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Simple shear flows of dense gas-solid suspensions at finite Stokes numbers
106
ANNUAL LITERATURE SURVEY 1996
To understand the physics of air entrainment in thin-film liquid coating and other applications, the stability characteristics of general stratified two-layer Poiseuille-Couette flow are examined in inclined channels. The generalized eigenvalue problem, formed by spectral decomposition and solution oftbe general two-layer OrrSommerfeld equation, is solved to obtain all of the critical modes. Analysis of the air/liquid interface corresponding to experiments reveals that because of the large density variation between the two layers, the interfacial mode is the only mode of instability in air entrainment. (from Authors) Numerical simulations of uniformly stratified fluid flow over topography Rottman J.W., Broutman D. & Grimshaw R., Journal of Fluid Mechanics, 1996, 306/- (1-30). In English. We use a high-resolution spectral numerical scheme to solve the two-dimensional equations of motion for the flow of a uniformly stratified Boussinesq fluid over isolated bottom topography in achannel of finite depth. The focus is on topography of small to moderate amplitude and slope and for conditions such that the flow is near linear resonance of either of the first two internal wave modes. The results are compared with existing inviscid theories: the steady hydrostatic analysis of Long (1955), time-dependent linear long-wave theory, and the fully nonlinear, weakly dispersive resonant theory of Grimshaw & Yi (1991 ). Also, we present some new results on the modal similarity of the solutions of Long and Grimshaw & Yi. (from Authors) Simple shear flows of dense gas-solid suspensions at finite Stokes numbers Sangani A.S., Guobiao Mo, Heng-Kwong Tsao & Koch D.L., Journal of Fluid Mechanics, 1996, 313/- (309341). In English. We examine the problem of determining the particle-phase velocity variance and rheology of sbeared gas-solid suspensions at small Reynolds numbers and finite Stokes numbers. The simulation results are compared to the predictions of two theories. The two theories agree with each other at higher values of volume fraction phi of particles over a surprisingly large range of values of St. F o r smaller phi, however, the two theories deviate significantly except at sufficiently large St. A detailed comparison shows that the predictions of the approximate theory based on Grad's method are in excellent agreement with the results of numerical simulations. (from Authors) Stable and unstable monopolar vortices in a stratified fluid Flor J.B. & Van Heijst G.J.F., Journal of Fluid Mechanics, 1996, 311/- (257-287). In English. This paper presents experiments on planar monopolar vortex structures generated in a non-rotating, stratified fluid. Characteristics such as cross-sectional profiles (angular velocity and vorticity) and vorticity-stream function scatter plots have been measured experimentally by using digital image processing techniques. The characteristics of the monopolar vortices are compared with analytical vortex models known from literature. Simple models, based on vertical diffusion ofvorticity, are proposed to describe the monopolar vortex decay; they show reasonable agreement with the experimental results. From the multipolar structures, the tripolar vortex and a specific case of a triangular vortex, neither having been observed before in a stratified fluid, are studied in detail. A comparison with point-vortex models yields good agreement. (from Authors) The behaviour of a gas cavity impacted by a weak or strong shock wave Zhong Ding & Gracewski S.M., Journal of Fluid Mechanics, 1996, 309/- (183-209). In English. Two -dimensio hal simulations of gas cavity responses to both weak shocks (p = or 30 MPa) and strong shocks ranging from 500 to 2000 MPa) are performed using a finite volume method. An artificial viscosity to capture the shock and a simple, stable, and adaptive mesh generation technique have been developed for the computations. The details of the shock propagation, rarefaction, transmission and bubble wall motions are obtained from the numerical computations. The bubble collapse and re-expansion time predicted by this model agree with spherically symmetric computations. When impacted by strong shock waves, the bubble will collapse and a liqud jet is formed that propagates through the bubble to the opposite bubble wall. (from Authors) The initial response of a stratified lake to the surface shear stress Stevens C. & Imberger J., Journal of Fluid Mechanics, 1996, 312/- (39-66). In English. Laboratory experiments are used to study the initial response of a stratified fluid to the action of a wind stress. The experiments are described in the context of a parameterization scheme that quantified the strength of the applied stress relative to the bulk stability of the fluid an also the duration of the wind stress relative to the periods of the waves generated by the stress. This study concentrates on the first fundamental internal wave period in experiments where the fluid is considered to have upwelled, i.e. the stratified region ofthe fluid reaches the surface at the upwind endwall. A linear model using normal modes proved successful prior to the commencement o f upwelling and this enabled an estimate to be made ofthe time at which upwelling occurred. (from Authors)
Axisymmetrie pressure-driven flow of rigid pellets through a cylindrical tube lined with a deformable porous wall layer Damiano E.R., Duling B.R., Ley K. & Skalak T.C., Journal of Fluid Mechanics, 1996, 314/- (163-189). In English. A closed-form analytic solution for the motion ofaxisymmetric rigid pellets suspended in a Newtonian fluid and driven under a pressure gradient through a rigid impermeable cylindrical tube lined with a porous deformable biphasic wall layer is derived using mixture and lubrication theories. The analysis details the velocity distributions in the lubrication and wall layers as well as the solid-phase displacement field in the wall layer. Expressions for the shear stress and pressure gradient are obtained throughout the lubrication and wall layers. Results are presented in terms of resistance, volume flow, and driving pressure relative to smooth-walled tubes for cases both with and without rigid spheres flowing in the free lumen. (from Authors)
ANNUAL LITERATURE SURVEY 1996
To understand the physics of air entrainment in thin-film liquid coating and other applications, the stability characteristics of general stratified two-layer Poiseuille-Couette flow are examined in inclined channels. The generalized eigenvalue problem, formed by spectral decomposition and solution oftbe general two-layer OrrSommerfeld equation, is solved to obtain all of the critical modes. Analysis of the air/liquid interface corresponding to experiments reveals that because of the large density variation between the two layers, the interfacial mode is the only mode of instability in air entrainment. (from Authors) Numerical simulations of uniformly stratified fluid flow over topography Rottman J.W., Broutman D. & Grimshaw R., Journal of Fluid Mechanics, 1996, 306/- (1-30). In English. We use a high-resolution spectral numerical scheme to solve the two-dimensional equations of motion for the flow of a uniformly stratified Boussinesq fluid over isolated bottom topography in achannel of finite depth. The focus is on topography of small to moderate amplitude and slope and for conditions such that the flow is near linear resonance of either of the first two internal wave modes. The results are compared with existing inviscid theories: the steady hydrostatic analysis of Long (1955), time-dependent linear long-wave theory, and the fully nonlinear, weakly dispersive resonant theory of Grimshaw & Yi (1991 ). Also, we present some new results on the modal similarity of the solutions of Long and Grimshaw & Yi. (from Authors) Simple shear flows of dense gas-solid suspensions at finite Stokes numbers Sangani A.S., Guobiao Mo, Heng-Kwong Tsao & Koch D.L., Journal of Fluid Mechanics, 1996, 313/- (309341). In English. We examine the problem of determining the particle-phase velocity variance and rheology of sbeared gas-solid suspensions at small Reynolds numbers and finite Stokes numbers. The simulation results are compared to the predictions of two theories. The two theories agree with each other at higher values of volume fraction phi of particles over a surprisingly large range of values of St. F o r smaller phi, however, the two theories deviate significantly except at sufficiently large St. A detailed comparison shows that the predictions of the approximate theory based on Grad's method are in excellent agreement with the results of numerical simulations. (from Authors) Stable and unstable monopolar vortices in a stratified fluid Flor J.B. & Van Heijst G.J.F., Journal of Fluid Mechanics, 1996, 311/- (257-287). In English. This paper presents experiments on planar monopolar vortex structures generated in a non-rotating, stratified fluid. Characteristics such as cross-sectional profiles (angular velocity and vorticity) and vorticity-stream function scatter plots have been measured experimentally by using digital image processing techniques. The characteristics of the monopolar vortices are compared with analytical vortex models known from literature. Simple models, based on vertical diffusion ofvorticity, are proposed to describe the monopolar vortex decay; they show reasonable agreement with the experimental results. From the multipolar structures, the tripolar vortex and a specific case of a triangular vortex, neither having been observed before in a stratified fluid, are studied in detail. A comparison with point-vortex models yields good agreement. (from Authors) The behaviour of a gas cavity impacted by a weak or strong shock wave Zhong Ding & Gracewski S.M., Journal of Fluid Mechanics, 1996, 309/- (183-209). In English. Two -dimensio hal simulations of gas cavity responses to both weak shocks (p = or 30 MPa) and strong shocks ranging from 500 to 2000 MPa) are performed using a finite volume method. An artificial viscosity to capture the shock and a simple, stable, and adaptive mesh generation technique have been developed for the computations. The details of the shock propagation, rarefaction, transmission and bubble wall motions are obtained from the numerical computations. The bubble collapse and re-expansion time predicted by this model agree with spherically symmetric computations. When impacted by strong shock waves, the bubble will collapse and a liqud jet is formed that propagates through the bubble to the opposite bubble wall. (from Authors) The initial response of a stratified lake to the surface shear stress Stevens C. & Imberger J., Journal of Fluid Mechanics, 1996, 312/- (39-66). In English. Laboratory experiments are used to study the initial response of a stratified fluid to the action of a wind stress. The experiments are described in the context of a parameterization scheme that quantified the strength of the applied stress relative to the bulk stability of the fluid an also the duration of the wind stress relative to the periods of the waves generated by the stress. This study concentrates on the first fundamental internal wave period in experiments where the fluid is considered to have upwelled, i.e. the stratified region ofthe fluid reaches the surface at the upwind endwall. A linear model using normal modes proved successful prior to the commencement o f upwelling and this enabled an estimate to be made ofthe time at which upwelling occurred. (from Authors)
Axisymmetrie pressure-driven flow of rigid pellets through a cylindrical tube lined with a deformable porous wall layer Damiano E.R., Duling B.R., Ley K. & Skalak T.C., Journal of Fluid Mechanics, 1996, 314/- (163-189). In English. A closed-form analytic solution for the motion ofaxisymmetric rigid pellets suspended in a Newtonian fluid and driven under a pressure gradient through a rigid impermeable cylindrical tube lined with a porous deformable biphasic wall layer is derived using mixture and lubrication theories. The analysis details the velocity distributions in the lubrication and wall layers as well as the solid-phase displacement field in the wall layer. Expressions for the shear stress and pressure gradient are obtained throughout the lubrication and wall layers. Results are presented in terms of resistance, volume flow, and driving pressure relative to smooth-walled tubes for cases both with and without rigid spheres flowing in the free lumen. (from Authors)