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1. Donde, Pratik Prakash. LES/PDF approach for turbulent reacting flows.

Degree: PhD, Aerospace Engineering, 2012, University of Texas – Austin

The probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of turbulent reacting flows. In this approach, the joint-PDF of all reacting scalars is estimated by solving a PDF transport equation, thus providing detailed information about small-scale correlations between these quantities. The objective of this work is to further develop the LES/PDF approach for studying flame stabilization in supersonic combustors, and for soot modeling in turbulent flames. Supersonic combustors are characterized by strong shock-turbulence interactions which preclude the application of conventional Lagrangian stochastic methods for solving the PDF transport equation. A viable alternative is provided by quadrature based methods which are deterministic and Eulerian. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a new approach called semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach. For soot modeling in turbulent flows, an LES/PDF approach is integrated with detailed models for soot formation and growth. The PDF approach directly evolves the joint statistics of the gas-phase scalars and a set of moments of the soot number density function. This LES/PDF approach is then used to simulate a turbulent natural gas flame. A Lagrangian method formulated in cylindrical coordinates solves the high dimensional PDF transport equation and is coupled to an Eulerian LES solver. The LES/PDF simulations show that soot formation is highly intermittent and is always restricted to the fuel-rich region of the flow. The PDF of soot moments has a wide spread leading to a large subfilter variance. Further, the conditional statistics of soot moments conditioned on mixture fraction and reaction progress variable show strong correlation between the gas phase composition and soot moments. Advisors/Committee Members: Raman, Venkat (advisor), Clemens, Noel (committee member), Ezekoye, Ofodike (committee member), Goldstein, David (committee member), Moser, Robert (committee member).

Subjects/Keywords: Probability density function approach; Large eddy simulation; Supersonic combustion modeling; Soot modeling; Turbulent reacting flows; Direct quadrature method of moments; Semi-discrete quadrature method of moments; Quadrature based methods; Lagrangian Monte Carlo methods; Supersonic combustors; Flame stabilization; Polycyclic aromatic hydrocarbons; Soot-turbulence-chemistry interactions; Shock-turbulence-chemistry interactions

…The first involves flame stabilization in supersonic combustors, while the second problem… …Stable and robust supersonic combustors are critical for design and development of scramjet… …milliseconds. Also, supersonic combustors are characterized by shocks, and shock-combustion-turbulent… …supersonic combustors is necessary for the design of reliable scramjet engines. 1.2 Soot… …1.1 and 1.2. Flame stabilization in supersonic combustors is characterized by strong shock… 

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APA (6th Edition):

Donde, P. P. (2012). LES/PDF approach for turbulent reacting flows. (Doctoral Dissertation). University of Texas – Austin. Retrieved from

Chicago Manual of Style (16th Edition):

Donde, Pratik Prakash. “LES/PDF approach for turbulent reacting flows.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed March 02, 2021.

MLA Handbook (7th Edition):

Donde, Pratik Prakash. “LES/PDF approach for turbulent reacting flows.” 2012. Web. 02 Mar 2021.


Donde PP. LES/PDF approach for turbulent reacting flows. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Mar 02]. Available from:

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Donde PP. LES/PDF approach for turbulent reacting flows. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: