Improvement of the pressure algorithm of the stand-alone PDF method to treat unsteady three-dimensional turbulent reacting flows

Abstract

This paper deals with the particle-mesh probability density function (PDF) method. It shows how an existing but less precise pressure algorithm for the stand-alone method can be improved. The present algorithm is able to handle the general case of an unsteady three-dimensional turbulent reacting flow. The transport equation of the joint PDF of velocity and composition is solved with a particle method. Open boundary conditions are realized and for statistical reasons a simple but effective particle splitting procedure is applied.

Based on a simple configuration, the properties of the presented improved pressure algorithm are analysed. It is shown which numerical condition must be taken care of so that the algorithm is able to correct the particle positions such that the normalization condition is fulfilled as accurately as specified.

To verify the algorithm the combustion of a methane–air mixture enclosed in an open simulation volume is calculated. It is shown that the simple particle splitting algorithm works very effectively in the studied case. The behaviour of the improved pressure algorithm is examined by different calculations. To analyse the convergence of the algorithm, the particle number per cell and the grid spacing are varied. To demonstrate the accuracy, a statistically stationary inflow/outflow configuration is used and the numerical solution is compared to an analytical one. For a less symmetric test case, the previous unsteady combustion problem is simulated, including an additional mean velocity in one direction.

The presented improved pressure algorithm provides the opportunity to calculate unsteady three-dimensional turbulent reacting flows with a stand-alone method, and offers an alternative to the complex hybrid finite-volume/particle PDF method.

Keywords:

• PDF method
• turbulent combustion
• stand-alone
• pressure algorithm
• particle splitting

Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft.