MECHANISM FOR THE TRANSITION FROM A REGULAR REFLECTION TO A MACH REFLECTION OR A VON NEUMANN REFLECTION

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.

Symmetric Mach reflection configuration with asymmetric unsteady solution

Symmetric Mach reflection in steady supersonic flow has been usually studied by solving a half-plane problem with the symmetric line treated as reflecting surface,thus losing the opportunity to discover antisymmetric flow structures.Here in this paper we treat this problem as an entire-plane problem.Using an unsteady numerical approach,we find that the two sliplines exhibit antisymmetric unsteadiness if the Mach stem height is small while the flow remains symmetric if the Mach stem height is large.The mechanism by which disturbance,generated in the downstream of the flow duct between the two sliplines,propagates upstream is identified and it is also shown that the interaction between the transmitted expansion waves and the sliplines increases the amplitude of the unstable modes.The present study suggests a new type of compressible jet that deserves further studies.

Global existence and stability of a stationary Mach reflection

We prove the global existence and stability of a wave structure containing a stationary Mach con- figuration, which occurs when an incident shock front hits a wall with a large incident angle. Our result shows that tile data of the upstream flow and the pressure at downstream part jointly determine the whole flow, as well a the wave structure. Particularly, we show that the height of the Mach stem depends not only on the data of upstream flow, but also on the pressure at downstream flow. The flow with the assigned wave structure is governed by a free boundary value problem for the Euler system. In the problem the location of the triple point, the shock fronts and the contact discontinuity are all unknown, they are finally determined together with the solution.

High temperature effects in moving shock reflection with protruding Mach stem

The influence of high temperature effects on the protrusion of Mach stem in strong shock reflection over a wedge was numerically investigated. A two-dimensional inviscid solver applies finite volume method and unstructured quadrilateral grids were employed to simulate the flow. Theoretical analysis was also conducted to understand the phenomenon. Both numerical and theoretical results indicate a wall-jet penetrating forward is responsible for the occurrence of Mach stem protrusion. The protrusion degree seems to depend on the thermal energy buffer capacity of the testing gas. Approaches to increase the energy buffer capacity, such as vibrational relaxation, molecular dissociation, and increase of frozen heat caoacitv, all tend to escalate the orotrusion effect.

DIFFRACTION OF A SOLITARY WAVE BY A THIN WEDGE PART 2. EFFECTS OF VISCOUS BOUNDARY LAYERS

Based on the study on the Mach reflection of a solitary wave in [3] , we continue to investi- gate effects of the boundary layers on the bottom and the vertical side wall. By using matched asymptotic methods, the two-dimensional KdV equation is modified to account for effects of viscosity. Numerical simulation of the problem shows that the effects of side wall are important while the effects of the bottom can be neglected. The results including the side wall's effects agree satisfactorily with those of Melville's experiments. Finally, we establish the simplified concept of the side wall effect and conclude that it repre- sents the physical reason for the discrepancy between the experiments and the previous calculations based on the inviscid fluid flow theory.

Two-Dimensional Regular Shock Reflection for the Pressure Gradient System of Conservation Laws

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.

Characteristics of the Mach Disk in the Underexpanded Jet in which the Back Pressure Continuously Changes with Time

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.

Shock wave configurations and reflection hysteresis outside a planar Laval nozzle

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.

Numerical Study for Hysteresis Phenomena of Shock Wave Reflection in Overexpanded Axisymmetric Supersonic Jet

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.

Trailing-edge shock loss control with self-sustaining synthetic jet in a supersonic compressor cascade

To effectively reduce the loss of strong shock wave at the trailing edge of the supersonic cascade under high backpressure,a shock wave control method based on self-sustaining synthetic jet was proposed.The self-sustaining synthetic jet was applied on the pressure side of the blade with the blow slot and the bleed slot arranged upstream and downstream of the trailing-edge shock,respectively.The flow control mechanism and effects of parameters were investigated by numerical simulation.The results show that the self-sustaining synthetic jet forms an oblique shock wave in the cascade passage which slows down and pressurizes the airflow,and the expansion wave downstream of the blow slot weakens the shock strength which can effectively change the Mach reflection to regular reflection and thus weaken the shock loss.And the suction effect can reduce loss near blade surface.Compared with the baseline cascade,the self-sustaining jet actuator can reduce flow losses by 6.73%with proper location design and vibration of diaphragm.

Theoretical solutions to three-dimensional asymmetrical shock/shock interaction

This paper explores theoretical solutions to the three-dimensional （3D） shock/shock interaction induced by 3D asymmetrical intersecting compression wedges in supersonic inviscid flows. For Mach interactions, an analytical method known as spa- tial-dimension reduction, which transforms the problem of 3D steady shock/shock interaction into a two-dimensional （2D） pseudo-steady problem on cross sections, is used to obtain the solutions in the vicinity of the Mach stem. The theoretical solu- tions include the pressure, temperature, density, Mach number behind the Mach stem, and total pressure recovery coefficient. Numerical simulations are performed to validate the theoretical results. Here, the NND scheme is employed by solving 3D in- viscid Euler equations, and good agreements are obtained. The asymmetry of the flow characteristics induced by the wedge angle and sweep angle are thoroughly discussed.

Interaction of Waves in Two-dimensional Steady Isentropic Flow

The Euler equations for two dimensional, steady, isentropic, and inviscid flow are considered. All the elementary waves are classified into incoming and outgoing waves under the assumption that there is a singular point in the configuration of the solution.The interactions of at most two incoming waves are dealt with in this paper, and all six kinds of configurations for the solutions are obtained. They are the Mach reflection (one kind), the shock wave S transmits contact discontinuity J (two kinds), the overtaking of two incoming shock waves (two kinds), and the collision of two incoming shock waves (one kind).

Study on cell size variation in overdriven gaseous detonations

The cell size variation in overdriven gaseous detonations is studied in hydrogen/oxygen and acetylene/oxygen mixtures.The local self-similarity of Mach reflection of detonations on the wedge in the far field renders the presence of a steady overdriven Mach stem to be possible.The study focuses on the cell size change of overdriven Mach stem on the wedge surface other than on the sidewall.The detonation cell pattern on the wedge surface has a complicated process of three-stage pattern,i.e.,the cells decreasing from large to small size,and then increasing asymptotically to a medium size and keeping constant.The cell size ratio with increasing the degree of overdrive is also examined.It is found that the ratio decays as the degree of overdrive increases.However,as the wedge angle increases to a critical value,finer cells are not created on the smoke foils.Ng’s model used to predict the cell size is also found to be valid only for detonations with relative large instability parameters,but presents large errors for highly overdriven detonations with low instability.A modification to Ng’s model is proposed based on the experimental results.