In recent decades, the gas-kinetic unified algorithm (GKUA) is proposed to simulate the gas flow in the whole flow regimes. In previous studies, GKUA was extended to problems of flows around the aircraft and internal flows considering the influence of rotational energy, as well as the flows around the aircraft considering the influence of vibrational energy. In this paper, we try to apply the model considering the effect of vibrational energy to the engine internal and external mixed flow problem, and build a numerical simulation framework of engine internal and external mixed flow considering the effect of vibrational energy. The reliability of the algorithm is verified by using one-dimensional shock tube problem and two-dimensional nozzle internal flow problem. The results show that the model can describe the flow problem of high temperature nozzle internal flow. Then the two-dimensional nozzle internal and external mixed flow problem of 25N attitude control engine is studied, the unsteady evolution and non-equilibrium effect of the mixed flow field are analyzed, and the flow parameter distribution of the mixed flow field without internal energy excitation, considering rotational energy excitation and considering vibrational energy excitation are compared.