Shock Reflection Research Articles

Study on the influence of expansion waves on the reflection type of shock wave in double-wedge configurations

Abstract This paper investigates how variations in the relative positioning between the expansion fan emitted from the triple point in the shock/shock interference on double-wedge geometries in confined spaces and the incidence point of oblique shocks influence the transition of oblique shock reflection types, and understands the roles of expansion waves in inhibiting MR. Predictive analysis through the shock polar line provides critical values for the transition of oblique shock reflection types under the influence of expansion fan effects. The position where the shock/expansion fan undergoes post-oblique reflection on the opposite sidewall can be controlled by adjusting the model’s contraction ratio (H 1/H 2). This study uses the density-based solver blastFOAM in openFOAM to numerically solve the Euler equations, conducting inviscid calculations of shock/shock interactions induced by double wedges in confined spaces with ideal gases. This study compares pressure values in different regions obtained from numerical simulations and examines the reflection types of oblique shocks on opposite sidewalls, confirming the feasibility of shock polar analysis and the accuracy of theoretical predictions.

Numerical Simulation of Weak Shock Wave Reflection in Water Media

Abstract Shock wave reflection (SWR) is an interesting physical phenomenon that plays an important role in the ocean engineering. The existing research mainly focused on the gas SWR. Compared with the gas SWR, the water SWR has distinctive features. This article uses numerical methods to study the reflection mode and regularity inside a gas-filled and water-filled wedge. Specifically, we use the fifth-order weighted essentially nonoscillatory method in space and the third-order Runge–Kutta (RK) method in time to solve the compressible Euler equations. The ideal gas equation of state and water equation of state are also considered in the simulations. We developed a numerical solver using the Fortran language based on these equations and numerical methods. The reliability and accuracy of the developed program were validated by the existing theoretical solution and experiment data. Results show that the reflections are different in gas and water media. Regular reflection (RR) and Mach reflection are observed in a gas-filled wedge. However, only the RR is observed in a water-filled wedge for the weak water shock. Besides, it is found that the reflected shock (RS) wave in water is straighter than that in gas medium. Under the same pressure condition, the curvature of the RS wave is larger in a gas medium. The difference in SWR mode can be attributed to the difference in compressibility between the gas and water. It is found that there is a significant increase in temperature behind the incidence shock in the gas due to its high compressibility, which causes the change of local wave speed especially near the reflected wave. However, the temperature and wave speed are approximately constant during the SWR process in water. These distinctions can well explain the difference in SWR modes between gas and water.

Numerical investigation on secondary injection and thrust vector control in a planar double divergent nozzle

In this work, the performance of secondary injection thrust vector control of an altitude adaptive planar double divergent supersonic nozzle is numerically investigated. The compressible turbulent flow is solved using the kT−kL−ω transition-sensitive eddy-viscosity model. An analytical model to predict the separation distance and penetration height due to secondary fluid injection is developed based on the blunt-body theory, and it shows good agreement with the numerical estimation. The computational results indicate that injection pressure, injector location and injection angle significantly impact the thrust vector control performance. The core flow is disrupted by the momentum injection from the secondary fluid, causing the flow field structure to become asymmetrical. The wall pressure imbalance between the upper and lower nozzle increases as the secondary jet pressure elevates. Further, the thrust vectoring amplification factor is improved when the injector is placed downstream near the outlet since the shock reflection is circumvented. Indeed, that resulted in the generation of a large lateral thrust force. Most importantly, for a high injector slot angle, the primary downstream vortex disappears, and a strong secondary upstream vortex is generated, which shifts the primary upstream vortex opposite to the core flow, subsequently the shock separation is advanced. In addition, a secondary injector fitted near the exit with high inclination angles and injection pressure generated a lateral thrust of 20%.

Centerline shock reflection for supersonic internal flows in the non-Rankine-Hugoniot zone: Overexpanded supersonic microjets

The viscous and rarefaction effects on centerline shock reflection occurring in an overexpanded axisymmetric microjet have been investigated numerically by means of a fully coupled pressure-based shock capturing scheme. Due to the low free-stream Reynolds number, the Navier–Stokes equations were coupled with slip velocity and temperature jump boundary conditions to account for rarefied gas effects in the Knudsen layer. It has been found that pronounced viscosity levels can cause a transition from a three-shock to a two-shock configuration, which is impermissible by inviscid theory. This is the first observation of such phenomena in the case of over-expanded jets. Analysis of the von Neumann and detachment criteria indicates that the transition from Mach reflection to regular reflection is analogous to the dual-solution domain transition for planar shocks. In addition, prediction of the longitudinal curvature of the incident shock has been conducted from a mathematical standpoint.

Numerical study on flame acceleration and deflagration-to-detonation transition: Spatial distribution of solid obstacles

This study conducts a detailed numerical investigation on the spatial distribution of solid obstacles using the large eddy simulation method. It is discovered that although flame acceleration induced by solid obstacles is dominated by factors such as flow field disturbances, vortices and recirculation zones, turbulence, flame surface areas and combustion heat release rates, etc., the characteristics of the leading shock wave are key to detonation initiation. Specifically, the intensity of the leading shock wave, its formation time, and its distance from the flame front significantly affect detonation initiation. Depending on the state of the shock wave, the detonation initiation process may occur through various mechanisms such as shock reflection, shock focusing. Overall, the types of detonation initiation in this study all belong to the shock detonation transition. However, the detonation initiation process can be further classified into two categories: (I) Detonation induced by shock wave reflection; (II) detonation triggered by shock wave focusing. Despite certain disparities in the detonation initiation process, all detonation initiation processes conform to the gradient theory, and the flame evolution processes in all cases consistently follow three stages: the laminar slow-ignition stage; the turbulent deflagration stage; the detonation initiation stage. Furthermore, the study further discerns that, compared to positioning obstacles on the wall, placing obstacles inside the combustion chamber can further augment the detonation-assisting effect. However, excessively sparse or dense spatial distributions of solid obstacles fail to yield the optimal detonation effect. An optimal distribution exists, which triggers the fastest detonation initiation.

Numerical investigation of annular expansion-deflection nozzle flow under varying backpressure changing rate

The characteristics of flow and thrust evolution of an annular Expansion-Deflection (ED) nozzle are numerically investigated under varying backpressure changing rates during ascending and descending trajectories. The objective is to test the sensitivity of unsteady behaviors of shock waves in the ED nozzle to backpressure changing rate, and to further elucidate the thrust evolution mechanism and mode transition hysteresis. The movement of shock reflection points on the nozzle wall follows two flow mechanisms, namely, shock self-excited oscillations and rapid backpressure changes. A low backpressure changing rate enables shock self-excited oscillations, leading to a reciprocating motion of the shock waves accompanied by thrust oscillations, while a high backpressure changing rate suppresses the shock self-excited oscillations, leading to a unidirectional motion of the wave system on the nozzle shroud wall. A criterion for distinguishing ED nozzle operation modes is proposed, which relies on the loading inflection points of the nozzle pintle base and exhibits a fast and user-friendly feature. A dual-wake mode hysteresis region is defined to quantify the hysteresis in nozzle mode transition, with the span of the region decreasing as the backpressure changing rate slows down. The present work helps in understanding the unsteady flow mechanism and thrust evolution in ED nozzles.

Unsteady Standoff Shock Behaviour Associated With Supersonic Impinging Jets

It was observed in an earlier study [Lim, H. D., New, T. H., Mariani, R., & Cui, Y. D. (2019). Effects of bevelled nozzles on standoff shocks in supersonic impinging jets. Aerospace Science and Technology, 94, 105371.] that standoff shocks in M=1.45 supersonic impinging jets produced by non-bevelled and bevelled nozzles under small separation distances may undergo large and abrupt fluctuations in their positions above the impingement points. This occurs when the separation distance is h/d=1.5 and for nozzle-pressure-ratio (NPR) between NPR=4 and 5, where h is the distance between the nozzle exit and flat-wall and d is the jet diameter. It has to be highlighted that the observed behaviour is unlike the more minor positional fluctuations typically associated with supersonic impinging jets. To reveal further details on the unsteadiness of the standoff shock, color schlieren results will be presented here to shed more light on the flow phenomenon, while initial modelling efforts to reproduce these standoff shock behaviour will be elaborated. Present results reinforce the notion that the large standoff shock fluctuations are due to the standoff shock trying to achieve pressure equilibrium through abrupt displacements when variation in the NPR changes the location of the shock reflection point. Considering the small separation distance used, small NPR changes are able to trigger abrupt standoff shock unsteadiness.

Numerical investigation of the reflection of unsteady decelerating incident shock waves

The incident shock attenuation phenomenon in shock tube has received widespread interest because of its inevitable influence on experimental gas properties. However, few studies have investigated the cascading effects of the resulting nonuniformity on shock reflection in shock tunnels before the nozzle. This paper describes a numerical study on the unsteady reflection of a decelerating incident shock driven by a decelerating piston, as a simplification of the complex nonideal factors. The initial decay and uniform parameter distributions are generated based on the non-inertial frame. The results indicate that the existence of the nonuniform area forces the reflected shock wave region to undergo a transition process of attenuation and then stability. The final values of the gas parameters in zone 5 will, therefore, deviate from those given by the traditional relation for an ideal shock tube, which are only dependent on the terminal shock Mach number. This affects the determination of the total temperature T5, which is difficult to measure directly. We discuss the reconstruction of the nonuniform region with the attenuation trajectory of the incident shock wave and find that there is no one-to-one correspondence between this trajectory and the resulting nonuniformity, which introduces additional uncertainties to the predictions. Thus, an analogy method is developed through the multilevel block building algorithm, allowing the total temperature T5 to be determined using the total pressure p5 considering the effect of nonuniformity. Further assessments verify the applicability of this method in cases with multidimensional and viscous interactions.

Fully appreciating the impossibility of shock wave regular reflection from the axis of symmetry in axisymmetric internal flows

This study investigates the reflection of shock waves in internal axisymmetric flows and conclusively shows that regular reflection cannot occur over the axis of symmetry. The analysis employs the curved shock theory to examine flow gradients behind the axisymmetric shock. The curved shock equations are presented in explicit form using influence coefficients, which establish a direct relation between flow gradients in polar coordinates and shock curvatures. The gradient information reveals that the flow behind the incident shock around the reflection point is governed by the Taylor–Maccoll equation, indicating that the flow pattern is locally conical. By analyzing the singularity of internal conical flows, the only possible structure of conical shock reflection with a smooth singularity is constructed. After a thorough theoretical analysis of this conical shock reflection structure, the study concludes with definitive proof that this specific flow pattern cannot occur in practical applications because it requires the incident shock angle to be less than the freestream Mach angle. This suggests that regular reflection is impossible to occur over the axis of symmetry in internal axisymmetric flows.

Surrogate-based shape optimization and sensitivity analysis on the aerodynamic performance of HCW configuration

With an additional wing upon the fuselage, the novel high-pressure capturing wing (HCW) configuration exhibits remarkable aerodynamic characteristics at hypersonic speeds under beneficial aerodynamic interference. This bi-wing structure can also enhance the lift at subsonic speeds, positioning HCW configuration as an excellent aerodynamic layout under wide-speed range conditions. In this paper, a single-wing principle HCW configuration is carried out to analyze the influence of the variations in the geometric parameters of the HCW on the aerodynamic performance. Drawing on extant research, four key geometric parameters of the HCW are chosen as design variables, and the hypersonic as well as supersonic conditions are selected for surrogate-based shape optimization. Utilizing polynomial response surface method and method of moving asymptotes, the single-objective optimization studies are carried out with the objectives of maximum lift-to-drag ratio at Ma = 6 and minimum drag coefficient at Ma = 3. Subsequently, the sensitivity analysis is performed for each design parameter. The above methods exhibit notable precision and favorable results. The results show that except for the leading-edge sweep angle, the other three optimization results exhibit divergent trends in their variations. The setting angle has the most significant influence on the aerodynamic forces, owing to the influences of its variation on the shock wave intensity and reflection angle. Based on the stronger intensity of shock wave, this sensitivity indices are higher at Ma = 6. The other three parameters (half-span, leading-edge sweep angle, and trailing-edge sweep angle) modify the aerodynamic forces by adjusting the area of high-pressure region on HCW. Due to the different flow field structures, optimum parameters exhibit diverse effects on lift coefficient and lift-to-drag ratio.

Real Gas Corrections Based on the Interaction of One-Dimensional Unsteady Waves in a Shock Tube

There are multiple unsteady wave system interactions such as shock waves, expansion waves, and reflection, transmission, and intersection of the contact surface inside a shock tube. Studying the law of unsteady wave system interaction has important guiding significance for the design of gas wave equipment. This paper proposes a solution method for the interaction law of unsteady wave systems based on real gas equation of state (EoS) and applies it to shock tubes. The results show that the temperature maximum error between the code based on ideal gas EoS and simulation results is 3.64%, and the error of wave velocity results is between 2.99% and 18.27%. While the error of temperature results between code based on real gas EoS and simulation is not exceed 3%. More importantly, the wave velocity calculated by the code based on real gas EoS is pretty consistent with the simulation results. The code based on the real gas model can help to solve the problem of offset design point. Research has also shown that as pressure and temperature gradually increase, the deviation between ideal and real gases increases, which also proves that the influence of real gas effects is becoming increasingly significant.

Self‐control or social control? Peer effects on temptation consumption

AbstractThis paper examines peer effects on self‐control problems. I construct a theoretical model to describe how peer networks influence consumption behaviors through social norms. Using monthly survey data conducted in 16 Thai villages from 1999 through 2004, I find that peer's temptation consumption significantly impacts individuals' temptation consumption such as alcohol, tobacco, and gambling. A one baht (around $0.025 U.S. dollars) increase in peer's temptation consumption leads to a 1.5 times increase in one's own temptation consumption. With detailed household‐level social network information defined by actual transactions, this paper identifies peer effects using a friend of a friend (excluded network) as the instrument. The panel nature of this instrument overcomes various common identification challenges, such as reflection, correlated effects, and common unobservable shocks, in the literature. My findings suggest that these peer effects are driven primarily by social norms, rather than risk sharing.

Modelling of high-speed engine flows using a space-marching method

A computationally efficient mathematical model was developed to analyze high-speed engine flows. The inlet and nozzle flows were modelled using the space-marching method to automatically solve the shock reflection and nozzle plume flow. The combustor flow was treated using a quasi-one-dimensional model that considered the rise in pressure of the isolator owing to the shock train. The resulting model was compared with the experimental results. Three test cases were used to validate the model's accuracy: 1) a hydrogen-fuelled combustor experiment, 2) an integrated inlet/combustor configuration experiment, and 3) a single-expansion-ramp nozzle flow experiment. The results showed that the space-marching method predicted the pressure profiles of the inlet flow and nozzle plume flow with reasonable accuracy. The computational time for the inlet and nozzle flows merely takes several minutes on a CPU with 3.6 GHz. The quasi-one-dimensional model calculated the fuel ignition and pressure rise in the combustor with a high computational efficiency of several seconds. The integration of the space-marching method and quasi-one-dimensional method can be developed as a powerful tool for fast evaluations of high-speed engine performance.

Experimental Verification of a Modified Cylindrical Focused Laser Differential Interferometer

A modification to cylindrical focused laser differential interferometry (CFLDI) that, without beam intersection, can achieve smaller stand-off distances from flat geometries than conventional FLDI is presented. The modified system uses a cylindrical lens pair to expand and collimate the beam in a single direction, parallel to the model surface, forming a long, flat, elliptical profile. Subsequently, a spherical lens focuses the beam. Mach 7.3 hypersonic flow, produced by the T4 Stalker Reflected Shock Tunnel, was used for an experimental comparison between the responses of the modified CFLDI and a similar FLDI system in the freestream and just above the boundary-layer edge. Good agreement between the modified CFLDI and FLDI among all measured frequencies was observed when probing near the boundary-layer edge. The comparison in the freestream had good agreement up to 1500 kHz, and higher frequencies saw the modified CFLDI response attenuated at a shallower angle than the FLDI. A combination of different system parameters and base noise levels between the experiments is believed to account for this difference. The modified CFLDI system was used to probe inside the boundary layer, achieving a y/δ of approximately 0.4, where broadband turbulence is detected.

Regular reflection of shock waves in steady flows: viscous and non-equilibrium effects

Numerical analysis of a steady monatomic gas flow about the point of the regular reflection of a strong oblique shock wave from the symmetry plane is conducted with the Navier–Stokes–Fourier (NSF) equations, the regularized Grad 13-moment (R13) equations and the direct simulation Monte Carlo (DSMC) method. In contrast to the inviscid solution to this problem completely defined by the Rankine–Hugoniot (RH) relations, all three models predict a complicated flow structure with strong thermal non-equilibrium and a long wake with flow parameters not predicted by the RH relations. The temperature $T_y$ related to thermal motion of molecules in the direction normal to the symmetry plane has a maximum inside the reflection zone while in a planar shock wave the maximum is observed for the $T_x$ temperature. The R13 equations predict these features much better than the NSF equations and are in good agreement with the benchmark DSMC results. An analysis of the flow with the conservation equations was conducted in order to evaluate the effects of various processes on a fluid element moving along the symmetry plane. In contrast to the shock wave where effects of viscosity and heat conduction are one-dimensional with zeroth net contribution to the fluid-element energy across the shock, the flow across the zone of the shock reflection is dominated by two-dimensional effects with positive net contribution of viscosity and negative contribution of heat conduction to the fluid-element energy. These effects are believed to be the main source of the wake with parameters deviating from the RH values.

A shock-stable rotated-hybrid Riemann solver on rectangular and triangular grids

The rotated Riemann solver is robust against the carbuncle phenomenon, especially for multidimensional computation. Moreover, hybrid techniques are usually used to enhance the stability of an accurate scheme by combining an accurate scheme with a diffusive scheme. This paper proposes a rotated-hybrid Riemann solver named the rotated-HLLC+ scheme. The scheme is developed by hybridizing the Harten–Lax–van Leer contact (HLLC) scheme with the advection upstream splitting method based on a flux vector splitting (AUSMV+) scheme by following the rotated Riemann solver approach. The unit vector n1 is calculated from the velocity-difference vector, and the unit vector n2 is the orthogonal vector. The linearized analysis suggests that the HLLC scheme should be used in the direction of n1 and the AUSMV+ scheme in the direction n2. In this way, the hybrid scheme becomes shock-stable with less numerical dissipation. Moreover, the pressure-based method is used to detect the shock wave. Several numerical experiments suggest that the pressure cutoff parameter εp=0.01 may be generally suitable and provide a stable solution with little additional numerical dissipation. The last two numerical examples show that the computational performance of the rotated-HLLC+ scheme is comparable to the HLLC scheme for the weak shock reflection over convex double wedges. However, the scheme is approximately 9% faster than the HLLC scheme for the double Mach reflection of a strong shock wave. The proposed scheme gives fast, stable, and accurate solutions on rectangular and triangular grids.

Gas dynamics at starting and terminating phase of a supersonic exhaust diffuser with a conical nozzle

This research investigates the process of starting and breakdown of second throat diffuser during high-altitude test of conical nozzle with a high expansion ratio. The subscale experimental setup includes a conical nozzle with an expansion ratio of 53, plus a second throat diffuser with a contraction ratio of 1.85, using compressed air as the working fluid. Numerical simulation has been employed to identify the flow physics during the unsteady process of diffuser startup and breakdown. According to the results, the starting process is divided into three distinct stages. In the first stage, the exhausted flow from the nozzle enters the vacuum chamber, leading to an increase in vacuum chamber pressure. The second stage, corresponding to the period before full flow establishment in the conical nozzle, exhibits a relatively constant slope. In the final stage, associated with the transition from over-expanded to under-expanded states, the slope of the rate of evacuation development descends. Next, the vacuum degradation in termination process has been analyzed, and it has been found to include three stages: high slope, middle slope, and low slope. The flow physics during the start process, similar to the results observed in other conical nozzles, exhibits only a Mach reflection structure. However, during the termination process, the flow physics involve a combination of both structures, including Mach reflection and Cap Shock. The results indicate that during the start, an internal shock only interacts with the separation shock, and no special change occurs in the Mach reflection structure. In contrast, during the termination process, unlike what has been reported in previous studies on conical nozzles, the structure of cap shock waves and restricted shock separation patterns are also observed. Another distinction between the starting and termination processes is related to the pressure distribution in the diffuser wall. The wall pressure at the diffuser inlet during the termination process has been reported to be 90% higher than during the starting process.

Mesoscopic Kinetic Approach of Nonequilibrium Effects for Shock Waves.

A shock wave is a flow phenomenon that needs to be considered in the development of high-speed aircraft and engines. The traditional computational fluid dynamics (CFD) method describes it from the perspective of macroscopic variables, such as the Mach number, pressure, density, and temperature. The thickness of the shock wave is close to the level of the molecular free path, and molecular motion has a strong influence on the shock wave. According to the analysis of the Chapman-Enskog approach, the nonequilibrium effect is the source term that causes the fluid system to deviate from the equilibrium state. The nonequilibrium effect can be used to obtain a description of the physical characteristics of shock waves that are different from the macroscopic variables. The basic idea of the nonequilibrium effect approach is to obtain the nonequilibrium moment of the molecular velocity distribution function by solving the Boltzmann-Bhatnagar-Gross-Krook (Boltzmann BGK) equations or multiple relaxation times Boltzmann (MRT-Boltzmann) equations and to explore the nonequilibrium effect near the shock wave from the molecular motion level. This article introduces the theory and understanding of the nonequilibrium effect approach and reviews the research progress of nonequilibrium behavior in shock-related flow phenomena. The role of nonequilibrium moments played on the macroscopic governing equations of fluids is discussed, the physical meaning of nonequilibrium moments is given from the perspective of molecular motion, and the relationship between nonequilibrium moments and equilibrium moments is analyzed. Studies on the nonequilibrium effects of shock problems, such as the Riemann problem, shock reflection, shock wave/boundary layer interaction, and detonation wave, are introduced. It reveals the nonequilibrium behavior of the shock wave from the mesoscopic level, which is different from the traditional macro perspective and shows the application potential of the mesoscopic kinetic approach of the nonequilibrium effect in the shock problem.

FR0 jets and recollimation-induced instabilities

Context. The recently discovered population of faint Fanaroff-Riley type 0 (FR0) radio galaxies has been interpreted as the extension to low power of the classical FRI sources. Their radio emission appears to be concentrated in very compact parsec scale cores, any extended emission is very weak or absent, and very-long-baseline interferometry (VLBI) observations show that jets are already mildly or sub-relativistic at parsec scales. Based on these observational properties, we propose here that the jets of FR0s are strongly decelerated and disturbed at the parsec scale by hydrodynamical instabilities. Aims. With the above scenario in mind, we studied the dynamics of a low-power relativistic jet propagating into a confining external medium, focusing on the effects of entrainment and mixing promoted by the instabilities developing at the jet-environment interface downstream of a recollimation shock. Methods. We performed a 3D relativistic hydrodynamical simulation of a recollimated jet by means of the state-of-the-art code PLUTO. The jet was initially conical, relativistic (with an initial Lorentz factor Γ = 5), cold, and light with respect to the confining medium, whose pressure is assumed to slowly decline with distance. The magnetic field is assumed to be dynamically unimportant. Results. The 3D simulation shows that, after the first recollimation and reflection shock system, a rapidly growing instability develops, as a result of the interplay between recollimation-induced instabilities and Richtmyer-Meshkov modes. In turn, the instabilities promote strong mixing and entrainment that rapidly lead to the deceleration of the jet and spread its momentum to slowly moving, highly turbulent external gas. We argue that this mechanism could account for the peculiarities of the low-power FR0 jets. For outflows with a higher power, Lorentz factor, or magnetic field, we expect that the destabilizing effects are less effective, allowing the survival of the jet up to the kiloparsec scale, as observed in FRIs.

Reflection of a rightward-moving oblique shock of first family over a steady oblique shock wave

The reflection of a rightward-moving oblique shock (RMOS) belonging to the first family, over an initially steady oblique shock wave (SOSW) produced by a wedge, is studied in this paper. To cover all possibilities, the problem is divided into a pre-shock reflection problem, for which the incident shock is assumed to reflect over the pre-interaction part of the SOSW, and a post-shock reflection problem, for which the incident shock is assumed to reflect over the post-interaction part. Such division, together with the definition of the equivalent problem defined on the reference frame co-moving with the nominal intersection point of the two shock waves, allows us to connect the reflection patterns with the six types of shock interference of Edney, which include type I–VI shock interferences depending on how an upstream oblique shock intersects a bow shock (types I and II are regular and Mach reflections of two shocks from the opposite sides; type III and type IV have two triple points or two Mach reflection configuration; type V and type VI are irregular and regular reflections of two shocks from the same side). We are thus able to identify all possible shock reflection types and find their transition conditions. Pre-shock reflection may yield IV, V and VI (of Edney's six types) shock interferences and post-shock reflection may yield I, II and III shock interferences. Pre- and post-shock reflections possibly occur at two different parts of the SOSW, and the complete reflection configuration may have one or both of them. Both transition condition study and numerical simulation are used to show how pre-shock reflection and post-shock reflection exist alone or coexist, leading to various types of combined pre-shock and post-shock reflections.