A time-accurate variable property algorithm for calculating flows with large temperature variations

A variable property algorithm is developed for time-dependent resolution of flows with large temperature differences. The non-linear coupled set of equations with property variations is resolved by an implicit iterative procedure at each time step. The momentum and energy equations are integrated in time using an implicit Crank–Nicolson method, and a Helmholtz equation for pressure is solved at each inner iteration. Local density changes are coupled to both changes in local temperature and pressure, whereas other properties are only coupled to changes in temperature. No low Mach number assumption is used in the formulation, and the pressure is calculated directly through the Helmholtz equation. Results are shown to compare well with benchmark calculations and analytical solutions of convection in a differentially heated cavity with very large temperature differences. Unsteady Poiseuille–Bénard flow is used for validation of the time-dependent aspects of the algorithm, which is shown to accurately predict the time-dependent buoyancy driven longitudinal vortices.