Impact of conditions at start-up on thermovibrational convective flow

The development of thermovibrational convection in a cubic cell filled with high Prandtl number liquid (isopropanol) is studied. Direct nonlinear simulations are performed by solving three-dimensional Navier-Stokes equations in the Boussinesq approximation. The cell is subjected to high frequency periodic oscillations perpendicular to the applied temperature gradient under zero gravity. Two types of vibrations are imposed: either as a sine or cosine function of time. It is shown that the initial vibrational phase plays a significant role in the transient behavior of thermovibrational convective flow. Such knowledge is important to interpret correctly short-duration experimental results performed in microgravity, among which the most accessible are drop towers ( approximately 5s) and parabolic flights ( approximately 20s) . It is obtained that under sine vibrations, the flow reaches steady state within less than one thermal time. Under cosine acceleration, this time is 2 times longer. For cosine excitations, the Nusselt number is approximately 10 times smaller in comparison with the sine case. Besides, in the case of cosine, the Nusselt number oscillates with double frequency. However, at the steady state, time-averaged and oscillatory characteristics of the flow are independent of the vibrational start-up. The only feature that always differs the two cases is the phase difference between the velocity, temperature, and accelerations. We have found that due to nonlinear response of the system to the imposed vibrations, the phase shift between velocity and temperature is never equal exactly to pi2 , at least in weightlessness. Thus, heat transport always exists from the beginning of vibrations, although it might be weak.