Incident Shock Wave Research Articles

Effect of pre-shock on the expanding fracture behavior of 1045 steel cylindrical shell under internal explosive loading

Explosively driven expansion fractures in metallic shells will be preceded by a compression shock wave, which inevitably changes the mechanical and microstructural state of the shell materials and thus affects their subsequent dynamic deformation and expansion fracture processes. To understand the influence of pre-shock pressure on the dynamic expansion fracture behavior of metallic shells, the incident shock waves with varying peak pressure were generated in a 1045 steel cylindrical shell by sweeping detonation wave loading. The pre-shock and subsequent expansion fracture processes were continuously diagnosed by combining a high-speed framing camera and the arrayed Photon Doppler Velocimetry (PDV) measurements to obtain the fracture strains at different axial positions (corresponding to different pre-shock pressures). The results clearly show that the pre-shock pressure during detonation loading has a significant effect on the expansion fracture properties of the 1045 steel cylinder; the fracture strain remarkably decreases with the increase of pre-shock pressure from ∼19 GPa to ∼20 GPa and then changes gently in the range of ∼20 GPa to ∼22 GPa. Metallurgical analyses reveal increased densities of microstructural defects, including dislocations and deformation twins, when a shock wave passes through, resulting in a reduced capacity for further defect storage in the shocked metals, ultimately leading to a decrease in the fracture strain during the subsequent expansion deformation process.

Non-inertial Computational Framework for Long-distance Shock-driven Object Dynamics

In the realm of dynamic separation problems, the motion of a body triggered by shock interactions is a common phenomenon. This is particularly important in terms of the safe separation of two-stage-to-orbit vehicles, where the motion must remain stable despite long-distance disturbances from shock waves. The flow field in these cases is complex, marked by interactions between hypersonic shock waves and a moving boundary. This leads to significant unsteady effects due to the body's translation and rotation over extended distances. Existing simulation techniques fall short in rapidly and accurately predicting the aerodynamic force and thermal properties for these problems, largely due to the overwhelming computational demands that result from oversize computational domains and the necessity of grid deformation. This paper presents a novel non-deforming grid method to address these challenges. The central concept is to anchor the reference frame to the moving object itself and to approach the problem from a non-inertial frame perspective. This accounts for the motion of the object solely via the inertial source term, circumventing the complexities of mesh manipulation typically required to link flow and motion equations. The moving shock boundary is designed to be closely compatible with selected shock-captured schemes, which reduces non-physical oscillations compared to the traditional method of direct assembly with theoretical shock relations. Other boundary conditions and the solution process are also refined to specifically target the unsteady, shock-dominated flow. These modifications significantly alleviate the computational burden. The effectiveness of the proposed method is demonstrated through several test cases. To showcase the method's practical application, a scenario is simulated wherein an ellipse is dislodged from a wedge by an incident shock wave, covering a long distance. These tests confirm the method's feasibility in aerospace engineering problems.

Effects of internal intervention in tubes on shock wave attenuation, formation and propagation of flame during high-pressure hydrogen release

Experiments on the impacts of the combination of fin structure and expansion chamber on shock wave attenuation, hydrogen ignition, and flame characteristics during high-pressure hydrogen release were carried out. The fin is a four-edged platform hollowed out on all sides. The inflated upper and lower tube walls are located 85, 95, and 105 mm away from the nickel burst disk. With the incident shock wave traveling through the fin, the reflected shock and the superposition of multiple reflected shock waves appear, and the reflected shock wave intensity can equal that of the release pressure. The decrease of the incident shock wave intensity behind the fin leads to the decrease of the non-uniformity of the mixed layer temperature, further causing the decrease of the flame propagation velocity. The presence of fins increases the probability of ignition in the fin region and the critical release pressure for ignition is significantly lower than that in the barrier free tube, mainly because the fin inside intensifies the hydrogen/air mixture, resulting in a lower minimum ignition energy required for self-ignition. Furthermore, the decrease of flame propagation velocity leads to the increase of hydrogen consumption inside the tube and the decrease of shock overpressure outside.

Influence of the shock wave-turbulence interaction on the swirl distortion in hypersonic inlet

This study uses the Large Eddy Simulation (LES) technique to conduct an exhaustive analysis of the flow characteristics within the Rectangular-to-Elliptical shape Transition (REST) inlet under Mach 6 conditions. It mainly focuses on investigating the influence of the shock wave-turbulence interaction on the swirl distortion at the inlet exit. At the design condition, characterized by 0° Attack and 0° Sideslip, the incident shock wave at the inlet lip undergoes multiple reflections within the boundary layer of the domain wall, culminating in the formation of turbulent structures. The first reflected shock wave has the highest energy, exerting a significant impact on the boundary layer and the exit swirl distortion. On the contrary, the energy of the incident shock wave is progressively reduced due to repeated reflections, which results in reducing the exit swirl distortion. Under off-design conditions, characterized by 6° Attack and 0° Sideslip as well as 6° Attack with 6° Sideslip, variations in the incoming flow make the incident shock wave move inward, decreasing the frequency of shock wave reflections and even significantly reducing the reflected shock waves under conditions of 6° Attack and 6° Sideslip. However, this results in significantly increasing the exit swirl angle and distortion intensity. The obtained results demonstrate that changes in the incoming flow conditions significantly affect the level of exit swirl distortion by modulating the shock wave-turbulence interaction, especially in terms of the positioning of the incident shock wave and the quantity of reflected shock waves. In addition, this paper studies the wall heat transfer coefficient of the inlet. The obtained results show that the interaction between shock waves and the boundary layer significantly affects the heat transfer coefficient. This study provides a foundation for the comprehension and prediction of the performance of hypersonic inlets across a spectrum of flight conditions, and for the guidance of the design and optimization of such inlets.

On the evolution of magnetohydrodynamic flow instability in shock-accelerated light bubble

The study investigates the evolution of flow instabilities in a magnetohydrodynamic (MHD) environment involving a shock-accelerated light cylindrical bubble. Numerical simulations were conducted using a cylindrical helium (He) bubble accelerated by a shock wave in nitrogen (N2) gas at various magnetic field strengths. The results highlight the impact of magnetic fields on flow morphology, vorticity generation, and enstrophy. The interaction between incident shock waves and the gas bubble revealed significant differences in flow patterns and interface features when magnetic fields were applied. Key findings include the quantification of shock trajectories and detailed visualizations of the evolving flow structure. The study provides insights into the dynamics of shock–bubble interactions under MHD conditions, contributing to the broader understanding of flow instability mechanisms in such complex environments.

On the focusing effect and interfacial evolution of incident shock waves impinging on double-layer nested heavy gas bubbles

A detailed numerical study about the planar incident shock wave impinging on heavy bubbles with different components and nested structures was conducted. Results show that the shock wave convergence occurs when the incident shock wave impinging on the pure SF6 bubble or CO2-SF6 nested bubbles, which triggers the shock wave focusing and obtains a high transient pressure. Changing the nested position and radius of the SF6 bubble in CO2-SF6 nested bubbles will change the interactional time and relative position of waves to affect the shock wave focusing time and peak pressure. Specifically, the shock wave focusing effect is enhanced, and the peak pressure is increased when the inner bubble is drifted downstream, high density, and larger sized. Thus, the later the shock wave focusing occurs, the higher the transient maximum pressure. The shock wave focusing process of double-layer nested bubbles is presented as follows: the new small shock wave (SS) formed by the intersection between the incident transmitted shock wave and the transmitted shock wave and another new shock wave formed by the collision of diffracted transmitted shock waves move in opposite directions to squeeze the undisturbed region and finally produce a high instantaneous pressure, where SS plays a major role in shock wave focusing. Further, the greater the intensity and velocity of focusing shock waves, the stronger the focusing effect and the higher the transient pressure.

Stereoscopic cells of three-dimensional detonation waves propagating in square ducts

The present study delves into the examination of the stereoscopic cells and wavefront structures characterizing the propagation of three-dimensional detonation waves within square ducts. Leveraging numerical solutions derived from three-dimensional reactive Euler equations, incorporating an induction-exothermic reaction kinetic model, this work reveals the distinct classification of three modes of detonation waves based on the direction of propagation and the phase characteristics of transverse shock waves on the wavefront. This paper delineates the presence of two different types of phenomena: duct wall slapping waves due to shock–wall collisions and internal slapping waves resulting from shock interactions. Furthermore, this investigation exposes the existence of two distinct types of triple-wave lines on the wavefront: the first comprising a strong Mach disk, a weak Mach disk, and a transverse shock wave; the second characterized by a weak Mach disk, an incident shock wave, and a transverse shock wave. Notably, the pressure behind the first type of triple-wave line is observed to be the highest. It elucidates the transition from two- to three-dimensional detonation waves, revealing that the prevalence of transverse shock waves on the wavefront in the rectangular and diagonal modes is twofold and quadruple, respectively, when compared to their two-dimensional counterparts within identical ducts/channels.

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.

Modal Discontinuous Galerkin Simulations of Richtmyer–Meshkov Instability at Backward-Triangular Bubbles: Insights and Analysis

This paper investigates the dynamics of Richtmyer–Meshkov instability (RMI) in shocked backward-triangular bubbles through numerical simulations. Two distinct gases, He and SF6, are used within the backward-triangular bubble, surrounded by N2 gas. Simulations are conducted at two distinct strengths of incident shock wave, including Ms=1.25 and 1.50. A third-order modal discontinuous Galerkin (DG) scheme is applied to simulate a physical conservation laws of two-component gas flows in compressible inviscid framework. Hierarchical Legendre modal polynomials are employed for spatial discretization in the DG platform. This scheme reduces the conservation laws into a semi-discrete set of ODEs in time, which is then solved using an explicit 3rd-order SSP Runge–Kutta scheme. The results reveal significant effects of bubble density and Mach numbers on the growth of RMI in the shocked backward-triangular bubble, a phenomenon not previously reported. These effects greatly influence flow patterns, leading to intricate wave formations, shock focusing, jet generation, and interface distortion. Additionally, a detailed analysis elucidates the mechanisms driving vorticity formation during the interaction process. The study also thoroughly examines these effects on the flow fields based on various integral quantities and interface characteristics.

Conceptual design methodology and performance evaluation of turbine-based combined cycle inward-turning inlet with twin-design points

Turbine-based combined cycle (TBCC) engines attract intensive attention due to adequate high working efficiency within the full speed range of air-breathing vehicles. Challenges of TBCC engines lie mostly in common-used components in particular the inlet system, which needs to satisfy the mass flow distribution of different sub-engines and to reconcile the performance requirement in the full speed range. In the present work, a new conceptual design methodology of the three-dimensional inward-turning TBCC inlet with twin-design points is proposed according to the basic flow field with double incident shock waves. The shock structures and flow field parameters at the high-speed design point Ma=4 and mass flow distribution at the low-speed design point Ma=3 both can be designed by the basic flow field. On that basis, a typical inlet model is designed and the corresponding aerodynamic performance is evaluated at two design points. Simulation results prove that the shock structure, the mass flow distribution, and the averaged throat parameters of the TBCC inlet are all consistent with the basic flow field with sufficient accuracy at twin-design points, where the maximum relative error is only 6.3%. Meanwhile, the aerodynamic performance of the inlet shows that the inlet has stable and efficient operation characteristics, which fully affirms the feasibility of the design method.

Influence of Incident Shock on Fuel Mixing in Scramjet

During the operation of hypersonic vehicles, a reciprocal coupling effect is manifested between the inlet and the combustion chamber. This results in an unavoidable non-uniformity of conditions at the combustion chamber’s entrance, which, in turn, influences the fuel mixing within the chamber. The present study employed the Reynolds-averaged Navier–Stokes (RANS) equations to perform a numerical simulation of an X-51-like vehicle, with a focus on examining the impact of isolation section length and multi-injection strategies on the fuel mixing characteristics within the combustion chamber under conditions of non-uniform inflow. The findings indicated that a supersonic non-uniform inlet triggers incident shock waves, leading to a non-uniform pressure distribution across the flow section. Moreover, the position of injection was found to be pivotal in regulating penetration depth and mixing efficiency. The incident shock wave, bow shock, and boundary layer separation shock interacted with each other to increase local pressure. The coupling of high and low pressures generated an adverse pressure gradient that led to boundary layer separation, which further enhanced fuel penetration depth.

On incident shock wave/boundary layer interactions under the influence of expansion corner

Cowl-induced incident shock wave/boundary layer interactions (ISWBLIs) under the influence of shoulder expansion represent one of the dominant phenomena in supersonic inlets. To provide a more comprehensive understanding of how an expansion corner affects the ISWBLI, a detailed experimental and analytical study is performed in a Mach 2.73 flow in this work. Pressure measurement, schlieren photography and surface oil-flow visualisation are used to record flow features, including the pressure distribution, separation extent and surface-flow topological structures. Our results reveal three types of ISWBLIs influenced by the expansion corner. When the shock intensity is weak, the separation is small scale with the expansion waves emanating from the expansion corner. This is the first type of expansion-corner-affected ISWBLI (EC-ISWBLI). When the incident shock wave is strong, large-scale separation occurs, accompanied by the disappearance of expansion waves, forming the second type of EC-SWBLI. The expansion corner induces a ‘lock-in’ effect in which the separation onset is consistently locked near the expansion corner regardless of the incident shock intensity and impingement position. The third type of EC-ISWBLI occurs when the shock is sufficiently strong and the impingement point is close to the expansion corner. In this interaction, the ‘lock-in’ effect ceases to manifest. Moreover, a shock polar-incorporating inviscid model is employed to elucidate the shock patterns. Two criteria are established by combining free interaction theory with this model. The first criterion provides valuable insights into the evolution of separations with a minimal overall pressure rise and the second criterion determines the threshold for the occurrence of the ‘lock-in’ effect.

A review of bubble collapse near particles

Bubble–particle interactions are of great importance in cavitation bubble dynamics, especially in the case of silt-laden flow. In this paper, a review of the physical mechanisms involved in bubble collapse near particles is presented, with an emphasis on the jet and shock wave phenomenon. First of all, the collapse of a bubble occurring close to a flat wall is introduced to provide a basis for understanding cavitation behavior near boundaries. Then, with the aim of revealing the physical processes that occur during bubble collapse near particles, this is followed by a detailed discussion, with plentiful examples, of the collapse process (the inception, growth, collapse, rebound, and final disappearance of the bubble) and the formation and behavior of jets (the inception jet, counter jet, and double jets) and shock waves (incident, reflected, jet-induced, and jet-split shock waves).

An ultra-rapid optical gas standard for dynamic processes: Absolute NH3 quantification and uncertainty evaluation

An ultra-rapid Optical Gas Standard (OGS) for absolute NH3 quantification in the shock tube has been developed. For the first time, the absolute NH3 mole fractions before the incident shock wave, after the incident shock wave and immediately after the reflected shock wave (within 25 μs) were quantified using OGS. On that basis, spectrally resolved NH3 absorption cross-section datasets were measured over pressure ranges of 1.15–3.15 bar and elevated temperatures (up to 2680 K), facilitating NH3 mole fraction quantification after the reflected shock wave using a correlative linear fit method. Besides, comprehensive uncertainty evaluations were conducted for thermodynamic parameters and species mole fraction following the 'Guide to the Expression of Uncertainty in Measurement (GUM)'. This metrological uncertainty analysis not only contributes to providing high-quality data but also serves as a valuable reference for other traceable measurements in shock tubes, such as dynamic temperature and pressure calibrations.

Research on the Shock Wave Overpressure Peak Measurement Method Based on Equilateral Ternary Array.

The measurement process of ground shock wave overpressure is influenced by complex field conditions, leading to notable errors in peak measurements. This study introduces a novel pressure measurement model that utilizes the Rankine-Hugoniot relation and an equilateral ternary array. The research delves into examining the influence of three key parameters (array size, shock wave incidence angle, and velocity) on the precision of pressure measurement through detailed simulations. The accuracy is compared with that of a dual-sensor array under the same conditions. Static explosion tests were conducted using bare charges of 0.3 kg and 3 kg TNT to verify the numerical simulation results. The findings indicate that the equilateral ternary array shock wave pressure measurement method demonstrates a strong anti-interference capability. It effectively reduces the peak overpressure error measured directly by the shock wave pressure sensor from 17.73% to 1.25% in the test environment. Furthermore, this method allows for velocity-based measurement of shock wave overpressure peaks in all propagation direction, with a maximum measurement error of 3.59% for shock wave overpressure peaks ≤ 9.08 MPa.

Effect of shock impedance of mesoscale inclusions on the shock-to-detonation transition in liquid nitromethane

Two-dimensional, meso-resolved numerical simulations are performed to investigate the effect of shock impedance of mesoscale inclusions on the shock-to-detonation transition (SDT) in liquid nitromethane (NM). The shock-induced initiation behaviors resulting from the cases with NM mixed with randomly distributed, 100-μm-sized air-filled cavities, polymethyl methacrylate (PMMA), silica, aluminum (Al), and beryllium (Be) particles with various shock impedances are examined. In this paper, hundreds of inclusions are explicitly resolved in the simulation using a diffuse-interface approach to treat two immiscible fluids. Without using any empirically calibrated, phenomenological models, the reaction rate in the simulations only depends on the temperature of liquid NM. The sensitizing effect of different inclusion materials can be rank-ordered from the weakest to the strongest as PMMA → silica → air → Al → Be in the hot-spot-driven regime of SDT. Air-filled cavities have a more significant sensitizing effect than silica particles, which is in agreement with the experimental finding. For different solid-phase inclusions, hot spots are formed by Mach reflection upon the interaction between the incident shock wave and the particle. The sensitizing effect increases roughly with the shock impedance of the inclusion material. More details of the hot-spot formation process for each solid-phase inclusion material are revealed via zoom-in simulations of a shock passing over a single particle.

Numerical investigations of spike velocity of microjetting from shock-loaded aluminum and tin

Microjetting is induced by the interaction between incident shock wave and material free surface. Moreover, spike velocity is one of the most important parameters to quantify the microjetting processes. The spike velocity over a wide range of shock and surface conditions for aluminum and tin is achieved via systematical Eulerian peridynamic simulations. The four popular spike velocity models are assessed according to the simulation data. The results indicate that the model proposed by Dimonte et al. based on Richtmyer–Meshkov instability (RMI) mechanism is in best agreement with the simulated spike velocities. The further analysis highlights that the dependence of adiabatic index on material states should be taken into account because it can impact the RMI flows. Then an improved spike velocity model is proposed and the comparative investigations indicate that it exhibits an overall better prediction compared to the original velocity model.

The dispersion and ignition behavior of zirconium particles under the effect of a shock wave

Experiments of the interaction process between shock waves and zirconium particles have been carried out using a self-designed shock tube. The interaction process was recorded using a high-speed shadowgraph imaging system, pressure testing system, and infrared thermal imager. The wave-systems structures resulting from the interaction between shock waves and accumulated zirconium powders have been characterized. Generally, the axial distance of the powder cloud reduces with the increase in accumulation thickness, which in turn increases with the addition of shock Mach number. The incident shock wave with an intensity of 1.53 Ma was enough to ignite zirconium powders under these experimental conditions. The ignition delay time for zirconium powders decreases with the addition of shock Mach number, while it decreases for thinner accumulations. Besides, the flame propagation characteristics and the ignition mechanism of zirconium powders are discussed in detail. The results can serve as a supplementary guide for the utilization and safe operation of zirconium powders.

Numerical Investigation of Transverse-Jet-Assisted Initiation of Oblique Detonation Waves in a Combustor

Detonation initiation is a prerequisite to normal operations of an oblique detonation engine (ODE), and initiation-assistant measures are imperative in cases of initiation failure that occur in a length-limited combustor under wide-range flight conditions. This study numerically investigates the initiation characteristics of oblique detonation waves (ODWs) in H2-fueled ODE combustors at wide-range flight Mach numbers Maf or flight altitudes Hf. Failures of ODW initiation are observed at both low Maf and high Hf if no measure is taken to assist initiation. Through analyses of the flow fields and theoretical predictions of the ignition induction length Lind, the data reveal that the detonation failure at low Maf is raised by the significant decrease in the post-shock temperature due to insufficient shock compression, leading to a significant increase in Lind. The detonation failure at high Hf is caused by the rapid decrease in the combustor inflow pressure as Hf increases, which also results in an increase in Lind. With further identifications of the key flow structures crucial to detonation initiation, an initiation-assistant concept employing a transverse H2 jet is proposed. The simulation results show that through an interaction between the incident oblique shock wave and the jet shock wave, the transverse jet helps to initiate an ODW in the combustor at a low Maf, and the initiation location is relatively fixed and determined by the jet location. At high Hf, a Mach reflection pattern is formed in the combustor under the effects of the transverse jet, and detonative combustion is achieved by the generated Mach stem and its reflected shock waves. The proposed concept of using transverse jets to assist detonation initiation provides a practical reference for future development of ODEs that are expected to operate under wide-range flight conditions.

Application of pressure-sensitive paint for explosive blast measurements

This study demonstrates the application of fast response pressure-sensitive paint (PSP) to explosively driven blast wave testing. A sprayable polymer ceramic fast response PSP was applied to an aluminium disc before being coated with platinum porphyrin compound as the active luminophore. The disc was then exposed to a blast wave and the response was measured using a high-speed video camera. The PSP measured the transit of the incident shock wave clearly, albeit with a slight response delay following the instantaneous change in pressure. A time domain-based method for improving temporal response, whilst considering both spatial and temporal effects, is described. This study clearly demonstrates that the spatial distribution of a blast wave on a surface may be captured by PSP technology. Integrated parameters such as impulse can correctly be characterised using this method. This technology offers an enhanced and more efficient way of characterising blast.