Time-averaging strategies in the finite-volume/particle hybrid algorithm for the joint PDF equation of turbulent reactive flows

Abstract

The influence of time-averaging on bias is investigated in the finite-volume/particle hybrid algorithm for the joint PDF equation for statistically-stationary turbulent reactive flows. It is found that the time-averaging of the mean fluctuating velocity (TAu) leads to the same variances of the fluctuating velocity before and after the velocity correction, whereas without TAu the estimates are different, and an additional numerical dissipation rate is introduced for the turbulent kinetic energy (TKE). When 100 particles per cell are used without TAu, a large bias error is found to be involved in the unconditional statistics of the statistically-stationary solutions of two tested turbulent flames, the Cabra H₂/N₂ lifted flame and the Sandia piloted flame E. The use of TAu reduces this bias dramatically for the same number of particles per cell. The conditional statistics in these flames, however, are hardly affected by TAu. To a large extent, the effect of the bias error on the unconditional statistics is similar to the effect of increasing the model constant C _{ω 1} in the stochastic turbulence frequency model.

Keywords:

• bias
• numerical dissipation
• numerical method
• PDF method
• time-averaging

Acknowledgements

This work is supported by the Air Force Office of Scientific Research, Grant FA9550-06-1-0048. We are grateful to Steven R. Lantz and Daniel I. Sverdlik for their help on the parallel computations, and to Renfeng Cao for help on the HYB2D code. Various suggestions from David A. Caughey and Zhuyin Ren are appreciated. This research was conducted using the resources of the Cornell Theory Center, which receives funding from Cornell University, New York State, federal agencies, foundations, and corporate partners.