Nonequilibrium Radiative Transfer Research Articles

Self-similar solutions for the non-equilibrium nonlinear supersonic Marshak wave problem

Similarity solutions to the nonlinear non-equilibrium Marshak wave problem with a time dependent radiation driving source are presented. The radiation transfer model used is the gray, non-equilibrium diffusion approximation in the supersonic regime. These solutions constitute an extension of existing non-equilibrium supersonic Marshak wave solutions, which are linear to the nonlinear regime that prevails in realistic high energy density systems. The generalized solutions assume a material model with power law temperature dependent opacities, a material energy density that is proportional to the radiation energy density, and a surface radiation temperature drive that obeys a temporal power law. The solutions are analyzed in detail, and it is shown that they take various qualitatively different forms according to the values of the opacity exponents. The solutions are used to construct a set of standardized benchmarks for supersonic non-equilibrium radiative heat transfer, which are nontrivial but straightforward to implement. These solutions are compared in detail to implicit Monte Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which demonstrates the usefulness of these solutions as a code verification test problem.

Benchmark Solutions for Radiative Transfer with a Moving Mesh and Exact Uncollided Source Treatments

The set of benchmark solutions used in the thermal radiative transfer community suffers some coverage gaps, in particular, nonlinear, nonequilibrium problems. Also, there are no nonequilibrium, optically thick benchmarks. These shortcomings motivated the development of a numerical method free from the requirement of linearity and easily able to converge on smooth optically thick problems, i.e., a moving mesh Discontinuous Galerkin framework that utilizes an uncollided source treatment. Having already proven this method on time-dependent scattering transport problems, we present here solutions to nonequilibrium thermal radiative transfer problems for familiar linearized systems together with more physical nonlinear systems in both optically thin and thick regimes, including both the full transport and the / solution. Geometric convergence is observed for smooth sources at all times and some nonsmooth sources at late times when there is local equilibrium. Also, accurate solutions are achieved for step sources when the solution is not smooth.

Control of non-equilibrium Casimir force

We introduce the concepts of the control theory into the study of non-equilibrium Casimir forces and radiative heat transfer. As an illustration, we consider the plate-plate system for non-equilibrium Casimir forces, where two dielectric plates having different temperatures are separated by a vacuum gap. Previous works have indicated that this system only supports an unstable mechanical equilibrium. Here, we prove analytically and confirm numerically that the equilibrium can be made stable through a feedback control process involving temperature measurement and modulation. Our results show that it should be fruitful to explore the concepts from control theory in the study of the Casimir force and radiative heat transfer.

Comparison of physical conditions in two phases of the solar flare of July 19, 2000 of M6.4/3N class

We study the solar flare of July 19, 2000 of M6.4/3N class, which occurred in the active region NOAA 9087. Echelle Zeeman spectrograms of this flare were obtained with the horizontal solar telescope of the Astronomical Observatory of Taras Shevchenko National University of Kyiv. Physical conditions were compared for two times corresponding to the pre-peak and peak phases of the flare in area of a small sunspot. It was found that the effective magnetic field $B$ eff by Fe I 6301.5 and Fe I 6302.5 lines was almost the same for both times and both spectral lines. However, $B$ eff in peak phase measured by the splitting of the emission peaks of Fe II and H $\upbeta $ lines turned out to be 300–500 G stronger than those by the above-mentioned Fe I lines, whereas by D3 He I line it was found to be close to zero. This may indicate a local magnetic field increase in height range from temperature minimum region to the lower chromosphere. A semi-empirical model of the photospheric layers of the flare, constructed on a base of observations of Fe I 5123.7 and Fe I 5434.5 lines by solving the inverse problem for non-equilibrium radiative transfer using Tikhonov stabilizers, shows the moderate increasing of temperature (∼300 K) in altitude range 250–500 km. The radial velocities were decreased during peak phase. The micro-turbulent velocity was increased in the photosphere layers before the flare peak, while during the peak phase it was significantly decreased. The obtained results indicate that in the pre-peak phase the altitude perturbations in the photosphere were larger than in the peak phase.

Multiscale Simulation for the System of Radiation Hydrodynamics

This paper aims at the simulation of multiple scale physics for the system of radiation hydrodynamics. The system couples the fluid dynamic equations with the radiative heat transfer. The coupled system is solved by the gas-kinetic scheme (GKS) for the compressible inviscid Euler flow and the unified gas-kinetic scheme (UGKS) for the non-equilibrium radiative transfer, together with the momentum and energy exchange between these two phases. For the radiative transfer, due to the possible large variation of fluid opacity in different regions, the transport of photons through the flow system is simulated by the multiscale UGKS, which is capable of naturally capturing the transport process from the photon’s free streaming to the diffusive wave propagation. Since both GKS and UGKS are finite volume methods, all unknowns are defined inside each control volume and are discretized consistently in the updates of hydrodynamic and radiative variables. For the coupled system, the scheme has the asymptotic preserving property, such as recovering the equilibrium diffusion limit for the radiation hydrodynamic system in the optically thick region, where the cell size is not limited by photon’s mean free path. A few test cases, such as radiative shock wave problems, are used to validate the current approach.

Solar Faculae: Microturbulence as an Indicator of Inclined Magnetic Fields

The observations of the solar facula in the Ba II λ 455.403 A line are used to construct a 3D model of the facula area by solving the inverse nonequilibrium radiative transfer problem and to investigate the fine structure of the field of unresolved velocities (microturbulence). New turbulent structures are formed in the layers of the upper photosphere. They are localized mainly between upward and downward flows with the formation of ring-shaped structures of increased turbulence around these flows. The mechanism of magnetic anisotropy of microturbulent velocity is proposed (small-scale eddy-type plasma motions mainly occur in the planes perpendicular to the magnetic field), which explains the height dependence of the field of unresolved velocities. Anisotropy of microturbulence begins to manifest itself in the lower photospheric layers outside the upward and downward flows, while it manifests itself in the higher layers inside these flows. The increase of microturbulence in the layers of the upper photosphere and the lower chromosphere in the areas between matter flows indicates the presence of inclined magnetic fields, which, along with the blurring of its spatial structure, indicates the existence of a magnetic canopy region. Microturbulence can be used as an additional tool for diagnostics of inclined magnetic fields.

On the resolution requirements for modelling molecular gas formation in solar neighbourhood conditions

The formation of molecular hydrogen (H$_2$) and carbon monoxide (CO) is sensitive to the volume and column density distribution of the turbulent interstellar medium. In this paper, we study H$_2$ and CO formation in a large set of hydrodynamical simulations of periodic boxes with driven supersonic turbulence, as well as in colliding flows with the \textsc{Flash} code. The simulations include a non-equilibrium chemistry network, gas self-gravity, and diffuse radiative transfer. We investigate the spatial resolution required to obtain a converged H$_2$ and CO mass fraction and formation history. From the numerical tests we find that H$_2$ converges at a spatial resolution of $\lesssim0.2$~pc, while the required resolution for CO convergence is $\lesssim 0.04$~pc in gas with solar metallicity which is subject to a solar neighbourhood interstellar radiation field. We derive two critical conditions from our numerical results: the simulation has to at least resolve the densities at which (1) the molecule formation time in each cell in the computational domain is equal to the dissociation time, and (2) the formation time is equal to the the typical cell crossing time. For both H$_2$ and CO, the second criterion is more restrictive. The formulae we derive can be used to check whether molecule formation is converged in any given simulation.

Analysis of thermal transport and fluid flow in high-temperature porous media solar thermochemical reactor

As a key technical indicator of porous media solar thermochemical reactor, thermal transport and fluid flow characteristics have significant impacts on hydrogen production efficiency. These issues could be achieved more efficiently and at a lower cost by applying computational fluid dynamics (CFD). However, the choice of different thermal transport models might cause the variation of results. In this study, the thermal transport and fluid flow characteristics in high-temperature porous media solar thermochemical reactor were investigated with different thermophysical models using FLUENT software user-defined functions (UDFs). The results indicate that the local thermal non-equilibrium model (LTNE) and radiative transfer model are proved to be indispensable for the thermal performance analysis of high working temperature thermochemical reacting system. Besides, Wu model of momentum source is more suitable for pressure simulation, while Wu model and Vafai model of heat transfer show little difference in temperature distribution.

Fluctuations of radiative heat exchange between two bodies

We present a theory to describe the fluctuations of nonequilibrium radiative heat transfer between two bodies both in far and near-field regime. As predicted by the blackbody theory, in far field, we show that the variance of radiative heat flux is of the same order of magnitude as its mean value. However, in near-field regime we demonstrate that the presence of surface polaritons makes this variance more than one order of magnitude larger than the mean flux. We further show that the correlation time of heat flux in this regime is comparable to the relaxation time of heat carriers in each medium. This theory could open the way to an experimental investigation of heat exchanges far from the thermal equilibrium condition.

Structure of the Long-Living Elements of Solar Granulation

Spatial and temporal variations in thermodynamic and kinematic parameters of structural elements of solar granulation are investigated by solving the inverse nonequilibrium radiative transfer problem using the observational data from the Vacuum Tower Telescope (duration of observations 2.6 h). In the lower photosphere, we have detected long-living (with lifetime up to 1.5 h) structures—trees of fragmenting granules. They occur as a result of the division of an ascending granular flow into several fragments, which can be repeated multiple times. We have found that approximately 67% of the regions with the highest positive variations of pressure correspond to the time and place of fragmentation of granular flows; approximately 12% of the regions correspond to the approach of adjacent structures.

Comparative analysis of the role of atom and ion spectral lines in radiative heating of four types of space capsules

This paper presents the results of two-dimensional calculation of radiative heating of the Fire-II, Stardust, Orion, and PPTS (Prospected Piloted Transport System, Russia) spacecraft entering the dense atmosphere of the Earth with orbital and superorbital velocities. A specificity of the simulation is the allowance for atom and ion spectral lines with use of the NERAT-ASTEROID computer platform. This computer platform is destined for solving the complete system of equations of radiative gas dynamics of viscous, heatconducting, and physically and chemically nonequilibrium gas and radiative transfer in two- and threedimensional geometries. The spectral and optical properties of high-temperature gases are calculated in the entire flow field by ab-initio quasi-classical and quantum mechanical methods. The selective heat radiation transfer was calculated by the line-by-line method on specially generated computational grids over the radiation wavelength, which make possible appreciable saving of computer resources while providing detailed description of the contours of atomic lines.

Radiative gas dynamics of the Fire-II superorbital space vehicle

The rates of convective and radiative heating of the Fire-II reentry vehicle are calculated, and the results are compared with experimental flight data. The computational model is based on solving a complete set of equations for (i) the radiative gas dynamics of a physically and chemically nonequilibrium viscous heatconducting gas and (ii) radiative transfer in 2D axisymmetric statement. The spectral optical parameters of high-temperature gases are calculated using ab initio quasi-classical and quantum-mechanical methods. The transfer of selective thermal radiation in terms of atomic lines is calculated using the line-by-line method on a specially generated computational grid that is nonuniform in radiation wavelength.

Diagnostics of the solar atmosphere by the Non-LTE inversion method: Line of Ba II λ 455.403 nm

The inverse problem of nonequilibrium radiative transfer in the Ba II λ 455.403 nm line is solved taking into account the hyperfine structure and isotopic splitting. Diagnostic capabilities of this line for the study of the solar atmosphere are investigated based on the three-dimensional hydrodynamic model. It is shown that the use of inversion methods for the analysis of the observed Ba II λ 455.403 nm line makes it possible to reproduce physical conditions in the layers of the photosphere and the lower chromosphere (0 < h < 600 km) with a correlation coefficient of 0.9.

Modeling near-field radiative heat transfer from sharp objects using a general three-dimensional numerical scattering technique

We develop a general numerical method to calculate the nonequilibrium radiative heat transfer between a plate and compact objects of arbitrary shapes, making the first accurate theoretical predictions for the total heat transfer and the spatial heat flux profile for three-dimensional compact objects including corners or tips. In contrast to the known sphere-plate heat transfer, we find qualitatively different scaling laws for cylinders and cones at small separations, and, in contrast to a flat or slightly curved object, a sharp cone exhibits a local minimum in the spatially resolved heat flux directly below the tip. Our results may have important implications for near-field thermal writing and surface roughness.

Entropy flow, entropy generation, exergy flux, and optimal absorbing temperature in radiative transfer between parallel plates

Taking nonequilibrium radiative heat transfer between two surfaces as an example, the nonequilibrium thermodynamics of radiation is studied and discussed. The formulas of entropy flow, entropy generation, exergy flux, and optimal temperature of absorbing surface for maximum exergy output are derived. The result is a contribution to the thermodynamic analysis and optimization of solar energy utilization and can be applied in more complex radiative heat transfer cases.

Time-dependent simplified PN approximation to the equations of radiative transfer

The steady-state simplified PN approximation to the radiative transport equation has been successfully applied to many problems involving radiation. This paper presents the derivation of time-dependent simplified PN (SPN) equations (up to N=3) via two different approaches. First, we use an asymptotic analysis, similar to the asymptotic derivation of the steady-state SPN equations. Second, we use an approach similar to the original derivation of the steady-state SPN equations and we show that both approaches lead to similar results. Special focus is put on the well-posedness of the equations and the question whether it can be guaranteed that the solution satisfies the correct physical bounds. Several numerical test cases are shown, including an analytical benchmark due to Su and Olson [B. Su, G.L. Olson, An analytical benchmark for non-equilibrium radiative transfer in an isotropically scattering medium, Ann. Nucl. Energy 24 (1997) 1035–1055.].

Angularly adaptive [formula omitted]–double [formula omitted] flux-limited diffusion solutions of non-equilibrium grey radiative transfer problems

The double spherical harmonics angular approximation in the lowest order, i.e. double P 0 ( DP 0 ), is developed for the solution of time-dependent non-equilibrium grey radiative transfer problems in planar geometry. Although the DP 0 diffusion approximation is expected to be less accurate than the P 1 diffusion approximation at and near thermodynamic equilibrium, the DP 0 angular approximation can more accurately capture the complicated angular dependence near a non-equilibrium radiation wave front. In addition, the DP 0 approximation should be more accurate in non-equilibrium optically thin regions where the positive and negative angular domains are largely decoupled. We develop an adaptive angular technique that locally uses either the DP 0 or P 1 flux-limited diffusion approximation depending on the degree to which the radiation and material fields are in thermodynamic equilibrium. Numerical results are presented for two test problems due to Su and Olson and to Ganapol and Pomraning for which semi-analytic transport solutions exist. These numerical results demonstrate that the adaptive P 1 – DP 0 diffusion approximation can yield improvements in accuracy over the standard P 1 diffusion approximation, both without and with flux-limiting, for non-equilibrium grey radiative transfer.

Theoretical light curves for deflagration models of type Ia supernova

Aims. We present synthetic bolometric and broad-band UBVRI light curves of SNe Ia for four selected 3D deflagration models of thermonuclear supernovae. Methods. The light curves are computed with the 1D hydro code stella, which models (multi-group time-dependent) nonequilibrium radiative transfer inside SN ejecta. Angle-averaged results from 3D hydrodynamical explosion simulations with the composition determined in a nucleosynthetic postprocessing step served as the input to the radiative transfer model. Results. The predicted model UBV light curves do agree reasonably well with the observed ones for SNe Ia in the range of low to normal luminosities, although the underlying hydrodynamical explosion models produced only a modest amount of radioactive 56 Ni (i.e. ∼0.24–0.42 M� ) and relatively low kinetic energy in the explosion (less than 0.7 × 10 51 erg). The evolution of predicted B and ∞

Parameters of the classical type-IIP supernova SN 1999em

Based on observations of SN 1999em, we determined the physical parameters of this supernova using hydrodynamic calculations including nonequilibrium radiative transfer. Taking the distance to SN 1999em estimated by the expanding photosphere method (EPM) to be D = 7.5 Mpc, we found the parameters of the presupernova: radius R = 450R⊙, mass M = 15M⊙, and explosion energy E = 7 × 1050 erg. For the distance D = 12 Mpc determined from Cepheids, R, M, and E must be increased to the following values: R = 1000R⊙, M = 18M⊙, and E = 1051 erg. We show that one cannot restrict oneself to using the simple analytical formulas relating the supernova and presupernova parameters to obtain reliable parameters for type-IIP presupernovae.

Type Ia Supernova models: Latest developments

Supernovae of type Ia (SNe Ia) are very important for cosmography. To exclude systematic effects in linking the observed light of distant SNe Ia to the parameters of cosmological models, one has to understand the nature of supernova outbursts and to build accurate algorithms for predicting their emission. We review the recent progress of modeling the propagation of nuclear flame subject to numerous hydrodynamic instabilities inherent to the flame front. The Rayleigh-Taylor (RT) instability is the main process governing the corrugation of the front on the largest scales, while on the smallest scales the front propagation is controlled by the Landau-Darrieus instability. Based on several hydrodynamic explosion models, we predict the broad-band UBVI and bolometric light curves of SNe Ia, using our 1D-hydro code which models multi-group time-dependent non-equilibrium radiative transfer inside SN ejecta. We employ our new corrected treatment for line opacity in the expanding medium, which is important especially in UV and IR bands. The results are compared with the observed light curves. Especially interesting is a recent 3D-deflagration model computed at MPA, Garching, by M. Reinecke et al.