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The foundation of AVIC Commercial Aircraft Engine Company (ACAE) in Shanghai triggers the hot upsurge of the civil aircraft engine development and study in China. Air worthiness requirements of the engine emission brings the new challenge to the combustor research and design. With the motivation of design high performance and clean combustor, CFD is utilized as the powerful design approach. In this paper, Reynolds averaged resolve of Navier-Stokes (RANS) equations of reaction two-phase flow in an experimental low emission combustor are performed. The numerical approach uses an implicit compressible gas solver together with a Lagrangian liquid-phase tracking method and the extended coherent flamelet model for turbulence-combustion interaction. The NOx formation is modeled by the concept of post-processing, which resolves the NOx transport equation with the assumption of frozen temperature distribution. Both turbulence-combustion interaction model and NOx formation model are firstly evaluated by the comparison of experimental data published in open literatures of a lean direct injection (LDI) combustor. The test rig studied in this paper is called Low Emission Stirred Swirl (LESS) combustor, which is a two stage model combustor, fueled with liquid RP-3 kerosene and designed by Beijing University of Aeronautics and Astronautics (BUAA). The main stage of LESS combustor employs the principle of lean prevaporized and premixed (LPP) concept to reduce pollutant, and the pilot stage depends on a diffusion flame for flame stabilization. Detailed numerical results including of species distribution, turbulence performance and burning performance are qualitatively and quantitatively evaluated. Numerical prediction of NOx emission shows a good agreement with test data both at idle condition and full power condition of LESS combustor. Preliminary results of the flame structure are shown in this paper. The flame stabilization mechanism and NOx reduction effort are also discussed with in-depth analysis.