Journal of Computational Physics vol:291 pages:34-51
This paper presents spatially averaged Navier–Stokes equations for modelling macro-scale flow in devices with periodic solid structures such as fin and tube arrays. The properties of steady and unsteady periodically developed flow are investigated to assess different strategies for determining the closure terms in the macro-scale flow equations. It is shown that the spatial averaging technique requires an appropriate weighting function to ensure that the closure terms are spatially constant for periodically developed flow. Moreover, through an appropriate choice of the weighting function, the closure terms can be obtained by solving a local closure problem on a unit cell of the periodic structures. The theoretical framework of this paper is applied as multi-scale modelling technique for flow through a cylindrical tube array. This case study illustrates the advantages of the weighted spatial averaging technique over the volume averaging technique.