Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity.

Two Reynolds-averaged Navier-Stokes models with full Reynolds-stress transport (RST) and tensor eddy viscosity are presented. These new models represent RST extensions of the k-2L-a-C and k-ϕ-L-a-C models by Morgan [Phys. Rev. E 103, 053108 (2021)10.1103/PhysRevE.103.053108; Phys. Rev. E 105, 045104 (2022)10.1103/PhysRevE.105.045104]. Self-similarity analysis is used to derive constraints on model coefficients required to reproduce expected growth parameters for a variety of canonical flows, including Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) mixing layers. Both models are then applied in one-dimensional simulation of RT and KH mixing layers, and the expected self-similar growth rates and anisotropy are obtained. Next, models are applied in two-dimensional simulation of the so-called "tilted rocket rig" inclined RT experiment [J. Fluids Eng. 136, 091212 (2014)10.1115/1.4027587] and in simulation of a shock-accelerated localized patch of turbulence. It is found that RST is required to capture the qualitative growth of the shock-accelerated patch, and an anisotropic eddy viscosity provides substantial improvement over a Boussinesq treatment for the tilted rocket rig problem.

Large-eddy simulation and Reynolds-averaged Navier-Stokes modeling of three Rayleigh-Taylor mixing configurations with gravity reversal.

High-fidelity large-eddy simulation (LES) is performed of Rayleigh-Taylor (RT) mixing in three different configurations involving gravity reversal. In each configuration, LES results are compared with one-dimensional Reynolds-averaged Navier-Stokes (RANS) results, and a deficiency in a commonly used transport equation for the mass-flux velocity, a_{j}, is identified. In the first configuration, a classical two-component RT mixing layer is allowed to develop before it is subjected to rapid acceleration reversal. In the second configuration, a three-component RT mixing layer with an intermediate density layer is allowed to develop before being subjected to rapid acceleration reversal. Finally, in the third configuration, a light layer is interposed between two heavy layers; in this configuration, only one interface is RT-unstable at a time as it undergoes rapid acceleration reversal. In all cases, a commonly used buoyancy production closure in the a_{j} transport equation is shown to lead to significant over-prediction of mixing layer growth after gravity reversal. An alternative formulation for this closure is then presented which is shown to more accurately capture the stabilization effect of gravity reversal.

Simulation and Reynolds-averaged Navier-Stokes modeling of a three-component Rayleigh-Taylor mixing problem with thermonuclear burn.

Rayleigh-Taylor mixing in the presence of a third component with intermediate density is investigated through three-dimensional large-eddy simulation (LES) with a high-order compact finite-difference code. Two configurations are considered: (1) a symmetric configuration in which the Atwood number between the heavy and intermediate components matches the Atwood number between the intermediate and light components and (2) an asymmetric configuration in which the Atwood number between the heavy and intermediate components is an order of magnitude greater than the Atwood number between the intermediate and light components. Mass fraction covariances are extracted, and proposed Reynolds-averaged Navier-Stokes (RANS) closures for density-specific-volume and density-mass-fraction covariances are evaluated in an a priori fashion. In addition, a multicomponent extension of the k-ϕ-L-a-V RANS model [Morgan, Phys. Rev. E 104, 015107 (2021)2470-004510.1103/PhysRevE.104.015107] is presented which includes model equations for the upper-triangular elements of the mass fraction covariance matrix. This model, referred to as the k-ϕ-L-a-C model, is compared against results from LES and against other RANS models. Profiles of average mass fraction, mass-fraction covariance, and density-specific-volume covariance obtained with the k-ϕ-L-a-C model are found to agree well with LES data. Finally, the impact of three-component turbulent mixing on average reaction rate is investigated in both premixed and nonpremixed cases by heating the mixing layer and allowing it to undergo thermonuclear (TN) burn. A closure model for average reaction rate is proposed for use with the k-ϕ-L-a-C model, and when this model is applied, improved agreement is obtained between LES and RANS in total TN neutron production.

Self-consistent, high-order spatial profiles in a model for two-fluid turbulent mixing.

A Reynolds-averaged Navier-Stokes model is presented with the property that it admits self-consistent, high-order spatial profiles in simulations of two-fluid turbulent mixing layers. Whereas previous models have been limited by the assumption of a linear mixing profile, the present paper relaxes this assumption and, as a result, is shown to achieve much better agreement with experimental profiles. Similarity analysis is presented to derive constraints on model coefficients to enforce desired self-similar growth rates that are fully consistent with the high-order spatial profiles. Through this similarity analysis, it is shown that care must be taken in model construction, as it is possible to construct certain terms in such a way as to leave growth rates unconstrained. This model, termed the k-ϕ-L-a-V model, is then applied in simulations of Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz mixing layers. These simulations confirm that the expected growth parameters are recovered and high-order spatial profiles are maintained.

Scalar mixing in a Kelvin-Helmholtz shear layer and implications for Reynolds-averaged Navier-Stokes modeling of mixing layers.

Large-eddy simulation of a temporally evolving Kelvin-Helmholtz (KH) mixing layer is performed with the tenth-order compact difference code miranda to examine the steady-state behavior of a passive scalar in a shear-driven mixing layer. It is shown that the integral behavior of scalar variance in a KH mixing layer behaves similarly to the integral behavior of scalar variance in a Rayleigh-Taylor (RT) mixing layer, and mixedness of the simulated KH shear layer tends towards a value of about 0.8. It is further shown that if the k-L-a-V Reynolds-averaged Navier-Stokes (RANS) model [B. E. Morgan et al., Phys. Rev. E 98, 033111 (2018)2470-004510.1103/PhysRevE.98.033111], calibrated to reproduce steady-state mixing in an RT layer, is applied to simulate a KH mixing layer, the RANS model will significantly overpredict the magnitude of scalar variance in the KH layer. A straightforward addition to the k-L-a-V model is then suggested, and self-similarity analysis is applied to determine constraints on model coefficients. It is shown that with the addition of a buoyancy production term in the model equation for scalar variance, it becomes possible to eliminate the model deficiency and match steady-state mixedness in simulations of both RT and KH mixing layers with a single model calibration.

Direct numerical simulation and Reynolds-averaged Navier-Stokes modeling of the sudden viscous dissipation for multicomponent turbulence.

Simulations of a turbulent multicomponent fluid mixture undergoing isotropic deformations are carried out to investigate the sudden viscous dissipation. This dissipative mechanism was originally demonstrated using simulations of an incompressible single-component fluid [S. Davidovits and N. J. Fisch, Phys. Rev. Lett. 116, 105004 (2016)10.1103/PhysRevLett.116.105004]. By accounting for the convective and diffusive transfer of various species, the current work aims to increase the physical fidelity of previous simulations and their relevance to inertial confinement fusion applications. Direct numerical simulations of the compressed fluid show that the sudden viscous dissipation of turbulent kinetic energy is unchanged from the single-component scenario. More importantly, the simulations demonstrate that the mass fraction variance and covariance for the various species also exhibit a sudden viscous decay. Reynolds-averaged Navier-Stokes simulations were carried out using the k-l model to assess its ability to reproduce the sudden viscous dissipation. Results show that the standard k-l formulation does not capture the sudden decay of turbulent kinetic energy, mass-fraction variance, and mass-fraction covariance for simulations with various compression and expansion rates, or different exponents for the power-law model of viscosity. A new formulation of the k-l model that is based on previous improvements to the k-ε family of models is proposed, which leads to consistently good agreement with the direct numerical simulations for all the isotropic deformations under consideration.

Self-consistent feedback mechanism for the sudden viscous dissipation of finite-Mach-number compressing turbulence.

Previous work [Davidovits and Fisch, Phys. Rev. Lett. 116, 105004 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.105004] demonstrated that the compression of a turbulent field can lead to a sudden viscous dissipation of turbulent kinetic energy (TKE), and that paper suggested this mechanism could potentially be used to design new fast-ignition schemes for inertial confinement fusion (ICF). We expand on previous work by accounting for finite Mach numbers, rather than relying on a zero-Mach-limit assumption as previously done. The finite-Mach-number formulation is necessary to capture a self-consistent feedback mechanism in which dissipated TKE increases the temperature of the system, which in turn modifies the viscosity and thus the TKE dissipation itself. Direct numerical simulations with a tenth-order accurate Padé scheme were carried out to analyze this self-consistent feedback loop for compressing turbulence. Results show that, for finite Mach numbers, the sudden viscous dissipation of TKE still occurs, for both the solenoidal and dilatational turbulent fields. As the domain is compressed, oscillations in dilatational TKE are encountered due to the highly oscillatory nature of the pressure dilatation. An analysis of the source terms for the internal energy shows that the mechanical-work term dominates the viscous turbulent dissipation. As a result, the effect of the suddenly dissipated TKE on temperature is minimal for the Mach numbers tested. Moreover, an analytical expression is derived that confirms the dissipated TKE does not significantly alter the temperature evolution for low Mach numbers, regardless of compression speed. The self-consistent feedback mechanism is thus quite weak for subsonic turbulence, which could limit its applicability for ICF.

Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing.

The three-equation k-L-a turbulence model [B. Morgan and M. Wickett, Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meshkov instabilities, Phys. Rev. E 91, 043002 (2015)PLEEE81539-375510.1103/PhysRevE.91.043002] is extended by the addition of a second length scale equation. It is shown that the separation of turbulence transport and turbulence destruction length scales is necessary for simultaneous prediction of the growth parameter and turbulence intensity of a Kelvin-Helmholtz shear layer when model coefficients are constrained by similarity analysis. Constraints on model coefficients are derived that satisfy an ansatz of self-similarity in the low-Atwood-number limit and allow the determination of model coefficients necessary to recover expected experimental behavior. The model is then applied in one-dimensional simulations of Rayleigh-Taylor, reshocked Richtmyer-Meshkov, Kelvin-Helmholtz, and combined Rayleigh-Taylor-Kelvin-Helmholtz instability mixing layers to demonstrate that the expected growth rates are recovered numerically. Finally, it is shown in the case of combined instability that the model predicts a mixing width that is a linear combination of Rayleigh-Taylor and Kelvin-Helmholtz mixing processes.

Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meskov instabilities.

In the present work, the two-equation k-L model [G. Dimonte and R. Tipton, Phys. Fluids 18, 085101 (2006)] is extended by the addition of a third equation for the mass-flux velocity. A set of model constants is derived to satisfy an ansatz of self-similarity in the low Atwood number limit. The model is then applied to the simulation of canonical Rayleigh-Taylor and Richtmyer-Meshkov test problems in one dimension and is demonstrated to reproduce analytical self-similar growth and to recover growth rates used to constrain the model.