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

Journal article, 2017

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 U t T and fully developed U s T bulk turbulent consumption velocities by independently varying a ratio of 0.5 ≤ u'=S L ≤ 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 = (L 11 S L )=(u'δ F ) and Karlovitz Ka = δ F =(S L τ η ) numbers were varied from 0.01 to 24.7 and from 0.36 to 587, respectively. Here, τ is the Kolmogorov time scale. The obtained DNS data show that, at sufficiently low Da, the fully developed ratio of U s T /u' is mainly controlled by Da and scales as p Da. However, such a scaling should not be extrapolated to high Da. The higher Da (or the lower Ka), the less pronounced dependence of U s T /u' on a ratio of L 11 /δ F . Moreover, scaling laws U T α u'αS 1-α L (L 11 =δ F ) β are substantially different for developing U t T and fully developed U s T , i.e., the scaling exponents α and, especially, β depend on the wave-development time. Furthermore, α and, especially, depend on a method used to evaluate the developing U t T . Such effects can contribute to significant scatter of expressions for U T or S T as a function of (u', S L , L 11 , δ F ), obtained by parameterizing various experimental databases.