Shock Wave Front Research Articles

Численное моделирование течения термически и химически неравновесного воздуха за фронтом ударной волны

We used the model of a five-component air mixture flow behind the front of a one-dimensional shock wave to compute the flow parameters for shock front temperatures of up to 7000 K, taking into account the variable composition, translational and vibrational temperatures and pressure in the relaxation zone. Vibrational level population in oxygen and nitrogen obeys the Boltzmann distribution with one common vibrational temperature. We consider the effect that temperature nonequilibrium has on the chemical reaction rate by introducing a nonequilibrium factor to the reaction rate constant, said factor depending on the vibrational and translational temperatures. We compared our calculation results for dissociation behind the shock front to the published data concerning temperature nonequilibrium in a pure oxygen flow behind a shock wave front for two different intensities of the latter. The comparison shows a good agreement between the vibrational temperature, experimental data and calculations based on the experimental values of vibrational temperature and molality. We computed the parameters of thermodynamically nonequilibrium dissociation in the air behind the shock wave front, comparing them to those of equilibrium dissociation and calculation results previously published by others. The study demonstrates that the molality values computed converge gradually with those found in published data as the distance from the shock front increases. We list the reasons for the discrepancy between our calculation results and previously published data

Coherence of oscillations in matter andsupernova neutrinos

We study the propagation coherence for neutrino oscillations inmedia with different density profiles.For each profile, we find the dependence of thecoherence length, Lcoh, on neutrino energy andaddress the issue of correspondenceof results in the distance and energy-momentum representations.The key new feature in matter is existence ofenergy ranges with enhanced coherence around the energiesE0 of “infinite coherence” at which Lcoh→∞.In the configuration space, the infinite coherence correspondsto equality of the (effective) group velocities of the eigenstates.In constant density medium, there is a unique E0, which coincides with the MSW resonance energy of oscillations of mass states and is close to the MSW resonance energy of flavor states.In the case of massless neutrinos or negligible masses in a very densemediumthe coherence persists continuously.In the adiabatic case, the infinite coherence is realized for periodicdensity change. Adiabaticity violation changes the shape factors ofthe wave packets (WPs) and leads to their spread. In a medium with sharp densitychanges (jumps), splitting of the eigenstates occurs at crossingof each jump. We study the increase of the coherence lengthin a single jump and periodic density jumps — castle-wall (CW) profiles.For the CW profile, there are several E0 corresponding to parametric resonances. We outlined applications of the results for supernova neutrinos.In particular, we show that coherence between two shock wave fronts leads to observable oscillation effects, and our analysis suggests that the decoherence can be irrelevant for flavor transformations in the central parts of collapsing stars.

In-silico experimentations of multimode shock response of polyurea

Computational studies can supplement existing ultrahigh strain rate experimental techniques in the absence of invasive full-field measurement and visualization. In this study, a computational model is employed to elucidate various phenomena accompanying the generation, propagation, and interaction of multimode shock waves in a viscoelastic material. Specifically, a 4 mm diameter polyurea plug with a thickness of 0.5 mm was modeled as a linear viscoelastic solid, where the relaxation behavior of the shear modulus was described using a Prony series while the bulk modulus was assumed to be linear elastic based on the Poisson's ratio of polyurea. The results are presented in three case studies, where a different type of shock wave was emphasized in each case while focusing on the regions at the leading and trailing edges of the shock wavefront. Generally, the wavefront interacted with the accompanying and reflected waves, resulting in compromising the purity of the sought-after loading condition, especially during the return trip of the wave upon approaching the free surface. In Case Study I, the propagation of laser-induced pressure wave remained pure during the forward trip towards the free surface but was compromised by the accompanying shear wave and side spherical patterned pressure waves. Case Study II simulated the generation of surface waves by incorporating a ring-shaped loading site, where the release of a surface displacement was found to be focused and amplified at the central point. In the final case study, Case Study III, the applied shear wave at ultrahigh strain rate generated secondary pressure and horizontal shear waves at the edges of the loading site, which complicated the loading scenario but provided new insight into the interaction of laser-generated shock waves within the solid. The results can be used to improve the analysis of experimental data to quantify the accompanying deformation and failure mechanisms of polymers subjected to hypervelocity impacts.

Features of optical breakdown of aqueous colloidal solutions of ferric oxide (Fe2O3) nanoparticles occurring on individual or on two closely located nanoparticles

• Optical breakdown in a solution of nanoparticles occurs according to 2 scenarios. • In 78%, breakdown occurs on one nanoparticle (NP), in 22% – on two NPs. • In the case of two NPs, cavitation bubbles with plasma move away from each other at a speed of 3000 m/s. • The motion of flash occurs under the influence of a shock wave from an neighboring breakdown. • Estimated pressure at the shock wave front is 2300 MPa. A streak camera was used to study the dynamics of the development of plasma flashes of the optical breakdown that occurs in aqueous solutions of Fe2O3 nanoparticles. It is shown that optical breakdown can occur according to two scenarios – initiated on single nanoparticle (78%) or on two closely located nanoparticles (22%). When optical breakdown occurs on two nanoparticles, cavitation bubbles move away from each other on 50 μm with velocity of 3000 m/s under the action of shock waves initiated by the optical breakdown on neighboring particles. The estimated pressure at the shock wave front is approximately 2300 MPa.

Effects of geometric similarity ratio on the disturbance amplitude of shock-wave front in viscosity measurement

Geometric similarity ratio is one of the important factors that affects the disturbance amplitude of shock-wave front in viscosity measurement. In this paper, the Euler difference scheme of two-dimensional (2D) equations of viscous fluid mechanics is used to simulate the disturbance amplitude damping curves under different geometric similarity ratios, and the corresponding numerical solutions are shown. The samples of aluminum shocked to 80 GPa are taken as an example. The simulation results show that the initial conditions, material viscosity, wavelength, and sample geometric similarity ratio affect the evolution of the shock front sine wave disturbance. For flyer-impact flow field, the phase shift increases from 0 to a certain value with the viscosity coefficient for sample with wavelength [Formula: see text] mm and geometric similarity ratio [Formula: see text], 0.1. So, the geometric similarity method can be used to measure the viscosity of material. But it is found that the phase shift is sensitive to the geometric similarity ratio, which should be considered in Zaidel’s equation. So, some flyer-impact experiments will be carried out to determine the simulation results, and find the quantity relation of phase shift and viscosity of material in the future investigation.

Addressing the symmetry of a converging cylindrical shock wave in water close to implosion

We report experimental and numerical results relevant to the dynamics in the vicinity of the implosion axis of a strong shock wave generated by an underwater electrical explosion of a cylindrical array. Experiments were conducted using both sub-microsecond and microsecond timescale pulsed generators with stored energy up to ∼5 kJ, delivering ∼420/350 kA with a 320/1000 ns rise time pulses to the array, respectively. The backlighted images of the converging shock wave and the light emission around the cylindrical axis indicate strongly that the shock wave front keeps its azimuthal uniformity as far as r ≈30 μm. Also, images obtained almost simultaneously with the implosion suggest symmetric convergence <2 ns prior to the shockwave's arrival to the axis. In addition, the light emission obtained by a photo-multiplying tube suggests the existence of a ∼200 ns long, almost constant, strong afterglow immediately following the light emission peak related to the implosion.

Theoretical, numerical and experimental study of hypersonic boundary layer transition: Blunt circular cone

• Hypersonic boundary layer transition is studied using various approaches. • Leading edge receptivity is crucial for understanding “transition reversal”. • Centreline and crossflow vortices significantly promote transition on a yawed cone. • The newly proposed C - γ - Re θ transition model works well at various flow conditions. • Valuable transition data is acquired in real flight test for a cone model. This article reviews the hypersonic laminar-turbulent boundary layer transition over a blunt circular cone under support of the National Key Research and Development Program of China (contract No. 2016YFA0401200). Various approaches, including theoretical, numerical, experimental and flight test, are combined to obtain a complete perspective of the transition process as well as some fundamental issues for this kind of flow. The interaction between freestream disturbances and the front shock wave is analysed theoretically, and multiple receptivity routes are unveiled using a sub-zone analysis technique. The entire transition process is captured using high-resolution nano-tracer-based planar laser scattering technique in a quiet windtunnel as well as large-scale high-fidelity direct numerical simulations. Using dynamic mode decomposition, the relationship between the second Mach mode and the low-frequency mode in the late stage of the transition is revealed. The “transition reversal” phenomenon is recovered in two of our conventional windtunnels. The numerical results show that leading-edge receptivity varies significantly for different cone bluntness, which might be responsible for the “transition reversal” phenomenon. For the cone at angles of attack, new instabilities including the leeward centerline vortex instability and the crossflow instability, occur and can significantly promote the transition process. A newly developed C - γ - Re θ transition model can give a good transition front prediction compared to the experimental data. The flight test for a cone model conducted within this project is reviewed, and the correlation between the ground experimental data and the flight data is established.

Losing the shock wave front profile due to interaction with turbulence

In this study, losing the shock wave profiles under interactions with grid turbulence was investigated experimentally and theoretically. We demonstrated that the shock wave contrast on side-view schlieren images gradually decreased to an undetectable level in the experiment. This shock wave ‘vanishment’ occurred at a low shock Mach number with a high turbulent Mach number. With a relatively strong shock wave, the contrast of the shock wave remained detectable although the shock wave profile region was expanded. To understand the shock wave vanishment phenomenon during interaction with turbulence, we established a shock wave vanishment model based on the solution of a one-dimensional interaction between a shock wave and forward induced flow. The criterion of the occurrence of local vanishment of the shock wave was derived as , where is the turbulent Mach number and is the shock Mach number. The proposed shock vanishment model involves the effect of the interaction length and the shock wave recovery characteristics. The derived model explains the vanishment of weak shock wave profile during turbulence with an interaction length of ten times the order of the integral scale of the turbulence, as observed in the experiment.

On the development of testing facilities for the scientific testing center of the rocket and space industry for developmental testing of advanced cryogenic propulsion systems

The paper provides a review of materials on the development of testing facilities in the Scientific Testing Center of the Rocket and Space Industry and the issues involved in raising the efficiency and safety of experimental development of advanced cryogenic propulsion systems for launch vehicles intended for exploration of the near and deep space. It shows that the most dangerous tests are those that are conducted on engines and propulsion systems that use oxygen, methane and hydrogen as propellant components. They may involve containment failure in the propellant system in off-nominal situations — emergency releases of propellant components, explosions and fires. It provides calculation results for overpressure in the shock-wave front depending on the mass of the released hydrogen and the factor of its contribution to the explosion. It formulates special and additional safety measures for engine and propulsion system tests in a test facility. Key words: test facility (test stand), propulsion system, safety, off-nominal situation, cryogenic propellant components.

ON THE DEVELOPMENT OF TESTING FACILITIES FOR THE SCIENTIFIC TEST-ING CENTER OF THE ROCKET AND SPACE INDUSTRY FOR DEVELOPMENTAL TESTING OF ADVANCED CRYOGENIC PROPULSION SYSTEMS

The paper provides a review of materials on the development of testing facilities in the Scientific Testing Center of the Rocket and Space Industry and the issues involved in raising the efficiency and safety of experimental development of advanced cryogenic propulsion systems for launch vehicles intended for exploration of the near and deep space. It shows that the most dangerous tests are those that are conducted on engines and propulsion systems that use oxygen, methane and hydrogen as propellant components. They may involve containment failure in the propellant system in off-nominal situations — emergency releases of propellant components, explosions and fires. It provides calculation results for overpressure in the shock-wave front depending on the mass of the released hydrogen and the factor of its contribution to the explosion. It formulates special and additional safety measures for engine and propulsion system tests in a test facility. Key words: test facility (test stand), propulsion system, safety, off-nominal situation, cryogenic propellant components.

Comparative investigation of microjetting generated from monocrystalline tin surface and polycrystalline tin surface under plane impact loading

With considering the scattering effect of grain boundary and the grain orientation, the molecular dynamics is used for the first time to comparatively investigate microjetting generated by monocrystalline tin surface and polycrystalline tin surface under plane impact loading in this work. The research results show that when the impact velocity is low, the scattering effect of grain boundary and different grain orientations in a polycrystalline tin will cause the sample to melt inhomogeneously, leading the shock wave front to attenuate, meanwhile, the inhomogeneous melting can result in jet deviating. Comparing with monocrystalline tin, the jet head velocity, jet velocity coefficient, and jet mass coefficient of polycrystalline tin at low impact velocity are all low. Moreover, as the impact velocity increases, this influence decreases and the microjetting results of polycrystalline tin and monocrystalline tin tend to be consistent with each other.

Anomalous dislocation core structure in shock compressed bcc high-entropy alloys

Recent studies of complex concentrated alloys suggest unusual dislocation core structure and motion, thanks to a collective concentration/structural inhomogeneity. Less is known whether these effects also work in extreme conditions where the solid solution effect is overwhelmed by the large driving force. Here, we investigate the dislocation structure behind a shock-wave front in bcc high-entropy alloys (HEAs) using large-scale molecular dynamics (MD) simulations. In contrast to bcc elemental metals, we find anomalous “extended“ edge dislocation structure (6 ~ 8 Burgers vector) with high stability in shock compressed TiZrNb and NiCoFeTi HEAs. The unique dislocation structures can facilitate faster dislocation motion, thus deterring the early nucleation of deformation twins. Combined with continuum elasticity theory, we show that the “extended“ dislocation structure can be attributed to the presence of local structures with low elastic stability that are imparted by the nanoscale chemical heterogeneities in HEAs. We also show how the dislocation structures are affected by the interatomic potentials.

Effects of the boundary-layer thickness at the cavity entrance on rarefied hypersonic flows over a rectangular cavity

A comprehensive numerical study is performed to investigate rarefied hypersonic flows past a flat plate with a two- (2D) or three-dimensional (3D) rectangular cavity using the direct simulation Monte Carlo method. In this work, we obtain different boundary-layer thicknesses at the cavity entrance by varying the length of upstream flat plate. Then, the effects of boundary-layer thickness at the cavity entrance on flow characteristics and aerodynamic surface quantities are analyzed in depth. The concept of total-enthalpy boundary layer successfully identifies the boundary-layer edge while the traditional boundary layer based on velocity fails to captures the shock-wave front due to the presence of the weak shock wave in the rarefied hypersonic flow past a flat plate. The boundary-layer thickness at the cavity entrance has strong effects on the flow past the 2D cavity. As the boundary layer at the cavity entrance becomes thicker, the external stream can penetrate deeper into the cavity and transfer more momentum and energy to the cavity, so the cavity flow develops gradually from an open flow to a transitional one and ultimately to a closed one. In addition, the 3D effect plays an important role for the cases of extremely thick boundary layers at the cavity entrance, while it can almost be neglected when boundary layers at the cavity entrance are exceedingly thin.

An improved Kirkwood–Bethe model for calculating near-field shockwave propagation of underwater explosions

To calculate the near-field shockwave propagation of underwater explosions for different explosives quickly and accurately, an improved calculation model, based on the Kirkwood–Bethe theory, is proposed. Based on the detonation theory and shock jump conditions, the model establishes initial equilibrium conditions and an initial shockwave-front state of the explosion bubble interface. By incorporating a second-order Mach-precision bubble dynamics equation, the model determines the physical parameters and enthalpy change functions at the initial expanding stage in real time. By solving the isentropic flow of the enthalpy change function G at varying delay times, a functional relation was established between the enthalpy change function and the pressure at arbitrary flow points and times. The model obtained the near-field shockwave-front peak-pressure spatial distributions of underwater explosions and the pressure decay time constants at arbitrary flow points. The results indicated that the proposed method can quickly and accurately determine the near-field shockwave propagation of underwater explosions for different explosives, with satisfactory agreement with experimental data. The proposed method relates the explosive detonation, explosion bubble expansion, and shockwave propagation, thus connecting the explosive parameters with the shockwave front state parameters.

Strain localization under impulse load

Unknown characteristics of the strain localization process are determined by the study of the structure of localized strain bands and adjacent matrix metal. Interference of oncoming waves (compression and unloading) reflected from the sample faces are shown to induce oscillations of the sample in the standing wave mode at the nodes of which the localized strain bands (precursors of damage) arise. Strain localization is accompanied by the formation of a flow of particles (interstitial and substitution atoms, fine particles of the doping phase, and impurities), which migrate from the matrix to the zone of spall damage. The main property of a standing wave, namely, capability of preventing energy exchange through the nodal points, provides a long-term sample deformation after the shock wave front passed. The distance passed by the particles under impulse load exceeds the drift of particles under quasi-static load by several orders of magnitude.

Постановка экспериментов для анализа возмущений головной ударной волны за счет присутствия частиц в сверхзвуковом потоке

The research in the field of devices and methods of experimental physics includes, in particular, the creation of installations for conducting experiments in the physics of multiphase nonequilibrium flows. Multiphase flow around bodies is of significant importance in various fields of technology, for example, in power engineering, contact visualization methods, aerosol technologies, in the application of various coatings, etc. In the high-speed two-phase flow around bodies, the physics of particle collisions with the surface and the interaction of flying particles with the head shock wave play an important role. Most of the experiments in this area, including the passage of the model through the zone of rain, snow, dust, cooled clouds, etc., are carried out in the reverse setting. In this case, the model is fixed, and the flow is made by one or another high-enthalpy aerodynamic installation. This approach does not correspond to the initial stage of the interaction formed before the entrance to the zone of the two-phase medium, between the head shock and the incident particle. Nevertheless, for some approaches, it is of interest to visually confirm the possibility of an oncoming particle being ejected at a supersonic speed by the front of the head shock wave and to see the deceleration of the model from the shadow pattern with a change in the Mach line. The paper considers a direct ballistic experiment which by shadow visualization tests the possibility of cavern formation near a body crossing the trajectory of the atmosphere saturated with dust particles

Simulation of propagation and diffraction of a shock wave in a planar curvilinear channel

Subject of Research. Numerical simulation of a shock wave propagation in a plane curved channel is considered on the basis of numerical simulation data. Method. Calculations of an inviscid compressible gas were carried out on the basis of unsteady two-dimensional Euler equations. Discretization of the basic equations was carried out using the finite volume method. Calculations were carried out for different channels with different radius of curvature and Mach numbers of the initial wave. To find the angular position of the front at the current time, the absolute value of the derivative of the density with respect to the angular coordinate was used. The calculation results were compared with the data of a physical experiment. Main Results. The features of the emerging shock-wave flow pattern and its development in time are discussed. The shock-wave configuration observed in channels with different radii of curvature is compared. Some differences in the curvature change of the front of shock waves formed in channels with different radius of curvature are shown. The size of the Mach leg and its change with time depending on the intensity of the initial wave and the size of the annular gap is the angular coordinate function corresponding to the position of the shock wave at the current time. While the maximum Mach number on the outer wall is relatively weakly dependent on the initial wave velocity, the Mach number on the bottom wall decreases with increasing Mach number at the channel entrance. The performed numerical studies show that in all variants there are no non-physical oscillations of the solution. Practical Relevance. The study of shock-wave and detonation processes is of interest for using their potential in pulsed installations and power systems for aircraft and rockets. The calculation results are important for the search of the new flow patterns that guarantee the formation of self-sustained detonation combustion in the combustion chambers of promising propulsion systems. Adjusting the size of the annular gap gives the possibility to select a geometric configuration that will provide the formation of an optimal triple shock wave structure, as well as the required intensity and size of the Mach wave.

Shock wave hydrodynamics of nano-carbons

Dynamic deformation of nano-carbons by shock waves is an important object in technological applications as well as in basic sciences. We report, on hydrodynamic response of two types of nano-carbon systems: graphene nano-flakes (GNF) and carbon nano-spheres (CNS) by subjecting them to the Klosky bar shock test (at strain rate 102–104/s). Data of stress (σ), strain (ε), and strain rate (ἑ) were obtained with time to analyse the behaviour of constitutive parameter (σ–ε). In elastic region GNF showed superior stress sensitivity at least by fivefold over CNS, whereas, stress accumulation ability of CNS was found to be ten times better than GNF. In plastic region both the systems were behaved quiet complexly. They comprised of various stages of deformation like inter–particle separation, micro–structure gliding, fracture, and perforation. To obtain hydrodynamic variables a few thermodynamic assumptions like matrix homogeneity, linear volume deformity, negligible temperature rise were made to set up the Lagrange–Rankine–Hugoniot model. Interplay of built–in pressure (P), particle velocity (UP), shock velocity (US), specific volume (V/VO), density (ρ), shock energy (E), behind and ahead of the shock wavefront led to the establishment of the equation of state for the system. Theoretical shock profile was vis-à-vis compared with the experimentally obtained shock results. Distribution of impulse pressure over the topology of the nano-carbons was examined that exhibited non-uniform shock energy dissipation pattern with peak pressure ~250 N/m2. Our calculations revealed that, almost ~65% shock energy was damped within GNF and ~89% in CNS. Details of the analysis are presented.

Experimental research on vector control features of a pulse detonation tube with fluidic nozzle

Fluidic nozzle is attractive on adjusting the effective area ratio according to the fluctuated exhaust gas in a pulse detonation engine, which can help to reduce over-expansion and under-expansion losses and improve the propulsion performance. The present paper seeks to explore the operation characteristics and thrust vector features of a two-dimensional and visualized fluidic nozzle attached to a single-cycle detonation tube, spike pressures, velocities of the detonation waves, and flow field structures in the nozzle were captured. The results demonstrated that the front shock wave was remarkably weakened with a decrease up to −57% when throat injection was utilized, and the exhaust process was extended up to 17.7%. Meanwhile, the divergent injections were proved to be effective on weakening the reflected shock waves in the nozzle, preventing the formation of Mach disk, and adjusting the effective boundary of divergent section from conical into bell-shape. In addition, the asymmetric injections were validated to be effectual on adjusting the direction of the exhaust gas. Reflected shock waves were weaker in the divergent injection side, and the exhausted gas was deviated from the injection side obviously.

Numerical investigation on the rotating detonation critical mode for a methane–air mixture in an annular tube using reactive Navier–Stokes equations

Previous experimental studies show that gaseous detonation propagation in an annular tube can be divided into three categories, i.e., stable mode, critical mode and unstable mode. However, the mechanism of detonation propagation with the critical mode is not well understood due to insufficient experimental data. In this paper, detonation propagation with the critical mode in the annular tube was numerically studied for the methane–air mixture based on reactive Navier–Stokes equations, in which the convective term was integrated by the fifth-order weighted essentially non-oscillatory. The numerical results show that the trajectories of the triple points of the shock wave front were drawn to obtain cell structure with “petal” pattern, which is agree with the experimental results. The wall curvature plays an important role for this phenomenon. The outer wall is concave, which can continuously compress the detonation wave and make it stronger. The inner wall is convex, which can produce an isentropic expansion and decouples the reaction front from the shock wave. The transverse shock wave emanating from the triple point moving from the outer wall reignites detonation near the inner wall, which implies that compression of the outer wall plays a key role in the rotating detonation propagation. As the transverse shock wave moves away from the inner wall, the detonation wave near it gradually weakens. Because of the back and forth reflection of the transverse shock wave between the inner and outer walls, the rotating detonation wave can be maintained and its cellular structure presents “petal” pattern. Meanwhile, the averaged detonation velocity at the outer wall is higher than that at the inner wall.