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An artificial compressibility method for buoyancy‐driven flow in heterogeneous saturated packed beds: A homogeneous approach

C.J. Visser (Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, South Africa)
A.G. Malan (Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, South Africa)
J.P. Meyer (Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, South Africa)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 19 September 2008

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Abstract

Purpose

The purpose of this paper is to focus on modeling buoyancy driven viscous flow and heat transfer through saturated packed pebble‐beds via a set of homogeneous volume‐averaged conservation equations in which local thermal disequilibrium is accounted for.

Design/methodology/approach

The local thermal disequilibrium accounted for refers to the solid and liquid phases differing in temperature in a volume‐averaged sense, which is modeled by describing each phase with its own governing equation. The partial differential equations are discretized and solved via a vertex‐centered edge‐based dual‐mesh finite volume algorithm. A compact stencil is used for viscous terms, as this offers improved accuracy compared to the standard finite volume formulation. A locally preconditioned artificial compressibility solution strategy is employed to deal with pressure incompressibility, whilst stabilisation is achieved via a scalar‐valued artificial dissipation scheme.

Findings

The developed technology is demonstrated via the solution of natural convective flow inside a heated porous axisymmetric cavity. Predicted results were in general within 10 per cent of experimental measurements.

Originality/value

This is the first instance in which both artificial compressibility and artificial dissipation is employed to model flow through saturated porous materials.

Keywords

Citation

Visser, C.J., Malan, A.G. and Meyer, J.P. (2008), "An artificial compressibility method for buoyancy‐driven flow in heterogeneous saturated packed beds: A homogeneous approach", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 18 No. 7/8, pp. 900-918. https://doi.org/10.1108/09615530810899015

Publisher

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Emerald Group Publishing Limited

Copyright © 2008, Emerald Group Publishing Limited