A Novel Numerical Approach for Low Mach Number: Application to Supercritical Fluids

A new numerical algorithm has been developed to compute low Mach number fluids using the c_V-formulation of the energy equation. c_V is the specific heat at constant volume. It has been applied to both supercritical fluid flows (using a nonlinear equation of state like the van der Waals cubic equation of state) and gas flows (using an ideal gas law). The algorithm is introduced successfully in a finite volume code using the SIMPLE and SIMPLER methods. Its main advantage lies in the decoupling of the energy equation and equation of state from the momentum and continuity equations, leading to decrease significantly the CPU time in the case of supercritical fluids simulations. Moreover it allows for supercritical fluid flow simulations the use of other discretization methods (such as spectral methods and/or finite differences) and any other nonlinear form of the equation of state. The new algorithm is presented after a brief description of the previously existing algorithm to solve supercritical fluid flows. Then three published Benchmark problems for steady and unsteady ideal gas flows are treated, as well as the side heated cavity problem for a near critical carbon dioxide filling. The results are then compared to those obtained from the previous algorithm as well as to those obtained from a spectral code using the new algorithm. This comparative investigation is extended to the Rayleigh-Bénard problem for a near critical carbon dioxide filled square cavity with the use of the Van der Waals and the Peng-Robinson equations of state.