Joint Gas-Phase Velocity-Scalar PDF Modeling for Turbulent Evaporating Spray Flows

Abstract

The article proposes a joint gas-phase velocity-scalar probability density function (PDF) model for turbulent spray flows. The joint gas-phase velocity-mixture fraction PDF transport equation for turbulent spray flows is derived and modeled. The simplified Langevin model and interaction-by-exchange-with-the-mean (IEM) model are extended to account for spray evaporation, and they close the PDF transport equation, which is solved by a Lagrangian Monte-Carlo particle method, and the droplet characteristics including heating, vaporization, and motion are solved by a Lagrangian droplet parcel method using the point-source approximation. A steady, two-dimensional, axi-symmetric, turbulent methanol/air dilute non reacting spray flow without swirl is simulated using the present method. The results of the gas velocity obtained by the joint PDF method are in good agreement with experimental data, and the PDF method improves the simulation results obtained using a moment closure model.

Keywords:

• Evaporating spray
• IEM mixing model
• Joint probability density function
• Langevin model
• Methanol spray
• Turbulent spray

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support from DFG through SFB 568, the International Graduiertenkolleg 710 “Complex Processes: Modeling, Simulation and Optimization”, and the Graduate School Math Comp of IWR, Universität Heidelberg, as well as DFG grant GU 255/6-1. H.W. Ge acknowledges partial support through the National Natural Science Foundation of China through project 50936005. The present article greatly benefits from the reviewers’ comments and advice, which is gratefully acknowledged.

Notes

The present affiliation for Hai-Wen Ge is ESI Mindware Inc., Farmington Hills, Michigan, USA.

Published as part of the 23rd International Colloquium on the Dynamics of Explosions and Reactive Systems (ICDERS) Special Issue with Guest Editor Derek Dunn-Rankin.