A new robust consistent hybrid finite-volume/particle method for solving the PDF model equations of turbulent reactive flows

• A robust hybrid FV/particle method has been developed for the PDF model equations.
• It is designed to remedy the main deficiencies of the old hybrid algorithm.
• Successfully applied to non-reacting and reacting bluff-body flows.
• The method is very robust against the grid refinement and statistical fluctuations.

A new robust hybrid finite-volume (FV)/particle method is developed for solving joint probability density function (JPDF) model equations of statistically stationary turbulent reacting flows. The method is designed to remedy the deficiencies of the hybrid algorithm developed by Muradoglu et al. (1999, 2001). The density-based FV solver in the original hybrid algorithm has been found to be excessively dissipative and yet not very robust. To remedy these deficiencies, a pressure-based PISO algorithm in the open source FV package, OpenFOAM, is used to solve the Favre-averaged mean mass and momentum equations while a particle-based Monte Carlo algorithm is employed to solve the fluctuating velocity-turbulence frequency-compositions JPDF transport equation. The mean density is computed as a particle field and passed to the FV method. Thus the redundancy of the density fields in the original hybrid method is removed making the new hybrid algorithm more consistent at the numerical solution level. The new hybrid algorithm is first applied to simulate non-swirling cold and reacting bluff-body flows. The convergence of the method is demonstrated. In contrast with the original hybrid method, the new hybrid algorithm is very robust with respect to grid refinement and achieves grid convergence without any unphysical vortex shedding in the cold bluff-body flow case. In addition, the results are found to be in good agreement with the earlier PDF calculations and also with the available experimental data. Finally the new hybrid algorithm is successfully applied to simulate the more complicated Sydney swirling bluff-body flame ‘SM1’. The method is also very robust for this difficult test case and the results are in good agreement with the available experimental data. In all the cases, the PISO-FV solver is found to be highly resilient to the noise in the mean density field extracted from the particles.