A 3D Low Mach Number model for high performance computations in natural or mixed convection newtonian liquid flows

Abstract

Despite its widespread usage Boussinesq's approximation exhibits a domain of validity which is extremely restricted for liquids in terms of admissible temperature difference, less than 10 K for liquid water under standard atmospheric pressure. This strong limitation can be overcome for flows subjected to weak dynamical pressure by introducing thermal property dependence in the governing equations. This communication presents the dilatable model we have developed to perform 3D computations of natural or mixed convection of liquid water. It contains two main features: a formulation that casts the Newtonian fluid behaviour law in a Low-Mach-Number approximation along with an open boundary condition formulation. The difficulties related to the former stand in implementing a computationally efficient equation of state for water in the LMN approximation framework, whereas those related to the latter concern the treatment of Open Boundary Conditions in the projection algorithm used. Both Boussinesq's approximation and the proposed LMN models have been used to compute a mixed convection water flow in a horizontal channel uniformly heated from below at prescribed heat flux (Re = 50, Ri = 3), for which the steady state solution is characterized by longitudinal roll-like structures combined to localized thermal plumes. Both models coincide in the upstream part of the channel where the fluid temperature is low and then progressively differ further downstream as the local temperature increases. A very good agreement is obtained between the LMN computed flow structure and the experimentally observed one.