Comparison of direct numerical simulations of turbulent flames using compressible or low-Mach number formulations

Modelling turbulent flames with an acceptable accuracy remains an open problem. In order to progress in our understanding of turbulent combustion, direct numerical simulations have been extensively employed during the last decade. These direct simulations generally rely on a fully compressible formulation, leading to extremely small time-steps associated with the propagation of acoustic waves. But, for many practical applications, acoustic phenomena are not essential. Using an incompressible approach while taking into account a dilatation term should then be much more efficient in terms of computing time. In this article we want to investigate this point by comparing results of direct simulations relying either on the compressible equations or on the low-Mach number formulation. We employ in both cases detailed models to describe chemistry and transport, in order to obtain an accurate description of the reaction zones. Two test-cases are considered for the evaluation of the low-Mach number approximation. We first compute the evolution of homogeneous isotropic turbulence decaying with time, without chemical reactions. In the second case a turbulent premixed ozone flame is investigated. For both configurations the computing time associated with the low-Mach number simulation is at least an order of magnitude shorter, while keeping a similar accuracy for the flame properties. This demonstrates that the low-Mach number formulation is extremely efficient and suitable to investigate the detailed structure Of turbulent flames when acoustic phenomena are not of primary interest. Copyright (C) 2002 John Wiley Sons, Ltd.