Incident Shock Wave Research Articles

Explosion wave and crack field of an eccentric decoupled charge.

To investigate the characteristics of the explosion damage from an eccentric decoupled charge, the rock-breaking mechanism of an eccentric decoupled charge is revealed from the perspectives of the explosion wave field and crack field through theoretical and experimental analyses. The ratio of the maximum to minimum pressure on an eccentric decoupled hole wall increases exponentially with an increase in the decoupling coefficient, but it does not change with a change in the explosive density or explosive detonation velocity. The explosive energy on the eccentric charge side has a certain accumulation effect, the velocity of the reflected shock wave at the blasthole wall is greater than that of the incident shock wave, and the incident velocity of the explosion wave on the eccentric side is greater than that on the non-eccentric side. The expansion range of the explosion gas is significantly better than that on the non-eccentric side, indicating that the eccentric decoupled charge can strengthen the action of the explosion gas product on the eccentric side. In addition, the overpressure of the explosion wave on the eccentric side is greater than that on the non-eccentric side. The fractal dimension and damage degree of the explosion crack on the eccentric side are larger than those on the non-eccentric side. The explosion cracks can be divided into intensive, transition, and sparse areas, and the fractal dimension and damage degree decrease successively in the three areas. The explosion cracks formed on the non-eccentric side outside the range of three times the blasthole diameter concentrate in the sparse area, and the destructive effect of the explosion on the non-eccentric side medium is effectively reduced.

Transition study for asymmetric reflection between moving incident shock waves

The transition criteria seen from the ground frame are studied in this paper for asymmetrical reflection between shock waves moving at constant linear speed. To limit the size of the parameter space, these criteria are considered in detail for the reduced problem where the upper incident shock wave is moving and the lower one is steady, and a method is provided for extension to the general problem where both the upper and lower ones are unsteady. For the reduced problem, we observe that, in the shock angle plane, shock motion lowers or elevates the von Neumann condition in a global way depending on the direction of shock motion, and this change becomes less important for large shock angle. The effect of shock motion on the detachment condition, though small, displays non-monotonicity. The shock motion changes the transition criteria through altering the effective Mach number and shock angle, and these effects add for small shock angle and mutually cancel for large shock angle, so that shock motion has a less important effect for large shock angle. The role of the effective shock angle is not monotonic on the detachment condition, explaining the observed non-monotonicity for the role of shock motion on the detachment condition. Furthermore, it is found that the detachment condition has a wavefunction form that can be approximated as a hybrid of a sinusoidal function and a linear function of the shock angle.

A numerical study of segmented cooling-stream injection in supersonic film cooling

The present study proposes a segmented cooling-stream injection structure based on a certain coolant mass flow rate, and numerically investigates the effect of segmented cooling-stream injection on supersonic film cooling. The results indicate that without shock-wave impingement and with helium as the coolant, segmented cooling-stream injection can reduce the mixing between the mainstream and the cooling stream to produce better cooling performance than single injection, especially at larger coolant Mach numbers. However, with nitrogen as the coolant, the cooling effect of the segmented-injection system is very close to that of the single-injection system. Mixing at the impinging region is enhanced significantly when there is an incident shock wave. When the shock wave impinges between the two coolant inlets, segmented cooling-stream injection improves film cooling effectiveness in the midstream and downstream regions more than single injection because only part of the cooling stream undergoes the enhanced mixing effect of the shock wave. The advantage of segmented injection is reduced when the impinging region is behind the second coolant inlet. The further downstream the impinging region, the smaller the associated advantage.

Analysis of the ignition induced by shock wave focusing equipped with conical and hemispherical reflectors

The interaction of a plane shock wave in air with concave profiles has been used in the past to understand the nature of shock wave focusing. The current study examines the complex two-dimensional flow field resulting from the interaction of a plane shock wave entering a symmetrical cavity with a curved end wall. The development of reflection patterns of the incident shock wave at the profile wall and the process of gas dynamic focus are of particular interest. In this study, numerical and experimental studies are performed to understand the ignition behavior in a stoichiometric methane-oxygen-argon mixture due to shock wave reflection from a variety of shapes, including planar, 60° and 90° conical and hemispherical reflectors. The numerical simulation reveals the complex two-dimensional flow field when the shock wave collides head-on with different reflectors and the propagation behavior of the reflected waves in the process of focusing. The instantaneous maximum temperature and pressure as a function of shock wave intensity in four reflectors are given and analyzed. The experimental results show that two ignition modes, namely, weak ignition and strong ignition, occur in those reflectors when the incident shock wave velocity (Vi) is greater than a critical value, and the separatrix between the weak and strong ignition for each reflector is demonstrated to be highly dependent on Vi. The critical values of Vi for the 60° conical, 90° conical and hemispherical reflectors are 740, 775 and 780 m/s, respectively. The ignition delay time (tign) of the combustible mixture under shock wave focusing for various reflectors is provided. The results show that in the weak ignition mode, tign is shorter in the hemispherical reflector than in the others, and therefore, its Pign (the maximum pressure after ignition) is higher. However, the result is completely opposite in the strong ignition mode, which is mainly because the ignition temperature of hot spots in the hemispherical reflectors is much lower than those in the conical reflectors. This study provides new simulation and experimental evidence of the ignition behavior in various reflectors, supporting the effect of enhancing shock wave focusing on the ignition performance.

Numerical simulation of the interaction of the disturbed boundary layer with an incident shock

Interaction of the disturbed supersonic boundary layer with an incident oblique shock wave is studied numerically with eddy-resolving numerical simulations. Eigenmodes of the linear stability theory are used to generate the inflow boundary layer disturbances. The evolution of unstable boundary-layer disturbances, effects of the incident shock on the disturbances, effects of the disturbances on the boundary layer separation, flow dynamics in the separation zone, and laminar-turbulent transition are studied.

Direct numerical simulation of supersonic turbulent expansion corner with shock impingement

This study conducted a direct numerical simulation of an incident shock wave impinging at an angle of 33.2° on a 12° supersonic turbulent expansion corner at Mach 2.25 to determine the influence of expansion on the physics of interaction. The point of nominal impingement was located at the tip of the expansion corner. This scenario was compared in detail with interactions in the case of a flat plate under the same inflow conditions. The expansion led to a significant reduction in the wall pressure and the size of the separation bubble. The pre-multiplied spectra of the fluctuating wall pressure indicated that the motion induced by the low-frequency shock was strongly inhibited by the presence of an expansion corner. The root mean-squared wall pressure declined rapidly downstream of the corner, and relaxed at a nearly constant level very close to its upstream value. The evolution of the reattached boundary layer was analyzed in terms of its velocity profile, map of anisotropic invariance, and turbulent kinetic energy, and a quick recovery process was clearly identified. Moreover, the analysis of decomposition of the mean skin friction revealed the dominant contribution of the turbulent kinetic energy regardless of the effect of expansion. Unlike in the case of flat-plate interaction, the component of negative spatial growth became positive owing to large positive streamwise heterogeneity, and could be neglected. Bidimensional empirical-mode decomposition was used to decompose the fluctuations into four modes with specific spanwise length scales, and the primary mechanism for the generation of skin friction was linked to small-scale structures in the near-wall region.

Evolution of artificial disturbances in a shear layer at M=1.43

The evolution of artificial disturbances in a laminar boundary layer on a flat plate model in the presence of an incident shock wave is considered. The flow is supersonic with the freestream Mach number M = 1.43. The study is carried out by hot-wire anemometry. A dielectric barrier discharge is used to generate disturbances. Data on the distribution in space of the average and non-stationary components of the mass flow are obtained. Disturbances created by the discharge and their evolution along the separation zone are recorded.

Boundary-layer viscous correction method for hypersonic forebody/inlet integration

The aerodynamic shape of the hypersonic forebody/inlet integrated vehicle is usually designed according to the inviscid flow. However, due to the effect of air viscosity, there is a boundary layer flow near the wall surface. In order to get the actual flow characteristics and performance parameters of the inviscid design vehicle close to the inviscid design values, the inviscid design surface must be corrected by considering the viscous boundary layer. In this paper, the theory and method of the boundary-layer viscous correction (BLVC) for the forebody/inlet integrated configuration are studied. Firstly, two modification schemes of the BLVC for the forebody/inlet integrated configuration are proposed. The calculation method of boundary-layer displacement thickness (BLDT) based on the momentum integral equation of steady two-dimensional (2D) axisymmetric compressible flow is described in detail, and two calculation methods of the BLDT are compared and analyzed. Secondly, the numerical simulation method used in this paper and its validation are introduced. Thirdly, an axisymmetric configuration of the forebody/inlet integration is selected as the first case, and two modification schemes of BLVC are studied and analyzed by numerical simulation. The effects of the two modification schemes of BLVC on the internal and external flow characteristics and aerodynamic performance of the axisymmetric configuration of the forebody/inlet integration are compared and analyzed. Finally, a full-waverider configuration of the forebody/inlet integration is selected as the second case, and the second modification scheme of the BLVC is used to modify the full-waverider configuration. The shock wave characteristics and inlet performance parameters of the modified full-waverider configuration are studied by both the numerical simulation and the wind tunnel experiment. The obtained results prove that the calculation method of the BLDT by a numerical integration method to solve the momentum integral equation of the steady 2D axisymmetric compressible flow is correct and the BLVC method and scheme for the forebody/inlet integrated configuration are effective. The modification scheme 1 of the BLVC can only improve the characteristics of forebody shock wave incident on the inlet lip under viscous conditions, that is, to improve the performance of inlet to capture precompressed air flow, while the modification scheme 2 of the BLVC can simultaneously improve the characteristics of forebody shock wave incident on the inlet lip and the characteristics of the lip shock wave cancelled on the shoulder of the inlet under viscous conditions, and make the air flow capture performance of the inlet and the pressure rise ratio at the inlet exit close to those of the inviscid design state.

Two-phase Interactions between Propagating Shock Waves and Evaporating Water Droplets

One-dimensional numerical simulations based on hybrid Eulerian-Lagrangian method are performed to study the interactions between propagating shocks and dispersed evaporating water droplets. Two-way coupling for exchanges of mass, momentum, energy and vapour species is adopted for the dilute two-phase gas-droplet flows. Interphase interactions and droplet breakup dynamics are investigated with initial droplet diameters of 30, 50, 70 and 90 {\mu}m under an incident shock wave Mach number of 1.3. Novel two-phase flow phenomena are observed when droplet breakup occurs. First, droplets near the two-phase contact surface show obvious dispersed distribution because of the reflected pressure wave that propagates in the reverse direction of the leading shock. The reflected pressure wave grows stronger for larger droplets. Second, spatial oscillations of the gas phase pressure, droplet quantities (e.g., diameter and net force) and two-phase interactions (e.g., mass, momentum, and energy exchange), are observed in the post-shock region when droplet breakup occurs, which are caused by shock / droplet interactions. Third, the spatial distribution of droplets (i.e., number density, volume fraction) also shows strong oscillation in the post-shock region when droplet breakup occurs, which is caused by the oscillating force exerted on the droplets.

Numerical simulation on interaction between blast shock wave and human thorax

The finite element model for simulating the interaction between blast shock wave and human thorax is established to analyze the propagation characteristics of stress wave in human thorax and the dynamic response of human thorax. The shock wave at the front of thorax is reflected by thorax surface and has the highest peak overpressure. The shock wave on the back of thorax is superimposed by diffraction shock waves from two sides of thorax and has the smallest peak overpressure. The overpressure of diffraction shock waves on both sides of thorax is similar. Due to the difference of impedance characteristics of thorax materials, the lung near the explosive point is mainly affected by compression waves transmitted by the incident shock wave through the muscles and sternum. The side lung is affected by the weak extension wave caused by the deformation of the sternum and the strong compression wave caused by the incident shock wave. In addition to the similar conditions of the side lung, the back of the lung is also subjected to compression waves caused by the reflection of vertebra. The relationship between the pressure on thorax surface and various tissues and the deformation speed of thorax and the blast shock wave can be fitted as y = A [ 1 − exp ( x B ) ] , where y is the dependent variable, x is the peak overpressure of blast shock wave, and A and B are the fitting constants.

Shock tube measurements of high-temperature argon broadening and shift parameters for the potassium D1 and D2 resonance transitions

The current study presents a novel approach to determine the spectroscopic line shape parameters of atomic potassium in a controlled laboratory environment and reports the results for temperatures between 1100 – 1900 K. Experiments were conducted in a shock tube using argon as the dilution gas. Potassium was introduced through a precursor, potassium chloride salt, on the surface of a stainless-steel threaded-rod inserted upstream of the measurement plane. The incident shock wave entrained the potassium chloride in the test gas before the reflected shock wave dissociated the compound, producing atomic potassium at ppb levels for spectroscopic studies with tunable diode lasers. This potassium seeding approach was tested over a wide range of temperatures and is readily deployable for other collisional partners and for other absorbing species of alkali metals. The well-resolved absorption features of both the potassium D1 and D2 transitions near 0.77 μm were modeled as Voigt profiles, enabling high-fidelity calculations of the argon broadening coefficients and pressure shift coefficients at various temperatures. The results are presented as temperature-dependent power-law expressions. These correlations will be useful for interpretation of brown dwarf spectra and for the development of remote sensing techniques in high-enthalpy facilities.

Numerical Study of Air Flow Induced by Shock Impact on an Array of Perforated Plates.

This study is focused on the propagation behavior and attenuation characteristics of a planar incident shock wave when propagating through an array of perforated plates. Based on a density-based coupled explicit algorithm, combined with a third-order MUSCL scheme and the Roe averaged flux difference splitting method, the Navier–Stokes equations and the realizable k-ε turbulence model equations describing the air flow are numerically solved. The evolution of the dynamic wave and ring vortex systems is effectively captured and analyzed. The influence of incident shock Mach number, perforated-plate porosity, and plate number on the propagation and attenuation of the shock wave was studied by using pressure- and entropy-based attenuation rates. The results indicate that the reflection, diffraction, transmission, and interference behaviors of the leading shock wave and the superimposed effects due to the trailing secondary shock wave are the main reasons that cause the intensity of the leading shock wave to experience a complex process consisting of attenuation, local enhancement, attenuation, enhancement, and attenuation. The reflected shock interactions with transmitted shock induced ring vortices and jets lead to the deformation and local intensification of the shock wave. The formation of nearly steady jets following the array of perforated plates is attributed to the generation of an oscillation chamber for the inside dynamic wave system between two perforated plates. The vorticity diffusion, merging and splitting of vortex cores dissipate the wave energy. Furthermore, the leading transmitted shock wave attenuates more significantly whereas the reflected shock wave from the first plate of the array attenuates less significantly as the shock Mach number increases. The increase in the porosity weakens the suppression effects on the leading shock wave while increases the attenuation rate of the reflected shock wave. The first perforated plate in the array plays a major role in the attenuation of the shock wave.

Numerical investigation of thermal non-equilibrium effects of diatomic and polyatomic gases on the shock-accelerated square light bubble using a mixed-type modal discontinuous Galerkin method

In this article, a numerical investigation is carried out for analyzing the thermal non-equilibrium effects of diatomic and polyatomic gases on the flow dynamics of a shock-accelerated square light bubble. The simulation emphasis is placed on the flow morphology visualization, wave patterns, degree of thermal non-equilibrium, vorticity generation, and evolution of enstrophy as well as dissipation rate. A two-dimensional system of unsteady physical conservation laws derived from the Boltzmann-Curtiss kinetic equation of diatomic and polyatomic gases is solved by employing an in-house developed mixed-type modal discontinuous Galerkin method with uniform meshes. An explicit third-order SSP Runge-Kutta scheme is employed for the time discretization. The numerical results are compared with existing experimental results for validation, and they are found in good agreement. The results elucidate that the effects of thermal non-equilibrium, including different gas properties play a significant role during the interaction between an incident shock wave and a square light bubble. The effects of diatomic and polyatomic gases cause a significant change in flow morphology, resulting in complex wave patterns, vorticity generation, vortices formation, and bubble deformation. In comparison to monatomic gases, diatomic and polyatomic gases exhibit the formation of larger rolled-up vortex chains, different jet structure and large mixing zones. A detailed investigation on the effects of diatomic and polyatomic gases is explored using the vorticity generation, degree of non-equilibrium, the evolutions of enstrophy and dissipation rate. Finally, the effects of thermal non-equilibrium parameters, including temperature-dependent transport coefficient and bulk viscosity ratio, on the flow dynamics of the shock-accelerated square light bubble are comprehensively investigated.

Blast mitigation by perforated plates using an explosive driven shock tube: study of geometry effects and plate numbers

This work is set in the context of blast mitigation based on geometric means, namely perforated metallic plates or grids. When a shock wave passes through a perforated plate, the flow field is modified, and new shock waves are created, as well as regions of vortices and turbulence in which the energy of the wave can be dissipated. In this study, an explosive driven shock tube (EDST) was used to visualize the interaction of a blast wave with perforated plates or with a piece of cast metallic foam. Additionally, the overpressure and the impulse of the reflected blast wave on a wall located downstream were assessed. The use of an EDST allowed the evaluation of the mitigation capacity under a high dynamic loading. Several combinations of perforated plates were tested, varying the geometry and the number of plates, as well as switching between two different spacings. When the shock wave collided with a plate, we observed that part of the incident shock wave was reflected by the plate, while the remaining wave was transmitted through it. Downstream of the plate, both the overpressure and the impulse were reduced, this effect being more prominent as the porosity of the plates decreased. When two plates were placed as obstacles, this phenomenon of reflection/transmission was repeated twice consecutively, further reducing the downstream reflected overpressure and impulse. An array of three plates or a piece of metallic foam were even more effective in mitigating the blast wave. Varying the distance between two or three plates had no effect on blast mitigation.

Skin Friction Extracted from Surface Pressure in Incident Shock-Wave/Boundary-Layer Interaction

High-resolution skin-friction fields are extracted from pressure-sensitive paint (PSP) data obtained in shock-wave/boundary-layer interaction (SWBLI). The method of extracting skin friction from surface pressure is described, including the fundamental relation between skin friction and surface pressure, the variational method, error analysis, and an approximate iterative method. The proposed method is based on a coupling relation between skin friction and surface pressure, where the boundary enstrophy flux is suitably modeled or approximated. This method is applied to unsteady PSP data obtained in incident SWBLIs at Mach 2.5 for different Reynolds numbers, revealing the skin-friction structures of the flows: particularly, the separation bubble induced by the incident shock wave. The extracted results are in good agreement with the data obtained by the surface-stress-sensitive film.

Optimization of scramjet inlet based on temperature and Mach number of supersonic combustion

A two-dimensional mixed compression scramjet inlet design is presented in this work. The design is based on the static temperature and Mach number at the combustion chamber inlet according to the conditions required to burn hydrogen spontaneously at supersonic speed. This method considers air as a calorically perfect gas, with no viscous effects, and shock on-lip and shock on-corner. To burn hydrogen spontaneously at supersonic speed the mixture temperature of the income airflow and hydrogen is obtained considering the zeroth and first Laws of Thermodynamics. The criterion of equal shock strength, based on the normal component of the airflow velocity approaching the incident oblique shock waves, is applied to obtain the compression ramps angles and the airflow corresponding thermodynamic properties. Therefore, the total pressure ratio across all incident oblique shock waves and total temperature at the compression section are constants. Although the present method can be applied to any scramjet with a mixed compression system for any number of ramps, cases with up to 5 ramps, flying at a hypersonic speed corresponding to Mach number 7 through the Earth's atmosphere at 30 km of geometric altitude are considered. Finally, the same optimization criteria are extended to analyze the inlet of a scramjet vehicle with 5 compression ramps, flying at speeds from Mach numbers 5 to 10, at an altitude of 30 km.

Numerical simulation of a normally incident shock wave – dense particles layer interaction using the Godunov solver for the Baer–Nunziato equations

The work is devoted to the numerical simulation of the known problem of a normally incident shock wave – dense layer of particles interaction and the phenomenon of the pressure rise on the wall under the layer. The novelty of the work is in the numerical approach which is based on the Godunov solver for the Baer-Nunziato equations and the pressure relaxation procedure which takes into account intergranular stresses in the solid phase. The algorithm based on the exact solution of the Riemann problem provides a low numerical dissipation of the solid contacts and is robust at the explicit interfacial boundaries. The algorithm was described in detail; the source code of the Godunov solver for the Baer-Nunziato equations was provided. The full scale experiment of a shock wave – particles layer interaction was simulated. The shape of the pressure curve, obtained on the wall under the particles layer, was explained from the point of view of ongoing wave processes in the layer. A quantitative comparison of the experimental and simulated pressure curves was carried out. Studies of the influence of parameters in the intergranular stresses model on simulation results as well as reversible or irreversible character of loading-unloading process were conducted. Obtained results were compared to the published simulation results by the other authors based on the R.I. Nigmatulin models.

Explosion mitigation by metal grid with water curtain

This paper examines blast mitigation based on geometric means, namely a perforated plate or a chain mail, with or without a water film cover. This method may be used for the protection of structures, and its effectiveness and limitations were assessed. First, a shock tube was used to visualize the interaction of a blast wave profile with a metallic grid or with a metallic grid covered by a layer of water. Secondly, free-field air blast experiments were performed in order to evaluate the protection system under real conditions. Three types of grids were tested. The first was a metallic plate having small round holes, the second had large round holes, and the third had square holes. A chain mail made of steel rings was also tested. The porosity of the grids ranged from 48 to 69%. In case of a collision between a shock wave and a grid, it was observed that one part of the incident shock wave was reflected by the plate. The remaining part was transmitted through the plate. The overpressure and the impulse downstream from the grid were reduced, and the reduction increased when the porosity decreased. When a film of water covered the grid, it was observed that the water film disintegrated into droplets long after the passage of the blast wave. Filling the holes with water enhanced the overpressure and impulse reduction as it contributed to the reflection of the shock wave.

The influence of viscosity and turbulence on the supersonic flow compression and expansion corner

Super- and hypersonic flow around aircraft elements is accompanied by the formation of a complex flow structure, which is characterized by the presence of strong shock waves, rarefaction waves, contact discontinuities, separation and reattachment of the flow. For such problems, the interaction of shock waves with viscous boundary layers is characteristic. Such interaction is quite complex and largely determines the effectiveness of aircraft. When flowing around complex structures of aircraft and their power plants in the vicinity of convex corner points of the geometry, compression and expansion flows are locally realized. The calculation of oblique shock waves, formed when flowing around the compression angle, and simple expansion waves, formed around the flowing angle of expansion, is included as an element of solving many problems of constructing streamlines and finding the pressure distribution on the streamlined surface. Based on the technology of adaptive meshes, a numerical model is proposed for studying two-dimensional effects arising from supersonic flow around the angles of compression and expansion. Numerical simulation was performed using various models such as inviscid, laminar or turbulent. In the calculations, the Mach number of the incident shock wave varies from 2 to 15, and the flow angle varies from 5 to 15 degrees. The Reynolds number, calculated from the characteristics of the unperturbed flow, is equal to 105. The working gas is air (γ = 1.4). A qualitative picture of the flow during diffraction of a shock wave on steps of different geometry is considered. When the shock wave interacts with the compression angle, flow separation and the formation of a recirculation region are observed, and when the shock wave interacts with the expansion angle, the Prandtl–Mayer wave is misaligned. The results of calculations are compared with theoretical data on the parameters of the flow behind the shock front or fan of the rarefaction wave. Studies have shown the influence of the effects of viscosity and turbulence on the flow structure and distribution of flow characteristics when flowing around the angles of compression and expansion. The simulation results can find application in solving problems related to the design of air intakes of high-speed flying aircrafts, in particular, in parametric and optimization calculations of gas-dynamic flows that arise in the elements of propulsion systems of supersonic and hypersonic aircraft.

Large eddy simulation of the turbulent mixing at an oblique interface induced by non-classical planar shock waves

The interaction between the shock wave and phase interface is one of the classic problems in aerospace and turbulent combustion engineering. In this paper, the instability of the gas–liquid interface driven by non-classical planar shock waves is studied. Based on the volume of fluid model and large eddy simulation method, the deformation process and the turbulent mixing phenomenon of the oblique interface induced by non-classical planar shock waves in a two-dimensional plane are numerically investigated by using a high-performance computer cluster. The effects of incident shock wave intensity, initial amplitude, initial wavelength, and inclined angle of the gas–liquid two-phase oblique interface are analyzed. The results show that the incident shock intensity has the most significant effect on the interface deformation and the development of turbulent mixing, and the initial amplitude and wavelength of the incident shock and the inclined interface angle also play a certain role in the deformation and development process. Overall, the width of the turbulent mixing zone increases with time under a given condition, and the convex structure will fall off and break up at the phase interface in the later stage of turbulent mixing.