Abstract: In arbitrary curvilinear coordinate system,numerical simulations of three-dimensional and two-phase reacting flows in annular combustor domes with the swirl cup are performed.The block-structured grids are generated by solving a system of elliptic partial differential equations.The gas phase equations are solved in an Eulerian frame of reference.Modified k-ε model is employed to describe the turbulent characteristics.Modified Eddy Dissipation Model-Arrhenius turbulent combustion model is used to determine the reaction rate.To consider the influence of heat radiation,the six flux model is applied to the predictions of radiant heat transfer in the combustor.The liquid phase is treated in a Lagrangian frame of reference with the particle trajectory model.Hybrid scheme and SIMPLE algorithm are used to solve the finite-difference equations in non-staggered grid system.The couple of the gas phase and the liquid phase is adopted by the Particle Source in cell Method(PSIC).The calculating swirl number is in agreement with experimental data.Predictions show that the influence of different geometries of the swirl cup on combustor flow characteristics is considerable.So the combustion performance may be improved by the optimum design of the swirl cup.