Radiative Transfer Problem Research Articles

Transient radiative-conductive heat transfer modeling in constructional semitransparent silica ceramics

The article deals with transient radiative – conductive heat transfer investigation in constructional silica ceramics with 10% of total porosity in 2D slab geometry. An empirical model, the so-called effective thermal conductivity (ETC) approximation, and rigorous radiative heat transfer (RCHT) problem solution are compared. Effective thermal conductivity coefficients were determined by both quasi-stationary and non-stationary sample heating and corresponding conductive heat transfer inverse problem solution. Rigorous RCHT calculations were based on radiative transfer equation solution. Spectral directional-hemispherical reflectances were used for scattering and absorption coefficients determination by an identification technique. Identification was based on direct problem solution by invariant embedding technique and parametric optimization. Mie theory and independent scattering approximation with regard to scatterers (pores) size distribution were used for mean scattering cosine estimation. It was shown that in the case of non-stationary temperature regime with rapid heating and cooling stages ETC models fail to predict through the thickness temperature distribution with absolute error less than 502013100 K. The absolute value of this error is strongly affected by the heating schedule. Moreover, calculations revealed several features of the heat flux through the unheated boundary that could not be taken into considerations by effective thermal conductivity approaches.

Near-field thermal radiative transfer in assembled spherical systems composed of core-shell nanoparticles

Thermal radiative transfer can be enhanced significantly when the distance of radiation sources is smaller than the characteristic wavelength of thermal radiation. However, the problem of the near-field thermal radiative transfer (NFTRT) between core-shell nanoparticles has rarely been studied. Moreover, most previous studies investigate the NFTRT between two or three nanoparticles, while few works have been done on real many-body systems where multibody mutual interaction plays a pivotal role. In this study, we choose silicon carbide (SiC) and n-type germanium (Ge) as two constituent materials of the core-shell nanoparticle, and describe a complete theoretical investigation of the NFTRT in many body systems composed of core-shell nanoparticles. The results demonstrate that the core-shell nanoparticles inherit both characteristics of SiC and n-type Ge: quasimonochromaticity and broad-band. What’s more, the spectral features can be tuned by core-shell radius and material composition. Further studies show that multibody mutual interaction has a detrimental effect on the NFTRT between two assembled spherical systems. Still, the enhancement of NFTRTs between a small proportion of nanoparticle dimers inside the systems is observed, which can be attributed to the coherence enhancement of fluctuating thermal fields. And by analyzing the trace of a dyadic Greens functions product, the locations of inherent resonance of nanoparticles and the coherent enhancement due to multibody mutual interaction need to be consistent if we hope strong exaltation effects of NFTRT.

Line by line benchmark solutions for radiative heat transfer in 2D irregular enclosures with non-gray media

Thermal radiation heat transfer in two-dimensional complex (irregular) enclosures containing non-gray gases, namely CO2/H2O/N2 mixtures, is calculated. The meshless Natural Element Method (NEM) is used for spatial discretization and the Discrete Ordinates Method (DOM) is employed for angular discretization of the radiative transfer equation. The Line-by-Line (LBL) and the correlated-k model (CK) models are used to model the spectral radiative properties of the participating gases. To obtain the most accurate results, the updated HITEMP spectroscopic database i.e. HITEMP2010 is employed in LBL calculations and the updated parameters (based on the HITEMP2010) is used in the CK calculation. The objectives of this study are threefold: (1) to combine a meshless natural elements method with LBL and the CK spectral models for the solution of radiative transfer problems in irregular (complex) enclosures, (2) to evaluate the accuracy of the CK model by comparing its results against the LBL results, and (3) to provide benchmark solutions for radiative heat transfer in irregular enclosures with the HITEMP2010 as the most accurate spectral database at high temperatures. Calculations are carried out for isothermal/non-isothermal and homogeneous/inhomogeneous mixtures of CO2/H2O/N2 gases. The present LBL results can serve as benchmark results for validating other approximate models in gas radiation heat transfer calculations in 2D complex enclosures. Results show that the CK results are in good agreement with those of the LBL model.

Radiation forces on dust envelopes

We address in detail the radiation forces on spherical dust envelopes around luminous stars, and numerical solutions for these forces, as a first step toward more general dust geometries. Two physical quantities, a normalized force and a force-averaged radius, suffice to capture the overall effects of radiation forces; these combine to yield the radiation term in the virial theorem. In addition to the optically thin and thick regimes, the wavelength dependence of dust opacity allows for an intermediate case in which starlight is easily trapped but infrared radiation readily escapes. Scattering adds a non-negligible force in this intermediate regime. We address all three regimes analytically and provide approximate formulae for the force parameters, for arbitrary optical depth and inner dust temperature. Turning to numerical codes, we examine the convergence properties of the Monte Carlo code Hyperion run in Cartesian geometry. We calibrate both Hyperion and our analytical estimate using the DUSTY code, run in spherical geometry. We find that Monte Carlo codes tend to underestimate the radiation force when the mean free path of starlight is not well resolved, as this causes the inner dust temperature, and therefore the inner Rosseland opacity, to be too low. We briefly discuss implications for more complicated radiation transfer problems.

Discontinuous finite element method with a local numerical flux scheme for radiative transfer with strong inhomogeneity

A discontinuous finite element method (DFEM) with a local numerical flux scheme is developed for solving radiative transfer problems in participating media with strongly inhomogeneous medium properties, steep gradient source, and inhomogeneous angular radiation intensities. The discrete elements in DFEM are assumed to be discontinuous on the inner-element boundaries and the shape functions are constructed on each element. The continuity of the computation domain is maintained by modeling a numerical flux across the inner-boundaries, which makes the DFEM suitable, accurate and numerical stable for radiative transfer problems involving strong inhomogeneity. Several test cases are studied to evaluate the DFEM performance for radiative transfer equation (RTE) with strong inhomogeneity. The DFEM solutions are compared with those obtained by the meshless method and the finite element method. Our results show that the DFEM is more accurate and stable than the other two methods.

Discrete spherical harmonics method for radiative transfer in scalar planar inhomogeneous atmosphere.

The radiative transfer problems in a participating inhomogeneous scalar planar atmosphere, subjected to diffuse or collimated incidence, are investigated using the discrete spherical harmonics method. In developing the method, the radiative intensity is expanded in a finite series of Legendre polynomials and the resulting first-order coupled differential equations of radiance moments are expressed in a set of discrete polar directions. The method is applied to homogeneous/inhomogeneous atmospheres of various anisotropic scattering degrees and thicknesses, and reflective boundary conditions. The discrete spherical harmonics method albedo, transmittance, and radiative intensity predictions agree well with benchmark literature results. Additionally, numerical predictions show that the discrete spherical harmonics method using Mark boundary conditions are more efficient than using Marshak boundary conditions.

Discontinuous Galerkin finite element method for radiative heat transfer in two-dimensional media with inner obstacles

A discontinuous Galerkin finite element method (DGFEM) with unstructured meshes is presented to solve the radiative transfer equation (RTE) in two-dimensional media with inner obstacles. The computation domain is discretized into a tessellation of unstructured elements and the elements are assumed to be discontinuous on the inner-element boundaries. The shape functions are constructed on each element and the continuity of the computation domain is maintained by modeling an up-winding numerical flux across the inner boundaries, which makes the DGFEM suitable and numerical stable for radiative transfer problems involved with strong non-uniformity and discontinuity induced by ray effects. The DGFEM discretization for RTE is presented and the accuracy of DGFEM is verified. Radiative transfer problems in square and irregular media with inner obstacles are investigated, the influence of medium parameters and the obstacle shielding effects are discussed.

Graphic Processor Realization of the Formal Solution of the Problem of Radiation Transfer in the Neutron Star Atmosphere

The realization (on the CUDA platform) of the search for the formal solution to the problem of radiation transfer in the strongly magnetized plasma in the atmosphere of a neutron star on graphic processors with the CUDA architecture. The solution is obtained using the Galerkin method with finite elements. The realization of graphic processors makes it possible to substantially accelerate computations in constructing models for the atmospheres of neutron stars.

Vectorial finite elements for solving the radiative transfer equation

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

Effect of Orientation of Ice Crystals in Cirrus on Direct and Scattered Solar Radiation Fluxes

The problem of solar radiation transfer by cirrus containing horizontally oriented ice crystals urgent today is considered. The results of a complex radiation experiment are described in which solar radiation fluxes at the Earth’s surface are measured and high-level clouds are vertically sensed by a polarization lidar. The lidar allows the full backscattering phase matrix (BSPM) to be determined. The degree of orientation of ice crystals in cirrus is estimated from the form of the BSPM elements and their interrelations. It is shown experimentally for the first time that the degree of orientation of crystalline particles in cirrus has a significant effect on the direct and scattered solar radiation fluxes arriving at the Earth’s surface.

Determining the Size of Pores in a Partially Transparent Ceramics from Total-Reflection Spectra

A technique is proposed for determining the pore-size distribution based on measuring the dependence of total reflectance in the domain of partial transparency of a material. An assumption about equality of scattering-coefficient spectra determined by solving the inverse radiation transfer problem and by theoretical calculation with the Mie theory is used. The technique is applied to studying a quartz ceramics. The poresize distribution is also determined using mercury and gas porosimetry. All three methods are shown to produce close results for pores with diameters of 180 nm, the methods show differences that might be related to both specific procedural features and the structural properties of ceramics. The spectral-scattering method has a number of advantages over traditional porosimetry, and it can be viewed as a routine industrial technique.

Modeling H2O and CO2 in Optically Thick Comets Using Asymmetric Spherical Coupled Escape Probability and Application to Comet C/2009 P1 Garradd Observations of CO, H2O, and CO2

Abstract We have adapted Coupled Escape Probability, a new exact method of solving radiative transfer problems, for use in asymmetrical spherical situations for use in modeling optically thick cometary comae. Here we present the extension of our model and corresponding results for two additional primary volatile species of interest, H2O and CO2, in purely theoretical comets. We also present detailed modeling and results for the specific examples of CO, H2O, and CO2 observations of C/2009 P1 Garradd by the Deep Impact flyby spacecraft.

A discrete spherical harmonics method for radiative transfer analysis in inhomogeneous polarized planar atmosphere

A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands both the Stokes vector and the phase matrix in a finite series of generalized spherical functions and the resulting vector radiative transfer equation is expressed in a set of polar directions. Hence, the polarized characteristics of the radiance within the atmosphere at any polar direction and azimuthal angle can be determined without linearization and/or interpolations. The spatial dependent of the problem is solved using the spectral Chebyshev method. The emergent and transmitted radiative intensity and the degree of polarization are predicted for both Rayleigh and Mie scattering. The discrete spherical harmonics method predictions using 36 streams are found in good agreement with benchmark literature results. The maximum deviation between the proposed method and literature results and for absolue value of the polar directions greater than 0.1 is less than 0.5% and 0.9% for the Rayleigh and Mie scattering, respectively. These deviations for directions close to zero are about 3% and 10 % for Rayleigh and Mie scattering, respectively.

Reliable anisotropic-adaptive discontinuous Galerkin method for simplified PN approximations of radiative transfer

In this paper we present the analysis for the error estimator for radiative transfer problems presented in Giani and Seaid (2016) where we showed the capabilities of the error estimator to accurately drive the adaptivity to resolve steep boundary layers, which are among the difficulties that most numerical methods fail to resolve accurately. We prove reliability for the error estimator in terms of a global upper bound of the error measured in the natural norm. We present a series of numerical experiments to test the efficiency of this approach within a fully automated h p -adaptive refinement algorithm.

Three-dimensional polarized radiative transfer simulation using discontinuous finite element method

The polarized radiative transfer problem in three-dimensional scattering media is numerically solved by the discontinuous finite element method (DFEM). The discrete elements in the DFEM simulation are assumed to be discontinuous and the solution domain is connected by modeling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving the radiative transfer equation. The shape functions are constructed on each element and the transformations between a general element and the standard element are presented. The accuracy of the DFEM for three-dimensional polarized radiative transfer is validated by comparing DFEM solutions with the published data in the literature. The DFEM is then applied to study the polarized radiative transfer problems in a cubic medium exposed to an external beam and in a cubic medium with an emitting surface. The distributions of the Stokes vector components are obtained and discussed.

Analytical solution of the simple nonlinear radiative transfer problem

Exploring the "Principle of invariance" and the method of "Linear images", the simple nonlinear conservative problem of radiative transfer is analyzed. The solutions of nonlinear reection-transmission and internal field problems of one dimensional scattering-absorbing medium of finite optical thickness are obtained, whereas both boundaries of medium illuminated by powerful radiation beams. Using two different approaches - a direct and inverse problem, the analytical solution of the internal field problem is derived.

A New Numerical Approach to Inverse Transport Equation with Error Analysis

The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover optical properties, denoted...

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.

Time evolution of photon-pulse propagation in scattering and absorbing media: The dynamic radiative transfer system

A new dynamic-system approach to the problem of radiative transfer inside scattering and absorbing media is presented, directly based on first-hand physical principles. This method, the Dynamic Radiative Transfer System (DRTS), employs a dynamical system formality using a global sparse matrix, which characterizes the physical, optical and geometrical properties of the material-volume of interest. The new system state is generated by the above time-independent matrix, using simple matrix-vector multiplication for each subsequent time step. DRTS is capable of calculating accurately the time evolution of photon propagation in media of complex structure and shape. The flexibility of DRTS allows the integration of time-dependent sources, boundary conditions, different media and several optical phenomena like reflection and refraction in a unified and consistent way. Various examples of DRTS simulation results are presented for ultra-fast light pulse 3-D propagation, demonstrating greatly reduced computational cost and resource requirements compared to other methods.

Chebyshev collocation spectral method for radiative transfer in participating media with variable physical properties

Chebyshev collocation spectral method based on discrete ordinates equation is employed to solve radiative heat transfer problems in participating media with variable physical prosperities (including space-dependent or temperature-dependent refractive index, absorption coefficient and scattering coefficient). Discrete ordinates method is employed to discretize the solid angle domain. Chebyshev polynomial and collocation spectral method are adopted to express and discretize space domain, respectively. Numerical results obtained by the Chebyshev collocation spectral-discrete ordinates method (CCS-DOM) are presented in this paper and the results show the CCS-DOM has a good accuracy and efficiency for radiative heat transfer problems in participating media. At last, the effects of variable physical properties on radiative heat transfer are analyzed and it can be found that the distributions of refractive index, absorption coefficient and scattering coefficient have a significant effect on radiative transfer and energy distribution.