International Journal of Automotive Technology, Vol. 12, No. 4, pp. 489−496 (2011) DOI 10.1007/s12239−011−0057−1 Copyright © 2011 KSAE 1229−9138/2011/059−03 489 BREAKUP MODELING OF A LIQUID JET IN CROSS FLOW K.-S. IM 1) , K.-C. LIN 2) , M.-C. LAI 3) and M. S. CHON 4)* 1) Livermore Software Technology Company, Livermore, CA 94551, USA 2) Taitec, Inc, Beavercreek, OH 45230, USA 3) Department of Mechanical Engineering, Wayne State University, Detroit, MI 48202, USA 4) Department of Energy System Engineering, Chungju National University, Chungbuk 380-702, Korea (Received 12 August 2010 ; Revised 26 January 2011) ABSTRACT−We propose a novel breakup model to simulate the catastrophic breakup regime in a supersonic cross flow. A developed model has been extended from an existing Kelvin-Helmholtz/Rayleigh-Taylor (K-H/R-T) hybrid model. A new mass reduction rate equation, which has critical effects on overall spray structure, is successfully adopted, and the breakup length, which is an important parameter in existing model, is replaced by the breakup initiation time. Measured data from the supersonic wind tunnel with a dimension of 762×152×127 mm was employed to validate the newly developed breakup model. A nonaerated injector with an orifice diameter of 0.5 mm is used to inject water into a supersonic flow prescribed by the momentum flux ratio of the liquid jet to free stream air, q 0 . The conservation-element and solution-element (CE/SE) method, a novel numerical framework for the general conservation law, is applied to simulate the supersonic compressible flow. The spray penetration height and average droplet size along with a spray penetration axis are quantitatively compared with data. The shock train flow structures induced by the presence of a liquid jet are further discussed. KEY WORDS : Cross flow, Breakup, K-H/R-T hybrid model, CE/SE method NOMENCLATURE B 0 : drop size - constant B 1 : breakup time - constant C D : drag coefficient D : drag function or drop diameter d 0 : nozzle diameter e : specific internal energy E : specific total energy h 0 : penetration height M x, y, z : Momentum exchange terms M s : free stream Mach number m 0 : initial mass m : mass p : pressure Q s : energy exchange term r : jet radius or drop radius Re : Reynolds number T : Taylor number t s : breakup time We : Weber number Z : Ohnesorge number u, v , w : flow velocities x, y , z : spatial coordinates Λ : wavelength of fastest growing wave ρ : density σ : surface tension coefficient τ : liquid breakup time µ : viscosity Ω : maximum wave growth rate SUBSCRIPTS g : gas k : particle index l : liquid 0 : initial value SUPERSCRIPTS T : transpose matrix 1. INTRODUCTION The injection of liquid jets into the high-speed flow stream is an important process in modern propulsions and power applications such as gas turbine, ramjet, and scramjet engines. In such applications, the combustion performance depends heavily on liquid atomization, spray penetration, and the mixing process between the free stream air and the liquid fuel. As a result, the study of the liquid spray in high- speed cross flow has become an important research area. The overall breakup process including deformation, liquid *Corresponding author. e-mail: mschon@cjnu.ac.kr