Abstract: This article presents experimental measurements involving immersed collisions between a rigid impactor and a deformable target for a wide range of Reynolds and Stokes numbers. Three aluminium alloys are used as solid targets submerged in seven different fluids covering a wide range of viscosity and density. The collision and rebound velocities as well as the depth and diameter of the crater produced by the collisions are measured with high resolution. Most of the experiments in this study occur at velocities for which the deformation is within the elastic–plastic regime. Results of the experiments in air are analysed by elastic, plastic and elastic–plastic theories, and demonstrate the complexities of modelling elastic–plastic collisions. For collisions in a liquid, the measurements show that the size of the crater is independent of the fluid characteristics if the Stokes number is beyond a critical value. The normal coefficient of restitution can be estimated by including both viscous losses and plasticity effects and assuming that the collision time scale is significantly shorter than the hydrodynamic time scale. The results of the crater dimensions are also used to develop an analytical expression for the volume of deformation of the material as a function of material properties and the impact and critical Stokes numbers.

Publication: Journal of Fluid Mechanics Vol.: 871ISSN: 0022-1120

ID: CaltechAUTHORS:20190620-093004189

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Abstract: For low-Reynolds-number shear flows of neutrally buoyant suspensions, the shear stress is often modelled using an effective viscosity that depends only on the solid fraction. As the Reynolds number (Re) is increased and inertia becomes important, the effective viscosity also depends on the Reynolds number itself. The current experiments measure the torque for flows of neutrally buoyant particles in a coaxial-cylinder rheometer for solid fractions, ϕ, from 10 % to 50 % and Reynolds numbers based on particle diameter from 2 to 1000. For experiments for Reynolds of O(10) and solid fractions less than 30%, the effective viscosity increases with Reynolds number, in good agreement with recent numerical simulations found in the literature. At higher solid fractions over the same range of Re, the results show a decrease in torque with shear rate. For Reynolds numbers greater than 100 and lower solids concentrations, the effective viscosity continues to increase with Reynolds number. However, based on comparisons with pure fluid measurements the increase in the measured effective viscosity results from the transition to turbulence. The particles augment the turbulence by increasing the magnitude of the measured torques and causing the flow to transition at lower Reynolds numbers. For the highest solid fractions, the measurements show a significant increase in the magnitude of the torques, but the effective viscosity is independent of Reynolds number.

Publication: Journal of Fluid Mechanics Vol.: 811ISSN: 0022-1120

ID: CaltechAUTHORS:20170112-110444245

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Abstract: The current field study examines linear and non-linear acoustic waves found in large desert sand dunes using field measurements of wave speed, frequency content, dispersion, and polarization. At the dune fields visited, an avalanching of sand can trigger a loud booming or rumbling sound with narrow peak frequencies centered between 70 and 105 Hz with higher harmonics. Prior to the onset of the nearly monotone booming, the emission consists of short bursts or burps of sound of smaller amplitude and over a significantly broader range of frequencies. These burps created at dune sites have similar frequency content to sounds generated by small-scale shearing in laboratory-scale experiments. By investigating the wave characteristics of both burping and booming emissions, this manuscript demonstrates that booming and burping correspond with the transmission of different waves within the dune. The burping sounds correspond to a surface Rayleigh wave with nonlinear and dispersive properties. The booming emission results from a linear, non-dispersive P-wave, which supports an earlier analysis where booming is modeled as the trapping of the body waves in the dune’s surficial layer. Besides characterizing the booming and burping emissions, this manuscript illustrates the effect of scale in the wave propagation of granular materials, when non-linear, dispersive waves across small scales transition to linear, non-dispersive waves across larger scales.

Publication: Physics of Fluids Vol.: 27 No.: 10 ISSN: 1070-6631

ID: CaltechAUTHORS:20151204-103416664

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Abstract: This study experimentally investigates the effect of a bumpy base on the Brazil-nut phenomenon in a vertically vibrated granular bed. The rise dynamics of an intruder is determined by the particle tracking method. The results indicate that the rise time increases with an increase in the base roughness, and the variation of the rise time with different base factors is more pronounced with smaller vibration acceleration and higher vibration frequency. A theoretical model is employed to measure the penetration length of the intruder and the drag force between the intruder and the immersed beads. The penetration length is reduced and the drag force is enhanced with surface roughness of the base. Additionally, the transport properties of the vibrated glass beads are also measured and discussed. With greater base roughness, the strength of the diffusive and convective motion is reduced leading to a weaker Brazil-nut effect.

Publication: Physics of Fluids Vol.: 26 No.: 7 ISSN: 1070-6631

ID: CaltechAUTHORS:20140926-080229459

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Abstract: Studies of the mechanical stresses on plates moving through loose materials were used to simulate and optimize robot locomotion over soft ground.

Publication: Science Vol.: 339 No.: 6126 ISSN: 0036-8075

ID: CaltechAUTHORS:20130328-091117651

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Abstract: The current research presents ground penetrating radar images up to 30 m in depth of two large desert dunes in California, USA— a barchanoid ridge in the Dumont field and a linear dune in the Eureka expanse. The radar images show a complicated structure of internal layering with ascending cross-strata, cross-bedding and bounding surfaces cutting through layers. Additional research using seismic refraction surveys and sand sampling refine the image of the subsurface (<5 m) structure. The sedimentary structure of the dune shows a strong internal layering with a cemented structure that may immobilize and influence migration of dune expanses. The subsurface features of the sand dune fields in the Mojave Desert provide evidence of dune building, wind regime and precipitation history.

Publication: Geophysical Journal International Vol.: 190 No.: 2 ISSN: 0956-540X

ID: CaltechAUTHORS:20120813-104703591

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Abstract: The incompressible Navier–Stokes equations are solved numerically to predict the coupled motion of a falling particle and the surrounding fluid as the particle impacts and rebounds from a planar wall. The method is validated by comparing the numerical simulations of a settling sphere with experimental measurements of the sphere trajectory and the accompanying flow field. The normal collision process is then studied for a range of impact Stokes numbers. A contact model of the liquid–solid interaction and elastic effect is developed that incorporates the elasticity of the solids to permit the rebound trajectory to be simulated accurately. The contact model is applied when the particle is sufficiently close to the wall that it becomes difficult to resolve the thin lubrication layer. The model is calibrated with new measurements of the particle trajectories and reproduces the observed coefficient of restitution over a range of impact Stokes numbers from 1 to 1000.

Publication: Journal of Fluid Mechanics Vol.: 691ISSN: 0022-1120

ID: CaltechAUTHORS:20120224-125133227

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

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

ID: CaltechAUTHORS:20120320-075849559

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Abstract: “Booming” sand dunes have a remarkable capacity to produce sounds that are comparable with those from a stringed instrument. This phenomenon, in which sound is generated after an avalanching of sand along the slip face of a dune, has been known for centuries and occurs in at least 40 sites around the world. A spectral analysis of the sound shows a dominant frequency between 70 and 110 Hz, as well as higher harmonics. Depending on the location and time of year, the sound may continue for several minutes, even after the avalanching of sand has ceased. This review presents historical observations and explanations of the sound, many of which contain accurate and insightful descriptions of the phenomenon. In addition, the review describes recent work that provides a scientific explanation for this natural mystery, which is caused by sound resonating in a surface layer of the dune.

Publication: Annual Review of Earth and Planetary Sciences Vol.: 38ISSN: 0084-6597

ID: CaltechAUTHORS:20100629-133612595

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Abstract: This paper presents the approach and rebound of a particle colliding with a deformable surface in a viscous liquid. The complex interaction between the fluid and the solid phases is coupled through the dynamics of the flow as well as the deformation process. For the experiments, steel particles impacted ductile aluminum alloys samples immersed in an aqueous mixture of glycerol and water. The experiments involved particle Stokes number from 5 to 10^5 and deformation parameters from 10^(−2) to 10^2. From the experiments, the coefficient of restitution is shown to depend on both these parameters. The coefficient of restitution is closest to unity when the deformation parameter is less than one and the Stokes number is greater than 10^3. The coefficient of restitution decreases as the deformation parameter increases and when the Stokes number decreases.

Publication: Granular Matter Vol.: 12 No.: 2 ISSN: 1434-7636

ID: CaltechAUTHORS:20100521-100231503

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

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

ID: CaltechAUTHORS:20111208-105043039

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

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

ID: CaltechAUTHORS:20111208-094334359

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Abstract: When two solid spheres collide in a liquid, the dynamic collision process is slowed by viscous dissipation and the increased pressure in the interparticle gap as compared with dry collisions. This paper investigates liquid-immersed head-on and oblique collisions, which complements previously investigated particle-on-wall immersed collisions. By defining the normal from the line of centers at contact, the experimental findings support the decomposition of an oblique collision into its normal and tangential components of motion. The normal relative particle motion is characterized by an effective coefficient of restitution and a binary Stokes number with a correlation that follows the particle-wall results. The tangential motion is described by a collision model using a normal coefficient of restitution and a friction coefficient that are modified for the liquid effects.

Publication: Physics of Fluids Vol.: 18 No.: 12 ISSN: 1070-6631

ID: CaltechAUTHORS:YANpof06

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

ID: CaltechAUTHORS:20111215-143708669

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

ID: CaltechAUTHORS:20130722-150325006

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Abstract: This work experimentally investigates the effects of an interstitial fluid on the discharge of granular material within an hourglass. The experiments include observations of the flow patterns, measurements of the discharge rates, and pressure variations for a range of different fluid viscosities, particle densities and diameters, and hourglass geometries. The results are classified into three regimes: (i) granular flows with negligible interstitial fluid effects; (ii) flows affected by the presence of the interstitial fluid; and (iii) a no-flow region in which particles arch across the orifice and do not discharge. Within the fluid-affected region, the flows were visually classified as lubricated and air-coupled flows, oscillatory flows, channeling flows in which the flow preferentially rises along the sidewalls, and fluidized flows in which the upward flow suspends the particles. The discharge rates depends on the Archimedes number, the ratio of the effective hopper diameter to the particle diameter, and hourglass geometry. The hopper-discharge experiments, as well as experiments found in the literature, demonstrate that the presence of the interstitial fluid is important when the nondimensional ratio (N) of the single-particle terminal velocity to the hopper discharge velocity is less than 10. Flow ceased in all experiments in which the particle diameter was greater than 25% of the effective hopper diameter regardless of the interstitial fluid.

Publication: Physics of Fluids Vol.: 16 No.: 9 ISSN: 1070-6631

ID: CaltechAUTHORS:MUIpof04

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Abstract: This paper presents experimental measurements of the approach and rebound of a particle colliding obliquely with a wall in a viscous fluid. Steel and glass particles 12.7 mm in diameter were used. The experiments were performed using a thick Zerodur wall (a glass-like material) with various mixtures of glycerol and water. Normal and tangential coefficients of restitution were defined from the ratios of the respective velocity components at the point of contact just prior to and after impact. These coefficients account for losses due to lubrication effects and inelasticity. A third parameter, a coefficient of sliding friction, provides a measure of the tangential force acting on the particle as it slides during a collision. Oblique collisions in a fluid are qualitatively similar to oblique collisions in a dry system, with a lowered friction coefficient dependent on surface roughness. For smooth surfaces the friction coefficient is drastically reduced due to lubrication effects. A theoretical model that takes into account the dependence of viscosity on pressure is proposed to explain the observed tangential force acting on a smooth sphere during an oblique collision. The model relies on an inferred uniform temperature increase within the lubrication layer, a consequence of viscous heating during impact. The tangential force felt by the particle is expressed as a friction coefficient dependent on the viscosity within the lubrication layer. The viscosity increases owing to pressure effects and decreases owing to thermal effects. For rough surfaces the friction coefficient is comparable to that measured in dry systems, since the surface asperities may interact with each other through the lubrication layer.

Publication: Journal of Fluid Mechanics Vol.: 510ISSN: 0022-1120

ID: CaltechAUTHORS:JOSjfm04a

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

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

ID: CaltechAUTHORS:WASpf02

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

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

ID: CaltechAUTHORS:HUNjfm02

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Abstract: This paper presents experimental measurements of the approach and rebound of a particle colliding with a wall in a viscous fluid. The particle's trajectory was controlled by setting the initial inclination angle of a pendulum immersed in a fluid. The resulting collisions were monitored using a high-speed video camera. The diameters of the particles ranged from 3 to 12 mm, and the ratio of the particle density to fluid density varied from 1.2 to 7.8. The experiments were performed using a thick glass or Lucite wall with different mixtures of glycerol and water. With these parameters, the Reynolds number defined using the velocity just prior to impact ranged from 10 to approximately 3000. A coefficient of restitution was defined from the ratio of the velocity just prior to and after impact. The experiments clearly demonstrate that the rebound velocity depends on the impact Stokes number (defined from the Reynolds number and the density ratio) and weakly on the elastic properties of the material. Below a Stokes number of approximately 10, no rebound of the particle occurred. For impact Stokes number above 500 the coefficient of restitution appears to asymptote to the values for dry collisions. The coefficients of restitution were also compared with previous experimental studies. In addition, the approach of the particle to the wall indicated that the particle slowed prior to impacting the surface. The distance at which the particle's trajectory varied due to the presence of the wall was dependent on the impact Stokes number. The particle surface roughness was found to affect the repeatability of some measurements, especially for low impact velocities.

Publication: Journal of Fluid Mechanics Vol.: 433ISSN: 0022-1120

ID: CaltechAUTHORS:JOSjfm01

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Abstract: The dynamics of a granular mixture can differ significantly from those of a same-size flow. For example, shearing of granular materials often leads to unwanted segregation of particles of different sizes. This research uses both experiments and discrete element computer simulations to study the segregation occurring in a cylindrical Couette flow. Both experiments and simulations show a complex segregation pattern in which the concentration of large particles varies with both the radial coordinate and the angular location in the cylinder. The large particles rise to the free surface at the top of the cylindrical container and also line the outer cylinder. The number of layers of large particles around the stationary outer cylinder varies with the angular coordinate.

No.: 81 ISSN: 0925-0042

ID: CaltechAUTHORS:20190829-131533463

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Abstract: Numerical simulations have been performed to study the stability of heated, incompressible Taylor-Couette flow for a radius ratio of 0.7 and a Prandtl number of 0.7. As Gr is increased, the Taylor cell that has the same direction of circulation as the natural convection current increases in size and the counterrotating cell becomes smaller. The flow remains axisymmetric and the average heat transfer decreases with the increase in Gr. When the cylinder is impulsively heated, the counterrotating cell vanishes and n = 1 spiral is formed for Gr = 1000. This transition marks an increase in the heat transfer due to an increase in the radial velocity component of the fluid. By slowly varying the Grashof number, the simulations demonstrate the existence of a hysteresis loop. Two different stable states with same heat transfer are found to exist at the same Grashof number. A time-delay analysis of the radial velocity and the local heat transfer coefficient time is performed to determine the dimension at two Grashof numbers. For a fixed Reynolds number of 100, the two-dimensional projection of the reconstructed attractor shows a limit cycle for Gr = −1700. The limit cycle behavior disappears at Gr = −2100, and the reconstructed attractor becomes irregular. The attractor dimension increases to about 3.2 from a value of 1 for the limit cycle case; similar values were determined for both the local heat transfer and the local radial velocity, indicating that the dynamics of the temperature variations can be inferred from that of the velocity variations.

Publication: Journal of Heat Transfer Vol.: 121 No.: 3 ISSN: 0022-1481

ID: CaltechAUTHORS:20190214-124414387

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

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

ID: CaltechAUTHORS:HUNpf99

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Abstract: When two particles collide in a liquid, the impulsive acceleration due to the rebound produces a pressure pulse that is transmitted through the fluid. Detailed measurements were made of the pressure pulse and the motion of the particles by generating controlled collisions with an immersed dual pendulum. The experiments were performed for a range of impact velocities, angles of incidence, and distances between the wall and the pairs of particles. The radiated fluid pressure was measured using a high-frequency-response pressure transducer, and the motion of the particles was recorded using a high-speed digital camera. The magnitude of the impulse pressure was found to scale with the particle velocity, the particle diameter and the density of the fluid. Additionally, a model is proposed to predict the impulse field in the fluid based on the impulse pressure theory. The model agrees well with the experimental measurements.

Publication: Journal of Fluid Mechanics Vol.: 375ISSN: 0022-1120

ID: CaltechAUTHORS:ZENjfm98

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Abstract: Numerical simulations have been performed to study the effects of the gravitational and the centrifugal potentials on the stability of heated, incompressible Taylor-Couette flow. The flow is confined between two differentially heated, concentric cylinders, and the inner cylinder is allowed to rotate. The Navier-Stokes equations and the coupled energy equation are solved using a spectral method. To validate the code, comparisons are made with existing linear stability analysis and with experiments. The code is used to calculate the local and average heat transfer coefficients for a fixed Reynolds number (Re = 100) and a range of Grashof numbers. The investigation is primarily restricted to radius ratios 0.5 and 0.7 for fluids with Prandtl number of about 0.7. The variation of the local coefficients of heat transfer on the cylinder surface is investigated, and maps showing different stable states of the flow are presented. Results are also presented in terms of the equivalent conductivity, and show that heat transfer decreases with Grashof number in axisymmetric Taylor vortex flow regime, and increases with Grashof number after the flow becomes nonaxisymmetric.

Publication: Journal of Heat Transfer Vol.: 120 No.: 1 ISSN: 0022-1481

ID: CaltechAUTHORS:20190726-104729403

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

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

ID: CaltechAUTHORS:ZENasr98

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

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

ID: CaltechAUTHORS:ZENjfm97

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

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

ID: CaltechAUTHORS:WASjam96

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

ID: CaltechAUTHORS:WASwcce96

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Abstract: Measurements were made of two components of the average and fluctuating velocities, and of the local self-diffusion coefficients in a flow of granular material. The experiments were performed in a 1 m-high vertical channel with roughened sidewalls and with polished glass plates at the front and the back to create a two-dimensional flow. The particles used were glass spheres with a nominal diameter of 3 mm. The flows were high density and were characterized by the presence of long-duration frictional contacts between particles. The velocity measurements indicated that the flows consisted of a central uniform regime and a shear regime close to the walls. The fluctuating velocities in the transverse direction increased in magnitude from the centre towards the walls. A similar variation was not observed for the streamwise fluctuations. The self-diffusion coefficients showed a significant dependence on the fluctuating velocities and the shear rate. The velocity fluctuations were highly anistropic with the streamwise components being 2 to 2.5 times the transverse components. The self-diffusion coefficients for the streamwise direction were an order-of-magnitude higher than those for the transverse direction. The surface roughness of the particles led to a decrease in the self-diffusion coefficients.

Publication: Journal of Fluid Mechanics Vol.: 304ISSN: 0022-1120

ID: CaltechAUTHORS:NATjfm95

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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: In flows of granular material, collisions between individual particles result in the movement of particles in directions transverse to the bulk motion. If the particles were distinguishable, a macroscopic overview of the transverse motions of the particles would resemble a self-diffusion of molecules as occurs in a gas. The present granular- flow study includes measurements of the self-diffusion process, and of the corresponding profiles of the average velocity and of the streamwise component of the fluctuating velocity. The experimental facility consists of a vertical channel fed by an entrance hopper that is divided by a splitter plate. Using differently-coloured but otherwise identical glass spheres to visualize the diffusion process, the flow resembles a classic mixing-layer experiment. Unlike molecular motions, the local particle movements result from shearing of the flow; hence, the diffusion experiments were performed for different shear rates by changing the sidewall conditions of the test section, and by varying the flow rate and the channel width. In addition, experiments were also conducted using different sizes of glass beads to examine the scaling of the diffusion process. A simple analysis based on the diffusion equation shows that the thickness of the mixing layer increases with the square-root of downstream distance and depends on the magnitude of the velocity fluctuations relative to the mean velocity. The results are also consistent with other studies that suggest that the diffusion coefficient is proportional to the particle diameter and the square-root of the granular temperature.

Publication: Journal of Fluid Mechanics Vol.: 251ISSN: 0022-1120

ID: CaltechAUTHORS:20120309-095444229

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