Numerical prediction of turbulent thermocapillary convection in superposed fluid layers with a free interface

The present paper introduces a new numerical method for predicting the characteristics of thermocapillary turbulent convection in a differentially-heated rectangular cavity with two superposed and immiscible fluid layers. The unsteady Reynolds form of the Navier–Stokes equations and energy equation are solved by using the control volume approach on a staggered grid system using SIMPLE algorithm. The turbulence quantities are predicted by applying the standard k–ε turbulence model. The level set formulation is applied for predicting the topological changes of the interface separating the two fluid layers and to provide an accurate and robust modeling of the interfacial normal and tangential stresses. The computational results obtained showed good agreement when compared with the previous experimental, numerical and analytical benchmark data for different validation cases in both laminar and turbulent regimes. The present numerical method is then applied to predict the velocity and temperature distribution in two immiscible liquid layers with undeformable interface for a wide range of Marangoni numbers. The laminar-turbulent transition is demonstrated by obtaining the turbulence features at high interfacial temperature gradient which is characterized by high Marangoni number. The effect of increasing Marangoni number on the interface dynamics in turbulent regime is also investigated.