DNS STUDY OF DEPENDENCE OF BULK CONSUMPTION VELOCITY ON TURBULENCE AND MIXTURE CHARACTERISTICS

A 3D Direct Numerical Simulation (DNS) study of propagation of a single-reaction wave in statistically stationary, homogeneous, isotropic, and constant-density turbulence was performed in order to evaluate both developing U_T^t and fully developed U_T^s bulk turbulent consumption velocities by independently varying a ratio 0.5≤u'⁄S_L ≤90 of the rms turbulent velocity to the laminar wave speed, a ratio 0.39≤L_11⁄δ_F ≤12.5 of integral turbulent length scale to the laminar wave thickness, the Damköhler number 0.01≤Da=(L_11 S_L)⁄((u^' δ_F ) )≤24.7, the Karlovitz number 0.36≤Ka=δ_F⁄((S_L τ_η ) )≤587, or the Péclet number 1≤Pe=(u'L_11)⁄((S_L δ_F ) )≤707. Here, τ_η is the Kolmogorov time scale. The obtained DNS data show that, at sufficiently low Da, the fully developed ratio of (U_T^s)⁄u' or (U_T^s)⁄S_L is mainly controlled by Da or Pe, respectively, and scales as √Da or √Pe, respectively, in line with the classical hypothesis by Damköhler. However, such a scaling should not be extrapolated to high Da. The higher Da (or 〖Ka〗^(-1)), the less pronounced dependence of (U_T^s)⁄u' on a ratio of L_11⁄δ_F . This trend could explain significant scatter of scaling exponents q obtained by fitting various experimental databases with U_T∝〖u'〗^b S_L^(1-b) (L_11⁄δ_F )^q. Moreover, due to the influence of turbulent wave development on the consumption velocity, scaling laws for developing U_T^t and fully developed U_T^s can be substantially different. Furthermore, the aforementioned scaling exponents b and, especially, q depend on the wave-development time and on a method used to evaluate the developing U_T^t. Such effects can contribute to significant scatter of expressions for U_T or turbulent flame speed S_T as a function of {u^',S_L,L_11,δ_F }, obtained by parameterizing various experimental databases.