Scale Modeling of Radiation in Enclosures With Absorbing/Emitting and Isotropically Scattering Media

1987 ◽  
Vol 109 (2) ◽  
pp. 470-477 ◽  
Author(s):  
Hsing-Pang Liu ◽  
J. R. Howell
Keyword(s):  
Heat Transfer ◽  
Factor Analysis ◽  
Optical Thickness ◽  
Energy Exchange ◽  
Isotropic Scattering ◽  
Scattering Medium ◽  
Scattering Media ◽  
Participating Media ◽  
Pure Radiation ◽  
Scale Modeling

Exchange factor analysis has been shown to be an alternative to zonal analysis in enclosures with participating media. An experimental measurement of exchange factors for a cubic enclosure has been done, and practical problems associated with the measurements are discussed. The effects of isotropic scattering and absorption-isotropic re-emission processes are known to be the same for their contribution to energy exchange paths in systems with equal optical thickness. The measurement of these exchange factors is achieved by using an enclosure containing a near-isotropically scattering medium. The heat transfer results for the pure radiation case are demonstrated by using these experimentally determined exchange factors in the analysis, and are compared with the analytical results.

Simulation of Radiation Heat Transfer of Three Dimensional Participating Media by Radiative Exchange Method

2008 ◽  
Author(s):  
Mohammad Hadi Bordbar ◽  
Timo Hyppa¨nen
Keyword(s):  
Heat Transfer ◽  
Balance Equation ◽  
Radiation Heat Transfer ◽  
Three Dimensional ◽  
Radiation Balance ◽  
Scattering Media ◽  
Radiation Heat ◽  
Exchange Method ◽  
Participating Media ◽  
Radiative Exchange

This paper describes the theoretical bases of the Radiative Exchange Method, a new numerical method for simulating radiation heat transfer. By considering radiative interaction between all points of the geometry and solving the radiation balance equation in a mesh structure coarser than the structure used in computational fluid flow calculation, this method is able to simulate radiative heat transfer in arbitrary 3D space with absorbing, emitting and scattering media surrounded by emitting, absorbing and reflecting surfaces. A new concept is introduced, that of the exchange factors between the different elements that are necessary for completing the radiative balance equation set. Using this method leads to a set of algebraic equations for the radiative outgoing power from each coarse cell being produced and the result of this set of equations was then used to calculate the volumetric radiative source term in the fine cell structure. The formulation of the exchange factor for a three-dimensional state and also a mesh size analysis that was conducted to optimize the accuracy and runtime are presented. The results of this model to simulate typical 3D furnace shape geometry, is verified by comparison with those of other numerical methods.

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

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Lei Mu ◽  
Zhi-hong He ◽  
Shi-kui Dong
Keyword(s):  
Heat Transfer ◽  
Meshless Method ◽  
Radiative Heat ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Reproducing Kernel Particle Method ◽  
Scattering Medium ◽  
Residual Function ◽  
Participating Media ◽  
Reproducing Kernel Particle

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.

Scaling Anisotropic Scattering in Radiation Heat Transfer for a Planar Medium

1982 ◽  
Vol 104 (1) ◽  
pp. 68-75 ◽  
Author(s):  
H. Lee ◽  
R. O. Buckius
Keyword(s):  
Heat Transfer ◽  
Radiation Heat Transfer ◽  
Anisotropic Scattering ◽  
Isotropic Scattering ◽  
Scattering Medium ◽  
Radiation Heat ◽  
Scattering Problems ◽  
Solution Methods ◽  
The One ◽  
Planar Medium

Radiation heat transfer in a planar participating medium which scatters anisotropically is scaled to an isotropically scattering medium. Only isotropic scattering problems need to be solved with a scaled optical depth and albedo. The scaling is derived from approximate solution methods to the equation of transfer. From the P-1 approximation, the two-flux method, and the modified linear anisotropic scattering model, three scalings are derived. The scaling that gives the best results when comparing the scaled solutions to exact solutions is the one derived from the P-1 approximation.

A Conservative Formulation of the Discrete Transfer Method

1997 ◽  
Vol 119 (1) ◽  
pp. 118-128 ◽  
Author(s):  
P. J. Coelho ◽  
M. G. Carvalho
Keyword(s):  
Heat Transfer ◽  
Energy Conservation ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Three Dimensional ◽  
Isotropic Scattering ◽  
Two Dimensional ◽  
Scattering Media ◽  
Combustion Chambers ◽  
Transfer Method

The discrete transfer method, often employed to calculate radiative heat transfer in combustion chambers, is not conservative. The reason for this behavior is examined and a conservative formulation is proposed and evaluated. A simple treatment of isotropic scattering media is also presented. The original and the conservative formulation of the method are applied to two-dimensional and three-dimensional enclosures containing a participating medium. It is shown that the accuracy of the original and the conservative formulation is very similar, but the proposed formulation has the advantage of ensuring energy conservation.

Analytical Solution Under Two-Flux Approximation to Radiative Heat Transfer in Absorbing Emitting and Anisotropically Scattering Medium

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Xin-Lin Xia ◽  
Dong-Hui Li ◽  
Feng-Xian Sun
Keyword(s):  
Heat Transfer ◽  
High Temperature ◽  
Radiative Transfer ◽  
Analytical Solution ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Thermal Protection ◽  
Isotropic Scattering ◽  
Scattering Media ◽  
Flux Approximation

Radiative transfer in absorbing, emitting, and highly anisotropically scattering media is widely encountered in high temperature applications such as pulverized coal firing furnaces and high temperature thermal protection materials. Efficient and effective solution methods for the transfer process are very crucial, especially in thermal radiation related reverse problems and optimization designs. In this study, the analytical solution for radiative heat transfer in an absorbing, emitting, and anisotropically scattering slab between two parallel gray walls are derived under the two-flux approximation. Explicit expression for the radiative heat flux in a slab is obtained under two-flux approximation. The reliability and adaptability of an analytical solution is examined in case studies by comparing with the Monte Carlo results. Comparative studies indicate that the analytical solution can be used in radiative transfer calculation in an absorbing emitting and anisotropically scattering slab. It is much more applicable in a forward and isotropic scattering slab than in an absorbing one, especially in a forward scattering slab. Because of simplicity and high computing efficiency with the analytical solution, it may be useful in reverse radiative transfer problems, in optimization design, and in developing some numerical schemes on radiative heat transfer.

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