Influence of vibrations on thermodiffusion in binary mixture: A benchmark of numerical solutions

Abstract

Double-diffusive and vibrational convection with the Soret effect is considered in a cubic rigid cell filled with water (90%) and isopropanol (10%), subjected to a temperature difference between opposite lateral walls. Numerical simulations are carried out for g-jitter induced flow. The direction of g-jitter is the same as the residual gravity vector, which is perpendicular to the applied temperature gradient. Along with various combinations of static and oscillatory components, vibrations with two different frequencies are examined: (a) when the period of oscillations is smaller than any characteristic time (viscous, thermal, and diffusion), f=0.2Hz; (b) when the period of oscillations is comparable with viscous time, f=0.01Hz. Component separation due to the Soret effect under these driving actions is analyzed. The concept of time-averaged models is applied for the explanation of the high-frequency results. The interplay between the mean and fluctuating motions is discussed. Three research groups performed a benchmark of numerical solutions of three-dimensional Navier-Stokes, energy, and concentration equations using the true physical parameters for a future Space experiment. The objective of this paper is twofold: (i) to carry out an accurate study of heat and mass transfer in a binary liquid with the Soret effect in the presence of steady residual gravity and its oscillatory component; (ii) to carry out a benchmark of numerical solutions.