An Asymptotic Model of Viscous Flow Limitation in a Highly Collapsed Channel

1998 ◽  
Vol 120 (4) ◽  
pp. 544-546 ◽  
Author(s):  
O. E. Jensen
Keyword(s):  
Pressure Drop ◽  
Viscous Flow ◽  
External Pressure ◽  
Asymptotic Model ◽  
Flow Limitation ◽  
Two Dimensional ◽  
Inertial Effects ◽  
Channel One ◽  
Narrow Region ◽  
Flow Through

A viscous flow through a long two-dimensional channel, one wall of which is formed by a finite-length membrane, experiences flow limitation when the channel is highly collapsed over a narrow region under high external pressure. Simple approximate relations between flow rate and pressure drop are obtained for this configuration by the use of matched asymptotic expansions. Weak inertial effects are also considered.

An Empirical Equation for Flow Through Porous Media

2005 ◽  
Author(s):  
C. A. Ortega Vivas ◽  
S. Barraga´n Gonza´lez ◽  
J. M. Garibay Cisneros
Keyword(s):  
Reynolds Number ◽  
Porous Medium ◽  
Pressure Drop ◽  
Empirical Equation ◽  
Experimental Methods ◽  
Two Dimensional ◽  
Inertial Effects ◽  
Flow Through Porous Media ◽  
Flow Through ◽  
Porous Medium Model

This study analyses the macroscopic flow through a two dimensional porous medium model by numerical and experimental methods. The objective of this research is to develop an empirical model by which the pressure drop can be obtained. In order to construct the model, a series of blocks are used as an idealized pressure drop device, so that the pressure drop can be calculated. The range of porosities studied is between 28 and 75 per cent. It is found that the pressure drop is a combination of viscosity and inertial effects, the later being more important as the Reynolds number is increased. The empirical equation obtained in this investigation is compared with the Ergun equation.

Viscous flow through a grating or lattice of cylinders

1964 ◽  
Vol 18 (1) ◽  
pp. 94-96 ◽  
Author(s):  
Joseph B. Keller
Keyword(s):  
Pressure Drop ◽  
Viscous Flow ◽  
Lubrication Theory ◽  
Cross Sectional ◽  
Flow Through ◽  
Square Array

Viscous flow perpendicular to a line (or ‘grating’) of evenly spaced identical cylinders is considered in the case when the spacing between the cylinders is much smaller than their cross-sectional dimensions. Lubrication theory is used to find the pressure drop across the grating and hence the force on each cylinder. A square array (or ‘lattice’) of closely packed cylinders is similarly treated.

Pressure drop due to viscous flow through cylinders

1959 ◽  
Vol 6 (4) ◽  
pp. 542-546 ◽  
Author(s):  
Howard Brenner
Keyword(s):  
Pressure Drop ◽  
Circular Cylinder ◽  
Viscous Fluid ◽  
Viscous Flow ◽  
Steady Flow ◽  
Equations Of Motion ◽  
Point Force ◽  
Flow Through ◽  
Bounding Surfaces ◽  
Simple Fashion

A general formula is developed which permits a calculation of the pressure drop arising from the slow steady flow of a viscous fluid through a circular cylinder for arbitrarily assigned conditions of velocity on the bounding surfaces of the cylinder. In particular, the diminution in pressure can be calculated directly from the prescribed boundary velocities without requiring a detailed solution of the equations of motion. Hence it is possible to compute, in comparatively simple fashion, the magnitude of this macroscopic parameter for a large variety of complex motions which would normally present great analytical difficulties.By way of illustration the additional pressure drop arising from the presence of a point force situated along the axis of a cylinder is calculated. The additional force required to maintain the motion in the presence of the obstacle is exactly twice the magnitude of the point force itself.

Numerical modelling of nonlinear effects in laminar flow through a porous medium

1988 ◽  
Vol 190 ◽  
pp. 393-407 ◽  
Author(s):  
O. Coulaud ◽  
P. Morel ◽  
J. P. Caltagirone
Keyword(s):  
Porous Medium ◽  
Pressure Drop ◽  
Nonlinear Term ◽  
Numerical Solutions ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Quadratic Term ◽  
Inertial Effects ◽  
Operator Splitting Methods ◽  
Flow Through

This paper deals with the introduction of a nonlinear term into Darcy's equation to describe inertial effects in a porous medium. The method chosen is the numerical resolution of flow equations at a pore scale. The medium is modelled by cylinders of either equal or unequal diameters arranged in a regular pattern with a square or triangular base. For a given flow through this medium the pressure drop is evaluated numerically.The Navier-Stokes equations are discretized by the mixed finite-element method. The numerical solution is based on operator-splitting methods whose purpose is to separate the difficulties due to the nonlinear operator in the equation of motion and the necessity of taking into account the continuity equation. The associated Stokes problems are solved by a mixed formulation proposed by Glowinski & Pironneau.For Reynolds numbers lower than 1, the relationship between the global pressure gradient and the filtration velocity is linear as predicted by Darcy's law. For higher values of the Reynolds number the pressure drop is influenced by inertial effects which can be interpreted by the addition of a quadratic term in Darcy's law.On the one hand this study confirms the presence of a nonlinear term in the motion equation as experimentally predicted by several authors, and on the other hand analyses the fluid behaviour in simple media. In addition to the detailed numerical solutions, an estimation of the hydrodynamical constants in the Forchheimer equation is given in terms of porosity and the geometrical characteristics of the models studied.

Oscillatory flow through constricted or dilated channels and axisymmetric pipes

1978 ◽  
Vol 363 (1714) ◽  
pp. 335-355 ◽  
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Viscous Flow ◽  
Oscillatory Flow ◽  
Equation Of Motion ◽  
Two Dimensional ◽  
Small Perturbations ◽  
Flow Through ◽  
Parallel Case ◽  
General Method

Two types of oscillatory viscous flow are considered: the first inside a two-dimensional channel, the second inside an axisymmetric pipe. The walls of the channel or pipe are taken to be small perturbations of the straight and parallel case, these distortions being much smaller than the width of the channel or pipe, so that the equation of motion may be linearized to give an Orr–Sommerfield type of equation. It is assumed that the width of the channel or pipe is comparable with the Stokes layer thickness. For sinusoidal perturbations of the wall, the asymptotic solutions for the parameter (Reynolds number times wavenumber) being very small or very large are considered. The general method may also be applied numerically to obtain solutions for non-periodic dilations or constrictions at arbitrary Reynolds number, and as an illustration the distributions of shear and pressure gradient are given for a number of examples.

A Study of the Effects of a Transversely Moving Boundary on Plane Posieuille Flow

1982 ◽  
Vol 104 (4) ◽  
pp. 314-323 ◽  
Author(s):  
J. M. Robertson ◽  
M. E. Clark ◽  
L. C. Cheng
Keyword(s):  
Shear Stress ◽  
Pressure Drop ◽  
Finite Difference ◽  
Viscous Flow ◽  
Stream Function ◽  
Moving Boundary ◽  
Maximum Shear Stress ◽  
Plane Channel ◽  
Flow Through ◽  
Oscillatory Period

Numerical (finite-difference) solutions in vorticity-stream function variables using a nonorthogonal geometric transform are found for viscous flow through a plane channel in which a portion of the boundary oscillates to change the flow. Calculations were made for three rates of inflow and for three frequencies of oscillation. The boundary pumpage relative to inflow decreased with inflow Karman number and with the oscillatory period of the boundary. The maximum shear stress, as indicated by the maximum vorticity, increased with Karman number and occurred when the boundary was in the maximum stenotic position. It did not change with boundary period except for the case when the period was the smallest. The channel pressure drop was significantly affected by the pumpage as well as the boundary nonuniformity.

ESTIMATION OF PRESSURE DROP FOR NON-NEWTONIAN LIQUID FLOW THROUGH BENDS USING ADAPTIVE NON-PARAMETRIC MODEL

2020 ◽  
Vol 47 (1) ◽  
pp. 59-69
Author(s):  
Suman Debnath ◽  
Anirban Banik ◽  
Tarun Kanti Bandyopadhyay ◽  
Mrinmoy Majumder ◽  
Apu Kumar Saha
Keyword(s):  
Pressure Drop ◽  
Liquid Flow ◽  
Parametric Model ◽  
Newtonian Liquid ◽  
Flow Through ◽  
Non Parametric
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