In this paper, by taking into account the thickness of the incident shock as well as the influence of the boundary layer, we point out that even in a regular reflection there should be present a contact discontinuity....In this paper, by taking into account the thickness of the incident shock as well as the influence of the boundary layer, we point out that even in a regular reflection there should be present a contact discontinuity. By using the smallest energy criterion, the inclined angle of this contact discontinuity can be determined for differen incident angle. Then, with this inclined contact discontinuity, together with the law of conservation of mass, the mechanism for the transition from a regular reflection to a Mach reflection or a von Neumann reflection becomes clear. The important roles played by the leftest point in the reflected shock polar are identified.展开更多
We are concerned with the shock regular reflection configurations of unsteady global solutions for a plane shock hitting a symmetric straight wedge.It has been known that patterns of the shock reflection are various a...We are concerned with the shock regular reflection configurations of unsteady global solutions for a plane shock hitting a symmetric straight wedge.It has been known that patterns of the shock reflection are various and complicated,including the regular and the Mach reflection.Most of the fundamental issues for the shock reflection have not been understood.Recently,there are great progress on the mathematical theory of the shock regular reflection problem,especially for the global existence,uniqueness,and structural stability of solutions.In this paper,we show that there are two more possible configurations of the shock regular reflection besides known four configurations.We also give a brief proof of the global existence of solutions.展开更多
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
We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach＇s experiment f...We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach＇s experiment for the compressible Euler system, i.e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.展开更多
The formation mechanism of an EFP(explosively formed projectile)using a double curvature liner under the overpressure effect generated by a regular oblique reflection was investigated in this paper.Based on the detona...The formation mechanism of an EFP(explosively formed projectile)using a double curvature liner under the overpressure effect generated by a regular oblique reflection was investigated in this paper.Based on the detonation wave propagation theory,the change of the incident angle of the detonation wave collision at different positions and the distribution area of the overpressure on the surface of the liner were calculated.Three dimensional numerical simulations of the formation process of the EFP with tail.as well as the ability to penetrate 45#steel were performed using LS-DYNA software,and the EFP ve locity,the penetration ability,and the forming were assessed via experiments and x_ray photographs.The experimental results coincides with those of the simulations.Results indicate that the collision of the detonation wave was controlled to be a regular oblique reflection acting on the liner by setting the di-mensions of the unit charge and maintai ning the pressure at the collision point region at more than 2.4 times the CJ detonation when the incident angle approached the cnitical angle.The distance from the liner midline to the boundary of the area within which the pressure ratio of the regular oblique reflection pressure to the qJ detonation pressure was greater than 2.5,2,and 15was approximately 0.66 mm,132 mm,and 3.3 mm,respectively.Itis noted that pressure gradient caused the liner to turn inside out in the middle to form the head of the EFP and close the two tails of the EFP at approximately 120μs.The penetration depth of the EFP into a 45#steel target exceeded 30 mm,and there was radial expansion between the head and tail of the EFP,increasing the penetration resistance of the EFP.Therefore,the structural size of the unit charge and the liner can be further optimized to reduce resist ance to increase the penetration ability of the EFP.展开更多
According to detonation theory and hydrodynamic principle, a physical model has been set up in this paper. Based on the model a methodology for calculating dynamic initial shock parameters such as shock pressure pm sh...According to detonation theory and hydrodynamic principle, a physical model has been set up in this paper. Based on the model a methodology for calculating dynamic initial shock parameters such as shock pressure pm shock wave velosity Dm etc. of coupling charge on borehole wall has ben developed. The shock parameters have been calculated when high explosives works on granite, limestone and marble respectively. The magnitude of every parameter on borehole wall has been obtained from ignited dot to the end of borehole along axial direction. Some important conclusions are also gained.展开更多
When the high-pressure gas is exhausted to the vacuum chamber from the supersonic nozzle, the overexpanded supersonic jet is formed at specific condition. In two-dimensional supersonic jet, furthermore, it is known th...When the high-pressure gas is exhausted to the vacuum chamber from the supersonic nozzle, the overexpanded supersonic jet is formed at specific condition. In two-dimensional supersonic jet, furthermore, it is known that the hysteresis phenomena for the reflection type of shock wave in the flow field is occurred under the quasi-steady flow and for instance, the transitional pressure ratio between the regular reflection （RR） and Mach reflection （MR） is affected by this phenomenon. Many papers have described the hysteresis phenomena for underexpanded supersonic jet, but this phenomenon under the overexpanded axisymmetric jet has not been detailed in the past papers. The purpose of this study is to clear the hysteresis phenomena for the reflection type of shock wave at the overexpanded axisymmetric jet using the TVD method and to discuss the characteristic of hysteresis phenomena.展开更多
When the high-pressure gas is exhausted to the vacuum chamber from the nozzle,the underexpanded supersonic jet contained with the Mach disk is generally formed.The eventual purpose of this study is to clarify the unst...When the high-pressure gas is exhausted to the vacuum chamber from the nozzle,the underexpanded supersonic jet contained with the Mach disk is generally formed.The eventual purpose of this study is to clarify the unsteady phenomenon of the underexpanded free jet when the back pressure continuously changes with time.The characteristic of the Mach disk has been clarified in consideration of the diameter and position of it by the numerical analysis in this paper.The sonic jet of the exit Mach number Me=1 is assumed and the axisymmetric conservational equation is solved by the TVD method in the numerical calculation.The diameter and position of the Mach disk differs with the results of a steady jet and the influence on the continuously changing of the back pressure is evidenced from the comparison with the case of steady supersonic jet.展开更多
基金supported by the NNSF of China(11271323,91330105)the Zhejiang Provincial Natural Science Foundation of China(LZ13A010002)supported by a GRF grant(City U 11303015)from the Research Grants Council of Hong Kong SAR,China
文摘In this paper, by taking into account the thickness of the incident shock as well as the influence of the boundary layer, we point out that even in a regular reflection there should be present a contact discontinuity. By using the smallest energy criterion, the inclined angle of this contact discontinuity can be determined for differen incident angle. Then, with this inclined contact discontinuity, together with the law of conservation of mass, the mechanism for the transition from a regular reflection to a Mach reflection or a von Neumann reflection becomes clear. The important roles played by the leftest point in the reflected shock polar are identified.
基金supported by the National Natural Science Foundation of China(Grant no.11761077)the NSF of Yunnan province of China(2019FY003007)the Program for Innovative Research Team in Universities of Yunnan Province of China.
文摘We are concerned with the shock regular reflection configurations of unsteady global solutions for a plane shock hitting a symmetric straight wedge.It has been known that patterns of the shock reflection are various and complicated,including the regular and the Mach reflection.Most of the fundamental issues for the shock reflection have not been understood.Recently,there are great progress on the mathematical theory of the shock regular reflection problem,especially for the global existence,uniqueness,and structural stability of solutions.In this paper,we show that there are two more possible configurations of the shock regular reflection besides known four configurations.We also give a brief proof of the global existence of solutions.
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Partially supported by NSF-DMS-0305497 and 0305114.
文摘We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach＇s experiment for the compressible Euler system, i.e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.
基金The work presented in this paper has been supported by the science foundation(YT20-01-02)of Nanjing Vocational University of Industry Technology and the National Science Foundation of China under NO.11802141.
文摘The formation mechanism of an EFP(explosively formed projectile)using a double curvature liner under the overpressure effect generated by a regular oblique reflection was investigated in this paper.Based on the detonation wave propagation theory,the change of the incident angle of the detonation wave collision at different positions and the distribution area of the overpressure on the surface of the liner were calculated.Three dimensional numerical simulations of the formation process of the EFP with tail.as well as the ability to penetrate 45#steel were performed using LS-DYNA software,and the EFP ve locity,the penetration ability,and the forming were assessed via experiments and x_ray photographs.The experimental results coincides with those of the simulations.Results indicate that the collision of the detonation wave was controlled to be a regular oblique reflection acting on the liner by setting the di-mensions of the unit charge and maintai ning the pressure at the collision point region at more than 2.4 times the CJ detonation when the incident angle approached the cnitical angle.The distance from the liner midline to the boundary of the area within which the pressure ratio of the regular oblique reflection pressure to the qJ detonation pressure was greater than 2.5,2,and 15was approximately 0.66 mm,132 mm,and 3.3 mm,respectively.Itis noted that pressure gradient caused the liner to turn inside out in the middle to form the head of the EFP and close the two tails of the EFP at approximately 120μs.The penetration depth of the EFP into a 45#steel target exceeded 30 mm,and there was radial expansion between the head and tail of the EFP,increasing the penetration resistance of the EFP.Therefore,the structural size of the unit charge and the liner can be further optimized to reduce resist ance to increase the penetration ability of the EFP.
文摘According to detonation theory and hydrodynamic principle, a physical model has been set up in this paper. Based on the model a methodology for calculating dynamic initial shock parameters such as shock pressure pm shock wave velosity Dm etc. of coupling charge on borehole wall has ben developed. The shock parameters have been calculated when high explosives works on granite, limestone and marble respectively. The magnitude of every parameter on borehole wall has been obtained from ignited dot to the end of borehole along axial direction. Some important conclusions are also gained.
文摘When the high-pressure gas is exhausted to the vacuum chamber from the supersonic nozzle, the overexpanded supersonic jet is formed at specific condition. In two-dimensional supersonic jet, furthermore, it is known that the hysteresis phenomena for the reflection type of shock wave in the flow field is occurred under the quasi-steady flow and for instance, the transitional pressure ratio between the regular reflection （RR） and Mach reflection （MR） is affected by this phenomenon. Many papers have described the hysteresis phenomena for underexpanded supersonic jet, but this phenomenon under the overexpanded axisymmetric jet has not been detailed in the past papers. The purpose of this study is to clear the hysteresis phenomena for the reflection type of shock wave at the overexpanded axisymmetric jet using the TVD method and to discuss the characteristic of hysteresis phenomena.
文摘When the high-pressure gas is exhausted to the vacuum chamber from the nozzle,the underexpanded supersonic jet contained with the Mach disk is generally formed.The eventual purpose of this study is to clarify the unsteady phenomenon of the underexpanded free jet when the back pressure continuously changes with time.The characteristic of the Mach disk has been clarified in consideration of the diameter and position of it by the numerical analysis in this paper.The sonic jet of the exit Mach number Me=1 is assumed and the axisymmetric conservational equation is solved by the TVD method in the numerical calculation.The diameter and position of the Mach disk differs with the results of a steady jet and the influence on the continuously changing of the back pressure is evidenced from the comparison with the case of steady supersonic jet.
