Shock Wave Diffraction Research Articles

Numerical investigation of rarefied vortex loop formation due to shock wave diffraction with the use of rorticity

When compressed gas is ejected from a nozzle into a low-pressure environment, the shock wave diffracts around the nozzle lip and a vortex loop will form. The phenomenon has been widely investigated in the continuum flow regime, but how the shock diffraction and vortex behave under rarefied flow conditions has not received as much attention. It is necessary to understand this transient flow in rarefied environments to improve thrust vector control and avoid potential contamination and erosion of spacecraft surfaces. This work provides numerical results of the vortex loop formation caused by shock wave diffraction around a 90° corner using the direct simulation Monte Carlo method and the compressible Navier–Stokes equations with the appropriate Maxwell velocity slip and the von Smoluchowski temperature jump boundary conditions. The Mach number and rarefaction effects on the formation and evolution of the vortex loop are discussed. A study of the transient structures of vortex loops has been performed using the rorticity concept. A relationship of mutual transformation between the rorticity and shear vectors has been discovered, demonstrating that the application of this concept is useful to understand vortex flow phenomena.

Evolution of heat transfer at the stagnation point during the detached bow shock establishment

The diffraction of a shock wave over a stationary body is a problem of interest associated with the starting of shock tubes and expansion tubes which are well suited to studies of hypersonic flows. However, these facilities are characterized by very short test times. The transient parameters during the establishment of the detached bow shock in such impulsive facilities are important for both data processing and experimental design. In the present study, numerical simulations are conducted to investigate the diffraction of a normal shock wave over a sphere and the subsequent transient phenomena in a viscous perfect-gas flow field. The incident shock Mach number ranges from 3 to 5 with a specific heat ratio of 1.4. Based on the theoretical description of the reflected shock position during bow shock formation, approximate solutions for the time histories of the stagnation-point heat flux are also derived. The analytical and numerical results agree well. The results show that the stagnation-point pressure and heat flux approach their steady-state values much more rapidly than the shock detachment distance does.

Shock wave mitigation using zig-zag structures and cylindrical obstructions

The present study focuses on the mitigation of shock wave using novel geometric passages in the flow field. The strategy is to produce multiple shock reflections and diffractions in the passage with minimum flow obstruction, which in turn is expected to reduce the shock wave strength at the target location. In the present study the interaction of a plane shock front (generated from a shock tube) with various geometric designs such as, 1) zig-zag geometric passage, 2) staggered cylindrical obstructions and 3) zig-zag passage with cylindrical obstructions have been investigated using computational technique. It is seen from the numerical simulation that, among the various designs, the maximum shock attenuation is produced by the zig-zag passage with cylindrical obstructions which is then followed by zig-zag passage and staggered cylindrical obstructions. A comprehensive investigation on the shock wave reflection and diffraction phenomena happening in the proposed complex passages have also been carried out. In the new zig-zag design, the initial shock wave undergoes shock wave reflection and diffraction process which swaps alternatively as the shock front moves from one turn to the other turn. This cyclic shock reflection and diffraction process helps in diffusing the shock wave energy with practically no obstruction to the flow field. It is found that by combining the shock attenuation ability of zig-zag passage (using shock reflection and diffraction) with the shock attenuation ability of cylindrical blocks (by flow obstruction), a drastic attenuation in shock strength can be achieved with moderate level of flow blocking.

Mathematical modeling of shock wave interaction with wagon

In case of some accidents on railways there may be situations when the shock wave appears and interacts with different objects on the railway (wagons, cargo, buildings etc.). In these cases it is necessary to predict the possible effect of shock wave diffraction on the different objects. Study of these problems on the basis of physical experiments (laboratory experiment or field experiment) demand expensive and unique experimental facility. In some cases physical experiment can’t be set. That is why mathematical simulation plays the important role in solving problem connected with shock wave propagation. For practice it is necessary to have predictive quick computing mathematical models which allow to perform numerical experiment on the basis of non-powerful computers. Now, in Ukraine, there is a real deficit of mathematical models which allow to compute quickly shock wave interaction with different objects. The aim of this work was development of quick computing numerical model to simulate shock wave propagation and its interaction with the wagons. The model is based on the numerical integration of Euler equations which are written in integral form. To solve modeling equations difference scheme of splitting was used. Results of numerical modeling are presented.

Vortex–shock and vortex–vortex interactions in the compressible starting jet from two beveled nozzle configurations

An experiment was conducted to investigate the flow structures in the compressible starting jet from two beveled nozzles (45 $$^{\circ }$$ and 30 $$^{\circ }$$ nozzle angles) of a shock tube using the schlieren technique. In the present study, the pressure ratios between the driver section and the driven section (PR) of 3.5, 7, and 10.5 corresponding to the shock wave Mach numbers ( $$M_\mathrm{s}$$ ) of 1.28, 1.48, and 1.59 were applied to produce three types of compressible vortex rings (CVRs). Owing to the beveled nozzle, the shock wave diffracts twice to produce two coaxial CVRs. For PR = 3.5 with 45 $$^{\circ }$$ beveled nozzle, two shock-free CVRs are formed and merged into one primary CVR, while the two CVRs are separated from each other for the 30 $$^{\circ }$$ beveled nozzle. The main reason is that the strength of the secondary CVR generated from the 30 $$^{\circ }$$ beveled nozzle is much lower than that of the leading CVR. As for PR =7 and 10.5, the embedded shock and counter-rotating vortex rings (CRVRs) appear and constraint the formation of the secondary CVR. As a result, the two CVRs are merged into a primary CVR at a very early stage. In addition, for the two different beveled nozzles, the embedded shock–CVR, CRVR–CVR, and shock cell-trailing vortices interactions are observed and exhibited some differences. Moreover, by identifying the position of the primary CVR, it is found that the propagation velocity of the primary CVR generated from the beveled nozzles is significantly slower than that from a straight nozzle.

The re-initiation mechanism of detonation diffraction in a weakly unstable gaseous mixture

Numerical simulations were performed to investigate the re-initiation mechanism of a diffracted detonation wave near the critical channel width for a weakly unstable gas. Two scenarios were examined: diffraction of a planar detonation wave and of a cellular detonation wave inside the inlet channel. The results revealed that the critical channel width predicted using a cellular detonation wave is smaller than that predicted using a planar detonation wave. The re-initiation mechanisms are described in detail by tracing massless particles along both the plane of symmetry and the re-initiation path. For planar detonation diffractions, a compression wave is formed in the far field behind the diffracted shock. Re-initiation is closely related to the amplification of this compression wave and its coalescence with the diffracted shock. Depending on the inlet channel width, the strength of the reflected rarefaction wave is responsible for weakening the strength of the compression wave and its coalescence with the diffracted shock, consequently hindering the reaction of particles behind the diffracted shock wave. In cellular cases, the continuous collisions of transverse waves, which generate local explosion sites, sustain detonation wave propagation.

Analysis of shock-wave diffraction over double cylindrical wedges. Part II: Vorticity generation

The unsteady aspect of turbulent flow structures generated by a shock-wave diffraction over double cylindrical wedges, with initial diffracting angle of 75∘, are numerically investigated by means of two-dimensional high-fidelity numerical simulation. Different incident-shock-Mach numbers, ranging from transonic to supersonic regimes, are considered. Unlike previous studies where only the total vorticity production is evaluated, the current paper offers more insights into the spatio-temporal behavior of the circulation by evaluating the evolution of the instantaneous vorticity equation balance. The results show, for the first time, that the diffusion of the vorticity due to the viscous effects is quite important compared to the baroclinic term for low Mach numbers regimes, while this trend is inverted for higher Mach numbers regimes. It is also found that the stretching of the vorticity due to the compressibility effects plays an important role in the vorticity production. In terms of pressure impulses, the effect of the first concave surface on the shock strength has been quantified at both earlier and final stages of the shock diffraction process. Unlike the overpressure, the static and the dynamic pressure impulses are shown to be significantly reduced at the end of the first concave surface.

Analysis of shock-wave diffraction over double concave cylindrical wedges. Part I: Shock dynamics

Shock-wave diffraction over double concave cylindrical surfaces has been numerically investigated at different flow regimes by varying the incident-shock-wave Mach number from Ms=1.6 (transonic) to Ms=4.5 (supersonic regime). The purpose of this study is to better understand the dynamics of shock-wave structure and the associated wave configurations. A mesh-independent solution is obtained and the flow is assessed through different physical quantities (transition angles, triple points trajectories, wall-pressure and skin-friction distributions, velocity and shock location). It is found that the transition angles, from regular to Mach reflection, increase with the Mach number. This phenomenon remains almost the same over both concave surfaces for weak Mach numbers (up to Ms=2.5) and becomes relatively larger on the second surface for high Mach numbers. In terms of shock dynamics, it is found that by increasing the incident incident-shock-wave Mach number to Ms=4.5, unlike the first reflector, the transition from a single-triple-point (STP) wave configuration to a double-triple-point (DTP) wave configuration and back occurred on the second reflector, indicating that the flow is capable of retaining the memory of the past events over the entire process. For the shock velocity, the velocity deficit is found to be increasing with increase in Ms. A best fitting scaling law is derived, to ensure a universal decay of the shock velocity depending on the flow parameters.

Shock tube exit flow fields through thin membranes

The flow field characteristics that form for a shock wave propagating through a membrane-like termination at the exit of a shock tube are studied. The strength of the shock wave reflected back into the tube, as well as the strength of the shock wave transmitted, is examined. Six different materials are used, ranging from copper and aluminium foils to a variety of elastic and plastic sheets, in a few cases with different initial pressure differentials. High-speed shearing interferometry imaging is done of the external flow. Three principal characteristics are present in the transmitted flow: a diffracted shock wave, an expansion wave and a re-compression shock wave. It is found that the prominence of these features varies depending on the material type. For the later flow development and material rupture, there are a number of principal characteristics: small vortices, secondary shock waves, a vortex ring, oblique waves and a Mach disc.

Localization of a combined pulse discharge within a gas with a rectangular obstacle on the channel wall

Analysis of plasma energy redistribution was conducted on the basis of experimental study of combined volume discharge of submicrosecond duration at its initiation in a gas-dynamic flow in rectangular channel with an obstacle. Shock wave diffraction on the obstacle (parallelepiped) on the channel wall was visualized. Effects of plasma localization at upward facing step and backward facing step were experimentally discovered and studied. CFD simulation patterns of the gas dynamic non stationary flow were compared to instant flow glow images.

Nanosecond volume discharge in the flow with diffracting shock wave in the rectangular channel

New effects of plasma redistribution shock wave (M = 2.8–3.4) diffraction on an obstacle at flow ionization with pulse volume discharge are presented. The obstacle has size 48.0 × 6.2x1.9 mm3 and consist of forward facing and backward facing steps on the wall. Localization of the nanosecond combined discharge plasma (with pre-ionization in the volume) in non-stationary gas flow was visualized with plasma glow imaging. It is shown that the discharge images visualize flow evolution structure, mainly - zones of reduced density. Image are compared with 2D CFD simulation.

On Shock Propagation through Double-Bend Ducts by Entropy-Generation-Based Artificial Viscosity Method

Shock-wave propagation through obstacles or internal ducts involves complex shock dynamics, shock-wave shear layer interactions and shock-wave boundary layer interactions arising from the associated diffraction phenomenon. This work addresses the applicability and effectiveness of the high-order numerical scheme for such complex viscous compressible flows. An explicit Discontinuous Spectral Element Method (DSEM) equipped with entropy-generation-based artificial viscosity method was used to solve compressible Navier–Stokes system of equations for this purpose. The shock-dynamics and viscous interactions associated with a planar moving shock-wave through a double-bend duct were resolved by two-dimensional numerical simulations. The shock-wave diffraction patterns, the large-scale structures of the shock-wave-turbulence interactions, agree very well with previous experimental findings. For shock-wave Mach number and reference Reynolds number , the predicted pressure signal at the exit section of the duct is in accordance with the literature. The attenuation in terms of overpressure for is found to be ≈0.51. Furthermore, the effect of reference Reynolds number is studied to address the importance of viscous interactions. The shock-shear layer and shock-boundary layer dynamics strongly depend on the while the principal shock-wave patterns are generally independent of .

Turbulent structures of shock-wave diffraction over 90° convex corner

The turbulent structures and long-time flow dynamics of shock diffraction over 90° convex corner associated with an incident shock Mach number Ms = 1.5 are investigated by large eddy simulation (LES). The average evolution of the core of the primary vortex is in agreement with the previous two dimensional studies. The Type-N wall shock structure is found to be in excellent agreement with the previous experimental data. The turbulent structures are well resolved and resemble those observed in the experimental findings. Subgrid scale dissipation and subgrid scale activity parameter are quantified to demonstrate the effectiveness of the LES. An analysis based on turbulent-nonturbulent interface reveals that locally incompressible regions exhibit the universal teardrop shape of the joint probability density function of the second and third invariants of the velocity gradient tensor. Stable focus stretching (SFS) structures dominate throughout the evolution in these regions. Stable node/saddle/saddle structures are found to be predominant at the early stage in locally compressed regions, and the flow structures evolve to more SFS structures at later stages. On the other hand, the locally expanded regions show a mostly unstable nature. From the turbulent kinetic energy, we found that the pressure dilatation remains important at the early stage, while turbulent diffusion becomes important at the later stage. Furthermore, the analysis of the resolved vorticity transport equation reveals that the stretching of vorticity due to compressibility and stretching of vorticity due to velocity gradients plays an important role compared to diffusion of vorticity due to viscosity as well as the baroclinic term.

Visualization of the shock wave diffraction on the wedge in a rectangular channel

The evolution of a shock wave interaction with a boundary layer on the surface of a shock tube channel after its reflection from a thin wedge is investigated. Visualization of the incident plane shock wave, the bow detached shock wave and flow behind the wedge in 48x24 mm channel was performed using the shadow method based on high-speed recording. The zone of boundary layer separation that occurs when the plane attached bow shock intersects with the channel wall is visualized on the basis of the pulse discharge glow recording. The flow evolution at incident shock wave Mach number of 2.3÷3.8 for the time interval up to 5 ms after the diffraction is investigated. The obtained data is compared with the corresponding CFD results: a numerical simulation based on the Euler equations of a nonstationary two-dimensional flow was performed under experimental conditions.

The influence of radial entrance width of the circular cavity on incident shock wave focusing

Despite the achievement of shock wave focusing with certain reflectors, the influence of the radial entrance width of a circular cavity on the flow field has yet to be addressed. In this study, we systematically investigated the effects of the shock wave focusing process in a cavity based on the radial entrance widths. An experimental system was installed to research the evolution of the flow field under conditions with different radial entrance widths of 3.0, 11.1, 19.5, and 33.0 mm. A schlieren system was used to photograph the structures of the flow field in the cavity, and a data acquisition system was used to record the dynamic pressure histories of different points. A numerical simulation was carried out to investigate greater details of the shock wave focusing process. A third-order strong stability-preserving Runge-Kutta method, third-order weighed essential non-oscillation scheme, and an adaptive mesh refinement algorithm were adopted to simulate the shock wave reflection, diffraction, and focus process. Good agreement between the experimental and numerical results was observed. By comparing the evolution process of the flow field under the conditions of four different entrance cavity widths, we found that when the entrance width was 19.5 mm, there was the stronger intensity of the shock wave focusing in the focal region, and the larger pressure value at the apex of the cavity than the other three entrance widths, occur. This study improves our understanding of shock wave focusing.

On the curvature of reflected diffracted shock wave interacted by an yawed wedge (Subsonic case)

On the curvature of reflected diffracted shock wave interacted by an yawed wedge (Subsonic case)

Dynamic response of single-layer reticulated shell with explosion-protection wall under blast loading

To investigate the structural dynamic response of long span reticulated shell under external blast loading considering explosion-protection wall, explicit finite element (FE) programme LS-DYNA is used to set up the analytical model of explosion-protection wall corresponding to an experiment to grasp the propagation law of blast shock waves around the wall. The results of simulation and experiment are compared and the results verify the creditability and applicability of numerical simulation by using ALE (Arbitrary-Lagrange-Euler) algorithm. A Kiewitt8 single-layer reticulated shell of refinement with span of 40 m is established to simulate the responses of structure considering explosion-protection wall, which contains reticulated shell member, purlin hanger, purlin, rivet and roof boarding. According to simulation results from the maximum nodal displacement, average plastic strain and yielding degree of cross section of reticulated shell member, the dynamic response laws are proposed based on varying parameters, including height, position, length, material of the explosion-protection wall, rise-span ratio of reticulated shell and TNT explosive weights. Meanwhile, the influence rules of explosion-protection wall and structure on diffraction and reflection action of blast shock wave are obtained. In addition, the adverse height of the explosion-protection wall for reticulated shell with span of 40 m under external blast loading is proposed. Four damage types of reticulated shell with the explosion-protection wall subject to external blast loading are defined by summarizing all the structural response of FE numerical models, which could provide reference for reasonable explosion-proof design for reticulated shell structure.

The relief of energy convergence of shock waves by using the concave combustion chamber under severe knock

In internal combustion engines, severe knock is a destructive phenomenon that would converge the energy released by fuel burning to damage the piston so that the engine can’t work anymore, which should be avoided. The destruction mechanism have been revealed in previous researches in which the focusing of shock waves is considered as a main reason to cause the energy convergence and the destruction. However, the method to alleviate such shock wave focusing hasn’t been put forward yet. Based on the destruction mechanism proposed before, in this research, a concave combustion chamber has been designed to alleviate the energy convergence of shock waves under severe knock so that the destruction of the piston under severe knock can be avoided. To validate the alleviation effect of the concave chamber, detonation bomb experiments have been conducted separately for the typical cone chamber and the redesigned concave chamber. Four pressure sensors installed in different positions of either chamber were used to monitor the shock wave behaviors and compare the energy convergence intensity for both of these two chambers. The experimental results prove that the concave chamber can efficiently alleviate the energy convergence in the center region. Furthermore, a series of numerical simulations have been conducted to reveal the alleviation mechanism of the concave chamber. Two kinds of alleviation mechanism have been obtained which are separately: the shock wave diffraction and the shock wave breaking up. These mechanism can efficiently alleviate the energy convergence of shock waves. The research results can be used as a theoretical basis for the chamber design to avoid the destruction under severe knock.

On the pressure buildup behind an array of perforated plates impinged by a normal shock wave

The pressure buildup behind an array of perforated plates following a shock wave impingement was experimentally studied. The experiments were performed in a shock tube facility and the arrays were varied in the number of their perforated plates and the porosities of the plates. It was found that the pressure buildup behind all of the configurations that were examined displayed similar characteristics. Using simplified assumptions about the nature of the flow through the perforated plates array, we could account for the influence of the volume confined between the plates, and the porosity of the plates. Once accounted for, experiments were performed with argon and SF6, in addition to air, in order to examine the effect of the gas. It was found that the pressure buildup depended on a constant parameter, which was gas-dependent. The constant parameter for each gas was found in this study experimentally. To the best of our knowledge this result has never been reported before. The large spread of different experiments performed throughout the present study enabled the separation of the effects facilitated by the perforated plates array into two distinct processes that affected the pressure buildup at the end-wall. The first was the diffraction of the incident shock wave and subsequent shock reverberations that were found to depend on the number of perforated plates in the array and their porosity. The second was the inhibition of the flow through the perforated plate that was found to depend on the confined volume, type of gas and the porosity of the plates.

Dynamics of shock wave diffraction over sharp splitter geometry using entropy-based artificial viscosity method

This paper reports the numerical analysis of shock wave diffraction over a convex sharp splitter geometry, focusing on the mechanism of the shock diffraction and the longtime behavior of shock–vortex dynamics. The flow evolution with shock–vortex dynamics for incident shock Mach number, \({M}_{{\mathrm {s}}} = 1.59\), is found to be in excellent agreement with the previous experimental results. We use a recent entropy-generation-based artificial viscosity (AV) method in conjunction with a high-order explicit discontinuous spectral element method (DSEM) to resolve these complex interactions. The AV is coupled with a shock sensor switch to attain optimal dissipations. Simulations capture the essential wave diffraction, transverse wave interaction with the deforming and growing primary vortex, and weaker secondary vortices arising from the Kelvin–Helmholtz instability. A quantification of the artificial dissipation of the numerical scheme is made by comparing the components of the kinetic energy dissipation rate and the pressure dilatation term. A new detailed transient flow analysis is also presented to address the shock dynamics, shock–vortex interaction, and the evolution of the flow topology with the probability density functions of various parameters of the enstrophy transport equation and the invariants of the velocity gradient tensor. The analysis reveals the mechanism of unwinding of vortices and its link with the divergence of the Lamb vector. A positive correlation is found between enstrophy and the imaginary part of the eigenvalues. Real parts of the two eigenvalues are associated with high dilatation shock regions and the outer edges of the vortices, respectively.