In the Propulsion Aerodynamics Workshop I, the conical nozzles are numerically investigated in present paper. Axisymmetric, three-dimensional, and unsteady computations are conducted for three types of test cases. The effects of base drag and free stream Mach number on velocity coefficient are analyzed. The results of axisymmetric computation show that, the discharge coefficient and velocity coefficient match well with the experimental data. The wall Mach number and sonic line are also well predicted. The shock reflection phenomenon is well captured by the fine grid. The velocity coefficient of three-dimensional computation is about 0.1% higher than the axisymmetric computation. When the pressure ratio is very high, the three-dimensional RANS results may be not reliable as the normal shock induces unsteady recirculation zone . Three-dimensional results with splitter plate in the nozzle show that, the shock wave location and shock reflection phenomenon are changed by the splitter plate. Unsteady zonal SST-DES method is also used to simulate the vortex shedding of the splitter plate. A main shedding frequency of 32.2 kHz is obtained by analyzing the viscous force of the splitter trailing edge.