Numerical solution of the Navier–Stokes equations for the flow in a cylinder cascade

A numerical study of the steady, two-dimensional incompressible flow past a cascade of circular cylinders is presented. The Navier–Stokes equations are written in terms of the streamfunction and vorticity and solved using a novel numerical technique based on using the Chebychev collocation method in...

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Bibliographic Details
Published in:Journal of fluid mechanics 2004-12, Vol.520, p.51-82
Main Authors: GAJJAR, J. S. B., AZZAM, NABILA A.
Format: Article
Language:English
Subjects:
Computational methods in fluid dynamics
Exact sciences and technology
Fluid dynamics
Fluid mechanics
Fundamental areas of phenomenology (including applications)
Navier-Stokes equations
Physics
Rotational flow and vorticity
Separated flows
Steady flow
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Summary:A numerical study of the steady, two-dimensional incompressible flow past a cascade of circular cylinders is presented. The Navier–Stokes equations are written in terms of the streamfunction and vorticity and solved using a novel numerical technique based on using the Chebychev collocation method in one direction and high-order finite differences in the other direction. A direct solver combined with Newton–Raphson linearization is used to solve the discrete equations. Steady flow solutions have been obtained for large Reynolds numbers, far higher than those obtained previously, and for varying gap widths between the cylinders. Three distinct types of solutions, dependent on the gap width, have been found. Comparisons with theoretical predictions for various flow quantities show good agreement, especially for the narrow gap width case. However, existing theories are unable to explain the solution properties which exist for intermediate gap widths.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112004001594