Based on the axisymmetric flowfield with optimal thrust under geometric constraints, a circular-to rectangular three-dimensional single expansion ramp nozzle is designed by using the streamline tracing method, and trimming the configuration of nozzle to improve the aerodynamic performance and reduce the weight of the nozzle. On this basis, the adjustment programme for changing geometry of the turbojet flowpath is achieved by using the rotating ramp rotation around the ramp endpoint to complete the design of the exhaust system. Subsequently, the wall pressure distribution and schlieren image of the exhaust system are obtained through cold flow experiments, and the detailed flow field characteristics and performance parameters are obtained through numerical simulations. The results show that the schlieren image and pressure distributions of the wall under each operating condition are in good agreement with the numerical simulation results; when the turbojet works alone, the structure of the exhaust jet is relatively simple, and there will be a shock train structure under the low Nozzle Pressure Ratio (NPR). In parallel operation, the two flowpath interfere with each other; in separate operation of ramjet, the airflow expands smoothly in the three-dimensional flow path. The thrust performance of the exhaust system deteriorates slightly in the turbine and ramjet co-operating condition, but the thrust coefficient is above 0.924 in the whole working envelope, and the thrust performance changes smoothly. This study provides a new effective solution for the TBCC exhaust system.