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Sophisticated numerical models that contain fluid interfaces rely upon interface evolution models to approximate the transition to turbulence near interfaces, in the presence of Rayleigh–Taylor (RTI) or Richtmyer–Meshkov (RMI) instability. Semi-analytical models have been developed in recent decades to predict the interface growth from an initial state into the nonlinear regime. Two of these models are considered in this study. They are the Goncharov and the z-models. Both of these interface models have strengths and weaknesses, which are examined here. Both of them have been implemented in the xRAGE compressible flow solver, which models fluid interfaces. The flow solver provides the fluids acceleration as a body force to the interface model. The purpose of such interface model is to evolve the early times of interface position as a subgrid model within a compressible flow simulation in order to then initialize a turbulence model. In this work, the interface models are assessed and compared for their evolution of RTI and RMI. The z-model performed better than the Goncharov model for all cases that were explored.

The engineered macro-pore foam provides a new way to study thermonuclear burn physics by utilizing capsules containing deuterated (D) foam and filling tritium (T) gas in the engineered macro-pores. The implosion of a thermonuclear capsule filled with an engineered macro-pore foam will be complex due to the interaction of a shock wave with the engineered macro-pores. It is our goal to quantify how substantially complex foam structures affect the shape of shock and bulk shock speed. A cylinder-shape shock tube experiment has been designed and performed at the Omega Laser Facility. In order to examine how a foam structure will affect shock propagation, we performed several tests varying (1) engineered macro-pore size, (2) average foam density, and (3) with/without neopentane (C5H12) gas. X-ray radiographic data indicate that shock speed through engineered macro-pore foams depends strongly on average foam density and less on pore size. Experimental shock propagation data helped guide two numerical simulation approaches: (1) a 2D simulation with homogenizing foams rather than explicitly simulating engineered macro-pores and (2) a 2D toroidal-pore approximation adopting a toroidal-tube geometry to model engineered macro-pores.

A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales, as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and shows to be in reasonable agreement with DNS and experiments. The importance of using DNS to calibrate and assess RANS type turbulence models is also highlighted.

We present results from the comparison of high-resolution three-dimensional (3D) simulations with data from the implosions of inertial confinement fusion capsules with separated reactants performed on the OMEGA laser facility. Each capsule, referred to as a “CD Mixcap,” is filled with tritium and has a polystyrene (CH) shell with a deuterated polystyrene (CD) layer whose burial depth is varied. In these implosions, fusion reactions between deuterium and tritium ions can occur only in the presence of atomic mix between the gas fill and shell material. The simulations feature accurate models for all known experimental asymmetries and do not employ any adjustable parameters to improve agreement with experimental data. Simulations are performed with the RAGE radiation-hydrodynamics code using an Implicit Large Eddy Simulation (ILES) strategy for the hydrodynamics. We obtain good agreement with the experimental data, including the DT/TT neutron yield ratios used to diagnose mix, for all burial depths of the deuterated shell layer. Additionally, simulations demonstrate good agreement with converged simulations employing explicit models for plasma diffusion and viscosity, suggesting that the implicit sub-grid model used in ILES is sufficient to model these processes in these experiments. In our simulations, mixing is driven by short-wavelength asymmetries and longer-wavelength features are responsible for developing flows that transport mixed material towards the center of the hot spot. Mix material transported by this process is responsible for most of the mix (DT) yield even for the capsule with a CD layer adjacent to the tritium fuel. Consistent with our previous results, mix does not play a significant role in TT neutron yield degradation; instead, this is dominated by the displacement of fuel from the center of the implosion due to the development of turbulent instabilities seeded by long-wavelength asymmetries. Through these processes, the long-wavelength asymmetries degrade TT yield more than the DT yield and thus bring DT/TT neutron yield ratios into agreement with experiment. Finally, we present a detailed comparison of the flows in 2D and 3D simulations.

The modeling of buoyancy driven turbulent flows is considered in conjunction with an advanced statistical turbulence model referred to as the BHR (Besnard-Harlow-Rauenzahn) k-S-a model. The BHR k-S-a model is focused on variable-density and compressible flows such as Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) driven mixing. The BHR k-S-a turbulence mix model has been implemented in the RAGE hydro-code, and model constants are evaluated based on analytical self-similar solutions of the model equations. The results are then compared with a large test database available from experiments and direct numerical simulations (DNS) of RT, RM, and KH driven mixing. Furthermore, we describe research to understand how the BHR k-S-a turbulence model operates over a range of moderate to high Reynolds number buoyancy driven flows, with a goal of placing the modeling of buoyancy driven turbulent flows at the same level of development as that of single phase shear flows.

The BHR RANS model is a turbulence model for multi-fluid flows in which density variation plays a strong role in the turbulence processes. In this paper they demonstrate the usefulness of BHR over a wide range of flows which include the effects of shear, buoyancy, and shocks. The results are in good agreement with experimental and DNS data across the entire set of validation cases, with no need to retune model coefficients between cases. The model has potential application to a number of aerospace related flow problems.

A second-moment closure model is proposed for describing turbulence quantities in flows where large density fluctuations can arise due to mixing between different density fluids, in addition to compressibility or temperature effects. The turbulence closures used in this study are an extension of those proposed by Besnard et al., which include closures for the turbulence mass flux and density-specific-volume covariance. Current engineering models developed to capture these extended effects due to density variations are scarce and/or greatly simplified. In the present model, the density effects are included and the results are compared to direct numerical simulations (DNS) and experimental data for flow instabilities with low to moderate density differences. The quantities compared include Reynolds stresses, turbulent mass flux, mixture density, density-specific-volume covariance, turbulent length scale, turbulence and material mix time scales, turbulence dissipation, and mix widths and/or growth rates. The...

This paper presents several issues related to mixing and turbulence structure in buoyancy-driven turbulence at low to moderate Atwood numbers, A, found from direct numerical simulations in two configurations: classical Rayleigh–Taylor instability and an idealized triply periodic Rayleigh–Taylor flow. Simulations at A up to 0.5 are used to examine the turbulence characteristics and contrast them with those obtained close to the Boussinesq approximation. The data sets used represent the largest simulations to date in each configuration. One of the more remarkable issues explored, first reported in (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145–80), is the marked difference in mixing between different density fluids as opposed to the mixing that occurs between fluids of commensurate densities, corresponding to the Boussinesq approximation. Thus, in the triply periodic configuration and the non-Boussinesq case, an initially symmetric density probability density function becomes skewed, showing that the mixing is asymmetric, with pure heavy fluid mixing more slowly than pure light fluid. A mechanism producing the mixing asymmetry is proposed and the consequences for the classical Rayleigh–Taylor configuration are discussed. In addition, it is shown that anomalous small-scale anisotropy found in the homogeneous configuration (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145–80) and Rayleigh–Taylor turbulence at A=0.5 (Livescu et al 2008 J. Turbul. 10 1–32) also occurs near the Boussinesq limit. Results pertaining to the moment closure modelling of Rayleigh–Taylor turbulence are also presented. Although the Rayleigh–Taylor mixing layer width reaches self-similar growth relatively fast, the lower-order terms in the self-similar expressions for turbulence moments have long-lasting effects and derived quantities, such as the turbulent Reynolds number, are slow to follow the self-similar predictions. Since eddy diffusivity in the popular gradient transport hypothesis is proportional to the turbulent Reynolds number, the dissipation rate and turbulent transport have different length scales long after the onset of the self-similar growth for the layer growth. To highlight the importance of turbulent transport, variable density energy budgets for the kinetic energy, mass flux and density-specific volume covariance equations, necessary for a moment closure of the flow, are provided.

The turbulence generated in the variable density Rayleigh–Taylor mixing layer is studied using the high-Reynolds number fully resolved 30723 numerical simulation of Cabot and Cook (Nature Phys. 2 (2006), pp. 562–568). The simulation achieves bulk Reynolds number, Re = H [Hdot]/ν = 32,000, turbulent Reynolds number, Re t = [ktilde] 2/νϵ = 4600, and Taylor Reynolds number, R λ = 170. The Atwood number, A, is 0.5, and the Schmidt number, Sc, is 1. Typical density fluctuations, while modest, being one quarter the mean density, lead to non-Boussinesq effects. A comprehensive study of the variable density energy budgets for the kinetic energy, mass flux and density specific volume covariance equations is undertaken. Various asymmetries in the mixing layer, not seen in the Boussinesq case, are identified and explained. Hypotheses for the variable density turbulent transport necessary to close the second moment equations are studied. It is found that, even though the layer width becomes temporally self-similar re...

A single beam of accelerated deuterium ions, D+2, of 108 keV, injected into a highly inhomogeneous magnetic field, decreasing quadratically with the radial distance from the center, was made to collide head‐on with itself. The trajectory of the ’’self‐colliding beam’’ is a precessing figure 8, with the ions moving clockwise in both (upper and lower) loops and colliding head‐on in the center.