6th International Conference on CFD in Oil & Gas, Metallurgical and Process Industries SINTEF/NTNU, Trondheim NORWAY 10-12 June 2008 CFD2008-041 1 COMPARISON OF SUPERSONIC DROPLET MIXING AND EVAPORATION BETWEEN THE MULTIPHASE, MUSIG AND H-MUSIG MODELS Marwan DARWISH * and Fadl MOUKALLED Department of Mechanical Engineering American University of Beirut P.O.Box 11-0236 Riad El Solh, Beirut 1107 2020 Lebanon * E-mail: darwish@aub.edu.lb ABSTRACT The paper deals with assessing the performance of three algorithms (full multiphase, MUSIG, and H-MUSIG) for the simulation of mixing and evaporation of droplets injected into a stream flowing at supersonic speeds. All algorithms, implemented within a finite volume method, use an Eulerian pressure-based formulation but differ in the representation of the disperse phase. In the full multiphase approach each droplet size is considered a phase with a phasic velocity, energy, and volume fraction equation. In the MUSIG model, there is only one disperse phase that is decomposed into N size groups, all moving at the same speed. To account for each size group, a size fraction equation is solved. The H-MUSIG model can be viewed as a blend between the full multi-phase approach and the two-phase MUSIG approach by subdividing droplets into classes with droplet size groups in each class sharing the same velocity. Turbulence in the gas phase is accounted for by using the k-ε two-equation model while an algebraic model is used for the disperse phase. Results in an axi- symmetric geometry indicate that solutions obtained by the various techniques exhibit similar behaviour with differences in values being relatively small. Keywords: CFD, Eulerian formulation, Disperse flow, Evaporation, Breakup and Coalescence, Multiphase Models. NOMENCLATURE u velocity vector [m/s] gas density [kg/m 3 ] dynamic viscosity [kg/m.s] breakup rate. .[droplets/??] breakup frequency. C ij coalescence rate. d s Sauter diameter. [m] f population fraction. h static enthalpy. h correction correction coefficient for heat transport in droplet model. m correction correction coefficient for mass transport in droplet model. mass rate of droplet evaporation. [kg/s] volumetric mass rate of droplet evaporation. [kg/m 3 .s] I number density distribution function. p pressure. [Pa] Pr laminar Prandtl number of fluid/phase k. Pr t turbulent Prandtl number of fluid/phase k. heat flux. Q (k) general source term of fluid/phase k. R (k) gas constant for fluid/phase k. Re d Reynolds number based on the droplet diameter. Sc Schmidt Number. X jki mass fraction due to coalescence between groups j and k, which goes into group i. Y vapor mass fraction. Greek Symbols α volume fraction. β k thermal expansion coefficient for phase/fluid k. η Kolmogorov micro-scale. λ c coalescence efficiency. ω c collision frequency. ∆h v latent heat. µ, µ turb , µ eff laminar, turbulent and effective viscosity of fluid/phase k. Subscripts d refers to the droplet discrete liquid phase. g refers to the gas phase. i refers to phase i. s refers to the droplet surface condition. sat refers to the saturation condition. ε refers to turbulent eddy dissipation equation. ω refers to turbulent eddy frequency equation. vap,g refers to the vapour specie in the gas phase. INTRODUCTION Liquid injection of fuel droplet into a stream of air involves complex multiphase flow phenomena including droplet break up, coalescence, and evaporation. Droplets of various sizes, temperatures, and velocities evolve in the air stream continuously interacting and affecting the airflow. Methods for the