Computation of low-speed flow with heat addition

Abstract

A perturbation expansion is used to obtain a system of conservation laws for compressible flows that is valid at arbitrarily low Mach numbers. These equations are rendered hyperbolic by adding an artificial time derivative to the energy equation, thus introducing pseudoacoustic waves with a speed the same order as the particle velocity. Traditional time-iterative schemes are shown to be effective in solving this system numerically. Stability calculations of the complete vector system indicate unconditional stability at all Mach numbers in the absence of gravity, but the source term introduced by buoyancy becomes destabilizing at Froude numbers below about 1. This instability is amplified by approximate factorization thus precluding solutions with gravity below this Mach number level. Computations of strong heat addition in low-Mach-number flow both with and without gravity confirm the stability predictions. Convergent solutions are maintained and are used to show the effect of gravity on such flowfields.