DNS study of dependence of bulk consumption velocity in a constant-density reacting flow on turbulence and mixture characteristics

Abstract

3D Direct Numerical Simulation (DNS) study of propagation of a single-reaction wave in forced, statistically stationary, homogeneous, isotropic, and constant-density turbulence was performed in order to evaluate both developing UTt and fully developed UTs bulk turbulent consumption velocities by independently varying a ratio of 0.5 ≤u′∕SL≤ 90 of the r.m.s. turbulent velocity to the laminar wave speed and a ratio of 0.39 ≤L11∕δF≤ 12.5 of the longitudinal integral length scale of the turbulence to the laminar wave thickness. Accordingly, the Damköhler Da=(L11SL)∕(u′δF) and Karlovitz Ka=δF∕(SLτη) numbers were varied from 0.01 to 24.7 and from 0.36 to 587, respectively. Here, τη is the Kolmogorov time scale. The obtained DNS data show that, at sufficiently low Da, the fully developed ratio of UTs∕u′ is mainly controlled by Da and scales as Da. However, such a scaling should not be extrapolated to high Da. The higher Da (or the lower Ka), the less pronounced dependence of UTs∕u′ on a ratio of L11∕δF. Moreover, scaling laws UT∝u′αSL1−α(L11∕δF)β are substantially different for developing UTt and fully developed UTs, i.e., the scaling exponents α and, especially, β depend on the wave-development time. Furthermore, α and, especially, β depend on a method used to evaluate the developing UTt. Such effects can contribute to significant scatter of expressions for UT or ST as a function of {u′, SL, L11, δF}, obtained by parameterizing various experimental databases.