Behavior Of Shock Waves Research Articles

Signum-gordon shock waves with spherical symmetry in (2+1) and (3+1) dimensions

Abstract This study introduces novel, exact solutions to the scalar field Signum-Gordon equation that feature a discontinuity near the light cone. These solutions, applicable in higher spatial dimensions (n > 1), extend previous limitations to one dimension. Our chosen ansatz leads to an ordinary equation with exact solutions obtained for n = 2 and 3 spatial dimensions. The shock wave’s energy trapped within the light cone is proportional to the wave’s n-dimensional volume and the field discontinuity at the wavefront. The investigation delves further into the behavior of shock waves when their driving force, represented by a delta function at the light cone, is disabled. Disabling this delta function disrupts energy transfer, preventing the wave’s propagation as predicted by analytical calculations. We identify the region within the light cones where the field remains unaffected. Two-dimensional (n = 2) simulations reveal the formation of intriguing structures upon source removal. These structures include a central, stable feature resembling an oscillon and a surrounding ring that breaks down into smaller oscillations.

Analytical Solution and Energy Behavior to a Forced Shock Wave Problem Under Dusty Gas Regime

ABSTRACTIn the presented research work, we have solved a new kind of problem of forced shock waves in a compressible inviscid perfect gas having dirty (dust) particles of small size in a one‐dimensional unsteady adiabatic flow. The approach that we have used is referred to as the generalized geometry approach. Here, we investigated how the density of the zone, which is undisturbed, changes as a function of the position from the point of the source of explosion. In addition, we have obtained analytically a novel solution to the problem in the form of a new rule of power of time and distance. Further, we have investigated the energy behavior of forced shock waves and interaction within the environment containing dust particles. Also, the behavior of the entire energy of a forced shock wave is expounded at different Mach numbers, respectively, for planar geometry, cylindrically symmetric geometry, and spherically symmetric geometry under a dusty gas medium. Furthermore, the findings show that dust particles in a gas produce a more sophisticated representation rather than the standard gas dynamics.

Numerical simulation and experimental investigation of the propagation law of plasma pulse shock waves

Abstract Plasma pulse shock wave rock-breaking technology represents a novel approach to rock fracturing. Present research on this subject largely addresses rocks and electrodes, yet often neglects the critical influence of shock waves in the rock-breaking process. Therefore, it is necessary to further study the propagation law of the shock wave and its reflection and transmission. This paper undertakes experimental simulations using the RHT rock model to explore the propagation process of plasma pulse shock waves based on two variables: the medium and the shape of the electrode. Integrated with one-dimensional stress wave theory, the study examines the impact of four specific parameters—dielectric thickness, surrounding rock height, surrounding rock density, and surrounding rock porosity—on the reflection and transmission rates of shock waves. Pressure data collected from experimental platform are utilized to validate the study’s conclusions. The findings indicate that the propagation behaviors of shock waves differ significantly between water and air mediums. The shape of the electrode causes significant differences in the pressure exerted by the shock wave at the same location. Both the thickness of the dielectric and the porosity of the surrounding rock show a positive correlation with the reflection coefficient and a negative correlation with the transmission coefficient, while the density of the surrounding rock exhibits an inverse relationship. The height of the surrounding rock is irrelevant to both reflection and transmission coefficients.

Experimental Study on Ignition and Pressure-Gain Achievement in Low-Vacuum Conditions for a Pulsed Detonation Combustor

Pressure-gain combustion (PGC) represents a promising alternative to conventional propulsion systems for interplanetary travel due to its key advantages, including higher thermodynamic efficiency, increased specific impulse, and more compact engine designs. However, to elevate this technology to a sufficient technology readiness level (TRL) for practical application, extensive experimental validation, particularly under vacuum conditions, is essential. This study focuses on the performance of a pulsed-detonation combustor (PDC) under near-vacuum conditions, with two primary objectives: to assess the combustor’s ignition capabilities and to characterize the shock wave behavior at the exit plane. To achieve these objectives, high-frequency pressure sensors are strategically positioned within both the vacuum chamber and the combustor prototype to capture the pressure cycles during operation, providing insights into pressure augmentation over a period of approximately 0.5 s. Additionally, the Schlieren visualization technique is employed to analyze and interpret the flow structures of the exhaust jet. The combination of these experimental methods enables a comprehensive understanding of the ignition dynamics and the development of shock waves, contributing valuable data to advance PGC technology for space-exploration applications.

Instability of isolator shocks to fuel flow rate modulations in a strut-stabilised scramjet combustor

Abstract Reynolds-Averaged Navier–Stokes (RANS) simulations, both steady and unsteady, are used to investigate supersonic, chemically reacting, flow fields inside a strut-stabilised supersonic combustion ramjet (scramjet) engine operating under different fuel flow rates. Fully supersonic, fully subsonic and mixed modes of operations inside the combustor, obtained at different fuel flow rates, are studied numerically through shock wave visualisations and top-wall static-pressure probing. The effect of changing fuel flow rates, imposed both suddenly and gradually, on the behaviour of shock waves and wall pressure profiles are studied in detail. For certain modes of combustion characterised by the presence of oblique shocks at the strut, shockwaves in the combustor respond predictably to an increase or decrease in fuel flow rate attaining the steady state flow fields as predicted by RANS simulations for those fuel flow rates. For certain other modes of combustion, characterised by the presence of shockwaves in the isolator and the absence of oblique shocks at the leading edge of the strut, shockwaves in the flow field appear unstable to fuel flow rate modulations. For such cases, any change in fuel flow rates, sudden or gradual, increase or decrease, causes the isolator shocks to immediately move upstream and eventually out of the isolator. A plausible physics-based explanation of the observed phenomena is presented.

Influences in Experimental Studies on the Characteristics of Transonic Shock Buffet

This article examines the evolution of transonic shock buffet on the OAT15A supercritial airfoil, aspiring to elucidate some of the causes of disparate buffet-relevant settings reported in the literature. Experimental campaigns on three distinct chord lengths are conducted thus resulting in chord Reynolds numbers of 1.3×106, 2.0×106, and 2.7×106. Continuous variations in Mach and AoA allow mapping the shock wave behavior across a large parameter space and capturing the transition between prebuffet, onset, developed buffet, and offset. High-speed focusing schlieren imaging is employed to extract the temporal and spectral nature of buffet and to deduce key quantities that characterize the unsteadiness. Three-dimensional effects along the span due to interference with the side walls are assessed thoroughly, revealing that phases of upstream shock motion and large separation are accompanied by 3D distortion. Even though this effect gains relevance at reduced aspect ratio, a substantially 2D character of the shock surface around the centerplane is confirmed. Fully developed buffet governed by a 2D buffet mode is proven to exist across all test cases, although the buffet peak condition is gradually shifted toward reduced angle of attack, yet greater Mach number with increased Reynolds number. Conversely, accompanied by severely increased angles of attack, the buffet mechanism appears more volatile for small chord length and is consolidated with enlarged chord, which strongly suggests a dependence on the state of the turbulent boundary layer.

Numerical Solution of Burgers Equation Using Finite Difference Methods: Analysis of Shock Waves in Aircraft Dynamics

In this research, the Lax, the Upwind, and the MacCormack finite difference methods are applied to the experimental solving of the one-dimensional (1D) unsteady Burger's Equation, a Hyperbolic Partial Differential Equation. These three numerical analysis-solving methods are implemented for accurate modeling of shock wave behavior high-speed flows that are necessary for aerospace engineering design. This research analysis proves that the MacCormack technique is the one that treats the differential equations with second-order accuracy. This method is quite preferred when it comes to numerical simulations because of its advanced level of accuracy. Although the Upwind and Lax methods are slightly less accurate, they show the development of shock waves that give visualizations to better understand the flow dynamics. Also, in this study, the impact of varying viscosity coefficients on fluid flow characteristics by using the lax (a numerical method for solving the viscous Burgers equation) is investigated. This identification of the phenomenon sheds light on the behavior of boundary layers, which, in turn, can be used to improve the design of high-speed vehicles and lead to a greater understanding of the area of ​​fluid dynamics.

Design, Fabrication, and Commissioning of Transonic Linear Cascade for Micro-Shock Wave Analysis

Understanding shock wave behavior in supersonic flow environments is critical for optimizing the aerodynamic performance of turbomachinery components. This study introduces a novel transonic linear cascade design, focusing on advanced blade manufacturing and experimental validation. Blades were 3D-printed using Inconel 625, enabling tight control over the geometry and surface quality, which were verified through extensive dimensional accuracy assessments and surface finish quality checks using coordinate measuring machines (CMMs). Numerical simulations were performed using Ansys CFX with an implicit pressure-based solver and high-order numerical schemes to accurately model the shock wave phenomena. To validate the simulations, experimental tests were conducted using Schlieren visualization, ensuring high fidelity in capturing the shock wave dynamics. A custom-designed test rig was commissioned to replicate the specific requirements of the cascade, enabling stable and repeatable testing conditions. Experiments were conducted at three different inlet pressures (0.7-bar, 0.8-bar, and 0.9-bar gauges) at a constant temperature of 21 °C. Results indicated that the shock wave intensity and position are highly sensitive to the inlet pressure, with higher pressures producing more intense and extensive shock waves. While the numerical simulations aligned broadly with the experimental observations, discrepancies at finer flow scales suggest the need for the further refinement of the computational models to capture detailed flow phenomena accurately.

Gravitational force-induced changes in collisionless shock wave behavior in a charge-varying nonthermal dusty plasma

Gravitational force-induced changes in collisionless shock wave behavior in a charge-varying nonthermal dusty plasma

Magnetosonic shock waves in degenerate electron–positron–ion plasma with separated spin densities

This study investigates magnetosonic shock waves in a spin-polarized three-component quantum plasma using the quantum magnetic hydrodynamic model. We explore the influence of spin effects, specifically spin magnetization current and spin pressure, on shock wave behavior. Numerical analysis of the linear dispersion relation under varying parameters such as positron imbalance, spin polarization ratio, plasma beta, quantum diffraction, and magnetic diffusivity reveals differential impacts, with diffusion exerting significant influence on the plasma frequency. Our findings highlight the sensitivity discrepancy between the real and imaginary parts of the dispersion relation. Furthermore, nonlinear behavior of magnetosonic shock waves is examined via the Korteweg–de Vries–Burgers equation, showcasing transitions between oscillatory and monotonic wave patterns based on changes in dimensionless parameters. Notably, we observe the combined effects of spin-up and spin-down positrons with spin-up and spin-down electrons on shock wave dynamics, contributing to a deeper understanding of spin-plasma interactions with implications across various fields.

Numerical investigation of annular expansion-deflection nozzle flow under varying backpressure changing rate

The characteristics of flow and thrust evolution of an annular Expansion-Deflection (ED) nozzle are numerically investigated under varying backpressure changing rates during ascending and descending trajectories. The objective is to test the sensitivity of unsteady behaviors of shock waves in the ED nozzle to backpressure changing rate, and to further elucidate the thrust evolution mechanism and mode transition hysteresis. The movement of shock reflection points on the nozzle wall follows two flow mechanisms, namely, shock self-excited oscillations and rapid backpressure changes. A low backpressure changing rate enables shock self-excited oscillations, leading to a reciprocating motion of the shock waves accompanied by thrust oscillations, while a high backpressure changing rate suppresses the shock self-excited oscillations, leading to a unidirectional motion of the wave system on the nozzle shroud wall. A criterion for distinguishing ED nozzle operation modes is proposed, which relies on the loading inflection points of the nozzle pintle base and exhibits a fast and user-friendly feature. A dual-wake mode hysteresis region is defined to quantify the hysteresis in nozzle mode transition, with the span of the region decreasing as the backpressure changing rate slows down. The present work helps in understanding the unsteady flow mechanism and thrust evolution in ED nozzles.

Exploring dust-ion acoustic shocks in a plasma in the light of phase plane analysis

This paper presents a comprehensive exploration of shock waves in a dusty plasma, incorporating the dynamics of inertial dust and ions with Maxwellian distributed electrons. By deriving the Korteweg-de Vries-Burgers (KdV-B) equation and by using its standard solution we analyze the characteristics of the shock front under varying parameters. Furthermore, we conduct a phase plane analysis to elucidate the system's behavior and dynamics by tuning in the parameters that provide various types of perturbation in the system. The investigation sheds light on the intricate behavior of shock waves in dusty plasmas and contributes valuable insights to the understanding of plasma dynamics.

Effect of ethanol/n-hexane blending ratio on behaviors of shock waves in flash-boiling jets

The rapid phase change of flash boiling jets would induce shock waves, but there is a lack of investigations on how the component blending ratios influence the characteristics of such shock waves. In this study, ethanol/n-hexane blends with different blending ratios were used to investigate this sort of shock waves using high-speed microscopic Schlieren photography. The tests were carried out in a constant volume vessel under varying ambient pressures (Pamb) and liquid temperatures (Tliquid). The shock size was carefully examined in terms of length and width. For all the test blends, both increasing Tliquid and decreasing Pamb could enlarge the shock length and width, but with different increments. Furthermore, with the increase in ethanol blending ratio, monotonic decrease in shock length and non-monotonic change in shock width were found, which can be attributed to the change in hydrogen bond concentration, which alters the axial distribution of evaporation intensity. The evaporation for the liquids with high ethanol blending ratios (>20 %) was weakened in contrast to that of pure n-hexane due to the existence of hydrogen bonds, causing the smaller shock size. At the low ethanol blending ratios (10 % & 20 %), the hydrogen bonds within ethanol were diluted and destroyed by n-hexane, enhancing the escape of ethanol from the blends. Thus, in contrast to the evaporation of pure n-hexane, the evaporation for the liquids with low ethanol was stronger, and the excessive energy due to the sudden pressure drop was released more rapidly at the nozzle exit. The former caused the increase in shock width, and the latter led to the shorter shock length. Finally, a good correlation was proposed between shock size and ΔG·Pamb-0.5(ΔG denoting the Gibbs energy difference during phase change).

Расчеты сжатия сферической слоистой системы ударными волнами с учетом переноса тепла излучением в различных приближениях

Numerical modeling is one of the basic tools to investigate physical phenomena that occur in materials compressed by shock waves. A study of the behavior of shock waves using simplified models is helpful in the analysis of more complex systems, for instance, in the problems of inertial thermonuclear fusion on laser facilities. Mathematical simulation of the nonstationary radiative heat transfer in a spectral kinetic statement is rather complicated because the system of equations is nonlinear and large in size. Generally, the kinetic transport equation is solved in 7D phase space, which requires huge computational resources. The initial system is often approximated under certain assumptions but this immediately causes questions as to whether the simplified model is applicable to particular calculations. In this study, several economic radiative heat transfer models were implemented in a 2D hydrodynamic code. Based on these models, test calculations were performed to simulate the compression of a layered spherical system by shock waves, taking into account radiative heat transfer. When the shock wave reaches the center of the sphere, it is focused and reflected. In the neighborhood of the focal point of a converging wave, temperature gradients increase; therefore, thermal conduction and radiation become the main mechanisms of energy dissipation to be considered when taking into account heat transfer. Maximum densities and temperatures at the center of the sphere and their average values in its regions were calculated. In addition, the time when shock and heat waves cross the sphere center was determined, and their behavior before and after focusing at the sphere center was estimated. It is shown that solutions to such problems can be found much faster and with adequate accuracy when applying simplified models.

Impact of Sudden Expansion Structure Length on Shock Wave Dynamics and Autoignition in High-Pressure Hydrogen Releases

This study investigates the effects of expansion structure length on shock wave behavior, specifically focusing on pressure dynamics, and subsequent autoignition in high-pressure hydrogen systems. Using configurations EPT1 and EPT2, along with a direct pipe (SP1) as a control, we analyze how different expansion lengths influence pressure profiles, shock wave attenuation, and ignition phenomena.

Discontinuity waves in temperature and diffusion models

We analyse shock wave behaviour in a hyperbolic diffusion system with a general forcing term which is qualitatively not dissimilar to a logistic growth term. The amplitude behaviour is interesting and depends critically on a parameter in the forcing term. We also develop a fully nonlinear acceleration wave analysis for a hyperbolic theory of diffusion coupled to temperature evolution. We consider a rigid body and we show that for three-dimensional waves there is a fast wave and a slow wave. The amplitude equation is derived exactly for a one-dimensional (plane) wave and the amplitude is found for a wave moving into a region of constant temperature and solute concentration. This analysis is generalized to allow for forcing terms of Selkov–Schnakenberg, or Al Ghoul-Eu cubic reaction type. We briefly consider a nonlinear acceleration wave in a heat conduction theory with two solutes present, resulting in a model with equations for temperature and each of two solute concentrations. Here it is shown that three waves may propagate.

A review of bubble collapse near particles

Bubble–particle interactions are of great importance in cavitation bubble dynamics, especially in the case of silt-laden flow. In this paper, a review of the physical mechanisms involved in bubble collapse near particles is presented, with an emphasis on the jet and shock wave phenomenon. First of all, the collapse of a bubble occurring close to a flat wall is introduced to provide a basis for understanding cavitation behavior near boundaries. Then, with the aim of revealing the physical processes that occur during bubble collapse near particles, this is followed by a detailed discussion, with plentiful examples, of the collapse process (the inception, growth, collapse, rebound, and final disappearance of the bubble) and the formation and behavior of jets (the inception jet, counter jet, and double jets) and shock waves (incident, reflected, jet-induced, and jet-split shock waves).

Investigations on the jets and shock waves of a cavitation bubble collapsing between a wall and a particle

The simultaneous presence of particles and cavitation bubbles has a deleterious effect on the performance and safety of hydraulic machinery through the generation of jets and shock waves. In the present paper, the mechanisms responsible for the generation and the evolution of jets and shock waves from a collapsing cavitation bubble situated between a spherical particle and a wall are simulated using a compressible two-phase flow solver. Specifically, the effects of bubble position on jet and shock wave behavior are qualitatively analyzed. The simulations and experiments reveal three typical cases of jet behavior: a jet toward the wall, double jets, and a jet toward the particle. Needle jets and shock waves are commonly generated by collisions of the bubble interface. In some cases, needle jets are associated with a high impact velocity. It is found that the smaller the distance between the particle and the wall, the higher the pressure generated by the jets and the shock waves on the wall.

Preliminary design of a hypersonic airbreathing vehicle based on four steps: An academic approach to learning

This article proposes a systematic approach for the preliminary design of a hypersonic airbreathing (scramjet) vehicle within an academic context. The goal is to serve as an educational tool, focusing on teaching students the fundamental physical concepts behind scramjets. The article provides essential equations for generic scramjet designs while explaining the simplifications made from an academic perspective. It demonstrates the use of spreadsheets as a user-friendly tool to modify parameters and observe the behavior of shock waves. The article outlines a four-step procedure. It includes estimating atmospheric properties, designing the supersonic inlet, calculating combustion chamber parameters, and determining postcombustor properties. An academic exercise illustrates these steps for a scramjet flying at a specific velocity and altitude. The results show that this procedure, combined with spreadsheets, enables a rapid prediction of thermodynamic properties, enhancing the understanding of the fundamental physics behind hypersonic airbreathing vehicles.

Analysis of spontaneous ignition of hydrogen-enriched methane in a rectangular tube

This study investigates the spontaneous ignition of high-pressure hydrogen-enriched methane in air within a rectangular tube. A computationally efficient approach has been adopted, utilizing a reduced reaction mechanism and ignition delay model within a 3D Large Eddy Simulation (LES) framework. This approach overcomes the limitations of traditional 1D and 2D simulations with detailed chemistry models, which are unable to accurately reproduce the complex 3D shock wave structures within the tube. The simulated shock wave behavior during 9 MPa hydrogen leakage (case 1) and 11 MPa 90 vol% hydrogen/10 vol% methane mixture leakage (case 2) are found to agree well with experimental observations. In case 2, the hot spots generated by reflected shock waves and Mach reflections ignite the hydrogen/methane-air mixture, resulting in three sequential spontaneous ignitions. The flame is observed to primarily propagate along the tube corners and wall centers, with the central ignition spreading across the entire cross-section. For the 25 MPa 24 vol% hydrogen/76 vol% methane mixture leakage (case 6), the shock intensity is significantly reduced due to the increased methane proportion, leading to spontaneous ignition only at the tube corners when the hemispherical shock wave reflects from the wall. The flame predominantly forms downstream along the tube corner, gradually spreading along the tube wall. It is indicated that while the probability of spontaneous ignition decreases with increasing methane content, the risk remains significant under sufficiently high pressures. To the best our knowledge, this study represents the first 3D large eddy simulation of spontaneous ignition for high-pressure hydrogen-enriched methane leakage into air, providing valuable insights into the underlying physical phenomena.