Numerical Simulation of Reciprocating Turbulent Flow in a Plane Channel

Direct numerical simulation results were obtained for oscillatory flow with zero time mean (reciprocating flow) in a plane channel using a finite volume method, Crank-Nicolson time stepping and central approximation of the advection terms. A pressure gradient varying co-sinusoidally in time was imposed as the forcing term, and its frequency and amplitude were made to vary so as to span a range of regimes from purely laminar to fully turbulent. For the limiting cases of reciprocating laminar flow and steady-state turbulent flow, numerical results were validated against analytical solutions and classic experimental literature data, respectively. For general reciprocating flows, predictions were in agreement with experimental or computational results in the literature. Here, the attention was focused on the flow rate-pressure gradient dependence. Interestingly, the relation between the amplitudes of the imposed pressure gradient and of the flow rate was found to be approximately linear both in the laminar and in the turbulent regime; the reasons for this peculiar behavior were investigated and discussed. The influence of oscillation frequency and pressure gradient on transition to turbulence was also studied, and a tentative flow regime chart was proposed. Finally, the effect of unsteadiness on heat transfer was investigated.