An efficient diffusion approximation for 3D radiative transfer parameterization: application to cloudy atmospheres

The three-dimensional (3D) diffusion radiative transfer equation, which utilizes a four-term spherical harmonics expansion for the scattering phase function and intensity, has been efficiently solved by using the full multigrid numerical method. This approach can simulate the transfer of solar and thermal infrared radiation in inhomogeneous cloudy conditions with different boundary conditions and sharp boundary discontinuity. The correlated k-distribution method is used in this model for incorporation of the gaseous absorption in multiple-scattering atmospheres for the calculation of broadband fluxes and heating rates in the solar and infrared spectra. Comparison of the results computed from this approach with those computed from plane-parallel and 3D Monte Carlo models shows excellent agreement. This 3D radiative transfer approach is well suited for radiation parameterization involving 3D and inhomogeneous clouds in climate models.     

Anti-diffusive radiation flow in the cooling layer of a radiating shock

This paper shows that for systems with optically thin, hot layers, such as those that occur in radiating shocks, radiation will flow uphill: radiation will flow from low to high radiation energy density. These are systems in which the angular distribution of the radiation intensity changes rapidly in space, and in which the radiation in some region has a pancaked structure, whose effect on the mean intensity will be much larger than the effect on the scalar radiation pressure. The salient feature of the solution to the radiative transfer equation in these circumstances is that the gradient of the radiation energy density is in the same direction as the radiation flux, i.e. radiation energy is flowing uphill. Such an anti-diffusive flow of energy cannot be captured by a model where the spatial variation of the Eddington factor is not accounted for, as in flux-limited diffusion models or the P₁ equations. The qualitative difference between the two models leads to a monotonic mean intensity for the diffusion model whereas the transport mean intensity has a global maximum in the hot layer. Mathematical analysis shows that the discrepancy between the diffusion model and the transport solution is due to an approximation of exponential integrals using a simple exponential.     

The importance of thermal radiation transfer in laminar diffusion flames at normal and microgravity

The importance of radiation heat loss in laminar and turbulent diffusion flames at normal gravity has been relatively well recognized in recent years. There is currently lack of quantitative understanding on the importance of radiation heat loss in relatively small scale laminar diffusion flames at microgravity. The effects of radiation heat transfer and radiation absorption on the structure and soot formation characteristics of a coflow laminar ethylene/air diffusion flame at normal- and microgravity were numerically investigated. Numerical calculations were conducted using GRI-Mech 3.0 combustion chemistry without the NO_x mechanism and complex thermal and transport properties, an acetylene based soot formation model, and a statistical narrow-band correlated-k non-grey gas radiation model. Radiation heat transfer and radiation absorption in the microgravity flame were found to be much more important than their counterparts at normal gravity. It is important to calculate thermal radiation transfer accurately in diffusion flame modelling under microgravity conditions.     

Radiative transfer within the atmospheres of the major planets

A modified Eddington approximation is presented which describes radiative transfer due to the pressure-induced far infrared spectrum of hydrogen. When applied to the atmospheres of the major planets, the radiative transfer model produces atmospheric temperature profiles which are in good agreement with more detailed calculations. Solar absorption and infrared transmission by the fundamental bands of methane are further included for Jupiter and Saturn, resulting in a temperature inversion within both atmospheres above an altitude corresponding to a pressure of roughly 0.01 atm. This relatively high inversion region appears to be qualitatively consistent with infrared observations of methane and ammonia bands for Jupiter. Additional sources of solar absorption, consisting of the pressure-induced vibration-rotation bands of hydrogen and the overtones of the v₃ methane fundamental, are shown to have a minor effect upon the atmospheric thermal structure for Jupiter and Saturn.     

Initial-state parton shower kinematics for NLO event generators

We are developing a consistent method to combine tree-level event generators for hadron collision interactions with those including one additional QCD radiation from the initial-state partons, based on the limited leading-log (LLL) subtraction method, aiming at an application to NLO event generators. In this method, a boundary between non-radiative and radiative processes necessarily appears at the factorization scale (μ_F). The radiation effects are simulated using a parton shower (PS) in non-radiative processes. It is therefore crucial in our method to apply a PS which well reproduces the radiation activities evaluated from the matrix-element (ME) calculations for radiative processes. The PS activity depends on the applied kinematics model. In this paper we introduce two models for our simple initial-state leading-log PS: a model similar to the ’old’ PYTHIA-PS and a p_T-prefixed model motivated by ME calculations. PS simulations employing these models are tested using W-boson production at LHC as an example. Both simulations show a smooth matching to the LLL subtracted W+1 jet simulation in the p_T distribution of W bosons, and the summed p_T spectra are stable against a variation of μ_F, despite that the p_T-prefixed PS results in an apparently harder p_T spectrum.     

A numerical model for multigroup radiation hydrodynamics

We present in this paper a multigroup model for radiation hydrodynamics to account for variations of the gas opacity as a function of frequency. The entropy closure model (M₁) is applied to multigroup radiation transfer in a radiation hydrodynamics code. In difference from the previous grey model, we are able to reproduce the crucial effects of frequency-variable gas opacities, a situation omnipresent in physics and astrophysics. We also account for the energy exchange between neighbouring groups which is important in flows with strong velocity divergence. These terms were computed using a finite volume method in the frequency domain. The radiative transfer aspect of the method was first tested separately for global consistency (reversion to grey model) and against a well-established kinetic model through Marshak wave tests with frequency-dependent opacities. Very good agreement between the multigroup M₁ and kinetic models was observed in all tests. The successful coupling of the multigroup radiative transfer to the hydrodynamics was then confirmed through a second series of tests. Finally, the model was linked to a database of opacities for a Xe gas in order to simulate realistic multigroup radiative shocks in Xe. The differences with the previous grey models are discussed.     

Infrared radiative transfer modelling in a 3D scattering cloudy atmosphere: Application to limb sounding measurements of cirrus

The Monte Carlo cloud scattering forward model (McClouds_FM) has been developed to simulate limb radiative transfer in the presence of cirrus clouds, for the purposes of simulating cloud contaminated measurements made by an infrared limb sounding instrument, e.g. the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS). A reverse method three-dimensional Monte Carlo transfer model is combined with a line-by-line model for radiative transfer through the non-cloudy atmosphere to explicitly account for the effects of multiple scattering by the clouds. The ice cloud microphysics are characterised by a size distribution of randomly oriented ice crystals, with the single scattering properties of the distribution determined by accurate calculations accounting for non-spherical habit.A comparison of McClouds_FM simulations and real MIPAS spectra of cirrus shows good agreement. Of particular interest are several noticeable spectral features (i.e. H₂O absorption lines) in the data that are replicated in the simulations: these can only be explained by upwelling tropospheric radiation scattered into the line-of-sight by the cloud ice particles.     

Numerical prediction of heat transfer by natural convection and radiation in an enclosure filled with an isotropic scattering medium

This paper deals with the numerical solution for natural convection and volumetric radiation in an isotropic scattering medium within a heated square cavity using a hybrid thermal lattice Boltzmann method (HTLBM). The multiple relaxation time lattice Boltzmann method (MRT-LBM) has been coupled to the finite difference method (FDM) to solve momentum and energy equations, while the discrete ordinates method (DOM) has been adopted to solve the radiative transfer equation (RTE) using the S8 quadrature. Based on these approaches, the effects of various influencing parameters such as the Rayleigh number (Ra), the wall emissivity (ε_ι), the Planck number (Pl), and the scattering albedo (ω), have been considered. The results presented in terms of isotherms, streamlines and averaged Nusselt number, show that in absence of radiation, the temperature and the flow fields are centro-symmetrics and the cavity core is thermally stratified. However, radiation causes an overall increase in the temperature and velocity gradients along both thermally active walls. The maximum heat transfer rate is obtained when the surfaces of the enclosure walls are regarded as blackbodies. It is also seen that the scattering medium can generate a multicellular flow.     

Analysis of the R0A product in n+-p Hg1−xCdxTe photodiodes

The influence of different junction current components (diffusion current for radiative and Auger 7 recombination mechanisms, tunneling and depletion layer currents) on the R₀A product of n⁺-p -Hg_1−xCd_xTe photodiodes is considered. The considerations are carried out for the 77–300 K temperature region and 1–15 μm cutoff wavelength. Optimum doping concentrations in the p-type region of n⁺-p abrupt junctions are determined, taking into account the influence of the tunneling current and of a fixed surface charge density of the junction passivation layer. Results of calculations are compared with experimental data reported by many authors. An attempt is made to explain the discrepancy between theoretical calculations and experimental data.     

Stochastic radiative transfer in multilayer broken clouds. Part I: Markovian approach

A two-part paper describes the statistical treatment of solar radiative transfer in multilayer broken clouds. The proposed approach is a logical development of the statistical ones originally suggested for a single-layer broken clouds. This first part introduces a new statistically inhomogeneous Markovian model that allows one to properly account for different combinations of the random and maximum overlap of broken clouds at distinct vertical layers. The statistically inhomogeneous Markovian model and the stochastic radiative transfer equation have been used to derive equations for the mean radiance of solar radiation. It was demonstrated that in extreme cases the obtained equations agree with corresponding equations previously derived for (i) the statistically homogeneous broken clouds and (ii) the vertically inhomogeneous overcast clouds.     

On the possibility of determining the diffusion length of excitons in semiconductors from photomagnetic measurement data

The effect of a magnetic field on the photocurrent I_ph in Si and GaAs solar cells is investigated. It is shown that the observed change in the photocurrent I_ph of the solar cells in response to a magnetic field can be caused by a decrease in the diffusion length of excitons L_exc. A simplified model of the photomagnetic experiment is proposed to estimate the diffusion length of excitons L_exc and the contribution made by excitons to the photocurrent of the solar cells.     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.     

Critical temperature and reactant mass flux for radiative extinction of ethylene microgravity spherical diffusion flames at 1 bar

In microgravity combustion, where buoyancy is not present to accelerate the flow field and strain the flame, radiative extinction is of fundamental importance, and has implications for spacecraft fire safety. In this work, the critical point for radiative extinction is identified for normal and inverse ethylene spherical diffusion flames via atmospheric pressure experiments conducted aboard the International Space Station, as well as with a transient numerical model. The fuel is ethylene with nitrogen diluent, and the oxidizer is an oxygen/nitrogen mixture. The burner is a porous stainless-steel sphere. All experiments are conducted at constant reactant flow rate. For normal flames, the ambient oxygen mole fraction was varied from 0.2 to 0.38, burner supply fuel mole fraction from 0.13 to 1, total mass flow rate, ṁ_total, from 0.6 to 12.2 mg/s, and adiabatic flame temperature, T_ad, from 2000 to 2800 K. For inverse flames, the ambient fuel mole fraction was varied from 0.08 to 0.12, burner supply oxygen mole fraction from 0.4 to 0.85, ṁ_total from 2.3 to 11.3 mg/s, and T_ad from 2080 to 2590 K. Despite this broad range of conditions, all flames extinguish at a critical extinction temperature of 1130 K, and a fuel-based mass flux of 0.2 g/m²-s for normal flames, and an oxygen-based mass flux of 0.68 g/m²-s for inverse flames. With this information, a simple equation is developed to estimate the flame size (i.e., location of peak temperature) at extinction for any atmospheric-pressure ethylene spherical diffusion flame given only the reactant mass flow rate. Flame growth, which ultimately leads to radiative extinction if the critical extinction point is reached, is attributed to the natural development of the diffusion-limited system as it approaches steady state and the reduction in the transport properties as the flame temperature drops due to increasing flame radiation with time (radiation-induced growth.)     

Differential approximations for transient radiative transfer in refractive planar media with pulse irradiation

Transient radiative transfer in an anisotropically scattering refractive planar medium with pulse irradiation is solved by various approximation methods, such as P?1, P?1 parabolic, P_1/3 and two-flux. The time-resolved transmittance and reflectance are calculated for various radiative parameters, and are compared with those obtained by the discrete ordinate method (DOM). Among the approximation methods considered, the P_1/3 approximation is the better one, because its results are in overall good agreement with those obtained by the more rigorous DOM, except the transmittance around the peak for neither thin nor very thick slabs. It is found that the curved paths of radiation and the internal reflection of the back scattered radiation enhance the effect of scattering.     

Mechanism and kinetics of Cu2O oxidation in chemical looping with oxygen uncoupling

In chemical looping with oxygen uncoupling, oxygen carrier (OC) circulates between the fuel and air reactors to release and absorb O₂ repeatedly. In order to assess the re-oxidation characteristic of Cu-based OC in the air reactor from the microscopic mechanism and macroscopic kinetics perspective, DFT calculations and isothermal oxidation experiments were conducted. In DFT calculations, Cu₂O(111) surface was chosen as the objective surface to explore the oxygen uptake as well as the atomic transportation pathways, and to determine the rate-limiting steps basing on the energy barrier analyses. It was found that the energy barrier of the surface reaction step (0.96?eV) is smaller than that of the ions diffusion step (1.61?eV). Moreover, the Cu cations outward diffusion occurs more easily than O anions inward diffusion, which confirmed the epitaxial growth characteristic of Cu₂O oxidation. The isothermal oxidation experiments were conducted in a thermogravimetric analyzer (TGA), and about 3.5?mg CuO@TiO₂-Al₂O₃ particles within the diameter range of 75–110?µm were tested between 540 and 600 °C, where the internal and external gas diffusion effects were eliminated. Mixtures of 5.2-21.0?vol.% O₂ in N₂ were adopted as the gas agent for oxidation. Based on the understandings obtained from DFT calculations, a simple mathematical model with unknown parameters of the surface reaction process (mainly the activation energy, E_k) and ions diffusion process (mainly the activation energy, E_D) was established to describe the overall oxidation process in TGA experiments. Eventually, these unknown parameters were determined as E_k=?50.5?kJ/mol and E_k=?79.2?kJ/mol via global optimization. With the attained parameters, simulations reproduced the experimental results very well, which demonstrated that this simplification model, where grain is converted almost layer by layer but different from the feature of the shrinking core model is able to accurately describe the overall oxidation process of Cu₂O.     

Time-dependent radiative transfer using Chapman-Enskog maximum entropy method

The time-dependent problems of radiative transfer involve a coupling between radiation and material energy fields and are nonlinear because of proposed temperature dependence of the medium characteristics in semi-infinite medium with Rayleigh anisotropic scattering. By means of the limited flux, Chapman-Enskog and maximum entropy technique the time-dependent radiative transfer equation has been solved explicitly. The maximum entropy method is used to solve the resulting differential equation for radiative energy density. The calculations are carried out for temperature (normalized dimensionless) Θ(x,τ), radiative energy density and net flux with Rayleigh and anisotropic scattering for different space at different times.     

Attenuation of solar radiation by a water mist from the ultraviolet to the infrared range

A model is developed for the hemispherical transmittance of direct and scattered solar radiation from a cloudless atmosphere by a mist layer of water droplets in order to investigate the potential of water misting systems to serve as a protection from solar irradiation with particular emphasis on harmful UV radiation. The proposed model is based on published spectral experimental data for solar irradiation, Mie theory for interaction of the radiation with single spherical droplets, and radiative transfer theory. Known limiting solutions are employed to simplify the Mie calculations. The modified two-flux approximation is used to account for both direct and diffuse irradiation in lieu of a numerical solution for the full radiative transfer equation in anisotropically scattering media. The role of the governing parameters of a disperse water curtain of water droplets, water content, and droplet size for sample conditions is studied in some detail, particularly in the near-ultraviolet part of the spectrum where radiation can result in human tissue damage.     

Calculation of radiative heat transfer in argon arc plasmas

Radiation emission and absorption in arc plasmas are important energy transfer processes. Exact calculations, though possible in principle, are usually impossible in practice because of the need to treat a large number of spectral lines and also the continuum radiation in the whole spectrum range. Recently, we have used an approximate method of partial characteristics to evaluate the radiation intensities, radiation fluxes and the divergence of radiation fluxes for SF₆ arc plasma with cylindrical symmetry. In this paper, we have extended our calculations toargon arc plasmas for the plasma pressures of 0.1, 0.5 and 1.0 MPa. We have calculated the coefficients of absorption for Ar plasmas at temperatures from 300 to 35 000 K, and have used these coefficients to calculate the partial characteristics. Both the continuum and the line spectra have been included in calculations. We have taken into account the radiative photo-recombination and bremsstrahlung for the continuous spectrum, and over 500 spectral lines for the discrete spectra.The method of partial characteristics has been applied to three-dimensional calculations of radiative heat transfer — i.e. radiation intensity, radiation flux and its divergence — in simplified temperature profiles. Conclusions have been made concerning validity and utilization of the method of partial characteristics in general gas dynamics problems.     

Band-to-band recombination in GaxIn1−xSb

The carrier lifetimes in Ga_xIn_1−xSb for radiative and Auger recombination are calculated for the temperature range 77–300 K and the composition range 0 ⩽ x ⩽ 1. The possible band-to-band Auger recombination mechanisms in direct-gap semiconductors are investigated. The Auger rates are calculated, including Boltzmann statistics and nonparabolic bands, using the Kane-band model. In the low temperature range, for lightly doped material, the carrier lifetime is determined by radiative recombination. At higher temperatures the CHCC process is dominant in n-type Ga_xIn_1−xSb but in p-type material the CHLH process is dominant. The influence of CHSH processes on the carrier lifetime is appreciable in p-type GaSb. The calculations are compared with experimental data reported by other authors.     

Die Strahlungsverluste einesz-Pinches hoher Dichte

The radiative losses of a high densityz-pinch (n _e=10¹⁹cm^?3) were investigated experimentally. When the compressed column has a temperature of 10 eV, the radiative losses were determined by a special measuring method in which the vacuum UV radiation was resolved in time and recorded by means of an open photocell. This method also involved absolute, but time integrated measurement of the radiation by means of a thermopile. It was possible to achieve a certain resolution of the radiation wavelength by filling a volume between the light source and the detectors with various absorbing gases in succession. It was found that the major part of the internal energy of the plasma was lost by radiation.