Abstract
Propagation of either an infinitely thin interface or a reaction wave of a nonzero thickness in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is simulated by solving unsteady 3D Navier–Stokes equations and either a level set (G) or a reaction-diffusion equation, respectively, with all other things being equal. In the case of the interface, the fully developed bulk consumption velocity normalized using the laminar-wave speed SL depends linearly on the normalized rms velocity u′/SL. In the case of the reaction wave of a nonzero thickness, dependencies of the normalized bulk consumption velocity on u′/SL show bending, with the effect being increased by a ratio of the laminar-wave thickness to the turbulence length scale. The obtained bending effect is controlled by a decrease in the rate of an increase δAF in the reaction-zone-surface area with increasing u′/SL. In its turn, the bending of the δAF(u′/SL)-curves stems from inefficiency of small-scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles characterized by a high local curvature are smoothed out by molecular transport within the reaction wave.
Highlights
The so-called bending effect consists in decreasing the rate/du0 of an increase in turbulent consumption velocity UT by the rms turbulent velocity u0 with increasing u0, i.e., the second derivative of the function UT (u0 ) is negative
A Direct Numerical Simulation (DNS) study of propagation of either an infinitely thin interface or a reaction wave of a nonzero thickness in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence was performed by solving Navier–Stokes equations and either a level set or a reaction-diffusion equation, respectively
The following results obtained in the present work stem from the finite thickness δF of the reaction wave
Summary
The so-called bending effect consists in decreasing the rate (dUT )/du0 of an increase in turbulent consumption velocity UT by the rms turbulent velocity u0 with increasing u0 , i.e., the second derivative of the function UT (u0 ) is negative. Due to this effect, the curve plotted in an orange solid line is bent and, at high u0 , shows significantly lower consumption velocities when compared to the straight dashed red line. Since this basic phenomenon was documented, e.g., in premixed turbulent flames [1,2], it has been challenging the research community and different approaches to explaining and modeling the bending effect have been put forward. The straightforward manifestation of the stretch effect consists in changing the mean value huc i of the local consumption velocity with increasing u0 , followed by eventual local reaction extinction at sufficiently high u0. A decrease in huc i and the local reaction extinction can affect the area AF of the reaction-wave surface, but this manifestation of the discussed mechanism is indirect, i.e., it is a consequence of the dependence of uc or Fluids 2019, 4, 31; doi:10.3390/fluids4010031 www.mdpi.com/journal/fluids
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