Flow Through a Deformable Porous Material

1975 ◽  
Vol 42 (3) ◽  
pp. 598-602 ◽  
Author(s):  
G. S. Beavers ◽  
T. A. Wilson ◽  
B. A. Masha
Keyword(s):  
Porous Material ◽  
Incompressible Fluid ◽  
Applied Pressure ◽  
Local Stress ◽  
Darcy Law ◽  
Stress Dependence ◽  
One Dimensional ◽  
Flow Through ◽  
Incompressible Media ◽  
The One

A model is presented to describe the one-dimensional flow of an incompressible fluid through a deformable porous material. The model is based on the Forchheimer extension of the Darcy law for flows through incompressible media, where the Forchheimer coefficients are functions of the local stress. Experiments to determine the stress-dependence of the coefficients for polyurethane foam specimens are described. The coefficients are then used in the model to predict the mass flow rate through long polyurethane specimens as a function of the applied pressure difference across the material. The predictions of the model are compared with experimental observations.

Fluid Flow Through Microscale Fractal-Like Branching Channel Networks

2003 ◽  
Author(s):  
Ali Y. Alharbi ◽  
Deborah V. Pence ◽  
Rebecca N. Cullion
Keyword(s):  
Three Dimensional ◽  
Dimensional Model ◽  
Flow Networks ◽  
Channel Networks ◽  
One Dimensional ◽  
Fluid Properties ◽  
Flow Through ◽  
Minor Losses ◽  
Branching Flow ◽  
The One

Flow through fractal-like branching flow networks is investigated using a three-dimensional computational fluid dynamics approach. Results are used to assess the validity of, and provide insight for improving, assumptions imposed in a one-dimensional model previously developed. Assumptions in the one-dimensional model include (1) reinitiating boundary layers following each bifurcation, (2) negligible minor losses at the bifurcations, and (3) constant thermophysical fluid properties. It is concluded that the temperature dependence of fluid properties, boundary layer development, and minor losses following a bifurcation are not negligible in analyses of branching flow networks.

Gravity-induced wrinkle lines in vertical membranes

1981 ◽  
Vol 375 (1762) ◽  
pp. 307-325 ◽  
Keyword(s):  
Heat Flow ◽  
Diffusion Equation ◽  
Vertical Plane ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Prime Objective ◽  
Flow Through ◽  
Flexible Membranes ◽  
The One

A theory is presented for the behaviour under self-weight of inextensible but perfectly flexible membranes supported in a vertical plane. Slack in the membrane manifests itself in the formation of (curved) wrinkle lines whose determination is the prime objective. The equilibrium and strain conditions are derived and solutions are given for several simple cases. It is shown that the wrinkle lines satisfy the one-dimensional diffusion equation and hence there are analogies, for example, with heat flow through a slab.

A Numerical Model for the Radial Flow Through Porous and Deformable Shells

2004 ◽  
Vol 4 (1) ◽  
pp. 34-47 ◽  
Author(s):  
Francisco J. Gaspar ◽  
Francisco J. Lisbona ◽  
Petr N. Vabishchevich
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Energy Estimates ◽  
One Dimensional ◽  
Consolidation Model ◽  
Finite Difference Discretization ◽  
Flow Through ◽  
The One ◽  
Theoretical Results ◽  
Difference Discretization

AbstractEnergy estimates and convergence analysis of finite difference methods for Biot's consolidation model are presented for several types of radial ow. The model is written by a system of partial differential equations which depend on an integer parameter (n = 0; 1; 2) corresponding to the one-dimensional ow through a deformable slab and the radial ow through an elastic cylindrical or spherical shell respectively. The finite difference discretization is performed on staggered grids using separated points for the approximation of pressure and displacements. Numerical results are given to illustrate the obtained theoretical results.

scholarly journals Radial Imbibition in Paper under Temperature Differences

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 86
Author(s):  
Abel López-Villa ◽  
Abraham Medina ◽  
F. J. Higuera ◽  
Jonatan R. Mac Intyre ◽  
Carlos Alberto Perazzo ◽  
...  
Keyword(s):  
Experimental Data ◽  
Surface Tension ◽  
Porous Material ◽  
Radial Temperature ◽  
Temperature Variations ◽  
One Dimensional ◽  
Blotting Paper ◽  
Dimensional Equation ◽  
The One ◽  
Account Temperature

Spontaneous radial imbibition into thin circular samples of porous material when they have been subjected to radial temperature differences was analyzed theoretically and experimentally. The use of the Darcy equation allowed us to take into account temperature variations in the dynamic viscosity and surface tension in order to find the one-dimensional equation for the imbibition fronts. Experiments using blotting paper showed a good fit between the experimental data and theoretical profiles through the estimation of a single parameter.

Steady Flow in Porous, Elastically Deformable Materials

1987 ◽  
Vol 54 (4) ◽  
pp. 794-800 ◽  
Author(s):  
K. H. Parker ◽  
R. V. Mehta ◽  
C. G. Caro
Keyword(s):  
Fluid Flow ◽  
Theoretical Model ◽  
Porous Material ◽  
Applied Pressure ◽  
Local Strain ◽  
Governing Equations ◽  
Good Qualitative Agreement ◽  
One Dimensional ◽  
The Matrix ◽  
Deformable Materials

The steady, one-dimensional flow of an incompressible fluid through a deformable porous material is studied theoretically and experimentally. The theoretical model is essentially that of Biot. Assuming that the stiffness and permeability of the matrix are functions of the local strain gradient, the governing equations can be solved and analytical solutions are presented for several simple constitutive relationships. The stiffness and permeability properties of one particular foam are measured and then used to predict the rate of fluid flow and the distortion of the matrix as a function of the applied pressure difference across the material. Comparison of the predictions of the model with experimental observations indicates good qualitative agreement.

Study of the Discharge Pressure Pulsation Within Twin Screw Compressors

2001 ◽  
Author(s):  
Ziwen Xing ◽  
Xueyuan Peng ◽  
Xiaojun Zhang ◽  
Tiansheng Cui
Keyword(s):  
Gas Flow ◽  
Pressure Pulsation ◽  
Theoretic Analysis ◽  
One Dimensional ◽  
Flow Equations ◽  
Twin Screw ◽  
Flow Through ◽  
The One ◽  
Discharge Pressure ◽  
Unsteady Gas Flow

Abstract Even in the absence of valves, flow through the discharge port of a screw compressor is oscillatory in nature. This unsteady but periodic flow variation at the discharge port excites the pressure pulsation. In this paper, the one-dimensional unsteady gas flow equations describing the discharge pressure pulsation are established, which allow for the effects of the viscosity friction and heat transfer between the gas and the pipe, and the boundary conditions of discharge pressure pulsation are considered. With Two-Step Lax-Wendroff scheme used, the one-dimensional unsteady gas flow equations are solved. In order to verify the theoretic analysis, the discharge pressure pulsation at variable working conditions is measured. It is shown that the model established in this paper is valid for getting a better understanding of the mechanism governing the behavior of the pressure pulsation in discharge pipe. It is found that the most important factor that affects the discharge pressure pulsation is the pressure difference between the actual discharge pressure and the design discharge pressure.

scholarly journals One-Dimensional Bubbly Cavitating Flows Through a Converging-Diverging Nozzle

1998 ◽  
Vol 120 (1) ◽  
pp. 166-170 ◽  
Author(s):  
Yi-Chun Wang ◽  
C. E. Brennen
Keyword(s):  
Cavitating Flows ◽  
One Dimensional ◽  
Cavitation Bubbles ◽  
Spatial Fluctuations ◽  
Bubble Interaction ◽  
Flow Through ◽  
Flow Transitions ◽  
The One ◽  
Physical Reasons ◽  
Critical Bubble

A nonbarotropic continuum bubbly mixture model is used to study the one-dimensional cavitating flow through a converging-diverging nozzle. The nonlinear dynamics of the cavitation bubbles are modeled by the Rayleigh-Plesset equation. Analytical results show that the bubble/bubble interaction through the hydrodynamics of the surrounding liquid has important effects on this confined flow field. One clear interaction effect is the Bernoulli effect caused by the growing and collapsing bubbles in the nozzle. It is found that the characteristics of the flow change dramatically even when the upstream void fraction is very small. Two different flow regimes are found from the steady state solutions and are termed: quasi-steady and quasi-unsteady. The former is characterized by large spatial fluctuations downstream of the throat which are induced by the pulsations of the cavitation bubbles. The quasi-unsteady solutions correspond to flashing flow. Bifurcation occurs as the flow transitions from one regime to the other. An analytical expression for the critical bubble size at the bifurcation is obtained. Physical reasons for this quasi-static instability are also discussed.

Fluid Flow Through Microscale Fractal-Like Branching Channel Networks

2003 ◽  
Vol 125 (6) ◽  
pp. 1051-1057 ◽  
Author(s):  
Ali Y. Alharbi ◽  
Deborah V. Pence ◽  
Rebecca N. Cullion
Keyword(s):  
Boundary Layers ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Dimensional Model ◽  
Local Pressure ◽  
Flow Area ◽  
One Dimensional ◽  
Fluid Properties ◽  
Flow Through ◽  
The One

Flow through fractal-like branching networks is investigated using a three-dimensional computational fluid dynamics approach. Results are used to assess the validity of, and provide insight for improving, assumptions imposed in a previously developed one-dimensional model. Assumptions in the one-dimensional model include (1) reinitiating boundary layers following each bifurcation, (2) constant thermophysical fluid properties, and (3) negligible minor losses at the bifurcations. No changes to the redevelopment of hydrodynamic boundary layers following a bifurcation are recommended. It is concluded that temperature varying fluid properties should be incorporated in the one-dimensional model to improve its predictive capabilities, especially at higher imposed heat fluxes. Finally, a local pressure recovery at each bifurcation results from an increase in flow area. Ultimately, this results in a lower total pressure drop and should be incorporated in the one-dimensional model.

Sonic Flow Through an Abrupt Change in Cross-Section

1984 ◽  
Vol 198 (3) ◽  
pp. 197-203 ◽  
Author(s):  
J S Anderson ◽  
G E A Meier
Keyword(s):  
Shock Wave ◽  
Abrupt Change ◽  
Wave Structure ◽  
Normal Shock ◽  
Laser Doppler Velocimeter ◽  
Normal Shock Wave ◽  
One Dimensional ◽  
Sonic Flow ◽  
Flow Through ◽  
The One

The steady, transonic flow in a rectangular duct following an abrupt change in section has been studied by measuring the density with a Mach-Zehnder interferometer and velocity with a laser-Doppler velocimeter. The flow structure was controlled either by a single, normal shock wave or by a series of reflected oblique shocks. In the case of the normal shock wave structure the one-dimensional compressible flow theory was found to apply adequately to the overall duct. Within the duct the flow was not one-dimensional, but had a minimum velocity in the centre and four shear layers.

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