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.     

Heat and mass transfer study of impinging turbulent premixed flames

 Impinging jet combusting flows on granite plates are studied. A mathematical model for calculating heat release in turbulent impinging premixed flames is developed. The combustion including radiative heat transfer and local extinction effects, and flow characteristics are modeled using a finite volume computational approach. Two different eddy viscosity turbulence models, namely the standard k–ɛ and the RNG k–ɛ model with and without radiation (discrete transfer model) are assessed. The heat released predictions are compared with experimental data and the agreement is satisfactory only when both radiative heat transfer and local extinction modeling are taken into account. The results indicate that the main effect of radiation is the decrease of temperature values near the jet stagnation point and along the plate surface. Radiation increases temperature gradients and affects predicted turbulence levels independently of the closure model used. Also, the RNG k–ɛ predicts higher temperatures close the solid plate, with and without radiative heat transfer. Received on 13 November 2000 / Published online: 29 November 2001     

Radiative and convective heat transfer in hypersonic flow around a blunt body

The heat transfer in the vicinity of the critical point is investigated for hypersonic air flow around a blunt body. The gas-dynamical conservation equations are solved simultaneously with the radiative transport equation in integral form. Allowance is made for the viscosity, heat conduction, and the actual radiation parameters of air, including spectral line emission. Profiles are obtained for the thermodynamic variables along the critical line. The dependence of the radiative and convective components of the aerodynamic heating on the velocity and pressure ahead of the shock front as well as the radius of curvature of the blunt nose section is discussed. Approximate relations having the form of similarity laws are derived for the heat fluxes in the vicinity of the critical point. The limits of applicability of the thermodynamic equilibrium approximation in the shock-compressed layer are discussed. The influence of absorption of radiation from the compressed layer by the cold freestream on the aerodynamic heating is considered. Attention is given in this case to the dependence of the spectral absorption coefficient for the cold air on the intensity of the radiation incident upon it.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 112–123, September–October, 1972.     

极高超声速稀薄气体原子辐射效应的p-DSMC方法

极高超声速流动激波层内的高温导致内能模态的激发并伴随热辐射发生, 过高的温度使得空气分子完全解离, 原子组分对辐射热的贡献将达到80%以上. 本文基于优化的原子辐射模型, 提出追踪光子?直接模拟蒙特卡罗(p-DSMC)方法, 研究了稀薄流区不同马赫数下的高超声速二维圆柱绕流的壁面辐射加热, 获得了有无激发辐射效应的壁面压力和热流以及沿驻点线变化的平动、振动和转动温度. 在不考虑激发辐射效应的情况下, 得到的壁面压力和热流与已有的模拟结果符合的非常好, 误差均在5%以内, 尤其是在驻点位置, 误差在1%以内; 获得的平动、振动以及转动温度均与文献结果符合的很好. 在相同的来流条件下, 考虑辐射效应后发现, 来流速度低于10 km/s时, 辐射加热不明显, 在驻点区域, 辐射加热占对流加热比重在7%左右; 来流速度大于10 km/s时, 在驻点区域, 辐射加热占对流加热比重将超过30%. 考虑辐射效应后, 对非平衡区的平动、转动和振动温度的最大值影响不大. 此外, 另一个重要结论是, 流场中原子的浓度是影响壁面辐射热流大小的一个重要因素.      

Versatile code DLAYZ for investigating population kinetics and radiative properties of plasmas in non-local thermodynamic equilibrium

A versatile code DLAYZ based on collisional-radiative model is developed for investigating the population kinetics and radiative properties of plasmas in non-local thermodynamic equilibrium. DLAYZ is implemented on the detailed level accounting (DLA) approach and can be extended to detailed configuration accounting (DCA) and hybrid DLA/DCA approaches. The code can treat both steady state and time-dependent problems. The implementation of the main modules of DLAYZ is discussed in detail including atomic data, rates, population distributions and radiative properties modules. The complete set of basic atomic data is obtained using relativistic quantum mechanics. For dense plasmas, the basic atomic data with plasma screening effects can be obtained. The populations are obtained by solving the coupled rate equations, which are used to calculate the radiative properties. A parallelized version is implemented in the code to treat the large-scale rate equations. Two illustrative examples of a steady state case for carbon plasmas and a time-dependent case for the relaxation of a K-shell excited argon are employed to show the main features of the present code.     

Non-LTE radiation transport in high radiation plasmas

A primary goal of numerical radiation transport is obtaining a self-consistent solution for both the radiation field and plasma properties, which requires consideration of the coupling between the radiation and the plasma. The different characteristics of this coupling for continuum and line radiation have resulted in two separate sub-disciplines of radiation transport with distinct emphases and computational techniques. LTE radiation transfer focuses on energy transport and exchange through broadband radiation, primarily affecting temperature and ionization balance. Non-LTE line transfer focuses on narrowband radiation and the response of individual level populations, primarily affecting spectral properties. Many high energy density applications, particularly those with high-Z materials, incorporate characteristics of both these regimes. Applications where the radiation fields play an important role in the energy balance and include strong line components require a non-LTE broadband treatment of energy transport and exchange.We discuss these issues and present a radiation transport treatment which combines features of both approaches by explicitly incorporating the dependence of material properties on both temperature and radiation fields. The additional terms generated by the radiation dependence do not change the character of the system of equations and can easily be added to a numerical transport implementation. A numerical example from a Z-pinch application demonstrates that this method improves both the stability and convergence of the calculations. The information needed to characterize the material response to radiation is closely related to that used by the linear response matrix (LRM) approach to near-LTE simulation, and we investigate the use of the LRM for these calculations.     

Multiple time scales of fluvial processes — theory and applications

Fluvial processes comprise water flow, sediment transport and bed evolution, which normally feature distinct time scales. The time scales of sediment transport and bed deformation relative to the flow essentially measure how fast sediment transport adapts to capacity region in line with local flow scenario and the bed deforms in comparison with the flow, which literally dictates if a capacity based and/or decoupled model is justified. This paper synthesizes the recently developed multiscale theory for sediment-laden flows over erodible bed, with bed load and suspended load transport, respectively. It is unravelled that bed load transport can adapt to capacity sufficiently rapidly even under highly unsteady flows and thus a capacity model is mostly applicable, whereas a non-capacity model is critical for suspended sediment because of the lower rate of adaptation to capacity. Physically coupled modelling is critical for fluvial processes characterized by rapid bed variation. Applications are outlined on very active bed load sediment transported by flash floods and landslide dam break floods.     

Argon K-shell and bound-free emission from OMEGA direct-drive implosion cores

We discuss calculations of synthetic spectra for the interpretation and analysis of K-shell and bound-free emission from argon-doped deuterium-filled OMEGA direct-drive implosion cores. The spectra are computed using a model that considers collisional-radiative atomic kinetics, continuum-lowering, detailed Stark-broadened line shapes, line overlapping, and radiation transport effects. The photon energy range covers the moderately optically thick n = 3 → n = 1 and n = 4 → n = 1 line transitions in He- and H-like Ar, their associated satellite lines in Li- and He-like Ar, and several radiative recombination edges. At the high-densities characteristic of implosion cores, the radiative recombination edges substantially shift to lower energies thus overlapping with several line transitions. We discuss the application of the spectra to spectroscopic analysis of doped implosion cores.     

X-ray line emissions from tamped thin aluminum targets driven by subpicosecond-duration laser pulses

We report on atomic kinetics and X-ray line spectra modeling work of plasmas generated by high-intensity, ultrashort-duration pulsed lasers. Our work is motivated by the need to analyze and interpret experiments with laser-irradiated layered targets performed at the Max-Planck-Institut für Quantenoptik. The focus of this Paper is on the theoretical characterization of the properties of X-ray line emissions as signatures of plasma conditions. Our model considers several spectral features with detailed attention paid to atomic kinetics, intrinsic spectral lineshapes in a high-density plasma environment (in particular Stark broadening and line shift effects), and spectroscopic-quality radiation transport (opacity effects). We apply our model to the analysis of time-integrated K-shell aluminum X-ray line spectra and time-resolved total line intensities obtained from the layered targets. Modeling calculations indicate that red line shifts observed in these experiments cannot be explained by shifts in the centers of gravity of composite spectral features due to blending with enhanced satellite contributions, but are consistent with intrinsic line shift effects in both resonance and satellite lines. We also investigate the sensitivity of our results to the selection of one of three adopted models for laser-energy deposition and transport within the target.     

Heat exchange between a selectively emitting liquid and a laminar gas flow in the presence of an external source of radiation

An investigation is conducted in the solution of a number of practical problems of the radiative and combined heat exchange in nonuniform systems having widely different physical properties. The processes of thermal interaction between the ocean and the atmosphere have been treated in the paper [1], the effect of thermal radiation on the melting and solidification of semitransparent crystals has been investigated in [2], the flow of a selectively emitting gas around the lateral surface of an object evaporating under the action of radiative heating has been discussed in [3], and heat transfer from a jet to the molten mass of glass in a glassmaking furnace tank has been investigated in [4]. The radiative and combined heat exchange between a selectively emitting liquid and a transparent heat-conducting laminar gas flow in the case of a specified external thermal radiation field is discussed in this paper. The energy conservation equations are set up taking into account the heat transfer by radiation, convection, and molecular thermal conduction. A differential approximation is used in calculating the values of the radiation fluxes. A system of fundamental computational equations is solved by the method of finite differences and iterations and by the Runge-Kutta method. The results of the calculations are presented in the form of graphs.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 116–122, May–June, 1976.     

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.     

Construction of a collisional radiative model of complex multiple charged ions for mid- to high-Z elements

A method of constructing a compact and complete collisional radiative model of multiple charged ions of mid- to high-Z elements is proposed, for studying radiative properties of the plasmas. The proposed tungsten model, which is based on atomic data calculated by the HULLAC code, incorporates a computer algorithm to identify well-populated atomic states and dielectronic recombination channels that have a significant effect on the ionization balance. The model is validated by investigating the convergence of the mean charge and radiative power loss with respect to the size of the model, and by comparing results with other calculations presented at the nLTE kinetics workshop.     

Radiation effect on temperature distribution and NO formation in a diffusion flame under reduced gravity conditions

Combustion of hydrocarbon fuel is accompanied with the formation of nitric oxide (NO) amongst other harmful emissions. In this work, a numerical investigation has been made for understanding the effect of radiative heat transfer on temperature distribution and formation of thermal NO in a methane–air diffusion flame under different reduced gravity environments. Conservation equations of overall mass, species concentration, momentum and energy for the reactive flows have been numerically solved with the use of finite difference scheme. In addition to that a semi-empirical soot model and an optically thin radiation model have been incorporated in the simulation. Gravity level is varied by the changed values of acceleration due to gravity. A thermal NO model incorporated accounts for the NO formation process which is decoupled from the hydrocarbon combustion. The relevant conservation equations have been solved as a post combustion reaction process. The flame height drops marginally with the reduction of gravity. Temperature becomes more uniformly distributed at lower gravity. NO formation boosts up with the fall of gravity below normal level when no radiation effect is considered. However, when radiation is considered, NO formation declines marginally with the reduction of gravity levels. Also in this case, concentration values of NO compare substantially lower with those without radiation. The upsurge of NO formation due to decline in gravity; and on the other hand, a shrinkage in concentration values of NO due to radiation effect can be attributed mainly to the rise and fall of temperature respectively in the computational zone.     

Spectroscopic analysis of Cu wire array implosions on the refurbished Z generator

Experimental investigations of pinches on the refurbished Z (ZR) generator using Cu arrays have been initiated and more are planned for the near future. Significant X-ray emissions in the K-shell from moderately high atomic number plasmas such as Cu generate extreme interest. However, the production of these hard photons from high Z materials comes with a price. There is substantial loss of radiative yield due to stripping through many electrons present in high Z materials to reach to the H- or He-like ionization stages. Production of hard X-rays for materials with atomic number higher than Cu such as Kr is very difficult and theoretical predictions are even more uncertain. Previous experimental efforts using Cu as a plasma pinch load are encouraging and promote further investigations of this element on the refurbished Z machine for achieving photon energies higher than 5 keV and obtaining sufficient radiative yield. We will analyze the ionization dynamics and generate Cu spectrum using the temperature and density conditions obtained from 1-D non-LTE radiation hydrodynamics simulations of Cu wire array implosions on ZR. These results will be compared with K- and L-shell experimental spectrum of shot Z 1975. Theoretical K- and L-shell spectroscopy provides validation of atomic and plasma modeling when compared to available experimental data and also provides useful diagnostics for the plasma parameters. Our self-consistently generated non-LTE collisional-radiative model employs an extensive atomic level structure and data for all dominant atomic processes that are necessary to model accurately the pinch dynamics and the spectroscopic details of the emitted radiation.     

Non-Maxwellian electron distributions in time-dependent simulations of low-Z materials illuminated by a high-intensity X-ray laser

The interaction of high intensity X-ray lasers with matter is modeled. A collisional-radiative time-dependent module is implemented to study radiation transport in matter from ultrashort and ultraintense X-ray bursts. Inverse bremsstrahlung absorption by free electrons, electron conduction or hydrodynamic effects are not considered. The collisional-radiative system is coupled with the electron distribution evolution treated with a Fokker-Planck approach with additional inelastic terms. The model includes spontaneous emission, resonant photoabsorption, collisional excitation and de-excitation, radiative recombination, photoionization, collisional ionization, three-body recombination, autoionization and dielectronic capture. It is found that for high densities, but still below solid, collisions play an important role and thermalization times are not short enough to ensure a thermal electron distribution. At these densities Maxwellian and non-Maxwellian electron distribution models yield substantial differences in collisional rates, modifying the atomic population dynamics.     

Numerical simulation of heat,mass and momentum transport behaviours in directionally solidifying alloy castings under electromagnetic fields using an extended Direct‐SIMPLE scheme

A Direct‐SIMPLE scheme is further extended for numerical simulations of heat and species mass transfer, and liquid flow behaviours in solidification processes of shaped alloy castings under various electromagnetic (EM) fields, based on a binary continuum model (a solidification transport phenomena/processes (STP)‐based dendrite solidification model). Unlike in a SIMPLE scheme, no iterative computations are needed to achieve the final pressure and velocity corrections in the extended Direct‐SIMPLE procedure, therefore extremely high computational efforts can be avoided. Using three different types of model alloys, pseudo‐binary In718 base‐4.85 wt% Nb, γ(TiAl)‐55 at% Al and Al‐4.5 wt% Cu systems, sample computations for solving strongly coupled solidification transport phenomena in directionally solidifying shaped castings under static and harmonic EM‐fields of different strengths are carried out, to demonstrate the feasibility and efficient calculation performance of the present model and numerical methods. Copyright © 2004 John Wiley & Sons, Ltd.     

2D numerical simulation for simultaneous heat, water and gas migration in soil bed under different environmental conditions

A general mathematical model for investigating simultaneous heat, water and gas (air plus vapor) transfer in unsaturated porous soil under different environmental conditions is presented based on the volume-averaging method. Two-dimensional numerical simulation in steady state is conducted for obtaining accurate images of field characteristics in a confined soil bed, which might be useful to provide necessary information for agricultural applications. Various effects of environmental parameters, such as ambient temperature, relative humidity, radiative heat flux and wind speed, on transport processes in soil without plant roots are analyzed through the calculating results in the present paper. Received on 13 January 1998     

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.