Turbulence and Combustion Group

PDF computations of turbulent flames

A variety of modelling methods have been proposed to predict the complex, highly non-linear, interaction between turbulence and chemical reaction in both premixed and non-premixed flames. Among these, PDF methods have the advantages of representing convection and reaction exactly without modelling assumptions, and they have been demonstrated to be an effective approach for calculating turbulent reactive flows.

The PDF calculations performed on TNF workshop target flames (simple jet flames, piloted jet flames, bluff body flames) clearly demonstrate the ability of PDF method to account accurately for strong turbulent combustion interactions such as local extinction and re-ignition. In recent PDF calculations on turbulent lifted flames in a vitiated coflow, the numerical model is found to capture the most interesting feature of this particular lifted flame: the strong sensitivity of liftoff height to coflow temperature. More work is performed on piloted jet flames and bluff body flames to investigate the effect of detailed chemical mechanisms and mixing models.

Recently, the Lagrangian investigations of local extinction, re-ignition and auto-ignition in piloted jet flame and lifted jet flames are performed. The processes of local extinction, re-ignition and auto-ignition are illustrated by the particle trajectories in composition space.


Lift-off height against coflow temperature for a turbulent lifted flame in a vitiated coflow. Circles, measurements (Wu, Starner and Bilger); Lines, joint PDF calculations using Mueller mechanism (solid line) and Li mechanism (dashed line) with different mixing models. MC, line with cross; IEM, line with diamond; EMST, line with triangle.

Measured and computed scatter plots of temperature against mixture fraction for lifted flame at z/D=14. (a) experimental data (Cabra and Dibble ). (b), (c) and (d) computed using IEM, MC and EMST mixing models, respectively. Mueller mechanism is used for these calculations. The solid line is the equilibrium temperature.

Selected Publications on PDF computations of turbulent flames


H. Wang and S.B. Pope, (2007) ``Lagrangian investigation of local extinction, re-ignition and auto-ignition in turbulent flames'', Combustion Theory and Modelling (submitted)

H. Wang and S.B. Pope, (2007) ``Time averaging strategies in the finite-volume/particle hybrid algorithm for the joint PDF equation of turbulent reactive flows'', Combustion Theory and Modelling (Accepted)

R. Cao, H. Wang and S.B. Pope (2007) ``The effect of mixing models in PDF calculations of piloted jet flames'', Proceedings of the Combustion Institute 31, 1543-1550.

R. Cao and S.B. Pope, (2005) ``The influence of chemical mechanisms on PDF calculations of nonpremixed piloted jet flames'', Combust and Flame 143, 450-470. This paper is accompanied by the Supplementary Material here.

R. Cao, S.B. Pope and A.R. Masri (2005) "Turbulent lifted flames in a vitiated coflow investigated using joint PDF calculations," Combustion and Flame 142, 438-453.

K. Liu, S.B. Pope and D.A. Caughey (2005) ``Calculations of bluff-body stabilized flames using a joint PDF model with detailed chemistry,'' Combustion and Flame 141, 89-117

A.R. Masri, R. Cao, S.B. Pope and G.M. Goldin (2004) "PDF Calculations of Turbulent Lifted Flames of H2/N2 issuing into a vitiated co-flow," Combustion Theory and Modelling, 8, 1--22.

M. Muradoglu, K. Liu and S.B. Pope (2003) "PDF modeling of a bluff-body stabilized turbulent flame," Combust. Flame, 132, 115--137.

M. Muradoglu, S.B. Pope and D.A. Caughey (2001) "The hybrid method for the PDF equations of turbulent reactive flows: consistency conditions and correction algorithms," J. Comp. Phys. 172, 841--878.

R. Cao and S.B. Pope (2003) "Numerical integration of stochastic differential equations: weak second-order mid-point scheme for applications in the composition PDF method," J. Comput. Phys. 185, 194--212.

Q. Tang, J. Xu and S.B. Pope (2000) "PDF calculations of local extinction and NO production in piloted-jet turbulent methane/air flames," Proceedings of the Combustion Institute, 28, 133--139.

J. Xu and S.B. Pope (2000) "PDF calculations of turbulent nonpremixed flames with local extinction," Combust. Flame 123, 281--307.

Related links on PDF computations of turbulent flames