Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Aeronautics and Astronautics

Committee Chair

Haifeng Wang

Committee Member 1

Gregory A. Blaisdell

Committee Member 2

William E. Anderson

Committee Member 3

Robert P. Lucht


The significance of differential molecular diffusion (DMD) has been demonstrated experimentally and numerically in many studies. Despite the significance, the effort of modeling DMD in turbulent combustion is still inadequate, and assumptions of equal molecular diffusion and unity Lewis numbers are often made when modeling turbulent combustion. It is imperative to interrogate the physics of DMD in turbulent combustion to provide needed physical insights for the advancement of models for DMD. In this work, we examine DMD in turbulent non-premixed combustion and advance the flamelet models for incorporating DMD.

The effect of DMD in turbulent non-premixed flames is studied by examining two previously reported DNS of temporally evolving planar jet flames, one with CO/H2 as the fuel and the other with C2H4 as the fuel. The DMD behaviors in the CO/H2 DNS flames are found to be like flamelets, while in the C2H4 DNS flames they are flameletlike only in the early stages of the flame evolution and become non-flamelet-like later. The scaling of DMD with respect to the Reynolds number Re is investigated in the CO/H2 DNS flames statistically, and an evident power-law scaling is observed. The effects of Damk¨ohler number Da on the DMD behaviors are also examined in both the laminar counter-flow jet C2H4 diffusion flames and the C2H4 DNS flames.

For developing DMD models, it is needed to have a set of model constraints based on physical observations to constrain the model development such that the models yield consistent results with physical observations. For developing consistent DMD models, we adopt the obtained power-law Re number scaling of DMD as the model constraints and examine the turbulence modeling requirement in order to yield the desired power-law scaling. Perturbation analysis is conducted to examine the model consistency to yield the desired power-law scaling for DMD in a mixing layer test case. It is found that a differential mixing time scale model is needed in order to yield the desired scaling, while the commonly used equal mixing time scale model cannot produce the scaling correctly. Numerical simulations of the turbulent mixing problem are also performed to further demonstrate the turbulence modeling requirement for producing the desired power-law scaling of DMD.

The flamelet models for turbulent combustion assume one dimensional laminar flamelet with equal molecular diffusivity embedded in turbulent flames and use presumed PDF to integrate the laminar flamelet to obtain an integrated flamelet table that can be readily used for turbulent flame calculations. It is pointed out in this work that there are non-unique approaches for such an integration, and this non-unique integration has not been thoroughly investigated before. A thorough understanding of this non-uniqueness is useful for providing a sound baseline model for incorporating DMD. This work studies, for the first time, systematically the non-uniqueness of the flamelet table integration approaches. A flamelet model called the flamelet/progress variable (FPV) model is used in the study although the issue generally exists in many other flamelet models. Two classes of table integration approaches are investigated, one preserving the laminar flamelet structures during integration and the other not. A partially stirred reactor is used as a test case for examining the different approaches. A method based on the transported probability density function (PDF) method is also employed to provide a reference for the assessment of the different flamelet table integration approaches. It is found in general that the flamelet preserving integration approach yields more reasonable joint PDF of the mixture fraction and the progress variable, and the prediction results are closer to the referenced transported PDF results.

A series of consistent DMD models suitable for flamelet modeling of turbulent non-premixed combustion has been developed recently. In this work, these DMD models are further assessed in the CO/H2 and C2H4 DNS flames. These models have been tested in a few flames and more thorough validation is required to examine the model’s performance under different combustion conditions. In these models, the dependence of DMD on the Re number, which is missing in original flamelet models, is correctly incorporated based on a limiting analysis of the behaviors of DMD at the limits of small and large Re numbers. The performances of the models are carefully examined in the DNS flames to further validate the models.