A direct numerical simulation study of interface propagation in homogeneous turbulence

Abstract

A 3D direct numerical simulation (DNS) study of the evolution of a self-propagating interface in forced constant-density statistically stationary homogeneous isotropic turbulence was performed by solving Navier–Stokes and level-set equations under a wide range of conditions that cover various (from 0.1 to 2.0) ratios of the interface speed $S_{L}$ to the r.m.s. turbulent velocity $U^{\prime }$ and various (50, 100 and 200) turbulent Reynolds numbers $\mathit{Re}$. By analysing computed data, the following issues were addressed: (i) dependence of the speed and thickness of the fully developed statistically planar mean front that envelops the interface on $U^{\prime }/S_{L}$ and $\mathit{Re}$, (ii) dependence of the fully developed mean turbulent flux of a scalar $c$ that characterizes the state of the fluid ($c=0$ and 1 ahead and behind the interface respectively) on $U^{\prime }/S_{L}$ and $\mathit{Re}$, (iii) evolution of the mean front speed, its thickness, and the mean scalar flux during the front development after embedding a planar interface into the forced turbulence and (iv) relation between canonical and conditioned moments of the velocity, velocity gradient and pressure gradient fields.

Direct numerical simulation study of statistically stationary propagation of a reaction wave in homogeneous turbulence

“…The constant-density flow solver is largely identical to the solver used by us earlier [23,24], but the multigrid solver [36] for the constant-coefficient Poisson equation with periodic boundaries is replaced with an accurate spectrum solver using an open-source, parallel version of FFTW3 (mpi-fftw). The DNS code is implemented in a vector form enabling 1D, 2D, and 3D simulations.…”

“…By adopting the same forcing technique with κ f /κ 0 = 3, where κ 0 = 2π/L, Yu et al [23,24] showed that (i) the rms velocity U was maintained as the initial value, i.e., U = U 0 , (ii) the normalized averaged dissipation rate ( 0 /U 0 3 ) ε fluctuated slightly above 3/2 after a short period (t < τ 0 t = 0 /U 0 ) of rapid transition from the initial artificially synthesized flow to developed turbulence, (iii) the forced turbulence achieved statistical homogeneity and isotropy over the entire domain (see also Table I show characteristics of these three fields, calculated after the forced turbulence reached statistical stationarity, i.e., at t > 5τ 0 t . Here,…”

“…Results obtained in the present DNS will be compared with recent DNS data [24] computed by solving the level-set equation [29] …”

“…(3) in the present work, and H (z) is the Heaviside function. The interface speed S L was kept constant by Yu et al [24].…”

“…In the first two papers of the present series [23,24], we explored such effects by analyzing DNS data obtained in computations of self-propagation of an infinitely thin interface in homogeneous isotropic turbulence. The present work extends the previous study by (i) considering a reaction wave of a nonzero thickness, with all other things being equal, and (ii) investigating the influence of the thickness on the mean wave characteristics such as its speed and thickness, turbulent scalar transport within the mean wave, etc.…”