A three-part numerical investigation has been conducted in order to identify the flow separation behavior––the progression of the shock structure, the flow separation pattern with an increase in the nozzle pressure ratio(NPR), the prediction of the separation data on the nozzle wall,and the influence of the gas density effect on the flow separation behavior are included.The computational results reveal that the annular conical aerospike nozzle is dominated by shock/shock and shock/boundary layer interactions at all calculated NPRs, and the shock physics and associated flow separation behavior are quite complex.An abnormal flow separation behavior as well as a transition process from no flow separation at highly over-expanded conditions to a restricted shock separation and finally to a free shock separation even at the deign condition can be observed.The complex shock physics has further influence on the separation data on both the spike and cowl walls, and separation criteria suggested by literatures developed from separation data in conical or bell-type rocket nozzles fail at the prediction of flow separation behavior in the present asymmetric supersonic nozzle.Correlation of flow separation with the gas density is distinct for highly overexpanded conditions.Decreasing the gas density or reducing mass flow results in a smaller adverse pressure gradient across the separation shock or a weaker shock system, and this is strongly coupled with the flow separation behavior.The computational results agree well with the experimental data in both shock physics and static wall pressure distribution at the specific NPRs, indicating that the computational methodology here is advisable to accurately predict the flow physics. A three-part numerical investigation has been conducted in the order to identify the flow separation behavior - the progression of the shock structure, the flow separation pattern with an increase in the nozzle pressure ratio (NPR), the prediction of the separation data on the nozzle wall, and the influence of the gas density effect on the flow separation behavior are included.The computational results reveal that the annular conical aerospike nozzle is dominated by shock / shock and shock / boundary layer interactions at all calculated NPRs, and the shock physics and associated flow separation behavior are quite complex. An abnormal flow separation behavior as well as a transition process from no flow separation at highly over-expanded conditions to a restricted shock separation and finally to a free shock separation even at the deign condition can be observed The complex shock physics has further influence on the separation data on both the spike and cowl walls, and separation criteria sugge sted by literatures developed from separation data in conical or bell-type rocket nozzles fail at the prediction of flow separation behavior in the present asymmetric supersonic nozzle. Correlation of flow separation with the gas density is distinct for highly overexpanded conditions. Decreasing the gas density or reducing mass flow results in a smaller adverse pressure gradient across the separation shock or a weaker shock system, and this is strongly coupled with the flow separation behavior. The computational results agree well with the experimental data in both shock physics and static wall pressure distribution at the specific NPRs, indicating that the computational methodology here is advisable to accurately predict the flow physics.