The eddy structure in Stokes flow in a cavity

Abstract

Stokes flow in a two-dimensional cavity of rectangular section, induced by the motion of one of the walls, is considered. A direct, efficient calculational procedure, based on an eigenfunction expansion, is used to study the eddy structure in the cavity. It is shown that some of the results of earlier studies are quantitatively in error. More importantly, two interesting questions, namely the extent of the symmetry of the corner eddies and their relationship to the large-eddy structure are settled. By carefully examining the rather sudden change in the main eddy structure for cavities of depth around 1.629, it is shown that the main eddies are formed by the merger of the primary corner eddies; the secondary corner eddies then become the primary corner eddies and so on. Thus, in the evolution of the large-eddy structure the corner eddies, in some sense, play the role of progenitors. This explicit prediction should be experimentally verifiable.

Steady stokes flow in an annular cavity

“…Shankar (15), using 100 terms in an eigenfunction expansion similar to (46) for a rectangular cavity to solve a system of 400 linear algebraic equations with the matrix depending on the complex roots A m could not obtain a reasonable approximation of the boundary condition near the comer points. He obtained a tangential velocity 0-6 instead of the prescribed value 1.…”

“…The last problem is a traditional benchmark problem for testing various numerical methods for the solution of the full Navier-Stokes equations with different values of the Reynolds number. In spite of the large number of papers devoted to this problem (see, for example, (14,15) for further references, including related mathematical and elasticity problems) it still remains important to raise accuracy and reduce computational costs in determining the velocity field.…”

Investigations into packaging technology for membrane-based thermal flow sensors

“…This is actually observed (Fig. 12) in different scientific papers that study a fundamental Computational Fluid Dynamics (CFD) analysis for similar geometries (Shankar, 1993;Cheng and Hung, 2006;van Dijk and de Lange, 2007). Making a CFD analysis to give a fundamental theoretical answer to what is happening in our setup when the sensor is mounted step down or step up would be rather complicated and very extensive work.…”

Steady Stokes flow between confocal semi-ellipses

“…There are a number of works describing the flow over a rectangular cavity [12][13][14][15][16][17][18]. The solutions for the Stokes equations for the annular cavities were investigated in [19][20][21][22][23][24][25].…”