Supersonic Wave Research Articles

Characterization of laser-induced shock waves generated during infrared laser ablation of copper by the optical beam deflection method

The shock waves generated during laser ablation of a copper target are investigated using the optical beam deflection method. The fluence of nanosecond pulsed infrared laser beam was in the range of 15-700J/cm2. The density jumps related with the influx of the shock wave at two interaction points were detected with the help of He-Ne laser probes. In general, a supersonic shock wave is produced, which propagates through air and gradually decays into an acoustic wave. Experiments were carried out to study the impact of laser fluence and propagation distance on the shock wave velocity and pressure. The shock wave velocity varies with laser fluence as v∝Fl0.3 and with propagation distance as v∝d-1.5. These results are compared with the predictions of the theoretical models. In the investigated fluence range, shock wave pressure rises by an order of magnitude (∼1-10MPa). We demonstrated that shock wave pressure and ablated mass can be related, yielding mass-specific shock wave pressure that increases linearly with laser fluence. We have also noticed the shock-wave-induced probe beam focusing under certain conditions, which indicates that the shock wave modifies the refractive index of the compressed layer of air. The reported results are useful for the fundamental understanding and pave the way for new applications of laser-induced shock waves.

Two component model of microtubules – subsonic and supersonic solitary waves

This work represents a contribution to modelling nonlinear dynamics of microtubules, the basic components of the eukaryotic cytoskeleton. Their dynamics can be explained in terms of kink and antikink solitary waves. Special attention was paid to the stability of solitonic solutions of differential equations describing the dynamics of microtubules. It is shown that subsonic solitons are stable, while supersonic ones are not.

Supersonic shear wave imaging of the tibial nerve for diagnosis of diabetic peripheral neuropathy: A meta-analysis.

BackgroundDiabetic peripheral neuropathy (DPN) is the most common diabetes-associated complication and imposes a significant burden to healthcare systems. Thus, early diagnosis of DPN is extremely critical for management and outcome of diabetic patients. Supersonic Shear Wave Imaging (SSI) enables the noninvasive measurement of nerve stiffness. However, previous studies on SSI in the diagnosis of DPN were limited in sample sizes and reported various results. In this meta-analysis, we aimed to obtain comprehensive evidence on the value of tibial nerve stiffness measurement by SSI in the diagnosis of DPN.MethodsA comprehensive literature search in English and Chinese electronic database was conducted for studies (published until January 25, 2022) that investigated the diagnostic performance of tibial nerve stiffness measurement by SSI for detecting DPN. Summary receiver operating characteristics (SROC) modelling was constructed to conduct the meta-analysis of diagnostic accuracy of SSI for detecting DPN.ResultsFinally, a total of 12 eligible studies with 1325 subjects were included for evaluation, and a meta-analysis was conducted to evaluate the diagnostic performance of tibial nerve stiffness measurement by SSI for detecting DPN. For tibial nerve stiffness measurement by SSI, the summary sensitivity and specificity for the diagnosis of DPN were 80% (95% confidence interval [CI]: 73%–86%) and 86% (95% CI: 82%–89%), respectively. The summary area under the ROC curve (AUROC) value of the SROC was 0.90 (95% CI: 0.87–0.92), for diagnosing DPN. A subgroup analysis of 11 SSI studies from China revealed similar diagnostic performance, with a summary sensitivity of 79% (95% CI: 72%–85%), specificity of 86% (95% CI: 82%–89%) and summary AUROC value of the SROC of 0.90 (95% CI: 0.87–0.92) for diagnosing DPN.ConclusionsOur meta-analysis suggests that a tibial nerve stiffness measurement by SSI shows good performance in diagnosing DPN and has considerable potential as a noninvasive tool for detecting DPN.

New Class of Laboratory Astrophysics Experiments: Application to Radiative Accretion Processes around Neutron Stars

Extreme radiative phenomena, where the radiation energy density and flux strongly influence the medium, are common in the universe. Nevertheless, because of limited or nonexistent observational and experimental data, the validity of theoretical and numerical models for some of these radiation-dominated regimes remains to be assessed. Here, we present the theoretical framework of a new class of laboratory astrophysics experiments that can take advantage of existing high-power laser facilities to study supersonic radiation-dominated waves. Based on an extension of Lie symmetry theory we show that the stringent constraints imposed on the experiments by current scaling theories can in fact be relaxed, and that astrophysical phenomena can be studied in the laboratory even if the ratio of radiation energy density to thermal energy and systems’ microphysics are different. The validity of this approach holds until the hydrodynamic response of the studied system starts to play a role. These equivalence symmetries concepts are demonstrated using a combination of simulations for conditions relevant to Type I X-ray burst and of equivalent laboratory experiments. These results constitute the starting point of a new general approach expanding the catalog of astrophysical systems that can be studied in the laboratory.

A stochastic particle Fokker–Planck method with nonlinear production terms for a variable hard-sphere gas

The stochastic particle Fokker–Planck (FP) method has been gaining increasing attention in the field of rarefied gas dynamics due to its potential to reduce the computational costs of the direct simulation Monte Carlo method. The FP method approximates the discrete binary collisions of the Boltzmann equation as continuous drift–diffusion phenomena in velocity space. Consistency between the FP method and the Boltzmann equation is achieved by matching production terms. The Maxwell molecular model has been widely used in this process due to the possibility of obtaining closed-form solutions for these production terms. However, it is well known that the Maxwell molecular model has difficulty predicting strong shock waves since it cannot provide accurate relaxation rates for the moments. By contrast, the variable hard-sphere (VHS) molecular model is able to capture the transport properties of real gases better than the Maxwell molecular model. Nonetheless, there have so far been no reports associated with an accurate VHS molecular model for the stochastic particle FP method. In this paper, two different molecular models are developed to describe a monatomic gas interacting through a VHS potential. The proposed VHS molecular models are evaluated using Grad's 13- and 26-moment distribution functions; hence, they are named the G13 and G26 molecular models. The G13 and G26 molecular models include additional nonlinear moments compared with the conventional Maxwell molecular model. A one-dimensional shock wave and two-dimensional hypersonic cylinder flow are considered for validation. The results show that the proposed molecular models perform better than the Maxwell molecular model in predicting supersonic and hypersonic shock waves.

Inferring the temperature profile of the radiative shock in the COAX experiment with shock radiography, Dante, and spectral temperature diagnostics

Predicting and modeling the behavior of experiments with radiation waves propagating through low-density foams require a detailed quantification of the numerous uncertainties present. In regimes where a prominent radiative shock is produced, key dynamical features include the shock position, temperature, and curvature and the spatial distribution and temperature of the corresponding supersonic radiation wave. The COAX experimental platform is designed to constrain numerical models of such a radiative shock propagating through a low-density foam by employing radiography for spatial and shock information, Dante for characterizing the x-ray flux from the indirectly driven target, and a novel spectral diagnostic designed to probe the temperature profile of the wave. In this work, we model COAX with parameterized 2D simulations and a Hohlraum-laser modeling package to study uncertainties in diagnosing the experiment. The inferred temperature profile of the COAX radiation transport experiments has been shown to differ from simulations more than expected from drive uncertainties that have been constrained by simultaneous soft x-ray flux and radiography measurements.

Snapping shrimp have helmets that protect their brains by dampening shock waves

Shock waves are supersonic high-amplitude pressure waves that cause barotrauma when they transfer kinetic energy to the tissues of animals.1-4 Snapping shrimp (Alpheidae) produce shock waves and are exposed to them frequently, so we asked if these animals have evolved mechanisms of physical protection against them. Snapping shrimp generate shock waves by closing their snapping claws rapidly enough toform cavitation bubbles that release energy as an audible "snap" and a shock wave when they collapse.5-8 We tested if snapping shrimp are protected from shock waves by a helmet-like extension of their exoskeleton termed the orbital hood. Using behavioral trials, we found shock wave exposure slowed shelter-seeking and caused a loss of motor control in Alpheus heterochaelis from which we had removed orbital hoods but did not significantly affect behavior in shrimp with unaltered orbital hoods. Shock waves thus have the potential to harm snapping shrimp but may not do so under natural conditions because of protection provided to shrimp by their orbital hoods. Using pressure recordings, we discovered the orbital hoods of A.heterochaelis dampen shock waves. Sealing the anterior openings of orbital hoods diminished how much they altered the magnitudes of shock waves, which suggests these helmet-like structures dampen shock waves by trapping and expelling water so that kinetic energy is redirected and released away from the heads of shrimp. Our results indicate orbital hoods mitigate blast-induced neurotrauma in snapping shrimp by dampening shock waves, making them the first biological armor system known to have such a function. VIDEO ABSTRACT.

‘Helmets’ shield shrimp from their own supersonic shock waves

‘Helmets’ shield shrimp from their own supersonic shock waves

Supernonlinear wave, associated analytical solitons, and sensitivity analysis in a two-component Maxwellian plasma

This analysis investigates the occurrence of super nonlinear waves (SNWs) in a two-component electron-ion plasma containing Maxwell distributed electrons. The effect of Mach number (M) on the presence of SNWs is also discussed. Analytical findings for all conceivable dark-pitch solitons, singular solitons, associated hyperbolically, trigonometrically, and rational solitons, and super nonlinear periodic wave solutions are discussed in this study. A graphical representation of the research findings is also presented. This study successfully shows 2D- graphs to offer further insight into the physical properties of the solutions described for the various ranges of M that is, for M<1 the velocity of the wave profile will be treated as subsonic, for M>1 the velocity of the wave profile will be treated as supersonic and for M=1 the velocity of the wave profile will be treated as sonic for super nonlinear waves in two-component Maxwellian plasma. We have further demonstrated the sensitivity assessments for the altered dynamical structural system’s supersonic, subsonic, and sonic wave profiles, utilizing six unique initial conditions. That whole research justifies the appearance of SNWs in such a two-component Maxwellian plasma, which used to be formerly unidentified until about the study’s start in 2011. The new analytical findings of the different categories and sensitivity analysis for the dynamical system with supersonic, subsonic, and sonic wave profiles are new things here.

A simple hydrodynamic-particle method for supersonic rarefied flows

In the practical aerospace industry, the supersonic rarefied effect presents multiscale characteristics from the near-continuum regime to the free molecular regime. In this paper, a simple hydrodynamic-particle method (SHPM) is proposed to efficiently capture the multiscale properties for the supersonic rarefied flow. To combine the conventional computational fluid dynamics solver with the particle-based method, the weights are theoretically derived from the integral solution of the Boltzmann Bhatnagar–Gross–Krook equation. The present numerical method is validated by test cases of supersonic shock wave structure, Sod shock-tube, and supersonic flow around the circular cylinder. Numerical results demonstrate that the SHPM could capture the multiscale properties from the continuum regime to the rarefied regime.

Comparison of Two Kinds of Two-Dimensional Shear Wave Elastography Techniques in the Evaluation of Jaundiced Infants Suspected of Biliary Atresia.

Purpose: To compare the reliability and performance of Supersonic shear wave elastography (S-SWE) and Toshiba shear wave elastography (T-SWE) in the diagnosis of biliary atresia (BA) and assessment of liver fibrosis among jaundiced infants suspected of BA. Material and Methods: A total of 35 patients with suspected BA who underwent both S-SWE and T-SWE examinations were prospectively included. Diagnostic performances of S-SWE and T-SWE in identifying BA were evaluated. The correlation between two types of SWE values and histological liver fibrosis stages by Metavir scores were investigated in 21 patients with pathology results. The intraclass correlation coefficients (ICCs) were calculated in 16 patients for inter- and intra-observer agreement. The area under the receiver operating characteristic curve (AUC) analysis was compared using a DeLong test. Results: There were 22 patients with BA and 13 patients without BA. The diagnostic performance of S-SWE was comparable to that of T-SWE (AUC 0.895 vs. 0.822, p = 0.071) in diagnosing BA. The AUCs of S-SWE in predicting liver fibrosis stages were from 0.676 to 1.000 and showed no statistical differences from that of T-SWE (from 0.704 to 1.000, all p > 0.05). T-SWE provided higher inter-operator agreement (ICC 0.990) and intra-operator agreement (ICCs 0.966–0.993), compared with that of S-SWE in a previous study (ICC 0.980 for inter-operator and 0.930–0.960 for intra-operator). Conclusions: For infants suspected of BA, T-SWE had good performances in the diagnosis of BA and the assessment of liver fibrosis compared with S-SWE. Furthermore, T-SWE showed higher measurement reproducibility than S-SWE.

Investigation on the flow mechanism of nacelle airframe interaction for podded blended wing body transport

For the flow interaction between the podded engine and the airframe of blended wing body configuration(BWB), taking the 300 seats class BWB civil transport NPU-BWB-300 designed by Northwestern Polytechnical University as the research object, the influence of the podded engines on the BWB airframe at typical high and low speed conditions were investigated by CFD method, and the airframe-nacelle interference mechanism was revealed. The results indicate that the podded engines mainly affect the high speed performance of BWB, but have little effect on the low speed performance. The flow interaction between the airframe and the nacelle at high speed condition is serious when podded the engines, which leads to strong shock wave and flow separation. The flow mechanism of the above-mentioned interaction is as follows: firstly, the large supersonic region and shock wave on the nacelle external surface interferes with airframe surface flow seriously, which induces shock wave and flow separation; secondly, a convergent-divergent channel is formed between the airframe and the nacelle, resulting in the "throat" effect, which produces shock wave and flow separation.

Appearance of Supersonic Stoneley Waves in Auxetics

It is shown that in auxetic materials (materials with negative Poisson’s ratio), supersonic Stoneley waves travelling without attenuation with a velocity equal to or exceeding maximum bulk wave velocity, may exist. Analytical expressions for the relation between negative Poisson’s ratio and Young’s moduli of the contacting isotropic media ensuring the condition of propagation for supersonic Stoneley waves, are derived by solving a secular equation for Stoneley waves.

Study on Flow Distribution and Structure Optimization in a Mix Chamber and Diffuser of a CO2 Two-Phase Ejector

This paper establishes a mathematic model of a CO2 two-phase ejector to investigate flow distribution in the components of a mixing chamber and diffuser. The suction chamber was modeled using the characteristic line method to describe the development process of the supersonic expansion wave, and the mixing chamber, as well as diffuser models, were built based on the double-flow model. The reliability of the model was verified by experimental data. The distributions of flow parameters along the axis of the mixing chamber and diffuser were analyzed under different expansion ratios of the ejector. Structure optimizations of the mixing chamber and diffuser were conducted. The results showed that the primary flow temperature gradually increased along the axis of the mixing chamber and diffuser, but the Mach number distribution decreased for a certain ejector expansion ratio. The temperature and Mach number of the secondary flow showed the opposite trend. Moreover, at the initial stage of mixing, the fluid pressure increased rapidly, and the Mach number of the primary flow decreased rapidly. The gas-phase fraction of primary flow increased gradually in the mixing chamber and was stable in the diffuser. When the length–diameter ratio of the mixing chamber was about 10.8–12, it was beneficial to mix uniformity, and when the expansion angle of the diffuser was 4–6°, the ejector had a better ejector efficiency.

Supersonic wave propagation in heterogeneous solids and the evolution of energy distribution

Dynamic homogenization of heterogeneous materials has received a lot of attention recently, due to the fact that it can avoid expensive direct simulations with high space-time resolution. In this paper, the applicability of effective homogenous media on some peculiar dynamic phenomena is discussed. Longitudinal wave velocity has been believed to be the upper limit of mechanical signal speeds in a homogenous elastic solid according to the classical elasticity theory. However, for heterogeneous materials, we demonstrate numerically and theoretically that if the wave impedances of the constituent phases are not equal, there must be the supersonic phenomenon such that some wave may propagate faster than the longitudinal wave in the effective homogenous medium. Especially, if two materials with the same longitudinal wave velocity are used to compose a heterogeneous medium, the effective longitudinal wave speed will almost definitely be lower than its local counterpart. We also investigate the evolution of energy distribution over time when the wave propagates through heterogeneous media with various gradients, which indicates, interestingly, that the smoother the change in wave impedances of the heterogeneous medium, the more energy in “before-wave” region and the less energy in “after-wave” region. The corresponding dispersion curves and group speed curves also show dramatic change for heterogeneous media with different smoothness, which can partially explain but not quantitively predict these phenomena. We attempt to develop an effective medium model to reproduce the energy evolution but fail. All these findings pose a big challenge to the proper establishment of dynamic homogenization models.

The behaviors of supersonic combustion wave through a perforated plate in a stoichiometric mixtures of H2/CH4/O2 and H2/O2

In this study, we reported the supersonic combustion wave behaviors as it propagated through a perforated plate in stoichiometric mixtures of H2-CH4-2.5O2, H2-CH4-4O2 and 2H2-O2. The perforated plate maintained an identical thickness of 10 mm with different hole diameters of 4 mm, 8 mm and 10 mm, respectively. Explosion pressures were recorded using pressure transducers flushed-mounted on the top wall, based on which the average velocity was calculated. Meanwhile, the cellular structures of the supersonic combustion waves were recorded by soot foils. According to the average velocity and soot foils, the propagation modes were classified into four regimes including Fast-flame to fast-flame, Fast-flame to detonation, Detonation to fast-flame, Detonation to re-initiation and Overdriven detonation to detonation. The perforated plate exerts a positive effort on fast-flame by disturbing the flow flied, therefore the fast-flame does not decelerate downstream of the perforated plate. However, the effect of the perforated plate is opposite for detonation, and it weakens the detonation and even causes detonation failure. And this effect is weakened with the hole diameter increasing, which is proven by the limit of re-initiation decreases from d/λ = 0.98(d = 4 mm) to d/λ = 0.71(d = 10 mm). However, the re-initiation mechanisms are different at various initial pressures. At higher initial pressure, the detonation front is elongated dramatically but not failed and it recovers downstream. However, the failed detonation needs the aid of the shock refection off the tube wall to re-initiate at lower initial pressure. With increasing the sensitivity of the mixture, the overdriven detonation characterized by d/λ > 1 was found to transmit the holes with no failure. By comparing with the failing cases owning small cells, d/λ > 1 is not the sole condition to ensure a detonation traveling through with no failure.

Numerical analysis of shock interaction with a spherical bubble

Two-dimensional and three-dimensional computational fluid dynamics studies of a spherical bubble impacted by a supersonic shock wave (Mach 1.25) have been performed to fully understand the complex process involved in shock–bubble interaction (SBI). The unsteady Reynolds-averaged Navier–Stokes computational approach with a coupled level set and volume of fluid method has been employed in the present study. The predicted velocities of refracted wave, transmitted wave, upstream interface, downstream interface, jet, and vortex ring agree very well with the relevant available experimental data. The predicted non-dimensional bubble and vortex velocities are also in much better agreement with the experiment data than values computed from a simple model of shock-induced Rayleigh–Taylor instability (the Richtmyer–Meshkov instability). Comprehensive flow visualization has been presented and analyzed to elucidate the SBI process from the beginning of bubble compression (continuous reflection and refraction of the acoustic wave fronts as well as the location of the incident, refracted and transmitted waves at the bubble compression stage) up to the formation of vortex rings as well as the production and distribution of vorticity. Furthermore, it is demonstrated that turbulence is generated with some small flow structures formed and more intensive mixing, i.e., turbulent mixing of helium with air starts to develop at the later stage of SBI.

A three-dimensional finite element foot-ankle model and its personalisation methods analysis

Foot and ankle injuries are common as a result of overuse or trauma as well as various pathologies. This study aims to establish a three-dimensional foot-ankle model and investigate its suitability personalisation for the analysis of foot-ankle biomechanical responses during dynamic gait loading. The model was first established based on medical images and validated in both static standing posture and dynamic gait loading concerning regional plantar pressures and the centre of pressure curve (COP). Then, two model personalisation methods using magnetic resonance imaging (MRI) and fast optical scan data, respectively, were investigated and compared through analysing the dynamic gait responses of the scaled models. In both methods, material personalisation of plantar tissues was also combined through supersonic shear wave elastography (SWE) measurements. With regard to plantar pressure distribution and internal soft tissue strain, both personalisation methods correlated well with the subject-specific experimental results. Thus, we believe that the present model, with a fast optical scan personalisation method of specific SWE measurement, is a reasonable arrangement for subject-specific plantar deformation behaviour analysis during dynamic gait loading.

Condensation properties of water vapor under different back pressures in nozzle

The existence of back pressure at outlet has a direct impact on the separation performance of the separation separator. However, the influence of back pressure is not understood well due to the complicated interaction of the supersonic flow, condensation and shock waves. In this study, the condensation flow models of water vapor were established, the influence of back pressure on supersonic condensation properties of water vapor was investigated. The results show that when the back pressure exists, the position of the shock wave is more forward than that without condensation, and the strength of shock wave is weaker. The nucleation rate is generated around the position of x = 115 mm and increases sharply from 0 to 1025 m−3 s−1. The shock wave is generated at x = 145 mm and x = 122 mm when the outlet back pressure is 20 kPa and 30 kPa, respectively. The condensed droplets evaporate again with the effect of shock wave, and then the secondary condensation of droplets occurs owing to the cooling effect of nozzle. When the back pressure is higher than a certain value, the refrigeration environment in the nozzle is completely destroyed with the effect of shock wave, and the condensed droplets evaporate again.

Multi-group radiation diffusion convergence in low-density foam experiments

We present an in-depth analysis of a Marshak radiation wave moving through an iron-oxide (Fe2O3) foam using a 1D multigroup diffusive radiation transport model, MDART (Multigroup Diffusion Algorithm for Radiation Transport). We consider the consequences of under-resolving the group structure and address how this could lead to incorrect conclusions in the analysis of general supersonic radiation wave experiments. We also provide an analysis of the types of experimental outcome one may incorrectly link to physical effects but are in fact due to poor simulation practice.