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In this paper, the initiation characteristics of the oblique detonation flow field induced by single- and double-wedge surfaces of finite length in a confined space are investigated. Numerical simulations with a detailed H2/air reaction and theoretical shock polar analyses are combined to study the influence mechanism of a complex wave system structure on the characteristics of the oblique detonation. The effects of expansion waves on the oblique detonation waves (ODWs) and their flow field characteristics for different equivalent ratios and geometric sizes are analyzed in single-wedge and double-wedge structures with the same inflow parameters. The results show that the length of the induced ODW is shorter in the double-wedge structure than in the single-wedge structure. For the single-wedge structure, the strength of the expansion wave increases, the wall temperature drops, and the characteristic length of the induction zone decreases with increasing deflection angle of the second wedge. If the strength of the expansion wave is sufficiently large, the ODW is initiated. For the double-wedge structure, the ODWs interact and form a complex wave system structure, consisting of a Mach stem, two reflected detonation waves and slip lines. The length and the temperature before and after the Mach stem decrease with an increase in the strength of the expansion waves. The effects of the expansion waves on the flow field of the ODW are relatively small at a large equivalent ratio and significantly larger at a small equivalent ratio.

The reflection of a moving shock wave over a wedge immersed in a still gas and the reflection of a wedge induced steady shock wave over symmetrical and asymmetrical reflecting surfaces have received intensive considerations since more than 70 years ago. Here we consider a different shock reflection problem—reflection of a moving shock wave over an initially steady oblique shock wave induced by a wedge immersed in supersonic flow. For the flow condition we considered, five moving triple points, with each connecting an incident shock wave, a reflected shock wave and a Mach stem, are identified. By using the reference frame co-moving with each triple point, the type of each shock wave of this triple point is clarified. The present study is significant in that it treats a new shock reflection problem leading to a new shock reflection configuration and showing potential applications in supersonic flow with unsteady shock interaction.

The prediction of Mach stem height can be important in the design of supersonic intake in supersonic and hypersonic flows. It is also important because of the progress in aircraft and rocket engines. An analytical method of predicting the Mach stem height is necessary in theoretical field of shock reflection and is the basis of the comparable computational fluid dynamics (CFD) method. A method for predicting the Mach stem height in steady flows is performed based on the earlier models. In this article, an analytical model for predicting the Mach stem height is improved based on two main assumptions: one is the calculation of the triple point deflection angle when the Mach stem is an oblique shock and the other is about the shape of the free part of the slip line. Under these assumptions, the relations predicting of Mach stem height in two-dimensional steady flow are derived based on the advanced averaging method of the subsonic flow region. The Mach stem heights are decided solely for the incoming flow Mach numbers and the wedge angles by the improved analytical model. As a result, the Mach stem heights by the model of this article are found to agree well with experimental results at lower Mach numbers, but there are relative errors at higher Mach numbers. The convexity of the slip line is also considered.

The transition of an overdriven Mach stem in the Mach reflection of cellular detonations on the wedge is experimentally studied in mixtures of hydrogen and oxygen with different argon dilutions. This study focuses on the changes in the cell size of an overdriven Mach stem on the wedge surface other than those on the sidewall. The detonation cell pattern on the wedge surface has a complicated process, i.e., the cells decrease from a large to a small size and then increase asymptotically to a medium size, which can be considered a three-stage pattern. The changes in cell size in this case do not correspond to the normal cell-size change in a decaying overdriven detonation. This is primarily attributed to the mixed effect of Mach reflection and cellular instability. Furthermore, the cell-size ratio upon increasing the degree of overdrive is examined. It is found that the ratio decreases with increase in the degree of overdrive. However, as the wedge angle increases to a critical value, finer cells are not created on the smoke foils.

Shock wave is a detriment in the development of supersonic aircrafts; it increases flow drag as well as surface heating from additional friction; it also initiates sonic boom on the ground which precludes supersonic jetliner to fly overland. A shock wave mitigation technique is demonstrated by experiments conducted in a Mach 2.5 wind tunnel. Non-thermal air plasma generated symmetrically in front of a wind tunnel model and upstream of the shock, by on-board 60 Hz periodic electric arc discharge, works as a plasma deflector, it deflects incoming flow to transform the shock from a well-defined attached shock into a highly curved shock structure. In a sequence with increasing discharge intensity, the transformed curve shock increases shock angle and moves upstream to become detached with increasing standoff distance from the model. It becomes diffusive and disappears near the peak of the discharge. The flow deflection increases the equivalent cone angle of the model, which in essence, reduces the equivalent Mach number of the incoming flow, manifesting the reduction of the shock wave drag on the cone. When this equivalent cone angle exceeds a critical angle, the shock becomes detached and fades away. This shock wave mitigation technique helps drag reduction as well as eliminates sonic boom.

To study the three-dimensional flow structure of an incident shock/boundary layer interaction, a M2.7 nozzle model with a ramp was tested based on the background-oriented schlieren (BOS) technique. After comparing the results of CFD, shear-sensitive liquid crystal (SSLC), and high-speed schlieren, we conclude that BOS can capture the internal structure of the flow field and that its results are consistent with those of other methods in which the relative error can be controlled to 7%. In this research, a new type of experiment with several light paths was used with BOS technology. Three-dimensional reconstruction of incident oblique shock (primarily the width of Mach stem of the shock wave) and quantitative results of the flow field can be obtained successfully, and BOS shows great potential for the measurement of flow fields.

The asymmetrical Mach reflection configuration is studied analytically in this paper, using an asymmetrical model extended from a recent symmetrical model and accounting for the new features related to asymmetry of the two wedges. It is found that the two sliplines do not turn parallel to the incoming flow at the same horizontal location and the sonic throat locates at the position where the difference of slopes of the two sliplines vanishes. This allows us to define a new sonic throat compatibility condition essential to determine the size of the Mach stem. The present model gives the height of the Mach stem, declined angle of the Mach stem from vertical axis, sonic throat location and shape of all shock waves and sliplines. The accuracy of the model is checked by computational fluid dynamics (CFD) simulation. It is found that the Mach stem height is strongly dependent on asymmetry of the wedge angles and almost linearly dependent on the asymmetry of the wedge lower surface lengths. The Mach stem height is shown to be insensitive to the asymmetry of the horizontal positions of the two wedges. The mechanisms for these observations are explained. For instance, it is demonstrated that the Mach reflection configuration remains closely similar when there is horizontal shift of either wedge.

An analytical model is presented for the configuration of Mach reflection (MR) due to the interaction of two-dimensional steady supersonic flow over asymmetric wedges. The present asymmetric MR model is an extension of an earlier model for the symmetric MR configuration. The overall Mach reflection (oMR) in the asymmetric wedge configuration is analysed as a combination of upper and lower half-domains of symmetric reflection configurations. Suitable assumptions are made to close the combined set of equations. The subsonic pocket downstream of the Mach stem is taken to be oriented along an average inclination, based on the streamline deflections by the Mach stem at the triple points. This assumption is found to give satisfactory results for all types of oMR configurations. The oMR configuration is predicted for all types of reflections such as direct Mach reflection (DiMR), stationary Mach reflection (StMR) and inverse Mach reflection (InMR). The reflection configuration and Mach stem shape given by the model for various sets of wedge angles, especially those giving rise to InMR, have been predicted and validated with the available numerical and experimental data. The von Neumann criterion for oMR is accurately predicted by this model. The asymmetric Mach stem profile is well captured. The variation of Mach stem height with wedge angle is also analysed and it is found that simplification of an asymmetric MR to a symmetric MR leads to over-prediction of the Mach stem height and hence the extent of the subsonic region.

Ducted supersonic flows which are highly diffusive in nature are dominated by the occurrence of reflecting shock waves. Accurate numerical treatment of wall boundary conditions significantly improves the quality of solution. Improvised smoothing technique and introducing artificial viscosity to control diffusion all aid in capturing shocks crisply. In this paper, a new two-step numerical time integration scheme which implements these code development methods for Euler and Navier–Stokes solvers is discussed succinctly. Oddly enough, this solver employs state vector to smoothen the flow and to accelerate convergence, until now believed to be an improbable task and much in defiance to the conventional method of residual smoothing of flux vector in CFD codes. The new set of wall boundary conditions developed for this purpose eliminates the undesirable occurrence of Mach stem in multiple shock reflection problems. The versatility of the code is amply demonstrated through standard validation test cases of internal flows for high and low diffusion in a stepped duct and shock reflecting surfaces, respectively. The results show good agreement between theory and numerical experiments. The fact that this two-step scheme can be applied to existing viscous code with no modifications permit them to be used in gridded solvers as hybrid codes for complex flow simulation.

Mach reflection subjected to the influence of an upstream shock wave from the same side is studied here. This situation occurs when two incident shock waves induced by a double wedge reflect at the same point of the reflecting surface and when the downstream incident shock wave is stronger than the upstream one. A shock polar analysis is used to show that this configuration produces an inverted Mach stem and a type IV shock interference between the Mach stem and the upstream shock wave. This shock interference produces a jet that divides the flow stream downstream of the Mach stem into two ducts with different sonic throats, thus complicating the mechanism by which the Mach stem size is determined. A transition analysis shows that the Mach reflection of the downstream shock wave is promoted by the upstream one. Computational fluid dynamics is used to assess the flow pattern anticipated by shock polar analysis and demonstrates how the heights of Mach stem and jet depend on the inflow Mach number and wedge turning angle.

Mach reflection in steady supersonic flow with two incident shock waves is studied. The second incident shock wave is produced by an additional deflection of the wedge lower surface, at some point ensuring that the two incident shock waves would intersect at the reflecting surface in case of normal reflection. Both theory and computational fluid dynamics (CFD) are used to study the flow structure and the influence of the second incident shock wave. The overall flow configuration, in case of Mach reflection, is shown to be composed of a triple shock structure, a shock/shock interaction structure and a shock/slipline reflection structure. Similar phenomenon, triggered by a high downstream pressure, has been observed before numerically, but not studied theoretically. The second incident shock wave reflects over the slipline to deflect the slipline more towards the reflecting surface, increasing thus the Mach stem height, advancing the transition of regular reflection to Mach reflection of the first incident shock wave, and causing an inverted Mach reflection below the usual von Neumann condition. A Mach stem height model built for a weak second incident shock wave is used to study the influence of the second incident shock wave on the Mach stem height. Both theory and CFD predict a maximum of the Mach stem height at some additional wedge deflection angle.

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. Keywords: Body and wing, Flow field, Hypersonic flow, Shock/shock interaction, Wave configurations

Direct shadowgraph with parallel light combined with high-speed recording has been used to analyze the water jet of a cutting machine. The use of image processing allowed observing sudden expansions in the jet diameter as well as estimating the jet velocity by means of the Mach angle, obtaining velocities of about $$500\,\hbox {m}\,\hbox {s}^{-1}$$ . The technique used here revealed the development of hydrodynamic instabilities in the jet. Additionally, this is the first reporting of the onset of shock waves generated by small fluctuations of a continuous flow of water at high velocity surrounded by air, a result confirmed by a transient computational fluid dynamics simulation.

This work makes an attempt to determine an effective streamwise and spanwise arrangement of a relatively novel control device, the sub-boundary-layer slotted vortex generator, having a slot radius ...

To investigate the effect of bifurcation on the induction time in cylindrical shock tubes used for chemical kinetic experiments, one should know the parameters of the bifurcation structure of a reflected shock wave. The dynamics and parameters of the shock wave bifurcation, which are caused by reflected shock wave–boundary layer interactions, are studied experimentally in argon, in air, and in a hydrogen–nitrogen mixture for Mach numbers $$M =$$ 1.3–3.5 in a 76-mm-diameter shock tube without any ramp. Measurements were taken at a constant gas density behind the reflected shock wave. Over a wide range of experimental conditions, we studied the axial projection of the oblique shock wave and the pressure distribution in the vicinity of the triple Mach configuration at 50, 150, and 250 mm from the endwall, using side-wall schlieren and pressure measurements. Experiments on a polished shock tube and a shock tube with a surface roughness of 20 $${\upmu }$$ m Ra were carried out. The surface roughness was used for initiating small-scale turbulence in the boundary layer behind the incident shock wave. The effect of small-scale turbulence on the homogenization of the transition zone from the laminar to turbulent boundary layer along the shock tube perimeter was assessed, assuming its influence on a subsequent stabilization of the bifurcation structure size versus incident shock wave Mach number, as well as local flow parameters behind the reflected shock wave. The influence of surface roughness on the bifurcation development and pressure fluctuations near the wall, as well as on the Mach number, at which the bifurcation first develops, was analyzed. It was found that even small additional surface roughness can lead to an overshoot in pressure growth by a factor of two, but it can stabilize the bifurcation structure along the shock tube perimeter.

The variable geometry ejector (VGE) used in solar-powered ejector refrigeration systems enables performance regulation with unstable heat input, which is important in solar energy utilization; however, the ejector performance is significantly affected by the nozzle configuration. To study the effects of the nozzle configuration on the VGE and to optimize the VGE configuration, experimental investigations are conducted on a supersonic nozzle and a subsonic nozzle used in the VGE under a variety of operating conditions. The experimental results show a close relationship between the driving flow behavior and the ejector performance. The driving flow behavior is influenced by the occurrence of Mach waves, which is significantly influenced by the nozzle configuration. Numerical simulations are conducted that further explain the Mach wave behavior as well as the driving flow development inside the VGE. The results are significant for the optimization and application of the variable geometry ejector in solar-powered ejector refrigeration systems.

The shock wave standoff distances of near space hypersonic vehicles, which execute missions mainly at the altitude of 25 km to 55 km, are vital in aerothermodynamic analysis. The implicit finite volume schemes are derived from axisymmetric Navier-Stokes equations for chemical equilibrium flow, and programmed in FORTRAN. Taking a sphere cone for example, the effects of Mach numbers (from 22 to 36) on the shock wave standoff distance and the average density behind the shock are simulated at different altitudes from 25 km to 55 km. The numerical results illustrate that the turning point of the standoff distance is corresponding to that of the average density with the variation of Mach numbers. Based on the numerical results, we propose a formula for shock wave standoff distance, which is the function of the radius of the blunt body, the Mach number and the altitude in the atmosphere. Compared with previous correlations, the new formula can overcome the drawbacks of larger relative errors and complex calculations of the average density.

For Mach reflection in steady supersonic flow, the slipline and reflected shock wave from the triple point are disturbed by secondary Mach waves generated over the slipline and by the expansion fan from the rear wedge corner. Analytical expressions for the shape of the curved slipline and reflected shock wave are derived in this paper. It is found that, due to transmitted expansion waves from the expansion fan, the slipline has a slope discontinuity at the turning point, i.e., the intersection point of the slipline and the leading characteristics of the transmitted expansion wave. The hypothetical shock wave calculated by considering this slope discontinuity as flow deflection angle matches a similar wave observed in numerical results by computational fluid dynamics, suggesting the existence of a weak shock wave from this turning point. The effects of the secondary Mach waves upstream of the turning point and of the turning point weak shock wave mutually cancel out approximately so that the transmitted Mach waves can be approximated as straight characteristic lines. This simplification leads to a fast analytical model which can predict the Mach stem height and shape of the slipline and reflected shock wave with increasing accuracy for the decreasing deflection angle of the slipline at the triple point. The slipline slope discontinuity at the turning point and the hypothetical turning point weak shock wave are new phenomena found in this work.

The interaction of a shock wave with turbulent flow was experimentally investigated. The case where a shock wave formed at one end of the tube, passed through the interface between two quiescent gases with different densities (air–CO2 or air–Ar), was reflected from the end of the tube, and interacted with the zone of turbulent mixing formed at the interface. The Mach number of the shock wave incident on the interface in air was M ≈ 2.37–2.57. The flow field was recorded using the schlieren method and high-speed video recording. It was found that after passing the mixing zone, the shock-wave front was deformed and became unstable.

An unsteady viscous numerical simulation is performed to study the starting process of a hypersonic nozzle coupled with a simplified inlet model in a shock tunnel under the condition of inflow Mach number higher than the design value. And the effect of the initial backpressure of test section in shock tunnel on the pulse-starting characteristics of the hypersonic nozzle-inlet is studied. It is found that the operation mode of inlet changes from local unstart to start with the initial backpressure decreasing. At high initial backpressure, two large separation bubbles are induced by the secondary shock at the nozzle walls, the separation induced shock waves repeat reflections between the nozzle walls and a shock train structure appears. The Mach number of the flow into the test section rises and falls repeatedly as a result of the presence of the successive shocks in the shock train structure. During the hypersonic nozzle-inlet starting process, a large separation bubble occurs at the forebody side and the inlet is choked. After the forebody shock moving close to the cowl lip, a bow shock is generated and moves before the cowl lip subsequently. Finally, the quasi-steady flowfield of the inlet is established with a bow shock before the cow lip and a subsonic region at the cowl side, namely the inlet is local unstarted. At low initial backpressure, the separation bubbles at the nozzle walls vanish and no shock train structure appears. Furthermore, an unsteady expansion wave may appear upstream of the secondary shock and the Mach number of the flow following the secondary shock is higher than that of the nozzle quasi-steady flow. The Mach number of the flow into the inlet increases to the maximum value quickly, the inlet starts successfully. The numerical results show that the inlet starts easier and faster with lower initial backpressure.

In order to clarify the mechanisms associated with a local explosion leading to deflagration to detonation transition (DDT) in a rectangular channel, detonation initiation behind the incident shock wave with a weak spark discharge was caused. In this approach the incident shock wave plays a role of the precursor shock wave, while the propagating flame is replaced with a flame kernel generated by the spark discharge. This method was successful in controlling the time and location of detonation initiation with good repeatability. The DDT process was visualized in two perpendicular directions to understand the three-dimensional behavior of the flame and the shock wave generated from flame acceleration. The following conclusions on the DDT process are deduced. (1) A shock wave coupled with a propagating flame eventually reflects off the wall as Mach reflection, behind which an accelerating flame and a shock wave ahead of it are caused. (2) The shock wave interacts with the other shock wave (shock–shock interaction) with more than a Mach number of 3. (3) This shock–shock interaction increases the temperature and pressure of the mixture locally, leading to the generation of a sufficiently strong shock wave with a larger M CJ . (4) The induced chemical energy release sustains the shock wave that decays to M CJ , resulting in propagation as detonation. Because the emergence of the accelerating flame and the shock–shock interaction process are completely three-dimensional phenomena, an understanding of three-dimensional flame and shock behavior is essential to reveal the DDT mechanism.

In this paper unified supersonic theory is used to derive the expressions of Stiffness derivative of a wedge in Hypersonic flow. This paper demonstrates the effects of pivot position on the stffness derivative with Mach number and incidence angle. From the above discussion it is seen that behaviour of the stiffness derivative is the same for h = 0 to 0.4 and also for h = 0.8, 0.9, and 1.0. Due to the pivot position variations there is a significant variation of Stiffness derivative with Mach number and incidence angle.

This paper presents numerical study of detonation initiation induced by shock wave reflection which is photoed by high speed camera in a rapid compression machine. It is found that detonation initiates near the wall of combustion chamber. In the numerical study, the process of shock wave propagation, the interaction between shock wave and wall, and the detonation initiation by shock wave reflection are analysed with a CFD software. The numerical simulation demonstrates that mach reflection occurs near the wall during the propagation of the shock wave in the combustion chamber. The temperature of the region between the slip plane and the wall becomes higher. The auto-ignition of a hot spot in the high temperature region forms shock wave which is coupled with the reaction surface, resulting in the detonation finally.

The study of shock-shock interaction has interested researchers since the days of Ernst Mach. The nonlinearity of the shocks yields a complex interaction featuring a Mach stem. This phenomenon is very similar to the reflection patterns of a planar shock wave over an inclined wedge. As the shocks expand, the two-shock system is no longer able to turn the flow as much as needed, and a Mach stem is generated. As the shocks continue to expand, so too does the Mach stem. The expansion of a shock wave has been studied analytically by Lin (J Appl Phys 25:54–57, 1950) and Taylor (Proc R Soc Ser A Math Phys Sci 201:159–174, 1954) for two and three dimensions, respectively. In these cases, however, there is only a single blast. For shock-shock interaction, von Neumann’s (Oblique Reflection of Shocks. Bureau of Ordinance, Washington, DC, 1943) work using a planar shock wave over a wedge, while similar, does not consider the decaying properties behind an expanding shock wave. This study will focus on two separate numerical methods; geometrical shock dynamics (GSD) and Euler simulations. Each of them was used to study a two-dimensional shock interaction case with two cylindrically expanding shock waves. The results from the GSD and Euler simulations were then compared to analogous experimental work conducted by Higashino et al. (Shock Waves 1:275, 1991). Good agreement is seen between the three cases apart from early times in the case of GSD.

The irregular reflection of weak acoustic shock waves, known as the von Neumann reflection, has been observed experimentally and numerically for spherically diverging waves generated by an electric spark source. Two optical measurement methods are used: a Mach-Zehnder interferometer for measuring pressure waveforms and a Schlieren system for visualizing shock fronts. Pressure waveforms are reconstructed from the light phase difference measured by the interferometer using the inverse Abel transform. In numerical simulations, the axisymmetric Euler equations are solved using finite-difference time-domain methods and the spark source is modeled as an instantaneous energy injection with a Gaussian shape. Waveforms and reflection patterns obtained from the simulations are in good agreement with those measured by the interferometer and the Schlieren methods. The Mach stem formation is observed close to the surface for incident pressures within the range of 800 to 4000 Pa. Similarly, as for strong shocks generated by blasts, it is found that for spherical weak shocks the Mach stem length increases with distance following a parabolic law. This study confirms the occurrence of irregular reflections at acoustic pressure levels and demonstrates the benefits of the Mach-Zehnder interferometer method when microphone measurements cannot be applied.

This paper examines the historical background leading to the discovery of the Mach reflection effect and applies original documents from Mach's residue which are kept in the archives of the Ernst-Mach-Institut in Freiburg. Two experimental setups for the generation and demonstration of the Mach reflection effect, incorporating an overhead projector, are described: (a) Mach's historic mechanical shock wave reflection and interaction experiments with soot covered glass plates, performed in 1875. The Mach triple points sharply erase the soot which results in a residual picture of funnel-shaped V-formations. The head-on collision of two shock waves is marked as a narrow line of piled-up soot. (b) CalTech's hydraulic jump reflection experiments in a shallow ripple tank, performed during World War II. Regular reflection and its transition into a Mach reflection wave. Using a slightly inclined tank and providing a “shoreline” in the middle of the tank, Mach stem propagation slows down to zero when hitting the shore line and, therefore, can be observed “live” without the use of a slow motion technique.

Re-initiation of detonation in a concentric tube arrangement where a detonation exiting from a small diameter inner tube to a large diameter outer tube has been investigated. The outer tube diameter D is 50.8 mm and inner tube diameters d are 38, 25.4, and 12.7 mm giving diameter ratios $$D/d=1.34$$ , 2, and 4. Stoichiometric C $$_2$$ H $$_2$$ –O $$_2$$ mixtures with argon dilution of 0, 25, 50, and 70% are used in the present study. Velocity measurements are made using photodiodes, and smoked foils downstream of the exit of the inner tube are also used to record the re-initiation process. Upon exit from the inner tube, the detonation suffers an abrupt decrease in velocity and at critical conditions, the velocity downstream of the exit is of the order of 50% of the Chapman–Jouguet velocity. It is found that re-initiation generally occurs within 10 tube diameters downstream of the exit. If re-initiation is not successful, the detonation continues to propagate at a low velocity for distances of the order of 30 tube diameters without any indication of flame acceleration of deflagration-to-detonation transition (DDT). Thus, the re-initiation process is clearly defined and distinct from the usual DDT in a smooth tube. The critical $$d/\lambda $$ value ratio in the concentric tube is significantly lower than the usual unconfined case of $$d/\lambda =13$$ where $$\lambda $$ is the detonation cell size. Thus, it is a result of re-initiation at the Mach stem of the reflected shock from the wall of the outer concentric tube. If re-initiation is not successful upon the first reflection, then subsequent multiple reflections at the tube axis and wall of the outer tube can also result in re-initiation. However, this is only observed for undiluted mixtures. For high-argon-diluted mixtures, re-initiation only occurs at the Mach stem of the first reflection.

The paper investigates the explosion characteristics of a below ground event of an explosive charge in proximity to a rigid cylindrical obstacle. The two-dimensional study simulates a line explosive and a parallel long cylindrical structure. The investigation shows that the unloading branch has a negligible effect on the peak pressure envelope whereas shear behavior and explosives burning have a considerable effect and should not be disregarded. The effect of the soil's equation of state and especially the full locking parameter on the pressure distribution on an obstacle has been studied. At a short standoff distance where a steep pressure growth beyond the full compaction point is developed, the pressure distributions envelope shows three maxima values that are located at some distance away from the axis of symmetry. It is different than the common single peak along the axis, in the case of a distant explosion. This effect is more pronounced for a medium having sharper pressure growth in the EOS beyond the full compaction point and for smaller charge standoff distances. The pressure distributions analysis indicates that the appearance of second (absolute-primary) and third (secondary) peaks are caused by the Mach stem effect appearing in a soil medium with full locking. The secondary peak pressure envelope maximum corresponds to the secondary Mach stem phenomenon that does not appear in the case of a planar wall, where the incident angle depends on the wave front curvature only.

The interaction of different types of long-wavelength perturbations of a supersonic incident flow around a wedge with an arising shock wave is simulated numerically. The results of parametric calculations are compared with the data of the linear theory for the interaction of perturbations with a shock wave in the absence of a body. Data on the structure of pressure fluctuations behind the shock wave on the wedge and data on the coefficients of transformation of external perturbations represented in the form of analytical dependences on the angle of inclination of the shock wave, the angle of propagation of external perturbations, and the incident Mach number are obtained.

In order to increase resistance to back pressure in an inlet isolator, an ejecting flow control method is applied in this paper. For the sake of checking out the control effect, test cases with air and cracking gas ejecting are completed in M = 2.41 inlet. According to the numerical results, the resistance to back pressure with air and cracking gas ejecting is increased by 15% and 11.76% at P t , eje = 1.07 × 10 6 Pa and P t , eje = 4 × 10 6 Pa , respectively, which indicates that the control method is effective. The flow field characteristic with air and cracking gas ejecting is compared to reveal the difference of shock/boundary layer interaction and the propagating path of adverse pressure gradient. As the back pressure increased, the adverse pressure gradient can propagate upstream along the wide range of aerodynamic subsonic bands far from the wall, which are formed by the large-scale Mach stem of Mach reflection. Furthermore, the influence of ejecting total pressure on flow field is further analyzed to understand the physical mechanism of the resistance to back pressure. The increase of the ejecting total pressure can indirectly increase the ejecting momentum and decrease the ejecting dynamic viscosity, which prompts the random motion of molecules in the shear layer between ejecting flow and core flow, thereby increasing the mixing of the momentum, mass and energy to narrow the subsonic band and suppress the adverse pressure gradient.

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 capacity, all tend to escalate the protrusion effect.

The interaction of three-dimensional vortex flows was investigated through vortex shedding off a discontinuous edge. Two wedges of $$14.5^\circ $$ wedge angle (up and downstream edges) were separated by an offset. The size of the offset (5, 10, and 20 mm) and the Mach number (Mach 1.32, 1.42, and 1.6) were the key parameters investigated. Experimental images were taken and computational simulations were run; a close relation was found between the two. This enabled the three-dimensional effects of the flow to be studied and analysed. It was found, as the offset increased in size, the vortices shed off the up and downstream edges took a longer time to merge and the strength of the interaction was weaker. The vortex topology changed with a larger offset; the downstream vortex was thinner (in terms of cross-sectional diameter) adjacent to the offset, which is an indication of a change in density, than the rest of the vortex along the downstream diffraction edge. This particular feature was more prevalent at lower Mach numbers. The effect of a higher Mach number was to increase the rate of dissipation of the vortices, lengthen the shear layer due to the higher upstream velocity, and make the vortex profile elliptical.

The Mach number and pressure at the outlet plane of a straight micro-tube were investigated numerically for both laminar and turbulent flow cases. The numerical methodology is based on the arbitrary Lagrangian-Eulerian method. The LB1 turbulence model was used for the turbulent flow case. The compressible momentum and energy equations with the assumption of the ideal gas were solved. The computational domain is extended to the downstream region from the micro-tube outlet. The back pressure was given to the outside of the downstream region. The computations were performed for a tube whose diameter ranges from 50 to 500 μm. The average Mach number at the outlet plane of the choked flow depends on the tube diameter and ranges from 1.16 to 1.25. The flow characteristics of the under-expanded gas flow in a straight micro-tube were revealed.

Numerical analysis was conducted of a jaws inlet under different working conditions, including angles of attack of 0° and 3°, varying Mach number, and varying back pressure with a constant-area isolator, to investigate its performance and flow fields of starting and unstarting states. Results reveal that the jaws inlet has an enhanced flow capture capability in starting states, with the mass capture ratio higher than 0.96, but relatively reduced working range of inflow Mach numbers. Its performance at a low Mach number is better than that at a high Mach number. Non-uniform flow fields are observed in unstarting cases at low Mach numbers and high back pressures, while separation structures are confined in the pitching compression section. Further increase in Mach number or decrease in back pressure does not result in significant changes in the separation structures. In the unstarting case under a high back pressure, it is hard to achieve restarting through reductions in the back pressure.

Experimental and computational methods were used to investigate the characteristics of a scaled, generically shaped weapons internal carriage and separation bay with a length-to-depth ratio of 4.5 at multiple Mach numbers and stagnation pressures. Three new nozzles were designed, manufactured, and characterized for the U.S. Air Force Institute of Technology small supersonic tunnel, yielding freestream Mach numbers of 1.43, 1.84, and 2.22. In addition, a control valve was reconfigured to achieve stagnation pressures as low as 1.0 psia, allowing more realistic scaling. These nozzles were used in conjunction with piezoresistive pressure transducers and high-speed schlieren photography to capture the time history of the pressure and the acoustic spectra of the cavity. The nominal Mach 2.3 nozzle was used in free-drop testing of a 1:20 scaled sphere and compared with computational simulations. The computational solution was obtained using the OVERFLOW solver with incorporated six-degree-of-freedom motion and t...

The aim of this work is to study the attainable velocities for a supersonic diffuser. Numerical analysis is carried out to identify the supersonic characteristics. The deceleration of air from free stream supersonic velocities in the 2D channel has been studied and analysed at a specific altitude. Ramp instalment maximizes the total pressure recovery. The geometry is generated in CATIA software and 2-D flow numerical simulation is done using ANSYS-CFD V15.0. Flow analysis is done by keeping the altitude constant and varying the inlet Mach number. A comprehensive study from the analysis provides the range in which Mach number at the inlet can be varied for a supersonic aircraft. The obtained flow phenomena in the supersonic diffuser domain are reported with the help of Mach number, static pressure, and velocity plots.

The starting process of the flow in an expansion nozzle (nominal Mach number 6) with an outlet diameter of 1.5 m and 8.9 m length, which is used for a large-scale hypersonic shock tunnel in the Key Laboratory of High-Temperature Gas Dynamics, was simulated and analyzed at incident Mach number M-s = 3.9. The calculating domains include the driven section (the shock-tube end, about 4.8m length), the nozzle with about 8.9 m length, and part of the test section (more than 3 m). The characteristics of unsteady nozzle flow, including the shock wave patterns in the nozzle inlet region and inside the nozzle, were analyzed numerically in the viscous and inviscid flow regimes, respectively. The pressure and Mach number results were presented and discussed by comparing with the experimental findings, where the simulated results of the reflected shock wave in the shock tube and the transmitted shock wave inside the nozzle were found to agree well with the test data. Additionally, the case without a contraction section for the throat configuration was also calculated and compared with the case with a contraction section. The effect of the starting flow in these two cases on the flowfield uniformity is discussed in detail in this paper.

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 spatial-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 solutions 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 inviscid Euler equations, and good agreements are obtained. The asymmetry of the flow characteristics induced by the wedge angle and sweep angle are thoroughly discussed.

In this study, the unsteady drag produced by the interaction of a shock wave with a single- and a double-sphere model is measured using imbedded accelerometers. The shock wave is generated in a horizontal circular shock tube with an inner diameter of 200 mm. The effect of the shock Mach number and the dimensionless distance between spheres is investigated. The time-history of the drag coefficient is obtained based on Fast Fourier Transformation (FFT) band-block filtering and polynomial fitting of the measured acceleration. The measured peak values of the drag coefficient, with the associated uncertainty, are reported.

The aim of this project is to study the effect of flow inside the subsonic co-axial nozzle used in aircraft turbofan engine. The study has been carried out by varying the Mach number of secondary flow by maintaining the constant Mach number of primary flow. The coaxial nozzle of the circular section was designed and analysed using CATIA and ANSYS V15.0 software for a Mach number range of 0.3 to 0.6 with secondary sub-sonic flow .The pressure and velocity contours were investigated along the flow. The increase in the velocity difference between the primary and secondary flow results in more turbulence which in turn decreases the potential core length.

The location of shock-induced boundary-layer separation inside the divergent section of convergent–divergent nozzles is studied experimentally. Pressure-sensitive paint technique is used with nozzles of different design Mach numbers in the range 1.4–2.8. Nozzle pressure ratios in the range of 1.12–4.91, corresponding to a “jet Mach number” range of 0.4–1.7 and a Reynolds number range of 0.35×106–0.58×107, are covered in the experiment. As it is well-known, one-dimensional nozzle flow theory grossly overpredicts the throat-to-shock-location distance at a given nozzle pressure ratio. A correlation from the literature based on rocket nozzle databases is also found to be inadequate for these nozzles of lower design Mach number typical of aircraft applications. For the parametric range covered, a simple correlation for the shock location distance is found. All data collapse in a cluster when plotted as a function of the ratio of jet Mach number to design Mach number. A curve-fit equation representing the avera...

Results of an experimental study of the excitation of high-intensity disturbances by a weak external shock wave in laminar boundary layer on flat-plate models with sharp and blunted leading edges at М = 2.5 are reported. The field of disturbances produced by a 2D sticker in turbulent boundary layer on the wall of wind-tunnel test section in the free stream is shown to have the form of an N-wave. It is found that, on the blunted plate, the intensity of pulsations produced by weak external shock waves in boundary layer several times exceeds the intensity of pulsations produced in boundary layer on the model with a sharp leading edge.

The effect of nonequilibrium plasma medium created by low-current gas discharge on a shock wave (Mach number M = 6.8) has been investigated. The shock wave is generated in a shock tube with a circular cross section and then passes through the area of the effect in the working chamber having a square cross section. The gas discharge is ignited in the area of the effect before the arrival of the shock wave by applying voltage to special pin electrodes mounted in the upper and lower walls of the working chamber. In the experiment, the phenomenon of broadening of the shock wave and an increase of its propagation velocity when passing through the region of nonequilibrium gas-discharge plasma was discovered.

Protective barriers are regarded as a useful means to enhance the safety level of buildings and residents in cases of air blast and impact scenarios. However, only limited research exists concerning the properties and effectiveness in mitigating the blast loads of air-permeable metallic barriers, which requires far fewer materials than ordinary solid walls. This paper explores the blast mitigation effect of an innovative barrier type using woven wire mesh. Numerical models were developed and validated against the experimental values of both peak overpressures and maximum impulses, which were published by the authors in a previous study. The influence of the Mach stem formation, which is attributed to the small elevation of the explosive charge above the ground surface, on the blast loads is also examined. It is found that the Mach stem formation significantly affects the peak overpressure at gauge ps1 (1 m ahead of the barriers), whereas its effects on the peak overpressures at the remaining gauges and on the maximum impulses at all gauges are negligibly small. This indicates that the validated numerical models can be used to assess the blast mitigation effect behind the barriers. Based on the numerical results at the employed gauges, the barriers using woven wire mesh can achieve an overpressure (impulse) reduction as high as 31.6% (41.6%) with respect to the free field scenario, in which no obstacles exist in the path of the shock wave propagation. Furthermore, the validated numerical models are used to shed light on the barrier behaviour against air blast by analysing the overpressure-time histories and by visualizing the shock wave propagation. This assists in pointing out the underlying reasons for the noticeable phenomena observed in the experiments. Moreover, two parametric studies are conducted in order to discuss the impact of the gabion wall thickness and the opening span between the gabion walls on the blast mitigation effect of barriers.

In spite of the fact that the process of shock wave reflection has been the subject of considerable research effort over the last few decades [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], the question of the transition between the so-called regular and irregular reflection types is still of particular interest. The analytical approach to describing regular (RR) and Mach (MR) reflection pattern was initiated by von Neumann [13]. He developed the local theory of two- and three-shock configurations that are valid in the vicinity of the intersection point of shock waves. Von Neumann’s theory has been successfully applied to shock wave reflection in steady flows. As for the reflection in pseudo-steady flows, this case is more adequately described by a model proposed by Cabannes [14] for the reflection of a shock wave off an immobile wedge. The main assumption of the theory is that the Mach stem is rectilinear along all its length and perpendicular to the wedge surface. The Cabannes’s theory of pseudo-steady Mach reflection is valid in the finite flow domain. Both theories are mathematically equivalent to each other, and the formal difference is that the given and unknown variables swap places. In the case of the pseudo-steady straight wedge reflection, the given parameters are the Mach number \(M_s\) of an incident shock wave (or the ratio of densities at the shock front), the wedge angle \(\beta \) and the gas specific heat ratio \(\gamma \). Note that in the absence of experimental data one can describe the pseudo-steady reflection process using exclusively Cabannes’s theory, since without experimental data, only two initial parameters, the incident shock Mach number and the wedge angle, are known.

A triple configuration of stationary shocks in a steady gas flow is studied analytically. The study reveals that a new pattern of the triple-shock configuration is formed within the range of Mach numbers exceeding 3.0 and specific heat ratios below 1.4. The reflected wave coming from the triple point deviates down and forms a negative angle of reflection with the initial flow direction. This shock-wave pattern differs from the known positive reflection angle configuration where the reflected wave is inclined upwards to the initial flow direction. The negative angle configuration effect is considered in this study in the problem of a supersonic flow about two wedges. It has been shown, that this configuration is unstable and its appearance leads to a radical change of the total flow pattern. It is suggested that this effect can cause an evident alteration of the flow wave pattern in the problem of a supersonic jet nozzle structure. The range of flow parameters in this study (large Mach numbers and small ratios of gas specific heats) corresponds to spacecraft flights (for example, in Mars atmosphere), as well as flows from the rocket nozzles with triple configurations at Mach reflections in both overexpanded and underexpanded jets. Instability supersonic flows with the analyzed triple configurations can influence both the aerodynamics of spacecraft flight and the functioning of its propulsion engine.

Due to their complexity, certain engineering problems like finding shock strength, Mach number etc. and the interaction of shock wave with a structure in free and restricted metal forming techniques cannot be achieved in a single experimentation, these can be obtained only through a number of trials and that leads to increase in cost and time. In such cases both cost and time can be reduced by adopting numerical simulations. In this projectcommercial software ANSYS is used to simulate the propagation shock wave through a shock tube, free and shape forming of metallic plates subjected to this shock wave. Shock Mach numbers up to 2.12 have been generated by varying the driver to driven pressure ratios. Thin copper plates of diameter 60mm and thickness of 0.5mm and 0.3mm are subjected to shock wave loadingin order to form into dies.These dies,madeof structural steel are modelled with pre-defined shapes. The plate peakoverpressures ranging from 9 to 20bar have been generated.The midpoint deflection, Von Mises stress and strain are calculated for free forming copper plates. The simulated results are compared with the experimental values available in literature. The simulated results match well with the experimental values.

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 condition. 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 conditions, 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.