Advances in NLTE modeling for integrated simulations

The last few years have seen significant progress in constructing the atomic models required for non-local thermodynamic equilibrium (NLTE) simulations. Along with this has come an increased understanding of the requirements for accurately modeling the ionization balance, energy content and radiative properties of different atomic species for a wide range of densities and temperatures. Much of this progress is the result of a series of workshops dedicated to comparing the results from different codes and computational approaches applied to a series of test problems. The results of these workshops emphasized the importance of atomic model completeness, especially in doubly-excited states and autoionization transitions, to calculating ionization balance, and the importance of accurate, detailed atomic data to producing reliable spectra.We describe a simple screened-hydrogenic model that calculates NLTE ionization balance with sufficient accuracy, at a low enough computational cost for routine use in radiation-hydrodynamics codes. The model incorporates term splitting, Δn = 0 transitions, and approximate UTA widths for spectral calculations, with results comparable to those of much more detailed codes. Simulations done with this model have been increasingly successful at matching experimental data for laser-driven systems and hohlraums.Accurate and efficient atomic models are just one requirement for integrated NLTE simulations. Coupling the atomic kinetics to hydrodynamics and radiation transport constrains both discretizations and algorithms to retain energy conservation, accuracy and stability. In particular, the strong coupling between radiation and populations can require either very short time steps or significantly modified radiation transport algorithms to account for NLTE material response. Considerations such as these continue to provide challenges for NLTE simulations.     

From single-scale turbulence models to multiple-scale and subgrid-scale models by Fourier transform

A theoretical method based on mathematical physics formalism that allows transposition of turbulence modeling methods from URANS (unsteady Reynolds averaged Navier–Stokes) models, to multiple-scale models and large eddy simulations (LES) is presented. The method is based on the spectral Fourier transform of the dynamic equation of the two-point fluctuating velocity correlations with an extension to the case of non-homogenous turbulence. The resulting equation describes the evolution of the spectral velocity correlation tensor in wave vector space. Then, we show that the full wave number integration of the spectral equation allows one to recover usual one-point statistical closure whereas the partial integration based on spectrum splitting gives rise to partial integrated transport models (PITM). This latter approach, depending on the type of spectral partitioning used, can yield either a statistical multiple-scale model or subfilter transport models used in LES or hybrid methods, providing some appropriate approximations are made. Closure hypotheses underlying these models are then discussed by reference to physical considerations with emphasis on identification of tensorial fluxes that represent turbulent energy transfer or dissipation. Some experiments such as the homogeneous axisymmetric contraction, the decay of isotropic turbulence, the pulsed turbulent channel flow and a wall injection induced flow are then considered as typical possible applications for illustrating the potentials of these models.      

The Braginskii model of the Rayleigh–Taylor instability. I. Effects of self-generated magnetic fields and thermal conduction in two dimensions

There exists a substantial disagreement between computer simulation results and high-energy density laboratory experiments of the Rayleigh–Taylor instability [1]. Motivated by the observed discrepancies in morphology and growth rates, we attempt to bring simulations and experiments into better agreement by extending the classic purely hydrodynamic model to include self-generation of magnetic fields and anisotropic thermal conduction.We adopt the Braginskii formulation for transport in hot, dense plasma, implement and verify the additional physics modules, and conduct a computational study of a single-mode RTI in two dimensions with various combinations of the newly implemented modules. We analyze physics effects on the RTI mixing and flow morphology, the effects of mutual physics interactions, and the evolution of magnetic fields.We find that magnetic fields reach levels on the order of 11 MG (plasma β ≈ 9.1 × 10^?2) in the absence of thermal conduction. These fields do not affect the growth of the mixed layer but substantially modify its internal structure on smaller scales. In particular, we observe denting of the RT spike tip and generation of additional higher order modes as a result of these fields. Contrary to interpretation presented in earlier work [2], the additional mode is not generated due to modified anisotropic heat transport effects but due to dynamical effect of self-generated magnetic fields. The overall flow morphology in self-magnetized, non-conducting models is qualitatively different from models with a pre-existing uniform field oriented perpendicular to the interface. This puts the usefulness of simple MHD models for interpreting the evolution of self-magnetizing HED systems with zero-field initial conditions into doubt.The main effects of thermal conduction are a reduction of the RT instability growth rate (by about 20% for conditions considered here) and inhibited mixing on small scales. In this case, the maximum self-generated magnetic fields are weaker (approximately 1.7 MG; plasma β ≈ 49). This is due to reduction of temperature and density gradients due to conduction. These self-generated magnetic fields are of very similar strength compared to magnetic fields observed recently in HED laboratory experiments [3].We find that thermal conduction plays the dominant role in the evolution of the model RTI system considered. It smears out small-scale structure and reduces the RTI growth rate. This may account for the relatively featureless RT spikes seen in experiments, but does not explain mass extensions observed in experiments.Resistivity, related heat source terms and the thermo-electric contribution to the heat flow were not included in the present work. We estimate their impact on RTI as modest and not affecting our main conclusions. These effects will be discussed in detail in the next paper in the series.     

Fluctuations and the ionization potential in dense plasmas

A semi-analytic model is developed to estimate continuum lowering in dense plasmas including fluctuations. The model is applied to aluminum and compared with recent experiments at the Linac Coherent Light Source [O. Ciricosta et al., Phys. Rev. Lett. 109 (2012) 065002] that reported the ionization potential depression of K-shell electrons in solid density aluminum at temperatures up to 180 eV. The analysis suggests fluctuations, which are neglected in most continuum lowering models but are essential to describe energy absorption by a system, are sufficiently large to impact the interpretation of the experimental results.     

Heat transport in low-dimensional materials: A review and perspective

Heat transport is a key energetic process in materials and devices. The reduced sample size, low dimension of the problem and the rich spectrum of material imperfections introduce fruitful phenomena at nanoscale. In this review, we summarize recent progresses in the understanding of heat transport process in low-dimensional materials, with focus on the roles of defects, disorder, interfaces, and the quantummechanical effect. New physics uncovered from computational simulations, experimental studies, and predictable models will be reviewed, followed by a perspective on open challenges.     

Comparison of Flow and Transport Experiments on 3D Printed Micromodels with Direct Numerical Simulations

Understanding pore-scale flow and transport processes is important for understanding flow and transport within rocks on a larger scale. Flow experiments on small-scale micromodels can be used to experimentally investigate pore-scale flow. Current manufacturing methods of micromodels are costly and time consuming. 3D printing is an alternative method for the production of micromodels. We have been able to visualise small-scale, single-phase flow and transport processes within a 3D printed micromodel using a custom-built visualisation cell. Results have been compared with the same experiments run on a micromodel with the same geometry made from polymethyl methacrylate (PMMA, also known as Perspex). Numerical simulations of the experiments indicate that differences in experimental results between the 3D printed micromodel and the Perspex micromodel may be due to variability in print geometry and surface properties between the samples. 3D printing technology looks promising as a micromodel manufacturing method; however, further work is needed to improve the accuracy and quality of 3D printed models in terms of geometry and surface roughness.

     

Numerical simulation of flows over 2D and 3D backward-facing inclined steps

The work deals with the numerical solution of incompressible turbulent flow in a channel with a backward-facing step having various inclination angles. Also, the inclination of upper wall is considered. The mathematical model is based on the Reynolds averaged Navier–Stokes equations. The governing equations are closed by the explicit algebraic Reynolds stress (EARSM) model according to Wallin and Johansson or by linear eddy viscosity models (SST, TNT k–ω). The numerical solution is carried out by the implicit finite-volume method based on the artificial compressibility and by the finite-element method amd both approaches compared. The numerical simulations use as reference the experimental data by Makiola and Driver and Seegmiller in large aspect ratio channels. In these cases, the results are obtained by 2D and 3D simulations. Further narrow channel PIV experimental data are used as reference for 3D simulations.     

On plasma radiative properties in stellar conditions

The knowledge of stellar evolution is evolving quickly thanks to an increased number of opportunities to scrutinize the stellar internal plasma properties by stellar seismology and by 1D and 3D simulations. These new tools help us to introduce the internal dynamical phenomena in stellar modeling. A proper inclusion of these processes supposes a real confidence in the microscopic physics used, partly checked by solar or stellar acoustic modes. In the present paper we first recall which fundamental physics has been recently verified by helioseismology. Then we recall that opacity is an important ingredient of the secular evolution of stars and we point out why it is necessary to measure absorption coefficients and degrees of ionization in the laboratory for some well identified astrophysical conditions. We examine two specific experimental conditions which are accessible to large laser facilities and are suitable to solve some interesting questions of the stellar community: are the solar internal radiative interactions properly estimated and what is the proper role of the opacity in the excitation of the non-radial modes in the envelop of the β Cepheids and the Be stars? At the end of the paper we point out the difficulties of the experimental approach that we need to overcome.     

Natural convection in a liquid metal heated from above and influenced by a magnetic field

Natural convection in a liquid metal heated locally at its upper surface and affected by a vertical magnetic field is investigated both experimentally and numerically. The experiments are conducted in a cylindrical test cell of large aspect ratio which is typical for application. The cell is filled with the liquid alloy GaInSn in eutectic composition. Temperature and velocity are measured using thermocouples and an electric potential probe, respectively. In the absence of the magnetic field the experimental results indicate a dependence of the Nusselt number on the Rayleigh number according to the law Nu∝Ra^0.191. The particular value of the scaling exponent is in excellent agreement with the prediction of a scaling analysis for laminar, boundary layer-type flow in a low-Prandtl number fluid. Furthermore the experiments demonstrate that the Nusselt number and therefore the convective heat losses can be decreased by about 20% when a magnetic field of moderate strength (B=0.1 T) is present. The numerical simulations solve the Boussinesq equations in an axisymmetric geometry using a finite element method. The results of the simulations are both quantitatively and qualitatively in good agreement with the experimental observations. Deviations are attributed to the three-dimensional characteristics of the flow.     

Systematic multiscale models for deep convection on mesoscales

This paper builds on recent developments of a unified asymptotic approach to meteorological modeling [ZAMM, 80: 765–777, 2000, SIAM Proc. App. Math. 116, 227–289, 2004], which was used successfully in the development of Systematic multiscale models for the tropics in Majda and Klein [J. Atmosph. Sci. 60: 393–408, 2003] and Majda and Biello [PNAS, 101: 4736–4741, 2004]. Biello and Majda [J. Atmosph. Sci. 62: 1694–1720, 2005]. Here we account for typical bulk microphysics parameterizations of moist processes within this framework. The key steps are careful nondimensionalization of the bulk microphysics equations and the choice of appropriate distinguished limits for the various nondimensional small parameters that appear. We are then in a position to study scale interactions in the atmosphere involving moist physics. We demonstrate this by developing two systematic multiscale models that are motivated by our interest in mesoscale organized convection. The emphasis here is on multiple length scales but common time scales. The first of these models describes the short-time evolution of slender, deep convective hot towers with horizontal scale ~ 1 km interacting with the linearized momentum balance on length and time scales of (10 km/3 min). We expect this model to describe how convective inhibition may be overcome near the surface, how the onset of deep convection triggers convective-scale gravity waves, and that it will also yield new insight into how such local convective events may conspire to create larger-scale strong storms. The second model addresses the next larger range of length and time scales (10 km, 100 km, and 20 min) and exhibits mathematical features that are strongly reminiscent of mesoscale organized convection. In both cases, the asymptotic analysis reveals how the stiffness of condensation/evaporation processes induces highly nonlinear dynamics. Besides providing new theoretical insights, the derived models may also serve as a theoretical devices for analyzing and interpreting the results of complex moist process model simulations, and they may stimulate the development of new, theoretically grounded sub-grid-scale parameterizations.     

Two-phase turbulence models for simulating dense gas–particle flows

The two-fluid model is widely adopted in simulations of dense gas–particle flows in engineering facilities. Present two-phase turbulence models for two-fluid modeling are isotropic. However, turbulence in actual gas–particle flows is not isotropic. Moreover, in these models the two-phase velocity correlation is closed using dimensional analysis, leading to discrepancies between the numerical results, theoretical analysis and experiments. To rectify this problem, some two-phase turbulence models were proposed by the authors and are applied to simulate dense gas–particle flows in downers, risers, and horizontal channels; Experimental results validate the simulation results. Among these models the USM-Θ and the two-scale USM models are shown to give a better account of both anisotropic particle turbulence and particle–particle collision using the transport equation model for the two-phase velocity correlation.     

Computational and experimental analysis of supersonic air ejector: Turbulence modeling and assessment of 3D effects

Numerical and experimental analyses are performed on a supersonic air ejector to evaluate the effectiveness of commonly-used computational techniques when predicting ejector flow characteristics. Three series of experimental curves at different operating conditions are compared with 2D and 3D simulations using RANS, steady, wall-resolved models. Four different turbulence models are tested: k–ε, k–ε realizable, k–ω SST, and the stress–ω Reynolds Stress Model. An extensive analysis is performed to interpret the differences between numerical and experimental results. The results show that while differences between turbulence models are typically small with respect to the prediction of global parameters such as ejector inlet mass flow rates and Mass Entrainment Ratio (MER), the k–ω SST model generally performs best whereas ε-based models are more accurate at low motive pressures. Good agreement is found across all 2D and 3D models at on-design conditions. However, prediction at off-design conditions is only acceptable with 3D models, making 3D simulations mandatory to correctly predict the critical pressure and achieve reasonable results at off-design conditions. This may partly depend on the specific geometry under consideration, which in the present study has a rectangular cross section with low aspect ratio.     

Effect of Particle Clusters on Carrier Flow Turbulence: A Direct Numerical Simulation Study

Experiments indicate that particle clusters that form in fluidized–bed risers can enhance gas-phase velocity fluctuations. Direct numerical simulations (DNS) of turbulent flow past uniform and clustered configurations of fixed particle assemblies at the same solid volume fraction are performed to gain insight into particle clustering effects on gas-phase turbulence, and to guide model development. The DNS approach is based on a discrete-time, direct-forcing immersed boundary method (IBM) that imposes no-slip and no-penetration boundary conditions on each particle’s surface. Results are reported for mean flow Reynolds number Re _p ?=?50 and the ratio of the particle diameter d _p to Kolmogorov scale is 5.5. The DNS confirm experimental observations that the clustered configurations enhance the level of fluid-phase turbulent kinetic energy (TKE) more than the uniform configurations, and this increase is found to arise from a lower dissipation rate in the clustered particle configuration. The simulations also reveal that the particle-fluid interaction results in significantly anisotropic fluid-phase turbulence, the source of which is traced to the anisotropic nature of the interphase TKE transfer and dissipation tensors. This study indicates that when particles are larger than the Kolmogorov scale (d _p ?>?η), modeling the fluid-phase TKE alone may not be adequate to capture the underlying physics in multiphase turbulence because the Reynolds stress is anisotropic. It also shows that multiphase turbulence models should consider the effect of particle clustering in the dissipation model.     

Two-dimensional radiation MHD modeling assessment of designs for argon gas puff distributions for future experiments on the refurbished Z machine

Argon Z-pinch experiments are to be performed on the refurbished Z machine (which we will refer to as ZR here in order to distinguish between pre-refurbishment Z) at Sandia National Laboratories with a new 8 cm diameter double-annulus gas puff nozzle constructed by Alameda Applied Sciences Corporation (AASC). The gas exits the nozzle from an outer and inner annulus and a central jet. The amount of gas present in each region can be varied. Here a two-dimensional radiation MHD (2DRMHD) model, MACH2-TCRE, with tabular collisional radiative equilibrium atomic kinetics is used to theoretically investigate stability and K-shell emission properties of several measured (interferometry) initial gas distributions emanating from this new nozzle. Of particular interest is to facilitate that the distributions employed in future experiments have stability and K-shell emission properties that are at least as good as the Titan nozzle generated distribution that was successfully fielded in earlier experiments on the Z machine before it underwent refurbishment. The model incorporates a self-consistent calculation for non-local thermodynamic equilibrium kinetics and ray-trace based radiation transport. This level of detail is necessary in order to model opacity effects, non-local radiation effects, and the high temperature state of K-shell emitting Z-pinch loads. Comparisons of radiation properties and stability of measured AASC gas profiles are made with that of the distribution used in the pre-refurbished Z experiments. Based on these comparisons, an optimal K-shell emission producing initial gas distribution is determined from among the AASC nozzle measured distributions and predictions are made for K-shell yields attainable from future ZR experiments.     

Near-critical fluid hydrodynamics

In the vicinity of the gas–liquid critical point, transport coefficients of pure fluids experience important changes. In particular, the thermal diffusivity tends to zero whereas the isothermal compressibility tends to infinity. Supercritical fluids are thus as dense as liquids and much more expandable than gases. These properties make the hydrodynamic similarity parameters vary over orders of magnitude when nearing the critical point, thus leading to a large field of research. We review here four main fields: heat transfer, cavity flows, interfaces and hydrodynamic instabilities. In the first, we present a fourth adiabatic heat transfer mechanism, called the piston effect, which carries heat much faster than diffusion, in the absence of convection. In the second, we show how this heat transfer mechanism interacts with buoyant convection. In the third, we basically show that a thermally non-homogeneous near-critical fluid behaves as a two miscible-phases fluid. In the fourth, we present some specific behavior of the Rayleigh–Benard convection, as recent experiments and numerical simulations have indicated. The last part gives some pathways in the continuation of the current research. We stress the need to fully develop the hydrodynamic of highly expandable, low heat diffusing fluids since the subject is both a bearer of new physics and is needed for the development of processes in chemical engineering. To cite this article: B. Zappoli, C. R. Mecanique 331 (2003).     

Contribution of the Dusty Gas Model to Permeability/Diffusion Tests on Partially Saturated Clay Rocks

Gas transfer experiments on claystone and numerical simulations have been conducted to enhance the knowledge of gas transport in nuclear waste repositories in the Callovo-Oxfordian clay formation in Bure, France. Laboratory Gas transfer experiments were performed with a specific device dedicated to very low permeability measurement (10^?23 to 10^?20 m²). Experiments were performed on both dry and close to saturation claystone. The Dusty Gas Model, based on multi-component gas transfer equations with Knudsen diffusion, was used to describe the experimental results. The parameters obtained are the effective permeability, the Knudsen diffusion (Klinkenberg effect) and molecular diffusion coefficients and the porosity accessible to gas. Numerical simulations were carried with various boundary conditions and for different gases (helium vs hydrogen) and were compared with experiments to test the reliability of the model parameters and to better understand the mechanisms involved in clays close to saturation. The numerical simulation fitted the experimental data well whereas simpler models cannot describe the complexity of the Knudsen/Klinkenberg effects. Permeabilities lie between 10^?22 and 10^?20 m². Claystones close to saturation have an accessible porosity to gas transfer that is lower than 0.1?C1% of the porosity. Analysis of the Klinkenberg effect suggests that this accessible pore network should be made of 50?C200?nm diameter pores. It represents pore networks accessible at capillary pressure lower than 4?MPa.     

An experimental platform for creating white dwarf photospheres in the laboratory

We present an experimental platform for measuring hydrogen Balmer emission and absorption line profiles for plasmas with white dwarf (WD) photospheric conditions (T_e ～1 eV, n_e ～10¹⁷ cm^?3). These profiles will be used to benchmark WD atmosphere models, which, used with the spectroscopic method, are responsible for determining fundamental parameters (e.g., effective temperature, mass) for tens of thousands of WDs. Our experiment, performed at the Z Pulsed Power Facility at Sandia National Laboratories, uses the large amount of X-rays generated from a z-pinch dynamic hohlraum to drive plasma formation in a gas cell. The platform is unique compared to past hydrogen line profile experiments in that the plasma is radiation-driven. This decouples the heating source from the plasma to be studied in the sense that the radiation temperature causing the photoionization is independent of the initial conditions of the gas. For the first time we measure hydrogen Balmer lines in absorption at these conditions in the laboratory for the purpose of benchmarking Stark-broadened line shapes. The platform can be used to study other plasma species and to explore non-LTE, time-dependent collisional-radiative atomic kinetics.     

Validation of a numerical model for the simulation of an electrostatic powder coating process

Numerical modeling of a complete powder coating process is carried out to understand the gas-particle two-phase flow field inside a powder coating booth and results of the numerical simulations are compared with experimental data to validate the numerical results. The flow inside the coating booth is modeled as a three-dimensional turbulent continuous gas flow with solid powder particles as a discrete phase. The continuous gas flow is predicted by solving Navier–Stokes equations using a standard k–ε turbulence model with non-equilibrium wall functions. The discrete phase is modeled based on a Lagrangian approach. In the calculation of particle propagation, a particle size distribution obtained through experiments is applied. The electrostatic field, including the effect of space charge due to free ions, is calculated with the use of the user defined scalar transport equations and user defined scalar functions in the software package, FLUENT, for the electrostatic potential and charge density.     

High‐order discontinuous Galerkin nonlocal transport and energy equations scheme for radiation hydrodynamics

The nonlocal theory of the radiative energy transport in laser‐heated plasmas of arbitrary ratio of the characteristic inhomogeneity scale length to the photon mean free paths is applied to define the closure relations of a hydrodynamic system. The corresponding transport phenomena cannot be described accurately using the Chapman–Enskog approach, that is, with the usual fluid approach dealing only with local values and derivatives. Thus, we directly solve the photon transport equation allowing one to take into account the effect of long‐range photon transport. The proposed approach is based on the Bhatnagar–Gross–Krook collision operator using the photon mean free path as a unique parameter. Such an approach delivers a calculation efficiency and an inherent coupling of radiation to the fluid plasma parameters in an implicit way and directly incorporates nonequilibrium physics present under the condition of intense laser energy deposition due to inverse bremsstrahlung. In combination with a higher order discontinuous Galerkin scheme of the transport equation, the solution obeys both limiting cases, that is, the local diffusion asymptotic usually present in radiation hydrodynamics models and the collisionless transport asymptotic of free‐streaming photons. In other words, we can analyze the radiation transport closure for radiation hydrodynamics and how it behaves when deviating from the conditions of validity of Chapman–Enskog method, which is demonstrated in the case of exact steady transport and approximate multigroup diffusion numerical tests. As an application, we present simulation results of intense laser‐target interaction, where the radiative energy transport is controlled by the mean free path of photons. Copyright © 2016 John Wiley & Sons, Ltd.