The objective of the proposed research program is to develop new overall computational schemes which employ spectral methods for the accurate and efficient solution of fluid flows with radiative transfer. This will significantly extend the class of radiation problems that may be studied numerically. For example, oscillating or weakly turbulent flows could be fully resolved in a simulation without approximation, i.e. numerical solutions to the exact forms of the governing equations could be obtained. Specifically, the governing equations (Navier-Stokes, energy conservation, and radiative transfer equations) will be discretized and solved by employing Fourier series and Chebyshev polynomials as basis expansion functions with efficient pseudospectral collocation and tau algorithms. To develop and validate these schemes, and to evaluate their performance and accuracy, the new models will be applied to the problem of combined radiation and natural convection in flows with participating media between concentric, horizontal cylinders. Experiments will also be performed to provide quantitative information for this purpose. A holographic interferometer will be used to provide measurements of the temperature field, and Laser Doppler Velocimetry (LDV) will be used for measurements of the fluctuating velocity field. The concentric cylinder geometry is chosen due to its relatively simple configuration and the well-documented existence of oscillating flows and transition to turbulence in the natural convection case. Successful completion of the proposed research program will dramatically improve our ability to perform engineering radiation heat transfer analyses.
