Date of Completion


Embargo Period


Major Advisor

Dr. Tianfeng Lu

Associate Advisor

Dr. Zhuyin Ren

Associate Advisor

Dr. Xinyu Zhao

Associate Advisor

Dr. Jacqueline H. Chen

Field of Study

Mechanical Engineering


Doctor of Philosophy

Open Access

Open Access


Accurate turbulent combustion models are key to establishing a predictive capability for combustion simulations at the device level. The transported probability density function (TPDF) methods provide an elegant solution to the challenge of closing the mean chemical source term in turbulent combustion modelling as it appears in closed form in the TPDF equations and thus the turbulence-chemistry interaction can be solved for without aggressive assumptions. This is crucial for predicting low temperature combustion, turbulent flames with the presence of local limit phenomena, and pollutant emissions. Despite some reported success in the literature, challenges remain when applying the TPDF method to turbulent premixed flames as the molecular mixing or micro-mixing term is unclosed, the modeling of which is considered to be a primary challenge.

The objective of this dissertation is to evaluate the application of existing mixing models to turbulent premixed flames and to create high-fidelity scalar dissipation rate models to predict turbulent premixed combustion. In this dissertation, direct numerical simulation (DNS) data is utilized at each stage to obtain statistical information on the scalar dissipation rate and mixing timescales for turbulent premixed flames. In the first step, DNS of a temporally evolving premixed flame is used as a numerical test bed to evaluate commonly used mixing models in the context of turbulent premixed flames. This study demonstrates that the Euclidean Minimum Spanning Tree (EMST) model is capable of predicting the behavior of a turbulent premixed flame assuming that an accurate model for the scalar mixing rate, and thus the scalar dissipation rate, can be provided. In the next stage of the dissertation, chemical explosive mode analysis (CEMA) and DNS data with realistic chemistry are used to identify physiochemical processes that govern the conditional scalar dissipation rate behavior in a turbulent premixed flame and evaluate mixing timescales. A local Damköhler number is defined based on the CEMA results and four flame zones are identified. It is found that large fluctuations in the instantaneous scalar dissipation rate occur in the explosive zone, where the local Damköhler number is much larger than unity. Two mechanisms are identified to account for the large degree of scatter in the explosive zone: flame-flame interactions and flame-assisted ignition.

A model for the Favre-averaged scalar dissipation rate is subsequently developed based on the insight gleaned from the DNS analysis. The new hybrid mixing rate model is developed to account for the scalar mixing rate behavior in both the turbulent mixing limit and the flamelet limit. The new hybrid timescale model is notable for its treatment of the flamelet mixing limit, an area where existing timescale models do not properly recover the correct mixing behavior. Comparisons to the DNS are performed with both a priori and a postereori comparisons, with the new hybrid model performing exceptionally well.

Finally, in the last stage of the dissertation, a transport equation for the conditional scalar dissipation rate of a reactive scalar is derived and an order of magnitude analysis is performed to evaluate the importance of each term in the governing equation. The order of magnitude analysis is verified with the DNS data of turbulent premixed flames and an equation of the leading order terms is identified. Models for the unclosed terms in the leading order equation are developed and evaluated with DNS data, and a modelled equation for the conditional scalar dissipation rate is proposed. The modelled equation is then compared to the DNS data, and excellent agreement between the new model and the DNS is observed.