Gravity-Driven Flows of Smooth, Inelastic Disks Between Parallel Bumpy Boundaries

1993 ◽  
Vol 60 (1) ◽  
pp. 59-64 ◽  
Author(s):  
M. Babic´
Keyword(s):  
Boundary Conditions ◽  
Granular Flow ◽  
Shooting Method ◽  
Particle Flux ◽  
Numerical Procedure ◽  
Present Theory ◽  
Gravity Driven ◽  
Temperature Shear ◽  
Air Table ◽  
Fluctuation Energy

The problem of a steady gravity-driven granular flow of identical, smooth, slightly inelastic, circular disks between parallel bumpy boundaries is analyzed. The balance laws, constitutive equations and boundary conditions obtained by the kinetic theory (Richman and Chou, 1988) are utilized. Both collisional and transport contributions to the fluxes of momentum and fluctuation energy are considered. The problem is reduced to a system of coupled differential equations governing the transverse variations of granular temperature, shear stress, and solid fraction with the appropriate boundary conditions. The numerical procedure is developed using a variation of shooting method in order to simultaneously satisfy all of the boundary conditions. The particle flux (discharge) calculated using the present theory compares favorably with the data from numerical simulations and air table experiments reported by Sanders et al. (1988).

scholarly journals Axisymmetric Natural Frequencies of Statically Loaded Annular Plates

2003 ◽  
Vol 10 (5-6) ◽  
pp. 301-312 ◽  
Author(s):  
Eihab M. Abdel-Rahman ◽  
Waleed F. Faris ◽  
Ali H. Nayfeh
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Shooting Method ◽  
Large Deformations ◽  
Natural Frequencies ◽  
Numerical Procedure ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Plate Model ◽  
Annular Plates

We present a numerical procedure to solve the axisymmetric vibration problem of statically loaded annular plates. We use the von Kármán nonlinear plate model to account for large deformations and study the effect of static deflections on the natural frequencies and mode shapes for six combinations of boundary conditions. The shooting method is used to solve the resulting eigenvalue problem. Our results show that static deformations have a significant effect on the natural frequencies and small effect on the mode shapes of the plate. Further, the results show that the presence of in-plane stresses has a significant effect on the natural frequencies.

Boundary Conditions for Rapid Granular Flow: Flat, Frictional Walls

1992 ◽  
Vol 59 (1) ◽  
pp. 120-127 ◽  
Author(s):  
J. T. Jenkins
Keyword(s):  
Distribution Function ◽  
Boundary Conditions ◽  
Granular Flow ◽  
Coulomb Friction ◽  
Slip Velocity ◽  
Unit Area ◽  
Velocity Distribution Function ◽  
Homogeneous Sphere ◽  
Fluctuation Energy ◽  
Tangential And Normal Restitution

We employ Coulomb friction and both tangential and normal restitution in a model for a collision between a homogeneous sphere and a flat wall. We calculate the impulse and change in kinetic energy in typical collisions and use a particularly simple velocity distribution function to obtain the rates at which momenta and energy are supplied to the flow over a unit area of the wall. From these, we determine boundary conditions that relate the shear stress and energy flux in the flow at the wall to the normal stress, slip velocity, and fluctuation energy and to the parameters that characterize a collision.

Comparison of Heat Transfer in Gravity-Driven Granular Flow near Different Surfaces

2020 ◽  
Author(s):  
Zhigang Guo ◽  
Xing Tian ◽  
Jian Yang ◽  
Tuo Shi ◽  
Qiuwang Wang
Keyword(s):  
Heat Transfer ◽  
Granular Flow ◽  
Gravity Driven

scholarly journals Kinetically constrained model for gravity-driven granular flow and clogging

2019 ◽  
Vol 100 (3) ◽  
Author(s):  
Gregory Bolshak ◽  
Rakesh Chatterjee ◽  
Rotem Lieberman ◽  
Yair Shokef
Keyword(s):  
Granular Flow ◽  
Gravity Driven ◽  
Constrained Model

Density waves in gravity-driven granular flow through a channel

2002 ◽  
Vol 14 (9) ◽  
pp. 3309-3326 ◽  
Author(s):  
Elizabeth D. Liss ◽  
Stephen L. Conway ◽  
Benjamin J. Glasser
Keyword(s):  
Granular Flow ◽  
Density Waves ◽  
Gravity Driven ◽  
Flow Through

Thermohydrodynamic Analysis of Compliant Flexure Pivot Tilting Pad Gas Bearings

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Kyuho Sim ◽  
Daejong Kim
Keyword(s):  
Boundary Conditions ◽  
Energy Equation ◽  
Numerical Procedure ◽  
Computational Method ◽  
Temperature Fields ◽  
Linear Perturbation ◽  
Gas Bearings ◽  
Thermal Boundary Conditions ◽  
Thermal Growth ◽  
Tilting Pad

A new thermohydrodynamic (THD) analysis for compliant flexure pivot tilting pad gas bearings is presented. Unlike many previous THD analyses on oil-lubricated bearings and gas bearings, the new THD analysis solves the rotor and bearing pad temperatures as well as the gas film temperature simultaneously upon adequate thermal boundary conditions on the bearing shell and rotor ends are given. All the previous studies assume that the rotor and bearing temperatures are given as thermal boundary conditions to solve 2D or 3D energy equation in the bearing film. The developed computational method is unique because these boundary conditions are found internally through global energy balance around the bearing. A numerical procedure involves solving the generalized Reynolds equation, 3D energy equation, and heat flux equations around the bearings simultaneously through iterative process. Furthermore, rotor thermal and centrifugal expansions are also considered during the iteration. Parametric studies were performed for the various temperature fields, i.e., rotor temperature, gas film temperature, and pad temperature as a function of nominal clearance, external load, and various thermal boundary conditions. Nominal clearance showed the most significant influence on overall THD behavior. The analyses also show that the rotor-bearing system can go to thermal runaway if adequate cooling mechanism does not exist. Linear perturbation analysis was also performed to investigate the thermal effects on the rotordynamic performance. Rotor thermal growth and increased viscosity increased direct stiffness and damping coefficients compared to the isothermal case.

scholarly journals An Efficient Numerical Procedure for Thermohydrodynamic Analysis of Cavitating Bearings

1996 ◽  
Vol 118 (3) ◽  
pp. 555-563 ◽  
Author(s):  
D. Vijayaraghavan
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Boundary Conditions ◽  
Radial Direction ◽  
Heat Dissipation ◽  
Numerical Procedure ◽  
Hydrodynamic Performance ◽  
Numerical Examples ◽  
Thermal Boundary Conditions ◽  
Theoretical Predictions

In this paper, an efficient and accurate numerical procedure to determine the thermo-hydrodynamic performance of cavitating bearings is described. This procedure is based on the earlier development of Elrod for lubricating films, in which the properties across the film thickness are determined at Lobatto points and their distributions are expressed by collocated polynomials. The cavitated regions and their boundaries are rigorously treated. Thermal boundary conditions at the surfaces, including heat dissipation through the metal to the ambient, are incorporated. Numerical examples are presented comparing the predictions using this procedure with earlier theoretical predictions and experimental data. With a few points across the film thickness and across the journal and the bearing in the radial direction, the temperature profile is very well predicted.

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