Conjugate heat transfer during oscillatory laminar flow in porous media

Hydrodynamics and conjugate heat transfer in porous media subject to unidirectional-steady state as well as steady-periodic flow conditions were numerically studied. Two-dimensional flows in porous media composed of periodically configured arrays of square cylinders were simulated using a computational fluid dynamics tool, with sinusoidal time variation of inlet and exit boundaries and conjugate heat transfer between the solid and fluid domains. The simulated domain contained seven unit cells, with each unit cell representing a square cylinder. Simulations showed that the end effects did not persist more than two unit cells. Simulations were conducted for flow oscillation frequencies of 0-60 Hz, and low and high velocity amplitudes (representing tidal fluid penetration amplitudes of 8 and 2 times the hydraulic diameter, respectively, at inlet) for a 75% porous domain. Using the simulation results, pore-scale volume-average Darcy permeability, Forchheimer coefficient, and Nusselt number associated with the standard volume-average porous media momentum and thermal energy equations were calculated. These parameters were calculated in instantaneous as well as cycle-averaged forms. The Forchheimer coefficient and Nusselt number were significantly different in unidirectional-steady and oscillatory flow conditions. These parameters strongly depend on the flow oscillation frequency and amplitude. Furthermore, significant phase lag occurs among velocity, pressure, temperature and heat transfer processes. The results confirm that unidirectional-steady flow models and correlations are not suitable for applications involving flow oscillations.