Turbulent transport and mixing in the multimode narrowband Richtmyer-Meshkov instability

Abstract

The mean momentum and heavy mass fraction, turbulent kinetic energy, and heavy mass fraction variance fields, as well as the budgets of their transport equations, are examined at several times during the evolution of a narrowband Richtmyer-Meshkov instability initiated by a Mach 1.84 shock traversing a perturbed interface separating gases with a density ratio of 3. The results are computed using the 'quarter scale' data from four algorithms presented in the θ -group study of Thornber et al. [Phys. Fluids 29, 105107 (2017)]. The present study is inspired by a previous similar study of Rayleigh-Taylor instability and mixing using direct numerical simulation data by Schilling and Mueschke [Phys. Fluids 22, 105102 (2010)]. In addition to comparing the predictions of the data from four implicit large-eddy simulation codes, the budgets are used to quantify the relative importance of the terms in the transport equations, and the balance of the terms is employed to infer the numerical dissipation. Terms arising from the compressibility of the flow are examined in particular, i.e., the pressure-dilatation. The results are useful for validation of large-eddy simulation and Reynolds-averaged modeling of Richtmyer-Meshkov instability.

Simulation and flow physics of a shocked and reshocked high-energy-density mixing layer

“…The second term T II is the turbulent-mass-flux coupling term, so named because the product of density and u i = u i − u i can be interpreted as a turbulent mass flux that vanishes for a constant-density flow. As a contribution to T II , the product − u i ∂p/∂x i is called the buoyancy production term (Schilling & Latini 2010;Thornber et al 2019) or the mean pressure work term (Chassaing et al 2010). The third term T III is the pressure-dilatation term.…”

The influence of initial perturbation power spectra on the growth of a turbulent mixing layer induced by Richtmyer–Meshkov instability

“…It is interesting to note that κ 0 is very similar to the weighted average wavenumberk introduced in Eqn. 33. For example, for the m = −2 case at a bandwidth of R = 128, κ 0 = 23.46 andk = 22.62.…”

Reynolds number dependence of turbulence induced by the Richtmyer–Meshkov instability using direct numerical simulations

“…In the largest such study to date (known as the θ -group collaboration), Thornber et al (2017) showed that good agreement is obtained for various integral measures such as the mixing layer width, mixedness and total fluctuating kinetic energy across eight independent algorithms. In a follow-up paper, Thornber et al (2019) computed the transport equation budgets for the mean momentum, mean heavy fluid mass fraction, heavy fluid mass fraction variance and specific turbulent kinetic energy to provide useful benchmark data for the development of closure models for these quantities. There is still a lack of understanding with regards to the behaviour of the mixing layer during the transitional period between linear growth and fully developed turbulence, however.…”

“…In a follow-up paper, Thornber et al. (2019) computed the transport equation budgets for the mean momentum, mean heavy fluid mass fraction, heavy fluid mass fraction variance and specific turbulent kinetic energy to provide useful benchmark data for the development of closure models for these quantities. There is still a lack of understanding with regards to the behaviour of the mixing layer during the transitional period between linear growth and fully developed turbulence, however.…”