger are the impact of falling water on the human body and the dangers a swimmer faces in a plunge pool. This paper presents rough evaluations of both dangers.

Publication: Journal of Fluids Engineering Vol.: 138 No.: 10 ISSN: 0098-2202

ID: CaltechAUTHORS:20160805-163914005

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Abstract: We generally think of bubbles as benign and harmless and yet they can manifest the most remarkable range of physical effects. Some of those effects are the stuff of our everyday experience as in the tinkling of a brook or the sounds of breaking waves at the beach. But even these mundane effects are examples of the ability of bubbles to gather, focus and radiate energy (acoustic energy in the above examples). In other contexts that focusing of energy can lead to serious technological problems as when cavitation bubbles eat great holes through ships' propeller blades or cause a threat to the integrity of the spillways at the Hoover Dam. In liquid-propelled rocket engines, bubbles pose a danger to the stability of the propulsion system, and in artificial heart valves they can cause serious damage to the red blood cells. In perhaps the most extraordinary example of energy focusing, collapsing cavitation bubbles can emit not only sound, but also light with black body radiation temperatures equal to that of the sun (Brennen 1995 Cavitation and bubble dynamics). But, harnessed carefully, this almost unique ability to focus energy can also be put to remarkably constructive use. Cavitation bubbles are now used in a remarkable range of surgical and medical procedures, for example to emulsify tissue (most commonly in cataract surgery or in lithotripsy procedures for the reduction of kidney and gall stones) or to manipulate the DNA in individual cells. By creating cavitation bubbles non-invasively thereby depositing and focusing energy non-intrusively, one can generate minute incisions or target cancer cells. This paper will begin by briefly reviewing the history of cavitation phenomena and will end with a vision of the new horizons for the amazing cavitation bubble.

Publication: Interface Focus Vol.: 5 No.: 5 ISSN: 2042-8898

ID: CaltechAUTHORS:20151013-103610353

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Abstract: Although the word ‘cavitation’ was originally coined by R. E. Froude and first cited by Barnaby and Thornycroft in 1895, the phenomenon was conjectured much earlier by L. Euler in his theory of water turbines in 1754. However, actual cavitation was first discovered and investigated by Barnaby and Parsons in 1893 when they found that the formation of vapour bubbles on the propeller blades was responsible for the sea-trial failure in 1885 of a British high-speed warship HMS Daring. In 1895, Parsons established the first water tunnel for cavitation study and discovered the relationship between cavitation and the damage to the propeller. It was Rayleigh who, in 1917, laid the theoretical foundation for cavitation study by solving the problem of the collapse of an empty cavity in a large mass of liquid.

Publication: Interface Focus Vol.: 5 No.: 5 ISSN: 2042-8898

ID: CaltechAUTHORS:20151204-095728652

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Abstract: This paper presents a review of some of the recent developments in our understanding of the dynamics and instabilities caused by cavitation in pumps. Focus is placed on presently available data for the transfer functions for cavitating pumps and inducers, particularly on the compliance and mass flow gain factor that are critical for pump and system stability. The resonant frequency for cavitating pumps is introduced and contexted. Finally emphasis is placed on the paucity of our understanding of pump dynamics when the device or system is subjected to global oscillation.

ID: CaltechAUTHORS:20170630-101600501

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Abstract: The issue of the transport of dissolved nutrients and contaminants between the sediment in the bottom of a lake or reservoir and the body of water above it is an important one for many reasons. In particular the biological and chemical condition of the body of water is intricately linked to these mass transport processes. As the review by Boudreau (Rev Geophys 38(3):389–416, 2000) clearly demonstrates those transport processes are very complex involving mechanisms as diverse as the wave-induced flux between the sediment and the overlying water and the effect of burrowing animals on the transport within the sediment as well as basic diffusion mechanisms. The present paper focuses on one facet of these transport processes; we re-examine the balance of diffusion and wave-induced advection and demonstrate that the wave-induced flux of a solute from submerged sediment is not necessarily purely diffusive as suggested by Harrison et al. (J Geophys Res 88:7617–7622, 1983) but can be dominated by a mean or time-averaged flux induced by the advective fluid motion into and out of the sediment caused by the fluctuating pressure waves associated with wave motion. Indeed along the subtidal shoreline where the fluctuating bottom pressures are greatest, wave-induced advection will dominate the mean, time-averaged transport of solute into or out of the sediment as suggested in the work of Riedl et al. (Mar Biol 13:210–221, 1972). However, the present calculations also indicate that this advective flux decreases rapidly with increasing depth so that further away from the shoreline the advective flux becomes negligible relative to the diffusive flux and therefore the latter dominates in deeper water.

Publication: Environmental Fluid Mechanics Vol.: 14 No.: 1 ISSN: 1567-7419

ID: CaltechAUTHORS:20140206-091622726

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Abstract: Preface: It is important to stress that there is always a significant danger associated with adventures into the wilderness. Those who wish to follow the adventure hikes in this book should be fully cognizant of those dangers and take appropriate precautions. The accounts are primarily intended for experienced hikers who will exercise informed judgment and caution. The hikes requiring technical expertise and equipment should never be undertaken without proper training and qualifications. Even given all this, the dangers should not be minimized. The accounts are offered with the understanding that readers will proceed entirely at their own risk. In "Precautions" we describe some of the precautions that minimize (but do not eliminate) the dangers and risks.

ID: CaltechAUTHORS:20140708-113008664

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ID: CaltechAUTHORS:20131115-115618475

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ID: CaltechAUTHORS:20140130-130352086

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Abstract: This paper presents a review of some of the recent developments in our understanding of the dynamics and instabilities caused by cavitation in pumps. Focus is placed on presently available data for the transfer functions for cavitating pumps and inducers, particularly on the compliance and mass flow gain factor, which are so critical for pump and system stability. The resonant frequency for cavitating pumps is introduced and contexted. Finally, emphasis is placed on the paucity of our understanding of pump dynamics when the device or system is subjected to global oscillation.

Publication: Journal of Fluids Engineering Vol.: 135 No.: 6 ISSN: 0098-2202

ID: CaltechAUTHORS:20131122-082823922

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Abstract: We investigate the shock dynamics of liquid flows containing small gas bubbles with numerical simulations based on a continuum bubbly flow model. Particular attention is devoted to the effects of distributed bubble sizes and gas-phase nonlinearity on shock dynamics. Ensemble-averaged conservation laws for polydisperse bubbly flows are closed with a Rayleigh–Plesset-type model for single bubble dynamics. Numerical simulations of one-dimensional shock propagation reveal that phase cancellations in the oscillations of different-sized bubbles can lead to an apparent damping of the averaged shock dynamics. Experimentally, we study the propagation of waves in a deformable tube filled with a bubbly liquid. The model is extended to quasi-one-dimensional cases. This leads to steady shock relations that account for the compressibility associated with tube deformation, bubbles and host liquid. A comparison between the theory and the water-hammer experiments suggests that the gas-phase nonlinearity plays an essential role in the propagation of shocks.

No.: 8
ID: CaltechAUTHORS:20130719-124326298

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Abstract: This paper presents a review of some of the recent developments in our understanding of the dynamics and instabilities caused by cavitation in pumps. Focus is placed on presently available data for the transfer functions for cavitating pumps and inducers, particularly on the compliance and mass flow gain factor which are so critical for pump and system stability. The resonant frequency for cavitating pumps is introduced and contexted. Finally emphasis is placed on the paucity of our understanding of pump dynamics when the device or system is subjected to global oscillation.

Publication: IOP Conference Series: Earth and Environmental Science Vol.: 15 No.: 1 ISSN: 1755-1315

ID: CaltechAUTHORS:20130719-125633115

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Abstract: This paper presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Stokes and Reynolds numbers. The experiments were performed in a coaxial rheometer that was designed to minimize the effects of secondary flows. By changing the shear rate, particle size, and liquid viscosity, the Reynolds numbers based on shear rate and particle diameter ranged from 20 to 800 (Stokes numbers from 3 to 90), which is higher than examined in earlier rheometric studies. Prior studies have suggested that as the shear rate is increased, particle-particle collisions also increase resulting in a shear stress that depends non-linearly on the shear rate. However, over the range of conditions that were examined in this study, the shear stress showed a linear dependence on the shear rate. Hence, the effective relative viscosity is independent of the Reynolds and Stokes numbers and a non-linear function of the solid fraction. The present work also includes a series of rough-wall experiments that show the relative effective viscosity is also independent of the shear rate and larger than in the smooth wall experiments. In addition, measurements were made of the near-wall particle velocities, which demonstrate the presence of slip at the wall for the smooth-walled experiments. The depletion layer thickness, a region next to the walls where the solid fraction decreases, was calculated based on these measurements. The relative effective viscosities in the current work are larger than found in low-Reynolds number suspension studies but are comparable with a few granular suspension studies from which the relative effective viscosities can be inferred.

Publication: Physics of Fluids Vol.: 24 No.: 1 ISSN: 1070-6631

ID: CaltechAUTHORS:20120320-075849559

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Abstract: In this opening lecture I will summarize some of the fundamentals of cavitation in the hope that this will allow attendees greater insight into the more advanced lectures which follow. Whether your primary interest is in the turbomachinery field or in the biological and bioengineering contexts in which cavitation is important these fundamentals are important in understanding the observed phenomena.

ID: CaltechAUTHORS:20111208-111956559

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Abstract: A time-domain model was developed to evaluate the dynamic response of pumping systems in the accelerating environment of rockets with a focus on cavitation. The model was first verified by comparing the results with measurements in ground-based tests of an LE-7A rocket engine. In these tests, various resonances occurred and levels of pump cavitation or incorporation of an accumulator altered them. The model results simulated the test data well, matching both the frequency and the amplitude. The test and model results also demonstrated the stability of the LE-7A propulsion system within nonaccelerating environments. Then, the model was used to examine the response of the propulsion system in accelerating frames; sinusoidal vehicle oscillations over a range of frequencies were explored. Under noncavitating conditions, the pressure amplitudes within the propulsion system did not substantially exceed the quasi-static acceleration head response ρah. However, under cavitating conditions (σ = 0.02), the same accelerations produced violent responses with pressure and flow amplitudes about 2 orders of magnitude greater than in noncavitating conditions. The obvious conclusion is that vehicle oscillations can cause substantial pressure and flow amplitudes, particularly when the pump is cavitating, even if the ground-based tests and the calculations in static frames indicate stable and well-behaved responses.

Publication: Journal of Spacecraft and Rockets Vol.: 48 No.: 4 ISSN: 0022-4650

ID: CaltechAUTHORS:20110907-073103948

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Abstract: The effect of distributed bubble nuclei sizes on shock propagation in a bubbly liquid is numerically investigated. An ensemble-averaged technique is employed to derive the statistically averaged conservation laws for polydisperse bubbly flows. A finite-volume method is developed to solve the continuum bubbly flow equations coupled to a single-bubble-dynamic equation that incorporates the effects of heat transfer, liquid viscosity and compressibility. The one-dimensional shock computations reveal that the distribution of equilibrium bubble sizes leads to an apparent damping of the averaged shock dynamics due to phase cancellations in oscillations of the different-sized bubbles. If the distribution is sufficiently broad, the phase cancellation effect can dominate over the single-bubble-dynamic dissipation and the averaged shock profile is smoothed out.

Publication: International Journal of Multiphase Flow Vol.: 37 No.: 6 ISSN: 0301-9322

ID: CaltechAUTHORS:20110713-152954571

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Abstract: Shock propagation through a bubbly liquid contained in a deformable tube is considered. Quasi-one-dimensional mixture-averaged flow equations that include fluid–structure interaction are formulated. The steady shock relations are derived and the nonlinear effect due to the gas-phase compressibility is examined. Experiments are conducted in which a free-falling steel projectile impacts the top of an air/water mixture in a polycarbonate tube, and stress waves in the tube material and pressure on the tube wall are measured. The experimental data indicate that the linear theory is incapable of properly predicting the propagation speeds of finite-amplitude waves in a mixture-filled tube; the shock theory is found to more accurately estimate the measured wave speeds.

Publication: Journal of Fluid Mechanics Vol.: 671ISSN: 0022-1120

ID: CaltechAUTHORS:20110328-100709784

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Abstract: This paper explores the phenomena associated with the emergence of gas bubbles from a submerged granular bed. While there are many natural and industrial applications, we focus on the particular circumstances and consequences associated with the emergence of methane bubbles from the beds of lakes and reservoirs since there are significant implications for the dynamics of lakes and reservoirs and for global warming. This paper describes an experimental study of the processes of bubble emergence from a granular bed. Two distinct emergence modes are identified, mode 1 being simply the percolation of small bubbles through the interstices of the bed, while mode 2 involves the cumulative growth of a larger bubble until its buoyancy overcomes the surface tension effects. We demonstrate the conditions dividing the two modes (primarily the grain size) and show that this accords with simple analytical evaluations. These observations are consistent with previous studies of the dynamics of bubbles within porous beds. The two emergence modes also induce quite different particle fluidization levels. The latter are measured and correlated with a diffusion model similar to that originally employed in river sedimentation models by Vanoni and others. Both the particle diffusivity and the particle flux at the surface of the granular bed are measured and compared with a simple analytical model. These mixing processes can be consider applicable not only to the grains themselves, but also to the nutrients and/or contaminants within the bed. In this respect they are shown to be much more powerful than other mixing processes (such as the turbulence in the benthic boundary layer) and could, therefore, play a dominant role in the dynamics of lakes and reservoirs.

Publication: Journal of Fluid Mechanics Vol.: 666ISSN: 0022-1120

ID: CaltechAUTHORS:20110307-145641113

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Abstract: Shock propagation through a bubbly liquid filled in a deformable cylindrical tube is considered. Quasi-one-dimensional bubbly flow equations that include fluid-structure interaction are formulated, and the steady shock relations are derived. Experiments are conducted in which a free-falling steel projectile impacts the top of an air/water mixture in a polycarbonate tube, and stress waves in the tube material are measured. The experimental data indicate that the linear theory cannot properly predict the propagation speeds of shock waves in mixture-filled tubes; the shock theory is found to more accurately estimate the measured wave speeds.

ID: CaltechAUTHORS:20111221-123516479

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Abstract: The effect of distributed bubble size on shock propagation in homogeneous bubbly liquids is computed using a continuum two-phase model. An ensemble-averaging technique is employed to derive the statistically averaged equations and a finite-volume method is used to solve the model equations. The bubble dynamics are incorporated using a Rayleigh-Plesset-type equation which includes the effects of heat transfer, liquid viscosity and compressibility. For the case of monodisperse bubbles, it is known that relaxation oscillations occur behind the shock due to the bubble dynamics. The present computations for the case of polydisperse bubbles show that bubble size distributions lead to additional damping of the shock dynamics. If the distribution is sufficiently broad, the statistical effect dominates over the physical damping associated with the single bubble dynamics. This smooths out the oscillatory shock structure.

ID: CaltechAUTHORS:20111213-124427981

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Abstract: The theory of the acoustics of dilute bubbly liquids is reviewed, and the dispersion relation is modified by including the effect of liquid compressibility on the natural frequency of the bubbles. The modified theory is shown to more accurately predict the trend in measured attenuation of ultrasonic waves. The model limitations associated with such high-frequency waves are discussed.

Publication: Journal of the Acoustical Society of America Vol.: 126 No.: 3 ISSN: 0001-4966

ID: CaltechAUTHORS:20090916-093310681

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Abstract: The behavior of liquid-solid flows varies greatly depending on fluid viscosity; particle and liquid inertia; and collisions and near-collisions between particles. Shear stress measurements were made in a coaxial rheometer with a height to gap ratio (b/r0) of 11.7 and gap to outer radius ratio (h/b) of 0.166 that was specially designed to minimize the effects of secondary flows. Experiments were performed for a range of Reynolds numbers, solid fractions and ratio of particle to fluid densities. With neutrally buoyant particles, the dimensional shear stress exhibits a linear dependence on Reynolds number: the slope is monotonic but a non-linear function of the solid fraction. Though non-neutrally buoyant particles exhibit a similar linear dependence at higher Reynolds numbers, at lower values the shear stress exhibits a non-linear behavior in which the stress increases with decreasing Reynolds number due to particle settling.

No.: 1027
ID: CaltechAUTHORS:KOOaipcp08

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Abstract: In many cavitating liquid flows, when the number and concentration of the bubbles exceeds some critical level, the flow becomes unsteady and large clouds of cavitating bubbles are periodically formed and then collapse when convected into regions of higher pressure. This phenomenon is known as cloud cavitation and when it occurs it is almost always associated with a substantial increase in the cavitation noise and damage. These increases represent serious problems in devices as disparate as marine propellers, cavitating pumps and artificial heart valves. This lecture will present a brief review of the analyses of cloud cavitation in simplified geometries that allow us to anticipate the behavior of clouds of cavitation bubbles and the parameters that influence that behaviour. These simpler geometries allow some anticipation of the role of cloud cavitation in more complicated flows such as those in cavitating pumps.

ID: CaltechAUTHORS:20111213-112942130

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Abstract: This reply addresses three main issues raised in the comment of Andreotti et al. [2008]. First, the turning of ray paths in a granular material does not preclude the propagation of body waves and the resonance condition described by Vriend et al. [2007]. The waveguide model still holds in the dune for the observed velocities, even with a velocity increase with depth as implied by Andreotti et al. [2008]. Secondly, the method of initiation of spontaneous avalanching does not influence the booming frequency. The frequency is independent of the source once sustained booming starts; it depends on the subsurface structure of the dune. Thirdly, if all data points from Vriend et al. [2007] are included in the analysis (and not an average or selection), no correlation is observed between the sustained booming frequency and average particle diameter.

Publication: Geophysical Research Letters Vol.: 35 No.: L08 ISSN: 0094-8276

ID: CaltechAUTHORS:20111208-105043039

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Abstract: The problem of predicting the moments of the distribution of bubble radius in bubbly flows is considered. The particular case where bubble oscillations occur due to a rapid (impulsive or step change) change in pressure is analyzed, and it is mathematically shown that in this case, inviscid bubble oscillations reach a stationary statistical equilibrium, whereby phase cancellations among bubbles with different sizes lead to time-invariant values of the statistics. It is also shown that at statistical equilibrium, moments of the bubble radius may be computed using the period-averaged bubble radius in place of the instantaneous one. For sufficiently broad distributions of bubble equilibrium (or initial) radius, it is demonstrated that bubble statistics reach equilibrium on a time scale that is fast compared to physical damping of bubble oscillations due to viscosity, heat transfer, and liquid compressibility. The period-averaged bubble radius may then be used to predict the slow changes in the moments caused by the damping. A benefit is that period averaging gives a much smoother integrand, and accurate statistics can be obtained by tracking as few as five bubbles from the broad distribution. The period-averaged formula may therefore prove useful in reducing computational effort in models of dilute bubbly flow wherein bubbles are forced by shock waves or other rapid pressure changes, for which, at present, the strong effects caused by a distribution in bubble size can only be accurately predicted by tracking thousands of bubbles. Some challenges associated with extending the results to more general (nonimpulsive) forcing and strong two-way coupled bubbly flows are briefly discussed.

Publication: Physics of Fluids Vol.: 20 No.: 4 ISSN: 1070-6631

ID: CaltechAUTHORS:COLpof08

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Abstract: In many cavitating liquid flows, when the number and concentration of the bubbles exceeds some critical level, the flow becomes unsteady and large clouds of cavitating bubbles are periodically formed and then collapse when convected into regions of higher pressure. This phenomenon is known as cloud cavitation and when it occurs it is almost always associated with a substantial increase in the cavitation noise and damage. These increases represent serious problems in devices as disparate as marine propellers, cavitating pumps and artificial heart valves. This lecture will present a brief review of the analyses of cloud cavitation in simplified geometries that allow us to anticipate the behavior of clouds of cavitation bubbles and the parameters that influence that behaviour. These simpler geometries allow some anticipation of the role of cloud cavitation in more complicated flows such as those in cavitating pumps.

ID: CaltechAUTHORS:20111213-112144056

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Abstract: We propose a new reduced-order model for spherical bubble dynamics that accurately captures the effects of heat and mass diffusion. The objective is to reduce the full system of partial differential equations to a set of coupled ordinary differential equations that are efficient enough to implement into complex bubbly flow computations. Comparisons to computations of the full partial differential equations and of other reduced-order models are used to validate the model and establish its range of validity.

Publication: Physics of Fluids Vol.: 19 No.: 12 ISSN: 1070-6631

ID: CaltechAUTHORS:PREpof07

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Abstract: Each of the webpages in this collection describes a different adventure hike. In each case, I have tried to give as much useful information as possible without spoiling the sense of adventure. When I explored each of these for the first time I had little or no knowledge of what to expect. In the early days, this led to some unexpected adventures such as spending an unplanned night in the canyon of the East Fork of the San Gabriel River. Later, I became more circumspect and often conducted preliminary exploratory hikes before attempting the complete version described here. Thus, for example, I ventured into some of the canyons from both above and below before attempting to travel all the way through. In each case, I have provided a map on which I have marked prominent features, obstacles or navigational aids. In addition, I have included some photographs so that the reader can gauge his or her own willingness to tackle some of the challenges described herein. Estimates of the times required for the hikes are also provided though the actual time required will vary considerably depending on the weather, stream conditions and personal agility and fitness. Some readers may be able to go significantly faster than indicated here. Groups larger than three or four will most likely be slower especially when rappelling. An estimate of the distance covered is also provided though this is much less useful than the elapsed time when discussing adventure hikes since average speeds vary greatly with the terrain. Another guide to the difficulty is the listed elevation gain that, unless otherwise specified, is the sum of all the major ascents experienced on the hike. Specific difficulties (and the equipment needed to overcome them) are also listed for reference at the beginning of each description.

ID: CaltechBOOK:2007.002

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Abstract: Each of the webpages in this collection describes a different adventure hike. I have tried to give as much useful information as possible without spoiling the sense of adventure. In each case, I have provided a map on which prominent features, obstacles or navigational aids have been marked. In addition, I have included some photographs so that the reader can gauge his or her own willingness to tackle some of the challenges described herein. Estimates of the times required for the hikes are also provided though the actual time required will vary considerably depending on the weather, stream conditions and personal agility and fitness. Some readers may be able to go significantly faster than indicated here. Groups larger than three or four will most likely be slower especially when rappelling. An estimate of the distance covered is also provided though this is much less useful than the elapsed time when discussing adventure hikes since average speeds vary greatly with the terrain. Another guide to the difficulty is the listed elevation gain that, unless otherwise specified, is the sum of all the major ascents experienced on the hike. Specific difficulties (and the equipment needed to overcome them) are also listed for reference at the beginning of each description.

ID: CaltechBOOK:2007.003

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Abstract: PREFACE: In this collection of stories, I have recorded some of my adventures on the mountains of the world. I make no pretense to being anything other than an average hiker for, as the first stories tell, I came to enjoy the mountains quite late in life. But, like thousands before me, I was drawn increasingly toward the wilderness, partly because of the physical challenge at a time when all I had left was a native courage (some might say foolhardiness), and partly because of a desire to find the limits of my own frailty. As these stories tell, I think I found several such limits; there are some I am proud of and some I am not. Of course, there was also the grandeur and magnificience of the mountains. There is nothing quite to compare with the feeling that envelopes you when, after toiling for many hours looking at rock and dirt a few feet away, the world suddenly opens up and one can see for hundreds of miles in all directions. If I were a religious man, I would feel spirits in the wind, the waterfalls, the trees and the rock. Many of these adventures would not have been possible without the marvellous companionship that I enjoyed along the way. Doug Hart was a frequent companion during the early adventures and I shall always count myself exceedingly fortunate to have travelled with him. Our spirits are forever bound together by the trials we faced together especially on the Mountain of the Devil. There were other companions too. Terry Jones was a most gracious host both in Oxford and on the slopes of Snowdon. In Japan, Yoichiro Matsumoto and Yoshi Tsujimoto were great companions. In Korea, I was touched by the watchful eye which Seung-Joon Lee kept on my wanderings. And closer to home in California, my advancing years were graced by the company of a number of young fellow adventurers, among them Troy Sette who was born with the instinct for adventure, Clancy Rowley whose grace and kindness shone in all he did and Mark Duttweiler with whom hiking was always a pleasure. To Garrett Reisman who taught me to climb, I owe an enduring debt and the very best of good fortune in his adventures as a NASA astronaut. In later years, I was immensely fortunate to link up with the three more great companions, the Marquesa de Canyonette, Randi Poer, whose blithe spirit is reflected in several of these stories, Scott ``Seldom Seen'' Smith whose kindness is unsurpassed, and the ``Magnificient Marine'' John Perry, a man for all seasons. I shall treasure all of their friendships for the rest of my days. To them and to all the others, I am deeply grateful. Most especially to Doreen whose love and friendship traveled with me to every corner of the globe.

ID: CaltechBOOK:2007.004

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Abstract: Desert booming can be heard after a natural slumping event or during a sand avalanche generated by humans sliding down the slip face of a large dune. The sound is remarkable because it is composed of one dominant audible frequency (70 to 105 Hz) plus several higher harmonics. This study challenges earlier reports that the dunes’ frequency is a function of average grain size by demonstrating through extensive field measurements that the booming frequency results from a natural waveguide associated with the dune. The booming frequency is fixed by the depth of the surficial layer of dry loose sand that is sandwiched between two regions of higher compressional body wave velocity. This letter presents measurements of the booming frequencies, compressional wave velocities, depth of surficial layer, along with an analytical prediction of the frequency based on constructive interference of propagating waves generated by avalanching along the dune surface.

Publication: Geophysical Research Letters Vol.: 34 No.: L16 ISSN: 0094-8276

ID: CaltechAUTHORS:20111208-094334359

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Abstract: In many cavitating liquid flows, when the number and concentration of the bubbles exceeds some critical level, the flow becomes unsteady and large clouds of cavitating bubbles are periodically formed and then collapse when convected into regions of higher pressure. This phenomenon is known as cloud cavitation and when it occurs it is almost always associated with a substantial increase in the cavitation noise and the potential for material damage associated with the cavitation. These increases represent serious problems in devices as disparate as marine propellers, cavitating pumps and artificial heart valves. This lecture will present examples of the phenomenon and review recent advances in our understanding of the dynamics and acoustics of clouds of bubbles and cloud cavitation. Both analyses of these complex multiphase flows and experimental observations will be used to identify the key features of the phenomenon and the parameters that influence it.

ID: CaltechAUTHORS:20111208-104034508

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Abstract: Recent testing of high-speed cavitating turbopump inducers has revealed the existence of more complex instabilities than the previously recognized cavitating surge and rotating cavitation. This paper explores one such instability that is uncovered by considering the effect of a downstream asymmetry, such as a volute on a rotating disturbance similar to (but not identical to) that which occurs in rotating cavitation. The analysis uncovers a new instability that may be of particular concern because it occurs at cavitation numbers well above those at which conventional surge and rotating cavitation occur. This means that it will not necessarily be avoided by the conventional strategy of maintaining a cavitation number well above the performance degradation level. The analysis considers a general surge component at an arbitrary frequency ω present in a pump rotating at frequency Ω and shows that the existence of a discharge asymmetry gives rise not only to beat components at frequencies, Ω−ω and Ω+ω (as well as higher harmonics), but also to rotating as well as surge components at all these frequencies. In addition, these interactions between the frequencies and the surge and rotating modes lead to “coupling impedances” that effect the dynamics of each of the basic frequencies. We evaluate these coupling impedances and show not only that they can be negative (and thus promote instability) but also are most negative for surge frequencies just a little below Ω. This implies potential for an instability involving the coupling of a surge mode with a frequency around 0.9 Ω and a low-frequency rotating mode about 0.1 Ω. We also examine how such an instability would be manifest in unsteady pressure measurements at the inlet to and discharge from a cavitating pump and establish a “footprint” for the recognition of such an instability.

Publication: Journal of Fluids Engineering Vol.: 129 No.: 6 ISSN: 0098-2202

ID: CaltechAUTHORS:20091019-152528509

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Abstract: Bubbles come in all sizes, shapes, and forms, but let’s begin with a very simple one. A bubble is a small pocket of vapor inside a liquid. This happens because the molecules have crossed the line separating the liquid zone from the vapor zone. Engineers and scientists like to depict this in a phase diagram, which is simply a graph that shows you whether a substance is a solid, a liquid, or a gas—or any combination thereof—at various temperatures and pressures. Increase the temperature, and the liquid boils. It forms bubbles. If you lower the pressure, a phenomenon called cavitation occurs. The resulting bubbles are essentially the same, but the consequences are not—when your teakettle boils, the bubbles don’t tear it apart, but cavitation can turn steel into Swiss cheese. The difference is that bubbles formed at high temperatures contain a lot of heat and collapse relatively slowly. But if you cross the line down near the triple point, where solid, liquid, and vapor can coexist, the vapor contains very little heat, allowing the bubbles to collapse quite rapidly and very violently. What matters is not so much how you cross the liquid-vapor line, but where you cross it.

Publication: Engineering and Science Vol.: 70 No.: 1 ISSN: 0013-7812

ID: CaltechAUTHORS:20130722-125628618

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Abstract: n/a

ID: CaltechAUTHORS:20130930-101528489

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Abstract: There are an increasing number of biological and bioengineering contexts in which cavitation is either utilized to create some desired effect or occurs as a byproduct of some other process. In this review an attempt will be made to describe a cross-section of these cavitation phenomena. In the byproduct category we describe some of the cavitation generated by head injuries and in artifical heart valves. In the utilization category we review the cavitation produced during lithotripsy and phacoemulsification. As an additional example we describe the nucleation suppression phenomena encountered in supersaturated oxygen solution injection. Virtually all of these cavitation and nucleation phenomena are critically dependent on the existence of nucleation sites. In most conventional engineering contexts, the prediction and control of nucleation sites is very uncertain even when dealing with a simple liquid like water. In complex biological fluids, there is a much greater dearth of information. Moreover, all these biological contexts seem to involve transient, unsteady cavitation. Consequently they involve the difficult issue of the statistical coincidence of nucleation sites and transient low pressures. The unsteady, transient nature of the phenomena means that one must be aware of the role of system dynamics in vivo and in vitro. For example, the artificial heart valve problem clearly demonstrates the importance of structural flexibility in determining cavitation occurrence and cavitation damage. Other system issues are very important in the design of in vitro systems for the study of cavitation consequences. Another common feature of these phenomena is that often the cavitation occurs in the form of a cloud of bubbles and thus involves bubble interactions and bubble cloud phenomena. In this review we summarize these issues and some of the other characteristics of biological cavitation phenomena.

ID: CaltechAUTHORS:BREwimrc06

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Abstract: Recent testing of high speed cavitating turbopump inducers has revealed the existance of more complex instabilities than the previously-recognized cavitating surge and rotating cavitation. This paper explores one such instability which is uncovered by considering the effect of a downstream asymmetry such as a volute on a rotating disturbance similar to (but not identical to) that which occurs in rotating cavitation. The analysis uncovers a new instability which may be of particular concern because it occurs at cavitation numbers well above those at which conventional surge and rotating cavitation occur. This means that it will not necessarily be avoided by the conventional strategy of maintaining a cavitation number well above the performance degradation level. The analysis considers a general surge component at an arbitrary frequency, ω, present in a pump rotating at frequency, Ω, and shows that the existence of a discharge asymmetry gives rise not only to beat components at frequencies, Ω − ω and Ω + ω (as well as higher harmonics) but also to circumferentially-varying components at all these frequencies. In addition, these interactions between the frequencies and the basic and complementary modes lead to “coupling impedances” that effect the dynamics of each of the basic frequencies. We evaluate these coupling impedances and show not only that they can be negative (and thus promote instability) but also are most negative for surge frequencies just a little below Ω. This implies potential for an instability involving the coupling of a basic mode with a frequency around 0.9Ω and a low frequency complementary mode about 0.1Ω. We also examine how such an instability would be manifest in unsteady pressure measurements at the inlet to and discharge from a cavitating pump and establish a “footprint” for the recognition of such an instability.

ID: CaltechAUTHORS:BREcav06b

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Abstract: The behavior of liquid-solid flows varies greatly depending on fluid viscosity, particle and liquid inertia, and collisions between particles. While particle collisions in inviscid fluids can be understood statistically, liquid-solid flows are complicated by the fluid viscosity and forces acting on the particles (e.g. lift, drag, added mass). These flows were first studied by Bagnold, whose investigation found two different flow regimes: a macro-viscous regime where the shear and pressure forces are proportional to the shear rate, and a grain-inertia regime defined by a dependance on the square of the shear rate [1, 2]. The scaling relations he developed have been used to model and understand natural phenomena since.

ID: CaltechAUTHORS:20111215-143708669

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Abstract: In the late 1970s, the authors began a collaboration with our colleague Tom Caughey that helped define a new set of fluid-structure interaction phenomena in turbomachines, namely fluid-induced rotordynamic forces and instabilities. That collaboration and the 31 joint ABC papers it produced epitomized Tom Caughey's genius and we reprise it here in his honor. The design of the space shuttle main engine (SSME) pushed beyond the boundaries of many known technologies. In particular, the rotating speeds and operating conditions of the high speed liquid oxygen and liquid hydrogen turbopumps were extreme and early testing revealed a whirl instability whose magnitude exceeded expectations and allowable limits. It was suspected and later proven that fluid-induced rotordynamic effects were a contributing factor and yet very little was known of such phenomena. As one of the efforts seeking understanding, we constructed a facility to measure fluid-induced rotordynamic forces. This was subsequently used in a broad range of investigations. Initially, the effort was directed to understanding the source and parametric variations of destabilizing fluid forces. Later various components of the flow in a high speed turbopump were investigated. And finally, some ameliorative measures and their effectiveness were examined. This paper reviews this body of knowledge and the lessons learnt along the way.

Publication: Structural Control and Health Monitoring Vol.: 13 No.: 1 ISSN: 1545-2255

ID: CaltechAUTHORS:BRE225

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Abstract: Set of DVD videos of seven special lectures given at the NASA George Marshall Space Flight Center, Huntsville, Alabama, on Dec. 13 and 14, 2005.

ID: CaltechAUTHORS:20120424-105426839

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Abstract: The transmission of pressure waves in granular materials is complicated by the heterogeneity and nonlinearity inherent in these systems. Such waves are propagated through particle contacts primarily along the "force chains" which carry most of the load in granular materials. These fragile and ephemeral chains coupled with irregular particle packing lead to the observed heterogeneity. Nonlinearity in these systems is largely the result of the force-deformation characteristic at particle contacts. Through experiments and simulations, we study the effects of heterogeneity and nonlinearity on the properties of pressure waves through a granular bed.

Publication: Physical Review E Vol.: 72 No.: 3 ISSN: 1539-3755

ID: CaltechAUTHORS:HOSpre05a

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Abstract: Pressure waves in a granular material travel through particle contact points and are primarily transmitted by the "force chains" that carry most of the load in a granular medium. However, these force chains tend to be fragile and ephemeral and can be disrupted by very minor perturbations including the waves themselves. External vibration also disrupts the force chains and therefore also changes the wave propagation characteristics. In this paper we study the effects of vibration on wave propagation in a shaken granular bed.

Publication: Physical Review E Vol.: 72 No.: 3 ISSN: 1539-3755

ID: CaltechAUTHORS:HOSpre05b

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Abstract: The cavitation inception threshold of mechanical heart valves has been shown to be highly variable. This is in part due to the random distribution of the initial and final conditions that characterize leaflet closure. While numerous hypotheses exist explaining the mechanisms of inception, no consistent scaling laws have been developed to describe this phenomenon due to the complex nature of these dynamic conditions. Thus in order to isolate and assess the impact of these varied conditions and mechanisms on inception, a system of ordinary differential equations is developed to describe each system component and solved numerically to predict the minimum pressure generated during valve closure. In addition, an experiment was conducted in a mock circulatory loop using an optically transparent size 29 bileaflet valve over a range of conditions to calibrate and validate this model under physiological conditions. High-speed video and high-response pressure measurements were obtained simultaneously to characterize the relationship between the valve motion, fluid motion, and negative pressure transients during closure. The simulation model was calibrated using data from a single closure cycle and then compared to other experimental flow conditions and to results found in the literature. The simulation showed good agreement with the closing dynamics and with the minimum pressure trends in the current experiment. Additionally, the simulation suggests that the variability observed experimentally (when using dP/dt alone as the primary measure of cavitation inception) is predictable. Overall, results from the current form of this lumped parameter model indicate that it is a good engineering assessment tool.

Publication: Journal of Biomechanical Engineering Vol.: 127 No.: 4 ISSN: 0148-0731

ID: CaltechAUTHORS:20111222-114317250

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Abstract: “Booming dunes” are large desert sand dunes that make a loud droning or humming noise during an avalanching of sand. The phenomenon has been observed for censturies, yet it remains largely unexplained. This note demonstrates that the booming frequency does not scale with the size of the particle or with the shearing speed of the avalanching sand. Instead, the dune may act as a waveguide with a fundamental frequency that depends on the sound speed within the dune and the depth of the loose dry sand layer.

ID: CaltechAUTHORS:20130722-150325006

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Abstract: The subject of multiphase flows encompasses a vast field, a host of different technological contexts, a wide spectrum of different scales, a broad range of engineering disciplines and a multitude of different analytical approaches. Not surprisingly, the number of books dealing with the subject is voluminous. For the student or researcher in the field of multiphase flow this broad spectrum presents a problem for the experimental or analytical methodologies that might be appropriate for his/her interests can be widely scattered and difficult to find. The aim of the present text is to try to bring much of this fundamental understanding together into one book and to present a unifying approach to the fundamental ideas of multiphase flows. Consequently the book summarizes those fundamental concepts with relevance to a broad spectrum of multiphase flows. It does not pretend to present a comprehensive review of the details of any one multiphase flow or technological context though reference to books providing such reviews is included where appropriate. This book is targeted at graduate students and researchers at the cutting edge of investigations into the fundamental nature of multiphase flows; it is intended as a reference book for the basic methods used in the treatment of multiphase flows.

ID: CaltechBOOK:2005.001

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Abstract: Wave propagation in a granular bed is a complicated, highly nonlinear phenomenon. Yet studies of wave propagation provide important information on the characteristics of these materials. Fundamental nonlinearities of the bed include those in the particle contact model and the fact that there exists zero applied force when grains are out of contact. The experimental work of Liu and Nagal showed the strong dependence of wave propagation on the forming and breaking of particle chains. As a result of the nonlinearities, anomalous behavior such as solitary waves and sonic vacuum have been predicted by Nesterenko. In the present work we examine wave propagation in a granular bed subjected to vertical agitation. The agitation produces continual adjustment of force chains in the bed. Wave propagation speed and attenuation measurements were made for such a system for a range of frequencies considerably higher than that used for the agitation. Both laboratory experiments and simulations (using a two-dimensional, discrete soft-particle model) have been used. The present paper is a progress report on the simulations.

Vol.: AIP Co No.: 706
ID: CaltechAUTHORS:HOSapstcsccm03

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Abstract: There are an increasing number of biological and bioengineering contexts in which cavitation is either utilized to create some desired effect or occurs as a byproduct of some other process. In this review an attempt will be made to describe a cross-section of these cavitation phenomena. In the byproduct category we describe some of the cavitation generated by head injuries and in artificial heart valves. In the utilization category we review the cavitation produced during lithotripsy and phacoemulsification. As an additional example we describe the nucleation suppression phenomena encountered in supersaturated oxygen solution injection. Virtually all of these cavitation and nucleation phenomena are critically dependent on the existence of nucleation sites. In most conventional engineering contexts, the prediction and control of nucleation sites is very uncertain even when dealing with a simple liquid like water. In complex biological fluids, there is a much greater dearth of information. Moreover, all these biological contexts seem to involve transient, unsteady cavitation. Consequently they involve the difficult issue of the statistical coincidence of nucleation sites and transient low pressures. The unsteady, transient nature of the phenomena means that one must be aware of the role of system dynamics in vivo and in vitro. For example, the artificial heart valve problem clearly demonstrates the importance of structural flexibility in determining cavitation occurrence and cavitation damage. Other system issues are very important in the design of in vitro systems for the study of cavitation consequences. Another common feature of these phenomena is that often the cavitation occurs in the form of a cloud of bubbles and thus involves bubble interactions and bubble cloud phenomena. In this review we summarize these issues and some of the other characteristics of biological cavitation phenomena.

ID: CaltechAUTHORS:BREcav03

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Abstract: The Rayleigh-Plesset equation and its extensions have been used extensively to model spherical bubble dynamics, yet radial diffusion equations must be solved to correctly capture damping effects due to mass and thermal diffusion. The latter are too computationally intensive to implement into a continuum model for bubbly cavitating flows, since the diffusion equations must be solved at each position in the flow. The goal of the present research is to derive a reduced-order model that accounts for thermal and mass diffusion. Motivated by results of applying the Proper Orthogonal Decomposition to data from full radial computations, we derive a model based upon estimates of the average heat transfer coefficients. The model captures the damping effects of the diffusion processes in two ordinary differential equations, and gives better results than previous models.

ID: CaltechAUTHORS:PREcav03

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Abstract: This study investigates the unsteady dynamics and inherent instabilities of a cavitating propeller operating in a water tunnel. First, the steady characteristics of the cavitating propeller such as the thrust coefficient are obtained by applying continuity and momentum equations to a simple one-dimensional flow tube model. The effects of the tunnel walls as well as those of the propeller operating conditions (advance ratio and cavitation number) are explored. Then the transfer matrix of the cavitating propeller (considered to be the most appropriate way to describe the dynamics of propeller) is obtained by combining the simple stream tube model with the conventional cavity model using the quasi-static cavitation compliance and mass flow gain factor representation. Finally, the surge instability of a cavitating propeller observed by Duttweiler and Brennen (2001) is examined by coupling the present model of the cavitation with a dynamic model for the water tunnel. This analysis shows that the effect of tunnel walls is to promote the surge instability.

Publication: Journal of Fluids Engineering Vol.: 125 No.: 2 ISSN: 0098-2202

ID: CaltechAUTHORS:WATjfe03

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Abstract: Sound and pressure wave propagation in a granular material is of interest not only for its intrinsic and practical value, but also because it provides a non-intrusive means of probing the state of a granular material. By examining wave speeds and attenuation, insight can be gained into the nature of the contacts between the particles. In the present paper, wave speeds and attenuation rates are first examined for a static granular bed for a variety of system parameters including particle size, composition and the overburden of the material above the measuring transducers. Agitation of the bed is then introduced by shaking the material vertically. This causes the bed to transition from a static granular state to a vibrofluidized state. The dilation of the bed allows for relative particle motion and this has a significant effect on the measured wave speeds and attenuation. Further, the fluid-like characteristics of the agitated bed distort the forcechain framework through which the waves are thought to travel. The consequences of bed consolidation, a natural result of shaking, are also examined.

Vol.: Materi No.: 759
ID: CaltechAUTHORS:HOSmrss03

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Abstract: Unsteady forces generated by fluid flow through the impeller shroud leakage path of a centrifugal pump were investigated. The effect of leakage path inlet swirl (pump discharge swirl) on the rotordynamic forces was re-examined. It was observed that increasing the inlet swirl is destabilizing both for normal and tangential rotordynamic forces. Attempts to reduce the swirl within the leakage path using ribs and grooves as swirl brakes showed benefits only at low leakage flow rate.

Publication: Journal of Fluids Engineering Vol.: 124 No.: 4 ISSN: 0098-2202

ID: CaltechAUTHORS:HSUjfe02b

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Abstract: High-speed observations clearly show that though a collapsing cavitation bubble approached its minimum size as a coherent single volume, it usually reappears in the first rebounding frame as a cloud of much smaller bubbles or as a highly distorted single volume. This paper explores two mechanisms that may be responsible for that bubble fission process, one invoking a Rayleigh-Taylor stability analysis and the other using the so-called microjet mechanism. Both approaches are shown to lead to qualitatively similar values for the number of fission fragments and the paper investigates the flow parameters that effect that number. Finally, the additional damping of the Rayleigh-Plesset single-bubble calculation caused by the fission process is investigated; it is shown that the fission damping dominates other contributions normally considered and is consistent with the number of collapses and rebounds that are observed to occur in experiments.

Publication: Journal of Fluid Mechanics Vol.: 472ISSN: 0022-1120

ID: CaltechAUTHORS:BREjfm02

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Abstract: It is possible to inject highly supersaturated aqueous solutions of gas through a small capillary into an aqueous environment without the formation of significant gas bubbles. Such a technique has considerable potential therapeutic value in the treatment, for example, of heart attacks and strokes. The present paper is the second in a series (see Brereton et al. [1]) investigating the basic phenomenon behind this surprising effect. Recent experiments clearly demonstrate that the nucleation, when it does occur, results from heterogeneous nucleation on the interior surface of the distal end of the capillary. This paper describes the effects of the treatment of this interior surface on the nucleation processes and the results of high speed video observations of the phenomena. A heterogeneous nucleation model is presented which is in accord with the experimental observations.

Publication: Journal of Biomechanical Engineering Vol.: 124 No.: 6 ISSN: 0148-0731

ID: CaltechAUTHORS:CREjbe02

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Abstract: The discharge of granular material from a hopper subject to vertical sinusoidal oscillations was investigated using experiments and discrete element computer simulations. With the hopper exit closed, side-wall convection cells are observed, oriented such that particles move up along the inclined walls of the hopper and down at the center line. The convection cells are a result of the granular bed dilation during free fall and the subsequent interaction with the hopper walls. The mass discharge rate for a vibrating hopper scaled by the discharge rate without vibration reaches a maximum value at a dimensionless velocity amplitude just greater than 1. Further increases in the velocity decrease the discharge rate. The decrease occurs due to a decrease in the bulk density of the discharging material when vibration is applied.

Publication: Physics of Fluids Vol.: 14 No.: 10 ISSN: 1070-6631

ID: CaltechAUTHORS:WASpf02

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Abstract: We present here an example of an important biomedical technique in which it is critical to understand and avoid bubble nucleation in supersaturated aqueous solutions of oxygen. By doing so it is possible to inject highly supersaturated oxygen solutions through a small capillary without the formation of significant gas bubbles. The potential medical benefits of a successful technique of this kind are substantial and multi-faceted. Deprivation of oxygen even for brief periods of time such as occur during heart attacks or strokes results in cell damage or death - and is a primary cause of permanent physiological damage. Consequently rapid therapeutic oxygen delivery systems could substantially enhance the treatment, for example, of acute myocardial infarction or acute cerebral stroke.

ID: CaltechAUTHORS:20111213-103456946

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Abstract: The Rayleigh-Plesset equation has been used extensively to model spherical bubble dynamics, yet it has been shown that it cannot correctly capture damping effects due to mass and thermal diffusion. Radial diffusion equations may be solved for a single bubble, but these are too computationally expensive to implement into a continuum model for bubbly cavitating flows since the diffusion equations must be solved at each position in the flow. The goal of the present research is to derive reduced-order models that account for thermal and mass diffusion. We present a model that can capture the damping effects of the diffusion processes in two ODE's, and gives better results than previous models.

ID: CaltechAUTHORS:PREfedsm02

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Abstract: Experimental studies of air entrainment by breaking waves are essential for advancing the understanding of these flows and creating valid models. The present study used experimental simulations of a ship bow wave to examine its dynamics and air entrainment processes. The simulated waves were created by a deflecting plate mounted at an angle in a supercritical free-surface flow in a flume. Measurements of the bow wave geometry at two scales and also for a bow wave created by a wedge in a towing tank are presented. Contact line and bow wave profile measurements from the different experiments are compared and demonstrate the similarity of the flume simulations to the towing tank experiments. The bow wave profile data from the towing tank experiments were used to investigate the scaling of the wave with the flow and the dependence on geometric parameters. In addition, surface disturbances observed on the plunging wave are documented herein because of the role they play in air entrainment. The air entrainment itself is explored in Waniewski et al (2001).

Publication: Journal of Ship Research Vol.: 46 No.: 1 ISSN: 0022-4502

ID: CaltechAUTHORS:WANjsr02.989

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Abstract: Fluid-induced rotordynamic forces produced by the fluid in an annular seal or in the leakage passage surrounding the shroud of a pump or turbine, are known to contribute substantially to the potential excitation forces acting on the rotor. The present research explores some of the important features of the equations governing bulk-flow models of these flows. This in turn suggests methods which might be used to solve these bulk-flow equations in circumstances where the linearized solutions may not be accurate. This paper presents a numerical method for these equations and discusses comparison of the computed results with experimental measurements for annular seals and pump leakage paths.

Publication: Journal of Fluids Engineering Vol.: 124 No.: 1 ISSN: 0098-2202

ID: CaltechAUTHORS:HSUjfe02

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Abstract: In 1954 R. A. Bagnold published his seminal findings on the rheological properties of a liquid-solid suspension. Although this work has been cited extensively over the last fifty years, there has not been a critical review of the experiments. The purpose of this study is to examine the work and to suggest an alternative reason for the experimental findings. The concentric cylinder rheometer was designed to measure simultaneously the shear and normal forces for a wide range of solid concentrations, fluid viscosities and shear rates. As presented by Bagnold, the analysis and experiments demonstrated that the shear and normal forces depended linearly on the shear rate in the 'macroviscous' regime; as the grain-to-grain interactions increased in the 'grain-inertia' regime, the stresses depended on the square of the shear rate and were independent of the fluid viscosity. These results, however, appear to be dictated by the design of the experimental facility. In Bagnold's experiments, the height (h) of the rheometer was relatively short compared to the spacing (t) between the rotating outer and stationary inner cylinder (h/t=4.6). Since the top and bottom end plates rotated with the outer cylinder, the flow contained two axisymmetric counter-rotating cells in which flow moved outward along the end plates and inward through the central region of the annulus. At higher Reynolds numbers, these cells contributed significantly to the measured torque, as demonstrated by comparing Bagnold's pure-fluid measurements with studies on laminar-to-turbulent transitions that pre-date the 1954 study. By accounting for the torque along the end walls, Bagnold's shear stress measurements can be estimated by modelling the liquid-solid mixture as a Newtonian fluid with a corrected viscosity that depends on the solids concentration. An analysis of the normal stress measurements was problematic because the gross measurements were not reported and could not be obtained.

Publication: Journal of Fluid Mechanics Vol.: 452ISSN: 0022-1120

ID: CaltechAUTHORS:HUNjfm02

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Abstract: The effects of unsteady bubbly dynamics on cavitating flow through a converging-diverging nozzle are investigated numerically. A continuum model that couples the Rayleigh-Plesset equation with the continuity and momentum equations is used to formulate unsteady, quasi-one-dimensional partial differential equations. Flow regimes studied include those where steady-state solutions exist, and those where steady-state solutions diverge at the so-called flashing instability. these latter flows consist of unsteady bubbly shock waves traveling downstream in the diverging section of the nozzle. An approximate analytical expression is developed to predict the critical backpressure for choked flow. The results agree with previous barotropic models for those flows where bubbly dynamics are not important, but show that in many instances the neglect of bubbly dynamics cannot be justified. Finally the computations show reasonable agreement with an experiment that measures the spatial variation of pressure, velocity and void fraction for steady shockfree flows, and good agreement with an experiment that measures the throat pressure and shock position for flows with bubbly shocks. In the model, damping of the bubbly raidal motion is restricted to a simple "effective" viscosity, but many features of the flow are shown to be independent of the specific damping mechanism.

Publication: Physics of Fluids Vol.: 14 No.: 1 ISSN: 1070-6631

ID: CaltechAUTHORS:PREpf02

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Abstract: Suppression of cavitation is a relatively common goal of fluid engineers and therefore examples of bubble nucleation suppression in other technological contexts are useful in suggesting ways in which such suppression might be achieved. In this paper we describe a remarkable example of bubble nucleation suppression achieved by a combination of the elimination of nucleation sites and the reduction of bubble growth time. The context is the invention of a device that allows the injection of aqueous solutions highly supersaturated with oxygen into the bloodstream without the formation of significant gaseous oxygen bubbles.

ID: CaltechAUTHORS:CREjsmemec02

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Abstract: A phase Doppler anemometer (PDA) system was used to measure the velocity profiles and air bubble size distributions downstream of two-dimensional hydraulic jumps for different upstream flow conditions in a 1.92m long laboratory flume. The PDA detected bubbles from 1 to 500 [microns] in diameter, and more were found at the bottom of the downstream flow near the elevation of the upstream free surface. This distribution was more marked for smaller bubbles, those with diameters less that 100 [microns]. The migration of the bubbles is controlled by the effects of buoyancy and by turbulent mixing; the relative magnitude of their effects on bubble distribution depends strongly on bubble size, and also on the energy of the upstream flow.

Publication: International Journal of Multiphase Flow Vol.: 27 No.: 7 ISSN: 0301-9322

ID: CaltechAUTHORS:WANijmf01

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Abstract: High-speed observations (for example, Lauterborn and Bolle 1975, Tomita and Shima 1990, Frost and Sturtevant 1986) clearly show that though a collapsing cavitation bubble approaches its minimum size as a coherent single volume, it usually reappears in the first rebounding frame as a cloud of much smaller bubbles or as a highly distorted single volume (see, for example, figure 2). This paper explores two mechanisms that may be responsible for that bubble fission process, one invoking a Rayleigh-Taylor stability analysis and the other utilizing the so-called microjet mechanism. Both approaches are shown to lead to qualitatively similar values for the number of fission fragments and the paper investigates the flow parameters that effect that number. Finally, we explore the effective damping of the Rayleigh-Plesset single bubble calculation which that fission process implies and show that it is consistent with the number of collapses and rebounds which are observed to occur in experiments.

ID: CaltechAUTHORS:CEBcav01

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Abstract: This paper presents a hydraulic analysis of a fluid coupling which is designed to operate either in a forward or reverse mode when a set of turning vanes are respectively withdrawn or inserted into the flow between the driving and driven rotors. The flow path is subdivided into a set of streamtubes and an interative method is used to adjust the cross-sectional areas of these streamtubes in order to satisfy radial equilibrium. Though the analyis requires the estimation of a number of loss coefficients, it predicts coupling performance data which are in good agreement with that measured in NAVSSES tests of a large reversible coupling intended for use in a ship drive train.

Publication: Journal of Fluids Engineering Vol.: 123 No.: 2 ISSN: 0098-2202

ID: CaltechAUTHORS:MCKjfe01

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Abstract: The Rayleigh-Plesset equation is used extensively to model spherical bubble dynamics, yet is has been shown that it cannot correctly capture damping effects due to mass and thermal diffusion. Full single bubble models have been successfully used to study these diffusion effects, but these are to computationally expensive to implement into the continuum model for bubbly cavitating flow since the diffusion equations must be solved in the radial direction at each position in the flow. The focus of the present research is the development of simpler and more efficient bubbly dynamic models that capture the important aspects of the diffusion processes. We present some preliminary results from a full bubbly model that has been developed to provide insight into possible simplifications. This in turn can be used to develop and validate simpler models. The full model is contrasted to the Rayleigh-Plesset equations, and a suggestion for possible improvement to the Rayleigh-Plesset equation is made.

ID: CaltechAUTHORS:PREcav01

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Abstract: The relationship among four flow instabilities of turbomachines, namely, surge, rotating stall, cavitation surge, and rotating cavitation, is elucidated, using a unified or common model for their analysis. The simplest unifying model was employed in the analysis to focus on the characteristic features of each instability. Moreover, the concentration is on the stability criteria, and hence, the amplitudes are assumed small. Of course, the instabilities often grow to amplitudes comparable with the average value of the flow variable. Flows upstream and downstream of the impeller were assumed to be one dimensional for surge and cavitation surge and to be two dimensional for rotating stall and rotating cavitation, respectively. Viscous effects were taken into consideration in the form of cascade loss. Impeller blade geometry was incorporated in the assumption that the flow is perfectly guided. The peripheral wavelength of the disturbance was assumed to be much larger than the blade pitch.

Publication: Journal of Propulsion and Power Vol.: 17 No.: 3 ISSN: 0748-4658

ID: CaltechAUTHORS:TSUjpp01

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Abstract: This paper describes measurements of the air entrained in experiments simulating the breaking bow wave of a ship for Froude numbers between two and three. The experiments and the characteristics of the wave itself are detailed in T. Waniewski, 1999, "Air Entrainment by Bow Waves; PhD. theses, Calif. Inst. of Tech." The primary mechanism for air entrainment is the impact of the plunging wave jet, and it was observed that the air bubbles were entrained in spatially periodic bubble clouds. The void fraction and bubble size distributions were measured in the entrainment zone. There were indications that the surface disturbances described in Waniewski divide the plunging liquid jet sheet into a series of plunging jets, each of which produces a bubble cloud.

Publication: Journal of Fluids Engineering Vol.: 123 No.: 1 ISSN: 0098-2202

ID: CaltechAUTHORS:WANjfe01

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Abstract: This study details experiments investigating a previously unrecognized surge instability on a cavitating propeller in a water tunnel. The surge instability is furst explored through visual observation of the cavitation on the propeller blades and in the tip vortices. Similarities between the instability and previously documented cavitation phenomena are noted. Measurements of the radiated pressure are then obtained, and the acoustic signature of the instability is identified. The magnitudes of the fluctuating pressures are very large, presumably capable of producing sever hull vibration on a ship. The origins of the instability are explored through separate investigation of the cavitation dynamics and the response of the water tunnel to volumetric displacement in the working section. Experiments are conducted to quantify the dynamics of the propeller vacitation. Finally, a model is developed for the complete system, incorporating both the cavitation and facility dynamics. The model predicts active system dynamics (linked to the mass flow gain factor familiar in the context of pump dynamics) and therefore potentially unstable behavior for two distinct frequency ranges, one of which appears to be responsible for the instability.

ID: CaltechAUTHORS:DUTcav01

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Abstract: Bubbly cavitating flow generated by the normal oscillation of a wall bounding a semi-infinite domain of fluid is computed using a continuum two-phase flow model. Bubble dynamics are computed, on the microscale, using the Rayleigh-Plesset equation. A Lagrangian finite volume scheme and implicit adaptive time marching are employed to accurately resolve bubbly shock waves and other steep gradients in the flow. The one-dimensional, unsteady computations show that when the wall oscillation frequency is much smaller than the bubble natural frequency, the power radiated away from the wall is limited by an acoustic saturation effect (the radiated power becomes independent of the amplitude of vibration), which is similar to that found in a pure gas. That is, for large enough vibration amplitude, nonlinear steepening of the generated waves leads to shocking of the wave train, and the dissipation associated with the jump conditions across each shock limits the radiated power. In the model, damping of the bubble volume oscillations is restricted to a simple "effective" viscosity. For wall oscillation frequency less than the bubble natural frequency, the saturation amplitude of the radiated field is nearly independent of any specific damping mechanism. Finally, implications for noise radiation from cavitating flows are discussed.

Publication: Physics of Fluids Vol.: 12 No.: 11 ISSN: 1070-6631

ID: CaltechAUTHORS:COLpf00

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Abstract: This paper presents the results of an investigation assessing the role experimental facility dynamics might play in determining the nature of a recently observed instability on a cavitating propeller (Duttweiler and Brennen 1999). To address this question, a theoretical model of the facility dynamics is developed. Experiments were conducted to measure the response of the water tunnel facility to volumetric excitations of varying amplitude and frequency, and the measurements are compared with the response predicted by the model. The dynamics of the propeller cavitation are characterized by estimating two parameters (cavitation compliance and mass flow gain factor) previously employed in developing a system transfer function for cavitating pumps (Brennen 1994). Finally, the characteristics of a model for the complete system, incorporating both the cavitating propeller and the experimental facility dynamics, are discussed.

ID: CaltechAUTHORS:DUTasmefedsm00

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Abstract: The effects of unsteady bubble dynamics on cavitating flow through a converging-diverging nozzle are investigated numerically. A continuum model that couples the Rayleigh-Plesset equation with the continuity and momentum equations is used to formulate unsteady, quasi-one-dimensional partial differential equations. These equations are solved numerically using a Lagrangian finite volume method. Special formulations are used at the boundary cells to allow Eulerian boundary conditions to be specified. Flow regimes studied include those where steady state solutions exist, and those where steady state solutions diverge at the so-called flashing instability. These latter flows consist of unsteady bubbly shock waves travelling downstream in the diverging section of the nozzle. The computations show reasonable agreement with an experiment that measures the spatial variation of pressure, velocity and void fraction for steady shockfree flows, and good agreement with an experiment that measures the shock position and throat pressure for flows with bubbly shocks.

ID: CaltechAUTHORS:PREfedsm00

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Abstract: This study details experiments investigating a previously unrecognized surge instability on a cavitating propeller in a water tunnel. The surge instability is explored through visual observation of the cavitation on the propeller blades and in the tip vortices. Similarities between the instability and previously documented cavitation phenomena are noted. Measurements of the radiated pressure are obtained, and the acoustic signature of the instability is identified. The magnitudes of the fluctuating pressures are very large, presumably capable of producing severe hull vibration on a ship. The origins of this instability are explored through separate investigation of the cavitation dynamics and the response of the water tunnel to volumetric displacement in the working section. Experiments are conducted to quantify the dynamics of the propeller cavitation. Finally, a model is developed for the complete system, incorporating both the cavitation and facility dynamics. The model predicts active system dynamics (linked to the mass flow gain factor familiar in the context of pump dynamics) and therefore potentially unstable behavior for two distinct frequency ranges, one of which appears to be responsible for the instability.

Publication: Journal of Fluid Mechanics Vol.: 458ISSN: 0022-1120

ID: CaltechAUTHORS:DUTjfm02

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Abstract: The nonlinear dynamics of a spherical cloud of cavitation bubbles have been simulated numerically in order to learn more about the physical phenomena occurring in cloud cavitation. A finite cloud of nuclei is subject to a decrease in the ambient pressure which causes the cloud to cavitate. A subsequent pressure recovery then causes the cloud to collapse. This is typical of the transient behavior exhibited by a bubble cloud as it passes a body or the blade of a ship propeller. The simulations employ the fully nonlinear continuum mixture equations coupled with the Rayleigh-Plesset equation for the dynamics of bubbles. A Lagrangian integral method is developed to solve this set of equations. It was found that, with strong bubble interaction effects, the collapse of the cloud is accompanied by the formation of an inward propagating bubbly shock wave, a large pressure pulse is produced when this shock passes the bubbles and causes them to collapse. The focusing of the shock at the center of the cloud produces a very large pressure pulse which radiates a substantial impulse to the far field and provides an explanation for the severe noise and damage potential in cloud cavitation.

Publication: Journal of Fluids Engineering Vol.: 121 No.: 4 ISSN: 0098-2202

ID: CaltechAUTHORS:WNGjfe99

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Abstract: In August 1999, a workshop was held at Pacific Northwest National Laboratory to discuss the effects of crust ingestion on mixer pump performance in Hanford Waste Tank 241-SY-101. The main purpose of the workshop was to evaluate the potential for crust ingestion to degrade mixing and/or damage the mixer pump. The need for a previously determined 12-inch separation between the top of the mixer pump inlet and the crust base was evaluated. Participants included a representative from the pump manufacturer, an internationally known expert in centrifugal pump theory, Hanford scientists and engineers, and operational specialists representing relevant fields of expertise. The workshop focused on developing an understanding of the pump design, addressing the physics of entrainment of solids and gases into the pump, and assessing the effects of solids and gases on pump performance. The major conclusions are summarized as follows: * Entrainment of a moderate amount of solids or gas from the crust should not damage the pump or reduce its lifetime, though mixing effectiveness will be somewhat reduced. * Air binding should not damage the pump. Vibration due to ingestion of gas, solids, and objects potentially could cause radial loads that might reduce the lifetime of bearings and seals. However, significant damage would require extreme conditions not associated with the small bubbles, fine solids, and chunks of relatively weak material typical of the crust. * The inlet duct extension opening, 235 inches from the tank bottom, should be considered the pump inlet, not the small gap at 262 inches. * A suction vortex exists at the inlet of all pumps. The characteristics of the inlet suction vortex in the mixer pump are very hard to predict, but its effects likely extend upward several feet. Because of this, the current 12-inch limit should be replaced with criteria based on actual monitored pump performance. The most obvious criterion (in addition to current operational constraints) is to monitor discharge pressure and cease pump operation if it falls below a predetermined amount. * There are no critically necessary tests to prove pump operability or performance before initiating the transfer and back-dilution sequence.

ID: CaltechAUTHORS:MEYpnnl99

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Abstract: Unsteady forces generated by fluid flow through the impeller shroud leakage path of a centrifugal pump were investigated. Different pump shroud geometries were compared, and the effect of leakage path inlet swirl (pump discharge swirl) on the rotordynamic forces was examined for various ratios of fluid flowthrough velocities to impeller tip speed. A short axial length leakage path reduced the measured forces, while curvature appeared to increase the destabilizing forces when inlet swirl was present. It was observed that changing the inlet swirl velocity does not appear to significantly affect the measured forces for a given leakage flow coefficient, but any nonzero inlet swirl is destabilizing when compared to cases with no inlet swirl.

Publication: Journal of Fluids Engineering Vol.: 121 No.: 3 ISSN: 0098-2202

ID: CaltechAUTHORS:UYRjfe99

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Abstract: This paper presents results from experiments investigating an instability observed on a cavitating propeller. Preliminary visual observations were made of the attached cavities on the blades of the propeller, and particular note was made of similarities between the behavior of the re-entrant jets and that found recently by Laberteaux and Ceccio (1998). It was also noted that the nature of the instability is closely related to the partial cavity instability observed on single, two-dimensional foils. (Knapp, 1955; Wade and Acosta, 1966; Brennen, 1994, 95). The flow conditions (cavitation number and advance ratio) under which the instability occurs were mapped and it is shown that the onset corresponds to a specific configuration of attached cavity lengths on the propeller. Pressure measurements were obtained from two different locations within the experimental facility, and the acoustic signature of the instability is identified. A simple model based on cavity volume estimates obtained from high speed video footage is developed, and the predictions of the model are compared with the experimentally obtained pressures.

ID: CaltechAUTHORS:DUTfedsm99

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Abstract: This paper focuses on the different forms that individual cavitating events may take when the cavitation number is below the inception value (but not so low as to produce only attached cavities) and individual nuclei trigger individual cavitation events. It is a sequel to those of Kuhn de Chizelle et al. (1992a, 1992b, 1995) which described a set of cavitation scaling observations on simple Schiebe headforms conducted in the US Navy Large Cavitation Channel (LCC). The most common events observed in those experiments were traveling, hemi-spherical shaped bubbles which grew and collapsed as they were convected through the low pressure region on the headform. Several interesting variations were also observed, including the development of bubble tails and the triggering of patches, or local regions of attached cavitation. In the present paper, the frequency of occurrence of the various types of events is analyzed as well as how those probabilities changed with cavitation number, velocity and headform size. In general, the probabilities of tails and patches increased with decreasing cavitation number, but they also increased with increasing headform size and increasing velocity. A specific parametric dependence on these variables is suggested.

ID: CaltechAUTHORS:WANfedsm99

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Abstract: The current experiments investigate the discharge of glass spheres in a planar wedge-shaped hopper (45 degree sidewalls) that is vibrated hoizontally. When the hopper is discharged without vibration, the discharge occurs as a funnel flow, with the material exiting the central region of the hopper and stagnant material along the sides. With horizontal vibration, the discharge rate increases with the velocity of vibration as compared with the discharge rate without vibration. For a certain range of acceleration parameters (20-30 Hz and accelerations greater than about 1 g), the discharge of the material occurs in an inverted-funnel pattern, with the material along the sides exiting first, followed by the material in the core; the free surface shows a peak at the center of the hopper with the free surface particles avalanching from the center toward the sides. During the deceleration phase of a vibration cycle, particles all along the trailing or low-pressure wall separate from the surface and fall under gravity for a short period before reconnecting the hopper. For lower frequencies (5 and 10 Hz), the free surface remains horizontal and the material appears to discharge uniformly from the hopper.

Publication: Physics of Fluids Vol.: 11 No.: 1 ISSN: 1070-6631

ID: CaltechAUTHORS:HUNpf99

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Abstract: This paper describes investigations of the dynamics and acoustics of clouds of cavitation bubbles. Recent experimental and computational findings show that the collapse of clouds of cavitating bubbles can involve the formation of bubbly shock waves and that the focussing of these shock waves is responsible for the enhanced noise and damage in cloud cavitation. The recent experiments and computations of Reisman et al. (1) complement the work begun by Morch and Kedrinskii and their co-workers (2,3,4) and demonstrate that the very large impulsive pressures generated in bubbly cloud cavitation are caused by shock waves generated by the collapse mechanics of the bubbly cavitating mixture. Here we describe computational investigations conducted to explore these and other phenomena in greater detail as part of an attempt to find ways of ameliorating the most destructive effect associated with cloud cavitation. Understanding such bubbly flow and shock wave processes is important because these flow structures propagate the noise and produce the impulsive loads on nearby solid surfaces in a cavitating flow. How these shocks are formed and propagate in the much more complex cloud geometry associated with cavitating foils, propeller or pump blades is presently not clear. However, the computational investigations reveal some specific mechanisms which may be active in the dynamics and acoustics of these more complex flows.

Publication: The National Academy of Sciences
ID: CaltechAUTHORS:BRE22snh99

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Abstract: This paper investigates the linearized dynamics of three-dimensional bubbly cavitating flows in helical inducers. The purpose is to understand the impact of the bubble response on the radial and tangential rotordynamic forces exerted by the fluid on the rotor and stator stages of whirling turbomachines under cavitating conditions. The flow in the inducer annulus is modeled as a homogeneous inviscid mixture, containing vapor bubbles with a small amount of noncondensable gas. The effects of several contributions to the damping of the bubbly dynamics are included in the model. The governing equations of the inducer flow are written in "body-fitted" orthonormal helical Lagrangian coordinates, linearized for small-amplitude perturbations about the mean flow, and solved by modal decomposition. The whirl excitation generates finite-speed propagation and resonance phenomena in the two-phase flow within the inducer. These, in turn, lead to a complex dependence of the lateral rotordynamic fluid forces on the excitation frequency, the void fraction, the average size of the cavitation bubbles, and the turbopump operating conditions (including, rotational speed, geometry, flow coefficient and cavitation number). Under cavitating conditions the dynamic response of the bubbles induces major deviations from the noncavitating flow solutions, especially when the noncondensable gas content of the bubbles is small and thermal effects on the bubble dynamics are negligible. Then, the quadratic dependence of rotordynamic fluid forces on the whirl speed, typical of cavitation-free operation, is replaced by a more complex behavior characterized by the presence of different regimes where, depending on the whirl frequency, the fluid forces have either a stabilizing or a destabilizing effect on the inducer motion. Results are presented to illustrate the influence of the relevant flow parameters.

Publication: Journal of Fluids Engineering Vol.: 120 No.: 6 ISSN: 0098-2202

ID: CaltechAUTHORS:DAGjfe98

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Abstract: To model the processes of cavitation inception, noise and damage, it is necessary to generate a model of the cavitation event rate which can then be coupled with the consequences of the individual events to produce a complete synthesis of the phenomenon. In this paper we describe recent efforts to connect the observed event rates to the measured distributions of cavitation nuclei in the oncoming stream. Comparison are made between the observed event rates and event rates calculated from measured nuclei distributions using an algorithm which includes the dynamics of the nuclei motion and growth. Various complications are explored including the effect of the boundary layer, the relative motion between the nucleus and the liquid, the observable bubble size effect, and the effect of bubble growth on neighboring nuclei. All of these are seen to have important influences on the event rate, and therefore, on cavitation inception and other macroscopic consequences. We demonstrate that it is possible to predict the correct order of magnitude of the event rate when an attempt is made to model the important flow complications.

Publication: Journal of Fluids Engineering Vol.: 120 No.: 4 ISSN: 0098-2202

ID: CaltechAUTHORS:LIUjfe98

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Abstract: This paper reviews some of the literature on partial cavity instabilities on single hydrofoils and then summarizes the striking differences in the appearance and behavior of partial cavities on swept foils (as opposed to two-dimensional, unswept foils) as rcently highlighted by de Lange et al. (1994) and Laberteaux and Ceccio (1998). These demonstrate the importance of the spanwise evolution of the re-entrant jet, and the consequences for the characteristics of the cavity closure flow. It is suggested in this paper that several variants of this evolution can be seen in the photographs of cavitation on single hydrofoils foils and on propellers. What is common to many of these variants is that, the spanwise evolution of the cavity and the re-entrant jet can give rise to conditions at some particular spanwise location(s) which initiate partial cavity instability. In this paper we present information on an instability that was observed to occur on a cavitating propeller of modern US Navy design. Detailed photographic examinations show that the instability oscillations involve spanwise development of a re-entrant jet and behavior similar to that of the partial cavity oscillations previously observed on two-dimensional foils.

ID: CaltechAUTHORS:DUT18b

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Abstract: Impedance based techniques have been used to quantify air entrainment by a stationary breaking wave at the bow of a ship. The present paper describes an impedance based void fraction meter which was developed to make measurements in this high speed, unsteady, multiphase flow, and details of its calibration are provided. In addition, air entrainment data from an experimental simulation of a bow wave are presented. The local, time averaged void fraction was mapped for flow cross sections beneath the plunging wave jet, revealing the location of the clouds of bubbles formed by that jet impacting the incoming water surface. Size distribution functions for the bubbles within the bubble clouds are also presented. The results are correlated with the wave structure described in Waniewski et al. (1997).

ID: CaltechAUTHORS:WANfedsm98

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Abstract: A recent significant advance in our understanding of cavitating flows is the importance of the interactions between bubbles in determining the coherent motions, dynamic and acoustic, of the bubbles in a cavitating flow. This lecture will review recent experimental and computational findings which confirm that, under certain conditions, the collapse of clouds of cavitating bubbles involves the formation of bubbly shock waves and that the focussing of these shock waves is responsible for enhanced noise and potential damage in cloud cavitation. The recent experiments of Reisman et al. (1998) complements the work begun by Mørch and Kedrinskii and their co-workers and demonstrates that the very large impulsive pressures generated in bubbly cloud cavitation are caused by shock waves generated by the collapse mechanics of the bubbly cavitatting mixture. Two particular types of shocks were observed: large ubiquitous global pressure pulses caused by the separation and collapse of indiviual clouds from the downstream end of the cavitation and much more localized local pressure pulses which occur much more randomly within the bubbly cloud. One of the first efforts to model cloud cavitation was due to vanWijngaarden (1964) who linked basic continuity and momentum equations for the mixture with a Rayleigh-Plesset equation for the bubble size in order to study the behavior of a bubbly fluid layer next to a solid wall. In the 1980s there followed a series of papers on the linearized dynamics of clouds of bubbles (for example, d’Agostino et al. 1983, 1988, 1989). But highly non-linear processes such as the formation of shock waves require computational efforts which are capable of resolving these phenomena in both time and space. A valuable first effort to do this was put forward by Kubota et al. (1992) but by limiting the collapse of individual bubbles they prevented the formation of the large pressure pulses associated with bubble collapse. Wang et al. (1994, 1995) and Reisman et al. (1998) present accurate calculations of a simple spherical cloud subject to a low pressure episode and show that, for a large enough initial void fraction, the collapse occurs as a result of the formation of a shock wave on the surface of the cloud and the strengthening of this shock by geometric focussing as the shock propagates inward. This review will discuss other efforts to investigate these phenomena computationally. Wang and Brennen (1997, 1998) have extended the one-dimensional methodology used for the spherical cloud to investigate the steady flow of a bubbly, cavitating mixture through a onvergent/divergent nozzle. Under certain parametric conditions, the results are seen to model the dynamics of flashing within the nozzle. Moreover, it is clear from these steady flow studies that there are certain conditions in which no steady state solution exists and it is speculated that the flow under those conditions may be inherently unstable. Of course, it has frequently been experimentally observed that cavitating nozzle flows can become unstable and oscillate violently. Finally, we will also describe recent efforts (Colonius et al. 1998) to extend the code to two and three space dimensions. A simple example of such a calculation is the collision of a plane pressure pulse with a cylindrical or spherical cloud of bubbles. When the pressure pulse is negative, the growth and subsequent collapse of the cloud is particularly interesting and is seen to involve the formation and propagation of a shock waves within the cloud. Moreover, the non-linear scatterring of the pressure waves into the far field provides valuable information. The long term objective is to develop computational techniques and experience which would allow practical calculation of much more complex bubbly flows such as occur on hydrofoils, on propellers and in pumps where there is a real need for CFD methodologies which allow calculation of the noise and damage potential of these flows.

ID: CaltechAUTHORS:CEBicmf98

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Abstract: Realistic cavitating flows are dominated by a large number of interacting bubbles. These clouds of bubbles exhibit highly nonlinear behavior with sudden changes in void fraction. Because of the potential damage caused by the coherent collapse of bubble clouds, there is a need for effective numerical models to predict their behavior. This paper presents a newly developed computational methodology to solve a continuum model of bubbly cavitating flow in which a Lagrangian finite volume technique is used to accurately and efficiently track all flow variables in space and time. We also present results for the solution of a one-dimensional model problem, namely cavitating shock waves produced by the normal motion of a wall bounding a semi-infinite domain of fluid. The roles of wave steepening and damping mechanisms in the collapse of bubble clouds are highlighted.

ID: CaltechAUTHORS:COLfed98

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Abstract: A nonbarotropic continuum bubbly mixture model is used to study the one-dimensional cavitating flow through a converging-diverging nozzle. The nonlinear dynamics of the cavitation bubbles are modeled by the Rayleigh-Plesset equation. Analytical results show that the bubble/bubble interaction through the hydrodynamics of the surrounding liquid has important effects on this confined flow field. One clear interaction effect is the Bernoulli effect caused by the growing and collapsing bubbles in the nozzle. It is found that the characteristics of the flow change dramatically even when the upstream void fraction is very small. Two different flow regimes are found from the steady state solutions and are termed: quasi-steady and quasi-unsteady. The former is characterized by large spatial fluctuations downstream of the throat which are induced by the pulsations of the cavitation bubbles. The quasi-unsteady solutions correspond to flashing flow. Bifurcation occurs as the flow transitions from one regime to the other. An analytical expression for the critical bubble size at the bifurcation is obtained. Physical reasons for this quasi-static instability are also discussed.

Publication: Journal of Fluids Engineering Vol.: 120 No.: 1 ISSN: 0098-2202

ID: CaltechAUTHORS:WNGjfe98

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Abstract: The rotordynamic forces generated by the fluid flow through the impeller leakage path of a centrifugal pump are now well established. The present paper examines the effects of modifying the leakage path geometry by changing the front shroud, from a conical shape to a more typical curved design, and the effects of low pressure seal design on these forces. It is found that only the cross-coupled stiffness is affected by the change of path geometry. Changing the low pressure seal from an axial to a radial clearance does, however, significantly affect the rotordynamic forces. A bulk flow numerical model is found to predict the same general result for the low pressure seal tests. The model agrees with the general trends with increasing leakage flow coefficient exhibited by the data, but appears to underpredict the magnitude of the normal force.

Publication: JSME International Journal. Series B, Fluids and Thermal Engineering Vol.: 41 No.: 1 ISSN: 0914-8817

ID: CaltechAUTHORS:UYRjsme98

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Abstract: This paper describes an investigation of the dynamics and acoustics of cloud cavitation, the structures which are often formed by the periodic breakup and collapse of a sheet or vortex cavity. This form of cavitation frequently causes severe noise and damage, though the precise mechanism responsible for the enhancement of these adverse effects is not fully understood. In this paper, we investigate the large impulsive surface pressures generated by this type of cavitation and correlate these with the images from high-speed motion pictures. This reveals that several types of propagating structures (shock waves) are formed in a collapsing cloud and dictate the dynamics and acoustics of collapse. One type of shock wave structure is associated with the coherent collapse of a well-defined and separate cloud when it is convected into a region of higher pressure. This type of global structure causes the largest impulsive pressures and radiated noise. But two other types of structure, termed 'crescent-shaped regions' and 'leading-edge structures' occur during the less-coherent collapse of clouds. These local events are smaller and therefore produce less radiated noise but the interior pressure pulse magnitudes are almost as large as those produced by the global events. The ubiquity and severity of these propagating shock wave structures provides a new perspective on the mechanisms reponsible for noise and damage in cavitating flows involving clouds of bubbles. It would appear that shock wave dynamics rather than the collapse dynamics of single bubbles determine the damage and noise in many cavitating flows.

Publication: Journal of Fluid Mechanics Vol.: 355ISSN: 0022-1120

ID: CaltechAUTHORS:REIjfm98

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Abstract: This paper presents a numerical investigation of some of the phenomena involved in the nonlinear dynamics of a homogeneous bubbly mixture bounded by an oscillatory wall. This problem represents an idealization of the flow in a typical vibratory cavitation damage device. Results are presented showing that wave steepening and ultimately shock wave formation occur as the magnitude of the excitation increases. The propagation characteristics of the waves through the bubbly medium have also been studied. Strong pressure peaks of short duration, corresponding to the coherent collapse of the bubble clusters, are computed and accurately resolved, both in space and time. As the amplitude of the excitation is increased a series of period doubling bifurcations occurs. The nonlinear dynamics of the oscillating bubble cluster are observed to follow a subharmonic route to chaos.

ID: CaltechAUTHORS:CEBcav98

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Abstract: Fluid-induced rotordynamic forces produced by the fluid in an annular seal or in the leakage passage surrounding the shroud of a pump or turbine, are known to contribute substantially to the potential excitation forces acting on the rotor. In this paper we explore some of the important features of the equations governing bulk-flow models of these flows. This in turn suggests methods which might be used to solve these bulk-flow equations in circumstances where the linearized solutions (such as those of Childs 1987, 1989) will no longer be accurate. An example of a numerical solution is then presented.

ID: CaltechAUTHORS:CEBisromac98

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Abstract: In a recent study the collisional particle pressure was measured for liquid fluidized beds and liquid-solid flows. The particle pressure was defined as the 'additional pressure' generated by the presence of the particle-solid phase in a liquid-solid mixture. The particle pressure generated by collisions of particles was found to be composed of two main contributions: one from pressure pulses generated by direct collisions of particles against the containing walls (direct component), and a second one from pressure pulses due to collisions between individual particles that are transmitted through the liquid (radiated component). This paper presents a summary of the technique to measure the particle pressure and the main results of that study. Additional experiments were performed to further study each one of the components of the particle pressure. The direct component was studied by impacting particles on the active face of the pressure transducer. The magnitude of the measured impulse was found to be related to the impact velocity, the mass and the size of the impacting particle. By comparing the measurements with the predictions from the Hertzian theory, a quantification of the interstitial fluid effects could be obtained. The radiated component was investigated by generating binary collisions of particles in the vicinity of the transducer. The magnitude of the measured impulse was found to be a function of fluid density, particle size and impact velocity. Predictions based on impulse-pressure theory were obtained and compared with the experimental measurements. The model results showed good agreement with the experimental measurements.

Publication: Applied Scientific Research Vol.: 58 No.: 1-4 ISSN: 0003-6994

ID: CaltechAUTHORS:ZENasr98

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Abstract: Experiments were conducted to measure the collisional particle pressure in both cocurrent and countercurrent flows of liquid-solid mixtures. The collisional particle pressure, or granular pressure, is the additional pressure exerted on the containing walls of a particulate system due to the particle collisions. The present experiments involve both a liquid-fluidized bed using glass, plastic or steel spheres and a vertical gravity-driven flow using glass spheres. The particle pressure was measured using a high-frequency-response flush-mounted pressure transducer. Detailed recordings were made of many different particle collisions with the active face of this transducer. The solids fraction of the flowing mixtures was measured using an impedance volume fraction meter. Results show that the magnitude of the measured particle pressure increases from low concentrations (>10% solid volume fraction), reaches a maximum for intermediate values of solid fraction (30-40%), and decreases again for more concentrated mixtures (>40%). The measured collisional particle pressure appears to scale with the particle dynamic pressure based on the particle density and terminal velocity. Results were obtained and compared for a range of particle sizes, as well as for two different test section diameters. In addition, a detailed analysis of the collisions was performed that included the probability density functions for the collisoin duration and collision impulse. Two distinct contributions to the collisional particle pressure were identified: one contribution from direct contact of particles with the pressure transducer, and the second one resulting from particle collisions in the bulk that are transmitted through the liquid to the pressure transducer.

Publication: Journal of Fluid Mechanics Vol.: 353ISSN: 0022-1120

ID: CaltechAUTHORS:ZENjfm97

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Abstract: This paper reports an experimental investigation of rotordynamic forces in a whirling axial flow inducer under the influence of cavitation at various flow coefficients. The results show the occurrence of large destabilizing peaks in the force tagential to the whirl orbit for positive whirl frequency ratios. The magnitude of the destabilizing forces increased with a decrease in cavitation number and flow coefficient. The rotordynamic data obtained do not exhibit quadratic functional behavior normally assumed in many rotordynamic models. Consequently, conventional generalized stiffness, damping, and intertia matrices cannot be determined for the inducer. The results demonstrate the complexity of rotordynamic forces and their consequences on stability of axial flow inducers.

Publication: Journal of Fluids Engineering Vol.: 119 No.: 4 ISSN: 0098-2202

ID: CaltechAUTHORS:BHAjfe97

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Abstract: The rotordynamic forces generated by the fluid flow through the impeller leakage path of a centrifugal pump are now well established. The present paper examines the effects of modifying the leakage path geometry by changing the front shroud, from a conical shape to a more typical curved design, and the effects of low pressure seal design on these forces. It is found that only the cross-coupled stiffness is affected by the change of path geometry. Changing the low pressure seal from an axial to a radial clearance does, however, significantly affect the rotordynamic forces. A bulk flow numerical model is found to predict the same general result for the low pressure seal tests. The model agrees with the general trends with increasing leakage flow coefficient exhibited by the data, but appears to underpredict the magnitude of the normal force.

ID: CaltechAUTHORS:UYRicfe97

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Abstract: One of the most destructive (and noisy) forms of cavitation is that referred to as "cloud cavitation" because it involves a large collection of bubbles which behave as a coherent whole. The present paper presents the results of an experimental study of the processes of collapse of a cavitation bubble cloud, specifically that generated by an oscillating hydrofoil in a water tunnel. Measurements of the far-field noise show that this is comprised of substantial pulses radiated from the cloud at the moment of collapse. Also, transducers within the cavitation zone encounter very large pressure pulses (or shock waves) with amplitudes of the order of tens of atmospheres and typical durations of the order of tenths of a millisecond. These shock waves appear to be responsible for the enhanced noise and damage potential which results from that phenomenon.

ID: CaltechAUTHORS:REIissw97

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Abstract: Unsteady forces generated by the fluid flow through the impeller leakage path of a centrifugal pump were investigated. The effect of leakage path inlet (pump discharge) swirl on the rotordynamic forces was examined for various ratios of fluid tangential velocity to impeller tip speed. It was observed that changing the inlet swirl velocity does not appear to significantly affect the measured forces for a given leakage flow coefficient. A bulk flow numerical model was found to predict the same general result. The model agreed with experimental data for small values of the leakage flow coefficient.

ID: CaltechAUTHORS:UYRfedsm97

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Abstract: In flows around ships, the bow wave can entrain a significant amount of air as it breaks continuously on the free surface. The resulting air bubbles persist in the ship wake affecting its radar cross section as well as acting as cavitation nuclei in the flow entering the ship's propeller. In the present investigation, the formation of a bow wave on a ship was simulated in the laboratory using a deflecting plate in a supercritical free surface flow. The experiments were conducted at two scales. The present paper focuses on how the bow wave changes with the angles and flow parameters, information which is a necessary prerequisite for understanding the air entrainment process. Flow visualization studies were performed and an electronic point gage was used to study the three-dimensional shape of the bow waves and the manner in which they break.

ID: CaltechAUTHORS:WANfedsm97

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Abstract: This paper describes experiments investigating the effects of air injection on the cloud cavitation of an oscillating hydrofoil. The effects of continuous air injection were investigated using two different hydrofoils. Measurements of the acoustic pressure were made on the downstream test section floor and on the surface of one of hydrofoils, and the extent of noise reduction provided by air injection at various volume flow rates was determined. The acoustic surface pressure measurements were also correlated with visual observations made using high speed motion pictures of the cloud cavitation. Thus the effects of continuous air injection on specific cavitation structures could be identified. In addition, the effectiveness of pulsed air injection in achieving greater reductions in cavitation noise at volume flow rates equal to those used in continuous air injection experiments was investigated.

ID: CaltechAUTHORS:REIfedsm97

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Abstract: This study experimentally examines the flow of glass spheres in a wedge-shaped hopper that is vibrated hoizontally. When the hopper is discharged without vibration, discharge occurs as a funnel flow, with the material exiting the central region of the hopper and stagnant material along the sides. With vibration, the discharge of the material occurs in reverse, with the material along the sides exiting first, followed by the material in the central region. These patterns are observed with flow visualization and high-speed photography. The study also includes measurements of the discharge rate, which increases with the amplitude of the velocity of vibration.

ID: CaltechAUTHORS:HUNmdfpm97

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Abstract: This paper examines the flow of granular material through a wedge-shaped hopper subject to vertical, sinusoidal oscillations. Experiments and discrete element computer simulations were conducted to investigate particle trajectories within and mass discharge rates from the hopper. With the hopper exit closed, side wall convection cells are observed in both the experiments and simulations. The convection cells are oriented such that particles move up along the inclined walls of the hopper and down along the centerline. Results from the computer simulation indicate that the convection cells are a result of the dilation of the granular bed during free fall and interaction with hopper walls. Measurements of the mean mass discharge rate for various vibration parameters were also made in both the experiments and simulations. The ratio of the mass discharge rate for a vibrating hopper to the mass discharge rate for a non-vibrating hopper scales with the oscillation velocity amplitude and exhibits a maximum value just greater than one for oscillation velocity amplitudes less than 0.5. The ratio is less than one for larger velocity amplitudes. A simple model taking into account the change in the effective gravity acting on the granular material over an oscillation cycle is examined. A significant deficiency in the model is that is assumes no material discharges from the hopper during part of each oscillation cycle for acceleration amplitudes greater than gravitational acceleration. Data from the simulations indicate that although the discharge rate from the hopper varies throughout an oscillation cycle, it never equals zero. The simulation was also used to examine particle horizontal position and velocity profiles at the hopper exit. Lastly, preliminary observations of the effects of localized vibration on a granular material in a closed hopper are presented.

ID: CaltechAUTHORS:WASmdfpm97

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Abstract: A non-barotropic continuum bubbly mixture model is used to study the one-dimensional cavitating flow through a converging-diverging nozzle. The nonlinear dynamics of the cavitation bubbles are modeled by the Rayleigh-Plesset equation. Analytical results show that the bubble/bubble interaction through the hydrodynamics of the surrounding liquid has important effects on this confined flow field. One clear interaction effect is the Bernoulli effect caused by the growing and collapsing bubbles in the nozzle. It is found that the characterisitics of the flow change dramatically even when the upstream void fraction is very small. Two different flow regimes are found from the steady state solutions and are termed: quasi-steady and quasi-unsteady. The former is characterized by large spatial fluctuations downstream of the throat which are induced by the pulsations of the cavitation bubbles. The quasi-unsteady solutions correspond to flashing flow. Bifurcation occurs as the flow transitions from one regime to the other. An analytical expression for the critical bubble size at the bifurcation is obtained. Physical reasons for this quasi-static instability are also discussed.

ID: CaltechAUTHORS:WNGfedsm97

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Abstract: When a deep bed of granular material is subject to vertical, sinusoidal oscillations, a number of phenomena appear including two regimes of standing surface waves that form at one-half and one-quarter of the oscillation forcing frequency. These waves are referred to as f/2 and f/4 waves where f is the oscillation frequency. This paper presents the results from experiments and computer simulations designed to study the wavelength and wave amplitude dependence of the surface waves on the vibration parameters, collision coefficient of restriction, and the particle bed depth.

ID: CaltechAUTHORS:WASpg97

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Abstract: This paper investigates the effects of bubbly dynamics on the stability of parallel bubbly flows of low void fraction. The equations of motion for the bubbly mixture are linearized for small perturbations and the parallel flow assumption is used to obtain a modified Rayleigh equation governing the inviscid stability problem. This is then used for the stability analysis of two-dimensional shear layers, jets and wakes. Inertial effects associated with the bubbly response and energy dissipation due to the viscosity of the liquid, the heat transfer between the two phases, and the liquid compressibility are included. Numerical solutions of the eigenvalue problems for the modified Rayleigh equation are obtained by means of a multiple shooting method. Depending on the characteristic velocities of the various flows, the void fractions, and the ambient pressure, the presence of air bubbles can induce significant departures from the classical stability results for a single-phase fluid.

Publication: Journal of Fluid Mechanics Vol.: 339ISSN: 0022-1120

ID: CaltechAUTHORS:DAGjfm97

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Abstract: Several recent experimental and analytical investigations of cavitating flows have revealed new phenomena which clearly affect how we should view cavitation growth and collapse and the strategies used to ameliorate its adverse effects. On the scale of individual bubbles it is now clear that the dynamics and acoustics of single bubbles are severely affected by the distortion of the bubble by the flow. This distortion depends on the typical dimension and velocity of the flow (as well as the Reynolds number) and therefore the distortion effects are very important in the process of scaling results up from the model to the prototype. The first part of the lecture will discuss the implications of these new observations for the classic problem of scale-up. Another recent revelation is the importance of the interactions between bubbles in determining the coherent motions, dynamic and acoustic, of a cloud of cavitation bubbles. The second part of the lecture focusses on these cloud cavitation effects. It is shown that the collapse of a cloud of cavitating bubbles involves the formation of a bubbly shock wave and it is suggested that the focussing of these shock waves is responsible for the enhanced noise and damage in cloud cavitation. The paper describes experiments and calculations conducted to investigate these phenomena in greater detail as part of an attempt to find ways of ameliorating the most destructive effects associated with cloud cavitation.

ID: CaltechAUTHORS:CEBksme97b

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Abstract: Thie paper described experimental and computational investigations of the dynamics of clouds of cavitation bubbles. Recent studies have confirmed that the interactions between bubbles as they are manifest in the dynamics of bubble clouds lead to generation of very large impulsive pressures which, in turn, cause substantial enhancement of the radiated noise and the material damage which results from this form of cavitation. The experimental program focuses on cloud cavitation formed on the suction surface of a hydrofoil, both static and oscillating. Piezo-electric transducers mounted at a series of locations on the suction surface measured very large positive pressure pulses with amplitudesx of the order of tens of atmospheres and with durations of the order of tenths of milliseconds. Two distinct types of pressure pulse were identified from high-speed films: "local pulses" which are registered by individual transducers and appear to be associated with the propagation of localized bubbly shocks and "global pulses" which result from larger scale, coherent collapses of bubble clouds. The experiments investigate the effects of reduced frequency, cavitation number and tunnel velocity on the magnitude of these pressure pulses. The computational component continues the earlier work of Wang and Brennen (1, 2), which presented numerical solutions of the growth and collapse of a spherical cloud of bubbles. This confirmed the idea put forward by Morch and his co-workers who speculated that collapse of the cloud involved the formation of a bubbly shock wave on the surface of the cloud and that inward propagation and geometric focussing of this shock would lead to very large localized pressure pulses. Here we review how the radiated acoustic pulses depend on the governing parameters such as the bubble population density, the cavitation number and the ratio of the bubble size to the cloud size. Understanding such bubbly flow and shock wave processes is important because these flow structures propagate the noise and produce the impulsive loads on nearby solid surfaces in a cavitating flow. How these shocks are formed and propagate in the much more complex cloud geometry associated with cavitating foils, propeller or pump blades is not presently clear. However, by combining the computational and experimental observations, we suggest some specific mechanisms which may be active in the dynamics and acoustics of these more complex flows.

ID: CaltechAUTHORS:BRE21snh97

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Abstract: The present work investigates the dynamics of the three-dimensional, unsteady flow of a bubbly mixture in a cylindrical duct subject to a periodic pressure excitation at one end. One of the purposes is to investigate the bubbly or cavitating flow at inlet to or discharge from a pump whose blade motions would provide such excitation. The flow displays various regimes with radically different wave propagation characteristics. The dynamic effects due to the bubble response may radically alter the fluid behavior depending on the void fraction of the bubbly mixture, the mean bubble size, the pipe diamter, the angular speed of the turbomachine and the mean flow Mach number. This simple linearized analysis illustrates the importance of the complex interactions of the dynamics of the bubbles with the average flow, and provides information on the propagation and growth of the turbopump-induced disturbances in the feed lines operating with bubbly or cavitating liquids. Examples are presented to illustrate the influence of the relevant flow parameters. Finally, the limitations of the theory are outlined.

Publication: Journal of Fluids Engineering Vol.: 118 No.: 5 ISSN: 0098-2202

ID: CaltechAUTHORS:DAUjfe96

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Abstract: A deep bed of granular material (more than six layers of particles) was subjected to sinusoidal, vertical vibrations. Several phenomena were observed depending on the amplitude of excitation. These included heaping, surface waves, and arching; the transitions from one state to another involved various dynamic instabilites and bifurcations. The paper includes a description of these phenomena and the characteristic properties associated with each in addition to measurements of the transitions from one phenomena to another.

Publication: Journal of Applied Mechanics Vol.: 63 No.: 3 ISSN: 0021-8936

ID: CaltechAUTHORS:WASjam96

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Abstract: When a deep bed of granular material is subjected to vertical, sinusoidal oscillations, a number of interesting phenomena appear including heaps, convection cells, surface waves, and arches. This paper examines the convection cell phenomena associated with vertical side walls using two-dimensional discrete element simulations. Measurements from the simulations indicate that when the container aspect ratio, defined as the depth of the granular bed, H, divided by the width of the container, W, is large, convection cells interact and the boundary layer width of the downward flow of particles against the walls varies linearly with the container width. However, when the container aspect ratio [is] small and the convection cells do not interact, the boundary layer width remains at a nearly constant value of ten particle diameters. Other simulation measurements show that the vertical location of the convection cell center remains close to the free surface regardless of container aspect ratio. Additional measurements show that the particle flow rate per oscillation cycle in the boundary layer increases with increasing vibration amplitude and velocity. Lastly, the asymmetric drag mechanism proposed as the cause of the side wall convection cells is briefly examined.

ID: CaltechAUTHORS:WASwcce96

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Abstract: A bed of granular material which is subjected to vertical vibration will exhibit at least one sudden expansion at a critical acceleration amplitude. This sudden expansion corresponds to a bifurcation similar to that exhibited by a single ball bouncing on a vibrating plate. Theoretical analysis based on this model yields results which are in accord with the experimental observations. Other bifurcations may occur at higher vibration levels.

Publication: Journal of Applied Mechanics Vol.: 63 No.: 1 ISSN: 0021-8936

ID: CaltechAUTHORS:BREjam96

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Abstract: This paper describes an experimental investigation of the large unsteady and impulsive pressures which are experienced on the suction surface of both an oscillating and static hydrofoil as a result of cloud cavitation. The present experiments used piezo-electric transducers to measure unsteady pressures at four locations along the chord of the foil and at two locations along the walls of the tunnel test section. These transducers measured very large positive pressure pulses with amplitudes of the order of tens of atmospheres and with durations of the order of tenths of milliseconds. Two distinct types of pressure pulse were identified. "Local" pulses occurred at a single transducer location and were randomly distributed in position and time; several local impulses could be recorded by each transducer during an oscillation cycle. On the other hand, "global" impulses were registered by all the transducers almost simultaneously. Correlation of the transducer output with high speed movies of the cavitation revealed that they were produced by a large scale collapse of the bubble cloud. The location of the global impulses relative to the foil oscillation was quite repeatable and produced substantial far-field noise. The high speed movies also showed that the local impulses were caused both by crescent-shaped regions of low void fraction and by small bubbly structures. These regions appeared to be bounded by bubbly shock waves which were associated with the large pressure pulses. The paper also quantifies the effect of reduced frequency, cavitation number and tunnel velocity on the strength of the pressure pulses by presenting the acoustic impulse for a range of flow conditions. The reduced frequency is an important parameter in the determination of the total impulse level and the local and global pulse distribution. Large impulses are present on the foil surface even at cavitation numbers which do not result in large levels of acoustic radiation or global impulse. The total impulse increases with increasing tunnel velocity.

Vol.: 1 No.: FED-236
ID: CaltechAUTHORS:REIfed96

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Abstract: This paper presents an anylytical investigation of the effects that vapor/gas bubbles can have on the fluid-induced rotordynamic forces in a liquid-filled annulus between a cylindrical rotor and a surrounding cylindrical stator. It is demonstrated that such cavitation (vaporous or gaseous) can have important consequences in altering the rotordynamic characteristics of devices such as long journal bearings or long squeeze-film dampers. A linearized analysis which includes bubble dynamic effects is used to evaluate the rotordynamic effects caused by a small amplitude whirl motion of the rotor in both the high and low Reynolds number regimes of fluid motion. In the former case the Euler equations for a bubbly mixture are employed while, in the latter, a modified Reynolds lubrication equation is used. These are combined with a Rayleigh-Plesset analysis of the bubble dynamics which includes various bubble damping effects. It is shown that, in certain parametric regimes, the normal and tangential fluid-induced rotordynamic forces acting on the rotor can deviate substantially from their classical forms in single-phase flow.

Publication: ASME Vol.: FED-23 No.: 236
ID: CaltechAUTHORS:DAUcglffmd96

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Abstract: The focus of this paper is the numerical simulation of the dynamics and acoustics of a cloud of cavitating bubbles. The prototypical problem solved considers a finite cloud of nuclei that is exposed to a decrease in the ambient pressure which causes the cloud to cavitate. A subsequent pressure recovery then causes the cloud to collapse. This is typical of the perturbation experienced by a bubble cloud as it passes a headform or the blade of a ship propeller. The simulations employ the fully non-linear, non-barotropic, homogeneous flow equations coupled with the Rayleigh-Plesset dynamics for individual bubbles. This set of equations is solved numerically by an integral method. The computational results confirm the early speculation of Morch and his co-workers (Morch 1980 & 1981, Hanson et al. 1981) that an inwardly propagating shock wave may be formed in the collapse of a cavitating cloud. The structure of the shock is found to be similar to that of the steady planar shocks analyzed by Noordij and van Wijngaarden (1974). The shock wave grows rapidly not only because of the geometric effect of an inwardly propagating spherical shock but also because of the coupling of the single bubble dynamics with the global dynamics of the flow through the pressure and velocity fields (see also Wang and Brennen 1994). The specific circumstances which lead to the formation of such a shock are explored. Moreover, the calculations demonstrate that the acoustic impulse produced by the cloud is significantly enhanced by this shock-focusing process. Major parameters which affect the dynamics and acoustics of the cloud are found to be the cavitation number, [sigma], the initial void fraction, [alpha-zero], the minimum pressure coefficient of the flow, [C Pmin], the natural frequencies of the cloud, and the ratio of the length scale of low pressure perturbation to the initial radius of the cloud, [D/A-zero], where D can be, for example, the radius of the headform or chord length of the propeller blade. We examine how some of these parameters affect the far field acoustic noise produced by the volumetric acceleration of the cloud. The non-dimensional far-field acoustic impulse produced by the cloud collapse is shown to depend, primarily, on the maximum total volume of the bubbles in the cloud normalized by the length scale of the low pressure perturbation. Also, this maximum total volume decreases quasi-linearly with the increase of the cavitation number. However, the slope of the dependence, in turn, changes with the initial void fraction and other parameters. Non-dimensional power density spectra for the far-field noise are presented and exhibit the [equation] behavior, where n is between 0.5 and 2. After several collapse cycles, the cloud begins to oscillate at its natural frequency and contributes harmonic peaks in its spectrum.

Publication: ASME Vol.: FED-226 No.: 226
ID: CaltechAUTHORS:WNGcglffmd95

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Abstract: This paper investigates the effects of bubble dynamics on the stability of bubbly and cavitating jets of low void fraction. The equations of motion for the bubbly mixture are linearized for small perturbations and the parallel flow assumption is used to obtain a modified Rayleigh equation governing the inviscid stability of a two-dimensional jet. Inertial effects associated with the bubble response and energy dissipation due to the viscosity of the liquid, the heat transfer between the two phases, and the liquid compressibility are included. Numerical solutions of the eigenvalue problem for the modified Rayleigh equation of a Bickley jet are obtained by a multiple shooting method. Depending on the jet velocity, the void fraction, and the ambient pressure, the presence of air bubbles can induce significant departures from the classical results for a single phase fluid.

ID: CaltechAUTHORS:20130725-165119685

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Abstract: Calculations of the collapse dynamics of a cloud of cavitation bubbles confirm the speculations of Morch and his co-workers and demonstrate that collapse occurs as a result of the inward propagation of a shock wave which grows rapidly in magnitude. Results are presented showing the evolving dynamics of the cloud and the resulting far-field acoustic noise.

Vol.: 2
ID: CaltechAUTHORS:WANissw95

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Abstract: Recent observations of growing and collapsing bubbles in flows over axisymmetric headforms have revealed the complexity of the ‘micro-fluid-mechanics’ associated with these bubbles (van der Meulen & van Renesse 1989; Briancon-Marjollet et al. 1990; Ceccio & Brennen 1991). Among the complex features observed were the bubble-to-bubble and bubble-to-boundary-layer interactions which leads to the shearing of the underside of the bubble and alters the collapsing process. All of these previous tests, though, were performed on small headform sizes. The focus of this research is to analyse the scaling effects of these phenomena due to variations in model size, Reynolds number and cavitation number. For this purpose, cavitating flows over Schiebe headforms of different sizes (5.08, 25.4 and 50.8 cm in diameter) were studied in the David Taylor Large Cavitation Channel (LCC). The bubble dynamics captured using high-speed film and electrode sensors are presented along with the noise signals generated during the collapse of the cavities. In the light of the complexity of the dynamics of the travelling bubbles and the important bubble/bubble interactions, it is clear that the spherical Rayleigh-Plesset analysis cannot reproduce many of the phenomena observed. For this purpose an unsteady numerical code was developed which uses travelling sources to model the interactions between the bubble (or bubbles) and the pressure gradients in the irrotational flow outside the boundary layer on the headform. The paper compares the results of this numerical code with the present experimental results and demonstrates good qualitative agreement between the two.

Publication: Journal of Fluid Mechanics Vol.: 293ISSN: 0022-1120

ID: CaltechAUTHORS:20120217-084909340

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Abstract: To model the processes of cavitation inception, noise, and damage, it is necessary to generate a model of the cavitation event rate which can then be coupled with the consequences of the individual events to produce a complete synthesis of the phenomenon. In this paper we describe recent efforts to connect the observed event rates to the measured distributions of cavitation nuclei in the oncoming stream. A comparison is made between the observed event rates and event rates calculated from measured nuclei distributions using an algorithm which includes the dynamics of the nuclei motion and growth. Various complications are explored including the relative motion between the nucleus and the liquid, the effect of the finite bubble size of the growing bubble relative to the dimensions of the low pressure region, and the effect of bubble growth on neighboring nuclei. All of these are seen to have an important influence on the event rate, and therefore, on cavitation inception and other macroscopic consequences. We demonstrate that it is possible to predict the correct order of magnitude of the event rate when an attempt is made to model the important flow complications.

ID: CaltechAUTHORS:LIUcav95

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Abstract: This paper examines the bubble dynamic effects on the stability of parallel bubbly and cavitating flows of low void fraction. Inertial effects associated with the bubble response and energy dissipation due to the viscosity of the liquid, the heat transfer between the two phases, and the liquid compressibility are included. The equations of motion are linearized for small perturbations and a modified Rayleigh equation for the inviscid stability of the two-dimensional parallel flow is derived. Numerical solutions of the characteristic problem for the modified Rayleigh equation of a free shear layer are obtained by means of a multiple shooting method. Depending on the dispersion of the gaseous phase in the bubbly mixture, the ambient pressure and the free stream velocities, the pressure of air bubbles can induce significant departures from the classical solution for a single phase fluid. Results are presented to illustrate the influence of the relevant flow parameters.

ID: CaltechAUTHORS:DAGcav95

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Abstract: Increasing interest has been given to swirl brakes as a means of reducing destabilizing rotordynamic forces due to leakage flows in new high speed rocket turbopumps. Although swirl brakes have been used successfully in practice (such as with the Space Shuttle HPOTP), no experimental tests until now have been performed to demonstrate their beneficial effect over a range of leakage flow rates. The present study investigates the effect of swirl brakes on rotordynamic forces generated by discharge-to-suction leakage flows in the annulus of shrouded centrifugal pumps over a range of subsynchronous whirl rtios and various leakage flow rates. In addition, the effectiveness of swirl brakes in the presence of leakage inlet (pump discharge) swirl is also demonstrated. The experimental data demonstrates that with the addition of swirl brakes a significant reduction in the destabilizing tangential force for lower flow rates is achieved. At higher flow rates, the brakes are detrimental. In the presence of leakage inlet swirl, brakes were effective over all leakage flow rates tested in reducing the range of whirl frequency ratio for which the tangential force is destabilizing.

Publication: Journal of Fluids Engineering Vol.: 117 No.: 1 ISSN: 0098-2202

ID: CaltechAUTHORS:SIVjfe95

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Abstract: This book describes and explains the fundamental physical processes involved in bubble dynamics and the phenomenon of cavitation. It is intended as a combination of a reference book for those scientists and engineers who work with cavitation or bubble dynamics and as a monograph for advanced students interested in some of the basic problems associated with this category of multiphase flows. A basic knowledge of fluid flow and heat transfer is assumed but otherwise the analytical methods presented are developed from basic principles. The book begins with a chapter on nucleation and describes both the theory and observations of nucleation in flowing and non-flowing systems. The following three chapters provide a systematic treatment of the dynamics of the growth, collapse or oscillation of individual bubbles in otherwise quiescent liquids. Chapter 4 summarizes the state of knowledge of the motion of bubbles in liquids. Chapter 5 describes some of the phenomena which occur in homogeneous bubbly flows with particular emphasis on cloud cavitation and this is followed by a chapter summarizing some of the experiemntal observations of cavitating flows. The last chapter provides a review of the free streamline methods used to treat separated cavity flows with large attached cavities.

ID: CaltechBOOK:1995.001

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Abstract: The present work investigates the dynamics of idealized bubbly and cavitating flows in whirling helical inducers, with the purpose of understanding the impact of the bubble response on the rotordynamic forces exerted by the fluid on the turbomachine under cavitating conditions. Inertial, damping, and compressibility effects in the dynamics of the bubbles are included. The effect of the whirl excitation on the two-phase flow is dependent on the wave propagation speed and the bubble resonance behavior in the bubbly mixture. These, in turn, lead to rotordynamic forces which are complicated functions of the whirl frequency and depend on the void fraction of the bubbles and on the mean flow properties. Under cavitating conditions the dynamic response of the bubbles induces major deviations from the non-cavitating flow solutions. The quadratic dependence of rotordynamic fluid forces on the whirl speed, which is typical of cavitation-free operation is significantly modified. Results are presented to illustrate the influence of the various flow parameters.

Publication: ASME Vol.: FED-21 No.: 210
ID: CaltechAUTHORS:DAUcmff95

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Abstract: The behavior of the flow of glass spheres in a vertically vibrating hopper is examined. A two-dimensional hopper is mounted on a shaker that provides sinusoidal, vertical vibrations. Both the frequency and amplitude of the vibrations are adjustable. Hopper discharge rates and flow patterns are measured as the acceleration amplitude of the vibrations is increased from 0 to 4g's. Comparisons are made with unvibrated hopper flows and with a two-dimensional discrete element simulation model.

Vol.: 2
ID: CaltechAUTHORS:WASasceemc95

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Abstract: Recent observations of growing and collapsing bubbles in flows over axisymmetric headforms have revealed the complexity of the 'micro-fluid-mechanics' associated with these bubbles (van der Meulen & van Renesse 1989; Briancon-Marjollet et al. 1990; Ceccio & Brennen 1991). Among the complex features observed were the bubble-to-bubble and bubble-to-boundary-layer interactions which leads to the shearing of the underside of the bubble and alters the collapsing process. All of these previous tests, though, were performed on small headform sizes. The focus of this research is to analyse the scaling effects of these phenomena due to variations in model size, Reynolds number and cavitation number. For this purpose, cavitating flows over Schiebe headforms of different sizes (5.08, 25.4 and 50.8 cm in diameter) were studied in the David Taylor Large Cavitation Channel (LCC). The bubble dynamics captured using high-speed film and electrode sensors are presented along with the noise signals generated during the collapse of the cavities. In the light of the complexity of the dynamics of the travelling bubbles and the important bubble/bubble interactions, it is clear that the spherical Rayleigh-Plesset analysis cannot reproduce many of the phenomena observed. For this purpose an unsteady numerical code was developed which uses travelling sources to model the interactions between the bubble (or bubbles) and the pressure gradients in the irrotational flow outside the boundary layer on the headform. The paper compares the results of this numerical code with the present experimental results and demonstrates good qualitative agreement between the two.

Publication: Journal of Fluid Mechanics Vol.: 293ISSN: 0022-1120

ID: CaltechAUTHORS:KUHjfm95

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Abstract: A numerical simulation of the collapse of a cloud of bubbles has been used to demonstrate the development of an inwardly propagating shock wave which grows rapidly in magnitude. The fully non-linear nonbarotropic homogeneous flow equations are coupled with single bubble dynamics and solved by a stable numerical scheme. The computational results demonstrate the structure of the shock wave as well as its strengthening effect due to the coupling of the single bubble dynamics with the global dynamics of the flow through the pressure and velocity fields. This appears to confirm the speculation of Morch and his co-workers that such shock formation is an important part of cloud collapse.

Publication: ASME Vol.: FED-194 No.: 194
ID: CaltechAUTHORS:WNGcmpf94

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Abstract: This paper reports on experiments conducted in the Rotor Force Test Facility at the California Institute of Technology to examine the effects of a tip leakage restriction and swirl brakes on the rotordynamic forces due to leakage flows on an impeller undergoing a prescribed circular whirl. The experiments simulate the leakage flow conditions and geometry of the Alternate Turbopump Design (ATD) of the Space Shuttle High Pressure Oxygen Turbopump and are critical to evaluating the pump's instability problems. Results indicate the detrimental effects of a discharge orifice and the beneficial effects of adding swirl brakes. Plots of the tangential and normal forces versus whirl frequency ratio show a substantial increase in these forces along with destabilizing resonances when a discharge orifice is added. When swirl brakes are added, some of the detrimental effects of the orifice are reduced. For the tangential force, a significant reduction occurs and a destabilizing resonance appears to be eliminated. For the normal force, although the overall force is not reduced, once again a destabilizing resonance appears to be eliminated.

ID: CaltechAUTHORS:SIVtpdrm94

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Abstract: In recent years, increasing attention has been give to fluid-structure interaction problems in turbomachines. The present research focuses on just one such fluid-structure interaction problem, namely, the role played by fluid forces in determining the rotordynamic stability and characteristics of a centrifugal pump. The emphasis of this study is to investigate the contributions to the rotordynamic forces from the discharge-to-suction leakage flows between the front shroud of the rotating impeller and the stationary pump casing. An experiment was designed to measure the rotordynamic shroud forces due to simulated leakage flows for different parameters such as flow rate, shroud clearance, face-seal clearance and eccentricity. The data demonstrate substantial rotordynamic effects and a destabilizing tangential force for small positive whirl frequency ratios; this force decreased with increasing flow rate. The rotordynamic forces appear to be inversely proportional to the clearance and change significantly with the flow rate. Two sets of data taken at different eccentricities yielded quite similar nondimensional rotordynamic forces indicating that the experiments lie within the linear regime of eccentricity.

Publication: Journal of Fluids Engineering Vol.: 116 No.: 1 ISSN: 0098-2202

ID: CaltechAUTHORS:GUIjfme94

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Abstract: The subject of this monograph is the fluid dynamics of liquid turbomachines, particularly pumps. Rather than attempt a general treatise on turbomachines, we shall focus attention on those special problems and design issues associated with the flow of liquid through a rotating machine. There are two characteristics of a liquid that lead to these special problems, and cause a significantly different set of concerns than would occur in, say, a gas turbine. These are the potential for cavitation and the high density of liquids that enhances the possibility of damaging unsteady flows and forces.

ID: CaltechBOOK:1994.001

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Abstract: Recently Ceccio and Brennen [1][2][3] have examined the interaction between individual traveling cavitation bubbles and the structure of the boundary layer and flow field in which the bubble is growing and collapsing. They were able to show that individual bubbles are often fissioned by the fluid shear and that this process can significantly effect the acoustic signal produced by the collapse. Furthermore they were able to demonstrate a relationship between the number of cavitation events and the nuclei number distribution measured by holographic methods in the upstream flow. Kumar and Brennen [4][5] have further examined the statistical properties of the acoustical signals from individual cavitation bubbles on two different headforms in order to learn more about the bubble/flow interactions. All of these experiments were, however, conducted in the same facility with the same size of headform (5.08cm in diameter) and over a fairly narrow range of flow velocities (around 9m/s). Clearly this raises the issue of how the phenomena identified change with speed, scale and facility. The present paper will describe further results from experiments conducted in order to try to answer some of these important questions regarding the scaling of the cavitation phenomena. These experiments (see also Kuhn de Chizelle et al. [6][7]) were conducted in the Large Cavitation Channel of the David Taylor Research Center in Memphis Tennessee, on similar Schiebe headforms which are 5.08, 25.4 and 50.8cm in diameter for speeds ranging up to 15m/s and for a range of cavitation numbers.

ID: CaltechAUTHORS:20111222-090408765

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Abstract: Cloud cavitation, often formed by the breakdown of a sheet or vortex cavity, is believed to be responsible for much of the noise and erosion damage that occurs under cavitating conditions. For this paper, cloud cavitation was produced through the periodic forcing of the flow by an oscillating hydrofoil. The present work examines the acoustic signal generated by the collapse of cloud cavitation, and compares the results to those obtained by studies of single travelling bubble cavitation. In addition, preliminary studies involving the use of air injection on the suction surface of the hydrofoil explore its mitigating effects on the cavitation noise.

ID: CaltechAUTHORS:REIsnh94

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Abstract: Previous experiments conducted in the Rotor Force Test Facility at the California Institute of Technology have thoroughly examined the effect of leakage flows on the rotordynamic forces on a centrifugal pump impeller undergoing a prescribed circular whirl. These leakage flows have been shown to contribute substantially to the total fluid induced forces acting on a pump. However, to date nothing is known of the flow field in the leakage annulus of shrouded centrifugal pumps. No attempt has been made to qualitatively or quantitatively examine the velocity field in the leakage annulus. Hence the test objective of this experiment is to acquire fluid velocity data for a geometry representative of the leakage annulus of a shrouded centrifugal pump while the rotor is whirling using laser velocimetry. Tests are performed over a range of whirl ratios and a flowrate typical of Space Shuttle Turbopump designs. In addition to a qualitive study of the flow field, the velocity data can be used to anchor flow models.

Publication: ASME Vol.: FED-191 No.: 191
ID: CaltechAUTHORS:SIVasla94

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Abstract: The present work investigates the dynamics of the three-dimensional, unsteady flow of a bubbly mixture in a cylindrical duct subject to a periodic pressure excitation at one end. The results are then applied to the case of the idealized pressure excitation generated by the rotor stage of a turbomachine with the objective of understanding the dynamics of an inlet or discharge duct filled with bubbly liquid. The flow displays various regimes (subsonic, supersonic and super-resonant), with radiacally different propagation characteristics. Depending on the dispersion of the gaseous phase in the bubbly mixture and the angular speed of the turbomachine, the dynamic effects due to the bubble response can be significant, and the flow no longer behaves as a homogeneous barotropic fluid, as is commonly assumed. Examples are presented to illustrate the influence of various flow parameters.

Publication: ASME Vol.: FED-19 No.: 194
ID: CaltechAUTHORS:DAUcmff94

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Abstract: This paper will present a review of some of the recent advances in our understanding of the dynamics and acoustics of cavitating flows. We focus first on the individual events which evolve from a single travelling nucleus and describe observations of the intricate micro-fluid-mechanics which affect both the bubble shape and the subsequent emission of noise. These phenomena have important consequences in terms of their implications for the scaling of cavitation damage and noise. We also present calculations of the interaction between the individual traveling bubbles and the irrotational flow outside of the boundary layer of the headform. Comparisons of predicted and experimentally observed bubble shapes show qualitative agreement but further work is necessary to understand the details of the interactions between the viscous boundary layer and the bubble. To model the processes of cavitation inception, noise and damage it is necessary to generate a model of the cavitation event rate which can then be coupled with the consequences of the individual events. In the second part of this paper we describe recent efforts to connect the observed event rates to the measured distributions of cavitation nuclei in the oncoming stream. Such studies necessarily raise questions regarding the nuclei distributions in water tunnels and in the ocean and it would seem that we still know little of the nuclei population dynamics in either context. This is illustrated by a few observations of the population dynamics in a particular facility. The third subject addressed in this paper is the question of the noise produced by an individual travelling cavitation event. It is shown that the distortions in the shape of cavitation bubbles leads to acoustic impulses which are about an order of magnitude smaller than those predicted by the spherical bubble dynamics of the Rayleigh-Plesset equation. However, at the higher cavitation numbers, the upper bound on the experimental impulses scales with speed and size much as one would expect from the spherical bubble analysis. Initially, as the cavitation number is decreased, the impulse increases as expected. But, beyond a certain critical cavitation number, the noise again decreases in contrast to the expected increase. This phenomenon is probably caused by two effects, namely the interaction between events at the higher event densities and the reduction in the impulse due to a change in the dominant type of cavitation event. From the single event we then move to the larger scale structures and the interactions which occur when the density of the events becomes large and individual bubbles begin to interact. One of the more important interaction phenomena which occur results from the behaviour of a cloud of cavitation bubbles. Most previous theoretical studies of the dynamics of cavitating clouds have been linear or weakly non-linear analyses which have identified the natural frequencies and modes of cloud oscillation but have not, as yet, shown how a cloud would behave during the massively non-linear response in a cavitating flow. We present non-linear calculations which show the development of an inwardly propagating shock wave during the collapse phase of the motion. These observations confirm the earlier speculation of Mørch and his co-workers.

ID: CaltechAUTHORS:BRE147

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Abstract: Observations have been made of the growth and collapse of surface and cloud cavitation on a finite aspect ratio hydrofoil oscillating in pitch. The cavitation was recorded using both still and high-speed motion picture photography, and the variations with cavitation number and reduced frequency of oscillation were investigated. The noise generated by the cavity collapse was also measured and analyzed. The acoustic signals associated with individual cavity collapse events have been synchronized with the motion pictures, providing insights into the correspondence between the flow structures involved in the cavity collapse process and the sound generated by them.

Publication: ASME Vol.: FED-190 No.: 190
ID: CaltechAUTHORS:MCKcglffmd94

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Abstract: This paper reports an experimental investigation of the rotordynamic forces that occur in a whirling three bladed inducer under the influence of cavitation. The effect of lowering the flow coefficient (and thus causing reverse flows) on these forces were also investigated. The results show the occurrence of large destabilizing peaks in the force tangential to the whirl orbit for positive whirl frequency ratios. Cavitation caused these forces to become destabilizing at both negative and positive whirl frequency ratios. The magnitude of the destabilizing forces increased with decreasing vacitation numbers and flow coefficient. The rotordynamic data obtained do not exhibit the kind of quadratic functional behavior which is normally ussumed in many rotordynamic models. Consequently the conventional generalized stiffness, damping and interia matrices cannot be determined for the inducer. The results demonstrate the complexity of rotordynamic forces and their consequences on stability of axial flow inducers.

Publication: ASME Vol.: FED-19
ID: CaltechAUTHORS:BHAfed94

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Abstract: Simultaneous measurements were made of the cavitation event rates on a Schiebe body and the nuclei number distributions in the oncoming stream in the Low Turbulence Water Tunnel at Caltech. Cavitation inception occurred at an average cavitation number of 0.57. Cavitation event rates increased dramatically as the cavitation number was decreased. It was also found that both the magnitude and the shape of the nuclei distribution changed substantially with the operating condition. These changes had very strong effect on the event rate and therefore on cavitation inception number based on a fixed event rate. At the same cavitation number, the changes in the event rate due to different free stream nuclei populations can be as much as a decade. The changes in the shape of the nuclei distribution occurred mostly in the nuclei size range above 15 [microns]. The nuclei concentration tended to increase as cavitation number was decreased. And the cavitation event rate increased with the free stream nuclei concentration. The measured nuclei density distributions are used in an analytical model which attempts to correlate the event rate with the nuclei population. The predicted event rates are compared with those observed experimentally.

Publication: ASME Vol.: FED-190 No.: 190
ID: CaltechAUTHORS:LIUascglffmd94

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Abstract: Recent observations of the geometries of growing and collapsing bubbles in typical cavitating flows (van der Meulen and van Renesse 1989, Briancon-Marjollet and Franc 1990, Ceccio and Brennen 1991, Kuhn de Chizelle et al. 1992) have revealed the complexity of the "microfluidmechanics" associated with these flows. Clearly the interaction of individual bubbles with the nearby solid surface and its boundary layer produce features in the dynamics of growth and collapse which were not present in experiments on bubbles in a quiescent liquid. These include several mechanisms for bubble fission prior to collapse and the role played by the concentration of accumulated vorticity in producing a hybrid vortex/bubble during collapse. The current paper presents a methodology for the calculation of the interaction between an individual bubble and the irrotational flow exterior to the boundary layer on a body. Comparison is made between computed bubble geometries and those previously observed experimentally. The calculations also reveal the effect which the bubble has on the irrotational flow around the body and consequently permits some preliminary evaluation of the interactions between neighbouring bubbles.

No.: 23
ID: CaltechAUTHORS:KUHbdip94

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Abstract: The role played by fluid forces in determining the rotordynamic stability of a centrifugal pump is gaining increasing attention. The present research investigates the contributions to the rotordynamic forces from the discharge-to-suction leakage flows between the front shroud of the rotating impeller and the stationary pump casing. In particular, the dependency of the rotordynamic characteristics of leakage flows on the swirl at the inlet to the leakage path was examined. An inlet guide vane was designed for the experiment so that swirl could be introduced at the leakage flow inlet. The data demonstrate substantial rotordynamic effects and a destabilizing tangential force for small positive whirl ratios: this force decreased with increasing flow rate. The effect of swirl on the rotordynamic forces was found to be destabilizing.

Publication: Journal of Engineering for Gas Turbines and Power Vol.: 115 No.: 2 ISSN: 0742-4795

ID: CaltechAUTHORS:GUIjegtp93

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Abstract: Recent experiments conducted in the Rotor Force Test Facility at the California Institute of Technology have examined the effects of a tip leakage restriction and swirl brakes on the rotordynamic forces due to leakage flows on an impeller undergoing a prescribed circular whirl. The experiments simulate the leakage flow conditions and geometry of the Alternate Turbopump Design (ATD) of the Space Shuttle High Pressure Oxygen Turbopump and are critical to evaluating the pump's rotordynamic instability problems. Previous experimental and analytical results have shown that discharge-to-suction leakage flows in the annulus of a shrouded centrifugal pump contribute substantially to the fluid induced rotordynamic forces. Also, previous experiments have shown that leakage inlet (pump discharge) swirl can increase the cross-coupled stiffness coefficient and hence increase the range of positive whirl for which the tangential force is destabilizing. In recent experimental work, the present authors demonstrated that when the swirl velocity within the leakage path is reduced by the introduction of ribs or swirl brakes, then a substantial decrease in both the destabilizing normal and tangential forces could be achieved. Motivation for the present research is that previous experiments have shown that restrictions such as wear rings or orifices at pump inlets affect the leakage forces. Recent pump designs such as the Space Shuttle Alternate Turbopump Design (ATD) utilize tip orifices at discharge for the purpose of establishing axial thrust balance. The ATD has experienced rotordynamic instability problems and one may surmise that these tip discharge orifices may also have an important effect on the normal and tangential forces in the plane of impeller rotation. The present study determines if such tip leakage restrictions contribute to undesirable rotordynamic forces. Additional motivation for the present study is that the widening of the leakage path annular clearance and the installation of swirl brakes in the ATD has been proposed to solve its instability problems. The present study assesses the effect of such a design modification on the rotordynamic forces. The experimental apparatus consists of a solid or dummy impeller, a housing instrumented for pressure measurements, a rotating dynamometer and an eccentric whirl mechanism. The solid impeller is used so that leakage flow contributions to the forces are measured, but the main throughflow contributions are not experienced. The inner surface of the housing has been modified to accommodate meridional ribs or swirl brakes within the leakage annulus. In addition, the housing has been modified to accommodate a discharge orifice that qualitatively simulates one side of the balance piston orifice of the Space Shuttle ATD. Results indicate the detrimental effects of a discharge orifice and the beneficial effects of brakes. Plots of the tangential and normal forces versus whirl ratio show a substantial increase in these forces along with destabilizing resonances at some positive whirl ratios when a discharge orifice is added. When brakes are added, some of the detrimental effects of the orifice are reduced. For the tangential force, a plot versus whirl ratio shows a significant reduction and a destabilizing resonance appears to be eliminated. For the normal force, although the overall force is not reduced, again a destabilizing resonance appears to be eliminated.

Vol.: 1 No.: CP-322
ID: CaltechAUTHORS:SIVcfdarp93

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Abstract: The role played by fluid forces in determining the rotordynamic stability and characteristics of a centrifugal pump is gaining increasing attention. The present research investigates the contributions to the rotordynamic forces from the discharge-to-suction leakage flows between the front shroud of the rotating impeller and the stationary pump casing. An experiment was designed to measure the rotordynamic shroud forces due to simulated leakage flows for different parameters such as flowrate, shroud clearance, face seal clearance, and eccentricity. The functional dependence on the ratio of whirl frequency to rotating frequency (termed the whirl ratio) is very similar to that measured in experiments and similar to that predicted by the theoretical work of Childs [1]. Childs' bulk flow model yielded some unusual results including peaks in the rotordynamic forces at particular positive whirl ratios, a phenomenon which Childs tentatively described as a "resonance" of the leakage flow. This unexpected phenomenon developed at small positive whirl ratios when the inlet swirl velocity ratio exceeds about 0.5. Childs points out that a typical swirl velocity ratio at inlet (pump discharge) would be about 0.5 and may not, therefore, be large enough for the resonance to be manifest. To explore whether this effect occurs, an inlet guide vane was constructed which introduced a known amount of swirl into the flow upstream of the leakage flow inlet. A detailed comparison of model predictions with the present experimental program is presented. The experimental results showed no evidence of the "resonances," even at much larger swirl inlet velocities than explored by Childs.

ID: CaltechAUTHORS:20111226-134646361

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Abstract: The collapse process of single bubbles in travelling bubble cavitation around two axisymmetric headforms have been studied acoustically to understand the collapse process of a cavitation bubble and characterize the sound emission in travelling bubble cavitation. The bubbles were observed to collapse and then sometimes to rebound and collapse again, resulting in one or two pulses in the acoustic signal from a cavitation event. It was observed that each of the pulses could contain more than one peak. This phenomenon is called multipeaking and is clearly distinct from rebounding. The occurrence of rebounding and multipeaking and their effects on some characteristic measures of the acoustic signal such as power spectra are examined in this paper. Two particular headforms (ITTC and Schiebe) with distinct flow characteristics were investigated. Both rebounding and multipeaking increased with reduction in the cavitation number for the ITTC headform. Smaller flow velocity, smaller cavitation number and multipeaking delay the rebound. The peak amplitude of the sound emitted from the first collapse was seen to be twice as large as the peak amplitude of sound from the second collapse, suggesting a repeatable process of bubble fission during the collapse process. Multipeaking and rebounding increased the characteristic measures of the acoustic signal such as the acoustic impulse. These characteristic measures have larger magnitudes for smaller flow velocity. Also, the values of these characteristics are larger for the ITTC headform than for Schiebe headform. Theoretical calculations based on the Rayleigh-Plesset equation were seen to correctly predict the order of magnitude of most of these characteristic measures. However, the distribution of spectral energy is not properly predicted; bubble fission during the collapse is thought to account for this discrepancy. Reduction in the cavitation number and multipeaking are observed to decrease the fraction of spectral energy contained in the high-frequency range (30-80 kHz).

Publication: Journal of Fluid Mechanics Vol.: 255ISSN: 0022-1120

ID: CaltechAUTHORS:KUMjfm93a

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Abstract: This paper presents a summary of some recent observations of the interaction between individual traveling cavitation bubbles and the nearly solid surface. These reveal a complex micro-fluid-mechanics associated with the interaction of the bubble with the boundary layer, the surface and the large pressure gradients exterior to the boundary layer which normally occur in the vicinity of a minimum pressure point. The details are important because they affect how the bubble collapses and therefore influence the noise produced and the damage potential of the cavitating flow. We present data showing how the noise from an individual event can be affected by these interaction effects. Since the scaling of cavitation phenomena is always an important issue we also describe the results of some experiments carried out to investigate the scaling of these interaction effects.

ID: CaltechAUTHORS:CEBiwmf93

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Abstract: This paper examines the relationship between the cavitation event rates on axisymmetric headforms and the nuclei distributions in the incident flow. An analytical model is developed to relate these quantities and the results are compared with experimental cavitation event rates measured in the Large Cavitation Channel (LCC) at David Taylor Research Center (DTRC) on three different sizes of Schiebe body. The experiments were carried out at various cavitation numbers, tunnel velocities and air contents. Boundary layer, bubble screening and observable cavitation bubble size effects on the event rates are examined. The trends in the event rates with changing cavitation number and body size are consistent with those observed experimentally. However the magnitudes of the event rates are about an order of magnitude larger than the experimental data. Nevertheless it is shown that the cavitation inception values predicted using a certain critical event rate are consistent with those observed experimentally.

Publication: ASME Vol.: FED-177 No.: 177
ID: CaltechAUTHORS:LIUasci93

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Abstract: The free stream nuclei number distributions in the Low Turbulence Water Tunnel at Caltech were measured using a Phase Doppler Anemometer. The changes in nuclei number distributions with water tunnel running time, with initial air content, with tunnel velocity varying from 2m/sec to 9m/sec and with water tunnel static tunnel pressures ranging from 40kPa to 110kPa were examined. Quite complex changes in nuclei number distributions were observed in the nuclei size range of interest from the point of view of cavitation, namely the range from 5 to 200[microns]. Order of magnitude changes were observed in the nuclei population.

Publication: ASME Vol.: FED-153 No.: 153
ID: CaltechAUTHORS:LIUcmff93

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Abstract: While the flow of a dry granular material down an inclined channel may seem at first sight to be a relatively simple flow, the experiments which have been conducted up to now suggest sufficient complexity which may be present in all but the very simplest granular material flows; consequently it is important to our general understanding of granular material rheology that these experimental observations be fully understood. This review of the current knowledge of channel flows will focus on the basic mechanics of these flows and the contributions the observations have made to an understanding of the rheology. In order to make progress in this objective, it is necessary to avoid some of the complications which can occur in practice. Thus we shall focus only on those flows in which the interstitial fluid plays very little role in determining the rheology. In his classic paper, Bagnold (1954) was able to show that the regime in which the rheology was dominated by particle/particle or particle/wall interactions and in which the viscous stresses in the interstitial fluid played a negligible role could be defined by a single, Reynolds-number-like parameter. It transpires that the important component in this parameter is a number which we shall call the Bagnold number, Ba, defined by Ba = p₈d²δ/µF where p₈,µF are the particle density and interstitial fluid viscosity, d is the particle diameter and δ is the principal velocity gradient in the flow. In the shear flows explored by Bagnold δ is the shear rate. Bagnold (1954) found that when Ba was greater than about 450 the rheology was dominated by particle/particle and particle/wall collisions. On the other hand, for Ba < 40, the viscosity of the interstitial fluid played the dominant role. More recently Zeininger and Brennen (1985) showed that the same criteria were applicable to the extensional flows in hoppers provided the extensional velocity gradient was used for δ. This review will focus on the simpler flows at large Ba where the interstitial fluid effects are small. Other important ancillary effects can be caused by electrical charge separation between the particles or between the particles and the boundary walls. Such effects can be essential in some flows such as those in electrostatic copying machines. Most experimenters have observed electrical effects in granular material flows, particularly when metal components of the structure are not properly grounded. The effect of such electrical forces on the rheology of the flow is a largely unexplored area of research. The lack of discussion of these effects in this review should not be interpreted as a dismissal of their importance. Apart from electrical and interstitial fluid effects, this review will also neglect the effects caused by non-uniformities in the size and shape of the particles. Thus, for the most part, we focus on flows of particles of spherical shape and uniform size. It is clear that while an understanding of all of these effects will be necessary in the long term, there remain some important issues which need to be resolved for even the simplest granular material flows.

ID: CaltechAUTHORS:AHNptpf93

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Abstract: This paper describes an investigation of the flows in unshrouded and shrouded inducers which are known to be highly complex, three dimensional flows with real fluid effects. A flow visualization technique using tufts and paint dots was used to study the flows on the blade, hub and housing at off-design flows. It was found that the blade boundary layer flows were attached to the blade surface and that leakage flows were the cause of the upstream swirling backflow in unshrouded inducers. It was also found that shrouded inducers showed flow reversal near the leading edge in addition to the discharge-to-suction leakage flow. The observations provide a better understanding of the internal flows and the occurrence of upstream backflows.

Publication: ASME Symposium on Pumping Machinery Vol.: FED-154 No.: 154
ID: CaltechAUTHORS:BHAfed93

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Abstract: Nonlinear interactive effects in a bubbly cloud have been studied by investigating the frequency response of a bubble layer bounded by a wall oscillating normal to itself. Averaged equations of motion are used and the Rayleigh-Plesset equation is used to include the bubble dynamics. Energy dissipation due to viscous and thermal effects are included while relative motion between the two phases, liquid compressibility and viscous dissipation in the liquid have been ignored. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear response of a single bubble in an infinite fluid. This is used in an approximate calculation of the nonlinear frequency response of a bubble layer. Finite thickness of the bubble layer results in characteristic natural frequencies of the layer all of which are less than the natural frequency of a single bubble. The presence of bubbles of different sizes in the layer causes a phenomenon called harmonic cascading. This phenomenon consists of a large response at twice the excitation frequency when the mixture contains bubbles with a natural frequency equal to twice the excitation frequency. The details of these results along with the most important limitations of theory are presented.

Publication: Journal of Fluid Mechanics Vol.: 253ISSN: 0022-1120

ID: CaltechAUTHORS:KUMjfm93b

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Abstract: Increasing interest has been give to swirl brakes as a means of reducing destabilizing rotordynamic forces due to leakage flows in new high speed rocket turbopumps. Although swirl brakes have been used successfully in practice (such as with the Space Shuttle HPOTP), no experimental test until now have been performed to demonstrate their beneficial effect over a range of leakage flow rates. The present study investigates the effect of swirl brakes on rotordynamic forces generated by discharge-to-suction leakage flows in the annulus of shrouded centrifugal pumps over a range of subsynchronous whirl ratios and various leakage flow rates. In addition, the effectiveness of swirl brakes in the presence of leakage inlet (pump discharge) swirl is also demonstrated. The experimental data demonstrates that with the addition of swirl brakes a significant reduction in the destabilizing tangential force for lower flow rates is achieved. At higher flow rates, the brakes are detrimental. In the presence of leakage inlet swirl, brakes were effective over all leakage flow rates tested in reducing the range of whirl frequency ratio for which the tangential force is destabilizing.

Publication: ASME Vol.: FED-154 No.: 154
ID: CaltechAUTHORS:SIVfed93

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Abstract: Bubble nuclei populations in the wake of a circular cylinder under cavitating and noncavitating conditions were measured using a Phase Doppler Anemometry (PDA) system. In addition, the mean velocity defect and the turbulent fluctuations were monitored in order to try to understand the nuclei population dynamics within the flow. At the Reynolds numbers of these experiments (20000->33000) the laminar near-wake is fairly steady and under very limited cavitation conditions nuclei accumulate in this wake so that the population there is several orders of magnitude larger than in the upstream flow. Further downstream the population declines again as nuclei are entrained into the wake. However at fifteen diameters downstream the population is still much larger than in the upstream flow.

Publication: ASME Vol.: FED-153 No.: 153
ID: CaltechAUTHORS:SATcmff93

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Abstract: A bed of granular material which is subjected to vertical vibration will exhibit at least one sudden expansion at a critical acceleration amplitude. This sudden expansion corresponds to a bifurcation similar to that exhibited by a single ball bouncing on a vibrating plate. Theoretical analysis based on this model yields results which are in accord with the experimental observations. Other bifurcations may occur at higher vibration levels.

Publication: Powders & Grains
ID: CaltechAUTHORS:BREpg93

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Abstract: Spectral analyses of all the forces and moments acting on a typical centrifugal pump impeller/volute combination are presented. These exhibit shaft frequencies, blade passing frequencies, and beat frequencies associated with a whirl motion imposed on the shaft in order to measure rotordynamic forces. Among other features the unsteady thrust was found to contain a surprisingly large blade passing harmonic. While previous studies have explored the magnitudes of the steady fluid-induced radial forces and the fluid-induced rotordynamic forces for this typical centrifugal pump impeller/volute combination, this paper presents information on the steady bending moments and rotordynamic moments due to the fluid flow. These imply certain axial locations for the lines of action of the radial and rotordynamic forces. Data on the lines of action are presented and allow inferences on the sources of the forces.

Publication: Journal of Fluids Engineering Vol.: 114 No.: 4 ISSN: 0098-2202

ID: CaltechAUTHORS:MISjfe92

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Abstract: Utilizing some novel instrumentation which allowed detection and location of individual cavitation bubbles in flows around headforms. Ceccio and Brennen (1991 and 1989) recently examined the interaction between individual bubbles and the structure of the boundary layer and flow field in which the bubble is growing and collapsing. They were able to show that individual bubbles are often fissioned by the fluid shear and that this process can significantly effect the acoustic signal produced by the collapse. Furthermore they were able to demonstrate a relationship between the number of cavitation events and the nuclei number distribution measured by holographic methods in the upstream flow. More recently Kumar and Brenncn (1991-1992) have closely examined further statistical properties of the acoustical signals from individual cavitation bubbles on two different headformsm in order to learn more about the bubble/flow interactions. However the above experiments were all conducted in the same facility with the same size of headform (5.08cm in diameter) and over a fairly narrow range of flow velocities (around 9m/s). Clearly this raises the issue of how the phenomena identified in those earlier experiments change with changes of speed, scale and facility. The present paper will describe experiments conducted in order to try to answer some of these important qucstions regarding the scaling of the cavitation phenomena. We present data from experiments conducted in the Large Cavitation Channel of the David Taylor Research Center in Memphis, Tennessee, on similar headforms which are 5.08, 25.4 and 50.8cm in diameter for speeds ranging up to 15m/s and for a range of cavitation numbers. In this paper we focus on visual observations of the cavitation patterns and changes in these patterns with speed and headform size.

ID: CaltechAUTHORS:KUHispc92

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Abstract: Nonlinear interactive effects in a bubbly cloud have been studied by investigating the frequency response of a bubble layer bounded by a wall oscillating normal to itself. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear response of a single bubble in an infinite fluid. This is used to solve for nonlinear effects in a semi-infinite layer containing bubbles with a distribution size. A phenomena termed harmonic cascading is seen to take place due to presence of distribution of bubble sizes. This phenomena consists of a large response at twice the excitation frequency when the mixture contains bubbles with a natural frequency equal to twice the excitation frequency. The ratio of the amplitude of the second harmonic response to the amplitude of the first harmonic response is observed to increase when the number of small bubbles is increased relative to the number of large bubbles. The response is also seen to be weakened by an increase in the total number of bubbles per unit liquid volume at constant void fraction.

ID: CaltechAUTHORS:KUMpc92

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Abstract: The role played by fluid forces in determining the rotordynamic stability of a centrifugal pump is gaining increasing attention. The present research investigates the contributions to the rotordynamic forces from the discharge-to-suction leakage flows between the front shroud of the rotating impeller and the stationary pump casing. In particular, the dependency of the rotordynamic characteristics of leakage flows on the swirl at the inlet to the leakage path was examined . An inlet guide vane was designed for the experiment so that swirl could be introduced at the leakage flow inlet. The data demonstrates substantial rotordynamic effects and a destabilizing tangential force for small positive whirl ratios; this force decreased with increasing flow rate. The effect of swirl on the rotordynamic forces was found to be destabilizing.

ID: CaltechAUTHORS:20120105-103828941

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Abstract: This paper explores the effect of inlet flow modification on the cavitating and noncavitating performance of two cavitating inducers, one of simple helical design and the other a model of the low-pressure LOX pump in the Space Shuttle Main Engine. The modifications were generated by sections of honeycomb, both uniform and nonuniform. Significant improvement in the performance over a wide range of flow coefficients resulted from the use of either honeycomb section. Measurements of the axial and swirl velocity profiles of the flows entering the inducers were made in order to try to understand the nature of the inlet flow and the manner in which it is modified by the honeycomb sections.

Publication: Journal of Turbomachinery Vol.: 114 No.: 2 ISSN: 0889-504X

ID: CaltechAUTHORS:DELjot92

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Abstract: Existing constitutive relations and governing equations have been used to solve for fully developed chute flows of granular materials. In particular, the results of Lun et al. (1984) have been employed and the boundary value problem has been formulated with two parameters (the coefficient of restitution between particles, and the chute inclination), and three boundary values at the chute base wall, namely the values of solid fraction, granular temperature, and mean velocity at the wall. The boundary value problem has been numerically solved by the "shooting method." The results show the significant role played by granular conduction in determining the rpofiles of granular temperature, solid fraction, and mean velocity in chute flows. These analytical results are also compared with experimental measurements of velocity fluctuation, solid fraction, and mean velocity made by Ahn et al. (1989), and with the computer simulations by Campbell and Brennen (1985b).

Publication: Journal of Applied Mechanics Vol.: 59 No.: 1 ISSN: 0021-8936

ID: CaltechAUTHORS:AHNjam92

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Abstract: Attached cavitation was generated on two axisymmetric bodies, a Schiebe body and a modified ellipsoidal body (the I.T.T.C. body), both with a 50.8 mm diameter. Tests were conducted for a range of cavitation numbers and for Reynolds numbers in the range of Re = 4.4x10⁵ and 4.8x10⁵. Partially stable cavities were observed. The steady and dynamic volume fluctuations of the cavities were recorded through measurements of the local fluid impedance near the cavitating surface [us]ing a series of flush mounted electrodes. These data were combined with photographic observations. On the Schiebe body, the cavitation was observed to form a series of incipient spot cavities which developed into a single cavity as the cavitation number was lowered. The incipient cavities were observed to fluctuate at distinct frequencies. Cavities on the I.T.T.C. started as a single patch on the upper surface of the body which grew to envelope the entire circumference of the body as the cavitation number was lowered. These cavitites also fluctuated at distinct frequencies associated with oscillations of the cavity closure region. The cavities fluctuated with Strouhal numbers (based on the mean cavity thickness) in the range of St = 0.002 to 0.02, which are approximately one tenth the value of Strouhal numbers associated with Karman vortex shredding. The fluctuation of these stabilized partial cavities may be related to periodic break off and filling in the cavity closure region and to periodic entrainment of the cavity vapor. Cavities on both headforms exhibited surface striations in the streamwise direction near the point of cavity formation, and a frothy mixture of vapor and liquid was detected under the turbulent cavity surface. As the cavities became fully developed, the signal generated by the froth mixture increased in magnitude with frequencies in the range of 0 to 50 Hz.

Publication: Journal of Fluids Engineering Vol.: 114 No.: 1 ISSN: 0098-2202

ID: CaltechAUTHORS:CECjfe92

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Abstract: Several experiments by Ceccio and Brennen (1991, 1989) and Kumar and Brennen (1992, 1991) have closely examined the interaction between individual cavitation bubbles and the boundary layer, as well as statistical properties of the acoustical signals produced by the bubble collapse. All of these experiments were, however, conducted in the same facility with the same headform size (5.08cm in diameter) and over a fairly narrow range of flow velocities (around 9m/s). Clearly this raises the issue of how the phenomena identified change with speed, scale and facility. The present paper describes experiments conducted in order to try to answer some of these important questions regarding the scaling of the cavitation phenomena. The experiments were conducted in the Large Cavitation Channel of the David Taylor Research Center in Memphis Tennessee, on geometrically similar Schiebe headforms which are 5.08, 25.4 and 50.8cm in diameter for speeds ranging up to 15m/s and for a range of cavitation numbers.

ID: CaltechAUTHORS:KUHattc92

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Abstract: Ceccio and Brennen (1991 and 1989) recently examined the interaction between individual cavitation bubbles and the structure of the boundary layer and flow field in which the bubble is growing and collapsing. They were able to show that individual bubbles are often fissioned by the fluid shear and that this process can significantly effect the acoustic signal produced by the collapse. More recently Kumar and Brennen (1991-1992) have closely examined further statistical properties of the acoustical signals from individual cavitation bubbles on two different headforms in order to learn more about the bubble/flow interactions. All of these experiments were, however, conducted in the same facility with the same size of headform (5.08cm in diameter) and over a fairly narrow range of flow velocities (around 9m/s). Clearly this raises the issue of how the phenomena identified change with speed, scale and facility. The present paper describes experiments conducted in order to try to answer some of these important questions regarding the scaling of the cavitation phenomena. The experiments were conducted in the Large Cavitation Channel of the David Taylor Research Center in Memphis Tennessee, on similar Schiebe headforms which are 5.08, 25.4 and 50.8cm in diameter for speeds ranging up to 15m/s and for a range of cavitation numbers.

Publication: Proceedings of the Institution of Mechanical Engineers. Part C, Journal of Mechanical Engineering Science Vol.: C453 No.: 047 ISSN: 0954-4062

ID: CaltechAUTHORS:KUHimechec92b

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Abstract: Experiments on continuous, steady flows of granular materials down an inclined channel or chute have been conducted with the objectives of understanding the characteristics of chute flows and of acquiring information on the rheological behavior of granular material flow. Two neighboring fiber-optic displacement probes provide a means to measure (1) the mead velocity by cross-correlating two signals from the probes, (2) the unsteady or random component of the particle velocity in the longitudinal direction by a procedure of identifying particles, and (3) the mean particle spacing at the boundaries by counting the frequency of passage of the particles. In addition, a strain-gauged plate built into the chute base has been employed to make direct measurement of shear stress at the base. With the help of these instruments, the vertical profiles of mean velocity, velocity fluctuation, and linear concentration were obtained at the sidewalls. Measurements of some basic flow properties such as solid fraction, velocity, shear rate, and velocity fluctuation were analyzed to understand the characteristics of the chute flow. Finally, the rheological behavior of granular materials was studied with the experimental data. In particular, the rheological models of Lun et al. (1984) for general flow and fully developed flow were compared withthe present data.

Publication: Journal of Applied Mechanics Vol.: 58 No.: 3 ISSN: 0021-8936

ID: CaltechAUTHORS:AHNjam91

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Abstract: This paper persents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a Fourier analysis of the Rayleigh-Plesset equations is used to obtain an approximate solution for the nonlinear effects in the oscillation of a single bubble in an infinite fluid. This is used in the approximate solution of the oscillating wall problem, and the resulting expressions are evaluated numerically in order to examine the nonlinear effects. Harmonic generation results from the nonlinearity. It is observed that the bubble natural frequency remains the dominant natural frequency in the volume oscillations of the bubbles near the wall. On the other hand, the pressure perturbations near the wall are dominated by the first and second harmonics present at twice the natural frequency while the pressure perturbation at the natural frequency of the bubble is inhibited. The response at the forcing frequency and its harmonics is explored along with the variation with amplitude of wall oscillation, void fraction, and viscous and surface tension effects. Splitting and cancellation of frequencies of maximum and minimum response due to enhanced nonlinear effects are also observed.

Publication: Journal of the Acoustical Society of America Vol.: 89ISSN: 0001-4966

ID: CaltechAUTHORS:KUMjasa91

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Abstract: Experimentally determined attenuation and propagation characteristics are presented for small amplitude concentration waves in vertical bubbly and particulate flows. These were studied up to concentrations of 44.3 and 58%, respectively, in a 10 cm pipe. The wave propagation was studied in terms of the time delay, phase lag and loss of coherence of naturally occurring volume fraction fluctuations by means of simultaneous impedance measurements at two separate locations. Small amplitude natural kinematic waves were confirmed to be non-dispersive, as has previously been shown by other investigators. In this system configuration, bubbly flows undergo a regime transition to churn-turbulence, and not to slug flows as is typically observed in smaller diameter pipes. A dramatic drop in the attenuation time constant of small kinematic waves was found prior to the transition to churn-turbulence in gas-liquid flows, indicating that the regime change is the consequence of a loss of kinematic stability. The solid-liquid mixtures studied were found to always remain stable, with a range of greatest stability between 15–20%, as indicated by a maximum in the kinematic wave attenuation constant. The idea of a stable intermediate range of concentrations is consistent with the observations by Homsy et al. [Int. J. Multiphase Flow 6, 305–318 (1980)], who first observed structure formation above and below such a range. At concentrations above 40%, gradual transition to plug flow occurs, in which the particles execute little or no motion relative to one another.

Publication: International Journal of Multiphase Flow Vol.: 17 No.: 1 ISSN: 0301-9322

ID: CaltechAUTHORS:KYTijmf91

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Abstract: Individual travelling cavitation bubbles generated on two axisymmetric headforms were detected using a surface electrode probe. The growth and collapse of the bubbles were studied photographically, and these observations are related to the pressure fields and viscous flow patterns associated with each headform. Measurements of the acoustic impulse generated by the bubble collapse are analysed and found to correlate with the maximum volume of the bubble for each headform. These results are compared to the observed bubble dynamics and numerical solutions of the Rayleigh-Plesset equation. Finally, the cavitation nuclei flux was measured and predicted cavitation event rates and bubble maximum size distributions are compared with the measurements of these quantities.

Publication: Journal of Fluid Mechanics Vol.: 233ISSN: 0022-1120

ID: CaltechAUTHORS:CECjfm91

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Abstract: This paper presents the details of the collapse process for single bubbles generated in travelling bubble cavitation around two axisymmetric headforms. The details of the bubble collapse process have been examined acoustically to understand the phenomena of rebounding and multipeaking. We find that both rebounding and multipeaking increased with reduction in the cavitation number for the ITTC headform. However with the Schiebe headform rebounding increases and multipeaking is decreased with reduction in the cavitation number. Some possible physical explanations for these phenomena are presented.

Publication: ASME Vol.: FED-109 No.: 109
ID: CaltechAUTHORS:KUMcmff91

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Abstract: Individual travelling cavitation bubbles generated on two axisymmetric headforms were detected using a surface electrode probe. The growth and collapse of the bubbles were studied photographically, and these observations are related to the pressure fields and viscous flow patterns associated with each headform. Measurements of the acoustic impulse generated by the bubble collapse are analyzed and found to correlate with the maximum volume of the bubble for each headform. These results are compared to the observed bubble dynamics and numerical solutions of the Rayleigh-Plesset equation. Finally, the cavitation nuclei flux was measured and predicted cavitation event rates and bubble maximum size distributions are compared with the measurements of these quantities.

ID: CaltechAUTHORS:CEC18snh91

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Abstract: Recent years have seen a substantial increase of interest in the flows of granular materials whose rheology is dominated by the physical contact between particles and between particles and the containing walls. Considerable advances in the theoretical understanding of rapid granular material flows have been made by the application of the statistical methods of molecular gas dynamics (e.g., Jenkins and Savage (1983), Lun et al. (1984)) and by the use of computers simulations of these flows (e.g., Campbell and Brennen (1985), Walton (1984)). Experimental studies aimed at measurements of the fundamental rheology properties are much less numerous and are understandably limited by the great difficulties involved in trying to measure velocity profiles, solid fraction profiles, and fluctuating velocities within a flowing granular material. Nevertheless, it has become clear that one of the most severe problems encountered when trying to compare experimental data with the theoretical models is the uncertainty in the material properties governing particle/particle or particle/wall collisions. Many of the theoretical models and computer simulations assume a constant coefficient of restitution (and, in some cases, a coefficient of friction). The purpose of the present project was to provide some documentation for particle/wall collisions by means of a set of relatively simple experiments in which solid spheres of various diameters and materials were bounced off plates of various thickness and material. The objective was to provide the kind of information on individual particle/wall collisions needed for the theoretical rheological models and computer simulations of granular material flows: in particular, to help resolve some of the issues associated with the boundary condition at a solid wall. For discussion of the complex issues associated with dynamic elastic or inelastic impact, reference is made to Goldsmith (1960) and the recent text by Johnson (1985).

Publication: Journal of Applied Mechanics Vol.: 112 No.: 3 ISSN: 0021-8936

ID: CaltechAUTHORS:SONjam90

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Abstract: An experiment in forced vabration was conducted to study the fluid-induced rotordynamic force on an impeller whirling along a trajectory eccentric to its undeflected position in the presence of cavitation. The prescribed whirl trajectory of the rotor is a circular orbit of a fixed radius. The force measured is a combination of a steady radial force due to volute asymmetries and an unsteady force due to the eccentric motion of the rotor. These measurements have been conducted over a full range of whirl/impeller speed ratios at different flow coefficients without cavitation for various turbomachines. A destabilizing force was observed over a region of positive whirl ratio. The range of flow conditions examined for a centrifugal impeller in a spiral volute has been enlarged to include cavitation. Compared to the non-cavitating condition, cavitation corresponding to a head loss of three percent did not have a significant effect upon the unsteady force. However, a lesser degree of cavitation at the design point increased the destabilizing force for a particular set of whirl ratios.

Publication: Journal of Fluids Engineering Vol.: 112 No.: 3 ISSN: 0098-2202

ID: CaltechAUTHORS:FRAjfe90

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Abstract: Experiments were carried out to measure the additional pressure, called the granular pressure, which is exerted on the containing wall of a fluidized bed due to particle collisions with that wall. Measurements were made for water fluidized beds using glass beads of 1.3mm and 3mm diameter, lead shot of 2.1mm diameter and plastic particles. The granular pressure was observed to increase to a maximum and then decrease to zero as the solid fraction of the bed was reduced. The magnitude of the granular pressure was much larger than the values expected on the basis of previous experiments.

Vol.: FED-98 No.: 98
ID: CaltechAUTHORS:KUMasmecmff90

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Abstract: This paper presents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a fourier series analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear effects in the oscillations of a single bubble. This is used in the approximate solution of the oscillating wall problem and the resulting expressions are evaluated numerically in order to examine the nonlinear effects. The frequency content of the bubble radius and pressure oscillations near the wall is examined. Nonlinear effects are seen to increase with increased amplitude of wall oscillation, reduced void fraction and viscous and surface tension effects.

Vol.: FED-98 No.: 98
ID: CaltechAUTHORS:KUMasmecmff90b

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Abstract: A test apparatus was designed and constructed to observe the effect of sinusoidal pitching oscillations on the cavitation of three-dimensional hydrofoils. The apparatus is capable of oscillating hydrofoils at a rate up to 50 Hz and provides for adjustments in oscillation amplitude and mean angle of attack. Observations of the effect of pitching oscillation on cavitation have been made for a NACA 64-309 (modified) hydrofoil operating at its designed mean angle of attack of 7 degrees with an oscillation amplitude of 2 degrees. Photographs illustrating the interaction between natural cavity shedding frequencies and the foil reduced frequency are included.

Vol.: FED-98 No.: 98
ID: CaltechAUTHORS:HARasmecmff90

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Abstract: In this study of attached cavities on an axisymmetric headform, measurements were made of the noise generated by the cavitation. In addition to hydrophone recordings, a new technique employing flush mounted electrodes was used to measure the steady state and dynamic volume fluctuations of the attached cavities. The spectra of the noise are quite featureless and show some decrease in the high frequency content as the cavities become larger. However, the spectra from the electrode measurement show some distinct frequencies of fluctuation.

Vol.: FED-98 No.: 98
ID: CaltechAUTHORS:CECcmff90

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Abstract: This paper describes an experimental investigation of rotor-stator interaction in a centrifugal pump with several vaned diffusers. Steady and unsteady diffuser vane pressure measurements were made for a two-dimensional test impeller. Unsteady impeller blade pressure measurements were made for a second two-dimensional impeller with blade number and blade geometry identical to the two-dimensional impeller used for the diffuser vane pressure measurements. The experiments were conducted for different flow coefficients and different radial gaps between the impeller blade trailing edge and the diffuser vane leading edge (5 and 8 percent of the impeller discharge radius). The largest pressure fluctuations on the diffuser vanes and the impeller blades were found to be of the same order of magnitude as the total pressure rise across the pump. The largest pressure fluctuations on the diffuser vanes were observed to occur on the suction side of the vane near the vane leading edge, whereas on the impeller blades the largest fluctuations were observed to occur at the blade trailing edge. However, the dependence of the fluctuations on the flow coefficient was found to be different for the diffuser vanes and the impeller blades; on the vane suction side, the fluctuations were largest for the maximum flow coefficient and decreased with decreasing flow coefficient, whereas at the blade trailing edge, the fluctuations were smallest for the maximum flow coefficient and increased with decreasing flow coefficient. Increasing the number of the diffuser vanes resulted in a significant decrease of the impeller blade pressure fluctuations. The resulting lift on the diffuser vanes was computed from the vane pressure measurements; the magnitude of the fluctuating lift was found to be larger than the steady lift.

Publication: Journal of Turbomachinery Vol.: 112 No.: 1 ISSN: 0889-504X

ID: CaltechAUTHORS:20190430-071649857

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Abstract: An experiment was designed to measure the rotordynamic shroud forces on a centrigual pump impeller. The measurements were doen for various whirl/impeller ratios and for different flow rates. A destabilising tangential force was measured for small positive whirl ratios and this force decreased with increasing flow rate.

No.: FED-96
ID: CaltechAUTHORS:GUI108

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Abstract: This paper reviews the current state of knowledge of rotordynamic forces caused by the discharge-to-suction leakage flows in centrifugal pumps. The indications that these flows could contribute significantly to the rotordynamics motivated the fabrication of an experiment in which measurements of rotordynamic forces would be made on simulated leakage flows in which the flow rate, clearance, eccentricity and other parameters would be exercised in order to understand the phenomena. Sample data is presented and demonstrates substantial rotordynamic effects which could be potentially destabilizing. The rotordynamic forces appear to be inversely propertional to the clearance and change significant with the flow rate.

ID: CaltechAUTHORS:GUIaetopt90

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Abstract: The flow through and around the rotor of a turbomachine exerts a force on the rotor and, hence, rotor shaft and bearing system. In some circumstances this force may lead to excitation of shaft whirl in the direction of impeller rotation. Recent international research of this phenomenon is briefly reviewed; these findings suggest that turbomachines intended to operate well above the first critical speed should take the effect into account.

Publication: Proceedings of U.S. - Korea Fluid Engineering Seminar
ID: CaltechAUTHORS:BREkfe89

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Abstract: The interatction between impeller blades and diffuser vanes in a diffuser pump was investigated. Steady and unsteady pressure measurements were taken on the diffuser vanes, and the shroud wall of a vaned and a vaneless diffuser. Steady, unsteady, and ensemble-averaged unsteady data, as well as frequency spectra, are presented. The measurements were made for different flow coefficients, shaft speeds, and radial gaps between impeller blade trailing and diffuser vane leading edge (1.5 and 4.5 percent based on impeller discharge radius). The resulting lift on the vane, both steady and unsteady, was computed from the pressure measurements at midvane height. The magnitude of the fluctuating lift was found to be greater than the steady lift. The pressure fluctuations were larger on the suction side than on the pressure side attaining their maximum value, of the same order of magnitude as the total pressure rise across the pump, near the leading edge. Pressure fluctuations were also measured across the span of the vane, and those near the shroud were significantly smaller than those near the hub. The pressure fluctuations on the shroud wall itself were larger for the vaned diffuser than a vaneless diffuser. Lift, vane pressure, and shroud wall pressure fluctuations decreased strongly with increasing radial gap.

Publication: Journal of Turbomachinery Vol.: 111 No.: 3 ISSN: 0889-504X

ID: CaltechAUTHORS:ARNjt89

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Abstract: An experiment in forced vibration was conducted to study the fluid-induced rotordynamic force on an impeller whirling along a trajectory eccentric to its undeflected position. The prescribed whirl trajectory of the rotor is a circular orbit of a fixed radius. The force measured is a combination of a steady radial force due to volute asymmetries and an unsteady force due to the eccentric motion of the rotor. These measurements have been conducted over a full range of whirl/impeller speed ratios at different flow coefficients for various turbomachines. A destabilizing force was observed over a region of positive whirl ratio. The range of flow conditions examined for a centrifugal impeller in a spiral volute has been enlarged to include cavitation. Compared to the non-cavitating condition, cavitation corresponding to a head loss of three percent did not have a significant effect upon the unsteady force.

Vol.: FED-81 No.: 81
ID: CaltechAUTHORS:FRAasmespm89

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Abstract: This paper describes an experimental investigation of rotor-stator interaction in a centrifugal pump with several vaned diffusers. Steady and unsteady diffuser vane pressure measurements were made for a two-dimensional test impeller. Unsteady impeller blade pressure measurements were made for a second two-dimensional impeller with blade number and blade geometry identical to the two-dimensional impeller used for the diffuser vane pressure measurements. The experiments were conducted for different flow coefficients and differeent radial gaps between the impeller blade trailing edge and the diffuser vane leading edge (5 and 8 percent of the impeller discharge radius). The largest pressure fluctuations on the diffuser vanes and the impeller blades were found to be of the same order of magnitude as the total pressure rise across the pump. The largest pressure fluctuations on the diffuser vanes were observed to occur on the suction side of the vane near the vane leading edge, whereas on the impeller blades the largest fluctuations were observed to occur at the blade trailing edge. However, the dependence of the fluctuations on the flow coefficient was found to be different for te diffuser vanes and the impeller blades; on the vane suction side, the fluctuations were largest for the maximum flow coefficient and decreased with decreasing flow coefficient, whereas at the blade trailing edge, the fluctuations were smallest for the maximum flow coefficient and increased with decreasing flow coefficient. Increasing the number of the diffuser vanes resulted in a significant decrease of the impeller blade pressure fluctuations. The resulting lift on the diffuser vanes was computed from the vane pressure measurements; the magnitude of the fluctuating lift was found to be larger than the steady lift.

Vol.: 1
ID: CaltechAUTHORS:ARNjt90

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Abstract: The present work investigates the dynamics of the one-dimensional, steady flow of a spherical bubble cloud subject to harmonic far-field pressure excitation. Bubble dynamics effects and energy dissipation due to viscosity, heat transfer, liquid compressibility and relative motion of the two phases are included. The equations of motion for the average flow and the bubble radius are linearized and a closed-form solution is obtained. The results are then generalized by means of Fourier synthesis to the case of arbitrary far-field pressure excitation. The flow displays various regimes (sub-resonant, trans-resonant and super-resonant) with different properties depending on the value of the relevant flow parameters. Examples are discussed in order to show the effects of the inclusion of the various energy dissipation mechanisms. Finally the results for the case of Gaussian-shaped far-field pressure change are presented and the most important limitations of the theory are briefly discussed. The simple linearized dynamical analysis developed so far clearly deminstrates the importance of the complex phenomena connected to the interaction of the dynamics of the bubbles with the flow and provides an introduction to the more realistic study of the same flows with nonlinear bubble dynamics.

Publication: Journal of Fluid Mechanics Vol.: 199ISSN: 0022-1120

ID: CaltechAUTHORS:DAGjfm89

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Abstract: This paper is primarily concerned with the acoustics of traveling bubble cavitation around foils or headforms. We begin with observations of individual bubbles and the acoustic signals they emit, our purpose being to identify areas of research which would enhance our understanding of the history of individual bubbles. Then we present some numerical integrations of the Rayleigh/Plesset equation for the same flows. The comparison is encouraging in terms of future synthesis of the noise by analytical means. Finally, bubble interaction effects which were omitted earlier are discussed and some recent analytical results including these effects are presented.

No.: FED-88
ID: CaltechAUTHORS:BRE097

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Abstract: The problem of rotordynamic instability has had a long history and a significant impact on the design and operation of rotating machinery. As the search for higher power density and sophistication intensified, so have efforts to understand better and solve the instability problem and the difficulties often associated with it, such as noise and vibration, excessive bearing loads, loss of performance and catastrophic failure.

ID: CaltechAUTHORS:20140429-101027105

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Abstract: The present work investigates the acoustical absorption and scattering cross sections of spherical bubble clouds subject to harmonic farfield pressure excitation. Bubble dynamics effects and energy dissipation due to viscosity, heat transfer, liquid compressibility, and relative motion of the two phases are included. The equations of motion for the average flow and for the bubble radius are linearized and a closed-form solution is obtained. Due to the presence of natural oscillatory modes and frequencies, the acoustical cross sections of the cloud are very different from those of each individual bubble in the cloud, as well as from the acoustical cross sections of a single large bubble with the same volume of vapor and gas. In general, the acoustical properties of any give volume of the dispersed phase depend strongly on the degree of dispersion because of the complex interactions of the dynamics of the bubbles with the whole flow.

Publication: Journal of the Acoustical Society of America Vol.: 84 No.: 6 ISSN: 0001-4966

ID: CaltechAUTHORS:DAGjasa88

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Abstract: The present work investigates the acoustical absorption and scattering cross-sections of spherical bubble clouds subject to harmonic far field pressure excitation. Bubble dynamics effects and energy dissipation due to viscosity, heat transfer, liquid compressibility and relative motion of the two phases are included. The equations of motion for the average flow and for the bubble radius are linearized and a closed form solution is obtained. Due to the presence of natural oscillatory modes and frequencies, the acoustical cross-sections of the cloud are very different from those of each individual bubble in the cloud, as well as from the acoustical cross-sections of a single large bubble with the same volume of vapor and gas. In general the acoustical properties of any given volume of the dispersed phase depend strongly on the degree of dispersion because of the complex interactions of the dynamics of the bubbles with the whole flow.

Vol.: FED-64 No.: 64
ID: CaltechAUTHORS:DAGasmecmff88

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Abstract: Fluid forces on a rotating and whirling centrifugal impeller in a volute are analyzed with the assumption of a two-dimensional rotational, inviscid flow. For simplicity, the flow is assumed to be perfectly guided by the impeller vanes. The theory predicts the tangential and the radial force on the whirling impeller as functions of impeller geometry, volute spacing, and whirl ratio. A good qualitative agreement with experiment is found.

Publication: Journal of Vibration, Acoustics, Stress, and Reliability in Design Vol.: 110 No.: 3 ISSN: 0739-3717

ID: CaltechAUTHORS:TSUjvasrd88

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Abstract: The interaction between impeller blades and diffuser vanes in a diffuser pump was investigated. Steady and unsteady pressure measurements were taken on the diffuser vanes, and the shroud wall of a vaned and a vane less diffuser. Steady, unsteady, and ensemble averaged unsteady data, as well as frequency spectra are presented. The measurements were made for different flow coefficients, shaft speeds, and radial gaps between impeller blade trailing and diffuser vane leading edge (1.5% and 4.5% based on impeller discharge radius). The resulting lift on the vane, both steady and unsteady, was computed from the pressure measurements at mid vane height. The magnitude of the fluctuating lift was found to be greater than the steady lift. The pressure fluctuations were larger on the suction side than on the pressure side attaining their maximum value, of the same order of magnitude as the total pressure rise across the pump, near the leading edge. Pressure fluctuations were also measured across the span of the vane. and those near the shroud were significantly smaller than those near the hub. The pressure fluctuations on the shroud wall itself were larger for the vaned diffuser than a vaneless diffuser. Lift, vane pressure, and shroud wall pressure fluctuations decreased strongly with increasing radial gap.

ID: CaltechAUTHORS:20120105-105138689

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Abstract: When designing a turbomachine, particularly one which is to operate at high speed, it is important to be able to predict the fluid-induced forces, both steady and unsteady, acting on the various components of the machine. This paper concentrates on the fluid-induced rotordynamic forces acting upon the impeller and therefore on the bearings. Self-excited whirl, where the rotor moves away from and whirls along a trajectory eccentric to its undeflected position, can result from these fluid-induced forces. The purpose of the present work is to study the full range of these forces so that they can be included in any rotordynamic analysis at the design stage. To study the fluid-induced rotordynamic force on an impeller vibrating around its machine axis of rotation, an experiment in forced vibration was conducted. The prescribed whirl trajectory of the rotor is a circular orbit of a fixed radius. A rotating dynamometer mounted behind the rotor measures the force on the impeller. The force measured is a combination of a steady radial force due to volute asymmetries and an unsteady force due to the eccentric motion of the rotor. These measurements have been conducted over a full range of whirl/impeller speed ratios at different flow coefficients for various turbomachines including both centrifugal impellers aand axial inducers. A destabilizing force was observed over a region of positive whirl ratio. The range of flow conditions includes an examination of the effects of cavitation on the observed rotordynamic forces.

No.: CP-3012
ID: CaltechAUTHORS:BREteopc88a

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Abstract: This paper describes an investigation of rotor/stator interaction in centrifugal pumps with radial diffusers. Steady and unsteady diffuser vane pressure measurements were made for two impellers, one half of the double suction pump of the High Pressure Oxygen Turbopump (HPOTP) of the Space Shuttle Main Engine (SSME) and a two-dimensional impeller. Unsteady impeller blade pressure measurements were made for a second two-dimensional impeller with blade number and geometry identical to the two-dimensional impeller used for the diffuser vane pressure measurements. The experiments were conducted with different flow coefficients and different radial gaps between the blade trailing edge and the diffuser vane leading edge (5% and 8% of the impeller discharge radius for the two-dimensional impellers, and 1.5% and 4.5% for the impeller of the HPOTP). The largest pressure fluctuations on the diffuser vanes and the impeller blades were found to be of the same order of magnitude as the total pressure rise across the pump. On the diffuser vanes, the largest pressure fluctuations were observed on the suction side of the vane near the leading edge, whereas on the impeller blades the largest fluctuations occurred at the blade trailing edge. The resulting lift on the diffuser vane was computed from the pressure measurements; the magnitude of the fluctuating lift was found to be larger than the steady lift.

No.: CP-3012
ID: CaltechAUTHORS:BREteopc88b

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Abstract: Hydrodynamic interactions that occur between a centrifugal pump impeller and a volute are experimentally and theoretically investigates. The theoretical analysis considers the inability of the blades to perfectly guide the flow through the impeller, and also includes a quasi-one dimensional treatment of flow in the volute. Flow disturbances at the impeller discharge and the resulting forces are determined by the theoretical model. The model is then extended to obtain the hydrodynamic force perturbations that are caused by the impeller whirling eccentrically in the volute. Under many operating conditions, these force perturbations were found to be destabilizing. Comparisons are made between the theoretical model and the experimental measurements of pressure distributions and radial forces on the impeller. The theoretical model yields fairly accurate predictions of the radial forces caused by the flow through the impeller. However, it was found that the pressure acting on the front shroud of the impeller has a substantial effect on the destabilizing hydrodynamic forces.

Publication: Journal of Fluids Engineering Vol.: 110 No.: 1 ISSN: 0098-2202

ID: CaltechAUTHORS:ADKjfe88

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Abstract: Vertical air-water flows, solids-water flows and three component air-solids-water flows were investigated in a Three Component Flow Facility. Visual observations of the flow patterns show that three component flows undergo transition and can exhibit strong unsteady vortical motions. Measurements of the fluctuations in cross-sectionally averaged volume fraction measurements were made. The statistical properties of the fluctuations are presented in terms of their amplitude and coherent time scale in the form of the Signal To Noise Ratio (STNR) and the Time Constant (symbol), respectively. Remarkably, the solids-water flows and the dispersed bubbly air-water flows exhibit almost identical values of STNR for the same volume fraction. Equally remarkable in the linear relationship between the Time Constant and the mean bubble or particle velocity; this relationship is found to have the same constant of proportionality for both species in the well behaved disperse regime. In the two-component churn-turbulent and the three-component agitated vortical regimes, the variables (symbol) and STNR significantly deviate from their dispersed regime values. The onset of large coherent structures characteristic of these regimes is reflected by a rise in the amplitude of the fluctuations and a marked increase in their coherent time scale. The results of this study demonstrate the large information content in the fluctuations of the measured quantity, both as a flow regime indicator and as a measure of flow quantities in two- and three-component flows.

Publication: Journal of Fluids Engineering Vol.: 110 No.: 1 ISSN: 0098-2202

ID: CaltechAUTHORS:KYTjfe88

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Abstract: The present work investigates the dynamics of two-dimensional, steady bubbly flows over a surface and inside a symmetric channel with sinusoidal profiles. Bubble dynamics effects are included. The equations of motion for the average flow and the bubble radius are linearized and a closed-form solution is obtained. Energy dissipation due to viscous, thermal and liquid compressibility effects in the dynamics of the bubbles is included, while the relative motion of the two phases and viscous effects at the flow boundaries are neglected. The results are then generalized by means of Fourier synthesis to the case of surfaces with slender profiles of arbitrary shape. The flows display various flow regimes (subsonic, supersonic and superresonant) with different properties according to the value of the relevant flow parameters. Examples are discussed in order to show the effects of the inclusion of the various energy dissipation mechanisms on the flows subject to harmonic excitation. Finally the results for a flow over a surface with a Gaussian-shaped bump are presented and the most important limitations of the theory are briefly discussed.

Publication: Journal of Fluid Mechanics Vol.: 192ISSN: 0022-1120

ID: CaltechAUTHORS:DAGjfm88

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Abstract: Shear flows of granular materials are studied in an open channel. The wall shear is calculated from an open channel momentum equation which includes the density variations in the flow. An experimental technique was developed that allowed the measurement of the average density of the flow at different longitudinal locations in the channel. Two sizes of glass beads are examined and results show the variations in the wall shear as a function of various dimensionless parameters.

Publication: Journal of Applied Mechanics Vol.: 54 No.: 4 ISSN: 0021-8936

ID: CaltechAUTHORS:PATjam87

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Abstract: Experiments on continuous, steady flows of granular materials down an inclined channel or chute were made with the object of acquiring information on the rheological properties of the granular material flow and the nature of the boundary condition on the base of the channel. Specifically measurements were made of the mean material velocities and velocity profiles on all boundaries of the flow using cross-correlation of two neighboring fibre-optic displacement probes. The output from these probes was used to obtain (1) the unsteady or random component of the particle velocity in the longitudinal direction and (2) a measure of the volume fraction of the flow in contact with the base by counting the frequency of passage of the particles. Measurement was also made of the depth of the flow, the mass flow rate and the shear stress on the base. The latter employed a strain-gauged shear force plate built into the base. The experiments are currently in progress and so further data will be presented at a later date. Nevertheless the preliminary data have yielded a number of interesting features.

Publication: Micromechanics of Granular Materials No.: 20
ID: CaltechAUTHORS:AHNmgm87

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Abstract: The asymmetric flow around an impeller in a volute exerts a force upon the impeller. To study the rotordynamic force on an impeller which is vibrating around its machine axis of rotation, the impeller, mounted on a dynamometer, is made to whirl in a circular orbit within the volute. The measured force is expressed as the sum of a steady radial force and an unsteady force due to the eccentric motion of the impeller. These forces were measured in separate tests on a centrifugal pump with radically increased shroud clearance, a two-dimensional impeller, and an impeller with an inducer, the impeller of the HPOTP (High Pressure Oxygen Turbopump) of the SSME (Space Shuttle Main Enginer). In each case, a destabilizing force was observed over a region of positive whirl.

ID: CaltechAUTHORS:FRAecfm87

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Abstract: The speed and attenuation of small amplitude kinematic waves were measured in vertical bubbly and particulate flows in a continuous medium of water. This was done by evaluating the time delay and phase lag of coherent random fluctuations in the volume fraction signal at two measuring locations. The volume fraction was monitored using two closely spaced Impedance Volume Fraction Meters (Kytomaa (1986)). Using the broad-band volume fraction perturbations yields the dependence of the kinematic speed and attenuation of wave number from a single experiment for one set of conditions. The kinematic waves were found to be non-dispersive. Bubbly flows are observed to undergo a change in flow regime at an approximate volume fraction of 45%. Prior to onset of churn-turbulence, a sharp drop in kenematic wave attenuation is observed above volume fractions of 40%. When further increase in volume fraction is attempted, the homogeneous dispersion suddenly becomes unstable. The particulate flows remain uniformly dispersed for all volume fractions, but above a value of ~55%, the mixture flows like a solid plug. The volume fraction fluctuations become incresingly persistent as the volume fraction approaches the solidification value, but no instability is observed. It is argued that the inability of air-water flows to withstand bubble-bubble forces without break-up may account for the differences between the bubbly and particulate flow results.

ID: CaltechAUTHORS:KYTnhtc87

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Abstract: Unsteady surface pressure measurements on a vaned diffuser of a centrifugal pump, and wake measurement of the flow exiting a centrifugal impeller into a vaneless diffuser are presented. Frequency spectra and ensemble averages are given for the unsteady measurements. Two different impellers were used, the pump impeller of the HPOTP (High Pressure Oxygen Turbopump) of the SSME (Space Shuttle Main Engine) and a two-dimensional impeller. The magnitude of the unsteady total pressure measured in the stationary frame at the impeller exit was found to be of the same order of magnitude as the total pressure rise across the pump. The magnitude of the unsteady diffuser vane pressures was observed to be significantly different on suction and pressure side of the vane, attaining its largest value on the suction side near the leading edge while decreasing along the vane.

Vol.: 1
ID: CaltechAUTHORS:ARNcfm87

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Abstract: Air-water flows, solids-water flows and three component air-solids-water flows in a vertical pipe have been investigated in a Three Component Flow Facility. Visual observations of the patterns show that the three component flow exhibits strong unsteady vertical motions which do not occur in the two phase flows studied. Quantitative results of the fluctuating component of the cross-sectionally averaged volume fraction measurements are presented, and related to the nature of the flows. The ratio of the steady component to the r.m.s of the fluctuating component of the volume fraction measurement (Signal To Noise Ratio) is found to be a good flow structure indicator. Remarkably, the solids-water flows and the bubbly air-water flows exhibit almost identical signal to noise ratios for the same volume fraction. However, the corresponding values for the three component flows reflect greater fluctuations corresponding to the vertical structures.

Vol.: FED-38 No.: 38
ID: CaltechAUTHORS:KYTasmessf86

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Abstract: Convective heat transfer to a rapidly flowing, granular material is experimentally investigated over a flat plate in an inclined chute. Two different sizes of glass beads are used as the granular materials. A technique was developed to measure the average density of the flowing material, which allowed the more accurate determination of the average velocity as well as of parameters depending on the velocity. The results are presented in terms of the Nusselt number and a model is proposed relating this Nusselt number to a Péclet number and a Froude number. The predicted results of the model are compared with the experimental data.

Publication: International Journal of Heat and Mass Transfer Vol.: 29 No.: 8 ISSN: 0017-9310

ID: CaltechAUTHORS:PATijhmt86

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Abstract: The asymmetric flow within a volute exerts a radial force on a centrifugal impeller. The present paper presents experimental measurements of the radial forces on the impeller in the presence of cavitation.

Vol.: NASA CP-2443 No.: 2443
ID: CaltechAUTHORS:FRAriphpt86

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Abstract: This paper addresses the issue of the steady and unsteady forces which may be imparted to a pump impeller by the through flow. The historical trend to increase the power density and speed of turbomachines has inevitably led to an increase in the number of fluid/structure interaction problems because the fluid forces scale like the square of the speed and thus become increasingly important relative to the structural strength. The present paper focuses on the radial forces acting on the impeller of a pump. Under the sponsorship of NASA, the authors have, over the past few years, conducted an extensive investigation of these forces and the associated hydrodynamically induced rotordynamic coefficients. A new facility, called the Rotor Force Test Facility was designed and constructed for the experimental component of this program. Measurements of the forces and rotordynamic coefficients have been made for a range of different impeller and volutes and include tests with the impeller of the high pressure oxygen turbopump (HPOTP) in the Space Shuttle Main Engine. Furthermore, tests have been conducted with different leakage flow geometries and, with different levels of pump cavitation. The paper will summarize these experimental measurements and the results of some theoretical analyses.

No.: CP-243
ID: CaltechAUTHORS:BREaeopt86

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Abstract: A Three Component Flow Facility (TCFF) was used to study friction pressure drops in vertical two component flows of both air bubbles in water and polyester particle-water mixtures. Friction factors of up to two orders in magnitude higher than those at zero volume fraction were observed for both bubbly and slurry flows. This deviation is shown to decrease with increased liquid Reynolds number. Bubbly and slurry flow friction factors were comparably large in magnitude and displayed the same decreasing trend as a function of Reynolds number. The two phase friction multiplier for bubbly flow was shown to attain values up to one order of magnitude higher than the prediction given by Lockhart and Martinelli. Two phase multiplier data is presented for the dispersed flow regime.

Vol.: FED-36 No.: 36
ID: CaltechAUTHORS:KYTasmecmff86

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Abstract: Fluid forces on a centrifugal impeller rotating and whirling in a vaneless diffuser are analysed on the assumption of a two-dimensional inviscid flow. It is assumed that the number of impeller vanes is infinitely large and that the loss in the impeller can be estimated from the steady hydraulic and incidence losses taking into account the delay time of the loss. Further, the pressure at the outlet of the diffuser is assumed to be constant. On these assumptions impeller and/or diffuser attributed rotating stalls are observed, and the effects of parameters affecting the stalls are discussed. It is found that both stalls may cause the whirling instability of a centrifugal impeller.

Publication: Japan Society of Mechanical Engineers. Journal Vol.: 52 No.: 483 ISSN: 0021-4728

ID: CaltechAUTHORS:TSUjjmes86

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Abstract: The characteristics of a centrifugal impeller under a condition with leading edge cavitation are analyzed by using conformal mapping methods. It is assumed that the thickness of the cavity is small, and linear cavity models are used. Concerning the treatment of the Bernoulli equation, two different models are considered. The first one is based on a full Bernoulli equation in a rotating frame. In the second model, the Bernoulli equation is linearized on the assumption that the disturbance due to cavity is small. The second model predicts shorter cavity, but the differences in the pressure distribution and in the head coefficient are small for the conditions with the same cavity length. The results of the first model are in general agreement with those by a singularity method and experiments.

Publication: Japan Society of Mechanical Engineers. Journal Vol.: 52 No.: 480 ISSN: 0021-4728

ID: CaltechAUTHORS:TSUjjmes86b

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Abstract: Hydrodynamic interactions that occur between a centrifugal pump impeller and volute are experimentally and theoretically investigated. The theoretical analysis considers the inability of the blades to perfectly guide the flow through the impeller, and also includes a quasi-one dimensional treatment of the flow in the volute. The disturbance at the impeller discharge and the resulting forces are determined by the theoretical model. The model is then extended to obtain the hydrodynamic force perturbations that are caused by the impeller whirling eccentrically in the volute. Under many operating conditions, these force perturbations were found to be destablizing. Comparisons are made between the theoretical model and the experimental measurements of pressure distributions and radial forces on the impeller. The theoretical model yields fairly accurate predictions of the radial forces caused by the flow through the impeller. However, it was found that the pressure acting on the front shroud of the impeller has a substantial effect on the destablizing hydrodynamic forces.

No.: CP 244
ID: CaltechAUTHORS:ADK074

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Abstract: The present work is an experimental investigation of the possible forces of fluid dynamic origin that can act on a turbomachine rotor particularly when it is situated off its normal center position. An experimental facility, the Rotor Force Test Facility, has been designed and contructed in order to measure these kinds of forces acting on a centrifugal pump impeller when the latter is made to whirl in a slightly eccentric circular orbit. The scope of the present experimental work consists of measuring quasi-steady forces on the impeller as it whirls slowly about the axis of the pump rotation. These forces are due to interaction between the impeller and volute; they are decomposed into force components relative to the geometric center of the volute and to those proportional to displacent from this center. These latter are interpreted as stiffness matrices. Such matrices were obtained for two different volutes and both were found to be the sum of a diagonal and a skewsymmetric matrix. It can be shown that a stiffness matrix of this type can lead to dynamic instability of impeller shaft system in certain circumstances. This new experimental finding may explain some operational problems of "high-speed" hydraulic machinery. Comparison is made with various existing theoretical and experimental results.

Publication: Journal of Fluids Engineering Vol.: 107 No.: 3 ISSN: 0098-2202

ID: CaltechAUTHORS:CHAjfe85

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Abstract: In recent years a number of theoretical, experimental and computational research programs (Refs. [5], [8] and [3] for example) have substantially increased our fundamental understanding of the mechanics of flowing granular material. However most of these studies have concentrated on the simplest type of flow namely that of uniform size particles in the absence of any interstitial fluid effects or other complicating factors. The purpose of the present paper is to investigate the effects of interstitial fluid. In his classic study of granular flows Bagnold (1954) observed from his Couette flow studies that viscous effects of the interstitial fluid became significant when a number (which is now termed the Bagnold number, Ba) defined as [equation] becomes less than about 450. Here [delta] is the velocity gradient or shear rate. (We have chosen to omit from the definition of Ba a volume fraction parameter which is usually of order unity and is therefore not important qualitively). In the Couette flow experiments the appropriate shear rate, [delta], is clearly defined; in other flows (such as the very practical flow in a hopper) the corresponding condition (or shear rate) in not known. The purpose here is to investigate the effects of the interstitial fluid in the primarily extensional flows which occur in the flow of a granular material in a hopper.

Vol.: FED-23 No.: 23
ID: CaltechAUTHORS:ZEIasmecmff85

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Abstract: Forces are exerted on a centrifugal pump impeller, due to the asymmetry of the flow caused by the volute of diffuser, and to the motion of the center of the impeller whenever the shaft whirls. Recent work in the measurement of these forces as a function of the whirl speed to shaft speed ratio, and the influence of the volute, is reviewed. These forces may be decomposed into a steady force, a static stiffness matrix, a damping matrix and an inertia matrix. It is shown that for centrifugal pumps of the moderate specific speed typical of boiler feed stages, there is a region of potential shaft vibration excitation from the hydrodynamic forces if the operating speed is well above the first flexural critical speed.

ID: CaltechAUTHORS:JERsips85

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Abstract: Open-channel flows of fluids may be classified as supercritical or subcritical, depending on whether their average velocity ῡ is larger, equal to or smaller than the propagation rate of small disturbances √(gh) cos α (where g is the gravitational acceleration, h is the flow depth and [alpha] is the channel inclination). Typically, the flow type is classified by the magnitude of the Froude number, ῡ√(gh), relative to its value under critical conditions Fr_c = √(cosα). Supercritical and subcritical flow represent conjugate states of open-channel flow; that is, a given supercritical flow will transition via an hydraulic jump that will transition a subcritical flow back to its corresponding supercritical value. flow. (However, energy considerations prohibit a reverse hydraulic jump that will transition a subcritical flow back to its corresponding supercritical value.) Supercritical flows are unaffected by downstream conditions, as they move faster than the downstream information can propagate upstream. Subcritical flows are strongly affected by downstream conditions. If downstream conditions are relaxed, a subcritical flow may transition back to supercritical flow (although not its conjugate state) via an expansion wave progagating upstream. The existence of a subcritical flow requires that the flow must be critical somewhere downstream before any abrupt expansion of the channel (such as the drop-off at the channel's end). The critical state prevents an expansion wave from propagating upstream from the expansion and causing a transition to supercritical flow. (A more complete discussion of these phenomena may be found in most introductory fluid mechanics textbooks; see, for example, Ref. 1, pp. 363-377.)

Publication: Powder Technology Vol.: 41 No.: 1 ISSN: 0032-5910

ID: CaltechAUTHORS:CAMpt85

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Abstract: A computer simulation has been developed to describe unidirectional flows of granular materials. Results are presented for a simulation of the two-dimensional flow of disks or cylinders down an inclined plane or chute. Velocity and solid fraction profiles were measured from the simulated systems and compared with theoretical analyses and are compared with the limited experimental results now available. The behavior is shown to be critically dependent on a third field quantity -- the "granular temperature" -- a measure of the kinetic energy contained in the random motions of the particles.

Publication: Journal of Applied Mechanics Vol.: 52 No.: 1 ISSN: 0021-8936

ID: CaltechAUTHORS:CAMjam85

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Abstract: Detailed understanding of flowing granular materials is severly hampered by the deficiencies of present experimental methods. To help increase the information base, a computer simulation has been developed to describe two-dimensional unidirectional flows of inelastic fully rough particles. This paper presents the results of a Couette shear-flow simulation. The results include distributions of velocity, density and granular temperature (a measure of the kinetic energy contained in the random particle motions). The effects of density and shear rate on the granular temperature are explored. Shear and normal forces on the solid walls are compared with experimental and theoretical results. The behaviour of the particles in the simulated flow is examined and assessments are made of the collision angle and velocity distributions. The development of a distinct, 'layered' microstructure is observed in high-density granular flows.

Publication: Journal of Fluid Mechanics Vol.: 151ISSN: 0022-1120

ID: CaltechAUTHORS:CAMjfm85

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Abstract: Measurements were made of the lateral hydrodynamic forces experienced by a centrifugal pump impeller performing circular whirl motions within several volute geometries. Experiments were conducted for various flow coefficients, [phi], impeller rotating speeds or angular frequencies, w, and the angular frequency of the whirl motion, [omega], was varied from zero to nearly synchronous (equation) and to nearly antisynchronous (equation). The lateral forces were decomposed into (i) time averaged lateral forces and (ii) hydrodynamic force matrices representing the variation of the lateral forces with position of the impeller center. No assumptions concerning the form of these matrices need to be made. The latter can be further decomposed according to the variation with whirl frequency, the result being "stiffness", "damping", and "fluid inertial" rotordynamic force matrices. It was found that these force matrices essentially consist of equal diagonal terms and skew-symmetric off-diagonal terms. One consequence of this is that during its whirl motion the impeller experiences forces acting normal and tangential to the locus of whirl. Data on these normal and tangential forces are presented; in particular it is shown that there exists a region of positive reduced whirl frequencies, [omega/w], within which the hydrodynamic forces can be destabilizing with respect to whirl.

No.: CP-2338
ID: CaltechAUTHORS:JERriphpt84

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Abstract: Destabilizing fluid forces on a whirling centrifugal impeller rotating in a volute have been observed (Ref. 1). A quasisteady analysis neglecting shed vorticity (Ref. 2) or an unsteady analysis without a volute (Ref. 3) does not predict the existence of such destabilizing fluid forces on a whirling impeller. The present report is intended to take into account the effects of a volute and the shed vorticity. We treat cases when an impeller with an infinite number of vanes rotates with a constant velocity [omega] and its center whirls with a constant eccentric radius {epsilon] and a constant whirling velocity [omega].

No.: CP-2338
ID: CaltechAUTHORS:TSUriphpt84

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Abstract: In the last decades the technological importance or bubbly flows has generated considerable efforts to achieve a better understanding of their properties, [1],[2]. However, the presence or two interacting phases so much increases the complexity or the problem that a satisfactory mathematical model of these flows has been possible only in special cases under fairly restrictive simplifying assumptions. The main purpose of the present note is to investigate the effects due to the inclusion or bubble dynamic response in two-dimensional flows over wave-shaped surfaces. The earlier studies of bubbly flows based on space averaged equations for the mixture in the absence or relative motion between the two phases, [5], [6], do not consider bubble dynamic effects. This approach simply leads to an equivalent compressible homogeneous medium and has been used to analyze the behaviour or one-dimensional bubbly flows through converging-diverging nozzles. In order to account for bubble dynamic response, in a classical paper by Foldy, [7], each individual bubble is described as a randomly distributed point scatterer. Assuming that the system is ergodic, the collective effect of bubble dynamic response on the flow is then obtained by taking the ensemble average over all possible configurations. An alternative way to account for bubble dynamic effects would be to include the Rayleigh-Plesset equation in the space averaged equations. Both methods have been successfully applied to describe the propagation or one-dimensional perturbances through liquids containing small gas bubbles, [8], [9], [10], [11]. However, because of their complexity, there are not many reported examples of the application to specific flow geometries of the space averaged equations which include the effects of bubble response, [12]. In an earlier note, [13], we considered the one-dimensional time dependent linearized dynamics or a spherical cloud of bubbles. The results clearly show that the motion of the cloud is critically controlled by bubble dynamic effects. Specifically, the dominating phenomenon consists of the combined response of the bubbles to the pressure in the surrounding liquid, which results in volume changes leading to a global accelerating velocity field. Associated with this velocity field is a pressure gradient which in turn determines the pressure encountered by each individual bubble in the mixture. Furthermore, it can be shown that such global interactions usually dominate any pressure perturbations experienced by one bubble due to the growth or collapse or a neighbor (see section 5). In the present note the same approach is applied to the two-dimensional case or steady flows over wave-shaped surfaces (for which there exist well established solutions for compressible and incompressible flow), With the aim, as previously stated, of assessing the effects due to the introduction or bubble dynamic response. Despite its intrinsic limitations, the following linear analysis indicates some of the fundamental phenomena involved in such flows and provides a useful basis for the study of the same flows with non-linear bubble dynamics, which we intend to discuss in a later publication. The present extention to the case of bubbly flows over arbitrarily shaped surfaces also constitutes the starting point for the investigation or such flows, a problem of considerable technical interest, for example in cavitating flows past lifting surfaces.

No.: 9
ID: CaltechAUTHORS:20130725-163717360

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Abstract: Recently, Morch [1,2,3,4] Chahine [5,6] and others have focused attention on the dynamics of a cloud or cluster of cavitating bubbles and have expanded on the work of van Wijngaarden [7,8] and others. Unfortunately, there appear to be a number of inconsistencies in this recent work which will require further study before a coherent body of knowledge on the dynamics of clouds of bubbles is established. For example, Morch and his co-workers [1,2,3] have visualized the collapse of a cloud of cavitating bubbles as involving the inward propagation of a shock wave; it is assumed that the bubbles collapse virtually completely when they encounter the shock. This implies the virtual absense of non-condensable gas in the bubbles and the predominance of vapor. Yet in these circumstances the mixture in the the cloud will not have any real sonic speed. As implied by a negative L.H.S. of equation (9), the fluid motion equations for the mixture would be elliptic not hyperbolic and hence shock wave solutions are inappropriate.

Vol.: FED-2 No.: 2
ID: CaltechAUTHORS:DAGasmecmff83

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Abstract: The purpose of this paper is to present results from computer simulations of Couette flows of granular materials and to examine the detailed rheological behavior inherent in these simulations. Comparison is made with the experimental results of Bagnold (1954) and Savage and Sayed (1980, 1982) as well as with the various theoretical constitutive models.

Publication: Mechanics of Granular Materials: New Models and Constitutive Relations No.: 7
ID: CaltechAUTHORS:CAMmgm83

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Abstract: This paper investigates the formation of hydraulic jumps in the open channel flow of dry, cohesionless granular materials. The experimental observations include the identification of several types of jump and several types of downstream flow. The relation between the depth ratio across the jump and the Froude number is similar to that observed in the open channel flow of liquid. However, the ratio h₂/h₁ in the granular material case is larger by a factor of between 1.2 and 1.5 Analysis of this factor indicates that it is caused by a 10 to 20% reduction in the solid fraction below its critical value in the highly sheared supercritical flow upstream of the jump.

Publication: Powder Technology Vol.: 35 No.: 1 ISSN: 0032-5910

ID: CaltechAUTHORS:BREpt83

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Abstract: The use of the transverse field electromagnetic meter for two-phase flows is investigated. It is shown both experimentally and theoretically that this device measures the average velocity of the continuous liquid phase provided this has some minimum electrical conductivity. The calibration is quite independent of void fraction, flow regime, axisymmetric velocity profile, or the electrical conductivity of the continuous liquid phase. The dynamic capability of the meter for use in measuring unsteady two-phase flows is also demonstrated to be considerable.

Publication: International Journal of Multiphase Flow Vol.: 9 No.: 3 ISSN: 0301-9322

ID: CaltechAUTHORS:BERijmf83

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Abstract: Dynamic transfer functions for two cavitating inducers of the same geometry but different size are presented, compared, and discussed. The transfer functions for each inducer indicate similar trends as the cavitation number is decreased. The nondimensional results for the two sizes are compared with themselves and with theoretical calculations based on the Bubbly Flow Model (reference [2]). All three sets of results compare well and lend further credance to the theoretical model. The best values of the two parameters in the model (K and M) and evaluated recommended for use in applications.

Publication: Journal of Fluids Engineering Vol.: 104 No.: 4 ISSN: 0098-2202

ID: CaltechAUTHORS:BREjfe82

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Abstract: Forced convection heat transfer was investigated for two granular materials flowing along a chute. For each material and for a given depth of flow, the heat transfer coefficient at first increases with velocity, then reaches a maximum and decreases as the velocity increases further. This behavior is believed to be related to changes in the packing density of the material caused by the flow field.

Publication: International Journal of Heat and Mass Transfer Vol.: 25 No.: 6 ISSN: 0017-9310

ID: CaltechAUTHORS:SPEijhmt82

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Abstract: This report reviews the existing state of knowledge concerning the evaluation of the forces imposed on a body in a fluid due to acceleration of either the body or the fluid. It concentrates on those fluid inertial forces due to acceleration rather than on the drag/lift forces due to steady motion. The first part of the report presents a survey of the analytical background including the definition of added mass, the structure of the added mass matrix and other effects such as the influence of viscosity, fluid compressibility and the proximity of solid and free surface boundaries. Then the existing data base from experiments and potential flow calculations is reviewed. Approximate empirical methods for bodies of complex geometry are explored in a preliminary way. The possible dramatic effects of the proximity of the ocean bottom are further highlighted. The confused state of affairs regarding the possibly major effects of viscosity in certain regimes of frequency and Reynolds number is discussed. Finally a number of recommendations stemming from ocean engineering problems are put forward.

ID: CaltechAUTHORS:BREncel82

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Abstract: The purpose of the present paper is to present results from computer simulations of the flow of granular materials down inclined chutes or channels and to compare the results of these calculations with existing experimental measurements of velocity, solid fraction and mass flow rate profiles.

ID: CaltechAUTHORS:CAMdfgm82

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Abstract: The objective of the Rotor Force Test Facility at the California Institute of Technology is to artificially orbit the center of rotation of an impeller enclosed within a volute over a range of frequencies from zero to synchronous and to measure the resulting forces on the impeller. This paper reports preliminary data from the first stage experiments in which the shaft is orbited at low frequency. Steady volute forces along with stiffness matrices due to the change in position of the rotor center are measured. Static pressure taps around the volute are used to obtain volute pressure distributions for various fixed positions of the impeller center and for various flow rates. Static pressure forces are calculated from these pressure distributions allowing a more complete analysis of the components of the impeller forces. Comparison is made with various existing theoretical and experimental results.

No.: CP-2250
ID: CaltechAUTHORS:CHAriphpt82

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Abstract: Cavitation has been investigated in directional control valves in order to identify damage mechanisms characteristic of components of aircraft hydraulic systems. Tests have been conducted in a representative metal spool valve and in a model three times larger. Data taken under noncavitating conditions with both valves showed that the position of the high-velocity annular jet shifts orientation, depending upon valve opening and Reynolds number. By means of high-frequency response pressure transducers strategically placed in the valve chamber cavitation could be sensed by the correlation of noise with a cavitation index. The onset of cavitation can be detected by comparing energy spectra for a fixed valve opening and a constant discharge. Another sensitive indicator of cavitation inception is the ratio of cavitating to noncavitating spectral densities. The incipient cavitation number as defined in this investigation is correlated with the Reynolds number for both valves.

Publication: Journal of Fluids Engineering Vol.: 103 No.: 4 ISSN: 0098-2202

ID: CaltechAUTHORS:MARjfe81

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Abstract: In an effort to develop domestic sources of energy, a number of processes to convert coal to clean fuels have been investigated. Products of these processes span the range from clean coal substitutes, to synthetic crude oil, to synthetic natural gas. Some of these processes, after successful operation in the laboratory, are now operating on a pilot plant scale to determine the feasibility of further scale up. These pilot plants range in capacity from 1/1000 to 1/10 of that projected for commercial operation [1]. At the pilot plant scale, problem areas which are generic to the conversion process have come to light. These problem areas include: handling of highly abrasive slurries, three phase heat transfer, high temperatures, high pressure, and high pressure slurry letdown. In this report the problems associated with high pressure slurry letdown from the reactor/dissolver to the fractionating section will be discussed. The operating experience and the current state of the art for high pressure letdown valves in the coal conversion industry and the process industry will be examined. Also, the commonly used valve sizing techniques will be examined in relation to the problem of sizing for high pressure letdown. A summary of the instrumentation needed to monitor the letdown process for valve development, and ultimately for process control, is also included.

ID: CaltechAUTHORS:CHA048

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Abstract: Detailed observations of funnel flows of dry granular materials in wedge-shaped hoppers of different geometries are presented. The variations of the flow regime with changes in the height of material in the hopper/vertical bin configuration, the width of the vertical bin, the hopper angle and the hopper opening width were investigated and a number of specific flow regimes identified (mass flow and several forms of funnel flow). In the first part of the paper particular attention is paid to the conditions for transition from one flow regime to another; in particular it is shown that the existence of a funnel depends not only on the hopper angle but is also strongly dependent on the geometry of the hopper/bin system. In the second part of the paper the variations in the shape of the funnel near the exit opening are explored in detail.

Publication: Journal of Applied Mechanics Vol.: 102 No.: 4 ISSN: 0021-8936

ID: CaltechAUTHORS:NGUjam80

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Abstract: This paper presents the results of experiments and analysis of the phenomenon of leading-edge flutter which has been observed to occur for supercavitating hydrofoils. The experiments confirmed the existence of such a single-degree-of-freedom flutter involving chordwise bending and indicated that for long, natural (or vapor-filled) cavities the reduced flutter speed, [formula], was in the range 0.15 to 0.23. Secondary effects observed were the variation with the angle of attack (a minimum flutter speed occurred at 10 deg) and with foil mass ratio. Shorter cavities typically yielded lower flutter speeds due to a complex interaction between the bubble collapse process occurring in the cavity closure region and the unsteady hydrodynamic load on the foil. Finally, a relatively simple theoretical analysis for supercavitating hydrofoils with elastic axes aft of midchord is presented. This linear analysis yields reduced flutter velocities somewhat lower than those observed.

Publication: Journal of Ship Research Vol.: 24 No.: 3 ISSN: 0022-4502

ID: CaltechAUTHORS:BREjsr80

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Abstract: We have recently become concerned with making estimates of steady forces that may be exerted between moving blade rows and stationary blade rows or volutes. Our present interest is with time averaged forces for estimation of shaft loads and flow asymmetry forces rather than with transient processes. For this purpose we have adopted the well-known "actuator" model for the blade row in which the flow leaving the row or cascade is assumed to have a constant leaving angle. The disturbances external to this row such as a volute may be represented by distributions of vortex elements as was done for example by Domm and Hergt [1].

No.: CP-2133
ID: CaltechAUTHORS:CHAriphpt80

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Abstract: Pressure suppression systems in boiling water reactors are designed to condense a large amount of steam very rapidly by injecting it into a pool of water. It transpires that such condensing flows are unstable and can lead to large oscillatory pressures on the walls of the containment system. This paper presents a theoretical model whose purpose is to attempt to understand why these flows are unstable and to extract the important parameters and frequencies pertaining to the instability. A simple linear dynamic model is constructed comprising linear transfer function for (i) the unsteady steam flow in the vent (ii) the condensation interface and (iii) the pool hydrodynamics. The analysis demonstrates the existence of both stable and unstable regions of operation defined by several non-dimensional parameters including the ratio of the steam flow rate to the effective thermal diffusivity in the water just downstream of the condensation interface and the frictional losses in the vent. Instability frequencies are in the vicinity of the vent acoustic frequencies or the pool manometer frequency depending on the conditions. Though the qualitative dynamic behavior of the model is consistent with the experimental observations, quantitative comparison is hindered by difficulties in accurately assessing the effective thermal diffusivity in the water. Nevertheless the model provides insight into the nature of the instability.

ID: CaltechAUTHORS:CEBbmtpfht80

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Abstract: Much speculation has surrounded the possible unsteady hydrodynamic forces which could be responsible for the excitation of whirl instabilities in turbomachines. However there exist very few measurements of these forces which would permit one to evaluate the merits of the existing fluid mechanical analyses. In keeping with the informal nature of this workshop we will present details of a proposed test program for the measurement of the unsteady forces on centrifugal impellers caused by either (i) azimuthal asymmetry in the volute geometry or (ii) an externally imposed whirl motion of the impeller. In the second case the forces resulting from the imposed whirl motions with frequencies ranging from zero to synchronous will be measured by means of a force balance upon which the impeller is mounted. This work is presently being carried out under contract with the NASA George Marshall Space Flight Center, Huntsville, Alabama (Contract NAS 8-33108).

No.: CP-2133
ID: CaltechAUTHORS:BREriphpt80

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Abstract: This paper presents details of measurements on the instability know as auto-oscillation which occurs in systems with cavitating pumps. Specific measurements are made of onset cavitation number and auto-osciallation frequency for a range of inducers. It has been shown that auto-oscillation is a system instability caused by the active dynamic characteristics of the cavitating pump. A system anslysis is presented which utilized previously measured dynamic transfer functions for the inducers; the resulting predictions of instability are consistent with the observations. Though the onset cavitation number is a function of the entire system it is also show that, given the onset cavitation number, the auto-oscillation frequency is only weakly dependent on the system and primarily a function of the pump dynamics. Detailed measurements of the amplitude and phase of fluctuating pressures and flow rates during auto-oscillation are also presented. These strongly suggest that the pump dynamics are primarily determined by the complicated flow at inlet to the inducer which involves pre-swirl generated by a strong backflow. Some data on the non-linear effect of auto-osciallation on overall mean performance are also presented.

Publication: Polyphase Flow and Transport Technology
ID: CaltechAUTHORS:BRApftt80

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Abstract: Increasing use is being made of transmission matrices to characterize unsteady flows in hydraulic system components and to analyze the stability of such systems. This paper presents some general characteristics which should be examined in any experimentally measured transmission matrices and a methodology for the analysis of the stability of transmission matrices in hydraulic systems of order 2. These characteristics are then examined for cavitating pumps and the predicted instabilities (known as auto-oscillation) compared with experimental observations in a particular experimental system.

ID: CaltechAUTHORS:BREiahrs80

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Abstract: Cavitation has been investigated in directional control valves in order to identify damage mechanisms characteristic of components of aircraft hydraulic systems. Tests have been conducted in a representative metal spool valve and in a model three times larger. Data taken under non-cavitating conditions with both valves showed that the position of the high-velocity annular jet shifts orientation depending upon valve opening and Reynolds number. By means of high-frequency response pressure transducers strategically placed in the valve chamber cavitation could be sensed by the correlation of noise with a cavitation index. The onset of cavitation can be detected by comparing energy spectra for a fixed valve opening and a constant discharge. Another sensitive indicator of cavitation inception is the ratio of cavitating to non-cavitating spectral densities. The incipient cavitation number as defined in this investigation is correlated with the Reynolds number for both valves.

ID: CaltechAUTHORS:MARasmesci79

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Abstract: An approximate solution to the flow of a cohesionless granular material in a conical hopper is presented. The material is modeled as a perfectly plastic continuum which satisfies the Mohr-Coulomb yield condition. Analytical expressions of the mass flow rate and the wall stress are derived and compared to some experimental data and other analyses.

Publication: Journal of Applied Mechanics Vol.: 46 No.: 3 ISSN: 0021-8936

ID: CaltechAUTHORS:NGUjam79

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Abstract: Detailed observtions of funnel flows of dry granular materials in wedge-shaped hoppers of different geometries are presented. The variations of the flow regime with changes in the height of material in the hopper/vertical bin configuration, the width of the vertical bin, the hopper angle and the hopper opening width were investigated and a number of specific flow regimes identified (mass flow and several forms of funnel flow). In the first part of the paper particular attention is paid to the conditions for transition from one flow regime to another; in particular it is shown that the existence of a funnel depends not only on the hopper angle but is also strongly dependent on the geometry of the hopper/bin system. In the second part of the paper the variations in the shape of the funnel near the exit opening are explored in detail.

Vol.: AMD-31 No.: 31
ID: CaltechAUTHORS:NGUmatbm79

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Abstract: This paper is concerned with the unsteady, dynamic behavior of hydraulic systems and, in particular, with the dynamic characteristics of internal flows involving phase-change and two-phase flows. This emphasis is motivated by the large number of different flows of this kind which exhibit "active" dynamic characteristics (see Section 3) and therefore have the potential to cause instability in the whole hydraulic system of which they are a part (see Section 4). We begin, first, with a discussion of the form and properties of dynamic transfer functions for hydraulic systems. Then, following the discussion of a number of examples we present an analysis leading to the transfer function for a simple phase-change and demonstrate its "active" dynamic character.

Vol.: 2
ID: CaltechAUTHORS:BREtpmhmtcpees79

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Abstract: This paper describes experiments performed to measure the dynamic transfer matrices for cavitating (and noncavitating) pumps. These transfer matrices describe the relationship between small linear oscillatory perturbations in the pressures and mass flow rates at inlet and discharge from the hydraulic machine. The matrices were deduced from direct measurements of these fluctuating quantities for different modes of excitation of the machine. Results for a cavitating inducer are presented as functions of frequency and mean operating state. Though some of the trends in the data are consistent with existing theoretical models of inducer dynamics, others are not, indicating a need for further theoretical investigation of the dynamic characteristics of such flows. The results exhibit increasingly complex dynamics with increasing cavitation; it appears that the hydraulic machine deviates from an essentially passive response without cavitation to an increasingly active response as the cavitation number is reduced.

Publication: Journal of Fluids Engineering Vol.: 100 No.: 2 ISSN: 0098-2202

ID: CaltechAUTHORS:NGSjfe78.925

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Abstract: The flow and transport of granular media have been of major importance in commerce and industry for a long time; materials such as coal, ore, cement, grain, soap granules, sugar, sand, gravel, etc., flow in hoppers, bins, chutes, rotating drums, and moving bands. The desire to improve such transportation equipment and to reduce the energy expenditure has motivated interest in understanding the fluid mechanics of such bulk flows (Wieghardt [25]1). Though transport, heat transfer, and other processes are often effected by fluidization we are concerned here with those situations in which the flow takes place with direct physical contact between the grains. Indeed the simplest situation is that in which the interstitial fluid (usually air) has a negligible effect on the equations of motion. The purpose of this paper is to present a comparison of experimental data and analysis for the flow of dry granular media through a two-dimensional or wedge-shaped hopper. It will be seen that the analytical solution which begins with the constitutive postulates suggested by Jenike and Shield [9] of (i) intergrain Coulomb friction and (ii) isotropy produces results which are in good agreement with the experimental measurements.

Publication: Journal of Applied Mechanics Vol.: 45 No.: 1 ISSN: 0021-8936

ID: CaltechAUTHORS:BREjam78

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Abstract: This paper is concerned with understanding the dynamic behaviour of cavitating hydraulic machines during unsteady or transienct opertion. The linear transfer matrices which relate the small fluctuating pressures and mass flow rates at inlet and discharge are functions not only of the frequency but also of the mean operating state of the machine, especially the degree of cavitation. The recent experimental transfer matrices obtained by Ng & Brennen (1978) for some axial flow pumps revealed some dynamic characteristics whic were unaccounted for by any existing theoretical analysis; their visual observations suggested that the bubbly cavitating flow in the blade passages could be responsible for these effects. A theoretical model of the dynamic response of this bubbly blade-passage flow is described in the present paper. Void-fraction fluctuations in this flow result not only from pressure fluctuations but also because the fluctuating angle of attack causes fluctuations in the rate of production of bubbles near the leading edge. The latter causes kinematic waves which interact through the boundary conditions with the dynamic waves caused by pressure fluctuation. The resulting theoretical transfer dynamic waves caused by pressur fluctuation. The resulting theoretical transfer functions which result are in good qualitative agreement with the experiments; with appropriate choices of two parameters (the practical values of which are difficult to assess) good quantitative agreement is also obtained. The theoretical model also provides one possible explanation of the observation that the pump changes from an essentially passive dynamic element in the absence of cavitation to a progressively more active element as the extent of cavitation increases.

Publication: Journal of Fluid Mechanics Vol.: 89 No.: 2 ISSN: 0022-1120

ID: CaltechAUTHORS:BREjfm78

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Abstract: Hydraulic systems involving cavitating turbomachines are known to be susceptible to instabilities at certain critical operating conditions. Two distinct classes of cavitating inducer instabilities have been reported in the literature (Refs. 1-6). The purpose of this note is to report on some preliminary observations of these phenomena. The experiments were performed in the Dynamic Pump Test Facility (DPTF) at the California Institute of Technology (Refs. 7, 8). Results will be presented for two different inducers operating at different flow coefficients, [symbol] ([symbol]= mean axial velocity/inducer tip velocity- [equation]) and cavitation numbers, [symbol] ([symbol]=[equation]; where [equation] are the inlet and vapor pressures, and [symbol] is the liquid density). In general, the instabilities occurred just before the head breakdown. After head breakdown, the system tended to become stable again, although there were some indications of a second region of instability at very small cavitation numbers. Impeller IV is a quarter scale model of the Low Pressure Oxidizer Turbo-Pump (LPOTP) of the space shuttle main engine (Refs. 7, 8). The cavitation performance of this impeller is presented in Figure 1. Some of the mean operating states for which large, constant amplitude oscillations occurred in all the pressures and mass flow rates are indicated by stars. The cavitation in each of the blade passages oscillated in unison. This unstable behavior is termed auto-oscillation. The frequency of the auto-oscillations ranged from 28 to 35 Hz. As might be expected, there does exist a marginal region of operation for which the auto-oscillations have a time varying amplitude. These non-steady oscillations occurred as sporadic bursts of auto-oscillation. It was this feature that makes the boundaries of the auto-oscillation region difficult to define. In addition to the auto-oscillation observations on Impeller IV, two instances of "rotating cavitation" were observed and are labeled by boxes in Figure 1. The presence of rotating cavitation was determined by means of a stroboscope slaved to the rotational speed of the inducer. Rotating cavitation appeared as a non-stationary cavitation patterns which rotated with respect to the "fixed" inducer. (More recent testing has also revealed the existence of a stationary form of rotating cavitation sometime referred to as alternate blade cavitation.) The large amplitude disturbances in the upstream pressure and mass flow rates which characterized auto-oscillation were not observed during rotating cavitation. This suggests the rotating cavitation is most intimately associated with the dynamic characteristics of the cavitating inducer itself irrespective of the hydraulic system in which it resides.

ID: CaltechAUTHORS:BRAcpff78

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Abstract: The ability to analyze and model the unsteady, dynamic response of hydraulic systems has arisen from the need for operational stability, flexibility and controlled transient behavior. Following a general discussion, this paper discusses experiments and analysis directed toward identification of the dynamic response of hydraulic pumps, both cavitating and non-cavitating. It is shown that rather modest amounts of cavitation cause the pump to become dynamically active and therefore capable of exciting instabilities and resonance with the hydraulic system.

Vol.: 1
ID: CaltechAUTHORS:BREsdofm78

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Abstract: Since the Annual Review of Fluid Mechanics first published a review on microorganism locomotion by Jahn & Votta (1972) considerable progress has been made in the understanding of both the biological and the fluid-mechanical processes involved not only in microorganism locomotion but also in other fluid systems utilizing cilia. Much of this knowledge and research, which has been built on the solid foundation of the pioneering work of Sir James Gray (1928, 1968) and Sir Geoffrey Taylor (1951, 1952a,b), has been reported extensively elsewhere, particularly by Gray (1928, 1968), Sleigh (1962), Lighthill (1975), and Wu, Brokaw & Brennen (1975). The subject is now sufficiently broad that it precludes any exhaustive treatment in these few pages. Rather, we restrict this review primarily to a summary of present understanding of the low-Reynolds-number flows associated with microorganism propulsion and the hydromechanics of ciliary systems. In this introductory section we wish to put such fluid-mechanical studies in biological perspective. Section 2 outlines the present status of low-Reynolds-number slender-body theory, and we discuss the application of this theory to biological systems in the final sections.

Publication: Annual Review of Fluid Mechanics Vol.: 9ISSN: 0066-4189

ID: CaltechAUTHORS:BREarfm77

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Abstract: Knowledge of the dynamic performance of pumps is essential for the prediction of transient behavior and instabilities in hydraulic systems; the necessary information is in the form of a transfer function which relates the instantaneous or fluctuating pressure and mass flow rate at inlet to the same quantities in the discharge from the pump. The presence of cavitation within the pump can have a major effect on this transfer function since dynamical changes in the volume of cavitation contribute to the difference in the instantaneous inlet and discharge mass flow rates. The present paper utilizes results from free streamline cascade theory to evaluate the elements in the transfer function for a cavitating inducer and shows that the numerical results are consistent with the characteristics observed in some dynamic tests on rocket engine turbopumps.

Publication: Journal of Fluids Engineering Vol.: 98 No.: 2 ISSN: 0098-2202

ID: CaltechAUTHORS:BREjfe76

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Abstract: When fluid in an annulus between two cylinders is set in motion by whirling movements of one or both of the cylinders, dynamic forces are imposed by the fluid on the cylinders. Knowledge of these forces is frequently important, indeed often critical, to the engineer designing rotor systems or journal bearings. Quite general solutions of the Navier-Stokes equations are presented for this problem and are limited only by restrictions on the amplitude of the whirl motion. From these solutions, the forces are derived under a wide variety of circumstances, including large and small annular widths, high and low Reynolds numbers and with and without a mean flow created by additional net rotation of one or both of the cylinders.

Publication: Journal of Fluid Mechanics Vol.: 75 No.: 1 ISSN: 0022-1120

ID: CaltechAUTHORS:BREjfm76

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Abstract: A "simple" cell method for concentrated suspnsions has been used to construct a model for the rheological behavior of blood. The model includes the physical properties of the suspending medium, red cell membrane and red cell fluid content. Predictions of the gross viscosity of red cell suspensions are found to agree very well with experiment in the cases of hardened red cells (or normal red cells at very low shear rate) and of normal red cells in the asymptotic limit of high shear rates. The behavior at intermediate shear rates requires a knowledge of the viscoplastic properties of the membrane and a number of membrane models are investigated. Of particular interest is plastic membrane which employs a membrane yield stress obtained from other experiments and whose results are qualitatively in agreement with the viscometric data at these intermediate shear rates.

Publication: Canadian Journal of Chemical Engineering Vol.: 53 No.: 2 ISSN: 0008-4034

ID: CaltechAUTHORS:BREcjce75

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Abstract: Theoretical hydrodynamic analyses of the locomotion of flagellates with mastigonemes are presented and particular comparison is made within experimental data on Ochromonas malhamensis. The first part of the paper analyses locomotion assuming the mastigonemes are rigid and maintain a fixed and normal position relative to the flagellum. The predicted propulsive velocity of 60 mum/sec for Ochromonas agrees well with the observed values of 55-60 mum/sec. It is shown that the propulsive system of Ochromonas represents a compromise between the need for efficient rectilinear propulsion and the need to manoeuvre and accelerate. The effect of rigid mastigonemes which are maintained at non-zero angles to the flagellar normal is also calculated and demonstrates a significant degradation of performance when this angle is greater than about 10 degrees. The latter part of the paper investigates the more complex but more realistic situation in which the mastigonemes flex during the motion according to the instantaneous hydrodynamic forces imposed upon them. The cyclical flexing history of a mastigoneme with passage of a flagellar wave and the consequent velocity of propulsion are obtained for a variety of geometric configurations and structural mastigoneme stiffnesses. It is demonstrated that there exists a relatively small transition range in the values of mastigoneme flexibility below which the mastigonemes are essentially rigid and above which they become totally ineffective hydrodynamically so that the flagellum can be regarded as essentially smooth. Since the transition value of the modulus of elasticity is about 5 dynes/mum2 (or stiffness of 3.5 X 10(-16) dyne cm2) for the mastigonemes of Ochromonas it would appear that the actual value must be in excess of this. Comparison is made with the structural properties of the micro-tubules in eukaryote cilia and flagella and with prokaryote flagella. The latter comparison suggests that the mastigonemes of Ochromonas are just rigid enough to produce the observed propulsive effect.

Publication: Journal of Mechanochemistry and Cell Motility Vol.: 3 No.: 3 ISSN: 0091-6552

ID: CaltechAUTHORS:BREjmcm75

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Abstract: The purpose of this paper is to present a new model for ciliary propulsion intended to rectify certain deficiencies in the existing theoretical models. The envelope model has been developed by several authors including Taylor (1951), Reynolds (1965), Tuck (1968), Blake (1971a,b,c) and Brennen (1974); it employs the concept of representing the ciliary propulsion by a waving material sheet enveloping the tips of the cilia. The principal limitations of this approach, as discussed in the review by Blake and Sleigh (1974), are due to the impermeability and no-slip conditions imposed on the flow at the envelope sheet (an assumption not fully supported by physical observations) and the mathematical necessity of a small amplitude analysis.

ID: CaltechAUTHORS:KELsfn75

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Abstract: To the present time much of the hydrodynamic analysis of the locomotion of ciliated micro-organisms has concentrated on the localized interaction between the cilia and the fluid medium. In doing so most investigators have found it necessary to simplify the larger scale flow and to consider "infinite sheet models" in which the fluid flow solutions are purely harmonic and the wave properties invariant in the rectilinear coordinate parallel to the sheet. The resulting mean motion is purely unidirectional and thus the hydrodynamic solution greatly simplified. Since these "infinite sheet models" conveniently termed the "envelope" and "sub-layer" models are discussed in detail by Blake and Sleigh (1974a, b) elsewhere in this volume further amplification is unnecessary. It is convenient, however, for our purposes to think of these as fluid/cilia interaction models describing the local interaction between the cilia and the fluid. The relative merits of the two types of model and criteria which describe their respective region of validity are discussed by Brennen (1974) and by Blake and Sleigh (1974b). In the present paper we will discuss some of the characteristics of the flow around "finite" ciliated micro-organisms, pointing out along the way those effects not experienced in the infinite sheet models but which are important in evaluating, say, the propulsive velocity of a ciliated micro-organism. The only previous solution for a "finite" body to appear in the literature seems to be that of Lighthill (1952), later modified by Blake (1971a) in which traveling surface waves on a sphere (to use the "envelope" model) are approximated by combining two spherical harmonic functions whose orders differ by one. But this solution is very restrictive in terms of the permitted variation of waveform and wave amplitude over the body and its extension to nonspheriodal bodies would involve prohibitive algebraic complexity.

ID: CaltechAUTHORS:BREsfn75

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Abstract: Knowledge of the dynamic performance of turbopumps is essential for the prediction of instabilities in hydraulic systems; the necessary information is in the form of a transfer function relating the instantaneous pressures and mass flow rates at inlet and discharge. Cavitation has a significant effect on this transfer function since dynamical changes in the volume of cavitation contribute to the difference in the instantaneous flow rates. The present paper synthesizes the transfer matrix for cavitating inducers at moderately low frequencies and shows that the numerical results are consistent with observations on rocket engine turbopumps.

ID: CaltechAUTHORS:CEBcfm75

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Abstract: This paper analyses the locomotion of a finite body propelling itself through a viscous fluid by means of travelling harmonic motions of its surface. The methods are developed with application to the propulsion of ciliated micro-organisms in mind. Provided that the metachronal wavelength (of the surface motions) is much smaller than the overall dimensions of the body, the flow can be divided into an oscillating-boundary-layer flow to which is matched an external complementary Stokes flow. The present paper employs the envelope model of fluid/cilia interaction to construct equations of motion for the oscillating boundary layer. The final solution for the propulsive velocity is obtained by application of the condition of zero total force on the self-propelling body; alternatively, if the organism is held at rest, the thrust it generates can be computed. Various optimum propulsive velocities for self-propelling bodies and optimum thrusts for restrained bodies are analysed in some simple examples. The results are compared with the relatively sparse observations for a number of micro-organisms.

Publication: Journal of Fluid Mechanics Vol.: 65 No.: 4 ISSN: 0022-1120

ID: CaltechAUTHORS:BREjfm74

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Abstract: This paper is concerned with the interpretation of isostatic recovery data in terms of the flow properties of the earth's mantle. A hydrodynamic analysis is first presented that allows straightforward calculation of the relaxation time for isostatic recovery within a mantle in which the viscosity varies continuously with depth. However, it transpires that no curve of this type (i.e., choice of a reference viscosity and a rate of change of viscosity with depth) can of itself adequately explain the available observational data from the Fennoscandian and Laurentide ice sheets and the pluvial Lake Bonneville. Proceeding onward it is then demonstrated that the strain rates within such flows are in fact greater than the critical strain rate envisaged by Weertman (1970) in his theoretical rheological model of the mantle. Below this critical value, diffusion creep is the dominant flow process, and the flow can be modeled by a Newtonian viscosity. But above this value, dislocation glide takes over, and the viscosity exhibits a decrease with increasing strain rate. This feature is then incorporated into the theoretical model, and the isostatic recovery data are interpreted in such a way as to provide experimental values of the strain rate dependent viscosity that can be compared with the values in Weertman's rheological model. It is demonstrated that the data become most self-consistent and exhibit the most satisfactory agreement with Weertman's model when the increase of mantle viscosity with depth is given roughly by exp (5 × 10^(−4)z), where z is the depth in kilometers. Thus in addition, the analysis would appear to provide some verification of Weertman's model of the mantle flow properties. It is further demonstrated that the much larger increase of viscosity with depth predicted by McConnell (1968) and others from previous analyses of isostatic recovery data is an artifice induced by the nature of such flows in which the strain rate decreases with depth; this led to an apparent increase of viscosity that is much larger than the actual variation.

Publication: Journal of Geophysical Research Vol.: 79 No.: 26 ISSN: 0148-0227

ID: CaltechAUTHORS:20111017-140608633

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Abstract: The role played by turbopump cavitation in the POGO instability of liquid rockets motivates the present study on the dynamic response of streams of cavitating bubbles to imposed pressure fluctuations. Both quasistatic and more general linearized dynamic analyses are made of the perturbations to a cavitating flow through a region of reduced pressure in which the bubbles first grow and then collapse. The results when coupled with typical bubble number density distribution functions yield compliances which compare favorably with the existing measurements. Since the fluids involved are frequently cryogenic, a careful examination was made of the thermal effects both on the mean flow and on the perturbations. As a result the discrepancy between theory and experiment for particular engines could be qualitatively ascribed to reductions in the compliance caused either by these thermal effects or by relatively high reduced frequencies.

Publication: Journal of Fluids Engineering Vol.: 95 No.: 4 ISSN: 0098-2202

ID: CaltechAUTHORS:BREjfe73

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Abstract: The serious POGO instability experienced by many liquid propellant rockets results from a closed loop interaction between the first longitudianl structural mode of vibration and the dynamics of the propulsion system. One of the most important features in the latter is the cavitation compliance of the turbopumps. This report presents calculations of the blade cavitation compliance obtained from free streamline cascade theory and demonstrates the various influences of angle of attack, blade angle, blade thickness and cavitation number. Discrepancies between calculated and experimentally derived values are discussed.

Publication: Journal of Spacecraft and Rockets Vol.: 10 No.: 3 ISSN: 0022-4650

ID: CaltechAUTHORS:BREjsr73

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Abstract: The principal concern of this paper is with the thermal convective instabilities of a non-uniformly viscous liquid sphere heated internally by some distribution of heat sources. Solutions are first obtained which correspond to an extension of the classic theory for uniformly viscous spheres for (1) radial variations of viscosity and (2) near critical Reynolds numbers. This results in instability growth rates which strongly suggest that the earth's mantle must have been in a highly supercritical state for the present convective pattern to have been established within the earth's lifetime. The paper then proceeds to a different theoretical calculation for incipient growth rates for such supercritical situations. For the earth's mantle this results in typical growth times of the order of 10^5 years. Various outer boundary conditions of the fixed and free type are explored; a true free surface condition is also examined and results in the establishment of a Froude number-like parameter governing distortion of the outer surface. In addition it is demonstrated that the spherical harmonics of degree 3 or 4 which seem to dominate the present convective pattern in the earth's mantle would do so in the theoretical construction if the increase of viscosity with depth within the mantle were such that the deep mantle viscosity was some four times the upper mantle value.

ID: CaltechAUTHORS:20161215-162022695

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Abstract: The wall effects in cavity flows have been long recognized to be more important and more difficult to determine than those in single-phase, nonseparated flows. Earlier theoretical investigations of this problem have been limited largely to simple body forms in plane flows, based on some commonly used cavity-flow models, such as the Riabouchinsky, the reentrant jet, or the linearized flow model, to represent a finite cavity. Although not meant to be exhaustive, references may be made to Cisotti (1922), Birkhoff, Plesset and Simmons (1950, 1952), Gurevich (1953), Cohen et al. (1957, 1958), and Fabula (1964). The wall effects in axisymmetric flows with a finite cavity has been evaluated numerically by Brennen (1969) for a disk and a sphere. Some intricate features of the wall effects have been noted in experimental studies by Morgan (1966) and Dobay (1967). Also, an empirical method for correcting the wall effect has been proposed by Meijer (1967). The presence of lateral flow boundaries in a closed water tunnel introduces the following physical effects: (i) First, in dealing with the part of irrotational flow outside the viscous region, these flow boundaries will impose a condition on the flow direction at the rigid tunnel walls. This "streamline-blocking" effect will produce extraneous forces and modifications of cavity shape. (ii) The boundary layer built up at the tunnel walls may effectively reduce the tunnel cross-sectional area, and generate a longitudinal pressure gradient in the working section, giving rise to an additional drag force known as the "horizontal buoyancy." (iii) The lateral constraint of tunnel walls results in a higher velocity outside the boundary layer, and hence a greater skin friction at the wetted body surface. (iv) The lateral constraint also affects the spreading of the viscous wake behind the cavity, an effect known as the "wake-blocking." (v) It may modify the location of the "smooth detachment" of cavity boundary from a continuously curved body. In the present paper, the aforementioned effect (i) will be investigated for the pure-drag flows so that this primary effect can be clarified first. Two cavity flow models, namely, the Riabouchinsky and the open-wake (the latter has been attributed, independently, to Joukowsky, Roshko, and Eppler) models, are adopted for detailed examination. The asymptotic representations of these theoretical solutions, with the wall effect treated as a small correction to the unbounded-flow limit, have yielded two different wall-correction rules, both of which can be applied very effectively in practice. It is of interest to note that the most critical range for comparison of these results lies in the case when the cavitating body is slender, rather than blunt ones, and when the cavity is short, instead of very long ones in the nearly choked-flow state. Only in this critical range do these flow models deviate significantly from each other, thereby permitting a refined differentiation and a critical examination of the accuracy of these flow models in representing physical flows. A series of experiments carefully planned for this purpose has provided conclusive evidences, which seem to be beyond possible experimental uncertainties, that the Riabouchinsky model gives a very satisfactory agreement with the experimental results, and is superior to other models, even in the most critical range when the wall effects are especially significant and the differences between these theoretical flow models become noticeably large. These outstanding features are effectively demonstrated by the relatively simple case of a symmetric wedge held in a non-lifting flow within a closed tunnel, which we discuss in the sequel.

ID: CaltechAUTHORS:WUTiutam71

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Abstract: During the first or booster stage of flight many liquid-propellant rockets have experienced severe longitudinal vibrations caused by a closed loop interaction between the first longitudinal structural mode and the dynamics of the propulsion system. This, "POGO" instability, reviewed in Reference 1, has been the subject of intensive research since it was first encountered. One of the most important transients in the dynamic modelling of the propulsion system is the "cavitation compliance" of the turbopumps [3] defined as the negative of the derivative of the cavity and bubble volume in the pump and its suction line with respect to the section pressure. Thus, it describes the oscillatory source/sink behavior of the pump due to changes in the cavity volume. Past analyses [1, 2] have suggested dividing this compliance into two components corresponding to the two major types of pump cavitation, namely blade cavitation and back-flow cavitation. The purpose of this paper is to present some preliminary results of theoretical calculations of blade cavitation compliance. The most satisfactory starting point would be a theory for unsteady cavitating flow in a cascade. Whilst work on this is in progress at the present time, the low frequency or quasistatic approach based on existing steady flow theory is much simpler and in itself yields interesting results.

ID: CaltechAUTHORS:BREpff72

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Abstract: This paper is intended to evaluate the wall effects in the pure-drag case of plane cavity flow past an arbitrary body held in a closed tunnel, and to establish an accurate correction rule. The three theoretical models in common use, namely, the open-wake, Riabouchinsky and re-entrant-jet models, are employed to provide solutions in the form of some functional equations. From these theoretical solutions several different rules for the correction of wall effects are derived for symmetric wedges. These simple correction rules are found to be accurate, as compared with their corresponding exact numerical solutions, for all wedge angles and for small to moderate 'tunnel-spacing ratio' (the ratio of body frontal width to tunnel spacing). According to these correction rules, conversion of a drag coefficient, measured experimentally in a closed tunnel, to the corresponding unbounded flow case requires only the data of the conventional cavitation number and the tunnel-spacing ratio if based on the open-wake model, though using the Riabouchinsky model it requires an additional measurement of the minimum pressure along the tunnel wall. The numerical results for symmetric wedges show that the wall effects invariably result in a lower drag coefficient than in an unbounded flow at the same cavitation number, and that this percentage drag reduction increases with decreasing wedge angle and/or with decreasing tunnel spacing relative to the body frontal width. This indicates that the wall effects are generally more significant for thinner bodies in cavity flows, and they become exceedingly small for sufficiently blunt bodies. Physical explanations for these remarkable features of cavity-flow wall effects are sought; they are supported by the present experimental investigation of the pressure distribution on the wetted body surface as the flow parameters are varied. It is also found that the theoretical drag coefficient based on the Riabouchinsky model is smaller than that predicted by the open-wake model, all the flow parameters being equal, except when the flow approaches the choked state (with the cavity becoming infinitely long in a closed tunnel), which is the limiting case common to all theoretical models. This difference between the two flow models becomes especially pronounced for smaller wedge angles, shorter cavities, and with tunnel walls farther apart. In order to gauge the degree of accuracy of these theoretical models in approximating the real flows, and to ascertain the validity of the correction rules, a series of definitive experiments was carefully designed to complement the theory, and then carried out in a high-speed water tunnel. The measurements on a series of fully cavitating wedges at zero incidence suggest that, of the theoretical models, that due to Riabouchinsky is superior throughout the range tested. The accuracy of the correction rule based on that model has also been firmly established. Although the experimental investigation has been limited to symmetric wedges only, this correction rule (equations (85), (86) of the text) is expected to possess a general validity, at least for symmetric bodies without too large curvatures, since the geometry of the body profile is only implicitly involved in the correction formula. This experimental study is perhaps one of a very few with the particular objective of scrutinizing various theoretical cavity-flow models.

Publication: Journal of Fluid Mechanics Vol.: 49 No.: 2 ISSN: 0022-1120

ID: CaltechAUTHORS:WUTjfm71

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Abstract: Until very recently numerical solutions of unsteady, free surface flows invariably employed the Eulerian description of the motions. Perhaps the most widely used of these has been the marker and cell (MAC) technique developed by Fromm and Harlow (1963) and further refined by many others. In such a formulation the most difficult problem arises in attempting to reconcile the initially unknown shape and position of the free surface with a finite difference scheme and the necessity of determining derivatives at that surface (in a similar fashion few solutions exist with curved or irregular boundaries). But this difficulty can be surmounted by solving in a parametric plane in which the position and shape of the free surface are known in advance; such mappings have been successfully employed in steady flows (eg. Brennen (1969)). Whilst there are other possibilities (see John (1953), Brennen and Whitney (1970)) the Lagrangian description in its general form involves just such a parrametric plane. The present paper describes briefly a numerical method for the solution of the Lagrangian equations of motion for the inviscid, planar flow of a homogeneous or inhomogeneous fluid, taking full advantage of the flexibility of choice of the Lagrangian coordinates (a, b). More details and other results can be found in Brennen and Whitney (1970). Very recently Hirt, Cook and Butler (1970) published details of a method which solves the Eulerian equations of motion in a fashion similar to the MAC technique but uses a Lagrangian tagging space.

Publication: Lecture Notes in Physics Vol.: 8ISSN: 0075-8450

ID: CaltechAUTHORS:BREnmfd70

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Abstract: This report is intended as a companion to Report No. E-111A.5, "Wall Efects in Cavity Flows", by Wu, Whitney and Lin. Some simple rules for the correction of wall effect are derived from that theoretical study. Experiments designed to complement the theory and to inspect the validity of the correction rules were then carried out in the high-speed water tunnel of the Hydrodynamics Laboratory, California Institute of Technology. The measurements on a series of fully cavitating wedges at zero angle of attack suggested that of the theoretical models that due to Riabouchinsky is superior. They also confirmed the accuracy of the correction rule derived using that model and based on a measurement of the minimum pressure along the tunnel wall.

ID: CaltechAUTHORS:WHIcitr70

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Abstract: Observations were made of the appearance of hydrodynamic cavities behind a series of axisymmetric headforms. Among the phenomena investigated was the transition of the interfacial or separated boundary layer on the cavity surface. The first stage of this process, namely the spatial growth of instability waves could be distinguished by means of high-speed photography. Comparison is made with a theoretical instability analysis.

Publication: Journal of Fluid Mechanics Vol.: 44 No.: 1 ISSN: 0022-1120

ID: CaltechAUTHORS:BREjfm70a

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Abstract: Experiments on fully developed cavity flows were carried out with the prime initial objective of investigating the effects of the addition of small quantities of 'turbulent drag reducing additive' upon the cavity-surface boundary-layer instability and transition reported in the previous paper (Brennen 1970). However, in most instances, the additives were found to cause an unforeseen instability in the wetted surface flow around the headform. Upon convection, the resulting disturbances dramatically disfigured the cavity surface, thus negating the original purpose. This new phenomenon warranted investigation and became the principal subject of this paper.

Publication: Journal of Fluid Mechanics Vol.: 44 No.: 1 ISSN: 0022-1120

ID: CaltechAUTHORS:BREjfm70b

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Abstract: Numerical techniques for the solution of unsteady free surface flows are briefly reviewed and consideration is given to the feasibility of methods involving parametric planes where the position and shape of the free surface are known in advance. A method for inviscid flows which uses the Lagrangian description of the motion is developed. This exploits the flexibility in the choice of Lagrangian reference coordinates and is readily adapted to include terms due to inhomogeneity of the fluid. Numerical results are compared in two cases of irrotational flow of a homogeneous fluid for which Lagrangian linearized solutions can be constructed. Some examples of wave run-up on a beach and a shelf are then computed.

No.: 8
ID: CaltechAUTHORS:BREonrsnh70

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Abstract: In steady, fully developed and unventilated cavity flows occurring in practice, air (originally dissolved in the water) and heat are diffused through the fluid towards the interface providing a continuous supply of air and vapour to the cavity. This must be balanced by the rate of entrainment of volume of air and vapour away from the cavity in the wake. These equilibria which determine respectively the partial pressure of air within the cavity and the temperature differences involved in the flow are studied in this paper. The particular case of the cavitating flow past a spherical headform has been investigated in detail. Measurements indicate a near-linear relation between the partial pressure of air in the cavity and the total air content of the water. From a second set of experiments, designed to estimate the volume rates of entrainment under various conditions by employing artificial ventilation, it appears that this is a function only of tunnel speed and cavity size within the range of the experiments. A simplified theoretical approach involving the turbulent boundary layer on the surface of the cavity is then used to estimate the rates of diffusion into the cavity. The resulting air balance yields a partial pressure of air/air content relation compatible with experiment. The water vapour or heat balance suggests that the temperature differences involved are likely to be virtually undetectable experimentally.

Publication: Journal of Fluid Mechanics Vol.: 37 No.: 1 ISSN: 0022-1120

ID: CaltechAUTHORS:BREjfm69a

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Abstract: In the first part of the paper a method is developed for the relaxation or numerical solution of axisymmetric fully cavitating flows. Employing the technique suggested in a paper by Woods (1951a) of working in a transformed [formula]-plane, solutions are obtained for cavities behind a disk and a sphere in different sizes of solid wall tunnel. Under certain conditions flow 'choking' occurs. The results of a series of experiments carried out with such headforms are then reported. The apparent viscous effect on the position of separation from the sphere and thus on the drag proves to be of particular interest.

Publication: Journal of Fluid Mechanics Vol.: 37 No.: 4 ISSN: 0022-1120

ID: CaltechAUTHORS:BREjfm69b

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Abstract: Some significant differences between fully developed cavity flows and their corresponding potential flow models are described and an attempt is made to interpret the results in terms of the real fluid properties. The phenomenon of cavity separation from a smooth surface and the nature and appearance of the cavity interface are given particular attention.

ID: CaltechAUTHORS:BREcsk69

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Abstract: A previous paper (Brennen (1968b)) reported the observation and analysis of wave patterns on the surface of fully developed cavities behind a series of axisymmetric headforms in No.2 water tunnel at Ship Division, NPL. Comparison of theory and experiment appeared to confirm that these waves, which appeared a short distance after separation, grew in amplitude as they were convected downstream and then under certain conditions broke up into turbulence, were the amplified result of a select frequency instability in the separated or cavity surface boundary layer. The small vertical tunnel (figure 1) was employed to study and extend observation of the same phenomenon to smaller headforms and Reynolds numbers. An additional intention was to investigate the effect of small quantities of polymer additive on the behaviour of this instability. But, a more dramatic phenomenon was manifest with the addition of these drag-reducing chemicals, leaving the original objective unattainable.

Publication: National Physical Laboratory No.: 123
ID: CaltechAUTHORS:BREnpl68b

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Abstract: In experiments on cavities behind various axisymmetric headforms, a pattern of waves or ripples with crests parallel to the separation line was observed on the cavity surface just downstream of separation. A theoretical analysis suggests that this pattern results from amplified instabilities in the separated laminar boundary layer on the cavity surface.

Publication: National Physical Laboratory No.: 121
ID: CaltechAUTHORS:BREnpl68a

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Abstract: This paper describes studies of the properties of dilute solutions of polymers which have been found to reduce friction in turbulent flows. The substances tested, in solution in tap water, were guar gum, polyethylene oxide (Union Carbide 'Polyox' WSR 301) and polyacrylamide (Dow 'Separan' AP 30). It had been previously found that solutions of 'Polyox' and 'Separan' exhibit normal-stress difference effects. Correspondingly for'Polyox' solutions, it has been reported that the pressure increment at the mouth of a pitot tube, or open-ended tube facing into the flow, can be reduced below the value [formula] normal for Newtonian liquids, where [Greek rho] is density and V is speed. The present experiments began as a further investigation of this loss of pitot pressure. It was found that the pitot loss reduced with time, and that with 'Polyox' solutions other normal-stress difference effects showed a similar aging, without apparently impairing the ability of the liquid to produce turbulent drag reduction. Continued exposure of the liquid to intense turbulence does, however, lead to a degradation of the drag reduction.

Publication: Nature Vol.: 215 No.: 5108 ISSN: 0028-0836

ID: CaltechAUTHORS:BREn67

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Abstract: This thesis develops a method of solving axisymmetric cavity flow problems using a relaxation or numerical technique. Chapter 1 contains a general review of the phenomenon of cavitation in fluids. Special reference is then made to fully developed cavities in an Euler or ideal fluid for both plane and axisymmetric flow. The basic theorems and equations are presented, with the various types of mathematical model which have been suggested. Details of the fundamental feature of this type of flow, namely the phenomenon of flow separation, are given. At the conclusion of the chapter the analytic methods of solution of plane cavitating flow and, in particular, those using the Riabouchinsky model, are outlined. The numerical results of a pertinant example of this type of flow are included in Appendix A with some additional comments on the phenomenon of choked cavity flow. Chapter 2 provides a brief account of the previous approaches to the problem of axisymmetric cavitating flow. These include; empirical results; theories based on source-sink and vortex sheet distributions; theories based on correlation with the corresponding plane flow solutions; previous applications of relaxation methods. Chapter 3 develops the basic equations for axisymmetric cavity flow in the transformed phi,psi plane in which it is proposed to solve for the dependent variable f (equal to r^2, where r is the radial variable in the physical plane). The equations prove to be of the non-linear elliptic type. Relations for the boundary conditions, and certain other relevant physical quantities, are then evolved in terms of the derivatives of f. The determinacy of the problem in this plane requires careful investigation. Special reference is made to two important phenomena; (i) that of the limiting condition of choked flow, for which certain important relations are developed and (ii) that of the two distinct types of separation in cavity flow. The derivation of expansions describing the singular behaviour of the flow in that region of the transformed plane is given in each case. Chapter 4 describes the adaptation of the results of chapter 3 to provide a numerical or relaxation method of solving axisymmetric cavity flows. The finite difference forms of the field equation and boundary conditions in the phi,psi plane are first derived. Their application is then discussed with special attention being paid to the separation point and to the free streamline, the treatment of which provides the crux of the problem. Details are then given of the treatment of the singular points, a subject which has commanded little attention in the literature for the case of nonlinear partial differential equations. Finally the application of the methods developed is summarized. Chapter 5 presents the results obtained by the author, both for the convergence of the methods and for the resulting cavity flows. Comparison is made with previous results with the corresponding plane flow solutions and with experiment. Special reference is made to the behaviour of cavity flows near the choked flow condition, results which have an added significance in view of the fact that most experiments are carried out in the restricted environment of a water tunnel. In the final section some analysis of the errors is given.

ID: CaltechAUTHORS:BREou66

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