Modelling heat and mass flow through packed pebble beds : a heterogeneous volume-averaged approach

Abstract

This work details modelling buoyancy-driven viscous flow and heat transfer through heterogeneous saturated packed pebble beds via a set of volume-averaged conservation equations in which local thermal disequilibrium is accounted for. The latter refers to the two phases considered viz. solid and fluid, differing in temperature. This is effected by describing each phase with its own governing equation. Further to the aforementioned, the governing equation set is written in terms of intrinsic volume-averaged material properties that are fully variant with respect to temperature. The heterogeneous solid phase is described with a porosity field varying from 0.39 to 0.99. The intent of the stated upper bound is to explicitly model typical packed bed near-wall phenomena such as wall-channelling and pebble-wall heat transfer as true to reality as possible, while maintaining scientific rigour. The set of coupled non-linear partial differential equations is solved via a locally preconditioned artificial compressibility method, where spatial discretisation is effected with a compact finite volume edge-based discretisation method. The latter is done in the interest of accuracy. Stabilisation 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. As a result of the aforementioned, calculation of the acoustic velocities, stabilisation scaling factors and allowable time-step sizes were revised. The developed technology is demonstrated by application to the modelling of SANA test cases, i.e. natural convective flow inside a heated porous axisymmetric cavity. Predicted results are shown to be within 12% of experimental measurements in all cases, while having an average deviation of only 3%.