Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

Hydrodynamic and hydromagnetic stability

We consider multiphysics applications from algorithmic and architectural perspectives, where âalgorithmicâ includes both mathematical analysis and computational complexity, and âarchitecturalâ includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.

https://journals.sagepub.com/doi/pdf/10.1177/1094342012468181

Multiphysics simulations: Challenges and opportunities

Bubble columns are widely used for carrying out gas−liquid and gas−liquid−solid reactions in a variety of industrial applications. The dispersion and interfacial heat- and mass-transfer fluxes, which often limit the overall chemical reaction rates, are closely related to the fluid dynamics of the system through the liquid−gas contact area and the turbulence properties of the flow. There is thus considerable interest, within both academia and industry, to improve the limited understanding of the complex multiphase flow phenomena involved, which is preventing optimal scale-up and design of these reactors. In this paper, the progress reported in the literature during the past decade regarding the use of averaged Eulerian multifluid models and computational fluid dynamics (CFD) to model vertical bubble-driven flows is reviewed. The limiting steps in the model derivation are the formulation of proper boundary conditions, closure laws determining turbulent effects, interfacial transfer fluxes, and the bubble co...

Modeling of Bubble Column Reactors: Progress and Limitations

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...

/pdf/application-of-a-second-moment-closure-model-to-mixing-30i05togbp.pdf

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

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

The Implicit Continuous-fluid Eulerian (ICE) method is a finite-volume scheme that is stable for any value of the Courant number based on the sound speed. In the incompressible limit, the ICE method becomes essentially identical to the Marker and Cell (MAC) method, so the two schemes are closely related. In this article, the classical ICE method is extended to multiple interpenetrating phases, and employed with a single control volume (nonstaggered) mesh framework. The incompressible limit is preserved, so that problems involving equations of state, or those exhibiting constant material densities, can be addressed with the same computer code. The scheme reduces properly to a single-fluid method, enabling benchmarking using well-known test cases. Thus, the numerical issues focus only on those aspects unique to problems having multiple density, velocity and temperature fields. The discussion begins with a derivation of the exact, ensemble-averaged equations. Examples of the most basic closures axe given, and the well-posedness of the equations is demonstrated. The numerical method is described in operator notation, and the discretization is sketched. The flow patterns in a bubble column are computed as an incompressible flow example. For a compressible flow example, the expansion and compression of a bubble formed by high-explosivemore » gases under water is shown. In each case, comparison to experimental data is made.« less

/pdf/a-cell-centered-ice-method-for-multiphase-flow-simulations-4od0vyhr2r.pdf

A cell-centered ICE method for multiphase flow simulations

In this paper, we present the results of high-resolution simulations of the implosion of high-convergence layered indirect-drive inertial confinement fusion capsules of the type fielded on the National Ignition Facility using the xRAGE radiation-hydrodynamics code. In order to evaluate the suitability of xRAGE to model such experiments, we benchmark simulation results against available experimental data, including shock-timing, shock-velocity, and shell trajectory data, as well as hydrodynamic instability growth rates. We discuss the code improvements that were necessary in order to achieve favorable comparisons with these data. Due to its use of adaptive mesh refinement and Eulerian hydrodynamics, xRAGE is particularly well suited for high-resolution study of multi-scale engineering features such as the capsule support tent and fill tube, which are known to impact the performance of high-convergence capsule implosions. High-resolution two-dimensional (2D) simulations including accurate and well-resolved ...

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

A semi-analytic solution is described for planar radiative shock waves in the equilibrium diffusion (1−T) limit. The solution requires finding numerically the root of a polynomial and integrating a nonlinear ordinary differential equation. This solution may be used as a test problem to verify computer codes that use the equilibrium–diffusion radiation model, or for more advanced radiation models in the optically-thick limit. The structure of the shock profiles is also discussed, including new accurate estimates on the conditions for continuous solutions. We also discuss how the Zel’dovich spike may be estimated from the equilibrium diffusion solution. Finally, results from a computer code are shown to compare well with a semi-analytic solution.

Rick M. Rauenzahn

Papers

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

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

A cell-centered ICE method for multiphase flow simulations

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

Radiative shock solutions in the equilibrium diffusion limit