When the pressure ratio increases from the perfectly expanded condition to the third limited condition in which a normal shock is located on the exit plane, shock wave configurations outside the nozzle can be further ...When the pressure ratio increases from the perfectly expanded condition to the third limited condition in which a normal shock is located on the exit plane, shock wave configurations outside the nozzle can be further assorted as no shock wave on the perfectly expanded condition, weak oblique shock reflection in the regular reflection （RR） pressure ratio condition, shock reflection hysteresis in the dual-solution domain of pressure ratio condition, Mach disk configurations in the Mach reflection （MR） pressure ratio condition, the strong oblique shock wave configurations in the corresponding condition, and a normal shock forms on the exit plane in the third limited con- dition. Every critical pressure ratio, especially under regular reflection and Mach reflection pressure ratio conditions, is deduced in the paper according to shock wave reflection theory. A hysteresis phenomenon is also theoretically possible in the dual-solution domain. For a planar Laval nozzle with the cross-section area ratio being 5, different critical pressure ratios are counted in these con- ditions, and numerical simulations are made to demonstrate these various shock wave configurations outside the nozzle. Theoretical analysis and numerical simulations are made to get a more detailed understanding about the shock wave structures outside a Laval nozzle and the RR←→MR transition in the dual-solution domain.展开更多
This paper examines the Shock/Shock Interactions（SSI）between the body and wing of aircraft in supersonic flows.The body is simplified to a flat wedge and the wing is assumed to be a sharp wing.The theoretical spatia...This paper examines the Shock/Shock Interactions（SSI）between the body and wing of aircraft in supersonic flows.The body is simplified to a flat wedge and the wing is assumed to be a sharp wing.The theoretical spatial dimension reduction method,which transforms the 3D problem into a 2D one,is used to analyze the SSI between the body and wing.The temperature and pressure behind the Mach stem induced by the wing and body are obtained,and the wave configurations in the corner are determined.Numerical validations are conducted by solving the inviscid Euler equations in 3D with a Non-oscillatory and Non-free-parameters Dissipative（NND）finite difference scheme.Good agreements between the theoretical and numerical results are obtained.Additionally,the effects of the wedge angle and sweep angle on wave configurations and flow field are considered numerically and theoretically.The influences of wedge angle are significant,whereas the effects of sweep angle on wave configurations are negligible.This paper provides useful information for the design and thermal protection of aircraft in supersonic and hypersonic flows.展开更多
基金supported by the National Natural Science Foundation of China (No. 10702009)
文摘When the pressure ratio increases from the perfectly expanded condition to the third limited condition in which a normal shock is located on the exit plane, shock wave configurations outside the nozzle can be further assorted as no shock wave on the perfectly expanded condition, weak oblique shock reflection in the regular reflection （RR） pressure ratio condition, shock reflection hysteresis in the dual-solution domain of pressure ratio condition, Mach disk configurations in the Mach reflection （MR） pressure ratio condition, the strong oblique shock wave configurations in the corresponding condition, and a normal shock forms on the exit plane in the third limited con- dition. Every critical pressure ratio, especially under regular reflection and Mach reflection pressure ratio conditions, is deduced in the paper according to shock wave reflection theory. A hysteresis phenomenon is also theoretically possible in the dual-solution domain. For a planar Laval nozzle with the cross-section area ratio being 5, different critical pressure ratios are counted in these con- ditions, and numerical simulations are made to demonstrate these various shock wave configurations outside the nozzle. Theoretical analysis and numerical simulations are made to get a more detailed understanding about the shock wave structures outside a Laval nozzle and the RR←→MR transition in the dual-solution domain.
基金supported by the Fundamental Research Funds for the Central Universities of China (No. 31020170QD087)
文摘This paper examines the Shock/Shock Interactions（SSI）between the body and wing of aircraft in supersonic flows.The body is simplified to a flat wedge and the wing is assumed to be a sharp wing.The theoretical spatial dimension reduction method,which transforms the 3D problem into a 2D one,is used to analyze the SSI between the body and wing.The temperature and pressure behind the Mach stem induced by the wing and body are obtained,and the wave configurations in the corner are determined.Numerical validations are conducted by solving the inviscid Euler equations in 3D with a Non-oscillatory and Non-free-parameters Dissipative（NND）finite difference scheme.Good agreements between the theoretical and numerical results are obtained.Additionally,the effects of the wedge angle and sweep angle on wave configurations and flow field are considered numerically and theoretically.The influences of wedge angle are significant,whereas the effects of sweep angle on wave configurations are negligible.This paper provides useful information for the design and thermal protection of aircraft in supersonic and hypersonic flows.
