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A Finite Element Simulation of Non Gray Participating Media Radiation for General Engineering Problems

DOI: 10.1615/ICHMT.1995.RadTransfProc.290

Mohammad-Ali Jamnia
Fluid Dynamics International, 500 Davis St, Suite 600, Evanston, Illinois 60201, USA

Michael S. Engelman
Fluent Inc., 10 Cavendish Court, Lebanon NH 03766; and Fluid Dynamics International, 500 Davis St, Suite 600, Evanston, Illinois 60201,USA


A numerical technique for the simulation of the effects of nongray media radiation is presented in which the wave length dependency is approximated by a number of bands. Each band is assumed to have a gray absorbing-emitting, scattering media radiation and the P-1 method is utilized to calculate the radiation flux. Inclusion of multi-layered materials as well as transparent windows and transparent bands - which allow the walls to exchange radiation energy in those bands alone - are discussed.
In this approach, the Navier-Stokes equations are solved along with the energy equation and the n transport equations resulting from the n bands of radiation, to predict the flow and temperature of radiating fluids. The coupling between the radiation equations and the energy equation is through the gradient of the irradiance flux which enters the energy equation as a source term. However, this particular formulation allows a separation of terms which leads to a redistribution of certain terms to the left hand side of the system of equations. This adds greatly to the stability of the nonlinear iterative procedure used to solve the discrete equations. These equations are implemented in FIDAP, a general purpose program for the analysis of viscous fluids.
Several examples are presented to validate the technique and also its application to 2-D, 2-D axisymmetic and 3-D problems.

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