Radiative Heat Transfer Calculations Research Articles

Numerical simulation of radiative heat transfer in indoor environments on programmable graphics hardware

The efficient use of energy for heating and cooling of indoor environments requires an accurate prediction and analysis of radiative heat transfer. Therefore it is necessary to use modern computer methods as otherwise the computational costs may become higher than for convective heat transfer, which is known to be a huge computational problem. A key problem in calculations of radiative heat transfer is the problem of mutual visibility arising in the determination of view factors. This is the same challenge that global illumination has to cope with which is one of the fundamental topics in computational graphics. The visibility problem is efficiently solved by modern graphics hardware. Therefore an OpenGL-based algorithm is developed to quickly and accurately calculate view factors for arbitrary, complex geometries. Theoretical and implementation details of the applied methods are given. We demonstrate the advantages of the developed computational method by a virtual test room for a tubular radiator, a heating of a warehouse by ceramic infrared heaters and the heat transfer in a car cabin.

Evaluation of gas radiation heat transfer in a 2D axisymmetric geometry using the line-by-line integration and WSGG models

The weighted-sum-of-gray-gases (WSGG) model is widely used in engineering computations of radiative heat transfer due to its relative simplicity, robustness and flexibility. This paper presents the computation of radiative heat transfer in a 2D axisymmetric chamber using two WSGG models to compute radiation in H2O and CO2 mixtures. The first model considers a fixed ratio between the molar concentrations of H2O and CO2, while the second allows the solution for arbitrary ratios. The correlations for both models are based on the HITEMP2010 database. The test case considers typical conditions found in turbulent methane flames, with steep variations in the temperature field as well as in the molar concentrations of the participating species. To assess the accuracy of the WSGG model, the results are compared with a solution obtained by line-by-line integration (LBL) of the spectrum.

Reproducing Kernel Particle Method for Radiative Heat Transfer in 1D Participating Media

The reproducing kernel particle method (RKPM), which is a Lagrangian meshless method, is employed for the calculation of radiative heat transfer in participating media. In the present method, for each discrete particle (i.e., spatial node) within a local support domain, the approximate formulas of the radiative intensity and its derivatives are constructed by the reproducing kernel interpolation function, and the residual function is obtained when these parameters are substituted into the radiative transfer equation. Then the least-squares point collocation technique (LSPCT) is introduced by minimizing the summation of residual function. Five test cases are considered and quantified to verify the meshless method, including isotropic scattering medium, first-order forward scattering medium, pure absorbing medium, absorbing scattering medium, and absorbing, scattering emitting medium. The results are in good agreement with the benchmark methods, showing the reproducing kernel particle method is an efficient, accurate, and stable method for the calculation of radiative transfer in participating media.

Accelerative iteration for coupled conductive–radiative heat transfer computation in semitransparent media

Due to the intensive coupling effect and non-linear characteristic, coupled conductive–radiative heat transfer problem in semitransparent media always consumes an enormous amount of computing time. In present work, an accelerative iteration model is developed to speed up the convergence process of this kind of coupled calculation. It promotes the iterative efficiency by revising the temperature and incident radiation of media during the iteration of energy equation and radiative transfer equation. It can remarkably reduce the computing time of coupled conductive–radiative heat transfer calculation in semitransparent media, even in the cases with complicate boundary conditions. The accuracy of present model is verified by comparing with literature and traditional source iteration method. The influences of conduction–radiation parameter, optical thickness, scattering albedo, emissivity of walls and boundary conditions are investigated as well. The results indicate that the accuracy of present model is reliable and its accelerative effect is more significant for the optically thick and scattering-dominated media with complicate boundary conditions.

Using a Parallel Spatial/Angular Agglomeration Multigrid Scheme to Accelerate the FVM Radiative Heat Transfer Computation—Part I: Methodology

A parallel spatial/angular agglomeration multigrid scheme is developed to accelerate the finite-volume method (FVM) for the computation of radiative heat transfer in absorbing, emitting, and scattering gray media. The multigrid scheme is based on the solution of the radiative transfer equation (RTE) with the full approximation scheme (FAS) on successively coarser spatial and angular resolutions, derived from the initial finest ones through the fusion of the adjacent control volumes and control angles, respectively. The numerical tests reveal the improvement of efficiency employing the aforementioned technique, especially in cases considering scattering media and reflecting boundaries.

Applicability of Phase-Function Normalization Techniques for Radiation Transfer Computation

The applicability of recently developed four phase-function (PF) normalization techniques for modeling radiation transfer in strongly anisotropic scattering media is intensively examined using the discrete-ordinates method. The three simple techniques via normalization of only the forward- and/or backward-scattering directions have been shown to reduce normalization complexity while retaining diffuse radiation computation accuracy for Henyey-Greenstein (HG) PFs. For Legendre PFs, however, such simple techniques are found to result in unphysical negative PF values at one or a few correction directions in some cases. Additionally, negative PF values can occur with these simple techniques for ballistic radiation transfer for both HG and Legendre PF types. If negative-intensity correction is applied, however, radiative heat transfer calculation can still converge regardless of the appearance of negative PF values. The relatively complex Hunter and Guo (2012) technique, in which normalization is realized through a correction matrix covering all discrete directions, is shown to be applicable for diffuse and ballistic radiation for both PF types.

Application of the weighted-sum-of-gray-gases model for media composed of arbitrary concentrations of H 2 O, CO 2 and soot

The weighted-sum-of-gray-gases (WSGG) model is widely used in engineering computations of radiative heat transfer in participating media due to its relatively simple implementation and reasonable accuracy. However, a major difficulty arises with its application to general gas mixtures where the mole ratios of the participating components are not constant. The present study presents a WSGG methodology to allow efficient, accurate computation of radiative heat transfer in mixtures of H2O, CO2, and soot with arbitrary concentrations. The method is based on first establishing independent correlations for each species, which are then combined to form the WSGG correlations for the mixture. A few test cases are presented to assess the accuracy of the two methods by comparisons with benchmark solutions obtained with the line-by-line integration (LBL) of the spectrum.

Comparisons of Radiative Heat Transfer Calculations in a Jet Diffusion Flame Using Spherical Harmonics and k-Distributions

A new nongray radiation modeling library for combustion gases has been implemented in OpenFOAM. The spectral models for single species include gray, correlation tables and full spectrum k-distributions (FSK) assembled from a narrow-band database. Mixing models for k-distributions include the multiplication and uncorrelated mixture models. Radiative transfer equation solvers for the library include spherical harmonics such as P1, P3, SP3 and SP5 as well as the optically thin approximation. The performance of the different solution methods is compared for accuracy and speed as a tool for future model strategy selection.

Taking Accurate Account of Radiative Heat Transfer for the Simulation of Core Reflooding

The reflooding of the reactor core during a loss-of-coolant accident (LOCA) in a pressurized water reactor is a rather complex conjugate heat transfer situation. In the mist flow regime downward from the quench front, the rod wall can reach temperatures up to 1400 K, and radiative heat transfer can play a significant role. The present study concerns the accurate numerical computation of radiative heat transfer throughout a subchannel with LOCA representative flow conditions resolved at a computational fluid dynamics–scale spatial discretization thus allowing the large gradients of two-phase-flow properties to be determined. The accuracy of several methods to solve the radiative transfer equations has been compared both in canonical test cases and in low-pressure LOCA conditions. The role of radiative transfer is obvious in all variables including those related to the dynamics of the flow. Analysis of the gap between the present estimation and a standard correlation has been performed. It leads to the conclusion that radiative transfer can be taken into account accurately by correlation as soon as well-defined radiative properties are considered. The transfer is very sensitive to droplet size and concentration and can be as large as the convective heat transfer.

Theoretical and Computational Research of Heat Radiant Transfer in Cylinder

In order to obtain the radiation heat transfer theory and calculation methods, the movement of the gas particles, location, intensity, temperature, are researched in cylinder under different conditions with combustion system and the mode of heat transfer. Under high temperature conditions in the cylinder, the gas radiation heat transfer is researched in the complex heat transfer theory. A statistical correlation K narrow band model, a mean absorption coefficient, a gas line databases, by-line calculation method are found, through research and analysis emissivity, transmittance, absorption coefficient, typical models, mathematical equations, database, calculation methods. Examine the distribution performance of each database for different media concentration and temperature, a statistical narrow-band band parametric model accuracy is tested, using statistical narrow band model, the results of the use of by-line method. Research shows: selected spectral database, calculation method has a greater impact on the results. The research also shows the result coincides calculations based by-line HITEWP2010 database method, whether radiant heat or wall flux, statistical narrow band model. These are supplied to the internal combustion engine cylinder design.

Radiative heat transfer in the core of axisymmetric pool fires – I: Evaluation of approximate radiative property models

Radiative heat transfer calculations are conducted in two laboratory-scale axisymmetric methane pool fires generated on a burner of 0.38 m diameter with heat release rates (HRR) of 34 and 176 kW by using the ‘exact’ Line-By-Line (LBL) method, the narrow band correlated-k (NBCK) model, the full-spectrum correlated-k (FSCK) model, the multi-scale full-spectrum k-distribution (MSFSK) model, and a grey wide-band model (WBM). For each radiative model the corresponding absorption coefficients for carbon dioxide, water vapor, carbon monoxide and methane are generated from the same high-resolution spectroscopic database. Model results show that the contribution of carbon monoxide can be neglected whereas that of methane increases with HRR. In addition, the grey approximation for soot holds for these weakly sooting flames. Comparisons with LBL solutions show that WBM fails to predict accurately the radiative heat transfer through the fuel rich core. The FSCK model presents the best compromise in terms of accuracy and computational efficiency for the 34 kW pool fire. However, significant discrepancies are observed for the 176 kW pool fire where the strong attenuation of radiation by methane invalidates the ‘correlated’ assumption of the absorption coefficient. MSFSK and NBCK models provide very accurate predictions, with the MSFSK model being more efficient when overlap parameters are tabulated as a function of temperature and composition.

Radiative Heat Transfer Through the Fuel-Rich Core of Laboratory-Scale Pool Fires

Radiative heat transfer calculations are conducted along the axis of six axisymmetric pool fires by using the “exact” line-by-line (LBL) method, the narrow band correlated k (NBCK) model, the full-spectrum correlated k (FSCK) model, the multi-scale full-spectrum k-distribution (MSFSK) model, and the wide-band model implemented in the fire dynamic simulator (FDS). The two baseline cases correspond to 34 kW and 176 kW methane pool fires generated on a burner of 0.38 m diameter. For each heat release rate, two other moderately and heavily sooting pool fires were generated by considering higher soot volume fractions while keeping temperature and gaseous species concentrations unaltered. For each radiative model, the corresponding absorption coefficients for carbon dioxide, water vapor, carbon monoxide, and methane were generated from the same high-resolution spectroscopic databases. Model results show that the contribution of carbon monoxide to the radiative intensity can be neglected, whereas that of methane increases with the heat release rate (HRR) and decreases as the soot loading increases. It is also found that the gray approximation for soot holds for the 34 kW pool fires and the weakly and moderately sooting 176 kW pool fires but ceases to be valid for the heavily sooting 176 kW pool fire. Concerning the accuracy of the different approximate radiative models, comparisons with the LBL solutions show that the NBCK model can be used as a reference if LBL solutions are not available. On the other hand, the FDS wide-band model fails in predicting accurately the radiative intensity through the fuel-rich core of pool fires. Finally, the FSCK provide predictions within 10% of LBL solutions with the exception of the heavily sooting 176 kW pool fire where the strong attenuation of radiation by methane invalidates the “correlated” assumption of the absorption coefficient. In this case, the MSFSK model must be considered, improving substantially the predictions of the FSCK.

Glass sagging simulation with improved calculation of radiative heat transfer by the optimized reciprocity Monte Carlo method

Glass sagging is used to process glass industrial products such as windscreens, mirrors or lenses. A 2D glass sagging process, simulated with the Finite Element Method (FEM), is presented in this work. Different thermal cases are reviewed with special care brought to radiative transfer model, with an optimized reciprocity Monte Carlo method used as the reference. Results show that ignoring radiative transfer is a too rough hypothesis. This leads to large errors on the glass temperature distribution, on the forming process and on the final shape in case of glass sagging without mold. However, predefining glass temperature or using Rosseland approximation give acceptable results, less accurate than Monte Carlo simulations especially for a fine prediction of the transfer as a function of time, but with smaller CPU times.

Using a High-Order Spatial/Temporal Scheme and Grid Adaptation with a Finite-Volume Method for Radiative Heat Transfer

In this work an algorithm using the finite-volume method along with a second-order-accurate spatial/temporal scheme and the h-refinement technique is evaluated in the parallelized computation of radiative heat transfer in absorbing-emitting and scattering gray media. The second-order spatial scheme is based on the reconstruction of radiative intensity's values, jointed with a slope limiter to maintain monotonicity. Additionally, the h-refinement method is incorporated to enrich targeted areas of the mesh during the solution procedure. The numerical results reveal the mitigation of false scattering and consequently the improvement of accuracy, employing these techniques in coarse unstructured hybrid grids.

A Hybrid Wavenumber Selection Scheme for Line-By-Line Photon Monte Carlo Simulations in High-Temperature Gases

Recently, it has become possible to conduct line-by-line (LBL) accurate radiative heat transfer calculations in spectrally highly nongray combustion systems using the Monte Carlo method. LBL accuracy, in principle, adds little to the computational load as compared to gray calculations. However, when employing the Monte Carlo method, the original scheme for choosing appropriate emission wavenumbers for statistical photon bundles is numerically expensive. An improved wavelength selection scheme has been applied to hypersonic plasmas for Monte Carlo solvers. However, directly applying this improved scheme to combustion gases may cause significant errors. In this paper, a hybrid scheme for wavenumber selection is proposed, significantly decreasing CPU requirements compared to previous work. The accuracy of the new method is established and its time requirements are compared against the previous method.

Using the Finite-Volume Method and Hybrid Unstructured Meshes to Compute Radiative Heat Transfer in 3-D Geometries

In this work an algorithm using the finite-volume method is presented for the parallelized computation of radiative heat transfer for absorbing, emitting, and either isotropically or anisotropically scattering gray media. Attention is mainly toward the extension of the finite-volume methodology to hybrid unstructured meshes, using a node-centered median-dual approach, with highly stretched elements at the solid wall regions, and the evaluation of its effectiveness and accuracy in such girds. As the parallelized calculation and the utilization of hybrid meshes are not common, results of the present algorithm against benchmark problems are used to demonstrate their equal potential.

Comparison of databases for radiative heat transfer calculations in combustion applications with the NBKMcK model

The NBKMcK (Narrow Band k-moment, i.e. NBKM, with the correlated-k assumption) model is used to solve the radiative transfer equation (RTE) with a Finite Volume Method along with the Discrete Ordinate Method (DOM) for the angular discretization. The parameters of the NBKMcK model can be derived from high resolution spectra and under several approaches to estimate them. The influence of the NBKM parameters has been investigated using three different approaches: (A1) numerically optimized, (A2) optically thin limit, (A3) optically thick limit. The influence of Line-by-Line (LBL) input data is also studied by comparing models based on CDSD-1000/HITEMP95 and HITEMP 2010 for each approach. Six sets of band parameters were tested for several test cases representative of combustion applications in one, two and three dimensional geometries. Results indicate that the impact of the different narrow band parameters is very limited. Spectroscopic data used to build LBL parameters have a more important impact than the technique used to build approximate parameters. Results were also compared to the Statistical Narrow Band (SNB) database from Soufiani and Taine and were found to be in satisfactory agreement.

A Comparison of Angular Discretization Strategies for Modeling Radiative Transfer in Pool Fire Simulations

Decoupled radiative heat transfer calculations of 30-cm-diameter heptane pool fire are carried out employing the P1, discrete ordinates (DO), and finite-volume (FV) methods. The DO calculations are performed employing three different quadrature schemes (level symmetric hybrid [LSH], spherical surface symmetrical equal dividing angular quadrature [SSD], and TN). By scaling the soot field in the fire, the performances of the various methods are evaluated at different optical thicknesses by employing highly angularly resolved FV calculations (512 directions) as a reference. Twenty-four angular directions in the DO and FV methods are seen to be adequate to accurately predict the distributions of the divergence of the radiative flux within the fire. The corresponding accuracies of the P1 model are seen to decrease with increase in optical thickness. In the regions away from the fire, the P1 model performs poorly in predicting the axial as well as the radial radiative fluxes, whereas the errors associated with employing coarse angular resolutions in the DO method are seen to increase with soot concentrations and distance from the pool centre. Among the DO and FV models, the accuracies of the axial and radial incident radiative flux predictions outside the fire were more dependent on the angular resolution of the calculations rather than on the particular quadrature set employed in the calculations.

Application of the Spectral Line-based Weighted-Sum-of-Gray-Gases model (SLWSGG) to the calculation of radiative heat transfer in steel reheating furnaces firing on low heating value gases

The Spectral Line-based Weighted-Sum-of-Gray-Gases (SLWSGG) model is applied to calculate the gaseous radiative properties of the aero- or oxy-combustion products of low heating value gases issued from steel making process such as Blast Furnace Gas (BFG) as well as of high heating value gases such as Coke Oven Gas (COG) and conventional Natural Gas (NG). The comparison of total emissivities shows that the 3-gray-gases SLWSGG model is in very good agreement with the Hottel and Sarofim's database. The 3-gray-gases SLWSGG model is then integrated into AnsysFluent® Discrete Ordinates method under User Defined Function and CFD simulations are performed using these combined models. The simulations are done, with full combustion-radiation coupling, for steel reheating furnaces firing on three types of gases: BFG, COG and NG. The results are compared with the simulations realized with the 1-gray-gas WSGG model available in AnsysFluent®. The comparison shows that the 1-gray-gas WSGG model highly overestimates the steel discharging temperature as compared to the 3-gray-gases SLWSGG model. Significant temperature differences are observed between the two radiative models, i.e. 116°C, 55°C and 67°C for the BFG, COG and NG cases, respectively. It can be concluded that the 3-gray-gases SLWSGG model should be used to calculate the radiation heat transfer in large industrial furnaces with more accuracy not only for low heating value gases such as BFG but also for high heating value gases such as COG and NG.

Comparison of spectral models in the computation of radiative heat transfer in participating media composed of gases and soot

Accurate combustion models are necessary to predict, among other effects, the production of pollutant gases and the heat transfer. As an important part of the combustion modeling, thermal radiation is often the dominant heat transfer mechanism, involving absorption and emission from soot and participating gases, such as water vapor and carbon dioxides. If the radiative heat transfer is not accurately predicted, the solution can lead to poor prediction of the temperature field and of the formation and distribution of the gases and soot. The modeling of the absorption coefficient of the gases is a very complex task due to its highly irregular dependence on the wavenumber. On the other hand, the absorption coefficient of the soot is known to behave linearly with the wavenumber, allowing for a simpler approach. Depending on the amount of soot, the more sophisticated and expensive gas models can be replaced by simpler ones, without considerable loss of accuracy. In this study, the radiative heat transfer for a medium composed of water vapor, carbon dioxide and soot is computed with the gray gas (GG), the weighted-sum-of-gray-gases model (WSGG), and the cumulative wavenumber (CW) models. The results are compared to benchmark line-by-line (LBL) calculations.