激波管缩比试验相关论文

Abstract Shock-tube experiments are conducted to investigate the Atwood-number dependence of hydrodynamic instability induced by a strong shock with a Mach number exceeding 3.0. The compressible linear theory performs reliably under varying compressibility conditions. In contrast, the impulsive model significantly loses predictive accuracy at high shock intensities and Atwood numbers ( $A_t$ ), particularly when specific heat ratio differences across the interface are pronounced. To address this limitation, we propose a modified impulsive model that offers favourable predictions over a wide range of compressibility conditions while retaining practical simplicity. In the nonlinear regime, increasing $A_t$ enhances both the shock-proximity and secondary-compression effects, which suppress bubble growth at early and late stages, respectively. Meanwhile, spike growth is promoted by the spike-acceleration and shock-proximity mechanisms. Several models reproduce spike growth across a wide range of $A_t$ , whether physical or incidental. In contrast, no models reliably describe bubble evolution under all $A_t$ conditions, primarily due to neglecting compressibility effects that persist into the nonlinear regime. Building on these insights, we develop an empirical model that effectively captures bubble evolution over a wide $A_t$ range. Modal evolution is further shown to be strongly affected by compressibility-induced variations in interface morphology. The effect is particularly pronounced at moderate to high $A_t$ , where it suppresses the fundamental mode growth while promoting higher-order harmonic generation.

A non-contact low-frequency (LF) method of diagnosing the plasma surrounding a scaled model in a shock tube is proposed. This method utilizes the phase shift occurring after the transmission of an LF alternating magnetic field through the plasma to directly measure the ratio of the plasma loop average electron density to collision frequency. An equivalent circuit model is used to analyze the relationship of the phase shift of the magnetic field component of LF electromagnetic waves with the plasma electron density and collision frequency. The applicable range of the LF method on a given plasma scale is analyzed. The upper diagnostic limit for the ratio of the electron density (unit: m−3) to collision frequency (unit: Hz) exceeds 1 × 1011, enabling an electron density to exceed 1 × 1020 m−3 and a collision frequency to be less than 1 GHz. In this work, the feasibility of using the LF phase shift to implement the plasma diagnosis is also assessed. Diagnosis experiments on shock tube equipment are conducted by using both the electrostatic probe method and LF method. By comparing the diagnostic results of the two methods, the inversion results are relatively consistent with each other, thereby preliminarily verifying the feasibility of the LF method. The ratio of the electron density to the collision frequency has a relatively uniform distribution during the plasma stabilization. The LF diagnostic path is a loop around the model, which is suitable for diagnosing the plasma that surrounds the model. Finally, the causes of diagnostic discrepancy between the two methods are analyzed. The proposed method provides a new avenue for diagnosing high-density enveloping plasma.

High-pressure shock waves of several tens of MPa are of importance in many applications, such as material fabrication and testing, combustion chemistry and metrology. Controlled and predetermined shock waves can be generated by a shock tube, where the sudden expansion of a high-pressure driver gas into a low-pressure driven gas caused by the instantaneous opening of a connection between two sections produces a compression shock wave that propagates through the driven gas. The reflection of the shock wave from the end wall of the driven section of the shock tube generates a rapid pressure rise, which in conventional straight shock tubes with a uniform cross-section is limited to a few MPa. This paper presents and experimentally investigates two configurations of the shock-wave focusing element that were designed on the basis of shock dynamics theory to effectively enhance the strength of the shock waves generated in the shock tube and therefore increase the generated driven end-wall pressures. The wall shape of the first configuration consists of a concave transformation segment that smoothly transforms the incident planar shock wave into a spherical converging shock wave and a convex transformation segment that further smoothly transforms the spherical shock wave back to planar, which then propagates into the straight outlet tube to the end wall. The convex transformation segment in the second configuration was replaced by a conical segment that further converges and accelerates the spherical shock wave formed in the concave segment towards the end wall and thereby additionally amplifies its strength. The results show that by converging the shock waves with the designed shock-wave focusing elements, the upper pressure limit of the shock tubes is increased from a few MPa up to 13.4 MPa and 44 MPa, respectively.

Compression driven shock tubes are indispensable in studies of blast-induced traumatic brain injury (bTBI). The ability of shock tubes in faithfully recreating free-field blast conditions is of enormous interest and has a direct impact on injury outcomes. Toward this end, the evolution of blast wave inside and outside of the compression driven shock tube has been studied using validated, finite element based shock tube models. Several shock tube configurations (uniform cross-section, transition, conical, suddenly expanded, and end plate) have been considered. The finite element modeling approach has been used to simulate the transient, dynamic response of blast wave propagation. The response is studied for longer durations (40–100 msec) compared with the existing literature. We demonstrate that locations inside and outside of the shock tube can generate free-field blast profile in some form, but with numerous caveats. Our results indicate that the locations inside the shock tube are affected by higher underpressure and corresponding kinetic energy yield compared with free-field blast. These effects can be minimized using optimized end plate configuration at the exit of the shock tube, yet this is accompanied by secondary loading that is not representative of the free-field blast. Blast wave profile can be tailored using transition, conical, and suddenly expanded sections. We observe oscillations in the blast wave profile for suddenly expanded configuration. Locations outside the shock tube are affected by jet-wind effects because of the sudden expansion, barring a narrow region at the exit. For the desired overpressure yield inferred in bTBI, obtaining positive phase durations of <1 msec inside the shock tube, which are sought for studies in rodents, is challenging. Overall, these results underscore that replicating free-field blast conditions using a shock tube involves tradeoffs that need to be weighed carefully and their effect on injury outcomes should be evaluated during laboratory bTBI investigations.

To achieve higher enthalpy and pressure, the technique of variable cross-section drive is effectively combined with the heating of light gas to enhance the intensity of the incident shock wave. A study was conducted to predict the impact of variable cross-sections on the performance of high-temperature shock tube flow using a shock tube with a 2.6:1 diameter ratio between the driver and driven sections. The driver section was filled with a helium–argon gas mixture (mass ratio of 1:9), while the driven section contained dry air. Under total pressure conditions of 14.5 MPa and total temperature of 3404 K, as well as total pressure of 45 MPa and total temperature of 4845 K in the driver section, corresponding to driven section pressures of 10 kPa and 80 kPa, the results of chemical non-equilibrium numerical simulations were compared to experimental measurements of the incident shock Mach number and total pressure. The results indicated the following: First, after adding the contraction–expansion nozzle, the incident shock accelerated through the contraction section and reflected within the contraction section. Strong oscillations occurred during the flow, with increasing intensity as the throat size decreased. Second, without the nozzle, the shock velocity increased and then decreased. However, with the nozzle, the Mach number was highest near the nozzle exit and gradually decreased thereafter. Third, the presence of the nozzle led to the formation of a distinct fan-shaped wavefront, accompanied by significant variations in flow variables such as pressure, temperature, and Mach number in the region. This phenomenon was attributed to the interaction between the shock wave and the nozzle geometry, which altered the flow dynamics. Finally, as the throat size decreased, the intensity of the incident shock also decreased. After reflecting at the end of the shock tube, the total pressure in the driven section also decreased. The numerical simulations employed a multi-component, multi-temperature chemical non-equilibrium model, validated against experimental data, to accurately capture the complex flow behavior and wave interactions within the shock tube.

This study examines the powder-gas flow dynamics in drug delivery through a nozzle integrated with a micro-shock tube-based needle-free device. The literature indicates that the pressure ratio (PR) influences particle velocity, which continues to increase even after exiting the nozzle causes momentum to the particles. As particle velocity increases post-nozzle exit, the stand-off distance emerges as a critical parameter. It minimizes the risk of device’s cross-contamination while ensuring optimal utilization of the PR to enhance particle velocity and promote penetration depth. The numerical investigation aimed to elucidate the influence of PR and stand-off distance on drug delivery. The current findings were validated by comparing numerical simulation results for nozzle exit pressure with experimental data from the literature, as discussed in the literature cited in this article. A parametric study was performed for PRs of 9, 15, 40, and 60. The selected PRs were based on data from the existing literature concerning powdered drug delivery devices. The influence of particle velocity by PR persists beyond the nozzle exit; therefore, the stand-off distance parameter ahead of the nozzle exit was included in this study. The maximum penetration depth of 75 µm at a PR of 60 was achieved for drug delivery within the epidermis region. It was observed that the optimal stand-off distance was determined to be 122 mm at PR = 60, resulting in a maximum penetration depth of 75.15 µm. The study revealed that the PR significantly influences particle velocity up to a specific stand-off distance along with penetration depth, even after the particles exit the nozzle region.

When a shock wave encounters an interface with a medium of different acoustic impedance, a reflected wave is generated. It is a shock wave if the medium has a higher acoustic impedance or an expansion fan if the impedance is lower. When the acoustic impedances are perfectly matched, no wave is reflected—a phenomenon known as “impedance matching.” This study aims to achieve a similar effect by varying the geometry of the shock tube exit. Assuming a steady-state, quasi-one-dimensional and subsonic post flow, we derived the exit geometry condition under which neither shock waves nor expansion waves are reflected. To validate this condition, we conducted shock tube experiments with shock Mach numbers up to approximately 1.07, and found that the shock wave reflection behavior is influenced not only by the cross-sectional area ratio of the tube but also by the specific shape of the orifice. In tests with a simple converging orifice shape, a pressure spike occurred due to the leading reflected shock wave before the pressure stabilized. The overpressure of this spike was reduced to 7×10−3 times the pressure ahead of the spike by installing perforated sections and a porous metal body on the sidewall just upstream of the orifice. This study offers a new approach to suppress post-shock pressure fluctuations in practical applications such as high-speed trains entering tunnels and within exhaust pipes of internal combustion engines, as well as to extend the test duration of shock tube experiments.

Shock tubes and tunnels are often used in research settings as a way of producing high pressure shock waves in a smaller footprint or without the use of explosives. However, there is no standard geometric design across laboratories. Peak pressure is a significant parameter for characterizing a shock wave. However, different tube configurations could also affect parameters such as impulse and duration, yet no research has investigated how the scale of the tube affects the overall waveform shape. To understand the implications of shock tube design, tubes with a constant length to diameter ratio were evaluated to determine how tube scaling affects the shock parameters. Larger tubes with a greater length and diameter produced more intense, shorter-duration shocks, resulting in higher pressure/duration ratios and up to a 20.9% reduction in impulse. Analysis of the pressure vs time profiles showed that square tubes have a more consistent self-similar relationship in peak pressure. Square tubes also exhibit a more pronounced negative phase than circle tubes of the same length-to-diameter (L/D) ratio. Increasing the diameter of constant length tubes from 0.5 to 1 cm increases the incident pressure by 90.94%, although this also leads to shorter shock wave durations. Conversely, increasing the length of constant diameter tubes results in a 2.4% reduction in incident pressure. These findings show that while peak pressure is important, the duration and impulse of the shock wave are crucial for determining the overall energy applied.

To develop a measurement system for calibrating high-frequency dynamic pressure that is capable of acting as a primary dynamic pressure calibration standard, a new concept of the shock tube, called the diaphragmless shock tube, has recently been developed. In most such shock tubes, the diaphragm is replaced with a commercially available, ISTA KB fast-opening valve (FOV). In this article, a numerical model was built in OpenFOAM to investigate the effects of the opening mechanism of ISTA KB-40-100 FOV on the formation of the shock wave in a shock tube with an internal radius of 20 mm. Numerical simulations were performed for the driver-driven pressure ratio of 40 and the valve-opening speeds of 5, 10, and 20 m/s, which were compared with the case of instantaneous valve opening, and the results predicted by the ideal shock tube theory. The observed variables were the mass flow through the valve, as well as the pressure, the temperature, and the shock wave velocity in the formation region behind the valve. The results show that when the shock wave undergoes an initial acceleration, the shock front accelerates more at higher opening speeds of the valve. The results also show that the valve-opening mechanism generates a series of reflection waves that propagate into the driven section, giving the shock wave velocity an oscillatory character, which can affect the calibration and measurement capability of the shock tube as a primary high-frequency, time-varying, pressure calibration standard.

No abstract available

Diffraction is a fundamental phenomenon that occurs when blast or shock waves pass over sudden discontinuous surfaces. It generates a complex flow field consisting of diffracted waves, expansion waves, slipstream, contact surface, and an unstable shear layer, in addition to emitting acoustic waves. In this study, we investigated the diffraction of a blast wave passing over a series of grooved structures with different aspect ratios and geometrical shapes (rectangular, circular, and triangular) using high-speed shadowgraph images. The blast wave Mach number considered in our investigation is 1.34. The grooves feature leading-edge geometrical variations such as rectangular, circular arc, and wedge shapes positioned at various lateral locations from the exit of the shock tube. The aspect ratios of the rectangular grooves vary from 0.33, 0.5, and 0.67. The circular and triangular grooves have an aspect ratio of 0.33. The trajectories and velocities of the primary vortex are calculated by tracking the location of the vortex in the shadowgraph images. Our observations revealed that a large portion of the incident blast wave is abducted inside the groove as the aspect ratio increases in rectangular grooves, resulting in better attenuation of the blast wave. The grooves, which have circular shapes, produced weaker diffraction, which resulted in delayed and weak primary vortex. The triangular grooves produced the strongest primary vortex and have the highest attenuation characteristics among other grooves. The strength and trajectory of the primary vortex formed over the grooves strongly depend on the aspect ratio and the curvature of the leading edge for a given Mach number. Vortices generated from rectangular and triangular grooves exhibit considerable strength and longevity.

No abstract available

European Shock Tube for High-Enthalpy Research (ESTHER) is a new state-of-the-art combustion-driven shock tube developed for supporting future ESA planetary exploration missions. Its high-pressure combustion driver sports a unique innovative design where a mixture of [Formula: see text] or [Formula: see text] gases, filled to pressures up to 100 bar, is ignited by a high-power Neodymium-doped yttrium aluminum garnet (Nd:YAG) laser. The qualification of this facility driver has allowed for the detailed study of laser-ignited combustion processes at high initial pressures (in the 5–100 bar range), over a series of 100 shots carried out for different configurations and gas mixtures. The influence of the oxygen-to-hydrogen ratio, filling pressure, inert gas dilution, and ignition mode have been studied and are presented in this work. The effects of nitrogen vs helium dilution are also discussed. Filling pressure and helium/nitrogen dilutions have the strongest influence in peak pressure, acoustic oscillation, and combustion velocity. The first two increase, whereas the latter strongly decreases with the filling pressure. Nitrogen diluted shots have drastically lower compression ratios and flame velocity when compared to the helium ones. Acoustic perturbations/instabilities are also found to be stronger. This test campaign allowed the definition of a large range of stable and reproducible firing conditions in deflagration mode, yielding post-combustion pressures up to 660 bar.

No abstract available

No abstract available

The shock formation process in shock tubes has been extensively studied; however, the influence of diaphragm rupture dynamics on the resulting flow non-uniformities remains inadequately understood. Existing models predicting the shock attenuation and propagation dynamics overlook critical diaphragm mechanics and their impact on shock behavior. Addressing this gap is vital for improving predictive capabilities and optimizing shock tube designs for applications in combustion kinetics, aerodynamics, and high-speed diagnostics. This study investigates the shock wave formation through combined experimental and numerical approaches over a range of driver-to-driven pressure ratios (Driver pressure: 9.4–25.5 bar of helium; Driven pressure: 100 Torr (133.322 mbar) of argon). High-speed imaging is used to capture the diaphragm opening dynamics, while pressure and shock velocity measurements along the entire driven section of the shock tube provide key validation data for computational fluid dynamic simulations. Two-dimensional numerical simulations incorporate experimentally measured diaphragm opening profiles, offering detailed insights into flow features and thermodynamic gradients behind the moving shock front. Key parameters, including deceleration and acceleration phases within the shock formation region, shock formation distances, and times, have been quantified. A novel theoretical framework is introduced to correlate these parameters, enabling accurate predictions of shock Mach number evolution under varying conditions. This unified methodology bridges theoretical and experimental gaps, providing a robust foundation for advancing shock tube research and design.

This study investigates blast wave interactions with different geometries to support safer and more effective design strategies for blast mitigation. Controlled shock tube experiments (driver length: 0.8 m, driven length: 6 m, and helium driver gas) were used to replicate blast wave conditions without live explosives. Two-dimensional simulations with an in-house multi-component Navier–Stokes solver were performed for rectangular, circular, and double-wedge objects placed at x/D=2.5 and 5 under pressure ratios of 13 and 57. Flow features were analyzed using numerical Schlieren, vorticity, pressure, and density fields, along with object load histories. The results show dominant vorticity generation over rectangular objects, while blast wave reattachment is governed primarily by standoff distance rather than strength-shortest for the double wedge, followed by circular and rectangular objects. These findings provide valuable benchmarks for validating computational models and predicting real-world blast effects.

Pressure sensors are widely used in various fields of social economy and production and life. The calibration and testing of dynamic pressure performance are usually carried out by using the step pressure generated by shock tube. Natural and active film breaking are the main ways to generate shock step pressure by shock tube. Compared with the natural film breaking technology, the active film breaking technology can control the dynamic parameters of the step pressure, shock wave velocity and response characteristics through the control of the film pressure ratio, and further improve the reliability of the dynamic calibration performance of the shock tube. This paper only introduces the principle and performance of different structures of the active film breaking device, and through different structures and blocking ratio of the film breaking device test, study and analysis of the impact of active film breaking technology on the shock wave waveform, for different calibration requirements for the dynamic pressure performance of the pressure sensor, so as to select the appropriate active film breaking technology to provide a reference.

A shock tube is a laboratory device used to explore the flow behaviour of shock waves. This research focuses on the computational study of fluid dynamics within a shock tube aimed at targeted drug delivery, specifically examining the behaviour of shock waves. Using ANSYS Fluent, the study employs a density-based implicit solver to perform transient analyses with two different gas combinations: nitrogen-air and helium-air. Key findings reveal that helium-air exhibits more significant pressure and temperature ratios, as well as higher Mach numbers, than nitrogen-air under various operating pressures. The computational results demonstrate good agreement with analytical calculations and experimental data. It specifies that the helium outperformed the nitrogen as it achieved higher microjet velocity (106 m s−1) compared to the nitrogen (62 m s−1). This suggests that the helium-air combination is more effective in achieving high reflected pressure at minimum operating pressure within short time intervals.

Single-pulse shock tubes are effective tools for measuring chemical kinetics at high temperatures, typically (900-1400) K. However, the use of a diaphragm for shock generation leads to significant shock-to-shock inconsistencies in temperature for a constant initial pressure ratio across the discontinuity. Diaphragms also require replacement after each shock and demand care in cleaning to ensure that the fragments do not contaminate the apparatus. A piston-driven valve design is presented that leads to a highly reproducible postreflected shock temperatures (0.41% at 1147 K and 0.61% at 967 K) in a single pulse varying from (500 to 1200) µs in width over the temperature range of interest. Characterization of the valve was accomplished using both shock-speed measurements and independent measurements of the pulse temperature using reference thermal decomposition reactions.

This is a numerical and experimental study on shock attenuation in shock tubes. Tube geometry, boundary layer, and reduction in cross-sectional area induced by burst diaphragms are often considered the main causes of shock speed reduction (or shock attenuation) observed during the experiments. In order to distinguish how each single phenomenon contributes toward shock attenuation, the National Cheng Kung University shock tube is simulated for driver and test (driver–test) gas pairs involving air–air and He–air. For low pressure ratios, the diaphragm effect was found to be negligible. For a pressure ratio of 200 and helium as driver gas, the shock speed was found to decrease linearly with the size of the diaphragm orifice. In general, wall viscous effects caused a 2.5% decrease in shock speed, while an additional 7% reduction was caused by the presence of the diaphragm. The gradual opening of the diaphragm mainly contributed to a decrease in shock oscillations.

This work deals with the performance of the shock tube with helium and carbon dioxide as working fluids at different diaphragm pressure ratios using numerical simulation. A two-dimensional planar geometry of the shock tube is considered for the study. An inviscid time accurate model is developed to find the effects of diaphragm pressure ratios on the shock Mach number, temperature behind the incident and reflected shocks.. This numerical model is validated analytically as well as experimentally with air as working gas. Simulations were conducted for same and different driver/driven gas combinations with helium and carbon dioxide test gases using this model. Simulations were carried out using CFD solver FLUENT. Adaptive Mesh Refinement (AMR) technique was applied to accurately capture and resolve shock and contact discontinuities. At lower pressure ratios the different gas model is able to produce 20.4% and at higher diaphragm pressure ratios up to 33% increase in shock Mach number when compared to the similar driver-driven gas model.

We investigate the effect of exit pressure history on the flow characteristics of underexpanded transient jets. Using both experiments and numerical simulations, we study the dynamics of shock-cell and vortex structures within these jets. A shock tube with an open-ended configuration allows us to generate transient jets by adjusting the diaphragm pressure ratio and the length of the driver section. Our results indicate that when the shock Mach number exceeds 1.6, a Mach disk forms, indicating a highly underexpanded transient jet at the exit of the shock tube. A distinguishing feature of this jet is the emergence of counter-rotating vortex rings (CRVRs) alongside the initial primary vortex ring. Our findings reveal a substantial influence of both the amplitude and duration of the peak exit pressure on the characteristics of the Mach disk and vortex ring. Notably, the characteristics of the primary vortex ring exhibit significant sensitivity to the formation and evolution of CRVRs. In cases of continuously decreasing exit pressure, the Mach disk follows a consistent self-similar decay pattern, regardless of the peak exit pressure magnitude. Finally, we present an empirical relationship between exit pressure and the characteristics of the Mach disk. In summary, this research provides insight into the complex interaction between the exit pressure history and the flow characteristics in underexpanded transient jets.

A comprehensive understanding of shock formation and propagation in shock tubes is crucial for their diverse applications. The shock velocity in single-diaphragm shock tubes, characterized by initial acceleration and subsequent attenuation due to viscous effects, has been extensively investigated. However, limited studies exist on the double-diaphragm mode of operation. In this study, shock tube experiments were conducted using helium at pressures of 10–60 bar as driver gas and argon at pressures of 100–600 Torr as driven gas. The shock velocity profiles in the double-diaphragm mode show a sequence of acceleration and deceleration stages of the shock front, strongly influenced by the driver-to-driven pressure ratios (P41) and the pressure in the intermediate section (Pmid). Particularly, at high values of P41, peak shock velocities can exceed those measured near the end wall by about 12%. Large axial temperature gradients arise in the driven gas due to the accelerating and decelerating shock. Selecting appropriate diaphragms to maintain the intermediate section's pressure close to the value of the driver pressure can reduce peak shock velocities and post-shock temperatures. An in-house one-dimensional (1D) weighted essentially non-oscillatory scheme-based code was utilized to analyze wave interactions in the shock formation region, revealing that the post-shock gas behind the secondary diaphragm and inhibition of the primary diaphragm's opening and subsequent reopening can lead to unique shock profiles in double-diaphragm shock tubes. These insights deepen our understanding of wave propagation in shock tubes and suggest ways to mitigate undesirable effects in double-diaphragm shock tubes.

No abstract available

No abstract available

Long left ignored by the digital computing industry since its heyday in 1940’s, analog computing is today making a comeback as Moore’s Law slows down. Analog CMOS has power efficiency advantages over digital CMOS for low-precision applications in edge computing, scientific computing, and artificial intelligence/machine learning (AI/ML) verticals. Driven by observed non-trivial improvements in performance over digital processors while solving linear partial differential equations (PDEs), this paper presents experimental results and analysis from a single-chip CMOS analog computer for solving nonlinear PDEs. The chip integrates a 15-point fully-parallel spatially-discrete time-continuous (SDTC) finite difference time-domain (FDTD) solver for acoustic shock wave equations with radiation boundary conditions. The design was realized in TSMC 180 nm CMOS technology. It has an active area of 7.38 mm $\times 4.64$ mm and consumes 936 mW while delivering an equivalent FDTD temporal update rate of 80 MHz and an analog bandwidth of 2 MHz. The paper discusses the challenges and associated design trade-offs in realizing such high-performance CMOS analog computers, including sensitivity to process, voltage, and temperature (PVT) variations, sensitivity to bias and voltage regulation, errors associated with noise, difficulties with calibration; it also outlines possible approaches for mitigating these challenges.

Abstract 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.

STHEs (Shell & Tube Heat Exchangers) are commonly used in oil & gas plants to cool or heat process fluids. A possible issue when designing such systems is represented by the tube rupture scenario, when the internal High Pressure fluid is suddenly discharged to the Low Pressure fluid in the shell. Since usually the tube and shell sides have different design pressures, this scenario must be analyzed to assess if the safety measures are fit to protect the weakest part of the system. The time evolution of this event is characterized by different phases; in the first one, a shock wave is generated and propagated very rapidly in the system, with a time scale in the order of few ms. The phenomenon is so rapid that pressure relief devices are not effective. This kind of waves is normally not evaluated in the majority of available publications; however, it is deemed that it is of particular relevance for large size SHTEs, due to their significant investment cost; a methodology has been developed in this work for the purpose. The amplitude of the shock wave at source location is calculated based on Riemann problem theory, with reference to different types of high and low pressure fluids. The relevant propagation up to the piping entrance is studied to estimate the wave damping and the effective wave amplitude impacting on it. Both validation calculations as well as calculations referred to new design applications and to existing installations are presented, and possible mitigation measures proposed.

With the evolution of modern warfare and the increased use of improvised explosive devices (IEDs), there has been an increase in blast-induced traumatic brain injuries (bTBI) among military personnel and civilians. The increased prevalence of bTBI necessitates bTBI models that result in a properly scaled injury for the model organism being used. The primary laboratory model for bTBI is the shock tube, wherein a compressed gas ruptures a thin membrane, generating a shockwave. To generate a shock wave that is properly scaled from human to rodent subjects many pre-clinical models strive for a short duration and high peak overpressure while fitting a Friedlander waveform, the ideal representation of a blast wave. A large variety of factors have been experimentally characterized in attempts to create an ideal waveform, however we found current research on the gas composition being used to drive shock wave formation to be lacking. To better understand the effect the driver gas has on the waveform being produced, we utilized a previously established murine shock tube bTBI model in conjunction with several distinct driver gasses. In agreement with previous findings, helium produced a shock wave most closely fitting the Friedlander waveform in contrast to the plateau-like waveforms produced by some other gases. The peak static pressure at the exit of the shock tube and total pressure 5 cm from the exit have a strong negative correlation with the density of the gas being used: helium the least dense gas used produces the highest peak overpressure. Density of the driver gas also exerts a strong positive effect on the duration of the shock wave, with helium producing the shortest duration wave. Due to its ability to produce a Friedlander waveform and produce a waveform following proper injury scaling guidelines, helium is an ideal gas for use in shock tube models for bTBI.

Abstract We report the first experiments on hydrodynamic instabilities of a single-mode light/heavy interface driven by co-directional rarefaction and shock waves. The experiments are conducted in a specially designed rarefaction-shock tube that enables the decoupling of interfacial instabilities caused by these co-directional waves. After the impacts of rarefaction and shock waves, the interface evolution transitions into Richtmyer–Meshkov unstable states from Rayleigh–Taylor (RT) stable states, which is different from the finding in the previous case with counter-directional rarefaction and shock waves. A scaling method is proposed, which effectively collapses the RT stable perturbation growths. An analytical theory for predicting the time-dependent acceleration and density induced by rarefaction waves is established. Based on the analytical theory, the model proposed by Mikaelian (Phys. Fluids, vol. 21, 2009, p. 024103) is revised to provide a good description of the dimensionless RT stable behaviour. Before the shock arrival, the unequal interface velocities, caused by rarefaction-induced uneven vorticity, result in a V-shape-like interface. The linear growth rate of the amplitude is insensitive to the pre-shock interface shape, and can be well predicted by the linear superposition of growth rates induced by rarefaction and shock waves. The nonlinear growth rate is higher than that of a pure single-mode case, which can be predicted by the nonlinear models (Sadot et al., Phys. Rev. Lett., vol. 80, 1998, pp. 1654–1657; Dimonte & Ramaprabhu, Phys. Fluids, vol. 22, 2010, p. 014104).

With the increased frequency of accidental and deliberate explosions, evaluating the response of civil infrastructure systems to blast loading has been attracting the interests of the research and regulatory communities. However, with the high cost and complex safety and logistical issues associated with field explosives testing, North American blast-resistant construction standards (e.g. ASCE 59-11 and CSA S850-12) recommend the use of shock tubes to simulate blast loads and evaluate relevant structural response. This study first aims at developing a simplified two-dimensional axisymmetric shock tube model, implemented in ANSYS Fluent, a computational fluid dynamics software, and then validating the model using the classical Sod’s shock tube problem solution, as well as available shock tube experimental test results. Subsequently, the developed model is compared to a more complex three-dimensional model and the results show that there is negligible difference between the two models for axisymmetric shock tube performance simulation; however, the three-dimensional model is necessary to simulate non-axisymmetric shock tubes. Following the model validation, extensive analyses are performed to evaluate the influences of shock tube design parameters (e.g. the driver section pressure and length and the expansion section length) on blast wave characteristics to facilitate a shock tube design that would generate shock waves similar to those experienced by civil infrastructure components under blast loads. The results show that the peak reflected pressure increases as the driver pressure increases, while a decrease in the expansion length increases the peak reflected pressure. In addition, the positive phase duration increases as both the driver length and expansion length are increased. Finally, the developed two-dimensional axisymmetric model is used to optimize the dimensions of a physical large-scale conical shock tube system constructed for civil infrastructure component blast response evaluation applications. The capabilities of such shock tube system are further investigated by correlating its design parameters to a range of explosion threats identified by different hemispherical TNT charge weight and distance scenarios.

We introduce Neural Discrete Equilibrium (NeurDE), a machine learning framework for stable and accurate long-term forecasting of nonlinear conservation laws. NeurDE leverages a kinetic lifting that decomposes the dynamics into a fixed linear transport component and a local nonlinear relaxation to equilibrium. This structure provides a natural and principled interface between physics, numerical methods, and machine learning methodologies, enabling NeurDE to be viewed as a ``neural twin''to Boltzmann-BGK. The transport step can be implemented efficiently in solvers such as lattice Boltzmann (LB), while the equilibrium is modeled by a neural network that maps macroscopic observables to a discrete equilibrium distribution. When integrated into a LB solver, the transport step becomes an efficient lattice streaming operation, and NeurDE yields a hybrid algorithm that robustly captures shock propagation and complex compressible dynamics over long time horizons. The NeurDE method is highly data-efficient: a small network trained on limited data generalizes far beyond the training regime, resolving shocks that evolve well outside the initial training distribution. Unlike traditional kinetic solvers, NeurDE achieves this accuracy without costly root-finding procedures or large velocity lattices. These results establish NeurDE as a scalable, efficient, and physics-informed paradigm for learning-based simulation of nonlinear conservation laws

Nonlinearly stable flux reconstruction (NSFR) combines the key properties of provable nonlinear stability with the increased time step from energy-stable flux reconstruction. The NSFR scheme has been successfully applied to unsteady compressible flows. Through the use of a bound-preserving limiter, positivity of thermodynamic quantities is preserved, and this enables the extension of NSFR to hyperbolic conservation laws. We extend the limiter of Zhang and Shu [1] to ensure robustness for the proposed scheme. The limiter is modified to consider the minimum density and pressure at the solution nodes when determining the value to scale the solution. The modifications are thoroughly tested with a suite of test cases. In addition to these modifications, this paper conducts a thorough investigation into the shock-capturing capabilities of the NSFR scheme and the advantages it presents over standard discontinuous Galerkin (DG) methods, where, on select variants of the flux reconstruction (FR) scheme, essentially oscillation-free solutions are demonstrated. Various parameters of the scheme are extensively tested and analyzed through several 1D and 2D compressible Euler tests that verify the high-order accuracy, entropy stability, time step advantage and shock-capturing capabilities of the NSFR scheme. These parameters include the two-point flux, quadrature nodes and the strength of the FR parameter. In addition to investigating the impact of the various two-point fluxes, this paper also presents numerical studies to determine the CFL condition required to maintain positivity for the two-point flux of choice. The investigation yields insightful results for all parameters, with the results pertaining to the type of FR scheme being of special interest. The tests showcase increased robustness, time step advantages and oscillation/overshoot mitigation when employing a stronger FR parameter.

A numerical investigation is conducted to characterize the interaction dynamics between planar incident shock waves (Mach numbers ranging from 1.21 to 2.00) and a cylindrical SF6 heavy gas column embedded in ambient air, focusing on Richtmyer–Meshkov instability (RMI) development, interfacial scale evolution, and vorticity-driven material transport mechanisms. From an Eulerian perspective, the motion of several interface characteristic points, the evolution of material line length, and two area parameters associated with SF6 distribution are tracked. Additionally, the SF6 material transport process and trajectories of material points within the gas column are visualized using the Lagrangian particle tracing method. Theoretical models for bubble velocity, vortex core spacing, and material line stretching laws are evaluated. Our results highlight the significant influence of incident shock strength on interface evolution and material transport. The streamwise motion of both the gas column and primary vortex core follows near-linear trajectories, whereas spanwise dynamics exhibit nonlinear behavior driven by hydrodynamic instabilities. The SF6-containing region expands linearly due to the growth of the primary vortex pair. Two constants—vortex core spacing and SF6 volume fraction weighted area—are identified, both dependent on the incident shock strength. Material line length evolution follows a two-stage exponential growth pattern, sequentially driven by RMI and secondary instabilities. Lagrangian analysis reveals a stratified entrainment mechanism, with outer SF6 layers mixing earlier than inner regions. Theoretical models show strong agreement with numerical predictions for bubble velocity and SF6 volume-fraction-weighted area, while discrepancies are observed in vortex core spacing models.

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Abstract For real-world engineering applications, there is a great deal of interest in developing effective models and simulations of continuum-rarefied gas flows. In this study, the numerical simulations of Grad’s 13 (G13) moment equations with application to the Riemann problem in a wide range of continuum-rarefied flow regimes are presented. This work emphasizes numerical robustness and wave phenomena in the G13 system to provide a building block for regularized 13 moment systems, and high-order Grad’s models. For this purpose, a high-order modal discontinuous Galerkin solver is developed for solving one-dimensional G13 moment equations. For spatial discretization, hierarchical modal basis functions premised on orthogonal-scaled Legendre polynomials are used. The proposed approach reduces the G13 systems into a framework of ordinary differential equations in time, which are addressed by an explicit third-order SSP Runge-Kutta algorithm. Three Riemann test cases, including the shock tube, two shock waves and two rarefaction waves, are examined in continuum-rarefied flow regimes. In the G13 system, the arising characteristic waves and dissipation phenomena are investigated in depth. The numerical results demonstrate that every Riemann problem does not have a solution for the G13 system because of loss of hyperbolicity of the system.

This work intends to compare the pressure-based coupled algorithm and the density-based algorithm for the two-dimensional high speed gas-particle two-phase compressible flow in the closed-ends micro-shock tube. The micro-shock tube is employed in the medical sector for the drug delivery without needle. The mass along with momentum transfer equations for compressible flow, together with the computational approach, are provided. These solvers are used to perform the transient simulation. The pressure-based algorithm offers the versatility to address flow issues using either a coupled or a segregated method. Choosing the coupled technique over the non-coupled or segregated approach has some benefits. In particular, the linked scheme outperforms segregated solution techniques and provides a reliable and effective solution for steady-state flows. The den sity-based and pressure-based segregated methods using SIMPLE-type pressure-velocity coupling is replaced by this pressure-based coupled technique. Using the coupled approach becomes essential when dealing with poor mesh quality or when using high time steps in the case of transient flows. The schlieren and vorticity contours were obtained to analyze and compared for both the solvers to determine their efficacy to capture the shock waves and fluid element rotation. This is the major gap and novelty found through the literature survey for such kind of problem. The pressure histories and Mach no. were recorded for both the solvers. The result obtained through these solvers show that though the pressure-based algorithm is capable for handling high speed compressible flow problem but when it comes about the CPU time as well as the accuracy of the result, the density-based solver is more reliable for this problem.

While the canonical two-component, single-mode Richtmyer–Meshkov instability (RMI) has been extensively studied, relatively less work has focused on the effects of an additional intermediate-density middle layer. This work investigates such three-material RMI configurations at two Atwood number scenarios using the ares hydrodynamics code. After validation against previous experimental and computational studies, setups corresponding to recent three-layer shock tube experiments are simulated. Cases with both single-mode and multimode perturbations are studied to quantify mixing across the interface between the materials with highest and intermediate density. In particular, this work is able to comprehensibly examine differences between two- and three-dimensional setups for the single-mode and multimode problems. Observations from previous two-layer investigations still apply in the three-layer setup, but over the time horizons considered, there appears to be insufficient nonlinear mode coupling to create significant differences between two- and three-dimensional simulations following the first passage of a shock. Additional reshock simulations have additional nonlinear growth that does result in expected differences between two- and three-dimensional cases in this three-layer setup, but significant differences do not manifest during the time horizon studied.

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In this paper we presented a lattice Boltzmann with square grid for compressible flow problems. Triple level velocity is considered for each cell. Migration step use discrete velocity but continuous parameters are utilized to calculate density, velocity, and energy. So, we called this semi-discrete method. To evaluate the performance of the method the well-known shock tube problem is solved, using 1-D and 2-D version of the lattice Boltzmann method. The results of these versions are compared with each other and with the results of the analytical solution.

The Direct Simulation Monte Carlo method is employed to solve the “1D - Sod-Shock tube problem”, a special case of Riemann problems, for gas mixtures. Initially, two different gas species are distributed separately in the high and low pressure sides of the tube without interacting with each other. For time greater than zero the species start mixing and shock and rarefaction waves are formed moving in opposite directions. In this work, the mixing process between different kinds of gas species was investigated by observing differences in waves’ formation. The influence of the mass and diameter ratio between the species was studied in detail. It was found that greater mass differences had a very strong effect on the mixing process, while the effects due to diameter differences were relatively small. Finally, it is shown that in the case of single species the interaction molecular models of the hard sphere, the variable hard sphere and the variable soft sphere gave the same results, while for gas mixtures the variable hard sphere and variable soft sphere models gave slightly different results.The Direct Simulation Monte Carlo method is employed to solve the “1D - Sod-Shock tube problem”, a special case of Riemann problems, for gas mixtures. Initially, two different gas species are distributed separately in the high and low pressure sides of the tube without interacting with each other. For time greater than zero the species start mixing and shock and rarefaction waves are formed moving in opposite directions. In this work, the mixing process between different kinds of gas species was investigated by observing differences in waves’ formation. The influence of the mass and diameter ratio between the species was studied in detail. It was found that greater mass differences had a very strong effect on the mixing process, while the effects due to diameter differences were relatively small. Finally, it is shown that in the case of single species the interaction molecular models of the hard sphere, the variable hard sphere and the variable soft sphere gave the same results, while for gas mixtures the...

Compact toroid (CT) injection, with its characteristics of high plasma density and extremely high injection velocity, is considered a highly promising method for core fueling in fusion reactors. Previous studies have lacked investigation into the transport process of CT within drift tubes. To investigate the dynamic processes of CT in drift tubes, this study developed a compressible magnetohydrodynamics (MHD) solver and a magnetic diffusion solver based on the OpenFOAM platform. They were integrated into a multi-region coupling framework to create a multi-region coupled MHD solver, mhdMRF, for simulating the dynamic behavior of CT in drift tubes and its interaction with finite-resistivity walls. The solver demonstrated excellent performance in simulations of the Orszag–Tang MHD vortex problem, the Brio–Wu shock tube problem, analytical verification of magnetic diffusion, and validation of internal coupling boundary conditions. Additionally, this work innovatively explored the effects of the geometric structure at the end of the inner electrode and finite-resistivity walls on the transport processes of CT. The results indicate that optimizing the geometric structure at the end of the inner electrode can significantly enhance the confinement performance and stability of CT transport. The resistivity of the wall profoundly influences the magnetic field structure and density distribution of CT.

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An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied to solve the flow filed by reconstructing the fluxes at each cell interface adaptively with the mesoscopic lattice Boltzmann model. To locally and dynamically improve the resolution of intricate shock structures and optimize the required computational resources, a block-structured adaptive mesh refinement (AMR) technique is introduced. The validity and effectiveness of the proposed method are confirmed through a range of two and three-dimensional numerical cases, including the shock tube problem, the four-wave Riemann problem, explosion within a rectangular box, and the vorticity induced by a shock. The results obtained using the AMR-RLBFS exhibit excellent agreement with published data and demonstrate high accuracy in capturing complex shock structures. The computational efficiency of the AMR-RLBFS can be also improved significantly compared to the RLBFS on uniform grids. Furthermore, the numerical outcomes underscore the capability of the AMR-RLBFS to eliminate shock instability effects while efficiently capturing a broader spectrum of small-scale vertical structures. These findings highlight the ability of AMR-RLBFS to improve the computational efficiency and capture intricate shock structures effectively, making it a valuable tool for studying a wide range of compressible flows from aerodynamics to astrophysics.

The resolution of interfacial dynamics in multi-material flows critically relies on Riemann solvers, while recent advances in physics-informed neural networks (PINNs) offer transformative potential for solving multi-material Riemann problems. This paper presents a novel PINNs-based multi-material high-accuracy Riemann solver (PINN-MHRS) designed to solve multi-material Riemann problems involving complex equations of state (EOS) without requiring labeled data. PINN-MHRS determines wave system structures through entropy condition analysis and constructs physics-constrained loss functions. A hard constraints strategy enforces continuity conditions, wave speed ordering, and positivity of pressure/density, significantly simplifying optimization and accelerating convergence. The PINN-MHRS is integrated with the modified ghost fluid method via a Fortran-Python hybrid framework, enabling numerical simulations of multi-material interactions. Time advancement is achieved through a cyclic training-prediction alternating strategy that dynamically adapts to evolving interface conditions. Comprehensive validation demonstrates PINN-MHRS's exceptional performance. For one-dimensional shock tube cases with ideal gas EOS, it achieves errors at least five orders of magnitude lower than Harten–Lax–van Leer Contact (HLLC). When handling the complex Jones-Wilkins-Lee (JWL) EOS for explosives, PINN-MHRS exhibits three orders of magnitude higher accuracy (error: 2.90×10−1) compared to HLLC (error: 2.70×102). In two-dimensional air–helium shock–bubble interaction simulations, PINN-MHRS maintains low-error predictions while accurately solving interface evolution details. PINN-MHRS establishes a new paradigm for high-accuracy, stable Riemann solvers in complex multi-material flow simulations. The Fortran-Python hybrid framework successfully bridges machine learning and traditional computational fluid dynamics (CFD). Its ability to handle complex EOS without labeled data and to maintain physical consistency suggests broad applicability to other interfacial dynamics problems.

A shock wave is a flow phenomenon that needs to be considered in the development of high-speed aircraft and engines. The traditional computational fluid dynamics (CFD) method describes it from the perspective of macroscopic variables, such as the Mach number, pressure, density, and temperature. The thickness of the shock wave is close to the level of the molecular free path, and molecular motion has a strong influence on the shock wave. According to the analysis of the Chapman-Enskog approach, the nonequilibrium effect is the source term that causes the fluid system to deviate from the equilibrium state. The nonequilibrium effect can be used to obtain a description of the physical characteristics of shock waves that are different from the macroscopic variables. The basic idea of the nonequilibrium effect approach is to obtain the nonequilibrium moment of the molecular velocity distribution function by solving the Boltzmann–Bhatnagar–Gross–Krook (Boltzmann BGK) equations or multiple relaxation times Boltzmann (MRT-Boltzmann) equations and to explore the nonequilibrium effect near the shock wave from the molecular motion level. This article introduces the theory and understanding of the nonequilibrium effect approach and reviews the research progress of nonequilibrium behavior in shock-related flow phenomena. The role of nonequilibrium moments played on the macroscopic governing equations of fluids is discussed, the physical meaning of nonequilibrium moments is given from the perspective of molecular motion, and the relationship between nonequilibrium moments and equilibrium moments is analyzed. Studies on the nonequilibrium effects of shock problems, such as the Riemann problem, shock reflection, shock wave/boundary layer interaction, and detonation wave, are introduced. It reveals the nonequilibrium behavior of the shock wave from the mesoscopic level, which is different from the traditional macro perspective and shows the application potential of the mesoscopic kinetic approach of the nonequilibrium effect in the shock problem.

In this paper, a high‐order lattice Boltzmann flux solver (LBFS) based on flux reconstruction (FR) is presented for simulating the three‐dimensional compressible flows. Unlike the original LBFS employing finite volume methods, the current method (FR‐LBFS) can achieve arbitrary high‐order accuracy with a compact stencil. High‐order schemes based on finite volume methods often compromise parallel efficiency and complicate boundary treatment. In contrast, LBFS incorporates physical effects in calculating inviscid fluxes, providing superior shock‐capturing capabilities over traditional approximate Riemann solvers. The present method combines the strengths of both FR and LBFS, yielding enhanced performance. Specifically, there is limited analysis of compact high‐order LBFS in simulations of three‐dimensional compressible flows. Several benchmark test cases are employed to validate the superiority of the current method, and the results show good agreement with established literature values. The shock tube problem and inviscid Taylor‐Green vortex demonstrate the shock‐capturing capability and low‐dissipation characteristics of FR‐LBFS. Meanwhile, the decaying homogeneous isotropic turbulent flow and the flow around a triangular airfoil highlight the accuracy of the current method in turbulence simulation. The obtained numerical results demonstrate that the proposed method holds considerable promise for applications in simulations of compressible and turbulent flows.

This paper presents a WENO-based upwind rotated lattice Boltzmann flux solver (WENO-URLBFS) in the finite difference framework for simulating compressible flows with contact discontinuities and strong shock waves. In the method, the original rotating lattice Boltzmann flux solver is improved by applying the theoretical solution of the Euler equation in the tangential direction of the cell interface to reconstruct the tangential flux so that the numerical dissipation can be reduced. The fluxes at each interface are evaluated using a weighted summation of lattice Boltzmann solutions in two local perpendicular directions decomposed from the direction vector so that the stability performance can be improved. To achieve high-order accuracy, both fifth and seventh-order WENO reconstructions of the flow variables in the characteristic spaces are carried out. The order accuracy of the WENO-URLBFS is evaluated and compared with the traditional Lax–Friedrichs scheme, Roe scheme, and the LBFS by simulating the advection of the density disturbance problem. It is shown that the fifth and seventh-order accuracy can be achieved by all considered flux-evaluation schemes, and the present WENO-URLBFS has the lowest numerical dissipation. The performance of the WENO-URLBFS is further examined by simulating several 1D and 2D examples, including shock tube problems, Shu–Osher problems, blast wave problems, double Mach reflections, 2D Riemann problems, K-H instability problems, and High Mach number astrophysical jets. Good agreements with published data have been achieved quantitatively. Moreover, complex flow structures, including shock waves and contact discontinuities, are successfully captured. The present WENO-URLBFS scheme seems to present an effective numerical tool with high-order accuracy, lower numerical dissipation, and strong robustness for simulating challenging compressible flow problems.

We present the application of Harten-Lax-van Leer (HLL)-type solvers on Riemann problems in nonlinear elasticity which undergoes high-load conditions. In particular, the HLLD (“D” denotes Discontinuities) Riemann solver is proved to have better robustness and efficiency for resolving complex nonlinear wave structures compared with the HLL and HLLC (“C” denotes Contact) solvers, especially in the shock-tube problem including more than five waves. Also, Godunov finite volume scheme is extended to higher order of accuracy by means of piecewise parabolic method (PPM), which could be used with HLL-type solvers and employed to construct the fluxes. Moreover, in the case of multi material components, level set algorithm is applied to track the interface between different materials, while the interaction of interfaces is realized through HLLD Riemann solver combined with modified ghost method. As seen from the results of both the solid/solid “stick” problem with the same material at the two sides of contact interface and the solid/solid “slip” problem with different materials at the two sides, this scheme composed of HLLD solver, PPM and level set algorithm can capture the material interface effectively and suppress spurious oscillations therein significantly.

No abstract available

Most high-order Euler-type methods have been proposed to solve one-dimensional scalar hyperbolic conservational law. These methods resolve smooth variations in flow parameters accurately and simultaneously identify the discontinuities. A disadvantage of Euler-type methods is the parameter change stretching in the shock over a few mesh cells. In reality, in the shock, the flow properties change abruptly at once for the computational mesh. In our considerations, the mean free path of a flow particle is much smaller than the mesh cell size. This paper describes a modification of the semi-Lagrangian Godunov-type method, which was proposed by the author in the previously published paper. The modified method also does not have numerical viscosity for shocks. In the previous article, a linear law for the distribution of flow parameters was employed for a rarefaction wave when modeling the Shu-Osher problem with the aim of reducing parasitic oscillations. Additionally, the nonlinear law derived from the Riemann invariants was used for the remaining test problems. This article proposes an advanced method, namely, a unified formula for the density distribution of rarefaction waves and modification of the scheme for modeling moderately strong shock waves. The obtained results of numerical analysis, including the standard problem of Sod, the Riemann problem of Lax, the Shu–Osher shock-tube problem and a few author’s test cases are compared with the exact solution, the data of the previous method and the Total Variation Deminishing (TVD) scheme results. This article delineates the further advancement of the numerical scheme of the proposed method, specifically presenting a unified mathematical formulation for an expanded set of test problems.

The degraded resolution and sensitivity characteristics of background-oriented schlieren (BOS) can be recovered by utilizing an optical flow (OF)-based image processing scheme. However, the background patterns conventionally employed in BOS setups suit the needs of the cross-correlation approach, whereas OF is based on a completely different mathematical background. Thus, in order to characterize the resolution and sensitivity response of OF-based BOS to the background generation configurations, a parametric study is performed. First, a synthetic assessment based on an analytical solution of a one-dimensional shock tube problem is conducted. Then, a numerical assessment utilizing direct numerical simulation data of density-driven turbulence is performed. Finally, the applicability of the documented conclusions in realistic scenarios is tested through an experimental assessment over a plume of a swirling heated jet.

The accurate capturing of shock waves by numerical methods has long been a focus of attention in engineering owing to singularity problems in discontinuities. In this article, a novel coupled Euler–Lagrange method (CELM) is proposed to capture shock waves and discontinuities with high resolution and high order of mapping accuracy. CELM arranges the Lagrange particles on an Euler grid to track the discontinuous points automatically, and the data pertaining to the grids and particles interact via a weighted mutual mapping method that not only achieves fourth‐order accuracy in a smooth area of the solution but also maintains a steep discontinuous transition in the discontinuous area. In the virtual particle method, virtual particles are derived from the existing real particles; thus, the inflow and outflow of the particles and interpolation accuracy of the boundary are more easily realized. An accuracy test and energy convergence test demonstrated the fourth‐order convergence accuracy and low energy dissipation of the CELM; the method exhibited lower error and better conservation ability than high‐precision schemes such as WENO3 and WENO5. The Sod shock tube problem and Woodward–Colella problem showed higher discontinuity resolution of the CELM and ability to accurately track discontinuity points. Examples of Riemann problems were employed to prove that the CELM exhibits lower dissipation and higher shock resolution than WENO3 and WENO5. The CELM also showed an accurate structure based on particle distribution. Shockwave diffraction tests were conducted to prove that the CELM results showed good agreement with the experimental data and exhibited an accurate expansion wave. The CELM can also accurately simulate the collision of an expansion wave and vortex.

Based on logarithm conformation representation, new equations that have the same Riemann invariant as the compressible Euler equations, but are defined in the non-conservation system, were obtained. In the new equations, adaptive mesh refinement, which is constructed by error analysis in the field of the finite-element method, was utilised to resolve the numerical flux with high quality, without any filter and limiter. The Sod shock tube problem was calculated at time $ \textrm{t} = 0.2 $ t=0.2, and the analytical solution was compared with the numerical one. The numerical results are similar to the exact solution but do not satisfy the exact conservations of the mass, momentum, and total energy. However, it is noteworthy that the shock wave and the contact discontinuity surface can be resolved, even if the newly proposed equations are defined in a non-conservation system and more a filter but also limiter are not used in this study.

This paper presents a parallel and fully conservative adaptive mesh refinement (AMR) implementation of a finite-volume-based kinetic solver for compressible flows. Time-dependent H-type refinement is combined with a two-population quasi-equilibrium Bhatnagar–Gross–Krook discrete velocity Boltzmann model. A validation has shown that conservation laws are strictly preserved through the application of refluxing operations at coarse-fine interfaces. Moreover, the targeted macroscopic moments of Euler and Navier–Stokes–Fourier level flows were accurately recovered with correct and Galilean invariant dispersion rates for a temperature range over three orders of magnitude and dissipation rates of all eigen-modes up to Mach of order 1.8. Results for one- and two-dimensional benchmarks up to Mach numbers of 3.2 and temperature ratios of 7, such as the Sod and Lax shock tubes, the Shu–Osher and several Riemann problems, as well as viscous shock–vortex interactions, have demonstrated that the solver precisely captures reference solutions. Excellent performance in obtaining sensitive quantities was proven, for example, in the test case involving nonlinear acoustics, while, for the same accuracy and fidelity of the solution, the AMR methodology significantly reduced computational cost and memory footprints. Over all demonstrated two-dimensional problems, up to a four- to ninefold reduction was achieved and an upper limit of the AMR overhead of 30% was found in a case with very cost-intensive parameter choice. The proposed solver marks an accurate, efficient, and scalable framework for kinetic simulations of compressible flows with moderate supersonic speeds and discontinuities, offering a valuable tool for studying complex problems in fluid dynamics.

Due to the complexity and short timescale of detonation, it is usually difficult to capture its transient characteristics experimentally. Advanced numerical methods are essential for enhancing the understanding of the flow field structure and combustion mechanism of detonation. In this study, a density-based compressible reactive flow solver called CDSFoam is developed for simulating gas-droplet two-phase detonation combustion based on OpenFOAM. The primary feature of this solver is its implementation of two-way coupling between gas and liquid phases, utilizing the Eulerian–Lagrangian method. The key enhancement is an improved approximate Riemann solver used to solve the convective flux, reducing dissipation while ensuring robustness. Time integration is achieved through the third-order strong stability preserving Runge–Kutta method. Additionally, CDSFoam incorporates dynamic load balancing and adaptive mesh refinement techniques to mitigate computational costs while achieving high-resolution flow fields dynamically. To validate the reliability and accuracy of the solver, a series of benchmark cases are examined, including the multi-component inert and reactive shock tube, the stable diffusion process, the Riemann problem, the one-dimensional detonation, the two-dimensional detonation and oblique detonation, the droplet phase model, the two-dimensional gas–liquid two-phase detonation, and the two-phase rotating detonation. The results show that CDSFoam can well predict the shock wave discontinuity, shock wave induced ignition, molecular diffusion, detonation key parameters, detonation cell size, and the main characteristics of gas–liquid two-phase detonation.

In this paper, a thermodynamically consistent solution of the interfacial Riemann problem for the first-order hyperbolic continuum model of Godunov, Peshkov and Romenski (GPR model) is presented. In the presence of phase transition, interfacial physics are governed by molecular interaction on a microscopic scale, beyond the scope of the macroscopic continuum model in the bulk phases. The developed two-phase Riemann solvers tackle this multi-scale problem, by incorporating a local thermodynamic model to predict the interfacial entropy production. Using phenomenological relations of non-equilibrium thermodynamics, interfacial mass and heat fluxes are derived from the entropy production and provide closure at the phase boundary. We employ the proposed Riemann solvers in an efficient sharp interface level-set Ghost-Fluid framework to provide coupling conditions at phase interfaces under phase transition. As a single-phase benchmark, a Rayleigh-B\'enard convection is studied to compare the hyperbolic thermal relaxation formulation of the GPR model against the hyperbolic-parabolic Euler-Fourier system. The novel interfacial Riemann solvers are validated against molecular dynamics simulations of evaporating shock tubes with the Lennard-Jones shifted and truncated potential. On a macroscopic scale, evaporating shock tubes are computed for the material n-Dodecane and compared against Euler-Fourier results. Finally, the efficiency and robustness of the scheme is demonstrated with shock-droplet interaction simulations that involve both phase transfer and surface tension, while featuring severe interface deformations.

We compare high-order methods including spectral difference (SD), flux reconstruction (FR), the entropy-stable discontinuous Galerkin spectral element method (ES-DGSEM), modal discontinuous Galerkin methods, and WENO to select the best candidate to simulate strong shock waves characteristic of hypersonic flows. We consider several benchmarks, including the Leblanc and modified shock-density wave interaction problems that require robust stabilization and positivity-preserving properties for a successful flow realization. We also perform simulations of the three-species Sod problem with simplified chemistry with the chemical reaction source terms introduced in the Euler equations. The ES-DGSEM scheme exhibits the highest stability, negligible numerical oscillations, and requires the least computational effort in resolving reactive flow regimes with strong shock waves. Therefore, we extend the ES-DGSEM to hypersonic Euler equations by deriving a new set of two-point entropy conservative fluxes for a five-species gas model. Stabilization for capturing strong shock waves occurs by blending high-order entropy conservative fluxes with low-order finite volume fluxes constructed using the HLLC Riemann solver. The hypersonic Euler solver is verified using the non-equilibrium chemistry Sod problem. To this end, we adopt the Mutation++ library to compute the reaction source terms, thermodynamic properties, and transport coefficients. We also investigate the effect of real chemistry versus ideal chemistry, and the results demonstrate that the ideal chemistry assumption fails at high temperatures, hence real chemistry must be employed for accurate predictions. Finally, we consider a viscous hypersonic flow problem to verify the transport coefficients and reaction source terms determined by the Mutation++ library.

The study focuses on enhancing the accuracy of numerical solutions for Euler’s equations, essential for aerospace, engineering, and scientific simulations. To improve the numerical solution accuracy and efficiency of nonlinear problems, this study proposes a high-precision and high stability scheme for the Euler equation system, combining the fifth-order explicit weighted compact nonlinear scheme with the third-order semi-implicit implicit-explicit Runge-Kutta method. The results show that the scheme maintains design order accuracy in both high and low Mach number flows, with a spatial discretization error of 4.95 orders and a time discretization error convergence order of 5.86 orders. The width of the shock transition zone is reduced by 40% compared to traditional weighted compact nonlinear scheme. This demonstrates the accuracy advantage of this format. And this format remains stable even when Courant-Friedrichs-Lewy>1, making it suitable for large-scale industrial simulation, which is beneficial for improving efficiency. In one-dimensional shock tubes, bimodal acoustic pulse collisions, and Lax/Sod problems, the density, velocity, and pressure results of this format are consistent with the reference solution, with no oscillation phenomenon. The rigid processing error of the pressure term is less than 1.134 × 10 −8 . It has good stability, which provides a new approach for numerical research to further understand complex flow phenomena.

Application of microwave radar is a useful approach to gauge piston motion in a free-piston driver. One difficulty associated with conventional microwave technique is its spatial resolution during rapid velocity shifts at diaphragm rupture timings. This study, while departing from the standard practice of analyzing standing wave peaks, introduces an alternative by examining the phase shift of the microwave in-phase and quadrature signals. A compact free-piston-driven expansion tube, MX6.0, is used as the test bed for this technique. A microwave frequency of 4.2 GHz is used to take measurements in a compression tube with a diameter of 50 mm and a length of 2.0 m, tracking the motion of the piston. After arranging the microwave radar systems, the piston velocity and displacement trajectory are measured. Compared to the lower-resolution measurements using conventional microwave wavelength intervals, the use of microwave phase allowed for an exceptionally high spatial resolution in analyzing the piston motion.

No abstract available

Blast simulators facilitate the creation of shock waves and measurement of pressure morphology in a controlled laboratory setting and are currently a vital model for replicating blast-induced neurotrauma. Due to the maintenance and operation cost of conventional blast simulators, we developed a pneumatic, table-top, gas-driven shock tube to test an alternative method of shock wave generation using a membrane-less driver section. Its unique operational mechanism based on air gun technology does not rely on a plastic membrane rupture for the generation of pressure pulses, allowing the simulator to be quickly reset and thus decreasing the experimental turnaround time. The focus of this study is to demonstrate that this proof-of-concept device can generate shock waves with diverse characteristics based on the selection of driver gas, driver pressurization, and driven section material. Pressure waves were generated using compressed nitrogen or helium at 15 psig and 80 psig and were analyzed based on their velocity and profile shape characteristics. At 15 psig, independent of the type of driver gas, driver pressurization, and driven section material, pressure pulses travelled at sonic velocities. At 80 psig, generation of shock waves was observed in all conditions. The choice of the driver gas affected the velocities of the resulting pressure waves and the shape of pressure waveforms, particularly the peak overpressure and rise time values. Our results demonstrate that depending on the selection of driver gas and magnitude of driver pressurization, the shock wave signatures can be controlled and altered using a piston-based driver section.

The increased incidence of improvised explosives in military conflicts has brought about an increase in the number of traumatic brain injuries (TBIs) observed. Although physical injuries are caused by shrapnel and the immediate blast, encountering the blast wave associated with improvised explosive devices (IEDs) may be the cause of traumatic brain injuries experienced by warfighters. Assessment of the effectiveness of personal protective equipment (PPE) to mitigate TBI requires understanding the interaction between blast waves and human bodies and the ability to replicate the pressure signatures caused by blast waves. Prior research has validated compression-driven shock tube designs as a laboratory method of generating representative pressure signatures, or Friedlander-shaped blast profiles; however, shock tubes can vary depending on their design parameters and not all shock tube designs generate acceptable pressure signatures. This paper presents a comprehensive numerical study of the effects of driver gas, driver (breech) length, and membrane burst pressure of a constant-area shock tube. Discrete locations in the shock tube were probed, and the blast wave evolution in time at these points was analyzed to determine the effect of location on the pressure signature. The results of these simulations are used as a basis for suggesting guidelines for obtaining desired blast profiles.

Detonation of a high-explosive produces shock-blast wave, shrapnel, and gaseous products. While direct exposure to blast is a concern near the epicenter, shock-blast can affect subjects, even at farther distances. When a pure shock-blast wave encounters the subject, in the absence of shrapnels, fall, or gaseous products the loading is termed as primary blast loading and is the subject of this paper. The wave profile is characterized by blast overpressure, positive time duration, and impulse and called herein as shock-blast wave parameters (SWPs). These parameters in turn are uniquely determined by the strength of high explosive and the distance of the human subjects from the epicenter. The shape and magnitude of the profile determine the severity of injury to the subjects. As shown in some of our recent works (1–3), the profile not only determines the survival of the subjects (e.g., animals) but also the acute and chronic biomechanical injuries along with the following bio-chemical sequelae. It is extremely important to carefully design and operate the shock tube to produce field-relevant SWPs. Furthermore, it is vital to identify and eliminate the artifacts that are inadvertently introduced in the shock-blast profile that may affect the results. In this work, we examine the relationship between shock tube adjustable parameters (SAPs) and SWPs that can be used to control the blast profile; the results can be easily applied to many of the laboratory shock tubes. Further, replication of shock profile (magnitude and shape) can be related to field explosions and can be a standard in comparing results across different laboratories. Forty experiments are carried out by judiciously varying SAPs such as membrane thickness, breech length (66.68–1209.68 mm), measurement location, and type of driver gas (nitrogen, helium). The effects SAPs have on the resulting shock-blast profiles are shown. Also, the shock-blast profiles of a TNT explosion from ConWep software is compared with the profiles obtained from the shock tube. To conclude, our experimental results demonstrate that a compressed-gas shock tube when designed and operated carefully can replicate the blast time profiles of field explosions accurately. Such a faithful replication is an essential first step when studying the effects of blast induced neurotrauma using animal models.

The end plate mounted at the mouth of the shock tube is a versatile and effective implement to control and mitigate the end effects. We have performed a series of measurements of incident shock wave velocities and overpressures followed by quantification of impulse values (integral of pressure in time domain) for four different end plate configurations (0.625, 2, 4 inches, and an open end). Shock wave characteristics were monitored by high response rate pressure sensors allocated in six positions along the length of 6 meters long 229 mm square cross section shock tube. Tests were performed at three shock wave intensities, which was controlled by varying the Mylar membrane thickness (0.02, 0.04 and 0.06 inch). The end reflector plate installed at the exit of the shock tube allows precise control over the intensity of reflected waves penetrating into the shock tube. At the optimized distance of the tube to end plate gap the secondary waves were entirely eliminated from the test section, which was confirmed by pressure sensor at T4 location. This is pronounced finding for implementation of pure primary blast wave animal model. These data also suggest only deep in the shock tube experimental conditions allow exposure to a single shock wave free of artifacts. Our results provide detailed insight into spatiotemporal dynamics of shock waves with Friedlander waveform generated using helium as a driver gas and propagating in the air inside medium sized tube. Diffusion of driver gas (helium) inside the shock tube was responsible for velocity increase of reflected shock waves. Numerical simulations combined with experimental data suggest the shock wave attenuation mechanism is simply the expansion of the internal pressure. In the absence of any other postulated shock wave decay mechanisms, which were not implemented in the model the agreement between theory and experimental data is excellent.

Shock tubes are instrumental in studying high-temperature kinetics and simulating high-speed flows. They rapidly increase the thermodynamic conditions of test gases, making them ideal for examining chemical reactions and generating high-enthalpy flows for aerodynamic research. However, non-ideal effects, stemming from factors like diaphragm opening processes and viscous effects, can significantly influence thermodynamic conditions behind the shock wave. This study investigates the impact of various diaphragm opening patterns on the shock parameters near the driven section's end wall. Experiments were conducted using helium and argon as driver and driven gases, respectively, at pressures ranging from 1.32 to 2.09 bar and temperatures from 1073 to 2126 K behind the reflected shock. High-speed imaging captured different diaphragm rupture profiles, classified into four distinct types based on their dynamics. Results indicate that the initial stages of diaphragm opening, including the rate and profile of opening, play crucial roles in the resulting incident shock Mach number and test time. A sigmoid function was employed to fit the diaphragm opening profiles, allowing for accurate categorization and analysis. New correlations were developed to predict the incident shock attenuation rate and post-shock pressure rise, incorporating parameters such as diaphragm opening time, rupture profile constants, and normalized experimental Mach number. The results emphasize the importance of considering diaphragm rupture dynamics in shock tube experiments to achieve accurate predictions of shock parameters.

Shock tubes are critical diagnostic tools in aerodynamics, astrophysics, chemical kinetics, and industrial research. In double-diaphragm mode, they provide better control over experiment initiation and allow for higher shock Mach numbers by using thinner diaphragms. Depending on the pressure in the intermediate section between the diaphragms, two distinct shock velocity profiles have been observed: 1) a higher peak shock velocity at lower midsection pressures and 2) a secondary acceleration phase at higher midsection pressures. This study aims to elucidate the flow dynamics associated with these behaviors by analyzing the underlying causes of shock velocity variations and assessing their influence on the uniformity of the shocked gas. Experiments were conducted using helium as the driver gas at 30 bar and argon as the driven gas at 133.3 mbar, with midsection pressures of 4.8 and 18.8 bar. Midsection pressure histories and high-speed visualizations of the diaphragm-opening process were employed to investigate the mechanisms influencing shock velocity. Additionally, numerical simulations were conducted at six distinct conditions to assess the impact of diaphragm-opening dynamics on shock profiles and to quantify axial variations in temperature and pressure. The results show that, although axial pressure remains nearly uniform, significant temperature gradients are present; peak temperatures were up to 6.5% higher for the case of lower midsection pressure at a Mach number of 4.15 and 2% higher at Mach 3.1. These findings underscore the critical role of midsection pressure in minimizing thermal nonuniformities in the shocked gas.

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This paper describes the development and characterization of modular, oxy-acetylene driven laboratory scale shock tubes. Such tools are needed to produce realistic blast waves in a laboratory setting. The pressure-time profiles measured at 1 MHz using high-speed piezoelectric pressure sensors have relevant durations and show a true shock front and exponential decay characteristic of free-field blast waves. Descriptions are included for shock tube diameters of 27-79 mm. A range of peak pressures from 204 kPa to 1187 kPa (with 0.5-5.6% standard error of the mean) were produced by selection of the driver section diameter and distance from the shock tube opening. The peak pressures varied predictably with distance from the shock tube opening while maintaining both a true blast wave profile and relevant pulse duration for distances up to about one diameter from the shock tube opening. This shock tube design provides a more realistic blast profile than current compression-driven shock tubes, and it does not have a large jet effect. In addition, operation does not require specialized personnel or facilities like most blast-driven shock tubes, which reduces operating costs and effort and permits greater throughput and accessibility. It is expected to be useful in assessing the response of various sensors to shock wave loading; assessing the reflection, transmission, and absorption properties of candidate armor materials; assessing material properties at high rates of loading; assessing the response of biological materials to shock wave exposure; and providing a means to validate numerical models of the interaction of shock waves with structures. All of these activities have been difficult to pursue in a laboratory setting due in part to lack of appropriate means to produce a realistic blast loading profile.

The experimental data [1, 2] on the effect of the parameters of plane incident shock waves and the characteristics of a porous medium on the attenuation and reflection of waves from a rigid obstacle are examined. The propagation of waves with a pressure jumps of up to ΔP/P0 = 20 (P0 = 0.1 MPa) in polyurethane foam blocks with a density of 20 kg/m3 and 35 kg/m3 and a length of up to 0.8 m, tightly adjacent to the walls and the end face of the driven section of the shock tube is studied. At lengths of the porous block greater than the extent of the shock wave, the porous block effectively attenuated the shock wave. For a wave of limited duration with a triangular pressure profile, a stronger attenuation of the wave in the polyurethane foam block was observed in comparison with that for an extended wave pulse. The reflection pressures of the waves in polyurethane foam with pressure jumps of ΔP/P0 ≥ 12 exceed the reflection pressures of shock waves in air. The degree of attenuation or amplification of a wave depends on the material density and the ratio of the lengths of the foamed polyurethane block and the pressure pulse.

Fiber Metal Laminates (FMLs) have garnered considerable attention and are increasingly being utilized in the development of protective armors for explosion and ballistic scenarios. While most research has focused on assessing the response of FMLs to single impacts, real battlefield situations often require shielding structures to endure multiple impacts. Thus, this study revolves around the creation of hybrid FMLs designed for shock shielding purposes. The primary focus is on how these laminates withstand repetitive impacts from high-intensity shock waves, aiming to pinpoint the optimal sequence that offers the highest resistance against multiple shock impacts. To establish effective shielding, a multi-layered FML configuration is employed. This configuration incorporates AA6061-T6 facing plates, ballistic-grade synthetic materials like aramid/epoxy ply, and ultra-high molecular weight polyethylene (UHMWPE)/epoxy ply. Additionally, a paperboard/epoxy lamina is introduced to induce functional grading based on layerwise shock impedance mismatches. Shock impact experiments are conducted using a shock tube equipped with helium as the driver gas. Critical shock parameters, including Mach Number, positive impulse, and peak overpressure, are meticulously evaluated. For validation purposes, a numerical model is employed to project the damage profile as a function of radial distance across different laminate sequences. The study unveils that ply deformations are strongly influenced by the arrangement of core layers, particularly the positions of the paperboard and UHMWPE layers within the core structure. To contextualize the findings, the shock impact results obtained from this study are compared with those from prior experiments that employed nitrogen-driven shocks.

The influence of real gas effects and a turbulent boundary layer on shock wave attenuation in the expansion tube is studied by numerically solving the axisymmetric compressible Navier–Stokes equations with an adaptive mesh refinement technique. Numerical simulation results reveal that the ideal gas assumption is not applicable to the expansion tube, and the turbulent boundary layer plays a major role in decreasing the shock wave speed in the acceleration tube of the expansion tube. Shock wave attenuation is attributed to the turbulent boundary layer decreasing the pressure behind the shock wave. The numerical simulations that include the real gas effects and the development of turbulent boundary layers qualitatively agree with analytical solutions in the shock tube, and they show good agreement with the experimental results, especially for the shock speed in the acceleration tube of the expansion tube. Both effects should be considered in the numerical simulation model aimed to support experiments in expansion tubes.

In this work, a novel coupled finite-volume method (FVM) and a smoothed-particle-hydrodynamics (SPH) method were developed for the simulation of interactions between inviscid shock waves and structures. In this approach, which considers the particles of a meshless method immersed in an FVM grid, the FVM grid cells are classified into either pure or mixed FVM cells, the latter of which contain SPH particles. A finite-element-method shape function is applied to map the variables from the SPH particles to the FVM cells, and the nodal and cell velocities are then obtained. The interaction of the fluid with the structure is computed using moving reflection boundary conditions at cell interfaces with SPH particles. The interactions of the structure with the fluid are computed from the pressure differences around the SPH particles. The processes for computing the coupled FVM–SPH method are described in detail herein. The validity of the presented coupled FVM–SPH method was verified using a theoretical model of a piston, and the numerical results were found to agree well with the theoretical approximations, indicating the accuracy of the proposed coupled method. The results of the method were then compared with the results of an experiment involving a blast-driven steel plate. Good agreement between the experimental and numerical results was obtained, and the maximum difference was 3.44%, demonstrating the effectiveness of the proposed coupled FVM–SPH method when applied to the interaction of a shock wave with a structure.

The viscous shock tube problem is studied using two different solvers, 5th order WENO solver and a 13th order hybrid scheme. The possibility to reach a grid-convergent solution for the Reynolds number Re = 2500 is investigated and an analysis of shock wave / boundary layer interaction details and flow dynamics inside the viscous shock tube is presented. Specific features and accuracy of the used solvers are discussed.The viscous shock tube problem is studied using two different solvers, 5th order WENO solver and a 13th order hybrid scheme. The possibility to reach a grid-convergent solution for the Reynolds number Re = 2500 is investigated and an analysis of shock wave / boundary layer interaction details and flow dynamics inside the viscous shock tube is presented. Specific features and accuracy of the used solvers are discussed.

In this paper, a development of the shock tube at RISE, the National Metrology Institute of Sweden, to extend its capability to the high-pressure regime is presented. The shock tube was developed to be operated in three different configurations: conventional, with an amplification system and with a converging cone. In the conventional and with the amplification system, the well-established shock tube analytical solution was used to calculate the reference pressure, while in the converging cone, a numerical simulation was applied. To demonstrate the capabilities and limitations of each configuration, a device under test (DUT) was characterized. The results show a good agreement in the DUT dynamic response calculated using the three configurations in the overlap regions between them. The uncertainty in measurements was estimated for each configuration. The three configurations complement each other to reach a pressure range from 0.1 MPa to 25 MPa and a frequency range from 0.5 kHz to 500 kHz.

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A numerical simulation of an unsteady gas flow containing inert solid particles in a shock tube is carried out using the interpenetrating continuum model. The gas and dispersed phases are characterized by governing equations that express the concepts of mass, momentum, and energy conservation as well as an equation that shows the change of the volume fraction of the dispersed phase. Using a Godunov-type approach, the hyperbolic governing equations are solved numerically with an increased order of accuracy. The working section of the shock tube containing air and solid particles of various sizes is considered. The shock wave structure is discussed and computational results provide the spatial and temporal dependencies of the particle concentration and other flow quantities. The numerical simulation results are compared with available experimental and computational data.

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Recent development in the field of aerodynamics have led to the studies of short duration high enthalpy flows. Such studies enable to simulate real time conditions that are encountered by aerospace vehicles at supersonic and hypersonic speeds. Shock tunnels are used for researches in the field of high-speed flows where shock tubes are used to generate shock waves that propagate through the test gas raising both its temperature and pressure. The present work is done to numerically simulate the shock tunnel of Mach 6. A reference shock tube is initially solved using a 2D transient solver and validated with published results. In the validation, flow development and shock movement are captured as well as shock wave boundary layer (SWBL) interaction is observed in detail. Hence the triple point behavior is studied for the reflected shock wave. Validation results are in good agreement with published results. Two combinations are analyzed using helium and air as driving gases with air as driven gas. It is shown that peak pressures for helium are higher than air as noted in literature. Finally, the shock tube is attached to a Mach 6 test circuit with a nozzle and test section. The results indicate that a stable and uniform Mach 6 flow is developed inside the test section.

Flat-scored metal diaphragms are essentially used in various hypersonic impulse facilities as quick-opening valves. Their burst pressure is a key parameter to optimize the performance of shock wave experimental devices and ensure the activation of overpressure safety devices. However, the conventional method to predict the burst pressure relies on time-consuming experiments that pose significant challenges for ultrahigh driving conditions. In this study, the finite element method (FEM) based on the Johnson–Cook model is adopted to predict the burst pressure of diaphragms used in a shock tube. The influences of the diaphragm thickness and groove depth on the burst pressure are analyzed. A simplified approximation based on the simulation results is obtained to estimate the burst pressure under a static load rapidly. This method is more generalizable than the existing equation and produces results in good agreement with experimental results. Furthermore, the burst pressure is investigated under different dynamic loads using the proposed FEM method. The results show that the dynamic load results in larger burst pressures than the static load, indicating that the burst pressure depends on the load type, the loading rate, and the magnitude of the applied forces.

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Aiming at the problem of difficulty to generate small amplitude step pressure to meet the requirement of dynamic pressure calibration in shock tube device, this paper studies the active incomplete broken diaphragm method and establishes the relevant theoretical formula. Simulation and experimental studies show that incomplete broken diaphragm can reduce the magnitude of shock step pressure to a certain extent, but the following vortex behind the diaphragm will affect the pressure distribution and the step pressure quality in the shock tube. A transition mechanism with linear variable inner diameter is designed to reduce the impact of vortex, and the simulation and experimental results show its effectiveness.

Accurate dynamic pressure measurements are increasingly important. While traceability is lacking, several National Metrology Institutes (NMIs) and calibration laboratories are currently establishing calibration capacities. Shock tubes generating pressure steps with rise times below 1 μs are highly suitable as standards for dynamic pressures in gas. In this work, we present the results from applying a fast-opening valve (FOV) to a shock tube designed for dynamic pressure measurements. We compare the performance of the shock tube when operated with conventional single and double diaphragms and when operated using an FOV. Different aspects are addressed: shock-wave formation, repeatability in amplitude of the realized pressure steps, the assessment of the required driver pressure for realizing nominal pressure steps, and economy. The results show that using the FOV has many advantages compared to the diaphragm: better repeatability, eight times faster to operate, and enables automation of the test sequences.

In experimental study of spherical shock waves in a conical shock tube, it was found that the amplitude of the shock wave turns out to be less than that calculated on the assumption of instantaneous removal of the diaphragm separating the high and low pressure chambers. To interpret the revealed effect, we analyzed the results of numerical modeling, taking into account the effect of diaphragm fragments on the formation and propagation of a shock wave.

Continuous generation of shock waves without replacing the diaphragm between the high-pressure and low-pressure sections of the shock tube could be applied to actuators with pistons moving at high speed and high power. The realization of actuators using such shock waves is expected to play an important role in industrial equipment that requires high-speed actuation. Previous reports described performance experiments involving a shock wave generator with two shock tubes facing each other in which it was shown that it is possible to cause the drive piston to reciprocate by adjusting the initial conditions. In this study, we report the behavior of a piston in a shock wave generator that moves the piston from the initial position to the target position.

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A hypersonic shock tunnel is a primary tool used for basic experimental research and may be used in engineering and university courses to study compressible flows involving shock waves. In the present study, a pneumatically operated shock tunnel is demonstrated for hypersonic flow studies. The high-pressure nitrogen gas is used to drive a pneumatic cylinder, which is used to burst the thin metal diaphragms. Tunnel-free stream conditions are quantified using the measured pressure values and by applying shock tube relations. The free-stream Mach number of 5.5-7.2 is achieved by varying the bursting pressure and test gas pressure from 2.1 to 4.5 bars and 0.2 to 0.5 bar, respectively. The simulation is performed and the shock standoff distance quantified, and the stagnation pressures measured. The results demonstrate that the pneumatically operated tunnel enhanced operation capacity compared to the manually operated tunnel and well suits the academic hypersonic research and developmental activities.

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Abstract The investigation of shock/blast wave diffraction over various objects has garnered significant attention in recent decades on account of the catastrophic changes that these waves inflict on the environment. Equally important flow phenomena can occur when the moving expansion waves diffract over bodies, which has been hardly investigated. To investigate the effect of expansion wave diffraction over different bodies, we conducted shock tube experiments and numerical simulations to visualise the intricate wave interactions that occur during this process. The current investigation focuses on the phenomenon of expansion wave diffraction across three distinct diffracting configurations, namely the bluff, wedge and ogive bodies. The diffraction phenomenon is subsequently investigated under varying expansion wave strengths through the control of the initial diaphragm rupture pressure ratios. The shock waves generated by the expansion wave diffraction in the driver side of the shock tube, which was initially identified in numerical simulations by Mahomed & Skews (2014 J. Fluid Mech., vol. 757, pp. 649–664), have been visualised in the experiments. Interesting flow features, such as unsteady shock generation, transition, and symmetric/asymmetric vortex breakdown, have been observed in these expansion flows. An in-depth analysis of such intricate flow features resulting from expansion wave diffraction is performed and characterised in the current study.

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Shock detection is a crucial technique for flow field visualization, significantly aiding in feature recognition and attracting considerable academic interest. However, the disturbance shadows in shock tubes present complex structures, low image quality, and high gradient continuity, which complicate the accurate identification of weak reflected waves and shock disturbances using existing methods. Additionally, ensuring precision in the calculation of geometric structure parameters remains a challenge. To tackle these issues, this paper proposes a cascaded shock disturbance feature extraction method. The methodology begins with preprocessing the original shadow images to generate a binary feature map. A vector method is then employed to pinpoint the pixel positions of shock wave edges and compute the axial motion speed between adjacent frames. The two-dimensional geometry of the reflected bow shock is derived through morphological erosion and dilation, skeletonization, and least-squares curve fitting. Experimental results demonstrate that the proposed method achieves an axial velocity extraction error margin of less than 5%.

Ground-based testing facilities are very crucial and helpful in conducting experiments for various aerodynamics studies such as flow analysis, estimation of aerodynamic forces, heat transfer analysis etc. As the initial phase of the study, similar to the available ground-based facility, a shock tube has been designed with different geometrical configurations to conduct the experiments with different aerodynamic test models at several test conditions. Each section of the designed shock tube is further fabricated with SS304 stainless steel material by keeping safety in mind under high-pressure working conditions. Before conducting experiments in a shock tube, a calibration experiment is important to understand the workings of the shock tube by estimating the shock tube parameters such as Shock Mach Number, Reflected Shock Mach Number, etc. After completion of calibration, an aerodynamic drag force study is performed to test this facility. For this, initially, an experiment was conducted with piezofilms-based stress wave force balance along with the hemispherical model by mounting at the end of the shock tube. Dynamic calibration of model-balance assembly is also performed to estimate the System Response Function by employing the well-developed force prediction algorithm, i.e., De-convolution and ANFIS after training. A trained algorithms are further used to predict the drag force over the designed test model from strain-time history responses. This Chapter mainly focused on the design, fabrication, and calibration of a new shock tube facility. Testing of the shock tube facility has been done in a simple manner.

A shock-tube facility capable of generating a planar shock with the Mach number higher than 3.0 is developed for studying Richtmyer-Meshkov instability induced by a strong shock wave (referred to as strong-shock RMI). Shock enhancement is realized through the convergence of shock within a channel with the profile determined by using shock dynamics theory. The facility is designed considering the repeatability of shock generation, transition of shock profile, and effects of viscosity and flow choking. By measuring the dynamic pressure of the tube flow using pressure sensors and capturing the shock movement through the high-speed shadowing technique, the reliability and repeatability of the shock tube for generating a strong planar shock are first verified. Particular emphasis is then placed on the ability of the facility to study strong-shock RMI, for which a thin polyester film is adopted to form the initial interface separating gases of different densities. The results indicate that the shock tube is reliable for conducting strong-shock RMI experiments.

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Shock tube experiments are used to investigate non-equilibrium thermochemistry and radiative processes in reacting gas hypersonic flows. Boundary layer and shock structure are known to influence the spatial variation of the test slug state properties. This work derives and validates a novel method for viscous, quasi-one-dimensional, non-equilibrium flow in a shock tube assuming constant shock speed. The proposed method fully resolves the shock structure. Mirels' estimate for boundary layer growth around the test slug determines the dilation rate at the centerline. This, along with relevant boundary conditions, appropriately models core flow in a shock tube. The flow equations are discretized by finite differences on a staggered grid. The resulting highly non-linear set of algebraic equations is solved by Newton iterations. The Jacobian matrix is block tridiagonal with a Schur complement, allowing efficient inversion. This culminates in a unique and computationally efficient quasi-one-dimensional method offering improved modeling of the physical characteristics of shock tube experiments. Results of a 3 km/s, 66.6 Pa argon test case solved by a viscous, axisymmetric Navier–Stokes solution had agreement with the proposed method in temperature and pressure profiles to within 2% and post-shock velocity to within 15%. Reacting gas shock tube experiments in synthetic air and synthetic Titan atmospheres were analyzed. Radiance values in the non-equilibrium and equilibrium regions were compared under various assumptions for the shock structure and radial velocity distribution. These results highlight the necessity of a dedicated shock tube solver when analyzing shock tube thermochemistry, particularly when determining reaction rates and relaxation parameters.

Technological progress demands accurate measurements of rapidly changing pressures. This, in turn, requires the use of dynamically calibrated pressure meters. The shock tube enables the dynamic characterization by applying an almost ideal pressure step change to the pressure sensor under calibration. This paper evaluates the effect of the dynamic response of a side-wall pressure measurement system on the detection of shock wave passage times over the side-wall pressure sensors installed along the shock tube. Furthermore, it evaluates this effect on the reference pressure step signal determined at the end-wall of the driven section using a time-of-flight method. To determine the errors in the detection of the shock front passage times over the centers of the side-wall sensors, a physical model for simulating the dynamic response of the complete measurement chain to the passage of the shock wave was developed. Due to the fact that the use of the physical model requires information about the effective diameter of the pressure sensor, special attention was paid to determining the effective diameter of the side-wall pressure sensors installed along the shock tube. The results show that the relative systematic errors in the pressure step amplitude at the end-wall of the shock tube due to the errors in the detection of the shock front passage times over the side-wall pressure sensors are less than 0.0003%. On the other hand, the systematic errors in the phase lag of the end-wall pressure signal in the calibration frequency range appropriate for high-frequency dynamic pressure applications are up to a few tens of degrees. Since the target phase measurement uncertainty of the pressure sensors used in high-frequency dynamic pressure applications is only a few degrees, the corrections for the systematic errors in the detection of the shock front passage times over the side-wall pressure sensors with the use of the developed physical dynamic model are, therefore, necessary when performing dynamic calibrations of pressure sensors with a shock tube.

Shock tube flows can be used to investigate nonequilibrium thermochemistry and radiative processes found in hypersonic flows. The flow in a shock tube contains many flow nonuniformities, in particular boundary-layer effects. For the purpose of studying the properties of the test slug, the flow behind the shock is usually considered analogous to the stagnation line flow over a blunt body. In reality, radial and longitudinal velocity distributions in the two flows are different, and so a coordinate transformation is needed to match time-of-flight profiles. This work develops a method to approximately transform the postshock distance for normal and blunt body shocks to a shock tube flow using a Mirels analysis. The effects of shock tube diameter and shock speed variation are highlighted along with the importance of postshock temperature and density rises. This is then applied to blunt body simulations of NASA EAST data for air and Titan tests. This showed that minimal difference is encountered for fast reacting flows. However, large differences can be seen in the slower reacting Titan tests, which to date have been misinterpreted when compared to blunt body simulations.