(PHD, 2010)

Abstract:

This thesis concerns the dynamics of bubbly flows with a distribution of equilibrium bubble sizes. The main goal is to formulate the physical and numerical models of continuum bubbly flows that enable us to efficiently compute the average mixture dynamics. Numerical simulations are conducted to quantify the effects of bubble size distributions on the averaged dynamics for several model flows.

First, the ensemble-averaged conservation laws for polydisperse bubbly flows are derived. One-way-coupled flow computations are conducted to illustrate that the different-sized bubbles can oscillate with different frequencies. The resulting phase cancellations can be regarded as an apparent damping of the averaged dynamics of polydisperse flows. A high-order-accurate finite-volume method is then developed to compute the flow, paying special attention to issues of wave dispersion and stiffness.

Next, computations of one-dimensional shock propagation through bubbly liquids are performed. The numerical experiments reveal that the bubble size distribution has a profound impact on the averaged shock structure. If the distribution is sufficiently broad, the apparent damping due to the phase cancellations can dominate over the single-bubble-dynamic dissipation (due to thermal, viscous, and compressibility effects) and the averaged shock dynamics become insensitive to the individual bubble dynamics. One-dimensional cloud cavitation caused by fluid-structure interaction is also solved to investigate the collapse of cavitation clouds with both monodisperse and polydisperse nuclei. The phase cancellations among the cavitation bubbles with broad nuclei size distributions are found to eliminate violent cloud collapse in the averaged dynamics.

Finally, shock propagation through a bubbly liquid-filled, deformable tube is considered. The quasi-one-dimensional conservation law that takes into account structural deformation is formulated and steady shock relations are derived. The results are compared to water-hammer experiments; the present shock theory gives better agreement with the measured wave speeds than linear theory. This indicates that the gas-phase nonlinearity needs to be included to accurately predict the propagation speeds of finite-amplitude waves in a deformable tube filled with a bubbly liquid.v

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(PHD, 2005)

Abstract:

Wave propagation is a fundamental property of all physical systems. The wave speed is directly related to the compressibility of the system and determines the rate at which local disturbances are propagated into the bulk of the material. The wave propagation characteristics of conventional forms of matter are well understood and well documented. In contrast, waves in granular materials are more complex due to the heterogeneous nature of these systems. The key element of the mechanics of a granular system is the force chain. It is along these preferentially stressed chains of particles that waves are transmitted. These nonlinear chains are heavily dependent on the geometry of the bed and are prone to rearrangement even by the slightest of forces.

Results from both experiments and simulations on wave propagation in granular materials are presented in the current study. The experiments measure the pressures at two points within the granular bed that result from the motion of a piston at one end of the bed. The simulations are a two-dimensional version of the experiments and use a discrete, soft-particle method to detect the wave at both the output of the simulated bed and at any point within it. In addition to examining wave propagation in a granular bed at rest, simulations and experiments are also performed for a granular bed undergoing agitation perpendicular to the direction of the wave input. Imposed agitation increases the granular temperature of the bed and allows for the exploration of the effect of granular state changes on the wave propagation characteristics. Such information may provide a means to diagnose the state of a flowing granular material.

Measurements of the wave speed and attenuation in the bed reveal the unique properties of waves in granular systems that result from the nonlinearity of the bed and the heterogeneity of the force chains. Sinusoidal waves demonstrate the nondispersive nature of a granular bed and show the transient effects of force chain rearrangement. Pulsed waves display a semi-permanent shape qualitatively similar to predictions from nonlinear wave theory. In an agitated granular bed, measurements of the wave characteristics were found to be possible even in the presence of significant agitation. The prevailing confining pressure, which changes throughout the agitation cycle, was determined to be the system parameter that correlates best with changes to the wave speed.

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(PHD, 2001)

Abstract: Fluid-induced rotordynamic forces in pumping machinery are well documented but poorly understood. The present research focuses on the rotordynamics due to fluid flow in annuli, in particular, the discharge-to-suction leakage flow in centrifugal pumps. There are indications that the contribution of the front shroud leakage flow can be of the same order of magnitude as contributions from the nonuniform pressure acting on the impeller discharge. Previous investigations have established some of the basic traits of these flows. This work furthers the experimental and computational approach to quantify and predict the shroud contribution to the rotordynamic stability of pumping machinery. Childs’ bulk flow model for leakage paths is carefully examined, and convective relations for vorticity and total pressure are deduced. This analysis leads to a new solution procedure for the bulk flow equations which does not resort to linearization or assumed harmonic forms of the flow variables. Experimental results presented show the contributions of the inlet swirl velocities to the rotordynamic forces. Antiswirl devices are evaluated for their effectiveness in reducing instability. Additional tests measuring the pressure distributions and the inlet swirl velocities of the leakage flow confirm some of the predictions by numerical analysis.

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(PHD, 2001)

Abstract:

The present study details results from experiments investigating a surge instability on a cavitating propeller. Initially, the stable behavior of the propeller is explored, and the nature and extent of the cavitation is documented at various experimental conditions, including propeller yaw. The cavitation surge instability is first explored through visual observation of the cavitation on the propeller blades and in the tip vortices. Particular note is made of similarities between the behavior of the re-entrant jets and that noted by other investigators. It is also observed that the nature of the instability is closely related to the partial cavity instability observed on single, two-dimensional hydrofoils.

The flow conditions that lead to instability are determined and it is shown that onset corresponds to a specific configuration of attached cavity lengths on an individual propeller blade. Pressure measurements are obtained from transducers within the experimental facility, and the acoustic signature of the instability is identified. The magnitude of the fluctuating pressures is very large, presumably capable of producing severe hull vibration. A simple model is developed based on cavity volume estimates obtained from high speed video footage, and the predictions of the model are compared with the experimentally obtained pressures.

To assess the significance of the surrounding facility in initiating and sustaining the instability, a model is developed for the experimental facility dynamics. The predictions of this model are then compared with an experimentally determined facility response to a volumetric excitation imposed by an oscillating piston. To quantify the response of the cavitation to fluctuations in test section conditions, quasistatic estimates are obtained for the cavitation compliance and mass flow gain factor of the propeller. These parameters have previously been employed in developing system transfer functions for cavitating pumps.

Finally, a model is developed for the complete system, incorporating both the cavitation and facility dynamics. The model predicts active system dynamics and therefore potentially unstable behavior for two distinct frequency ranges, and one such range is hypothesized to correspond to the observed instability. The ability of the model to predict the observed characteristics of the instability is then evaluated.

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(PHD, 1999)

Abstract:

Experimental studies of air entrainment by breaking waves are essential for advancing the understanding of these flows and creating valid models. The present study used three-dimensional simulations of a bow wave to examine its air entrainment process. The simulated waves were created by a deflecting plate mounted at an angle in a super-critical free surface flow. Since the air entrainment process is closely coupled with breaking wave dynamics, the present study included both air entrainment and free surface measurements.

Measurements of the free surface wave were obtained from the simulated bow waves at two scales, and also from the bow wave created a towed wedge model. Contact line and bow wave profile measurements for the different experiments were compared, demonstrating the similarity of the experimental simulations to the towed model experiments. The plunging wave jet shape was measured in the larger scale stationary model and towed model experiments and used to calculate the jet thickness, velocity, and impingement angle. The bow wave profile data from the towed model experiments were used to investigate the scaling on the plunging wave face, and their wavelength, frequency, and velocity were measured.

The primary mechanisms for air entrainment were the impact of the plunging wave jet and individual droplets in the splash region on the free surface. The air entrainment process was observed in the larger scale stationary model experiments, and the air bubbles were entrained in spatially periodic bubble clouds. Due to the shallow depth in these experiments, measurements of only the larger bubbles in the initial stages of air entrainment were obtained. An impedance based void fraction meter, developed specifically for the purpose, was used to measure the void fractions and bubble size distributions beneath the wave. The bubble cloud size and void fraction increased with downstream distance.

There were indications that the surface disturbances control the periodicity of the bubble clouds. Namely, the surface disturbances divide the plunging liquid jet sheet into a series of plunging wave jets, each entraining air into a separate bubble cloud beneath the free surface.

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(PHD, 1998)

Abstract:

Fluid-induced rotordynamic forces in pumping machinery are well documented but poorly understood. The present research focuses on the rotordynamics due to fluid flow in annuli, in particular, the discharge-to-suction leakage flow in centrifugal pumps. There are indications that the contribution of the front shroud leakage flow can be of the same order of magnitude as contributions from the nonuniform pressure acting on the impeller discharge. Previous investigations have established some of the basic traits of these flows. This work further elaborates both the experimental and computational approach to quantify and predict the shroud contribution to the rotordynamic stability of pumping machinery.

Experimental results presented show the contributions of the curvature of the leakage path to the rotordynamics both with and without inlet swirl. The effect of different inlet swirl rates at constant flow rate is examined. Anti-swirl devices are evaluated for their effectiveness in reducing instability. Geometrical changes to the high-pressure and low-pressure seals for the leakage path are quantified. All results are in good agreement with other reported measurements.

Childs’ bulk flow model for leakage paths is carefully examined, and convective relations for vorticity and total pressure are deduced. This analysis suggests a new solution procedure of the bulk flow equations which does not resort to linearization or assumed harmonic forms of the flow variables.
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(PHD, 1997)

Abstract:

Cloud-cavitation, often formed by the breakdown and collapse of a sheet or vortex cavity, is responsible for severe cavitation noise and erosion damage. This thesis describes an experimental investigation of the dynamics and acoustics of cloud cavitation on a three dimensional hydrofoil and examines the injection of air as a means of noise suppression.

Part one of this work examines the large amplitude impulsive pressures which were measured on the suction surface of an oscillating hydrofoil experiencing cloud cavitation and these pressure pulses are correlated with the observation of shock waves propagating through the bubbly mixture. Recess mounted transducers were used to measure unsteady pressures at four locations along the chord of the suction surface of a hydrofoil. By examining the transducer output, two distinct types of pressure pulses were identified. Local pulses occurred at a single transducer location and were randomly distributed in position and time. Conversely, global pulses were registered by all the transducers almost simultaneously. The location of the global pulses relative to the foil oscillation was quite repeatable and these events produced substantial far-field noise. Correlation of the transducer output with high speed movies of the cavitation revealed that the global pulses were produced by a large scale collapse of the bubble cloud. Conversely, local pulses were generated by local disturbances in the bubbly mixture characterized by large changes in void fraction.

The large pressure pulse associated with the local and global cavitation structures, the geometric coherence of their boundaries and the nearly discrete change in void fraction across the boundaries of these structures indicate that these structures consist of bubbly shock waves. Qualitative and quantitative comparisons between the current experiments and the numerical, analytic and experimental bubbly shock wave analysis of other investigators support this conclusion.

Part two of this work examines the dramatic reduction in cloud cavitation noise due to both continuous and pulsed injection of air into the cavitating region of the foil. At sufficient air flow rates, the radiated noise could be reduced by a factor greater than 200 relative to the noise produced without air injection. Unsteady surface pressure measurements also showed a reduction in the acoustic impulse with air injection by a factor of up to two orders of magnitude. An explanation for this noise reduction can be found by examining the high speed motion pictures. The presence of the non-condensible gas in the cavitation cloud is shown to prevent any rapid or coherent collapse process. Although the formation of local structures is still observed, the presence of air in the bubbles diminishes both the magnitude and the frequency of occurrence of local pressure pulses. Finally, pulsed air injection results in a lower acoustic impulse than the impulse obtained by injecting the same mass of air continuously over the entire oscillation cycle.
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(PHD, 1997)

Abstract:

This thesis focuses on understanding the use of air injection as a means of controlling rotating stall in an axial flow compressor, involving modeling, dynamical systems analysis, and experimental investigations.

The first step towards this understanding was the development of a low order model for air injection control, the starting point of which was the Moore and Greitzer model for axial flow compressors. The Moore and Greitzer model was extended to include the effects of air injection and bifurcation analysis was performed to determine how the closed loop system dynamics are different from those of the open loop system. This low order model was then used to determine the optimal placement of the air injection actuators.

Experimental work focused on verifying that the low order model, developed for air injection actuation, qualitatively captured the behavior of the Caltech compressor rig. Open loop tests were performed to determine how the placement of the air injectors on the rig affected the performance of the compressor. The positioning of the air injectors that provided the greatest control authority were used in the development of air injection controllers for rotating stall. The controllers resulted in complete elimination of the hysteresis associated with rotating stall. The use of a throttle actuator for the control of the surge dynamics was investigated, and then combined with an air injection controller for rotating stall; the resulting controller performed quite well in throttle disturbance rejection tests.

A higher order model was developed to qualitatively match the experimental results with a simulation. The results of this modeling effort compared quite well with the experimental results for the open loop behavior of the Caltech rig. The details of how the air injection actuators affect the compressor flow were included in this model, and the simulation predicted the same optimal controller that was developed through experimentation.

The development of the higher order model also included the investigation of systematic methods for determining the simulation parameters. Based on experimental measurements of compression system transients, the open loop simulation parameters were identified, including values for the compressor performance characteristic in regions where direct measurements were not possible. These methods also provided information on parameters used in the modeling of the pressure rise delivered by the compressor under unsteady flow conditions.

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(PHD, 1997)

Abstract:

NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.

This thesis examines the fundamental behavior of a granular material subject to external vibrations. Experiments were designed to investigate the phenomena that appear in a container filled with glass spheres subject to vertical, sinusoidal oscillations. In addition, a discrete element computer simulation code was written to supplement the experimental program.

Experiments and simulations reveal that the behavior of the particle bed can be classified into two regimes known as shallow and deep beds. For example, when a shallow bed consisting of less than six layers of glass spheres is subjected to oscillations with acceleration amplitudes greater than approximately 2.Og where g is the acceleration due to gravity, the particles in the container are fluidized and do not display coordinated movement. However, when more than six particle layers are used, the particles move coherently and the deep bed behaves as a single, completely inelastic mass.

In the shallow bed regime three distinct sub-states are observed that differ in the degree of coherency in the particle motions. Each appears depending upon the number of particle layers in the bed and on the acceleration amplitude of the oscillations. The transitions between the states are gradual and not well-defined.

The transition from the deep bed to the shallow bed state is characterized by a sudden expansion of the bed that occurs at a critical acceleration amplitude for a fixed bed depth and particle type. Simulations indicate that when the particle fluctuating kinetic energy is dissipated completely each oscillation cycle, the bed remains in the deep bed state. If the energy is not completely dissipated, a shallow bed state results. A simple model consisting of an inelastic ball bouncing on a sinusoidally oscillating table reproduces the sudden expansion.

In the deep bed regime, phenomena such as side wall convection, surface waves, kinks, and kink convection cells appear depending primarily on the acceleration amplitude of the oscillations and, to a lesser degree, the number of particle layers in the bed. Phase maps of when these behaviors occur were constructed using both experimental and simulation data.

When the acceleration amplitude is greater than approximately lg, side wall convection cells appear at the vertical wall boundaries of the container. Particles move down along the vertical walls of the container and up within the bulk of the bed. Simulations indicate that the convection cells are the result of the frictional contact between particles and the walls and the asymmetry of the particle/wall collision rate over an oscillation cycle. Using the simulations, the width of the boundary layer next to the walls, the height of the convection cell center from the container base, and the particle flux in the boundary layer were measured as functions of the vibration parameters and particle properties. The results from the simulation compare well with experimental measurements. The simulation indicates that the boundary layer width is proportional to the container width when the bed aspect ratio, defined as the bed depth to the bed width, is greater than approximately 0.2. For beds with aspect ratios less than 0.2, however, the boundary layer width remains constant. Simulation results also demonstrate that the convection cell height is proportional to the bed depth and that the flux of particles in the boundary layer increases with increasing particle/wall friction and decreases for coefficients of restitution near one.

At acceleration amplitudes between approximately 2.Og and 3.5g, standing waves appear on the top free surface of the bed. These waves form at half the forcing oscillation frequency and are referred to as […]/2 waves. A second set of standing waves appears when the acceleration amplitude is greater than approximately 5.Og and persist up to at least 7.0g. These waves form at one-quarter the forcing frequency and are known as […]/4 waves. Experimental measurements indicate that the wave amplitude expressed as a Froude number increases with increasing acceleration amplitude for the […]/2 waves but remains constant for the […]/4 waves. Additionally, measurements of the wavelength suggest that the waves have a dispersion relation similar to that for deep fluid gravity waves where the wavelength is proportional to the square of the inverse frequency.

Kinks and kink convection cells appear in the particle bed after a period doubling bifurcation occurs in the flight dynamics of the bed. The formation of kinks can be explained using a simple model consisting of a completely inelastic ball on a sinusoidally oscillating table. Experimental measurements indicate a minimum allowable distance between nodes that is a function of the bed depth and acceleration amplitude. The convection cells bracketing each kink are shown to be the result of the out-of-phase motion of the bed sections and the interaction between fluidized and solidified regions of the bed.

The effect of vertical, sinusoidal vibrations on a discharging wedge-shaped hopper was also investigated. When the hopper exit is closed, side wall convection cells appear with particles moving up at the inclined container boundaries and down at the centerline of the bed. The same mechanism that causes downward convection at vertical walls can also explain the upward motion at inclined walls. Experimental measurements also indicate that the discharge rate from the vibrating hopper scales with the oscillation velocity amplitude. At low velocity amplitudes, the discharge rate from the hopper is slightly greater than the non-vibrating hopper discharge rate. At high velocity amplitudes, however, the discharge rate decreases significantly. A simple model accounting for the change in the effective gravity acting on the particle bed throughout the oscillation cycle and the impact velocity of the bed with the hopper predicts the observed trend.

The experiments and simulations conducted in the present work suggest that the boundary conditions and the fluid- and solid-like nature of granular materials are significant factors affecting the response of a granular bed. Additionally, this work demonstrates the value of discrete element computer simulations as a tool for complementing experimental observations.
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(PHD, 1996)

Abstract:

Two problems are considered in this thesis: the nonlinear dynamics of a cloud of cavitation bubbles, and bubbly cavitating flows in a converging-diverging nozzle. The focus of the first problem is to explore the characteristics of the growth and collapse of a spherical cloud of 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 transient behaviour exhibited by a bubble cloud as it passes a body or the blade of a ship propeller. The simulations employ the fully nonlinear, non-barotropic, homogeneous two-phase flow equations coupled with the Rayleigh-Plesset equation for the dynamics of individual bubbles. A Lagrangian integral method is developed to solve this set of equations. The computational results confirm the idea put forward by Morch and his co-workers (Morch [1980], [1981], [1982]; Hanson et al. [1981]) who speculated that the collapse of the cloud involved the formation of a shock wave on the surface of the cloud and that inward propagation and geometric focusing of this shock would lead to very large localized pressure pulses. The effects of varying the bubble population density, the cavitation number, and the ratio of the cloud size to the bubble size are examined. The theoretical results are shown to provide a satisfactory explanation for dynamic structures and acoustic signature observed in recently conducted experiments of cloud cavitation at California Institute of Technology (Reisman and Brennen [1996]; Brennen et al. [1996]). It is concluded that the formation and focusing of bubbly shock waves are responsible for the severe noise and damage potential in cloud cavitation. The second problem investigates the nonlinear behavior of a bubbly cavitating flow, both steady and unsteady, through a converging-diverging nozzle. Two different flow regimes are found from steady state solutions: quasi-steady and quasi-unsteady. The former is characterized by the large spatial fluctuations in the downstream of the flow. Bifurcation occurs as the flow transitions from one regime to the other. An analytical expression for the critical bubble size at bifurcation is obtained. Finally, unsteady solutions in a period of consecutive times are presented. These solutions are characterized by the downstream spatial fluctuations coupled with large pressure pulses changing in both magnitude and location with time. The characteristics of these pulses are similar to the shock pulses of Part I and are produced by the local violent collapse of the bubbles in the flow.

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(PHD, 1995)

Abstract:

Unsteady lifting surface flows are important subjects for study, both for the purposes of improving propulsive or lifting efficiency and also for mitigating the destructive effects and noise caused by cavitation. Some progress may be made by selecting a simple type of unsteadiness for closer study. In the present work, this tactic was implemented in two ways: the operation of a propeller at an angle of yaw to the freestream and the pitching oscillation of a finite-span hydrofoil. A new facility was designed and constructed to set a propeller at an angle of yaw to the freestream, creating a fairly simple non-uniformity in the propeller inflow. Tip vortex cavitation inception measurements were made for a range of yaw angles and freestream velocities, and photographs of the cavitation were taken to illustrate the effects of the yaw angle. The unsteady tip vortex flow field was measured on an oscillating finite aspect ratio hydrofoil using Particle Image Velocimetry (PIV), revealing how the circulation varied during a typical oscillation cycle. The results were compared with unsteady infinite-span theory, and also with recent measurements using LDV techniques on the same foil. The hydrofoil was also the focus of a study of surface cavitation. High-speed motion pictures of the cavitation cycle helped to separate the process into its component stages, and variations with cavitation number and reduced frequency of oscillation were observed. The acoustic signals generated by the cavity collapse were correlated 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. The results from these studies provide valuable insights into the effects of unsteadiness in lifting surface flows.

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(PHD, 1995)

Abstract: The effect of the nuclei population in water on cavitation has not been investigated thoroughly due to the difficulties of measuring the microbubbles in water. In this thesis, a Phase Doppler Anemometer (PDA) was calibrated by a holographic method and used to measure the micro-bubble distribution in water. Substantial agreement was achieved between the PDA and the holographic method. After the calibration, the PDA was used to study the nuclei population dynamics in two water tunnels. It was also employed in a study of cavitation on an axisymmetric Schiebe body in which the cavitation on the headform and the upstream nuclei population were simultaneously observed. Substantial changes in the nuclei number density distributions were found in these two water tunnels. The nuclei population in each water tunnel can also vary significantly, sometimes by as much as an order of magnitude. The nuclei population dynamics are complicated and are affected by the tunnel design, the tunnel operating condition and the air content. The cavitation event rate on the Schiebe headform is mainly determined by the cavitation number. It increases dramatically as the cavitation number is decreased. It also varies with the magnitude and the shape of the nuclei number distribution. As the upstream nuclei population increases, the cavitation event rate increases. During the experiments, cavitation acoustic emissions were also measured and analyzed. An analytical model based on the spherical bubble assumption and the Rayleigh-Plesset theory is developed to relate the free stream nuclei population to the cavitation event rate and the acoustic noise on an axisymmetric body. Complications, such as the effect of the boundary layer flow rate, of the bubble screening, of the bubble/bubble interactions and of the observable bubble size are examined and included in the model. The predicted cavitation event rate and acoustic impulse are compared with the experimental observations. It is shown that the predicted event rates agree with the observations when the population is small, but that increasing discrepancies occur at lower cavitation numbers when the bubble density becomes larger. The predicted noise qualitatively agrees with the observations, but is generally larger than the observations, mainly due to the fact that the spherical bubble assumption usually departs from the observed bubble shape.

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(PHD, 1994)

Abstract:

Recent observations of the geometries of growing and collapsing bubbles over axisymmetric headforms have revealed the complexity of the “microfluidmechanics” associated with these flows (Hamilton et al., 1982, Briancon Marjollet and Franc, 1990, Ceccio and Brennen, 1991). Among the complex features observed were bubble to bubble interaction, cavitation noise generation and bubble interaction with the boundary layer which leads to the shearing of the underside of the bubble and alters the collapsing process. All of these previous tests were performed on small headform sizes. The focus of this research is to determine the dynamics governing the growth and collapse of traveling bubbles and to analyze the scaling effects due to variations in geometry size, Reynolds number and cavitation number. For this effect, cavitating flows over Schiebe headforms of different sizes (5.08cm, 25.4cm and 50.8cm in diameter) were studied in the David Taylor Large Cavitation Channel (LCC). This thesis presents the scaling effects captured on high-speed film and electrode sensors as well the noise signals generated during the collapse of the cavities. The influence of each of these parameters on the dynamics involved in the growth and collapse phases of the traveling bubble are presented, along with the acoustical impulse produced during the collapse of the bubble.

In order to model and analyze the dynamics of the three-dimensional bubble deformation in the presence of the pressure field around the Schiebe headform, an unsteady numerical code using traveling sources has been developed. This thesis presents calculations of the interaction between the irrotational flow outside the boundary layer of the headform and individual traveling bubbles. An error estimation of the method and comparisons with the LCC experiments are presented. This method is shown to predict some of the features of three-dimensional bubble growth and collapse dynamics remarkably well. Furthermore, analysis of these computations allow a better understanding bubble interaction and event rate prediction.

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(PHD, 1994)

Abstract:

Axial flow pump runners known as inducers are subject to complex internal flows and fluid-induced lateral and rotordynamic forces. The internal flows in inducers are three dimensional and are characterized by complicated secondary flows. The current research investigates the boundary layer flows on the blades, hub and housing of unshrouded and shrouded axial flow inducers using flow visualization techniques. Rotordynamic and lateral force data on unshrouded inducers were also obtained under varying conditions of flow and whirl.

Studies on the internal flows showed that the blade boundary layer flow had strong radial components at off-design conditions. The flow remains attached to the blade surface of unshrouded inducers at all flow coefficients tested. The origin of the upstream swirling backflow was found to be at the discharge plane of the inducer. In addition, flow reversal was observed at the suction side blade tip near the leading edge in a shrouded inducer. Re-entry of the hub boundary layer flow (a downstream backflow) into the blade passage area was observed at flow coefficients below design. For unshrouded inducers the radially outward flow near the blade tip mixed with the tip clearance leakage flow to form the upstream backflow. These observations provide a better understanding of the internal flows and the occurrence of upstream backflows in inducers.

The rotordynamic forces acting on an inducer due to an imposed whirl motion was also investigated. It was found that the rotordynamic force data at various whirl frequency ratios does not allow a normal quadratic fit; consequently the conventional inertial, stiffness and damping coefficients cannot be obtained and a definite whirl ratio describing the instability region does not result. Rotordynamic forces were found to be significantly dependent on the flow coefficient. At flow coefficients below design, these forces are characterized by multiple zero crossings at various whirl frequencies and large destabilizing peeks. Theoretical estimates of the tangential rotordynamic force on a non-whirling inducer using actuator disk theory were significantly different, both in magnitude and direction, from the experimentally measured forces.

The effect of upstream and downstream flow distortions on the rotordynamic and lateral forces on an inducer were studied. It was found that at flow coefficients below design, large lateral forces occurred in the presence of a downstream asymmetry. The reverse flows occurring downstream which consist of high energy fluid are the possible cause of these large forces. The imposition of a uniform downstream condition reduced these forces to near zero values. Results of inlet distortion experiments show that a strong inlet shear causes a significant increase in the lateral force. However, weak inlet shear flows and the flow asymmetry due to a 180° upstream bend did not cause a significant lateral force. It was found that flow distortions upstream or downstream did not cause any significant effect on the rotordynamic forces. Cavitation was found to have important consequences for fluid-induced rotordynamic forces. These forces become destabilizing for both forward and reverse whirl. The magnitudes of the destabilizing forces were found to increase with decreasing cavitation numbers.

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(PHD, 1993)

Abstract: NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document. Unsteady flows are prevalent in virtually every fluid application yet, because of their intrinsic complexity, few attempts have been made to measure them or explain their behavior. This thesis presents an experimental study of one of the simplest unsteady flow induced effects, the periodic change in angle of attack of a lifting surface. Of particular interest is the influence this effect has on the tip vortex structure of a finite aspect ratio hydrofoil and the part it plays in the inception of cavitation. An aspect ratio 2.3 hydrofoil was reflection-plane mounted to the test section floor of the Caltech Low Turbulence Water Tunnel and harmonically oscillated in pitch near its center of pressure. Observations of the growth and collapse of surface and tip vortex cavitation were made along with detailed observations of the interaction of the tip vortex formation with the spanwise wake structure. Measurements of the cavitation inception number for surface cavitation and tip vortex cavitation were made relative to the phase of the hydrofoil and the reduced frequency, k=[low-case omega]c/2U[…], of oscillation. Studies of the oscillation-induced spanwise trailing vortex structures and the Karman vortex street generated by the boundary layer were made of a two-dimensional hydrofoil. Laser Doppler Velocimetry (LDV) measurements were taken of the tip vortex velocity profile and the flow at the trailing edge of both the two-and the three-dimensional hydrofoils at reduced frequencies ranging from 0.5 to 2.0. Dynamic changes in bound circulaion and shed vorticity in the streamwise and spanwise directions relative to the freestream were calculated from these measurements at three locations along the span of the foil. The results of these measurements are compared to theoretical flow calculations and related to measurements of the cavitation inception number in the tip vortex region of the three-dimensional foil

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(Engineer, 1993)

Abstract:

This experimental research investigates transverse particle segregation in a binary mixture of spherical particles in air. in a gravity driven. vertical channel flow. Glass beads with similar properties, except for size and color, are randomly mixed in an upper hopper at the entrance of a vertical channel. When roughened channel walls are employed. particles show segregation by size, with a preferred position of larger particles at the centerline and approximately 80% of the distance between the centerline and the side walls. The concentration of the particles is found based on grey-scale color distribution as recorded by an image processing system. The effects of variations in flow rate. wall surface conditions, mixture ratios and channel width on segregation are studied as a function of downstream distance.

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(PHD, 1992)

Abstract:

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

Like earlier measurements of the total fluid induced rotordynamic forces on impellers [Chamieh et al. (1985), Jery et al. (1985), Adkins et al. (1988)], the forces measured in these experiments scaled with the square of the rotor speed. 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. 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 exceeded 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.

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(PHD, 1992)

Abstract:

NOTE: Text or symbols not renderable in plain ASCII are indicated by […]. Abstract is included in .pdf document.

This work investigates two aspects of cavitation noise. The first part models some nonlinear interactive effects in bubbly mixtures generated in cavitating flows, and the second part focuses on an acoustical study of the collapse process of a single bubble in travelling bubble cavitation.

The nonlinear interactive effects in a bubbly cloud have been studied by investigating the frequency response of a bubble layer bounded by a wall oscillating normal to itself. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear response of a single bubble in an infinite fluid. This is used in an approximate solution of the oscillating wall problem for bubble layers of finite and infinite thickness in which all the bubbles have the same equilibrium size and a semi-infinite layer containing bubbles with a distribution of size. Particular attention is paid to the generation of harmonics that is due to nonlinear effects.

The finite thickness of the layer results in characteristic natural frequencies of the bubble mixture, all of which are less than bubble natural frequency. These characteristic natural frequencies are functions of the void fraction and the ratio of layer thickness to the bubble radius. In general, the lowest characteristic natural frequency is found to dominate the response. The amplitude of the response increases as the excitation frequency, […], is reduced from […] to around 0.5[…] and decreases with further decrease in excitation frequency. The characteristic frequencies disappear in the limit of a semi-infinite layer. The bubble size oscillation in a semi-infinite layer is maximum at the excitation frequency of […]. The pressure oscillation is minimum at the excitation frequency of […] with equally significant first and second harmonic components.

For sub-resonant and trans-resonant excitation […], the response consists of standing wave patterns with an amplitude that decays slowly with distance from the oscillating wall. This decay is different from that found in spherical bubble clouds (d’Agostino and Brennen 1988a) because of the geometric effects of propagating disturbance. However, for super-resonant excitation the amplitude of oscillation rapidly decays with distance from the source of excitation.

A phenomenon termed harmonic cascading is seen to take place when the bubble layer consists of bubbles with a distribution of bubble sizes. In this phenomenon a large response is observed at twice the excitation frequency when the layer contains bubbles with a natural frequency equal to twice the excitation frequency. The effect is manifest as an increase in the ratio of the second harmonic to the first harmonic as the number of bubbles with small radii gets larger relative to the number of bubbles with large radii. Also, a similar change in the bubble size distribution, while holding the equilibrium void fraction constant, results in a weaker response. This reduction in amplitude of pressure oscillation may be due to the increased number of bubbles. Larger void fraction and smaller amplitudes of wall oscillation are observed to produce a weaker response. Reduced effects of viscocity and surface tension that are due to changes in ambient conditions result in a larger response.

In the second part the collapse processes of single bubbles in the travelling bubble cavitation around two axisymmetric headforms have been studied acoustically to understand the collapse process of a cavitation bubble and to characterize the sound emission in travelling bubble cavitation. The bubbles were observed to collapse and then sometimes to rebound and collapse again, resulting in one or two pulses in the acoustic signal from a cavitation event. It was observed that each of the pulses could contain more than one peak. This phenomenon is called multipeaking and is clearly distinct from rebounding. The occurrence of rebounding and multipeaking and their effects on some characteristic measures of the acoustic signal such as power spectra are examined in this chapter. Two particular head-forms (I.T.T.C. headform and Schiebe headform) with distinct flow characteristics were investigated.

Both rebounding and multipeaking increased with reduction in cavitation number in case of the I.T.T.C. headform. However, multipeaking decreased and rebounding increased with the reduction in cavitation number for the Schiebe headform. Smaller flow velocity, smaller cavitation number and multipeaking delay the rebound. The peak amplitude of the sound emitted from the first collapse was seen to be twice as large as the peak amplitude of sound from the second collapse suggesting a repeatable process of bubble fission during the collapse process. The multipeaking and rebounding increased the characteristic measures of the acoustic signal. These characteristic measures have larger magnitudes for smaller flow velocity. Also, the values of these characteristics are larger for the I.T.T.C. headform than for the Schiebe headform.

Theoretical calculations based on the Rayleigh-Plesset equation were seen to predict correctly the order of magnitude for most of these characteristic measures. However, the distribution of spectral energy is not properly predicted by the model based on the Rayleigh-Plesset equation; bubble fission during the collapse is thought to account for this discrepancy. Reduction in the cavitation number and multipeaking are observed to decrease the fraction of spectral energy contained in the high frequency range (30 kHz-80kHz).
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(PHD, 1990)

Abstract:

Individual travelling cavitation bubbles generated on two axisymmetric headforms were detected using a surface electrode probe. The growth and collapse of the bubbles, almost all of which were quasi-spherical caps moving close to the headform surface, were studied photographically. Although the growth patterns for the two headforms were similar, the collapse mechanisms were quite different. These differences were related to the pressure fields and viscous flow patterns associated with each headform. Measurements of the acoustic impulse generated by the bubble collapse were analyzed and found to correlate with the maximum volume of the bubble for each headform. Numerical solutions of the Rayleigh-Plesset equation were generated for the same flows and compared with the experimental data. The experiments revealed that for smaller bubbles the impulse-volume relationship is determinate, but for larger bubbles the impulse becomes more uncertain. The theoretical impulse was at least a factor of two greater than the measured impulse, and the impulse-volume relationship was related to the details of the collapse mechanism. Acoustic emission of individual cavitation events was spectrally analyzed and the results were compared with relevant theoretical and emperical predictions. Finally, the cavitation nuclei flux was measured and compared to the cavitation event rate and the bubble maximum size distribution through the use of a simple model. The nuclei number distribution was found to vary substantially with tunnel operating conditions, and changes in the nuclei number distribution significantly influenced the cavitation event rate and bubble maximum size distribution. The model estimated the cavitation event rate but failed to predict the bubble maximum size distribution. With the above theoretical and experimental results, the cavitation rate and resulting noise production may be estimated from a knowledge of the non-cavitating flow and the free stream nuclei number distribution.

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(PHD, 1989)

Abstract:

Granular materials flowing down an inclined chute were studied experimentally and analytically. Characteristics of convective heat transfer to granular flows were also investigated experimentally and numerically.

Experiments on continuous, steady flows of granular materials in an inclined chute were conducted with the objectives of understanding the characteristics of chute flows and of acquiring information on the rheological behavior of granular material flow. Two neighboring fibre optic displacement probes were employed to measure mean velocity, one component of velocity fluctuations, and linear concentration at the wall and free surface boundaries. A shear gauge was also developed to make direct measurement of shear stress at the chute base. Measurements of solid fraction, velocity, shear rate, and velocity fluctuations were analyzed to understand the chute flow characteristics, and the rheological behavior of granular materials was studied with the present experimental data. The vertical profiles of mean velocity, velocity fluctuation, and solid fraction were also obtained at the sidewalls.

Existing constitutive equations and governing equations were used to solve for fully developed chute flows of granular materials, and thus the boundary value problem was formulated with two parameters (the coefficient of restitution between particles, and the chute inclination) and three boundary values at the chute base wall (the values of solid fraction, granular temperature, and mean velocity at the wall). The boundary value problem was numerically solved by the “shooting method.” The boundary conditions at the free surface were satisfied by the proper choice of a gradient of granular temperature at the wall. The results show a significant role played by granular conduction in determining the profiles of granular temperature, solid fraction, and mean velocity in chute flows. These analytical results were also compared with the present experimental measurements and with the computer simulations by other investigators in the literature.

Experiments on heat transfer to granular flows over a flat heating plate were conducted with three sizes of glass beads, polystyrene beads, and mustard seeds. A modification on the existing model for the convective heat transfer was made using the effective Nusselt number and the effective Peclet number, which include the effects of solid fraction variations. The slightly modified model could describe the heat transfer characteristics of both fast and slow flows (supercritical and subcritical flows).

A numerical analysis of the convective heat transfer to granular flows was also performed. The results were compared with the present experimental data, and reasonable agreement was found in the comparison.

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(Engineer, 1989)

Abstract:

Fluid-induced forces acting on a rotating impeller are known to cause rotor-dynamic problems in turbomachines. The forces generated by leakage flow along the front shroud surface of a centrifugal turbomachine impeller play an important role among these fluid-induced forces. The present research was aimed to gain a better understanding of these shroud forces. An experimental apparatus was designed and constructed to simulate the impeller shroud leakage flow. Hydrodynamic forces, steady and unsteady pressure distributions on the rotating shroud were measured as functions of eccentricity, width of shroud clearance, face seal clearance and shaft rotating speed. The forces measured from the dynamometer and manometers agreed well. The hydrodynamic force matrices were found skew-symmetric and statically unstable. This is qualitatively similar to the result of previous hydrodynamic volute force measurements. Nondimensionalized normal and tangential forces decrease slightly as Reynolds number increases. As the width of the shroud clearance decreases and/or the eccentricity increases, the hydrodynamic forces increase nonlinearly. There was some evidence found that increased front seal clearance could reduce the radial shroud forces and the relative magnitude of the destabilizing tangential force. Subharmonic pressure fluctuations were also observed which may affect adversely the behavior of the rotor system.

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(PHD, 1987)

Abstract:

Friction pressure drop measurements were made in vertical bubbly and particulate flows, and friction factors up to two orders of magnitude higher than pure liquid values were obtained. The two-phase friction multiplier for air-water flows was shown to attain values up to 15 times higher than the predictions given by the Lockhart and Martinelli correlations (1949). These findings exemplify the lack of detailed understanding of multi-component flow phenomena. The lack of understanding of the flow kinematics and the small amount of information available on the topic has been primarily due to the primitive stage of development of flow measuring instrumentation.

A shielded, temperature compensated and non-intrusive Impedance Volume Fraction Meter (IVFM) was built and shown to have good spatial and temporal resolution. The dynamic calibration of the device demonstrated that the volume fraction measuring device could also be used to measure both the dispersed medium velocity and concentration. This device enabled us to carry out measurements of small and large amplitude kinematic stability and wave propagation in two-component and three-component flows. The velocities of small amplitude kinematic waves in both air-water and solids-water flows were measured using a cross-correlation technique and these were shown to be non-dispersive. The persistence of flow structure was quantified using the coherence of the IVFM noise at two locations. The structure in solids-water flows was found to be more persistent than in air-water flows, and the most coherent wave length was measured to be of the order of .5 m, or five pipe diameters in both flows. The statistical properties in the inherent noise in the IVFM output was shown to contain valuable information on two- and three-component flow quantities and regime.

In this thesis, we show that much can be learned about the complex nature of multi-component flows with adequate instrumentation, and we emphasize the need for further development of critical flow measuring techniques for use not only in fundamental investigations but also in the monitoring and control of practical multiphase flow processes.

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(PHD, 1986)

Abstract:

It has been experimentally determined by previous investigators that hydrodynamic forces can cause a centrifugal pump impeller to whirl in a volute. The present work was undertaken to develop a theoretical model of the interactions that occur between an impeller and a volute, and to identify the source of the hydrodynamic forces. Experiments were then conducted to test the predictions of the model. The theoretical analysis presents a quasi-one dimensional treatment of the flow in the volute and accounts for the disturbance at the impeller discharge that is caused by the volute. The model also considers the lack of perfect guidance through the blade passages. Extending this model allowed for the calculation of hydrodynamic force perturbations that result when the impeller whirls eccentrically in the volute. These force perturbations were shown to encourage, rather than dissipate the whirling motion. The predictions of the model gave reasonable comparisons with the experimental data obtained in this study. Further, it was experimentally observed that pressure forces acting on the front shroud of the impeller could have a major influence on the hydrodynamic force perturbations acting on an eccentrically positioned impeller.

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(Engineer, 1983)

Abstract: Kinematic and dynamic wave characteristics in bubbly two-phase flows are investigated. Using the same set of basic equations, kinematic and dynamic wave characteristics in a one-dimensional flow system were simultaneously obtained. A simple linear model was used so that the response of the flow to oscillatory perturbations of frequency [Omega] was studied. Explicit asymptotic solutions for the wave speeds and attenuations in various relative velocity and frequency regimes were obtained. Numerical analyses were carried out to investigate intermediate or transitional values of the parameters. The regimes of validity for a number of conventional wave propagation models (drift-flux model and acoustic wave analysis) were explored by using the present results. It was observed that for most engineering bubbly two-phase flows of concern, the inertial effects, which are commonly neglected in many existing models, should be included for better accuracy in prediction of wave characteristics.

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(Engineer, 1982)

Abstract:

The convective heat transfer to a flowing, cohesionless granular material has been studied experimentally. Heat-transfer rates were measured for two materials from a heated plate installed in the floor of an inclined, open chute. The variable parameters were the bed depth and the mass flow rate.

At relatively small flow rates the heat-transfer rate increased with velocity in agreement with earlier studies. As the mass flow rate continued to rise however, it was discovered that the heat-transfer coefficient for a given bed depth reached a maximum and then decreased.
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(PHD, 1982)

Abstract:

Many of the macroscopic and microscopic features of shearing granular materials were observed during the course of this investigation.

The principal results were obtained from a computer simulation of the flows in an inclined chute, and in a Couette shear cell. The simulation followed the exact trajectories of two-dimensional discs through a control volume. Properties of the flow were obtained from temporal averages of the instantaneous particle properties. Macroscopic flow characteristics such as velocity and density profiles are presented. Because the simulation follows the exact mechanics of the particles it was also possible to investigate the statistical nature of granular flows. Towards this purpose velocity distributions, collision angle distributions and pair correlation functions were measured.

The results of the simulation draw a picture of a flowing granular material as a self-excited gas. There appears to be a “temperature” associated with the random motions of the particles, that is a product of gradients in the mean velocity field. An equation of state is proposed, involving this temperature, to describe the behavior of the density within the flow. A phenomenon reminscent of conduction is observed. The particle velocities appear to obey a Maxwellian distribution based on this temperature.

Preliminary experiments were also performed to investigate the flow of glass beads down inclined chutes. It is shown that the flows may be classified as either supercritical or subcritical depending on the local value of the Froude number, and that the classification had a strong influence on the flow properties. In addition, wall friction coefficients were determined.

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(PHD, 1982)

Abstract:

The performance of a transverse field electromagnetic flowmeter in a steady two-phase flow was investigated analytically for a disperse and an annular flow regime. In both cases the flowmeter output voltage was found to be proportional to the mean velocity of the liquid phase. Experiments in a steady air-water mixture showed good agreement with the analysis.

An impedance void fraction meter was designed and built to conduct measurements of unsteady void fractions. Short electrodes excited by voltages of opposite polarity were used in combination with a highly sensitive signal processor. The steady state calibration indicated that the meter was somewhat sensitive to the void fraction distribution for the bubbly flow regime. However, the transition to a churn turbulent regime greatly affected the meter steady state response. The dynamic capability of the void fraction meter was estimated by comparison of the statistical properties of the voltage fluctuations in a nominally steady bubbly flow with those of a shot-noise process. The filter function associated with the finite volume of the electric field within the fluid cell could be determined from the measured autocorrelation function and was shown to be mainly a function of the velocity of the disperse phase. Also some properties of the disperse phase could be inferred from the statistical analysis.

Two void fraction meters were used to measure the propagation speed of kinematic shocks in an air-water bubbly mixture for various void fractions and water flow rates. The relative velocity of the disperse phase calculated from these measurements decreased with an increase in the disperse phase concentration. However, this effect disappeared at higher water flow rates and the relative velocity became independent of void fraction. Measurements of the propagation speed of shocks of decreasing strength provided a good verification of the kinematic wave theory. The shock thicknesses could also be determined leading to the conclusion that an important diffusion mechanism was responsible for arresting the steepening of the wave.

Cross-correlations of the fluctuating voltage of two void fraction meters in a steady bubbly flow were determined. The speed measured by this technique was identified as the infinitesimal wave speed of the void fraction and not the velocity of the dispersed phase as postulated by some authors. The normalized cross-correlation maxima showed that the small amplitude void fraction disturbances were short-lived structures, which were created and diffused on a continuous basis. The cross spectral density revealed that the waves present in these disturbances were nondispersive.

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(PHD, 1980)

Abstract:

Cavitation induced instabilities of hydraulic systems were investigated both experimentally and analytically. The instability, known as auto-oscillation, was found to occur in a well defined region of cavitation numbers just above head breakdown of the inducer. Auto-oscillation is characterized by large amplitude fluctuations in the pressures and mass flow rates throughout the system. The frequency of the oscillations was observed to decrease with a reduction in both the flow coefficient and cavitation number. The amplitudes of the fluctuation increased with a reduction in the flow coefficient. These detailed measurements reflect changes in the dynamic performance of the inducer due to cavitation and the interaction between the dynamics of the inducer and those of the inlet flow field. Some detailed analytical studies were performed to try to understand the nature of this interaction.

A linear stability analysis was developed which was based upon the understanding that auto-oscillation is a function of the entire hydraulic system including the cavitating inducer. Using the experimentally obtained transfer functions of two impellers, the analysis successfully predicted both the onset and frequency of auto-oscillation. The stability of the Dynamic Pump Test Facility is significantly reduced by the increased dynamically active character of the inducers at the lower cavitation number. In addition, the stability of the Dynamic Pump Test Facility was found to be particularly sensitive to the mass flow gain factor and pump impedance.
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(PHD, 1980)

Abstract:

A number of problems related to the flow of cohesionless granular materials in hoppers are investigated.

An approximate solution to the flow of granular materials in a conical hopper is presented. The material is modeled as a rigid-perfectly plastic continuum which satisfies the Mohr-Coulomb yield condition. Unknown geometries of the upper and lower free surfaces are determined from the stress-free conditions. The results are compared to those based on different constitutive postulates as well as to experimental observations. The computed mass flow rate and wall stress compare well with the experimental measurements made with small and full size hoppers.

The flow field in a hopper with a vertical bin is observed to gain a better understanding of the details of the flow field. The observations seem to correspond to the recent results obtained by other investigators using X-ray radiography.

The funnel flow regime in hoppers is studied in detail. The different types of flow which exist are identified and classified. The possibility of having a transition from one type of flow into another one is recorded as a function of the material properties and hopper geometry. Finally, the boundary between the moving and stagnant material is studied as a function of the hopper geometry. Other parameters such as the effect of the hopper thickness and wall roughness on the flow field are also studied.

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(PHD, 1979)

Abstract:

Leading edge flutter is a problem that is unique to a super-cavitating hydrofoil. At high speed, the leading edge portion has been observed to oscillate while the trailing edge remains motionless.

In this study, several flat plate hydrofoils were tested. The experimental results indicate that the phenomenon is a complex function of speed, angle of attack, cavitation number and mass ratio. Leading edge flutter was also observed to cause cavity pinching. A theoretical study was also conducted. Two mathematical models are presented here. The first one models the flexible chord foil as a rigid chord foil hinged at the trailing edge; the second model treats the fluid-structure interaction problem of a flexible chord foil cantilevered at the trailing edge. Both models resemble leading edge flutter near zero cavitation number in some respects. At short and moderate cavity lengths, leading edge flutter phenomenon is influenced by the cavity closure condition.

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