Incident Shock Wave Research Articles

Improved traceable measurement of the reflected step pressure in shock tube with the compensation of shock wave attenuation

Shock tube is an exceptional valuable facility that can produce approximately ideal step pressure from the reflected shock wave for the dynamic characterization of pressure sensors in aerospace industry. However, the traceable measurement accuracy of the reflected step pressure (RSP) is limited by the inevitable attenuation of the incident shock wave (ISW), leading to the dynamic characterization results with large error. This paper proposes an improved method for achieving high-accuracy traceable measurement of RSP in shock tube with the compensation of shock wave attenuation. The traceable measurement model of RSP relates to the ISW velocity is established firstly based on shock tube theory. To compensate the ISW velocity attenuation, a distributed measurement combined with a non-equidistant fractional-order grey (NFOG) method is implemented to establish ISW velocity model in consideration of the nonlinear, small-sample and non-equidistant features of the velocity sequence obtained by multiple sensors. Meantime, an ergodic optimization method based on a similarity index is adopted to estimate the optimal fractional-order in NFOG. With ISW velocity model, the velocity at the end-wall of shock tube is predicted and then more reliable RSP result is achieved with the traceable measurement model. Four experiments under different shock wave conditions are carried out to verify the proposed method. Results show that NFOG is able to establish the velocity model effectively, and the modeling error is less than that of the non-equidistant grey model and least square fitting methods. Furthermore, the traceable measurement accuracy of RSP by the proposed method is improved significantly than existing methods according to the investigation of pressure sensor sensitivity in both dynamic and static conditions.

Strong interactions of incident shock wave with boundary layer along compression corner

The coherent structure and instability of the interaction of incident shock wave with boundary layer developing on a compression corner are experimentally studied. The experiments are carried out in a supersonic wind tunnel of Mach number 2. Particular attention is paid to shock patterns and unsteady shock motions induced by the separation bubble. The high-speed schlieren is used to visualize the flowfield evolution and to characterize the instability. The snapshot proper orthogonal decomposition of schlieren sequences is applied to investigate the primary coherent structure in the flowfield. Fast Fourier transform and continuous wavelet transformation are applied to characterize the instability. The results show that there are large-scale low-frequency oscillations of the shock waves and small-scale high-frequency pulsations in the separation region. The peak frequency of shock oscillation is mainly concentrated in the range of 100–1000 Hz. The pulsation of the small flow structure in the separation bubble is mainly concentrated above 12.5 kHz. Based on the results of experimental analysis, the preliminary mechanism of the large-scale instability of such interaction is obtained.

Sensor orientation and other factors which increase the blast overpressure reporting errors.

This study compared the response of the wearable sensors tested against the industry-standard pressure transducers at blast overpressure (BOP) levels typically experienced in training. We systematically evaluated the effects of the sensor orientation with respect to the direction of the incident shock wave and demonstrated how the averaging methods affect the reported pressure values. The evaluated methods included averaging peak overpressure and impulse of all four sensors mounted on a helmet, taking the average of the three sensors, or isolating the incident pressure equivalent using two sensors. The experimental procedures were conducted in controlled laboratory conditions using the shock tube, and some of the findings were verified in field conditions with live fire charges during explosive breaching training. We used four different orientations (0°, 90°, 180°, and 270°) of the headform retrofitted with commonly fielded helmets (ACH, ECH, Ops-Core) with four B3 Blast Gauge sensors. We determined that averaging the peak overpressure values overestimates the actual dosage experienced by operators, which is caused by the reflected pressure contribution. This conclusion is valid despite the identified limitation of the B3 gauges that consistently underreport the peak reflected overpressure, compared to the industry-standard sensors. We also noted consistent overestimation of the impulse. These findings demonstrate that extreme caution should be exercised when interpreting occupational blast exposure results without knowing the orientation of the sensors. Pure numerical values without the geometrical, training-regime specific information such as the position of the sensors, the distance and orientation of the trainee to the source of the blast wave, and weapon system used will inevitably lead to erroneous estimation of the individual and cumulative blast overpressure (BOP) dosages. Considering that the 4 psi (~28 kPa) incident BOP is currently accepted as the threshold exposure safety value, a misinterpretation of exposure level may lead to an inaccurate estimation of BOP at the minimum standoff distance (MSD), or exclusion criteria.

A substructure method for the transient response of vertical cylinders subjected to shock wave of underwater explosion

Vertical cylinders are widely used as supporting structures in ocean engineering applications. Shock waves due to underwater explosives (UNDEX) can cause serious damage to offshore structures, which has attracted the interest of many researchers. The propagation characteristics of shock waves produced by UNDEX across a cylinder are a complex physical phenomenon that involves fluid-structure dynamic interactions. For the shock wave produced by UNDEX, the total pressure on a cylinder consists of three parts, including the incident shock wave pressure, scattered wave pressure and radiation pressure due to the motion of the cylinder. This paper develops an improved method for obtaining the transient response of a vertical circular cylinder subjected to UNDEX. First, an empirical formula of the shock wave pressure for far-field UNDEX is adopted as the incident shock wave. Based on the continued fraction (CF) expansion of the frequency-domain dynamic stiffness coefficient, an accurate model in the time domain for solving the scattered wave pressures on a cylinder is further developed. Then, the added mass model is used to replace the fluid-structure interaction caused by radiation wave. Finally, the vibration equation of a Euler-Bernoulli beam is utilized to evaluate the transient response of the cylinder subjected to UNDEX.

Mach reflection promoted by an upstream shock wave

Abstract

A numerical study of the metal jet induced by a shock wave

In this work, a metal jet induced by a shock wave is studied numerically. Different from the previous works on metal jets, we apply a cut-cell based sharp interface numerical method for the study. The evolution of jets is simulated by the in house code CCGF [X. Bai and X. Deng, Adv. Appl. Math. Mech. 9(5), 1052–1075 (2017)], and the interfacial growth rate is computed and compared with some theoretical models. Various initial conditions, including disturbance amplitude and shock wave strength, are considered here. Based on the model of Karkhanis et al. [J. Appl. Phys. 123, 025902 (2018)], a modified model of the spike velocity is presented to achieve better consistency between the numerical simulation and the model formula under more wide initial conditions (here, the scaled perturbed amplitudes involved are 0.125 and 4, and the incident shock wave Mach number is from 2.5 to 8) in this paper. In order to extend the applicability of the empirical models, an approximate formula for the initial velocity V0 is also obtained; a direct prediction of the spike velocity will become possible when the initial perturbed amplitude and incident shock intensity are known. Relevant figures show that the modified model can estimate a more consistent result with the numerical simulation than the VK or GD model.

Modeling the amplitude growth of Richtmyer–Meshkov instability in shock–flame interactions

This paper discusses the shock–flame interactions and the aspects associated with it, including the types of interactions, role of interactions in turbulent flames, high pressure generation during interactions, initial pressure effects on interactions, equivalence ratio effects on turbulent interactions, and the Richtmyer–Meshkov instability (RMI). In particular, the theory of RMI and the models associated with its amplitude growth with time have been discussed. Then, a new analytical model, Al-Thehabey model, is presented based on the impulsive acceleration of Richtmyer, not the gravitational acceleration. This model predicts the amplitude growth of the interface perturbation in terms of Atwood number (A), wave number of the perturbation (k), interface velocity (uc), and time (t). This new model’s prediction of the amplitude growth of the RMI is tested on six different combinations of fluids at different interface velocities. The results of the new model are compared with the results of four other existing analytical models and the new model’s performance fared very well. In addition, the new model’s performance has been compared with the experimental results from a shock wave incident on CO2–air, at Mach number, M = 3.08, interface velocity, u = 699.1 m/s, Atwood number, A = 0.206, and wavelength, λ = 990.0 × 10−6 m. The new model showed much closer results with the experimental ones than all other models used in the evaluation. The advantage of this new model is that it is capable of predicting the amplitude growth for both linear, at the early stages of the instability, and non-linear later regimes of the instability. In addition, it covers a larger time-domain than both the Alon et al. and the Sadot et al. models.

Mechanisms of detonation initiation in multi-focusing systems

The work is dedicated to the experimental and numerical study of the mechanisms of gaseous detonation initiation in a stoichiometric hydrogen–oxygen mixture due to the reflection of a shock wave from a complex-shaped end wall. Several elliptic surfaces of different geometries, including distributed ones, were considered. We refer to such reflectors with multiple elliptical surfaces as multi-focusing systems. The experiments were carried out in a shock tube. Visualization of the process was carried out with a high-speed schlieren system. In the experiments, the ignition delay times and the critical incident shock wave Mach number for detonation initiation were measured. Two-dimensional Euler simulations, on a fully unstructured computational grid, were carried out to determine the mechanism of detonation initiation. The numerical approach was verified using the experimentally measured ignition delay times. Reasonable agreement between the simulations and experiments for the critical Mach number of detonation initiation and for the efficiency of various multi-focusing systems for detonation initiation was achieved. Different regimes of detonation initiation depending on the incident shock wave Mach number were observed.

The interaction of shockwaves with a vapour bubble in boiling histotripsy: The shock scattering effect

Boiling histotripsy is a High Intensity Focused Ultrasound (HIFU) technique which uses a number of short pulses with high acoustic pressures at the HIFU focus to induce mechanical tissue fractionation. In boiling histotripsy, two different types of acoustic cavitation contribute towards mechanical tissue destruction: a boiling vapour bubble and cavitation clouds. An understanding of the mechanisms underpinning these phenomena and their dynamics is therefore paramount to predicting and controlling the overall size of a lesion produced for a given boiling histotripsy exposure condition. A number of studies have shown the effects of shockwave heating in generating a boiling bubble at the HIFU focus and have studied its dynamics under boiling histotripsy insonation. However, not much is known about the subsequent production of cavitation clouds that form between the HIFU transducer and the boiling bubble. The main objective of the present study is to examine what causes this bubble cluster formation after the generation of a boiling vapour bubble. A numerical simulation of 2D nonlinear wave propagation with the presence of a bubble at the focus of a HIFU field was performed using the k-Wave MATLAB toolbox for time domain ultrasound simulations, which numerically solves the generalised Westervelt equation. The numerical results clearly demonstrate the appearance of the constructive interference of a backscattered shockwave by a bubble with incoming incident shockwaves. This interaction (i.e., the reflected and inverted peak positive phase from the bubble with the incoming incident rarefactional phase) can eventually induce a greater peak negative pressure field compared to that without the bubble at the HIFU focus. In addition, the backscattered peak negative pressure magnitude gradually increased from 17.4 MPa to 31.6 MPa when increasing the bubble size from 0.2 mm to 1.5 mm. The latter value is above the intrinsic cavitation threshold of –28 MPa in soft tissue. Our results suggest that the formation of a cavitation cloud in boiling histotripsy is a threshold effect which primarily depends (a) the size and location of a boiling bubble, and (b) the sum of the incident field and that scattered by a bubble.

Advances in interfacial instability induced by reshock

The interactions of a moving shock wave with fluid interface lead to complex flow phenomena, including shock reflection and refraction, interface evolution, and even turbulent mixing at its late stage. These phenomena are of great significance in nature and engineering applications. When an incident shock wave sweeps over the interface, the interface morphology varies, making the interface perturbations grow from linear to nonlinear stages due to the baroclinic and pressure disturbance mechanisms. When a reshock wave passes the already distorted interface, the generation and transportation of vorticity will change the original developing mode of interface instability, resulting in different physical phenomena and developing rules. As the generation and control of the reshock waves are more complicated than those of the single shock scenarios, it is a great challenge to investigate the reshock-induced interface instabilities. In this article, progresses of experimental, numerical, and theoretical studies on the interface instability and turbulent mixing under reshock are reviewed. The effects of initial conditions, such as interface shape, shock strength, and reflection distance, on the reshock-induced interface instability are discussed in both planar and converging shock scenarios. The future research priorities and directions are finally proposed.

Design of Diaphragmless Shock Tube and Research on its Normal Temperature Characteristics

Shock wave is an important physical phenomenon in supersonic airflow. The shock tube is an experimental device that generates shock wave. It generates shock wave by generating a pressure difference between its high-pressure section and low-pressure section. Most researchers in the world use diaphragm shock tubes to generate shock wave, such as single diaphragm structure and double diaphragms structure type shock tubes. Although the type of shock tube can generate an incident shock wave with a wide range of Mach numbers, in the process of producing shock wave and breaking film, there will be broken film fragments interfering with the flow field. And every time the researcher needs to replace the diaphragm after the experiment, the efficiency of the experiment is low. In this paper, a diaphragmless shock tube is designed. The high-speed reciprocating motion of two pistons in the high-pressure section is used to replace the process of membrane rupture. And the normal temperature characteristics of the shock tube are researched.

Flow patterns of dual-incident shock waves/turbulent boundary layer interaction

The ice-cluster-based planar laser scattering technique, a high spatiotemporal resolution technique, is used to obtain the fine structures of dual-incident shock waves/turbulent boundary layer interaction. A double wedge produces these two incident shock waves. Three different interval distances between the incident shock waves are examined to obtain the influence of the second shock wave on the entire flow-field configuration. The overall flow pattern of dual-incident shock wave/turbulent boundary layer interaction flow is shown dominated by a quasi-triangular separation when the two shock waves intersect at the wall. As the interval distance increases, a trapezoid separation appears and finally no apparent flow separation occurs in the turbulent boundary layer.

Experimental study on shock and turbulent boundary layer interactions under different incident shock waves

In this paper, the interactions between shock wave and the turbulent boundary layer of an incoming wall were experimentally studied. The experiments were performed in a Mach 3.4 supersonic low-noise wind tunnel at the unit Reynolds number of 6.30×106 m−1. Under different incident shock wave conditions, fine flow field structure, wall pressure, and wall temperature distribution were determined. Relationship was also analyzed. Instantaneous fine structures of typical flow fields with shock wave and turbulent boundary layer interactions were investigated using the nano-tracer planar laser scattering technique, and the transient flow images were analyzed statistically. The oscillation position of the induced shock wave satisfies a normal distribution. Simultaneously, the wall pressure distribution under different incident shockwave conditions of the interaction region was determined using the flush air data sensing system, and the relationship between flow the structure of the separation region and the wall pressure distribution with different incident shock wave intensities is analyzed. Using a temperature sensitive paint technology, the wall temperature distribution under different incident shockwave conditions of the interaction region model was determined. Also, the relationship between the strip structure caused by Gortler vortices and the incident shock wave intensity in the shockwave/turbulent boundary layer interaction was analyzed.

Dynamic evolution of a transient supersonic trailing jet induced by a strong incident shock wave

The dynamic evolution of a highly underexpanded transient supersonic jet is investigated via high-resolution time-resolved schlieren and numerical simulations. Experimental evidence is provided for the presence of a second triple shock configuration along with a shocklet between the reflected shock and the slipstream. A model is developed and applied to the numerical simulations to reveal the mechanism leading to the formation of the second triple point.

Experimental Study on Unsteady Characteristics of Shock and Turbulent Boundary Layer Interactions

In this paper, the experimental study on the shock wave and turbulent boundary layer interactions was performed in the Mach 3.4 supersonic low-noise wind tunnel. The angle of the shock generator was θ = 15°, and the unit Reynolds number of 6.30 × 106 m–1. The wall temperature and pressure distribution during the disturbance process of the shock wave and the turbulent boundary layer were obtained based on the temperature-sensitive paints technique and the flush air data sensing system, and the basic flow field of the interactions region was partitioned. Meanwhile, based on the nano-tracer planar laser scattering technique, and the instantaneous fine structures in the interaction region were obtained and the spatiotemporal evolution characteristics of the flow structure were analyzed. The flow visualization images showed that the oscillation position of the induced shock wave satisfied the normal distribution. Compared with the flow visualization images and the temperature results, the correlation between the flow structure of the interactions region and the wall temperature change was obtained. At the same time, the wall fluctuation pressure of the center surface of the shock wave and turbulent boundary layer interactions region was measured by the high-frequency pulsating pressure sensor. The power spectrum density results showed that under the action of the shock wave incident by the shock generator, there were two characteristics frequency signal of 12 and 30 kHz in the induced shock oscillation interval. For the signal of 12 kHz, the frequency value and the amplitude were increased from the turbulent boundary layer to the separation bubble, and the oscillation energy of the induced shock wave was enhanced. The amplitude of the peak signal of each measurement point gradually decreased from the separation bubble to the reattachment zone, and the energy was gradually attenuated. For the high frequency signal of 30 kHz, the frequency variation of each channel was relatively small, relatively stable, and the energy was concentrated.

Brightness temperature of water compressed by a double shock to pressures of 60–79 GPa

New data on the temperature of water shock-compressed to 79 GPa are presented. Thermal radiation from a water layer compressed by incident shock waves and shock waves reflected from a lithium fluoride or sapphire window was recorded in the range of incident-wave intensity of 28–36 GPa. The reflected-wave pressures were in the range of 49–79 GPa. The temperature measured at the pressure of 79 GPa was 2750 K, which is much lower than the single-shock temperature at this pressure—5270 K. The radiant flux loss at the interfaces was estimated. The temperature of water compressed by one and two shock waves was calculated using an equation of state model, and the calculation results are in good agreement with the experimental data.

Shock Loading of Closed Cell Aluminum Foams in the Presence of an Air Cavity

It is important to protect assets located within cavities vulnerable to incident shock waves generated by explosions. The aim of the present work is to explore if closed cell aluminum foams can mediate and attenuate incident shocks experienced by cavities. A small cavity of 9 mm diameter and 2 mm length was created within the steel end-wall of a shock tube and exposed to shocks, directly or after isolating by aluminum foam liners. Shock waves with incident pressure of 9–10 bar travelling at a velocity of 1000–1050 m/s were generated in the shock tube. Compared to the no-foam condition, the pressure induced in the cavity was either equal or lower, depending on whether the foam density was low (0.28 g/cc) or high (0.31 to 0.49 g/cc), respectively. Moreover, the rate of pressure rise, which was very high without and with the low density foam barrier, reduced substantially with increasing foam density. Foams deformed plastically under shock loading, with the extent of deformation decreasing with increasing foam density. Some interesting responses such as perforation of cell walls in the front side and densification in the far side of the foam were observed by a combination of scanning electron microscopy and X-ray microscopy. The present work conclusively shows that shocks in cavities within rigid walls can be attenuated by using foam liners of sufficiently high densities, which resist densification and extrusion into the cavities. Even such relatively high-density foams would be much lighter than fully dense materials capable of protecting cavities from shocks.

АНАЛИЗ ФОРМИРОВАНИЯ ТЕЧЕНИЙ ВЯЗКОГО ТЕПЛОПРОВОДНОГО ГАЗА ПРИ МАЛЫХ ВОЗМУЩЕНИЯХ ПАРАМЕТРОВ

Formation of one-dimensional flows arising as a result of interaction of a viscous heat-conducting gas and a heat-conducting wall in the process of reflection of a normally incident weak shock wave is considered. Formation of the flow field with small perturbations of parameters is studied on the basis of the Navier -Stokes equations linearized around the values of the parameters in the initial state, and the wall temperature distribution is modeled by linear heat equation. Analytical solutions of the linearized system of equations are obtained that allow one to analyze the influence of viscosity, thermal conductivity, and other factors on the formation of a continuous flow field structure with the formation of dissipative and ideal inviscid and non-heat-conducting zones.

Study on Richtmyer-Meshkov instability at heavy/lightsingle-mode interface

The Richtmyer-Meshkov (RM) instability at a heavy/light single-mode interface is studied both experimentally and numerically in this work, focusing on the interface structure evolution and the perturbation amplitude growth. The difference between the RM instability of the heavy/light interface and the light/heavy case (J. Fluid Mech., 2018, 853: R2) is discussed. Experimentally, an advanced soap film technique is adopted to generate an SF6/air gaseous interface with a controllable shape such that the instability development can be accurately examined. Detailed evolutions of the interface morphology and the wave pattern are captured by a high-speed video camera combined with schlieren photography. It is observed that the interfacial morphology presents an evident stratification after the phase inversion of the interface (the bubble (spike) reverses to be a spike (bubble)), which is mainly ascribed to the droplet cloud produced by the rupture of the soap film impacted by an incident shock wave. Numerically, a high-order accurate solver for compressible multi-phase flow, which has been thoroughly validated in previous shock-interface interaction studies, is employed to simulate the present heavy/light RM instability. The numerical results show good agreements with the experimental ones, which enables us to perform a detailed flow analysis. Different from the light/heavy case, after the shock impact, the heavy/light interface immediately enters the phase reversal process. After the phase reversal, the interface experiences successively the linear and nonlinear growths, which is similar to the light/heavy case. The reliable experimental and numerical results here allow us to examine the validity of the previous linear and nonlinear models for the heavy/light RM instability growth. It is found that the linear model of Meyer & Blewett (Phys. Fluids, 1972, 15: 753–759) gives a good prediction of the perturbation growth at linear stage up to a dimensionless time of 0.7, and the empirical model of Dimonte & Ramaprabhu (Phys. Fluids, 2010, 22: 014104) reasonably predicts the perturbation growth at the nonlinear stage, which is different from the light/heavy case where the model of Zhang & Guo (J Fluid Mech., 2016, 786: 47–61) gives the best prediction as suggested by an elaborate experimental study. Our study may facilitate the thorough understanding of the heavy/light RM instability and also can serve as a benchmark for new models.

Numerical investigations of interface instability and turbulent mixing driven by implosion

The interface instability and turbulent mixing of perturbed Air/SF6 interface driven by implosion in spherical convergent geometry are numerically investigated by the use of in-house compressible hydrodynamic code (multi-viscous flow and turbulence). The results revealed the complex evolving laws and physical mechanisms of interface instability and turbulent mixing due to the evolution of complex waves in this case. The RM instability is induced when the perturbed Air/SF6 interface is driven by the incident shock wave. And the perturbed interface accelerates toward the center, thereafter RT instability occurs. Then the perturbed interface slows down and decelerates towards the center, and the RT stabilization appears and suppresses the development of the interface instability and turbulent mixing. When the RT stabilization acts an absolutely dominant role, the growth of the turbulent mixing zone (TMZ) width is restrained completely, and its width in turn reduces. After the rebound of transmitted shock waves, the secondary loading from heavy fluid to light fluid is a combination of quasi-isentropic ramp wave, shock wave and Taylor wave in time series. The loading of quasi-isentropic ramp wave also contributes to the RT stabilization mechanism, the drive of rebound shock wave was seen to have induced the RM instability too, and the impact of Taylor wave resulted in RT instability once again. In the following, the reflected wave moves toward the center and bounces, the third loading process is the same as the secondary one; the TMZ width repeats the same growth laws. The Bell-Plesset (BP) effect which belongs to the conergent geometry can promote the development of TMZ. In the spherical converegent geometry, the competition mechanism among the RM instability, RT instability, BP effect and RT stabilization controls the evolution of interface instability and turbulent mixing. The distributions of turbulent kinetic energy indicate that TMZ evolves asymmetrically along the radial direction. The distributions of three direction components of turbulent kinetic energy and energy spectra also exhibit the evolution of TMZ as strong anisotropy.