This page documents the two primary research projects I have conducted both as an undergraduate and graduate student at the University of Wyoming. 


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Master's Thesis Research: Photon Monte Carlo Simulation of Radiative Heat Transfer in Multiphase Flow (IN-PROGRESS)

My current master's program requires the completion of a traditional research based thesis. The research I have been conducting primarily involves utilizing the Photon Monte Carlo method to model radiative heat transfer in the complex multiphase flow of a gasifier. All numerical simulations for this research are being written entirely in FORTRAN. The resulting high-fidelity model that I create will be used to validate the implementation of the P1 radiation model into the MFIX software package (the DOE’s open-source CFD software for multiphase flow). This research, and the expenses of my graduate education, are therefore being funded exclusively by the DOE. More information about this software package can be found here:

I would also like to acknowledge Dr. Michael Stoellinger, my primary faculty advisor for this research.

No Radiation

No Radiation

P1 Model

P1 Model

A visualization of the significant impact thermal radiation modeling has on multiphase flow simulations

Monte Carlo simulations are stochastic techniques which involve repetitively simulating or sampling isolated events such that complex deterministic processes can instead be modeled with simpler stochastic analysis. This is applied to complex radiative heat transfer problems by simulating individual rays or bundles of energy and tracking them throughout a radiative enclosure while making stochastic decisions about their direction, path length, energy, etc. This application of the Monte Carlo method is often referred to as Photon Monte Carlo simulations, and it is preferable to solving the general form of the radiative transfer equation (RTE) since doing so can be unreasonably computationally expensive. This is especially true in cases of complex radiation where 3-dimensional, inhomogeneous, isotropically scattering, non-gray participating media is involved (such as the multiphase flow of a gasifier). 

Obviously this research is still a work in process but I plan to post a copy of my completed thesis here once it is complete (summer 2020.) For now, more detailed technical information about the current status of this project has been summarized in a recent paper I submitted for my Stochastic Modeling course. A copy of this report can be found under the "Compiled Course Work" section of the "Projects" tab. More information about how my research fits into the larger context of the MFIX project can also be found by viewing this presentation which was given by Murali Kotteda (a postdoctoral researcher at UW) last year during the annual MFIX workshop in Morgantown, WV.


Undergraduate Research Fellowship: Determining the Model Coefficients of a New Turbulence Model

During my Senior year at UW, I was selected for an Undergraduate Research Fellowship. This project was both hosted and exclusively funded by the Wyoming NASA Space Grant Consortium. More information about this program can be found here: This undergraduate research experience was a tremendous learning opportunity for me and it ultimately became the precursor for my ongoing graduate education. I would again like to acknowledge Dr. Michael Stoellinger, who was my faculty advisor for this project.

A direct numerical simulation (DNS) of turbulent channel flow from the John Hopkins Turbulence Database

Turbulent flow in a fluid is flow characterized by random, irregular, and fluctuating motion. The ability to model such chaotic flows is necessary for countless applications, many of which are of great interest to NASA (e.g. predicting stalls in fixed-wing flight, calculating turbulent effects on the efficiencies in gas turbine engines, designing for turbulent mixing in internal combustion engines, etc.) Exact numerical simulations of such flows are possible but require repetitively solving the three-dimensional Navier-Stokes equations to obtain the fluid flow field, and then averaging the solutions to obtain applicable statistic. Such an approach requires an extremely demanding amount of computational power and thus is not a practical solution for many common flows of engineering interest. Therefore, the goal of turbulence theories and models is to describe turbulent motions by exact analytical methods. Richard Feynman denoted this task as the last great unsolved problem of classical physics.

In 1991, J.L. Lumley proposed a new model for calculating the energy dissipation rate in a flow (a key parameter for modeling turbulent behavior as a whole.) This new model has the potential to rectify the shortcomings of all currently adopted turbulence models by accounting for the history of the strain rate that fluid elements experience in a turbulent flow, yet, there is no evidence that this proposed model was ever compared to data from a direct numerical simulation (DNS) in order to determine the optimal constants and initial conditions for the new Lumley model. This was likely due to a lack of computational resources at the time. Therefore, the goal of this research was to test and optimize Lumley’s proposed turbulence model by referencing published DNS data. The “standard” and the “realizable” turbulence models were also used for comparison. Theoretical derivations were provided for each model. Data from eight DNS studies of varying nature were used to assess the performance of each model. All numerical calculations were programmed in Python.

It was ultimately concluded that the new Lumley model performs well in certain flow cases, but it does not universally outperform the traditional models. A key next step to further validate and optimize the model is to implement it into a CFD (computational fluid dynamics) solver such that it can be applied to other cases of turbulent flow. If the proposed model can in fact accurately represent the energy dissipation rate in other cases of turbulent flow, it will continue to prove itself to be an extremely useful tool in the ongoing challenge of modeling turbulent flow. Another University of Wyoming student was recently considering to seek another WNSGC Undergraduate Research Fellowship to help continue this work.

For more detailed technical information about this research, please consider viewing my final report to the Wyoming NASA Space Grant Consortium by clicking this link:

© 2020 David J. Tobin