Numerical Simulation of Low-Mach-Number Laminar Mixing and Reacting Flows Using a Dual-Purpose Pressure-Based Algorithm

Abstract

Benefitting from an analogy between compressible and incompressible governing equations, a novel dual-purpose, pressure-based finite-volume algorithm is suitably extended to simulate laminar mixing and reacting flows in low-Mach-number regimes. In our test cases, the Mach number is as high as 0.00326. Definitely, such low-Mach-number flows cannot be readily solved by either regular density-based solvers or most of their extensions. To examine the accuracy and performance of the extended formulation and algorithm, we simulate two benchmark cases including the mixing natural-convection flow in a square cavity with strong temperature gradients and the premixed reacting flow through annuli with high, sharp density variations. In both cases, the fluid flow is treated as an ideal gas, whose properties vary with temperature variation assuming Sutherland's law. Additionally, we do not take into account the Boussinesq limit in treating highly thermobuoyant flow fields. The current results are validated against other available benchmarks and reliable numerical solutions. Despite using a pressure-based algorithm, the Mach number and density variations are predicted very accurately.