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An artificial compressibility algorithm for modelling natural convection in saturated packed pebble beds: A heterogeneous approach

This work is concerned with the modelling of heat and fluid flow through saturated packed pebble beds. A volume‐averaged set of local thermal disequilibrium governing equations is employed to describe the latter as a heterogeneous porous medium with porosity varying from 0.39 to 0.99. The thermal disequilibrium approach, together with stated porosity upper limit, allows for the modelling of wall effects such as wall channeling and wall–bed radiative heat transfer. The resulting set of coupled non‐linear partial differential equations is solved via a locally preconditioned artificial compressibility method, where spatial discretization is effected with a compact finite volume edge‐based discretization scheme. The latter was done in the interest of accuracy. Stabilization is effected via JST scalar‐valued artificial dissipation. This is the first instance in which an artificial compressibility algorithm is applied to modelling heat and fluid flow through heterogeneous porous materials. For this reason, special attention was given to the calculation of acoustic velocities, stabilization scaling factors, as well as allowable time‐step sizes. The developed technology is validated by application to the modelling of a number of benchmark test cases. Copyright © 2008 John Wiley & Sons, Ltd.