Numerical study is carried out to investigate the characteristics of supersonic turbulent combustion in Dual Combustion Ramjet(DCR) engine using a multi-dimensional 5th-order high resolution scheme. Two series of numerical experiment are carried out for the DCR combustors with various divergence angles and the length of the constant area combustor section. Operating conditions are selected by considering the flight conditions. Two different combustion modes are found by the investigation of the results depending on the formation of Mach reflection. It is analyzed that the relation between the turbulent combustion and the formation of the Mach reflection by the variation of scalar dissipation rate. Dynamic characteristics the turbulent supersonic combustion were investigated by the variation of wall pressure compared with other properties. Critical conditions for the combustion stabilization are reasoned from the characteristics of the turbulent combustion. The detailed mechanism of coupling between the compressibility effects and the turbulent combustion is understood as they are supporting with each other, similarly in detonation phenomena.