Radiative Transfer Problem Research Articles

Radiative heat transfer in fractal structures

The radiative properties of most structures are intimately connected to the way in which their constituents are ordered on the nano-scale. We have proposed a new representation for radiative heat transfer formalism in many-body systems. In this representation, we explain why collective effects depend on the morphology of structures, and how the arrangement of nanoparticles and their material affects the thermal properties in many-body systems. We investigated the radiative heat transfer problem in fractal (i.e., scale invariant) structures. In order to show the effect of the structure morphology on the collective properties, the radiative heat transfer and radiative cooling are studied and the results are compared for fractal and non-fractal structures. It is shown that fractal arranged nanoparticles display complex radiative behavior related to their scaling properties. we showed that, in contrast to non-fractal structures, heat flux in fractals is not of large-range character. By using the fractal dimension as a means to describe the structure morphology, we present a universal scaling behavior that quantitatively links the structure radiative cooling to the structure gyration radius.

Improved Finite Volume Method for Three-Dimensional Radiative Heat Transfer in Complex Enclosures Containing Homogenous and Inhomogeneous Participating Media

ABSTRACTThe paper presents a modified finite volume method for the solution of the radiative transport equation, which implements the FTn angular discretization along with the bounded high-resolution curved line advection method to alleviate ray effect and false scattering, respectively, and consequently improve the accuracy of the final results. Using the blocked-off-region procedure, the present formulation is capable of treating blockage effects caused by inner/outer obstructing bodies. The developed methodology based on the combination of the above methods is evaluated against five three-dimensional test cases considering either homogenous or inhomogeneous participating media. For all cases, the predictions reveal the mitigation of false scattering and ray effects consequently the improvement of accuracy, employing this model for solving radiation heat transfer in industrial applications. In industrial application, the radiative heat transfer problem is solved for a unity boiler furnace where an inhomogeneous medium is assumed. The effects of the scattering albedo, walls emissivity and walls temperature are investigated.

Improved social spider optimization algorithms for solving inverse radiation and coupled radiation–conduction heat transfer problems

A novel bio-inspired swarm algorithm, social spider optimization (SSO), is introduced to solve the inverse transient radiation and coupled radiation–conduction problems for the first time. Based on the original model, five improved SSO (ISSO) algorithms are developed to enhance search ability and convergence velocity. The sensitivity analysis of measured signals with respect to the physical parameters of the medium are described. After which, the SSO and ISSO algorithms are applied to solve the inverse estimation problems in a one-dimensional participating medium. Two cases concerns radiative transfer problems are investigated, in which the radiative source term, extinction coefficient, scattering albedo, and scattering symmetry factor are reconstructed. Furthermore, the coupled radiation–conduction heat transfer model is considered and the main parameters such as the conduction–radiation parameter, boundary emissivity, and scattering albedo are retrieved. All retrieval results show that SSO-based algorithms are robust and effective in solving inverse estimation problems even with measurement errors. Findings also show that the proposed ISSO algorithms are superior to the original SSO model in terms of computational accuracy and convergence velocity.

The Discrete Ordinates Characteristics Solution to the One-Dimensional Radiative Transfer Equation

ABSTRACTA simple quasi-analytical method is proposed to solve the boundary-value problem of radiative transfer through a participating planar layer with reflective/transparent boundary under diffuse/collimated incident radiation. The method couples angular discretization using quadrature sets such as in the discrete ordinates method, with the solution of the system of radiative characteristics variables of first-order differential equations that were obtained after eigenvalue decomposition of the matrix obtained from media radiative characteristics such as the extinction coefficient and the scattering phase function. Henceforth, the proposed method is designated as discrete ordinates characteristics solution, to emphasize on the two aspects. The predicted radiative fluxes, hemispherical transmittance and reflectance are shown to agree with benchmark literature results for various scattering phase functions, scattering albedo, optical thicknesses and boundary conditions.

Analysis of radiative heat transfer in two-dimensional semitransparent medium with piece-wise constant refractive index

In this work, radiative heat transfer in a medium with piece-wise constant refractive index is considered. The interfaces between two different materials are smooth, thus can be treated as Fresnel surfaces. Based on the Fresnel's equations and Snell's law, the interfacial intensity formulas for the whole solid angle space considering Fresnel reflection and refraction phenomena are introduced. To solve the radiative transfer equation, the angular space is discretized by the discrete-ordinates approach, and the spatial discretization is conducted by natural element method. Radiative heat transfer problems in rectangular medium with a circle or rectangular inclusion are studied. The results show that, due to the existence of the Fresnel interface, the radiative heat transfer with piece-wise constant refractive index is much more complicate than the case with uniform refractive index, and obvious discontinuous characteristics are observed on the interface. The refractive index distributions and optical parameters greatly influence the radiative heat transfer. Several interesting phenomenon is observed and analyzed.

Performance analysis of near-field thermophotovoltaic system with 2D grating tungsten radiator

The effect of hyperbolic modes on near-field thermophotovoltaic (TPV) system performance is investigated by implementing a hyperbolic metamaterial (HMM) radiator. Specifically, the near-field TPV system consists of a 2D grating tungsten radiator and a gallium antimonide (GaSb) cell separated by a gap thickness varying between 100nm and 500nm. The temperatures of the radiator and the TPV cell are fixed at 2000K and 300K, respectively. The effective medium theory (EMT) is proposed to solve the near-field radiative heat transfer problem with a uniaxial anisotropic radiator. Near-field TPV performance is evaluated via maximum power output and conversion efficiency. Enhanced radiative heat transfer is observed within the spectral band where hyperbolic modes are supported by the radiator. As a result, the radiative heat flux absorbed by the cell is enhanced from broadband tunneling of evanescent waves. Furthermore, near-field TPV maximum power output and conversion efficiency are improved. The highest maximum power output and conversion efficiency are 4.28×105Wm−2 and 35%, respectively. When the gap thickness is smaller than 300nm, the effect of hyperbolic modes is strong, and radiative losses affect the conversion efficiency as radiative flux is enhanced both below and above the cell bandgap. For gap thicknesses larger than 300nm, the effect of hyperbolic modes is weak and the conversion efficiency is mostly affected by the spatial distribution of radiative flux absorbed in the cell. In this study, radiative heat flux enhancement and the improvement of near-field TPV performance are attributed to hyperbolic modes supported by the radiator. These findings will further contribute to the design of near-field TPV experimental systems outperforming their far-field counterparts.

Iterative discrete ordinates solution of the equation for surface-reflected radiance

This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

Comparison of the blocked-off and embedded boundary methods in radiative heat transfer problems in 2D complex enclosures at radiative equilibrium

Radiative heat transfer in participating media at radiative equilibrium in two-dimensional complex geometries will be investigated using two Cartesian boundary treatments, i.e. the blocked-off method and the embedded boundary method. The main advantages of Cartesian formulation are to simplify grid generation and using efficient Cartesian solvers for complicated problems. Angular and spatial discretization of the radiative transfer equation are performed using the discrete ordinates method and the finite volume method, respectively. The accuracy of both methods in solution of radiative heat transfer problems in irregular geometries are verified by comparison with benchmark solutions from literatures. Then, in order to investigate all features of the blocked-off and embedded boundary methods, two radiative problems with complex enclosures that contain gray absorbing and emitting medium at radiative equilibrium are examined. The results obtained from the two methods are compared with each other as well as with results obtained by body-fitted grid system. It has been shown that for a medium at radiative equilibrium with Cartesian formulation, the embedded boundary method is the method of choice, especially for calculations near the complex boundaries. It should be noted that for optically thick media, both blocked-off and embedded boundary methods show poor performance.

TRUST

The radiative transport of photons through arbitrary three-dimensional (3D) structures of dust is a challenging problem due to the anisotropic scattering of dust grains and strong coupling between different spatial regions. The radiative transfer problem in 3D is solved using Monte Carlo or Ray Tracing techniques as no full analytic solution exists for the true 3D structures. We provide the first 3D dust radiative transfer benchmark composed of a slab of dust with uniform density externally illuminated by a star. This simple 3D benchmark is explicitly formulated to provide tests of the different components of the radiative transfer problem including dust absorption, scattering, and emission. This benchmark includes models with a range of dust optical depths fully probing cases that are optically thin at all wavelengths to optically thick at most wavelengths. This benchmark includes solutions for the full dust emission including single photon (stochastic) heating as well as two simplifying approximations: One where all grains are considered in equilibrium with the radiation field and one where the emission is from a single effective grain with size-distribution-averaged properties. A total of six Monte Carlo codes and one Ray Tracing code provide solutions to this benchmark. Comparison of the results revealed that the global SEDs are consistent on average to a few percent for all but the scattered stellar flux at very high optical depths. The image results are consistent within 10%, again except for the stellar scattered flux at very high optical depths. The lack of agreement between different codes of the scattered flux at high optical depths is quantified for the first time. We provide the first 3D dust radiative transfer benchmark and validate the accuracy of this benchmark through comparisons between multiple independent codes and detailed convergence tests.

Self-generated clouds of micron-sized particles as a promising way of a Solar Probe shielding from intense thermal radiation of the Sun

An effect of shielding of an intense solar radiation towards a solar probe with the use of micron-sized SiC particles generated during ablation of a composite thermal protection material is estimated on a basis of numerical solution to a combined radiative and heat transfer problem. The radiative properties of particles are calculated using the Mie theory, and the spectral two-flux model is employed in radiative transfer calculations for non-uniform particle clouds. A computational model for generation and evolution of the cloud is based on a conjugated heat transfer problem taking into account heating and thermal destruction of the matrix of thermal protection material and sublimation of SiC particles in the generated cloud. The effect of light pressure, which is especially important for small particles, is also taken into account. The computational data for mass loss due to the particle cloud sublimation showed the low value about 1kg/m2 per hour at the distance between the vehicle and the Sun surface of about four radii of the Sun. This indicates that embedding of silicon carbide or other particles into a thermal protection layer and the resulting generation of a particle cloud can be considered as a promising way to improve the possibilities of space missions due to a significant decrease in the vehicle working distance from the solar photosphere.

A lattice Boltzmann method to simulate combined radiation–force convection heat transfer mode

Lattice Boltzmann method is extended to solve a combined mode of radiation and force convection heat transfer problem in a channel. Effects of different parameters such as radiation parameters, Peclet number, and emissivity on temperature distribution are investigated. To benchmark the accuracy of the LBM model, the results are compared by the published results of the same geometry modeled by the finite volume method. It is observed that there are good agreements between the LBM and FVM results for all cases. Moreover, the shares of advection, radiation and conduction terms in energy equation are 0.0024, 0.9974, and 0.0002, respectively, for the last one-third piece of the channel.

Incident energy transfer equation and its solution by collocation spectral method for one-dimensional radiative heat transfer

The ray-effect is a major discretization error in the approximate solution method for the radiative transfer equation (RTE). To overcome this problem, the incident energy transfer equation (IETE) is proposed. The incident energy, instead of radiation intensity, is obtained by directly solving this new equation. Good numerical properties are found for the incident energy transfer equation. To show the properties of numerical solution, the collocation spectral method (CSM) is employed to solve the incident energy transfer equation. Three test cases are taken into account to verify the performance of the incident energy transfer equation. The result shows that the radiative heat flux obtained based on IETE is much more accurate than that based on RTE, which means that the IETE is very effective in eliminating the impacts of ray-effect on the heat flux. However, on the contrary, the radiative intensity obtained based on IETE is less accurate than that based on RTE due to the ray-effect. So, this equation is more suitable for those radiative heat transfer problems, in which the radiation heat flux and incident energy are needed rather than the radiation intensity.

Transient/time-dependent radiative transfer in a two-dimensional scattering medium considering the polarization effect.

Transient/time-dependent radiative transfer in a two-dimensional scattering medium is numerically solved by the discontinuous finite element method (DFEM). The time-dependent term of the transient vector radiative transfer equation is discretized by the second-order central difference scheme and the space domain is discretized into non-overlapping quadrilateral elements by using the discontinuous finite element approach. The accuracy of the transient DFEM model for the radiative transfer equation considering the polarization effect is verified by comparing the time-resolved Stokes vector component distributions against the steady solutions for a polarized radiative transfer problem in a two-dimensional rectangular enclosure filled with a scattering medium. The transient polarized radiative transfer problems in a scattering medium exposed to an external beam and in an irregular emitting medium are solved. The distributions of the time-resolved Stokes vector components are presented and discussed.

Finite volume lattice Boltzmann scheme for neutron/radiative transfer on unstructured mesh

In this paper, we propose a novel finite volume lattice Boltzmann (FV-LB) scheme to simulate the neutron and radiative transfer problems governed by the linear Boltzmann transport equation (BTE). In the derivation of the FV-LB scheme, we utilize a multi-speed lattice Boltzmann model to reduce the linear BTE into a linear discrete velocity Boltzmann equation (DVBE). Considering the computational effectiveness and flexibility in complex geometries, we design a finite volume scheme by using the first order upwind numerical flux and solve the DVBE with the finite volume scheme on a unstructured tetrahedral or triangular mesh. The accuracy of the FV-LB scheme is verified by comparing our results with the benchmark values of three representative problems.

Implementation of SLW model in the radiative heat transfer problems with particles and high temperature gradients

PurposeThe paper aims to test the spectral line-based weighted sum of gray gases (SLW) method in axisymmetric geometries with particles and high temperature gradients.Design/methodology/approachAn SLW model is coupled with Trivic’s mean wavelength approach to estimate the radiative heat fluxes at the wall of an enclosure and to the base wall of the rocket exhaust, thereby subsequently studying the effect of concentration variation of the gases and particles in these cases. Radiative transfer equation is solved using modified discrete ordinates method. Anisotropic scattering is modeled using transport approximation.FindingsTwo cases considered show the importance of particle emission and scattering in the rocket plume base heating problems. In cases involving only gases, the concentration of H2O tends to have more impact on the flux values than any other gas.Originality/valueA full model of gases with particles in an axially varying temperature field is reported. Such cases are very common in practical applications. The present methodology gives more insight and a firm handle on the problem vis-a-vis other traditional techniques.

A modification of the narrow band-based WSGG regrouping method for computation time reduction in non-gray gas radiation analysis

In this study, a novel total spectrum-based non-gray model is proposed by modifying the narrow band-based WSGG regrouping (RG-NBW) method. Using the total weighting factor and the total absorption coefficient for each gray gas group, the required number to solve the RTE can be remarkably reduced. To verify the performance of the modified RG-NBW, three-dimensional radiative transfer problems using pure H2O gas with a uniform temperature, a non-homogeneous mixture of H2O and N2 with a uniform temperature, and a mixture of CO2, H2O and N2 with a non-uniform temperature were solved using the discrete ordinate method (DOM) with various non-gray models. The results are compared to benchmark data obtained using the ray-tracing method with the statistical narrow band (SNB) model. For all cases, the results with the modified RG-NBW model show good agreement with the benchmark results as well as results from other models. Furthermore, the modified RG-NBW model requires the shortest computational time after the WSGG model. Therefore, considering the accuracy and computational time, the modified RG-NBW model can be an efficient choice for non-gray gas radiation problems.

An iterative phase-space explicit discontinuous Galerkin method for stellar radiative transfer in extended atmospheres

A phase-space discontinuous Galerkin (PSDG) method is presented for the solution of stellar radiative transfer problems. It allows for greater adaptivity than competing methods without sacrificing generality. The method is extensively tested on a spherically symmetric, static, inverse-power-law scattering atmosphere. Results for different sizes of atmospheres and intensities of scattering agreed with asymptotic values. The exponentially decaying behavior of the radiative field in the diffusive-transparent transition region, and the forward peaking behavior at the surface of extended atmospheres were accurately captured. The integrodifferential equation of radiation transfer is solved iteratively by alternating between the radiative pressure equation and the original equation with the integral term treated as an energy density source term. In each iteration, the equations are solved via an explicit, flux-conserving, discontinuous Galerkin method. Finite elements are ordered in wave fronts perpendicular to the characteristic curves so that elemental linear algebraic systems are solved quickly by sweeping the phase space element by element. Two implementations of a diffusive boundary condition at the origin are demonstrated wherein the finite discontinuity in the radiation intensity is accurately captured by the proposed method. This allows for a consistent mechanism to preserve photon luminosity. The method was proved to be robust and fast, and a case is made for the adequacy of parallel processing. In addition to classical two-dimensional plots, results of normalized radiation intensity were mapped onto a log-polar surface exhibiting all distinguishing features of the problem studied.

The effect of BRDF surface on radiative transfer within a two-dimensional graded index medium

The traditional diffuse or specular surface assumption is insufficient to accurately characterize the reflection characteristics of a practical surface under some circumstances, which could cause distinct deviation in radiative heat transfer analysis and temperature measurements. The anisotropic reflection of a real surface can be well featured by the Bidirectional Reflectance Distribution Function (BRDF). This study aims to solve the radiative heat transfer in a two-dimensional non-uniform refractive index and anisotropic scattering medium coupled with the BRDF surface. The Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface (DRESOR) method is extended to deal with this issue. The effect of BRDF surface on the radiative heat flux and radiative intensity is investigated varying with optical thickness and scattering albedo of medium by compared to the corresponding diffuse surface. It is found that the more deviation from the diffuse characteristics the BRDF surface has, the larger difference of the radiative heat flux and intensity between the BRDF and diffuse surface there exits. The increased optical thickness and scattering albedo both decrease the difference of radiative flux on the wall between the BRDF and corresponding diffuse surface. And the influence of the reflection of the BRDF boundaries can be alleviated with thick optical thickness or large scattering capacity in the medium. The results demonstrate that the BRDF surface can impose remarkable impact on the radiative heat transfer, and an appropriate BRDF model should be introduced to be coupled with radiative transfer procedure in the accurate analysis of multi-dimensional radiative transfer problem if the boundary possesses the anisotropic reflection properties.

Transient polarized radiative transfer analysis in a scattering medium by a discontinuous finite element method.

Transient (time-dependent) polarized radiative transfer in a scattering medium exposed to an external collimated beam illumination is conducted based on the time-dependent polarized radiative transfer theory. The transient term, which persists the nanosecond order time and cannot be ignored for the time-dependent radiative transfer problems induced by a short-pulsed beam, is considered as well as the polarization effect of the radiation. A discontinuous finite element method (DFEM) is developed for the transient vector radiative transfer problem and the derivation of the discrete form of the governing equation is presented. The correctness of the developed DFEM is first verified by comparing the DFEM solutions with the results from the literature. The DFEM is then applied to study the transient polarized radiative transfer induced by a pulsed beam. The time-dependent Stokes vector components are calculated, plotted and analyzed as functions of the axis coordinate and discrete direction. Effects of the diffuse/specular boundary and the incident beam polarization state with respect to the Stokes vector components are further analyzed for cases of different boundary reflection modes and incident beam illuminations.

Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.