Shock Expansion Research Articles

Evolution characteristics of shock wave in microsecond-scale underwater electrical wire explosion

The underwater electrical wire explosion (UEWE) is a physical phenomenon initiated by the rapid injection of electrical energy, triggering an explosive event. UEWE offers advantages in energy conversion efficiency, repeatability, and controllability, making it valuable in various industrial applications. Building upon established zero-dimensional (0D) and one-dimensional (1D) models, this paper proposes an enhanced 0D-1D coupled cold-start model to describe the plasma channel expansion and subsequent shock wave (SW) propagation characteristics. The model comprises two submodules: a 0D magnetohydrodynamics model that describes plasma channel boundary expansion during the explosion, and a 1D hydrodynamics model using an artificial viscosity algorithm to depict SW propagation. The constructed numerical model facilitates investigation of plasma characteristics, SW propagation behavior, and energy conversion efficiency throughout the UEWE process. Additionally, the influences of wire dimensions and discharge frequency on these characteristics were analyzed. The results indicate that SW propagation characteristics are primarily governed by thermal pressure variations within the wire and that different wire dimensions markedly affect SW amplitude, attenuation, and impulse. The efficiency of electrical-to-SW energy conversion remains relatively low; however, thicker and shorter wires can enhance SW amplitude and improve conversion efficiency. Higher discharge frequencies produce greater impact forces and impulses near the explosion site, while also improving energy conversion rates. This study offers a theoretical basis and technical guidance for prospective engineering applications.

Three-dimensional magnetohydrodynamic simulations of core-collapse supernovae – I. Hydrodynamic evolution and protoneutron star properties

ABSTRACT We present results from three-dimensional, magnetohydrodynamic, core-collapse simulations of 16 progenitors following until 0.5 s after bounce. We use non-rotating solar-metallicity progenitor models with zero-age main-sequence mass between 9 and 24 ${\rm M}_{\odot }$. The examined progenitors cover a wide range of the compactness parameter including a peak around $23 \, {\rm M}_{\odot }$. We find that neutrino-driven explosions occur for all models within 0.3 s after bounce. We also find that the properties of the explosions and the central remnants are well correlated with the compactness. Early shock evolution is sensitive to the mass accretion rate on to the central core, reflecting the density profile of the progenitor stars. The most powerful explosions with diagnostic explosion energy $E_{\rm dia} \sim 0.75 \times 10^{51}$ erg are obtained by 23 and 24 ${\rm M}_{\odot }$ models, which have the highest compactness among the examined models. These two models exhibit spiral standing-accretion-shock-instability motions during 150–230 ms after bounce preceding a runaway shock expansion and leave a rapidly rotating neutron star with spin periods $\sim 50$ ms. Our models predict the gravitational masses of the neutron star ranging between $1.22$ and $1.67 {\rm M}_{\odot }$ and their spin periods 0.04 – 4 s. The number distribution of these values roughly matches observation. On the other hand, our models predict small hydrodynamic kick velocity (15–260 ${\rm km \, s}^{-1}$), although they are still growing at the end of our simulations. Further systematic studies, including rotation and binary effects, as well as long-term simulations up to several seconds, will enable us to explore the origin of various core-collapse supernova explosions.

Transient pressure characteristic investigation and performance analysis of a novel three-port gas pressure dividing (GPD) device

The wave-rotor based gas pressure dividing (GPD) is a novel concept to allocate and utilize the pressure energy of gases, presenting significant potential in engineering fields. However, studies about GPD devices are rare, and related mechanism analysis and performance investigations are almost blank. In this study, an experimental platform upon a novel three-port GPD device is established. The transient pressure distribution characteristics in passages of GPD wave rotor are determined experimentally with the customized pressure acquisition system. Besides, the effects of rotation speed, compression ratio (β), and expansion ratio (α) on the pressure dividing performance of the GPD device are systematically examined via experiments and numerical simulations. The results indicate that the interaction of shock waves and expansion waves in passages can enable the medium-pressure gas to divide into high-pressure and low-pressure gases. The rotation speed of 2340 rpm is optimized, determining the greatest gas compression and expansion. The compression ratio increase can improve the compression efficiency and reduce the expansion depth, while the expansion ratio increase can present an opposite regulation. The flow rate efficiency of LP port is decreased with the compression ratio and expansion ratio increase.

Expansion wave-reinforced initiation of the oblique detonation wave

Efficient initiation of oblique detonation waves (ODWs) is crucial for optimizing the performance of oblique detonation wave engines. A novel approach is proposed for enhancing ODW initiation through expansion waves in this research. Validation of the expansion wave-reinforced initiation method is conducted via numerical simulations employing multi-species reactive Euler equations and a pressure-dependent reaction mechanism. Results demonstrate a significant reduction in the initiation length of ODWs with the addition of an expansion wave ahead of the wedge, contrasting with the absence of detonation wave initiation on a wedge lacking an expansion wave. A theoretical model, based on expansion wave and shock wave relations, along with constant volume combustion theory, elucidates the underlying mechanism of reinforcement. The model reveals that crossing the expansion wave elevates the fluid's Mach number and locally enlarges the flow deflection angle on the wedge surface, without altering the wedge's structure. Furthermore, post-shock temperature increases and pressure decreases compared to the wedge not encountering an expansion wave. The heightened temperature predominantly triggers ODW initiation, thus reinforcing the process. Theoretical analyses indicate the reinforcement's greater efficacy at lower inflow temperatures and lower inflow Mach numbers, suggesting the expansion wave's suitability for initiation in the early flight stages of an aircraft equipped with oblique detonation wave engines.

Research on flow and heat transfer characteristics of supersonic film cooling with different hole-configurations

In order to investigates the flow and heat transfer characteristics under supersonic mainstream conditions among three typical film hole-configurations—cylinder hole (CH), fan-shaped hole (FSH), and laidback fan-shaped hole (LFSH), this study conducted numerical simulation using the ANSYS CFX and based on the assumption of compressible flow. The results indicate that the cooling effectiveness of the CH dramatically decreases as the blowing ratio increases, while FSH and LFSH improves. When the supersonic mainstream encounters the coolant, flow structures such as oblique shock waves, expansion waves, and mixing layers et al., will be generated around the film holes, which have an impact on the flow and heat transfer characteristics. Under the conditions of same blowing ratio, the shock wave intensity of LFSH is significantly lower than the other two holes and the kidney vortices formed by the CH develop further along the mainstream direction. While the strength of the kidney vortices formed by the FSH and the LFSH is weaker. Additionally, the LFSH incurred the least total pressure loss from before the shock wave to after the oblique shock wave. Specifically, at a blowing ratio of 0.8, it achieved a reduction of approximately 20% in total pressure loss compared to the CH.

Interaction between lateral jet and hypersonic rarefied flow

Reaction control systems (RCS) are commonly utilized in a variety of air vehicles, and they give rise to complex flow phenomena. For flows dominated by shock waves and expansion, such as lateral jets, a significant gradient is formed in the local region of the flow field, resulting in a high local Knudsen number, and the continuum hypothesis is no longer applicable, even if the freestream belongs to near-continuum flow. As a result, multi-scale simulation approaches should be used to capture the interactions between these multi-scale structures and appropriately determine aerodynamic forces. Our earlier work, which used the conserved discrete unified gas kinetic scheme (CDUGKS) for monatomic gas, studied the flow field features of lateral jets and aerodynamic forces on blunt bodies under various rarefied freestream conditions. In this research, the Rykov model is used to expand the CDUGKS suit for diatomic gas flow while taking into account the excitation of molecular rotational energy. The impact on the flow field and aerodynamic forces from four parameters, namely freestream Mach number, jet Mach number, jet pressure ratio, and nozzle position, is thoroughly investigated. The results show that even if the incoming Mach number is different, the flow field structure and aerodynamic properties don't change much when the jet momentum ratio stays the same. The solid wall stagnation point value and local peak also show some linear relationships. The jet pressure ratio mainly affects the expansion characteristics of the jet, such as the influence range on the solid wall. In addition, with an increase in the distance between the nozzle position and the torque reference point, higher control efficiency can be obtained. The study of these aspects will help us comprehend lateral jet flow and provide reference for the design of an air vehicle's RCS.

Real Gas Corrections Based on the Interaction of One-Dimensional Unsteady Waves in a Shock Tube

There are multiple unsteady wave system interactions such as shock waves, expansion waves, and reflection, transmission, and intersection of the contact surface inside a shock tube. Studying the law of unsteady wave system interaction has important guiding significance for the design of gas wave equipment. This paper proposes a solution method for the interaction law of unsteady wave systems based on real gas equation of state (EoS) and applies it to shock tubes. The results show that the temperature maximum error between the code based on ideal gas EoS and simulation results is 3.64%, and the error of wave velocity results is between 2.99% and 18.27%. While the error of temperature results between code based on real gas EoS and simulation is not exceed 3%. More importantly, the wave velocity calculated by the code based on real gas EoS is pretty consistent with the simulation results. The code based on the real gas model can help to solve the problem of offset design point. Research has also shown that as pressure and temperature gradually increase, the deviation between ideal and real gases increases, which also proves that the influence of real gas effects is becoming increasingly significant.

Exploration of shock–droplet interaction based on high-fidelity simulation and improved theoretical model

Shock–droplet interaction in the early stage involves intricate wave structures. Investigating this phenomenon is inherently challenging due to the fine spatial and temporal scales involved. Past research has suggested that the occurrence of cavitation, marked by a negative peak pressure, is linked to the focus of the reflected expansion wave. In this study, a high-fidelity compressible numerical approach is utilized to replicate the initial phase of shock–droplet interactions. The location of the negative peak pressure is meticulously documented and compared with experimental measurement and numerical results. Results indicate a strong alignment between the negative peak pressure positions identified through numerical simulations and the focal points identified in theoretical models for low gas–liquid wave velocity ratios. However, this alignment is notably disrupted when dealing with higher gas–liquid wave velocity ratios. Further enhancements are made to the theoretical model, enabling a more precise depiction of internal wave structures and focus points, particularly under conditions of high gas–liquid wave velocity ratios. The study delves into the various factors influencing internal pressure fluctuations within the liquid droplet, categorizing them into four phases: the shock wave effect, relaxation effect, fluctuation effect, and expansion wave effect. Analysing the pressure decrease portion reveals that while the converging of the reflected expansion wave leads to a substantial pressure drop, it accounts for only a fraction of the total pressure variation. Consequently, any model predicting negative peak pressure positions must comprehensively consider all contributing factors.

Commissioning of Upgrades to T6 to Study Giant Planet Entry

The scientific potential of a mission to the ice giants is well recognized and has been identified by NASA and ESA as a high priority on several occasions, most recently in the 2023–2032 Decadal Survey. The payload capacity of such a spacecraft is limited by the heat shield thickness, which must be sized conservatively due to a lack of reliable data for convective and radiative heat flux along the proposed entry trajectories. Major upgrades to the Oxford T6 Stalker Tunnel have been commissioned that allow study of giant planet entry trajectories, including a flammable gas handling system, a Mach 10 expansion nozzle, and a steel shock tube with optical access. Initial testing has been completed in shock tube and expansion tunnel modes, with peak shock speeds of 18.9 km/s achieved. Convective heat flux and surface pressure were measured at several locations on a 45° sphere cone model in expansion tunnel mode. Measurements of the radiating shock layer were made in shock tube mode to assess the effect of CH4 concentration. This work establishes the first high-enthalpy giant planet entry test bed in Europe.

Large-scale free-piston-driven multi-mode shock expansion tunnel

X3/R is a new large-scale free-piston-driven dual-mode shock expansion tube, developed and operated collaboratively by the University of Queensland (UQ) and Australia’s Defence Science and Technology Group (DSTG). The facility can be converted between a long-duration reflected shock tunnel (RST), a super-orbital expansion tube (X-mode), and a non-reflected shock tube (NRST). In RST mode, the facility is currently capable of producing 600 mm diameter Mach 7 test flows at 25–50 kPa dynamic pressure for more than 10 ms. In expansion tube mode, the facility can reach enthalpies up to 80 MJ/kg for test times on the order of 500–1000 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mu }$$\\end{document}s. This paper presents the new facility, summarizes its current operational capabilities, and discusses key the technical challenges overcome during its development.

The impact of low-velocity shock waves on the dynamic behaviour characteristics of nanobubbles.

Low-velocity shock wave-induced contraction and expansion of nanobubbles can be applied to biocarriers and microfluidic systems. Although experiments have been conducted to study the application effects, the dynamic behavior characteristics of nanobubbles remain unexplored. In this work, we utilize molecular dynamics (MD) simulations to investigate the dynamic behavior characteristics of nanobubbles influenced by low-velocity shock waves in a liquid argon system. The DBSCAN (Density-Based Spatial Clustering of Applications with Noise) machine learning method is used to calculate the equivalent radius of nanobubbles. Two statistical methods are then utilized to predict the time series changes in the equivalent radius of nanobubbles without rebound shock waves. The piston velocity is analyzed using the bisection method to obtain the critical impact states of the nanobubble. The results show that at the low velocity shock wave (piston velocity of 0.1 km s-1), the shock wave pressure is small, the non-vacuum nanobubbles contract and expand in a circular shape, and the gas particles inside the bubble are not dispersed. In contrast, the vacuum nanobubbles collapse directly. As the shock wave rebounds upon impact, it triggers periodic contraction and expansion of the nanobubbles. The predictions indicate that the equivalent radius will vary within a small range according to the pre-predicted values in the absence of the rebound shock wave. Nanobubbles are present in four critical impact states: dispersed gaps, multiple smaller bubbles, two split bubbles, and a concave bubble.

Structure of rotating detonation in mixtures of natural gas and oxygen

The rotating detonation combustor is investigated as a potential implementation of pressure-gain combustion. Achieving net pressure-gain has proven to be extremely challenging in most combustors reported in the literature, regardless of their operating parameters. The performance losses observed in rotating detonation, compared to ideal predictions, can be attributed to mechanisms such as vitiation by residual burnt gases, partial detonation, and pre-combustion of reactants. The literature frequently discusses the impact of these mechanisms on measurable properties such as thrust and wave speed, but their effects on the front structure have not been fully understood. This study proposes using the rotating detonation structure for the first time to evaluate the vitiation quantitatively. The front structure of a compressed natural gas — oxygen-fueled rotating detonation is characterized using broadband chemiluminescence, and properties such as oblique shock angle, expansion angle, and front height are reported. The experimental values are then compared to the ideal predictions derived based on mass flow rates. The experimental front heights are found to be much higher than their ideal predicted counterparts. Analytical calculations that include pre-burning and vitiation show an increase in front height and a reduction in expansion angle, consistent with the chemiluminescence levels observed. The vitiated mass fraction is then deduced from the experimental front height, and the remaining velocity deficit is then used to evaluate the partial detonation mass fraction. Vitiated front angles compare favorably to the predicted values.Novelty and SignificanceThis study reports high-quality chemiluminescence imaging of natural gas/oxygen rotating detonation front enabling the measurement of critical geometrical front features such as the front height, oblique shock angle, and expansion angle. The conventional front mass flow rate balance is extended to account for the re-circulation of burnt gases effects and is used to estimate the experimental vitiation. Most notably, vitiation of the fresh mixture, which was already known to reduce front speed and pressure rise, is also shown to strongly decrease the expansion angle resulting in further losses of axial thrust.

Numerical Investigation on the Effect of Wet Steam and Ideal Gas Models for Steam Ejector Driven by Ship Waste Heat

Steam ejectors could improve the energy efficiency of ships by efficiently utilizing low-grade waste heat from ships for seawater desalination or cooling. The internal flow characteristics of steam ejectors can be deeply analyzed through numerical simulation, which is of great significance for improving their performance. Due to the influence of the nonequilibrium phase change, the results of the wet steam model and the ideal gas model are significantly different. In this paper, the flow field characteristics of the wet steam model and the ideal gas model under different primary flow pressures (Pm) are compared and analyzed. The results show that the structures of the shock wave train for the wet steam model and the ideal gas model are different under different Pm. When the first shock wave of the shock wave train changes from a compression shock wave to an expansion shock wave, the Pm for the ideal gas model is 75,000 Pa and that for the wet steam model is 55,000 Pa. The phase change reduces the energy loss of the shock wave. With the increase in the Pm, the variation in the length of the shock wave train for the wet steam model decreases by 61%, the variation of the primary temperature at the nozzle exit increases by 60% and the variation in the choke temperature decreases by 50% compared with the ideal gas model. The investigation in this paper provides guidance for the design theory of a ship waste heat steam ejector.

A shock-stable numerical scheme accurate for contact discontinuities: Applications to 3D compressible flows

The low-dissipation Roe scheme is a popular shock capturing scheme but the shock instability, such as the infamous carbuncle phenomenon, seriously affects its application in high Mach number flows. Although considerable research has been undertaken in two dimensions, mechanism analysis of the three-dimensional shock instability is relatively scarce. Numerical simulations of the Sedov blast wave indicate that the shock instability is more prominent in three dimensions, so it has theoretical and practical significance to analyze and heal the numerical instability. The mechanism for three-dimensional shock instability has been thoroughly studied by means of the linearized stability analysis and the dissipation-controlling approach which introduces the required transverse dissipation in the numerical shock layer and is adopted to enhance the Roe scheme’s shock stability. Furthermore, the unphysical expansion shock resulting from the violation of entropy condition is eliminated by a simple modification of numerical signal speed. For the improvement of the resolution for contact discontinuities and shear waves, an algebraic method which combines the THINC reconstruction scheme and the BVD algorithm is employed to minimize the density difference in the numerical diffusion term. A series of benchmark numerical experiments fully demonstrate that the proposed scheme is endowed with excellent robustness against the shock instability and high accuracy for contact discontinuities and shear waves.

Evaluation of the relative importance of preheat from hohlraum x rays and a radiative shock on a low-density foam

Indirectly driven shock-tube experiments were performed on the Omega Laser Facility to evaluate the relative importance of hohlraum x ray and radiative shock preheat sources on a low-density foam. X rays emitted from the hohlraum and a subsequent shock wave are channeled into a low-density foam sample, which contains a plastic preheat-witness disk placed downstream of the foam. Simultaneous radiographic measurements of the shock speed in the foam and the expansion rate of the witness disk due to preheat allow for the observation of effects from the hohlraum's low-energy and high-energy x-ray spectrum. We showed, from simulations, that low-energy x rays from the hohlraum are preferentially absorbed near the ablator surface (where the hohlraum and the shock tube meet), while higher-energy x rays largely pass through the ablator and foam and are volumetrically absorbed by the witness disk. Reproducing the experimentally measured shock speed and expansion of the witness disk simultaneously, we extracted the temperature evolution of preheated foam from the simulation and evaluated the relative importance of preheat sources on a low-density foam from hohlraum x-ray radiation and radiative shock. We found that radiation from the shock front was more effective at preheating the low-density foam than the high-energy x rays from the hohlraum. This shock-tube preheat experiment is important for understanding the results of the MARBLE experiments at the National Ignition Facility because initial conditions of foam-filled MARBLE capsules are sensitive to preheat.

Expansion and ongoing cosmic ray acceleration in HESS J1731−347

Diffusive shock acceleration in supernova remnants (SNRs) is considered one of the prime mechanisms of galactic cosmic ray (GCR) acceleration. It is still unclear, however, whether SNRs can contribute to the GCR spectrum up to the “knee” (1 PeV) band as acceleration to such energies requires an efficient magnetic field amplification process around the shocks. The presence of such a process is challenging to test observationally. Here, we report on the detection of fast variability in the X-ray synchrotron emission from the forward shock in the SNR HESS J1731−347, which implies the presence of a strong (∼0.2 mG) field exceeding background values, and thus of effective field amplification. We also report a direct measurement of the high forward shock expansion velocity of 4000–5500 km s−1, confirming that the SNR is expanding in a tenuous wind bubble blown by the SNR progenitor, is significantly younger (2.4–9 kyr) than previously assumed by some authors, and only recently started interacting with the dense material outside of the bubble. We finally conclude that there is strong evidence for ongoing hadronic GCR acceleration in this SNR.

Fast-Responding Pressure-Sensitive Paint Measurements of the IC3X at Mach 7.2

Global surface pressure measurements of a 5.7% scale AFRL Initial Concept 3.X vehicle (IC3X) were obtained using a fast-responding ruthenium-based pressure-sensitive paint (PSP) at the UTSA Mach 7 Ludwieg Tube Wind Tunnel at two different angles of attack, 0° and 2.5°. Static calibration of the paint was performed over a range of 0.386 kPa to 82.7 kPa to relate luminescent intensity to pressure. Details on the facility, paint preparation, application, calibration, and image processing techniques are provided in the manuscript. The results from statistical, spectral, and proper orthogonal decomposition (POD) analyses are presented to characterize the pressure field observed on the model. The experimental results qualitatively follow the expected trends and correspond to the occurrence of shock waves and expansion fans, which were visualized via Schlieren imaging. The theoretical pressure range obtained from conical shock analysis for 0° agrees with the experimentally derived pressure range for the model, and the outliers are attributed to errors in image registration. This study presents preliminary pressure measurements that pave the way for obtaining time-resolved global PSP measurements to train and validate aerothermodynamic machine learning models.

Conflicting primary and secondary properties of thermoelectric devices – A case study on the thermomechanical behavior of ZrNiSn

While the primary properties of thermoelectric devices, directly related to the conversion efficiency, are considered in design efforts, the secondary (thermomechanical) properties are often ignored or overlooked even though they can lead to failure. Here, thermomechanical properties of thermoelectric ZrNiSn in the amorphous and crystalline state (space group F-43m), comprising thermal conductivity, thermal expansion, elastic (Young’s) modulus, and thermal shock, are studied using density functional theory and two phonon models. Thermal conductivity is also a key primary property for thermoelectric applications. Amorphous ZrNiSn exhibits a fourfold lower thermal conductivity than the crystalline counterpart due to high phonon–phonon scattering, which is conducive to thermoelectric performance. However, this is conflicting since a high thermal conductivity value is required to attain high resistance to thermal shock. Due to stronger bonds in the crystalline counterpart, facilitated by the stronger Zr3d–Ni3d and Sn5p–Ni3d hybridization and higher coordination than in the amorphous state, the linear coefficient of thermal expansion is lower, and the elastic modulus is higher. Hence, the crystalline state yields higher resistance to thermal shock. It is suggested that samples entailing both amorphous and crystalline regions can concurrently satisfy the primary and secondary requirements for enhanced efficiency and durability.

Effects of blowing upon dynamic stability of blunt nosed re entry vehicles pitching in hypersonic flow

AbstractBlowing is often used to alleviate the intense heating rates on blunt noses of hypersonic vehicles. This flow efflux at the leading edge transforms the flow field in the blunt-nose regions with implications on the dynamic stability of the vehicles. As a demonstrative exercise, the flow fields past blunt-nosed and truncated-nosed conical bodies under blowing and no-blowing conditions were perturbed to obtain the unsteady effects using the shock expansion method to recover the unsteady pressure coefficient. Static and pitching moment derivatives were then duly obtained by integrating the differential of the unsteady pressure coefficient with respect to the pitch angle (α) or the pitch rate ( $\dot \theta $ ) together with the moment arm with reference to the centre of gravity. The results obtained for blunt-nose and truncated conical bodies show a noticeable drop in dynamic stability. Even when the flow is transformed from a tangential blowing at the shoulder of the blunt-nosed vehicle shows some degradation in dynamic stability.

Flow Field Simulations Over Reentry Modules at High Speed

Reentry capsule configurations significantly differ from each other due to entry conditions and mission requirements. This paper describes numerical simulations of the viscous flow over the Beagle and the OREX (Orbital Reentry EXperiments) configurations for freestream Mach numbers in the range of 1.2 - 5.0. The flow fields over the reentry modules are obtained by solving time-dependent axisymmetric compressible laminar Navier-Stokes equations. The fluid mechanics equations are discretized in spatial coordinates employing a finite volume method, which reduces the governing equations to semi-discretized ordinary differential equations. Temporal integration is carried out using a two-stage Runge-Kutta time-stepping scheme. A local time-stepping is employed to get the steady state solution. The numerical simulation is performed on a single-block structured grid. The flow field features around the reentry capsules such as bow shock wave, sonic line, expansion fan and recirculation flow in the base-shell region are well captured by the present numerical computation. The effects of the geometrical parameters of the module, such as aspect ratio, frontal segment bluntness, fore body cone angle and shoulder rounding radius on the wake throat width, distance from the wake throat to the base of the model, flow departure angle and aerodynamic drag are analyzed using the numerically simulated flow field.