Bertrand Rollin

On generating initial conditions for turbulence models: the case of Rayleigh–Taylor instability turbulent mixing

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 bubbles 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 and AT =0.5 for the former, and AT =0.01 and AT =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>τ0 profiles 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, τ0 is taken as the time at which the mixing layer growth rate parameter α has reached its asymptotic value in the corresponding ILES simulation.

Extinction simulation of diffusion flame established in microgravity

A combination of numerical simulations and experiments is used to establish the accuracy of a soot production and the associated radiative heat transfer models for a non-buoyant laminar diffusion flame. In addition, the need to describe the combustion reaction by means of finite rate chemistry is assessed. An ethylene flame is established within a laminar boundary layer flow and the physical parameters studied are the flame length and standoff distance. Experimentally, these parameters are defined by means of CH chemiluminescence measurements. The results show that finite chemistry is necessary to define trailing edge quenching and thus the flame length. In the absence of accurate local soot concentrations and a robust radiation model, the standoff distance and flame length cannot be predicted accurately.

Effect of a bimodal initial particle volume fraction perturbation in an explosive dispersal of particles

Explosive dispersal of particles is a complex multiphase phenomenon that has yet to be fully understood. As the particle cloud disperses at high speed, it experiences multiphase instabilities related to Richtmyer-Meshkov (RM) and Rayleigh-Taylor (RT) instabilities when interacting with the blast-wave structure. This paper reports the results of a numerical experiment where the effect of bimodal perturbations in the initial particle volume fraction is studied. Results indicate that a signature of the initial perturbation profile remains in the particle cloud throughout the observed time, and that adding a bimodal perturbation increases the width of the cloud when compared to a uniform volume fraction distribution.Explosive dispersal of particles is a complex multiphase phenomenon that has yet to be fully understood. As the particle cloud disperses at high speed, it experiences multiphase instabilities related to Richtmyer-Meshkov (RM) and Rayleigh-Taylor (RT) instabilities when interacting with the blast-wave structure. This paper reports the results of a numerical experiment where the effect of bimodal perturbations in the initial particle volume fraction is studied. Results indicate that a signature of the initial perturbation profile remains in the particle cloud throughout the observed time, and that adding a bimodal perturbation increases the width of the cloud when compared to a uniform volume fraction distribution.

Simulations of the Tilted Rig Experiment Using the xRage and FLAG Hydrocodes

The tilted rig experiment is a derivative of the rocket rig experiment designed to study mixing of fluids by the Rayleigh–Taylor instability. In this experiment, a tank containing two fluids of different densities is accelerated downwards between two parallel guide rods by a rocket motor. The rocket rig is inclined by a few degrees off the vertical to force a two-dimensional Rayleigh–Taylor instability. Thus, the tilted rig experiment can help calibrate two-dimensional mixing models. Simulations of the tilted rig experiments using two of Los Alamos National Laboratory’s hydrocodes are reported. Both codes, xRAGE and FLAG, are multidimensional, multimaterial, massively parallel, hydrodynamics codes that solve the Euler equations. xRAGE operates in an Eulerian framework, while FLAG operates in an Arbitrary Lagrangian–Eulerian (ALE) framework, with a Lagrange step followed by mesh relaxation and remapping. Direct comparisons between simulations and experimental results are reported, as well as report the behavior of the variable-density turbulence models implemented in the codes.© 2012 ASME

Simulation of the Tilted Rig Experiment

The tilted rig experiment is a derivative of the rocket rig experiment designed to study mixing of fluids by the Rayleigh-Taylor instability. In the latter experiment, a tank containing two fluids of different densities is accelerated downwards between two parallel guide rods by a rocket motor. Misalignment between density and pressure gradients trigger the instability leading turbulence and mixing of the fluids. In the tilted rig experiment, the rocket rig is inclined by few degrees off the vertical before firing, creating a slanted initial perturbation interface. The purpose of the tilted rig experiment was to help with calibration of mixing models, as it is a unique two-dimensional Rayleigh-Taylor instability flow. We reproduce conditions similar to this experiment using a Monotone Integrated Large Eddy Simulation (MILES) technique, and for the first time look at statistics of turbulence quantities that appears in “RANS-type” variable density turbulence model. Our statistics show that for the most part, the turbulence quantities in this two-dimensional Rayleigh-Taylor instability configuration behave in a similar fashion as in the planar Rayleigh-Taylor instability configuration when looking in a direction perpendicular to the mixing layer centerline.Copyright

Modeling Turbulent Rayleigh-Taylor Mixing with Dynamic Interfaces

Variable-density turbulent mixing is found in a wide variety of applications, and modeling these effects is a continuing challenge. Reynolds–Averaged Navier–Stokes models remain the most common design tool in a wide variety of fields. This paper extends validation of RANS models for variable-density turbulence to a two-dimensional Rayleigh–Taylor test case. The combined effects of bulk fluid motion and turbulence model behavior are discussed and several metrics are shown to demonstrate the ability of four-equation turbulence model to describe this class of flows.

Application of a Novel Approach for Turbulence Model Initialization: Preliminary Results

Progress on the implementation of a novel approach to initialization for RANS simulations of interfacial instability induced turbulent mixing is demonstrated on various problems. The strategy consist of using an analytical model to compute the instability evolution from the quiescent state, and make use of its prediction to generate initial conditions for the turbulence model. Explicitly, an incompressible inviscid model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities continuously updates the turbulence model variables values in the mixing layer, until the Reynolds number suggests that the flow has become turbulent. Implementation of this procedure is made in three steps: first, the instability model is run alone while the interface is evolved by the hydrocode hosting the turbulence model; second the turbulence model is started and the turbulence variables updated in accordance with the instability growth model predictions; finally, the Reynolds number suggests that the turbulent mixing regime is reached, causing the instability model to stop and the turbulence model to continue alone. The initialization methodology is tested on canonical Rayleigh-Taylor and Richtmyer-Meshkov problems, on the tilted rig test problem, and on the chevron problem. Overall, this new approach to turbulence model initialization show promising results.

An Appropriate Metric to Switch on a Turbulence Model for Rayleigh-Taylor Instability Driven Mixing

Rayleigh-Taylor (RT) instability occurs at a perturbed interface between fluids of different densities, when the lighter fluid is accelerated into the heavier fluid (∇p · ∇ρ < 0, where p is pressure, and ρ is density). In time, as the two fluids seek to reduce their combined potential energy, the mixing becomes turbulent. This fundamental instability is observed, and plays a key role, in numerous natural phenomena, e.g. supernovae explosions, and in engineering applications, e.g. Inertial Confinement Fusion (ICF). The importance of initial condition (ICs) effects on the growth and mixing of Rayleigh-Taylor instability open an opportunity for “design” of RT turbulence for engineering, and question our current predictive capability. Indeed, commonly used turbulence models used for engineering applications are tuned for fully developed turbulence, whereas RT instability is a dynamic process that evolves toward turbulence under the influence of ICs. Therefore, our efforts aim at defining a procedure for properly accounting for initial conditions in variable density (RT) turbulence models. Our strategy is to have a model for the “early” evolution of the RT instability that will produce the initial conditions for the turbulence model. We already dispose of a modal model to evolve the RT mixing layer starting from almost any initial conditions. The present work is a first look at determining an appropriate metric for switching from the modal model to a variable density turbulence model.Copyright

On the “Early-Time” Evolution of Variables Relevant to Turbulence Models for the Rayleigh-Taylor Instability

We present our progress toward setting initial conditions in variable density turbulence models. In particular, we concentrate our efforts on the BHR turbulence model [1] for turbulent Rayleigh-Taylor instability. Our approach is to predict profiles of relevant variables before fully turbulent regime and use them as initial conditions for the turbulence model. We use an idealized model of mixing between two interpenetrating fluids to define the initial profiles for the turbulence model variables. Velocities and volume fractions used in the idealized mixing model are obtained respectively from a set of ordinary differential equations modeling the growth of the Rayleigh-Taylor instability and from an idealization of the density profile in the mixing layer. A comparison between predicted profiles for the turbulence model variables and profiles of the variables obtained from low Atwood number three dimensional simulations show reasonable agreement.Copyright