Search

A new approach to generate initial conditions for RANS simulations of Rayleigh–Taylor (RT) turbulence is presented. The strategy is to provide profiles of turbulent model variables when it is suitable for the turbulence model to be started, and then use these profiles for the turbulence model initialization. The generation of turbulence model variable profiles is achieved with a two-step process. In the first step, a nonlinear modal model assuming small amplitude initial perturbations, incompressible and inviscid fluids is used to track the growth of modes that exist in a given initial perturbation spectrum, and also modes generated by mode interactions. The amplitude development of each mode represents the penetration distance of the light fluid into the heavy fluid (bubble penetration), for a given mode perturbation. The penetration distance of heavy fluid into the light fluid (spike penetration), for a given mode perturbation, is inferred from the bubble's height by an empirical relation valid for small initial amplitudes, and established by DNS simulations that depend on a nondimensional time, and the density contrast (Atwood number). It is hypothesized that the bubble front position of the RT mixing layer can be approximated by the largest penetration distance among all existing modes. The spike front position is approximated in the same fashion. The nonlinear model is evaluated by comparing the bubble front height evolution predicted by the model against the bubble front height predicted by an incompressible implicit large eddy simulations (ILES) code. Comparisons of results for “top-hat” and two-band initial perturbation spectra at Atwood numbers,AT=0.3 andAT=0.5 for the former, andAT=0.01 andAT=0.5 for the latter, show reasonable agreement. In the second step, the bubble and spike front positions, their derived velocities, and simplified profiles of the mixture fraction distribution of each fluid between the bubble and spike fronts are used with a two-fluid approximation to derive profiles for the turbulence model variables. When initialized with modal model profiles at start time τ0, (i.e., the time when the turbulence model variable profiles are inferred from the modal model results), the RANS simulations provide at all times τ>τ0profiles that show good agreement with ILES simulations. The procedure for determining the time at which the RANS model should be started is a representative use, other parameters can be used depending on the application. In this paper, for the purpose of demonstration of the full strategy, τ0is taken as the time at which the mixing layer growth rate parameter α has reached its asymptotic value in the corresponding ILES simulation. [ABSTRACT FROM AUTHOR]

Experimental evidence is needed to verify the hypothesis that the memory of initial conditions is retained at late times in variable density flows. If true, this presents an opportunity to “design” and “control” late-time turbulence, with an improved understanding in the prediction of inertial confinement fusion and other general fluid mixing processes. In this communication, an experimental and theoretical study on the effects of initial condition parameters, namely, the amplitude δ0and wavenumber κ0, where λ0is the initial wavelength) of perturbations, on late-time turbulence and mixing in shock-driven Richtmyer–Meshkov (R-M) unstable fluid layers in a 2D plane is presented. Single and multi-mode membrane-free initial conditions in the form of a gas curtain having a light-heavy-light configuration (air-SF6-air) with an Atwood number ofA= 0.57 were used in our experiments. A planar shock wave with a shock Mach numberM= 1.21 drives the R-M instability, and the evolution of this instability after incident shock is captured using high resolution simultaneous planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV) diagnostics. Time evolution of statistics such as amplitude of the mixing layer, 2D turbulent kinetic energy, Reynolds number, rms of velocity fluctuations, probability density functions, and density-specific volume correlation were observed to quantify the amount of mixing and understand the nature of turbulence in this flow. Based on these results, it was found that the R-M mixing layer is asymmetric and non-Boussinesq. There is a correlation between initial condition parameters and large-scale, and small-scale mixing at late times, indicating an initial condition dependence on R-M mixing. [ABSTRACT FROM AUTHOR]

A stochastic form of linear stability analysis is used to construct initial conditions for variable density moment closures for flows due to the unstable interface between two different density fluids. The material interface can be driven by a mechanism, such as gravity, a pressure gradient (Rayleigh-Taylor), or by a shock (Richtmyer-Meskoff). Initial moments for second moment closure strategies that carry the variables k, 〈uiuj〉, Rij, ε, and ai for the hydrodynamical field and 〈ρ2〉, 〈ρv〉, and ερ, ερv for the material field are derived. The method produces a one-to-one correspondence between the initial conditions of a statistical model and the initial energy production - crucially important to the early time problem that sets up the late time problem and is not addressed in models for these flows. The analysis is applied to the Rayleigh-Taylor transition and turbulence problem. Several scalings emerge from the analysis that parameterize the initial condition dependence of RT turbulence on statistics of the interfacial morphology. Computations are conducted to assess the importance of nondimensional parameters on the transition process. An interfacial Reynolds number, involving two statistically defined length scales, collapses the simulation data exceptionally well and is thus a parameter that can be used to effect the transition to turbulence. About 97% of the variability of the turbulence and bulk Reynolds numbers is explained by the initial Taylor-Reynolds number, Reλ0. The initial Taylor-Reynolds number, Reλ0, includes two length scales of the interface, δ is the root mean square (rms) thickness and κis rms zero-crossing wavenumber. Minimizing δ2/κ appearing in Reλ0 stabilizes the interface and reduces the speed of transition to a turbulent flow. Maximimizing δ2/κ destabilizes the interface and increases the rate of transition to a developed turbulent flow and may be of use in reducing the computational costs of transition in the direct numerical simulations of fully developed Rayleigh-Taylor turbulence. [ABSTRACT FROM AUTHOR]