Pressure-driven flow in a channel with porous walls

2011 ◽  
Vol 679 ◽  
pp. 77-100 ◽  
Author(s):  
QIANLONG LIU ◽  
ANDREA PROSPERETTI
Keyword(s):  
Reynolds Number ◽  
Porous Medium ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Three Dimensional Flow ◽  
Porous Layers ◽  
Simple Cubic ◽  
Porous Walls ◽  
Pressure Driven Flow ◽  
Pressure Driven

The finite-Reynolds-number three-dimensional flow in a channel bounded by one and two parallel porous walls is studied numerically. The porous medium is modelled by spheres in a simple cubic arrangement. Detailed results on the flow structure and the hydrodynamic forces and couple acting on the sphere layer bounding the porous medium are reported and their dependence on the Reynolds number illustrated. It is shown that, at finite Reynolds numbers, a lift force acts on the spheres, which may be expected to contribute to the mobilization of bottom sediments. The results for the slip velocity at the surface of the porous layers are compared with the phenomenological Beavers–Joseph model. It is found that the values of the slip coefficient for pressure-driven and shear-driven flow are somewhat different, and also depend on the Reynolds number. A modification of the relation is suggested to deal with these features. The Appendix provides an alternative derivation of this modified relation.

Pressure-driven flow in a two-dimensional channel with porous walls

2009 ◽  
Vol 631 ◽  
pp. 1-21 ◽  
Author(s):  
QUAN ZHANG ◽  
ANDREA PROSPERETTI
Keyword(s):  
Reynolds Number ◽  
Porous Medium ◽  
Hydrodynamic Force ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Slip Coefficient ◽  
Staggered Arrangement ◽  
Two Dimensional Flow ◽  
Porous Walls ◽  
Pressure Driven Flow

The finite-Reynolds-number two-dimensional flow in a channel bounded by a porous medium is studied numerically. The medium is modelled by aligned cylinders in a square or staggered arrangement. Detailed results on the flow structure and slip coefficient are reported. The hydrodynamic force and couple acting on the cylinder layer bounding the porous medium are also evaluated as a function of the Reynolds number. In particular, it is shown that, at finite Reynolds numbers, a lift force acts on the bodies, which may be significant for the mobilization of bottom sediments.

Reynolds Number Effects on the Performance Characteristic of a Small Regenerative Pump

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Shin-Hyoung Kang ◽  
Su-Hyun Ryu
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Internal Flow ◽  
Reynolds Numbers ◽  
Maximum Efficiency ◽  
Three Dimensional Flow ◽  
One Dimensional ◽  
Rotating Speed ◽  
Dimensional Modeling ◽  
Reynolds Number Effects

This paper studies the effect of the Reynolds number on the performance characteristics of a small regenerative pump. Since regenerative pumps have low specific speeds, they are usually applicable to small devices such as micropumps. As the operating Reynolds number decreases, nondimensional similarity parameters such as flow and head coefficients and efficiency become dependent on the Reynolds number. In this study, the Reynolds number based on the impeller diameter and rotating speed varied between 5.52×103 and 1.33×106. Complex three-dimensional flow structures of internal flow vary with the Reynolds numbers. The coefficients of the loss models are obtained by using the calculated through flows in the impeller. The estimated performances obtained by using one-dimensional modeling agreed reasonably well with the numerically calculated performances. The maximum values of flow and head coefficients depended on the Reynolds number when it is smaller than 2.65×105. The critical value of the Reynolds number for loss coefficient and maximum efficiency variations with Reynolds number was 1.0×105.

Three-dimensional flow over two spheres placed side by side

1993 ◽  
Vol 246 ◽  
pp. 465-488 ◽  
Author(s):  
Inchul Kim ◽  
Said Elghobashi ◽  
William A. Sirignano
Keyword(s):  
Reynolds Number ◽  
Vortical Structure ◽  
Three Dimensional ◽  
Numerical Data ◽  
Reynolds Numbers ◽  
Near Wake ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Confined Flow ◽  
Small Spacing

Three-dimensional flow over two identical (solid or liquid) spheres which are held fixed relative to each other with the line connecting their centres normal to a uniform I stream is investigated numerically at Reynolds numbers 50, 100, and 150. We consider the lift, moment, and drag coefficients on the spheres and investigate their dependence on the distance between the two spheres. The computations show that, for a given Reynolds number, the two spheres are repelled when the spacing is of the order of the diameter but are weakly attracted at intermediate separation distances. For small spacing, the vortical structure of the near wake is significantly different from that of the axisymmetric wake that establishes at large separations. The partially confined flow passing between the two spheres entrains the flows coming around their other sides. Our results agree with available experimental and numerical data.

Onset of Transition in the Flow Over a Three-Dimensional Array of Rectangular Obstacles

1992 ◽  
Vol 114 (2) ◽  
pp. 251-255 ◽  
Author(s):  
S. V. Garimella ◽  
P. A. Eibeck
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Water Channel ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Channel Height ◽  
Circuit Boards ◽  
Three Dimensional Flow ◽  
Transfer Data ◽  
Array Geometry

Onset of transition is investigated in the flow over an array of protruding elements mounted on the bottom wall of a rectangular water channel simulating flow passages between adjacent circuit boards in computers. The element dimensions are held constant while the channel height and the element spacing are varied. Flow visualization and turbulence measurements are used to determine transition Reynolds numbers, which compare well with previous results obtained from heat transfer data. The complicated, three-dimensional flow field causes transition to be a function not only of flow rate and array geometry but also of location in the array. Transition occurs in the fully developed region of the array at a channel height-based Reynolds number of 700 for a channel height of 1.2 element heights, increasing to 1900 for a channel height of 3.6 element heights. However, when Reynolds number is defined based on element height, transition occurs at the same Reynolds number of 550 for all channel heights. Increasing the stream wise spacing between elements causes transition to occur at lower Reynolds numbers.

scholarly journals The Effect of the Reynolds Number on the Three-Dimensional Flow in a Straight Compressor Cascade

1988 ◽  
Author(s):  
Václav Cyrus
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Compressor Cascade ◽  
Simple Correlation ◽  
Three Dimensional Flow ◽  
Flow Angle ◽  
Low Reynolds Numbers ◽  
Dimensional Flow

A straight compressor cascade of aspect ratio 2 was tested in a low speed tunnel within Reynolds number Re1 = 45 000 – 150 000 and inlet flow angle α1 = 35° – 48°. The profile of the blade was NACA 65-12-10. The purpose of the paper was to obtain data on three–dimensional flow in a straight cascade at low Reynolds numbers. Some experimental results on secondary flow have been made into simple correlation relations.

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Author(s):  
Francine Battaglia ◽  
George Papadopoulos
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Effective Expansion ◽  
Three Dimensional Simulations

The effect of three-dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio of in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations fail to capture completely the total expansion effect on the flow, which couples both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When the two-dimensional geometry was consistent with the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations was compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, helping to sustain laminar flow symmetry to higher Reynolds numbers in comparison to nominally two-dimensional double-expansion geometries. Lastly, and most importantly, when the logarithm of the critical Reynolds number from all these studies was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

Darcy-Forchheimer porous medium effect on rotating hybrid nanofluid on a linear shrinking/stretching sheet

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Differential Equations ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Medium Effect ◽  
Hybrid Nanofluid ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Dimensional Flow

Purpose The purpose of this study is to find the multiple branches of the three-dimensional flow of Cu-Al2 O3/water rotating hybrid nanofluid perfusing a porous medium over the stretching/shrinking surface. The extended model of Darcy due to Forchheimer and Brinkman has been considered to make the hybrid nanofluid model over the pores by considering the porosity and permeability effects. Design/methodology/approach The Tiwari and Das model with the thermophysical properties of spherical particles for efficient dynamic viscosity of the nanoparticle is used. The linear similarity transformations are applied to convert the partial differential equations into ordinary differential equations (ODEs). The system of governing ODEs is solved by using the three-stage Lobatto IIIa scheme in MATLAB for evolving parameters. Findings The system of governing ODEs produces dual branches. A unique stable branch is identified with help of stability analysis. The reduced heat transfer rate has been shown to increase with the reduced ϕ2 in both branches. Further, results revealed that the presence of multiple branches depends on the ranges of porosity, suction and stretching/shrinking parameters for the particular value of the rotating parameter. Originality/value Dual branches of the three-dimensional flow of Cu-Al2 O3/water rotating hybrid nanofluid have been found. Therefore, stability analysis of the branches is also conducted to know which branch is appropriate for the practical applications. To the best of the authors’ knowledge, this research is novel and there is no previously published work relevant to the present study.

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