The chemical reactions in combustor are described by integrating Eddy-Dissipation Model with Arrhenius rate coefficients. The cold and react flow fields of triplet impingement injector and combustor are simulated using the three-dimensional computational fluid dynamics method. Both helicity and mixing length are introduced to study the mixing mechanism and the effect of triplet impingement injector. The key characteristic parameters of combustor, e.g., spatial distributions of total temperature and pressure, residence time of gas flow in combustor, are obtained. The flow field characteristics of triplet impingement injector and combustor for Fuel-Oxidizer-Fuel (F-O-F) and Oxidizer-Fuel-Oxidizer (O-F-O) triplet arrangements are analyzed. The degree of F2 dissociation in combustor exit plane for O-F-O triplet arrangement is 13.5% higher than that for the F-O-F triplet arrangement under conditions of specified composition proportioning and combustor characteristic length. Experimental result demonstrates that the output power of laser is increased by 17%.