A pore-scale assessment of the dynamic response of forced convection in porous media to inlet flow modulations

Abstract

An increasing number of technologies require prediction of unsteady forced convection in porous media when the inlet flow is unsteady. To gain further insight into this problem, the unsteady equations of continuity, Navier Stokes and energy are solved within the pores formed by several cylindrical flow obstacles. The system is modulated by sine waves superimposed on the inlet flow velocity, and the spatio-temporal responses of the flow and temperature fields are calculated. The results are then utilised to assess the linearity of the thermal response represented by the Nusselt number on the obstacles. It is shown that for linear cases, a transfer function can be devised for predicting the dynamic response of the Nusselt number. It is further argued that such a transfer function can be approximated by a classic low-pass filter which resembles the average response of the individual obstacles. This indicates that there exists a frequency threshold above which the thermal system is essentially insensitive to flow modulations. The results also show that changes in Reynolds number and porosity of the medium can push the dynamic response of the system towards non-linearity. Yet, there appears to be no monotonic change in the linearity of the response with respect to the Reynolds number and porosity. In general, it is found that for low Reynolds numbers, the dynamics of heat convection can be predicted decently by taking a transfer function approach. The findings of this study can enable further understanding of unsteady forced convection in porous media subject to time-varying inlet flows.