Rick M. Rauenzahn

Spectral transport model for turbulence

The spectrum of inhomogeneous turbulence is modeled by an approach that is not limited to regimes of large Reynolds numbers or small mean-flow strain rates. In its simplest form and applied to incompressible flow, the model depends on five phenomenological constants defining the strength of turbulence coupling to mean flow, turbulence transport in physical and wave-number space, and mixing of stress-tensor components. The implications for homogeneous isotropic turbulence are investigated in detail and found to correspond well to the conclusions from more fundamental theories. Under appropriate limiting conditions, a turbulent system described by the model will relax over time into a state of approximate spectral equilibrium permitting a reduction to a “one-point” model for the system that is substantially like the familiar K-ε model. This yields preliminary estimates of the present models parameters and points to the way to improved modeling of flows beyond the applicability of the K-ε method.

Three-dimensional simulation of a three-phase draft-tube bubble column

Abstract Three-dimensional simulations of a three-phase flow in conical-bottom draft-tube bubble columns were performed using a finite-volume flow simulation technique. Simulated gas volume fraction and column circulation times agree with the experimental observations of Pironti et al. ( Chemical Engineering Journal , 60 , 155–160). Furthermore, the simulations showed the same loss of column circulation as observed experimentally when the column was operated with the draft-tube in its highest position. The simulation code employed an unstructured grid method along with a multifield description of the multiphase flow dynamics. Modeled physical phenomena included momentum exchange and turbulence due to both shear and slip among phases.

Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids

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. These comparisons are made within the framework of three very different classes of flows: shear-driven, Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Overall, reasonable agreement is seen between experiments, DNS, and averaging models.

A second order self-consistent IMEX method for radiation hydrodynamics

We present a second order self-consistent implicit/explicit (methods that use the combination of implicit and explicit discretizations are often referred to as IMEX (implicit/explicit) methods [2,1,3]) time integration technique for solving radiation hydrodynamics problems. The operators of the radiation hydrodynamics are splitted as such that the hydrodynamics equations are solved explicitly making use of the capability of well-understood explicit schemes. On the other hand, the radiation diffusion part is solved implicitly. The idea of the self-consistent IMEX method is to hybridize the implicit and explicit time discretizations in a nonlinearly consistent way to achieve second order time convergent calculations. In our self-consistent IMEX method, we solve the hydrodynamics equations inside the implicit block as part of the nonlinear function evaluation making use of the Jacobian-free Newton Krylov (JFNK) method [5,20,17]. This is done to avoid order reductions in time convergence due to the operator splitting. We present results from several test calculations in order to validate the numerical order of our scheme. For each test, we have established second order time convergence.

A Consistent, Moment-Based, Multiscale Solution Approach for Thermal Radiative Transfer Problems

We present an efficient numerical algorithm for solving the time-dependent grey thermal radiative transfer (TRT) equations. The algorithm utilizes the first two angular moments of the TRT equations (Quasi-diffusion (QD)) together with the material temperature equation to form a nonlinear low-order (LO) system. The LO system is solved via the Jacobian-free Newton-Krylov method. The combined high-order (HO) TRT and LO-QD system is used to bridge the diffusion and transport scales. In addition, a “consistency” term is introduced to make the truncation error in the LO system identical to the truncation error in the HO equation. The derivation of the consistency term is rather general; therefore, it can be extended to a variety of spatial and temporal discretizations.

An Efficient and Time Accurate, Moment-Based Scale-Bridging Algorithm for Thermal Radiative Transfer Problems

We present physics-based preconditioning and a time-stepping strategy for a moment-based scale-bridging algorithm applied to the thermal radiative transfer equation. Our goal is to obtain (asymptotically) second-order time accurate and consistent solutions without nonlinear iterations between the high-order (HO) transport equation and the low-order (LO) continuum system within a time step. Modified equation analysis shows that this can be achieved via a simple predictor-corrector time stepping that requires one inversion of the transport operator per time step. We propose a physics-based preconditioning based on a combination of the nonlinear elimination technique and Fleck--Cummings linearization. As a result, the LO system can be solved efficiently via a multigrid preconditioned Jacobian-free Newton--Krylov method. For a set of numerical test problems, the physics-based preconditioner reduces the number of GMRES iterations by a factor of 3

The effects of plasma diffusion and viscosity on turbulent instability growth

\sim

Temporal accuracy of the nonequilibrium radiation diffusion equations employing a Saha ionization model

4 as compared to a standard preconditioner for advection-di...

Monte Carlo simulation methods in moment-based scale-bridging algorithms for thermal radiative-transfer problems

We perform two-dimensional simulations of strongly–driven compressible Rayleigh–Taylor and Kelvin–Helmholtz instabilities with and without plasma transport phenomena, modeling plasma species diffusion, and plasma viscosity in order to determine their effects on the growth of the hydrodynamic instabilities. Simulations are performed in hydrodynamically similar boxes of varying sizes, ranging from 1 μm to 1 cm in order to determine the scale at which plasma effects become important. Our results suggest that these plasma effects become noticeable when the box size is approximately 100 μm, they become significant in the 10 μm box, and dominate when the box size is 1 μm. Results suggest that plasma transport may be important at scales and conditions relevant to inertial confinement fusion, and that a plasma fluid model is capable of representing some of the kinetic transport effects.

High-resolution modeling of indirectly driven high-convergence layered inertial confinement fusion capsule implosions

This manuscript presents an analysis of the temporal accuracy of two first-order in time and two second-order in time integration methods as applied to a coupled radiation diffusion/reaction system of equations. These methods are categorized by their temporal order of accuracy, whether the algorithm includes operator splitting, and whether the algorithm includes linearizations. Accuracy of the different methods on three different test problems is discussed. These test problems are not new to the literature, but the purpose here is to demonstrate that it is possible to maintain second-order time accuracy on a nontrivial coupled system while employing an operator-split and linearized method.