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

• Published in: International journal for numerical methods in engineering Vol. 75; no. 10; pp. 1214 - 1237
• Main Authors: Visser, C. J., Malan, A. G., Meyer, J. P.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 03.09.2008; Wiley
• Subjects: artificial compressibility; Computational techniques; Convection and heat transfer; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Heat transfer; heterogeneous porous materials; Mathematical methods in physics; natural convection; Physics; saturated randomly packed pebble beds; Solid mechanics; Structural and continuum mechanics; Thermal radiation; Turbulent flows, convection, and heat transfer; Compressibility; Stabilization; Porous materials; Porous medium; Heat flow; Natural convection; Saturated porous medium; Finite volume methods; Sound velocity; Packed beds; Thermal radiation; Inhomogeneous media; Modelling; artificial compressibility; saturated randomly packed pebble beds; Inhomogeneous materials; Scale factor; Random media; Upper bound; Flow(fluid); Wall effects; Porosity; heterogeneous porous materials; Non linear effect; Edge detection; Preconditioning; Heat transfer
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2296

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.