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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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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