Incident Shock Mach Number Research Articles

Computational study of shock diffraction over convex edges

Numerical analysis of normal shock diffraction over various step corners is presented using an implicit second-order upwind least squares cell-based method. Slipstream angle calculation for various corner angles and Mach numbers, variation of pressure load and specific heat flux with incident shock Mach numbers and different step corners along the step wall, separation point movement, and reattachment of the streamlines are some of the key features of the present study. Detailed studies have been conducted about the perturbed region enclosed within the diffracted shock wave and the last running expansion wave with the increase in the incident shock Mach numbers. The finite Volume Method is used to solve the governing equations numerically for the simulation of the moving shock. Various flow characteristics such as secondary shock, contact surface, expansion wave, slipstream, vortex, etc are well captured. Apart from isopycnics; Mach contours, isobars, and isotherms are plotted as well. The reattachment region formed after the flow separation near the step edge is mentioned and corresponding lengths over various steps are presented. Separation point movement along the step wall is highlighted and a relevant increase in reattachment length is reported. The slipstream angles get increased with incident shock Mach numbers and with corner angles. However, the rate of increment of slipstream angle decreases gradually. The core of the vortices generated and the reattachment of the separated streamlines are indicated by the two downfalls in the heat flux values.

Parametric effects on Richtmyer–Meshkov instability of a V-shaped gaseous interface within linear stage

The Richtmyer–Meshkov instability of a V-shaped air/SF6 gaseous interface is numerically studied via a high-order finite difference scheme and a localized artificial diffusivity method. The oblique angle of the interface ranges from 20° to 75°, and the incident shock Mach number varies from 1.05 to 1.75. The wave patterns and the vortex structures are visualized during the interface evolution. A cavity is observed at the spike fingertip when the oblique angle decreases, which proves to be formed due to Mach reflection of the transmitted shock through velocity decomposition. By analyzing the linear growth rates of the interface, a modified empirical model for the reduction factor is suggested with model coefficients acquired by linear fitting for different Mach numbers. With shock polar analysis (SPA) method and visualization of the wave configuration, a criterion is proposed to explain the non-monotonic dependence of the linear growth rate on the oblique angle. In addition, Mach number effects on the linear growth rate are discussed by the SPA method, especially the anomalous behavior of the Mach 1.05 case.

Experimental investigation on initiation mechanism, overpressure, and flame propagation characteristics of methane-air mixtures explosion induced by hexogen in a closed pipeline

Gas explosion accidents under shock wave stimulation cause more severe hazards than electric spark ignition. To explore the initiation mechanism and explosion characteristics of methane induced by shock waves. A series of experimental investigations of methane-air mixtures initiated by hexogen (RDX) was performed based on a self-developed closed pipeline. The effects of incident shock wave intensity and methane concentration on the characteristics of methane explosion were studied. The results indicate that methane participating in the reaction can significantly increase the positive pressure duration compared with RDX explosion. With the increase of incident shock Mach number (Ma), methane deflagration pressure increases and counteracts the attenuation of RDX detonation pressure. When the ignition distance is 0 cm, the overpressure inside the pipeline is directly proportional to the methane concentration from 5 vol% to 13 vol%. When the concentration approaches the upper explosion limit, the flame velocity exceeds the theoretical detonation velocity, resulting in the unstable detonation of methane in the pipeline.

Multi-objective optimization design of shock-focusing detonation initiator

Shock-focusing induced detonation is an efficient technique that has the potential to simplify detonation-based engines. However, the generation of high energy regions relies on an extremely strong shock, and the design of the initiator plays a crucial role in minimizing the threshold of incident shock strength. In this study, a multi-objective optimization design of the shock-focusing initiator was conducted using Computational Fluid Dynamics (CFD). Firstly, the accuracy of the numerical method and the reliability of the optimization platform were validated through a series of experimental data. Subsequently, the Axial Ratio (AR) of the elliptical reflector and the angle of the incident shock were optimized, considering the objectives of focusing pressure and focusing delay time. Three typical focusing patterns were identified from the samples, with pattern C generally exhibiting higher focusing pressure but longer focusing delay time. Four optimization cases were tested and demonstrated good agreement with the predicted results. case 1 corresponded to pattern A but failed to detonate, while the others followed pattern C and successfully detonation. Although pattern C was also observed in the original initiator, it failed to detonate because the focusing region was too distant from the bottom of the cavity. Finally, a best initiator was selected and compared to the original initiator. The results showed that the threshold of the incident shock Mach number Min was reduced by 24.9%, the pressure of the corresponding driver gas was reduced by 68%, and the focusing delay time shortened by 7.2%.

Numerical investigation of shock Mach number effects on Richtmyer–Meshkov instability in a heavy square bubble

This study conducts a two-dimensional numerical investigation of incident shock Mach number effects on the Richtmyer–Meshkov (RM) instability after a shock wave impulsively drives a heavy square bubble. The square bubble is composed of SF6 gas, which is surrounded by nitrogen gas. Five different shock Mach numbers are considered: Ms=1.12, 1.22, 1.4, 1.7, and 2.1. Two-dimensional compressible Euler equations for two-component gas flows are simulated with a high-order modal discontinuous Galerkin solver. For validation, the numerical results are compared with the existing experimental results and are found to be in good agreement. The present results reveal that the incident shock Mach number is critical in the growth of RM instability in a heavy square bubble. The shock Mach number affects flow morphology significantly, resulting in complicated wave patterns, shock focusing, jet creation, bubble deformation, and vorticity generation. The convergent shape of the bubble causes shock focusing, which creates a local high-pressure zone and, as a result, an outward jet generation. It is found that the bubble deforms differently with increasing shock Mach number, and the different shock Mach numbers alter the distance between the shock focusing position and the downstream bubble interface. The effects of shock Mach numbers are investigated in depth through physical phenomena such as vorticity production, kinetic energy, and enstrophy. Finally, the shock Mach number impacts on the time-variations of the shock trajectories and interface structure are thoroughly investigated.

Numerical simulation of laminar premixed hydrogen-air flame/shock interaction in semi-closed channel

Highly refined simulations of flame/shock interactions (FSI) are performed and analyzed in the context of hydrogen/air combustion in a two-dimensional shock-tube configuration (height 7 cm). The chemical mechanism used for the hydrogen oxidation contains 9 reactive species, without nitrogen oxides, and 23 kinetic reactions. An initially planar laminar premixed flame (ϕ = 0.8, P=20 kPa) is left to evolve until the ratio between its burning flame velocity and the laminar flame speed reaches 1.45. Two thermal wall boundary conditions are envisaged: isothermal with Twall fixed to 300 K and adiabatic. The species transport is described with a unity Lewis number for all species or by complex transport. Once the flame is established, a shock is installed in the domain which propagates toward the flame. Two values of the Mach number for the incident shock are considered: Ms=1.4 and Ms=1.9. The relative impacts of the wall thermal condition, of the species transport modeling and of the incident shock Mach number on the FSI process are discussed. It is observed that thermal boundary conditions and transport modeling have a weak impact during the first stages of the FSI, i.e. the two successive interactions of the incoming and reflected shock with the flame, but a significant one once the reflected shock has crossed the flame front.

On the irregular jet formation of shock-accelerated spherical heavy gas bubbles

The behaviors of shock-accelerated heavy gas bubbles are numerically investigated, focusing on clarifying the forming mechanisms of the bubble jets in different types. The present study categorizes heavy bubble jets into two types, regular jets, and irregular jets. The present shock-accelerated multi-component flows are simulated by solving inviscid compressible Euler equations. An upwind characteristic space-time conservation element solution element scheme is adopted, and a five-equation model is used to treat the gas interface. Bubbles of R22, SF6, and Kr in ambient N2 and air are examined, and the incident shock Mach numbers are 1.1 and 1.23. The numerical results demonstrate that the bubble jet formation and its shape are very sensitive to the test gas species and incident shock strength. It is found that the tiny upstream jet formed in the single-shocked SF6/air scenario results from a very small Mach stem impingement onto the bubble upstream interface, the type II shock-shock interaction features the flow mechanism. While the large upstream jet formed in the re-shock SF6/air scenario is a combined result of the re-shock convergence and later vortex stretching. For the complex Kr/air scenario, the upstream jet results from the vorticity-induced inward jet stretching, and the downstream hollow jet results from the slip line guided tip extension. The measurements of bubble volumes, gas mixings, and material line lengths suggest that, although the jet formation greatly changes the bubble morphology, it makes a minor contribution to the bubble overall integral properties.

Formation of Bow Shock Waves Around a Blunt Body in Magnetohydrodynamics Flows

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 magnetohydrodynamic 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, based on the low magnetic Reynolds number assumption and dipole magnetic field distribution, the influence of magnetic field on the diffraction of an incident shock wave over a sphere was studied numerically. The incident shock Mach number ranges from 11 to 15 under different magnetic field intensities. Time histories of the shock-detached distance and stagnation pressure were first obtained. Moreover, the time needed to establish the steady flows over the sphere was also displaced against the magnetic interaction parameter. The larger the magnetic interaction parameter, the longer the time needed to establish a steady bow shock for experiments, which further challenges the facilities to have sufficient test times for conducting hypersonic magnetohydrodynamic flow experiments.

An experimental and numerical investigation of the effects of the diaphragm pressure ratio and its position on a heated shock tube performance

AbstractThe main purpose of this work was to investigate the performance of heated shock tube (ST) with different pressure ratios and diaphragm positions numerically and experimentally. The numerical model was developed to simulate the fluid flow inside a shock tube test facility located at Qatar University. The shock tube was a cast‐iron hollow tube with 6 m length, 50 mm internal diameter and 10 mm thickness. ST driver and driven sections were filled with helium–argon mixture and air. The driven section was heated up to 150°C using coils. At the middle of the ST, the diaphragm was made of aluminium sheet (0.5 mm) layers. Five different pressure ratios were implemented during the experiment, and performance evaluation depended on the strength of the incident shock Mach number. The inviscid numerical model solver used transient two‐dimensional time‐accurate Navier–Stokes CFD. The model introduced a parametric study regarding three different diaphragm positions (1m, 2m and 3m) and five pressure ratios (6–10) for each position. In addition to yielding the incident and reflected wave Mach number, reflected wave temperature was also considered a shock tube performance indicator. The incident Mach numbers for the diaphragm middle position from the experiment were compared against those conducted from the model, and good matching was observed. The parametric study results showed that at high‐pressure ratios, diaphragm Positions 1 and 3 could generate a 7.4% increase in shock wave Mach number compared with the diaphragm position‐2 model. Moreover, the diaphragm position‐3 model tends to have a 2% increase in the temperature behind the reflected shock wave compared with the other two positions.

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.

Ignition behavior and the onset of quasi-detonation in methane-oxygen using different end wall reflectors

The shock wave focusing technique is beneficial to the development of detonation-based engines, which can shorten the long run-up distance that is usually required for a detonation, reducing the weight of the detonation engine. In this work, we performed experiments using different end wall reflectors to facilitate the formation and intensity of the combustion wave in a stoichiometric methane-oxygen mixture diluted by argon. By changing shock wave intensity, the effects of the incident shock Mach number (Ma) on the ignition delay times in two reflectors are systematically investigated. The experimental results show that the conical reflector creates an abrupt pressure rise in the apex, resulting in a 64.5% rise in the acceleration of the reflected shock velocity compared with the planar reflector. The introduction of a conical reflector significantly shortens the ignition delay time by an order of magnitude and facilitates the amalgamation of the leading reflected shock wave and the subsequent combustion wave. The experimental results also illustrate that conical reflectors promote the formation of the second ignition. However, only a weak deflagration wave is formed in a planar reflector, and a strong deflagration wave and quasi-detonation wave are observed by using a conical reflector. Our observation sheds light on the mechanism of ignition modes induced by the shape of reflectors.

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.

Surface conductivity effects during shock wave reflection off curved surfaces

Previous work has shown that heat transfer into a plane conducting surface affects shock wave reflection properties. In the more complex reflection case of a curved surface the situation would be different because of the increased number of reflection patterns, with a rapid change in reflection geometry as the wave propagates up the surface. Test pieces of different thermal conductivities (0.19 W/mK and 401 W/mK) and hydraulically smooth surfaces are used on both convex and concave cylindrical surfaces. The test pieces are placed in identical positions on either side of a plane of symmetry and at the same incident angles in a shock tube. Tests are performed at incident shock Mach numbers of 1.22< M <1.5 and imaged using high-speed shadowgraph photography. The images are analyzed both quantitatively through reflection angle measurements and qualitatively by searching for asymmetry. Both the qualitative and quantitative measurements clearly indicate that the thermal conductivity of the surface affects the reflection patterns due to the complex transient thermal environment. Asymmetry in the reflection patterns is found at all Mach numbers. In contrast to the plane wall case the lack of theory limits comparison, where in that case it was shown that the lower the thermal conductivity the closer the experimental results approached the ideal adiabatic case. Similar comparisons in the relationship of reflection types between different materials are found in the current case. The findings could be refined by using higher imaging frame rates and spatial resolution, and sophisticated numerical modeling.

On the interactions between a propagating shock wave and evaporating water droplets

One-dimensional numerical simulations based on the hybrid Eulerian–Lagrangian approach are performed to investigate the interactions between propagating shock waves and dispersed evaporating water droplets in two-phase gas–droplet flows. Two-way coupling for interphase exchanges of mass, momentum, and energy is adopted. A parametric study on shock attenuation, droplet evaporation, motion, and heating is conducted, through considering various initial droplet diameters (5 µm–20 µm), number densities (2.5 × 1011/m3–2 × 1012/m3), and incident shock Mach numbers (1.17–1.9). It is found that the leading shock may be attenuated to the sonic wave and even to the subsonic wave when the droplet volume fraction is large and/or the incident shock Mach number is low. Attenuation in both strength and propagation speed of the leading shock is mainly caused by momentum transfer to the droplets that interact at the shock front. Total pressure recovery is observed in the evaporation region, whereas pressure loss results from shock compression, droplet drag, and pressure gradient force behind the shock front. Recompression of the region between the leading shock and the two-phase contact surface is observed when the following compression wave is supersonic. After a critical point, this region gets stable in width and interphase exchanges in mass, momentum, and energy. However, the recompression phenomenon is sensitive to the droplet volume fraction and may vanish with high droplet loading. For an incident shock Mach number of 1.6, recompression only occurs when the initial droplet volume fraction is below 3.28 × 10−5.

An Assessment of the Drag Models in the Case of a Shock Interacting With a Fixed Bed of Point Particles

Abstract In this work, three-dimensional Euler–Lagrange (EL) point-particle simulations of a shock wave interacting with a fixed bed of particles are carried out. The results from the particle-resolved (PR) simulations are used to assess the performance of the point-particle drag models during short time scales. We demonstrate that in a one-way coupled regime, the point-particle simulations recover the dominant gas dynamic features of the flow and are in a good agreement with the exact Riemann solution of a shock traveling through a sudden area contraction. Although the PR simulations are inviscid, we show that a dissipative drag is necessary to predict the mean behavior of the gas. As a model for the inviscid shock-induced (SI) drag two different models are presented in lieu of the quasi-steady drag. Finally, two-way coupled simulations are performed at four different particle volume fractions {0.10, 0.15, 0.20, 0.25} and three different incident shock Mach numbers {1.22, 1.66, 3.0} and compared against the data from PR inviscid simulations. At a lower Mach number (1.22), averaged flow quantities from the two-way coupled simulations agree well with the PR simulations. As the Mach number increases, we observe that the discrepancies between the point-particle and the PR simulations grow. A sensitivity analysis of the drag models involved reveals a strong influence of the inviscid-unsteady force on the gas quantities especially in the case of a strong shock interacting with a dense bed of particles. The use of Mach correlation beyond the subcritical regime coupled with the model for volume fraction correction is identified as a probable cause for the additional drag.

Experimental investigation of diaphragm material combinations in a small-scale shock tube

PurposeThe purpose of this study is to experimentally investigate the trends in shock wave Mach number that were observed when different diaphragm material combinations were used in the small-scale shock tube.Design/methodology/approachA small-scale shock tube was designed and fabricated having a maximum Mach number production capacity to be 1.5 (theoretically). Two microphones attached in the driven section were used to calculate the shock wave Mach number. Preliminary tests were conducted on several materials to obtain the respective bursting pressures to decide the final set of materials along with the layered combinations.FindingsAccording to the results obtained, 95 GSM tracing paper was seen to be the strongest reinforcing material, followed by 75 GSM royal executive bond paper and regular 70 GSM paper for aluminium foil diaphragms. The quadrupled layered diaphragms revealed a variation in shock Mach number based on the position of the reinforcing material. In quintuple layered combinations, the accuracy of obtaining a specific Mach number was seen to be increasing. Optimization of the combinations based on the production of the shock wave Mach number was carried out.Research limitations/implicationsThe shock tube was designed taking maximum incident shock Mach number as 1.5, the experiments conducted were found to achieve a maximum Mach number of 1.437. Thus, an extension to further experiments was avoided considering the factor of safety.Originality/valueThe paper presents a detailed study on the effect of change in the material and its position in the layered diaphragm combinations, which could lead to variation in Mach numbers that are produced. This could be used to obtain a specific Mach number for a required study accurately, with a low-cost setup.

Similarity in Mach stem evolution and termination in unsteady shock-wave reflection

Abstract

Investigation of shock wave interactions involving stationary and moving wedges

The present study investigates the shock wave interactions involving stationary and moving wedges using a sharp interface immersed boundary method combined with a fifth-order weighted essentially non-oscillatory scheme. Inspired by Schardin’s problem, which involves moving shock interaction with a finite triangular wedge, we study the influence of incident shock Mach numbers and corner angles on the resulting flow physics under both stationary and moving conditions. The present study involves three incident shock Mach numbers (1.3, 1.9, and 2.5) and three corner angles (60°, 90°, and 120°), while its impact on the vorticity production is investigated using the vorticity transport equation, circulation, and rate of circulation production. Furthermore, the results yield that the generation of the vorticity due to the viscous effects is quite dominant compared to the baroclinic or compressibility effects. The moving cases presented involve shock driven wedge problems. The fluid and wedge structure dynamics are coupled using the Newtonian equation. These shock driven wedge cases show that wedge acceleration due to the shock results in a change in reflected wave configuration from single Mach reflection to double Mach reflection. The intermediary state between them, the transition Mach reflection, is also observed in the process. The effect of shock Mach numbers and corner angles on the triple point trajectory, as well as on the drag coefficient, is analyzed in this study.

Unified prediction of reshocked Richtmyer–Meshkov mixing with K-L model

Hydrodynamic instabilities, including Rayleigh–Taylor, Richtmyer–Meshkov (RM), and Kelvin–Helmholtz, induced turbulent mixing broadly occur in both natural phenomena, such as supernova explosions, and high-energy-density applications, such as inertial confinement fusion. Reshocked RM mixing is the most fundamental physical process that is closely related to practical problems, as it involves three classical instabilities. In complex applications, the Reynolds-averaged Navier–Stokes model analysis continues to play a major role. However, there are very few turbulence models that facilitate unified predictions of the outcome of reshocked RM mixing experiments under different physical conditions. Thus, we aim to achieve this objective using the K-L model based on three considerations: deviatoric shear stress is considered when constructing Reynolds stress tensor; the model coefficients used are derived based on a new systematic procedure; the performance of different numerical schemes are studied to ensure high resolution but basically no numerical oscillation. Consequently, a unified prediction is obtained for the first time for a series of reshocked RM mixing experiments under incident shock Mach numbers Ma = 1.2–1.98, Atwood numbers At = ±0.67, and test section lengths 8 cm ≤ δ ≤ 110 cm. The results reveal the feasibility of demonstrating different reshocked RM processes using a single model, without adjusting the model coefficients, which sheds light on the further application of the present model to practical engineering, such as inertial confinement fusion.

Sulfur hexafluoride bubble evolution in shock accelerated flow with a transverse density gradient

Sulfur hexafluoride (SF6) is a colorless, odorless, non-toxic, non-flammable stable gas, which has been widely adopted as the heavy gas in the Richtmyer–Meshkov instability study. In this paper, a computational analysis of SF6 bubble evolution in shock-accelerated flow with a transverse density gradient is presented. The influences of different incident shock Mach numbers on various interactions were clarified using high-resolution computation schemes. The results showed that the incident shock wave becomes curved during propagation because of the transverse density gradient. Based on this, two separate shock-focusing processes were identified when Ma = 1.21 and three separate shock-focusing processes were identified when Ma = 2.0. However, the shock-focusing intensity was weaker than previously observed in a flow field with a uniform density distribution. High- and relevant-pressure impingement played vital roles in the formation of three jets near the downstream pole of the SF6 bubble in both cases. In addition, impingement by incident and reflected shocks could induce additional vorticities in the bubble region and promote increased bubble volumes, but these increased bubble volumes could weaken the average vorticity. Upon increasing the incident shock Mach number, the effective bubble volume decreased with the enhanced shock intensity, but the vorticities were strengthened. Furthermore, analyzing the factors that affected vorticity evolution allowed us to find that the compression term had a stronger influence on vorticity evolution than the baroclinic term or the viscosity term. All of these studies complement the Richtmyer–Meshkov instability study.