Shock Wave Structure Research Articles

Numerical investigations on interactions between 2D/3D conical shock wave and axisymmetric boundary layer at Ma=2.2

Numerical simulation and analysis are carried out on interactions between a 2D/3D conical shock wave and an axisymmetric boundary layer with reference to the experiment by Kussoy et al. [AIAA J, 1980, 18(12): 1477–1487], in which the shock was generated by a 15° half-angle cone in a tube at 15° angle of attack (AOA). Based on the Reynolds-averaged Navier–Stokes equations and Menter's SST turbulence model, the present study uses the newly developed WENO3−PRM1,12 scheme and the PHengLEI CFD platform for the computations. First, computations are performed for the 3D interaction corresponding to the conditions of the experiment by Kussoy et al., and these are then extended to cases with AOA = 10° and 5° For comparison, 2D axisymmetric counterparts of the 3D interactions are investigated for cones coaxial with the tube and having half-cone angles of 27.35°, 24.81°, and 20.96° The shock wave structure, vortex structure, variable distributions, and wall separation topology of the interaction are computed. The results show that in 2D/3D interactions, a new Mach reflection-like event occurs and a Mach stem-like structure is generated above the front of the separation bubble, which differs from the model of Delery for 2D planar shock wave/boundary layer interaction. A new interaction model is established to describe this behavior. The relationship between the length of the circumferentially unseparated region in the tube and the AOA of the cone indicates the existence of a critical AOA at which the length is zero, and a prediction of this angle is obtained using an empirical fit, which is verified by computation. The occurrence of side overflow in the windward meridional plane is analyzed, and a quantitative knowledge is obtained. To further elucidate the characteristics of the 3D interaction, the scale and structure of the vortex and the pressure and friction force distributions are presented and compared with those of the 2D interaction.

Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

Recent theoretical physics efforts have been focused on the probes for nonlinear pulse waves in, for example, variable-radius arteries. With respect to the nonlinear waves in an artery full of blood with certain aneurysm, pulses in a blood vessel, or features in a circulatory system, this paper symbolically computes out an auto-Bäcklund transformation via a noncharacteristic movable singular manifold, certain families of the solitonic solutions, as well as a family of the similarity reductions for a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers equation. Aiming, e.g., at the dynamical radial displacement superimposed on the original static deformation from an arterial wall, our results rely on the axial stretch of the injured artery, blood as an incompressible Newtonian fluid, radius variation along the axial direction or aneurysmal geometry, viscosity of the fluid, thickness of the artery, mass density of the membrane material, mass density of the fluid, strain energy density of the artery, shear modulus, stretch ratio, etc. We also highlight that the shock-wave structures from our solutions agree well with those dusty-plasma-experimentally reported.

Research on time sequence prediction of supersonic cascade flow field based on compressed sensing artificial neural network

The aviation engine that achieves efficient energy conversion is the core power equipment for low-carbon navigation, and the thermal components represented by the combustion chamber greatly affect the stable state of the compressor cascade flow field. Accurate, comprehensive and promptly monitoring of the compressor cascade flow state is related to the safe operation of the engine. A flow field time sequence prediction framework named compressed convolutional gate recurrent unit (CC-GRU) was proposed in this study to predict future supersonic cascade flow parameters based on the flow field at previous moments. CC-GRU embedded convolution into gate recurrent unit (GRU) to deal with the complex spatial-temporal behavior of supersonic cascade flow field. Firstly, unsteady numerical simulations driven by linear changes in back pressure were carried out, and the dataset for model training and validation was obtained to verify the feasibility of time sequence prediction of the cascade flow field. The verification results indicate that the framework can comprehensively predict the flow field with high back pressure in the future according to the flow field with low back pressure in the past period, and further validated the effectiveness of the proposed time sequence prediction model in ground wind tunnel experiments. The CC-GRU model can accurately capture the fine shock wave structure and flow separation zone, with a relative error of less than 10% in predicting the pressure field, and is mainly concentrated within the shock wave structure. Therefore, this research provides new research perspective and technical support for comprehensive and promptly condition monitoring of supersonic cascade flow field.

Propagation of rotating detonation wave with wall-detached injection in a hollow combustor

The wall-detached propagation of the continuously rotating detonation (CRD) caused by the injection gap is numerically studied in a hollow combustor. The three-dimensional CRD is solved with the detailed chemical reaction of H2/air. Three cases are set, including Case1 with a small width of the injection gap, Case2 without an injection gap for comparison and Case3 with a wider injection gap. The results show that the injection gap leads to an interesting phenomenon, that is, a “stretching forward” region (SFR). It is the highest speed region in the flow field, even more than C-J speed. The SFR is still the highest temperature region, while the pressure is not the highest. In Case1, a “V” shaped shock wave structure occurs, similar to the phenomenon in Matsuoka's experimental images. In Case3, the shock wave structure leans backward, and the SFR still propagates ahead. The analysis of the velocity field shows that the formation of the SFR is probably caused by the high pressure behind the detonation wave, the compression effect of the sidewall and the hindering effect of the injection gap. The exit views are obtained, where the key features of Case1 are highly consistent with those in Anand's experimental images. The injection gap can dramatically reduce the peak pressure on the sidewall. This work reveals the effect of the injection gap that may widely exist in RDC.

Numerical Analysis on Effect of Structural Parameters on Flow Field and Internal Trajectory in Gas–Steam Ejection Systems

This paper aims to study the influence of the structure of spray holes and throats on the flow field and the internal trajectory of the gas–steam ejection device. The compressible Navier–Stokes equations, discrete ordinate methods and RNG k-ε turbulence model are utilized to simulate the two-phase flow of the rocket gas with multispecies and the water sprays. The comparison between numerical results and experimental data confirms the accuracy and effectiveness of this model. The simulation analysis on the cases of the ejection process with multiple spray hole diameters, number of spray holes, total spray area, and throat diameter are conducted. The shock wave structure inside the gas–steam ejection device is examined. The simulation results show that, instead of the spray hole diameter and number, the total spray area and secondary nozzle throat diameter are the key factors that affect the flow field and internal trajectory of the gas–steam ejection device. Under the existing spray structure, the maximum number of spray holes is 300 to achieve the stability of the flow field and internal ballistic trajectory of gas–steam ejection devices. By comparing the throat diameters of multiple secondary nozzles, it was found that the minimum throat diameter of the secondary nozzles should be no less than 100 mm. The results could be valuable for the design of gas–steam ejection devices.

A Three-Dimensional Design to Study the Shock Waves of Linear Cascade with Reduced Mass Flow Requirements

This paper presents the development of high-specific-speed mixed flow/centrifugal compressor vaned diffusers. Specifically, the design of a test rig that will make the visualization of shock waves on diffuser vanes manageable is addressed in the current study. In this particular case, linearization of an existing state-of-the-art compressor stage was used. For the computational modeling, a series of RANS analyses were conducted to examine the flow characteristics of the two cases explored: a complete transonic cascade and an idealized periodic passage. The distinct behavior exhibited by each vane passage within the entire cascade offers the opportunity to analyze the shockwave structures across a mass flow range of ±9% around the design point. Overall, the pressure coefficient distributions and flow field patterns appear to align with the single-passage conditions, although there are some minor lateral wall influences, particularly in the first passage close to the suction lateral wall. However, because of the nature of the flow, which is characterized by high velocity and density differences near the vanes, the equivalent mass flow per individual passage was difficult to estimate. This may also be attributed to the small endwall axial vortices; nonetheless, for the purposes of this paper, this was of little consequence.

On the shock wave structures in anisotropy magnetoplasmas

In this work, the propagation of nonlinear electrostatic shock wave structures in an anisotropy pressure magnetoplasma composed of warm inertial ions and inertia-less Maxwellian electrons is reported. For this purpose, the technique of reductive perturbation is applied for reducing fluid equations of the current model to the Korteweg–de Vries Burgers (KdVB) equation with a second-order dissipative term and the KdVB–Kuramoto (KBK) equation with both second- and fourth-order dissipative terms. The impact of various plasma parameters, including the parallel ion pressure, perpendicular ion pressure, and dissipation parameter, on the significant characteristics of the shock wave profile is examined and discussed. In addition, a comparison between the profiles of KdVB shocks and KdVB–Kuramoto shocks is reported. We expect that KBK shock wave amplitudes become larger than the KdVB ones by taking the fourth-order dissipative into consideration. Thus, the results of the KBK equation may treat the difference between the theoretical and laboratory results or satellite observations.

Study on the characteristics of the transient flow field under different underwater environments

The underwater muzzle transient flow field is an unsteady, multiphase complex flow field interacting with projectiles and containing various shock wave structures. The turbulent mixing of gunpowder gas and water has a significant impact on the development of the muzzle gas flow field. Moreover, the muzzle gas flow field disturbs the motion of the projectile, thereby affecting shooting accuracy. As part of this research, an unsteady multiphase flow model of the underwater muzzle transient flow field is established by combining the theories of multiphase flow and turbulent mixing. The volume of fluid model is employed to trace the two-phase interface, while the gas–liquid turbulent mixing is described by the standard k–ε turbulence model. Furthermore, the cavitation model is used to describe the cavitation phenomenon caused by the motion of the projectile. The established numerical model is validated by comparing underwater launching experimental results. Accordingly, the muzzle flow field of a 30 mm underwater gun under different water depth conditions is numerically calculated. The results demonstrate that, as the water depth increased, the gunpowder gas is exposed to relatively high water pressure during the expansion process, resulting in a continuous decrease in the core area of the gas, and the Mach disk is also increasingly closer to the muzzle. At different water depths, the diameter of the Mach disk conforms to the binomial law with time, while the displacement of the Mach disk from the muzzle increases exponentially with time.

Structure of shock and detonation waves propagating in hybrid methane/hydrogen/air/coal dust mixtures

Structure of shock and detonation waves propagating in hybrid methane/hydrogen/air/coal dust mixtures

Unraveling Anisotropy in Crystalline Orientation under Shock-Induced Dynamic Responses in High-Entropy Alloy Co25Ni25Fe25Al7.5Cu17.5.

Shock-induced plastic deformation and spall damage in the single-crystalline FCC Co25Ni25Fe25Al7.5Cu17.5 high-entropy alloy (HEA) under varying shock intensities were systematically investigated using large-scale molecular dynamics simulations. The study reveals the significant influence of crystalline orientation on the deformation mechanism and spall damage. Specifically, the shock wave velocities in the [110] and [111] directions are significantly higher than that in the [001] direction, resulting in a two-zone elastic-plastic shock wave structure observed in the [110] and [111] samples, while only a single-wave structure is found in the [001] sample. The plastic deformation is dominated by the FCC to BCC transformation following the Bain path and a small amount of stacking faults during the compression stage in the [001] sample, whereas it depends on the stacking faults induced by Shockley dislocation motion in the [110] and [111] samples. The stacking faults and phase transformation in the [001] sample exhibit high reversibility under release effects, while extensive dislocations are present in the [110] and [111] samples after release. Interestingly, tension-strain-induced FCC to BCC phase transformation is observed in the [001] sample during the release stage, resulting in increased spall strength compared to the [110] and [111] samples. The spall strength estimated from both bulk and free surface velocity history shows reasonable consistency. Additionally, the spall strength remains stable with increasing shock intensities. The study discusses in detail the shock wave propagation, microstructure change, and spall damage evolution. Overall, our comprehensive studies provide deep insights into the deformation and fracture mechanisms of Co25Ni25Fe25Al7.5Cu17.5 HEA under shock loading, contributing to a better understanding of dynamic deformation under extreme environments.

Orientation-dependent phase transition pathways of single-crystal nickel over large shock range

The response of single crystals to increasing shock strength involves complex phase transition processes from solid-solid to solid-liquid phases. However, it is not yet fully understood how these phase transitions occur along different crystallographic orientations, and what the dominant micro-mechanisms are at different shock stages. To fill this knowledge gap, non-equilibrium molecular dynamics simulations are performed to explore the dynamic phase-transition characteristics of face-centered cubic Ni single crystal over a large shock strength range of 0–350 GPa. The orientation-dependent phase transition in single-crystal Ni is examined through three typical shock directions: [001], [011], and [111], and a phase-transition locus map is established. The results show that the shock compression of single-crystal Ni undergoes four response stages: (I) elasticity, (II) plasticity, (III) partial melting, and (IV) complete melting. The shock orientation plays a crucial role in the shock wave structure, Hugoniot, microstructure evolution, and shock melting behavior. The [001] shock direction maintains a single-wave structure and exhibits a shear stress superelasticity. However, the [011]/[111] orientations undergo a single-double-single wave transformation, and an interesting U-shape transition wave is identified along the [111] orientation due to its unique progressive plasticity. Superheating and cold melting phenomena are observed along the [001] and [011]/[111] orientations, respectively. The differences in the critical melting temperature and threshold shock pressure along different orientations are up to ∼3000 K and ∼80 GP. Atomic-structure analysis reveals that due to the Bain path, FCC→BCC (BCT) is the dominant solid-solid phase transition along the [001] orientation, and the dislocation slips are limited in a narrow shock window. Melting nuclei emerge, grow, and coalesce homogeneously on the BCC (BCT) substrate, leading to the superheating phenomenon. In contrast, a dynamic process involving shock melting and recrystallization is observed along the [011]/[111] orientations, which finally results in the coexisting of the solid and liquid phases. Heterogeneous melting, marked by mixed phases, is the most distinctive feature in the [011]/[111] orientations, which is responsible for the cold melting phenomenon. Our study shed light on the shock-induced phase transitions of FCC single crystal, which may offer insight into understanding the complex polycrystalline.

Development and evolution mechanism of streamwise vortex in an inward-turning inlet

The three-dimensional flows in an inward-turning inlet were numerically investigated at different incoming flow conditions. When the incoming flow conditions change, the shock angle and the shock interaction form of the external compression wave change, and the development of the near-wall low-energy fluid and the streamwise vortex is also affected. The impingement of the shock wave leads to a sharp increase in the vorticity of the low kinetic energy fluid. Under the pressure gradient caused by the shock wave, the high-vorticity fluid migrates from the cowl to the ramp and entrains the mainstream fluid to form a streamwise vortex, for which the velocity gradient ( ∂v/ ∂y + ∂w/ ∂z) along the vortex axis can accurately determine the rotation direction and the Hopf bifurcation position. By considering high Reynolds number flows, the pressure gradient along the vortex axis is developed to estimate the simplified dilation term (velocity gradient) due to its ease of measurement. However, the pressure gradient ( ∂p/ ∂x) along the vortex axis can lead to bias when evaluating the cross-flow state of the streamwise vortex, with the shock wave structure and high-vorticity fluid leading to under- and overestimation, respectively. This study provides a theoretical basis for an accurate determination of the flow state of a streamwise vortex in an inward-turning inlet and thus lays the foundation for effective vortex control.

Highly underexpanded rarefied jet flows

A highly underexpanded jet outflow into the background in transition and scattering regimes is studied computationally. The direct simulation Monte Carlo method and Navier–Stokes equations are used. The main parameters’ impact on the jet flow is analyzed. It is shown that a drastic flow structure transformation occurs in a relatively narrow Reynolds numbers’ range, 5 ≤ ReL≤ 30, featuring the jet–surrounding gas interaction. At ReL= 5, a shock wave structure that is typical for the underexpanded jet degenerates completely. The existing empirical expressions application for the estimation of the characteristic dimensions of the shock wave structure in the transition regime leads to significant inaccuracy. For the considered parameters’ range, the approaches based on the direct simulation Monte Carlo method and Navier–Stokes (NS) equations’ solution lead to similar results in the nozzle region, where the flow regime is hydrodynamic. Nevertheless, the NS approach employment for the assessment of flow parameters within rarefied shock layers is debatable.

Aerodynamic performance of a characteristic airfoil at low-Reynolds number and transonic flow under Mars sand-containing environment

The propeller tip of an unmanned aerial vehicle on Mars operates at a low-Reynolds number (Re = 1–5 × 104) and transonic velocity range (Ma = 0.7–1.2). Generally, this implies flow separation and shock waves in the flow field. Furthermore, the impact of Martian atmospheric sand particles significantly affects the aerodynamic performance, and numerical simulations of this issue have received increasing attention recently. Aimed at a characteristic airfoil, the study of a low-Reynolds number transonic flow and the influence of sand-containing flow on airfoil aerodynamic performance were analyzed in this study. The discrete phase model was adopted to simulate the two-phase flow considering Re = 8100–56 800 and Ma = 0.2–1.4. The results indicate that, compared with the atmospheric environment on Earth, the low-pressure atmosphere on Mars can delay the generation of the surface shock wave of the airfoil as well as alter the shock wave structure, significantly increasing the lift-to-drag ratio at high subsonic velocities (Ma = 0.6–0.8). Moreover, due to the weak compressive wave generated at the separation position, the low-pressure atmosphere weakens the strength of the trailing-edge oblique shock wave and reduces the drag when Ma = 0.9–1.4. Compared with a sand-free environment, sand-containing flow can affect the separation and transition positions of laminar separation bubbles, in addition to alter the shock wave structure. At different Mach numbers, the lift and drag of the airfoil first increased and then decreased as the sand particles flowed in the horizontal direction during the entire process of particles entering and exiting the airfoil flow field.

Influences of spatial structure of plasma shock wave on electromagnetic wave propagation characteristics

Plasma shock waves represent high-speed, nonlinear motion states of plasma in which the physical parameters of fluid, such as density, temperature, and velocity, vary dramatically within a limited space. These variations make studying electromagnetic wave propagation in plasma shock waves difficult. In this study, we calculate the spatial distribution of the plasma frequency and collision frequency in the plasma shock layer based on the one-dimensional structure of the plasma shock wave. In the process from upstream to downstream of the plasma shock wave, the plasma frequency increases as a function of electron density; downstream, the plasma frequency increases as a function of the free stream Mach number, while the collision frequency decreases first and then increases. We also use the recursive convolution finite-difference time-domain method to calculate the propagation of the electromagnetic wave in the plasma shock layer. The absorption of the plasma shock layer to the electromagnetic wave decreases gradually as a function of the electromagnetic wave frequency. The absorption of the plasma shock layer downstream of the electromagnetic wave is greater than that upstream owing to the larger plasma frequency. In the case of low-Mach numbers, the wavelength of the electromagnetic wave downstream is larger than that upstream. In the case of high-Mach numbers, the thickness of the entire shock layer is much greater than that at low-Mach numbers. Due to the nonlinear effects of electromagnetic processes in plasmas, a modulation phenomenon occurs when electromagnetic waves propagate in the shock layer. In the case of low frequencies, the electromagnetic wave gave rise to a modulation phenomenon that resembled the beat phenomenon. When the electromagnetic wave frequency increased, a modulation phenomenon gradually appeared that resembled the oscillation superimposed on a sine wave. Further increases in the electromagnetic wave frequency led to the gradual disappearance of the modulation phenomenon.

Structure of Shock Wave in Oxygen

Structure of Shock Wave in Oxygen

Studies on Shock Wave Structures in Supersonic Ejector and Its Influence on Ejector Performance

Supersonic ejectors are an economically feasible and environmentally friendly technology. Shock wave structures significantly affect the ejector performance. In the present work, the first shock wave structures in a supersonic ejector were analyzed with experimental and numerical methods. The experimental results by the Schlieren method were used to verify the accuracy of the numerical simulation results. Then the influence of the inlet pressure on the first shock wave structures inside the ejector was analyzed under critical operating conditions. The numerical simulation results showed that the dimensionless length and height of the first shock wave inside the ejector increase with the increase of the primary pressure and decrease with the increase of the secondary pressure. Meanwhile, the relationship between the performance of the ejector and the shock structures was established, the entrainment ratio is positively correlated with the first shock wave aspect ratio and has a good linear relationship. The results may be beneficial to reveal the ejector’s working mechanism and design high performance ejectors in the future.

Analysis on the radial structure of rotating detonation wave in a hollow combustor

This experimental study discusses the radial structure of the rotating detonation wave (RDW) in a hollow chamber. The head chamber wall could be fabricated with quartz glass for high-speed visualizations or metal cover for high-frequency pressure measurement. The entire radial-stratified reaction zone was directly and continuously captured. The wall-attached bright zone indicated that the main reaction zone propagated along the chamber wall, but some deflagration was still observed in the inner zone. Based on the phase-averaged CH* chemiluminescence image, the radial thickness of the reaction zone was determined to be about 15–20 mm. The diminishing pressure peaks and deteriorating waveforms of the high-frequency pressure signals proved that the intensity of shock waves decreased along the chamber radius. The structure of RDW was reconstructed using radially distributed pressure sensors. Due to the compression effect of the concave chamber wall, a Mach reflection of detonation wave might occur. The detonation wave was connected to a diffracted shock, which stretched in the radial direction with decreasing intensity. The central angles calculated with the time-difference analysis demonstrated that the entire RDW bent forward in the inner zone of the chamber. Moreover, the radial thickness of the reaction zone and the curvature of shock waves increased with decreasing nozzle contraction ratio, which mainly attributed to the increasing expansion effect. This study demonstrated the distribution of reaction zone and the radial structures of shock waves for the RDW in a hollow combustor, contributing to the exploration of the flow and combustion process in a rotating detonation engine.

Numerical study on the influence mechanism of different types of burst disc on high pressure hydrogen spontaneous combustion in tube

High-pressure transportation and storage are the current main methods for storing hydrogen. Burst discs, which are common in high-pressure storage devices, can cause hydrogen leaks to ignite and create serious accidents when certain conditions are met. To investigate this, this paper studies the effect of different blasting slot shapes on the spontaneous combustion of leaked high-pressure hydrogen. Numerical simulations, using LES, EDC model, Ten-Step Burst Disc Opening Method and 19-Step Detailed Hydrogen Combustion Mechanism, were conducted to analyze the spontaneous combustion of hydrogen with annular grooves, star grooves, cross grooves and grooveless burst discs. The results of the study show that the shape of the groove in the bursting disc will significantly affect the shock wave structure and spontaneous combustion time of leaked high pressure hydrogen in the tube. Among the four types of bursting discs, the order of spontaneous combustion in the tube is annular groove (approximately 90 μs), star groove (approximately 110 μs), cross groove (approximately 120 μs), and grooveless bursting disc (approximately 130 μs). Secondly, the double spherical shock waves produced by annular groove bursting disc collide with each other, resulting in a higher rising speed of pressure and temperature in the tube than with other bursting discs. Finally, the spontaneous combustion time of the leaked hydrogen is proportional to the open area of the bursting disc. When the opening area is the same, the smaller the exit shape coefficient is, the shorter the spontaneous combustion time is. The research results can provide some reference for the design and application of bursting disc in high pressure hydrogen storage equipment.

Structure of shock wave in tungsten and titanium metals by using navier-stokes equation

Using the Navier–Stokes equation, we present the structure of a one-dimensional stationary shock wave formed in condensed alloy materials such as tungsten and titanium. In this study, the shock wave structure in the mentioned materials has been analysed by using several important parameters such as material viscosity, the Mie-Gruneisen parameter, and Mach number (M). One of our derived results is shock thickness, which is found to be of the order of 10−6 meters. In addition, we address a number of key insights into the shock wave interaction with tungsten and titanium. It should be noted that the validity of the model discussed in this study is limited to high M values, i.e., M ≥ 2.0.