Evaluation of three different radiative transfer equation solvers for combined conduction and radiation heat transfer

2016 ◽  
Vol 184 ◽  
pp. 262-273 ◽  
Author(s):  
Yujia Sun ◽  
Xiaobing Zhang ◽  
John R. Howell
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Radiation Heat Transfer ◽  
Radiation Heat

An Acceleration Technique for the Computation of Participating Radiative Heat Transfer

2009 ◽  
Author(s):  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Radiation Heat Transfer ◽  
Solution Procedure ◽  
Discrete Ordinates ◽  
Average Intensity ◽  
Scattering Media ◽  
Acceleration Techniques

It is known that the finite volume and discrete ordinates methods for computing participating radiation are slow to converge when the optical thickness of the medium becomes large. This is a result of the sequential solution procedure usually employed to solve the directional intensities, which couples the ordinate directions and the energy equation loosely. Previously published acceleration techniques have sought to employ a governing equation for the angular-average of the radiation intensity to promote inter-directional coupling. These techniques have not always been successful, and even where successful, have been found to destroy the conservation properties of the radiative transfer equation. In this paper, we develop an algorithm called Multigrid Acceleration using Global Intensity Correction (MAGIC) which employs a multigrid solution of the average intensity and energy equations to significantly accelerate convergence, while ensuring that the conservative property of the radiative transfer equation is preserved. The method is shown to perform well for radiation heat transfer problems in absorbing, emitting and scattering media, both and without radiative equilibrium, and across a range of optical thicknesses.

Application of an Optimized SLW Model to Calculation of Non-Gray Radiation Heat Transfer in a Furnace

2015 ◽  
Author(s):  
Masoud Darbandi ◽  
Bagher Abrar ◽  
Gerry E. Schneider
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer Equation ◽  
Radiation Heat Transfer ◽  
Radiation Heat ◽  
Participating Media ◽  
Combustion Gas ◽  
Cross Section Spectrum ◽  
Advanced Model ◽  
Gas Medium ◽  
Heat Transfer Calculation

The spectral line based weighted sum of gray gases (SLW) model is considered as an advanced model, which can solve the radiative transfer equation (RTE) in non-gray participating media by dividing the absorption cross section spectrum into a limited number of intervals. Each interval is then treated as a gray gas medium, in which the attributed RTE should be solved separately. Therefore, the SLW model would be computationally more efficient than the other non-gray participating media solvers because it is faced with a small number of RTE solutions. In this work, we present a novel optimized SLW model and applied it to radiation heat transfer calculation in a model furnace. The current optimized SLW model with only 3 gray gases can provide accuracy close to the line-by-line (LBL) method. This is while the classic nonoptimized SLW model cannot provide the same level of accuracy imposing only 3 gray gases. Therefore, we strongly recommend the optimized SLW model to calculate the radiation heat transfer in non-gray combustion gas mixtures.

ΕΞΕΤΑΣΗ ΦΑΙΝΟΜΕΝΩΝ ΘΕΡΜΙΚΗΣ ΑΚΤΙΝΟΒΟΛΙΑΣ ΣΕ ΕΣΤΙΕΣ ΣΤΕΡΕΟΥ ΚΑΥΣΙΜΟΥ

1998 ◽  
Author(s):  
Ιωάννης Μαράκης
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Operating Conditions ◽  
Radiative Properties ◽  
Band Model ◽  
Combustion Chambers ◽  
Practical Applications

THEMATIC AREA OF THIS THESIS IS THE HEAT TRANSFER IN COMBUSTION CHAMBERS. THE ORIGINALITY ITEMS ARE CONCERNED WITH THE DEVELOPMENT OF ACCURATE METHODS BOTH FOR THE CALCULATION OF THE FLUE GAS AND COMBUSTION PARTICLE RADIATIVE PROPERTIES, AS WELL AS THE SOLUTION OF THE RADIATIVE TRANSFER EQUATION IN FURNACE - LIKE ENCLOSURES. SPECIFICALLY, THIS WORK CONTRIBUTES TO THE EXACT DETERMINATION OF THE INFLUENCE THAT THE TEMPERATURE AND PRESSURE OPERATING CONDITIONS HAVE ON THE RADIATIVE FLUXES AND SOURCE TERMS, THE LATTER BEING THE NET THERMAL ENERGY EMITTED OR ABSORBED PER UNIT VOLUME. THE THESIS INCLUDES THE DEVELOPMENT OF TWO METHODS FOR THE SOLUTION OF THE RADIATIVE TRANSFER EQUATION (A MONTE CARLO VARIANT AND A NEW INTEGRAL METHOD NAMED DIRECT NUMERICAL INTEGRATION),TWO STATISTICAL NARROW BAND AND A WIDE BAND MODEL FOR THE CALCULATION OF THE NON - GRAY GAS SPECTRAL TRANSMISSIVITY, AN ALGORITHM BASED ON MIE THEORY FOR THE DETERMINATION OF THE ABSORPTION AND SCATTERING COEFFICIENTS, THE PHASE FUNCTION AND THE ASYMMETRY PARAMETER OF COAL, CHAR, FLY - ASH AND SOOT PARTICLES AND CORRELATIONS FOR THE RESPECTIVE SPECTRAL OPTICAL PROPERTIES. THE EXACT SOLUTION OF THE THERMAL RADIATION TRANSFER HAS SIGNIFICANT PRACTICAL APPLICATIONS, SUCH AS: 1) DESIGN OF COMBUSTION CHAMBERS AND HEAT TRANSFER SURFACES, 2) DETERMINATION OF THE RADIATIVE FLUX AT THE BOUNDARIES OF A GIVEN GEOMETRY (ABSTRACT TRUNCATED)

Sphere-to-Sphere Radiative Transfer Coefficient for Packed Sphere System

2001 ◽  
Author(s):  
S. H.-K. Lee ◽  
S. C.-H. Ip ◽  
A. K. C. Wu
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Transfer Coefficient ◽  
Radiative Heat Transfer ◽  
Transfer Equation ◽  
Radiative Heat ◽  
Radiative Transfer Equation ◽  
Radiative Properties ◽  
Equation Approach ◽  
Packed Sphere

Abstract Rapid sintering is one of the most attractive metalworking technologies due to its ability to fabricate the final product with different microstructure in an economical manner. During this process, the high heating rate would induce a great thermal gradient to the sintering part. Such temperature differences affect the microstructure of the product, which in turn leads to the occurrence of microstructure defects. However, for this non-isothermal sintering, the present Radiative Transfer Equation approach or Units/Cells approach cannot effectively compute the temperature distributions inside the porous media, so as to predict the part defects. Cumbersome computations are needed for the Radiative Transfer Equation approach. For the Units/Cells approach, the use of regular assembly in the model limits the analysis of complex packed sphere systems. This study seeks to simplify the entire computational process for different packed sphere systems. By introducing a Radiative Transfer Coefficient (RTC) approach, the computation of radiative heat transfer within the porous bed can be enhanced. The newly introduced Radiative Transfer Coefficient is defined as the ratio of radiative energy exchange, including direct and indirect exchange, from the emitting sphere to the receiving sphere, which is a function of the system microstructure and radiative properties. A set of energy-balanced algebraic equations can then be established. With an appropriate initial energy guess for each sphere, these equations can be solved by the Gauss-Seidel iteration scheme, thereby computing the radiative heat transfer in packed sphere systems with different microstructures and radiative properties. The temperature for each sphere can therefore be computed right away. This model has been validated in different perspectives. With this RTC approach, the overall computational time required is significantly shorter, providing a set of fine-resolution temperature solution.

A Multiscale Method for Coupled Steady-State Heat Conduction and Radiative Transfer Equations in Composite Materials

2021 ◽  
Author(s):  
Zi-Xiang Tong ◽  
Ming-Jia Li ◽  
Yi-Si Yu ◽  
Jing-Yu Guo
Keyword(s):  
Heat Transfer ◽  
Asymptotic Expansion ◽  
Heat Conduction ◽  
Composite Materials ◽  
Radiative Transfer ◽  
Radiation Heat Transfer ◽  
Homogenization Method ◽  
Radiation Heat ◽  
Transfer Equations ◽  
Radiative Transfer Equations

Abstract The prediction of coupled conduction-radiation heat transfer in periodic composite materials is important for the application of the materials in high-temperature environment. Homogenization method is widely used for the heat conduction problem, but the coupled radiative transfer equation is seldom studied. In this work, the homogenization method is extended to the coupled conduction-radiation heat transfer in composite materials with periodic microscopic structures, in which both the heat conduction and radiative transfer equations are analyzed. The homogenized equations are obtained for the macroscopic heat transfer. The unit cell problems are also derived, which provide the effective coefficients for the homogenized equations and the local temperature and radiation corrections. The second-order asymptotic expansion of the temperature field and first-order asymptotic expansion of the radiative intensity field are established. A multiscale numerical algorithm is proposed to simulate the coupled conduction-radiation heat transfer in materials doped with isotropic or anisotropic particles. According to the numerical examples in this work, comparing with the fully-resolved simulations, the errors of the multiscale model are less than 13% for the temperature and less than 8% for the radiation. The computational time can be reduced from more than 300 hours to less than 30 minutes. Therefore, the proposed multiscale method can maintain the accuracy of the calculation and significantly improve the computational efficiency. It can provide both the average temperature and radiation for engineering utilizations and the local information corresponding to the microstructure of the composite materials.

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