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.

Effects of the Divergence Angle on the Onset of Asymmetric Flow Through a Planar Diffuser

2009 ◽  
Author(s):  
Majid Nabavi ◽  
Luc Mongeau
Keyword(s):  
Reynolds Number ◽  
Flow Regime ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Asymmetric Flow ◽  
Symmetric Flow ◽  
Turbulent Flow Regime ◽  
Flow Through ◽  
Gradual Expansion

In this study, two-dimensional laminar incompressible and turbulent compressible flow through the planar diffuser (gradual expansion) for different divergence half angles of the diffuser (θ), and different Reynolds numbers (Re) was numerically studied. The effects of θ on the critical Reynolds number at which the onset of asymmetric flow is observed, were investigated. In the laminar flow regime, it was observed that for every values of θ, there is a critical Re beyond which the flow is asymmetric. However, in the turbulent flow regime, for θ ≥ 20°, even at low Reynolds number the flow is asymmetric. Only for θ ≤ 10°, symmetric flow was observed below a critical Re.

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.

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.

On the Disturbance of a Thin Layer of Liquid by a Moving Obstruction

1990 ◽  
Vol 57 (4) ◽  
pp. 1066-1072
Author(s):  
Roger F. Gans ◽  
Chung-Hai Wang
Keyword(s):  
Surface Tension ◽  
Reynolds Number ◽  
Free Surface ◽  
Thin Layer ◽  
Viscous Flow ◽  
Length Scale ◽  
Two Dimensional ◽  
Thin Liquid Layer ◽  
Horizontal Length ◽  
Small Ratio

We calculate the free surface shapes upstream and downstream of an obstacle obstructing a thin liquid layer on a moving surface, taking into account gravity and surface tension. We assume low Reynolds number viscous flow, a two-dimensional layer, and small ratio of vertical to horizontal length scale. The upstream and downstream shapes are very different. The upstream liquid piles up against the obstacle to provide an overpressure sufficient to drive the Poiseuille component of the lubrication flow under the obstacle. The downstream liquid is disturbed only by surface tension.

Moderate Reynolds number flows through periodic and random arrays of aligned cylinders

1997 ◽  
Vol 349 ◽  
pp. 31-66 ◽  
Author(s):  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Volume Fraction ◽  
Unit Length ◽  
Reynolds Numbers ◽  
Moderate Reynolds Number ◽  
Random Arrays ◽  
Flow Through ◽  
The Mean ◽  
Square Array

The effects of fluid inertia on the pressure drop required to drive fluid flow through periodic and random arrays of aligned cylinders is investigated. Numerical simulations using a lattice-Boltzmann formulation are performed for Reynolds numbers up to about 180.The magnitude of the drag per unit length on cylinders in a square array at moderate Reynolds number is strongly dependent on the orientation of the drag (or pressure gradient) with respect to the axes of the array; this contrasts with Stokes flow through a square array, which is characterized by an isotropic permeability. Transitions to time-oscillatory and chaotically varying flows are observed at critical Reynolds numbers that depend on the orientation of the pressure gradient and the volume fraction.In the limit Re[Lt ]1, the mean drag per unit length, F, in both periodic and random arrays, is given by F/(μU) =k1+k2Re2, where μ is the fluid viscosity, U is the mean velocity in the bed, and k1 and k2 are functions of the solid volume fraction ϕ. Theoretical analyses based on point-particle and lubrication approximations are used to determine these coefficients in the limits of small and large concentration, respectively.In random arrays, the drag makes a transition from a quadratic to a linear Re-dependence at Reynolds numbers of between 2 and 5. Thus, the empirical Ergun formula, F/(μU) =c1+c2Re, is applicable for Re>5. We determine the constants c1 and c2 over a wide range of ϕ. The relative importance of inertia becomes smaller as the volume fraction approaches close packing, because the largest contribution to the dissipation in this limit comes from the viscous lubrication flow in the small gaps between the cylinders.

A Note on the Reattachment of Two-Dimensional Compressible Jets to Planes

1967 ◽  
Vol 71 (681) ◽  
pp. 655-657 ◽  
Author(s):  
R. D. Begg
Keyword(s):  
Reynolds Number ◽  
Fluid Velocity ◽  
Experimental Tests ◽  
Two Dimensional ◽  
Inclined Plane ◽  
Air Jets ◽  
Bubble Length ◽  
Flow Through ◽  
Basic Characteristics ◽  
And Control

The rapid growth of interest in fluid logic and control elements has refocused attention on the reattachment of two-dimensional jets to plane surfaces. Of particular interest is the size of the low-pressure bubble enclosed between the jet and the adjacent inclined plane, and the effect on this of fluid velocity and compressibility. Several full studies have been made of such flows, notably by Bourque and Newman, Sawyer and Olson, and the basic characteristics have been well established. Agreement has been reached that bubble length is independent of jet Reynolds number (above 104), but doubts remain as to the best method of measuring the bubble length and also as to the effect of compressibility on this measurement. In order to clear up some of these points for an investigation of compressible flow through control valves, some experimental tests have been carried out on the reattachment of air jets to a plane.

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