An Efficient Computational Method for Thermal Radiation in Participating Media
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Date
2007-07-26T13:13:57Z
Authors
Hassanzadeh, Pedram
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Thermal radiation is of significant importance in a broad range of engineering
applications including high-temperature and large-scale systems. Although the
governing equations of thermal radiation have been known for many years, the
complexities inherent in the phenomenon, such as the multidimensionality and
integro-differential nature of these equations, have made it difficult to obtain an
accurate, efficient, and robust computational method. Developing the finite volume
radiation method in the 1990s was a significant progress but not a panacea
for computational radiation. The major drawback of this method, which is common
among all methods that solve for directional intensities, is its slow convergence
rate in many situations which increases the solution cost dramatically. These situations
include large optical thicknesses, strongly reflecting boundaries, and any
other factor that causes strong directional coupling like complex geometries.
Several acceleration schemes have been developed in the heat transfer and neutron
transport communities to expedite the convergence and reduce the solution
cost, but none of them led to a general and reliable method. Among these available
schemes, the two most promising ones, the multiplicative scheme and coupled
ordinates method, suffer from failing on fine grids and being very complicated for
complex scattering phase functions, respectively.
In this research, a new computational method, called the QL method, has been
introduced. The main idea of this method is using the phase weight concept to
relate the directional and average intensities and re-arranging the Radiative Transfer
Equation to find a new expression for the radiant heat flux. This results in an
elliptic-type equation for the average intensity at each control volume which conserves
the radiant energy in all directions in the control volume. This formulation
gives the QL method a great advantage to solve for the average intensity while
including the directional effects. Since the directional effects are included and the
radiant energy is conserved in each control volume, this method is expected to be
accurate and have a good convergence rate in all conditions. The phase weight
distribution required by the QL method can be provided by a method like the finite
volume method or discrete ordinates method.
The QL method is applied to several 1D and 2D test cases including isotropic
and anisotropic scattering, black and partially reflecting boundaries, and emitting absorbing
problems; and its accuracy, convergence rate, and solution cost are studied.
The method has been found to be very stable and efficient, regardless of grid
size and optical thickness. This method establishes very accurate predictions on the
tested coarse grids and its results approach the exact solution with grid refinement.
Description
Keywords
Computational Thermal Radiation, QL Method, Radiative Heat Transfer, Finite Volume Method, CFD, Participating Media