Date of Award

Spring 2019

Document Type


Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Roy, Somesh

Second Advisor

Allen, Casey

Third Advisor

Singer, Simcha


Radiative heat transfer in participating media is among the most challenging computational engineering problems due to the complex nonlinear, nonlocal nature of radiation transport. Many approximate methods have been developed in order to resolve radiative heat transfer in participating media; but approximate methods, by the nature of their approximations, suffer from various shortcomings both in terms of accuracy and robustness. The only methods that can resolve radiative transfer accurately in all configurations are the statistical Monte Carlo-based methods. While the Monte Carlo (MC) method is the most accurate method for resolving radiative heat transfer, it is also notoriously computationally prohibitive in large-scale simulations. To overcome this computational burden, this study details the development of a quasi-Monte Carlo (QMC) method for thermal radiation in participating media with a focus on combustion-related problems. The QMC method employs a low-discrepancy sequence (LDS) in place of the traditional random number sampling mechanism used in Monte Carlo methods to increase computational efficiency. In order to analyze the performance of the QMC method, a systematic comparison of accuracy and computational expense was performed. The QMC method was validated against formal solutions of radiative heat transfer in several one-dimensional configurations and extended to three practical combustion configurations: a turbulent jet flame, a high-pressure industrial gas turbine, and a high-pressure spray combustion chamber. The results from QMC and traditional Monte Carlo are compared against benchmark solutions for each case. It is shown that accuracy of the predicted radiation field from QMC is comparable to MC at lower computational costs. Three different low-discrepancy sequences – Sobol, Halton, and Niederreiter – were examined as part of this work. Finally, recommendations are made in terms of choice of the sequence and the number of the dimensions of the LDS for combustion-relevant configurations. In conclusion, significant improvements in computational costs and accuracy seen in the QMC method makes it a viable alternative to traditional Monte Carlo methods in high-fidelity simulations.

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