Shock Width Research Articles

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).

Shock wave formation in radiative plasmas.

The temporal evolution of weak shocks in radiative media is theoretically investigated in this work. The structure of radiative shocks has traditionally been studied in a stationary framework. Their systematic classification is complex because layers of optically thick and thin regions alternate to form a radiatively driven precursor and a temperature-relaxation layer, between which the hydrodynamic shock is embedded. In this work we analyze the formation of weak shocks when two radiative plasmas with different pressures are put in contact. Applying a reductive perturbative method yields a Burgers-type equationthat governs the temporal evolution of the perturbed variables including the radiation field. The conditions upon which optically thick and thin solutions exist have been derived and expressed as a function of the shock strength and Boltzmann number. Below a certain Boltzmann number threshold, weak shocks always become optically thick asymptotically in time, while thin solutions appear as transitory structures. The existence of an optically thin regime is related to the presence of an overdense layer in the compressed material. Scaling laws for the characteristic formation time and shock width are provided for each regime. The theoretical analysis is supported by FLASH simulations, and a comprehensive test case has been designed to benchmark radiative hydrodynamic codes.

On the Width of a Collisionless Shock and the Index of the Cosmic Rays It Accelerates

Despite being studied for many years, the structure of collisionless shocks is still not fully determined. Such shocks are known to be accelerators of cosmic rays (CRs), which, in turn, modify the shock structure. The shock width λ is known to be connected to the CR spectral index a. Here, we use an instability analysis to derive the shock width in the presence of CRs. We obtain an analytical expression connecting the shock width to the CR index and to the fraction of upstream particles that are accelerated. We find that when this fraction becomes larger than ∼30%, a new instability becomes dominant. The shock undergoes a transition where its width increases by a factor ∼8–10, and the CR acceleration effectively ends. Our analysis is valid for strong, nonrelativistic, and unmagnetized shocks. We discuss the implication of these results on the expected range of CR spectra and flux observed and on the structure of nonrelativistic collisionless shocks.

Effects of dust size distribution and non-Maxwellian electrons on shock waves in a dusty plasma

We present a study of dust acoustic shock waves in a non-Maxwellian plasma with dust charge fluctuations, which are seen to cause a dissipation term in fluid model, and consequently shocks are generated. In particular, we focus on dust acoustic waves as affected by various dust size distributions. Two distinct dust size distributions—the polynomial and the power law distributions—have been used. For analytical investigation of nonlinear wave propagation in complex plasmas, a reductive perturbation approach is used to obtain the Burgers equation. A dusty plasma system with non-Maxwellian Kappa distribution is considered and it is shown that the amplitude of a shock wave, for the dust size distribution is larger than that for the mono-sized counterpart, while the shock width manifests an opposite trend. Furthermore, the shock wave speed is also affected by the dust size distributions as well as by the nature of velocity distribution function. To benchmark our findings, we apply the proper limit on the spectral index, i.e., κ→∞, and retrieve the Maxwellian results. The current findings are crucial for comprehending respective shock distributions for a plasma system exhibiting non-thermal characteristics and having dust size distributions.

Structures of strong shocks in low-density helium and neon gases.

Strong shocks are essential components in many high-energy-density environments such as inertial confinement fusion implosions. However, the experimental measurements of the spatial structures of such shocks are sparse. In this paper, the soft x-ray emission of a shock front in a helium gas mixture (90% helium, 10% neon) and a pure neon gas was spatially resolved using an imaging spectrometer. We observe that the shock width in the helium mixture gas is about twice as large as in the pure neon gas. Moreover, they exhibit different precursor layers, where electron temperature greatly exceeds ion temperature, extending for more than ∼350µm with the helium gas mixture but less than 30µm in the pure neon. At the shock front, calculations show that the electrons are strongly collisional with mean-free path two orders of magnitude shorter than the characteristic length of the shock. However, the helium ions can reach a kinetic regime as a consequence of their mean-free path being comparable to the scale of the shock. A radiation-hydrodynamic simulation demonstrates the impact of thermal conduction on the formation of the precursors with charge state, Z, playing a major role in heat flow and the precursor formation in both the helium mixture and the pure neon gases. Particle-in-cell simulations are also performed to study the ion kinetic effects on the formation of the observed precursors. A group of fast-streaming ions is observed leading the shock only in the helium gas mixture. Both effects explain the longer precursor layer in the helium shock.

Observation of subcritical shocks in a collisional laboratory plasma: scale dependence near the resistive length

We present a study of subcritical shocks in a highly collisional laboratory plasma with a dynamically significant magnetic field. Shocks were produced by placing cylindrical obstacles into the supermagnetosonic ( $M_{{\rm MS}} \sim 1.9$ ) outflow from an inverse wire array z-pinch at the MAGPIE pulsed power facility ( $n_{e} \sim 8.5 \times 10^{17}\,{\rm cm}^{-3}$ , $v \sim 45\,{\rm km}\,{\rm s}^{-1}$ ). We demonstrate the existence of subcritical shocks in this regime and find that secondary stagnation shocks form in the downstream which we infer from interferometry and optical Thomson scattering measurements are hydrodynamic in nature. The subcritical shock width is found to be approximately equal to the resistive diffusion length and we demonstrate the absence of a jump in hydrodynamic parameters. Temperature measurements by collective optical Thomson scattering showed little temperature change across the subcritical shock ( ${<}10\,\%$ of the ion kinetic energy) which is consistent with a balance between adiabatic and Ohmic heating and radiative cooling. We demonstrate the absence of subcritical shocks when the obstacle diameter is less than the resistive diffusion length due to decoupling of the magnetic field from the plasma. These findings are supported by magnetohydrodynamic simulations using the Gorgon and AstroBEAR codes and discrepancies between the simulations and experiment are discussed.

Non-locality of ion reflection at the shock front: dependence on the shock angle

In typical heliospheric collisionless shocks most of the mass, momentum and energy are carried by ions. Therefore, the shock structure should be most affected by ions. With the increase of the Mach number, ion reflection becomes more and more important, and reflected ions participate in shaping the shock profile. Ion reflection at the collisionless shock is a non-local process: the reflected–transmitted ions re-enter the shock front far from the reflection point. The direction and the magnitude of this shift depend on the shock angle. The distance between the reflection point and the re-entry point is of the order of the upstream ion convective gyroradius and exceeds the shock width. The non-locality of ion reflection may have implications for shock rippling since reflected ions may carry perturbations along the shock front.

MESSENGER Observations of Standing Whistler Waves Upstream of Mercury's Bow Shock

AbstractThis paper reports on the standing whistler waves upstream of Mercury's quasi‐perpendicular bow shock. Using MESSENGER's magnetometer data, 36 wave events were identified during interplanetary coronal mass ejections (ICMEs). These elliptic or circular polarized waves were characterized by: (a) a constant phase with respect to the shock, (b) propagation along the normal direction to the shock surface, and (c) rapid damping over a few wave periods. We inferred the speed of Mercury's bow shock as ∼26 km/s and a shock width of 1.87 ion inertial length. These events were observed in 20% of the MESSENGER orbits during ICMEs. We conclude that standing whistler wave generations at Mercury are generic to ICME impacts and the low Alfvén Mach number (MA) collisionless shock, and are not affected by the absolute dimensions of the bow shock. Our results further support the theory that these waves are generated by the current in the shock.

Shock compression of semiflexible polymers.

We employ molecular dynamics simulations to investigate the shock compression of linear semiflexible polymers. While the propagation velocity of a shock primarily depends on density, both chain rigidity and chain orientation significantly influence the shock width and the final temperature of the system. In general, the shock wave triggers molecular buckling in chains oriented perpendicular to the compression front. Following the passage of the front, the semiflexible chains buckle with a wavelength that decreases with the compression speed as λm ∼ up-0.2, and subsequent relaxation leads to a banana-like liquid crystal phase. In ordered systems with molecules oriented perpendicular to the compression front, the shock width increases by a factor of up to 10 compared to a similar isotropic system, resulting in enhanced shock energy absorption. These findings indicate that chain stiffness plays a critical role in the impact absorption properties of polymeric materials.

Perpendicular Subcritical Shock Structure in a Collisional Plasma Experiment.

We present a study of perpendicular subcritical shocks in a collisional laboratory plasma. Shocks are produced by placing obstacles into the supermagnetosonic outflow from an inverse wire array z pinch. We demonstrate the existence of subcritical shocks in this regime and find that secondary shocks form in the downstream. Detailed measurements of the subcritical shock structure confirm the absence of a hydrodynamic jump. We calculate the classical (Spitzer) resistive diffusion length and show that it is approximately equal to the shock width. We measure little heating across the shock (<10% of the ion kinetic energy) which is consistent with an absence of viscous dissipation.

The higher-order nonlinearity and parametric effects on dust-ion-acoustic shock waves

In the case of obliquely propagated small-amplitude shock waves, in this study, we investigate the impacts of higher-order nonlinearity as well as various parameters (such as dust concentrations, viscosity, trapping parameters, etc) on the shock wave structures. The considered magnetized plasma system consists of three components, such as inertial positive ions (mobile), trapped electrons, and immobile negatively charged dust particles. The modified Burgers equation with a dominating dissipative term (in which the viscous effect is significant) is derived initially to examine the lower-order nonlinear and dissipative effects, and then, to the best of our knowledge, the modified Burgers-type linear inhomogeneous equation is derived for the first time to observe the higher-order nonlinear effects on shock waves while the plasma contains trapped electrons. The reductive perturbation method is used for the derivation of the equations, whereas the Abel’s theorem and the method of variation of parameters are used for adding the higher-order effect. From the theoretical investigation, we observe that the higher-order nonlinearity has an increasing effect on the shock amplitude. Furthermore, the viscosity and dust concentration increase the shock width and the phase speed, respectively.

A spectrum improved peridynamic model for shock wave problems

Most previous peridynamics (PD) based shock wave modeling focuses on the field discontinuity problem but neglects the temporal discontinuous feature. Considering it is of vital importance to reproduce the shock jumps, the spectral properties of PD are studied and improved in this paper. A systematic theoretical analysis is firstly conducted and reveals the overly-dispersive behavior of PD model, including the oscillatory dispersion relation and zero energy modes. To suppress the consequent spurious oscillation, the dissipation effect is nonlocally introduced by viscosity as a minimum variation of conventional PD. Rather than applying the existing viscosities directly, the spectral balance is considered for the good control of both the oscillation and shock width, leading to the proposal of polynomial and force-limited viscous force states. The proposed model is then verified by several impact and explosion cases. The quantification of spectral balance is established and is employed for parameter calibration. The results suggest that the model shows good performance in shock wave modeling, with which both the suppression of oscillation and control of shock width near the shock jump are well achieved.

Characterizing under-expansion behaviors induced by rapid phase change of flash-boiling jets

Flash-boiling sprays issued from multi-hole gasoline direct injection (GDI) injectors could collapse, which is recently proved to be caused by under-expansion, but very few experimental data are available on this sort of under-expansion. In this study, high-speed microscopic Schlieren photography was used to capture the near-field shock structures in flash-boiling n-hexane jets. The tests were carried out in a constant volume vessel with ambient pressures (Pamb) from 10 to 101 kPa, fuel temperatures (Tfuel) from 30 to 170 ℃, and injection pressures (Pinj) from 2 to 20 MPa. The shock structure was carefully analyzed in terms of shock width and length. Generally, both the shock width and length decreased with the increase in Pamb. With the increase in Tfuel, the shock length was relatively stable and the shock width overall increased, but a decreasing trend in shock width could be observed at 170 ℃, possibly caused by the near-critical behaviors. Further analysis showed that the shock width shows a strong linear correlation with Δμ·Pamb−0.5 (Δμ denoting chemical potential of phase change) for a given Pinj, and the shock length shows a strong quadratic polynomial relationship with ηinj (injection pressure ratio, defined as the ratio of Pinj to Pamb). Additionally, some new shock structures without Mach disk were observed, indicating that the phase change induced under expansion is different from the typical gaseous under-expansion.

Effects of non‐thermality and plasma parameters on dust‐ion‐acoustic shock waves

AbstractThe nonlinear characteristics of dust‐ion‐acoustic shock waves (DIASHWs) in a plasma consisting of charge‐fluctuating dust, inertial ions, and non‐Maxwellian electrons is examined. In particular, the electron velocity distribution function (VDF) is assumed to follow Kappa and Cairns distributions. In this regard, a reductive perturbation (RP) approach (in a weakly nonlinear limit) is used to derive the corresponding Burger's equation, and, from its solution, the effects of various physical parameters, for example, non‐thermal indices, number density, and temperature ratios, on the properties of shock waves are investigated. It is observed that the magnitude of the shock reduces as ion‐electron temperature ratio increases and vice versa. Furthermore, when the ion to electron (equilibrium) density ratio increases, the shock profile gets steepened. The resultant potential amplitude as well as the shock width is also shown to be strongly related to the spectral indices, namely κ and α in the case of Kappa‐ and Cairns‐distributed electrons, respectively. Hence, the potential distribution is strongly affected by the non‐thermal nature of the electron VDF. The relevant Maxwellian results are recovered in the limiting cases, namely κ → ∞ and α → 0. The present study will be useful in understanding the nonlinear propagation of DIASHWs in non‐thermal (space and laboratory) plasmas.

Neutralized Solar Energetic Particles for SEP Forecasting: Feasibility Study of an Innovative Technique for Space Weather Applications

Energetic neutral atoms (ENAs) are produced by the neutralization of energetic ions formed by shock-accelerated gradual solar energetic particle events (SEP). These high-energy ENAs (HENAs) can reach the Earth earlier than the associated SEPs and thus can provide information about the SEPs at the lower corona. The HENA properties observed at Earth depend on the properties of the coronal mass ejection (CME)-driven shocks that accelerate the SEPs. Using a model of HENA production in a shock-accelerated SEP event, we semi-quantitatively investigate the energy-time spectrum of HENAs depending on the width, propagation speed, and direction of the shock, as well as the density and ion abundances of the lower corona. Compared to the baseline model parameters, the cases with a wider shock width angle or a higher coronal density would increase the HENA flux observed at the Earth, while the case with an Earth-propagating shock shows a softened HENA spectrum. The comparison of expected HENA fluxes in different cases with a flight-proven ENA instrument suggests that solar HENAs can feasibly be monitored with current technologies, which could provide a lead time of 2−3 hours for SEPs at a few MeV. We propose that monitoring of solar HENAs could provide a new method to forecast shock-driven SEP events that are capable of significant space weather impacts on the near-Earth environment.

Shock width measured under liquid and solid conditions in a two-dimensional dusty plasma.

Widths of shocks are compared, under liquid and solid conditions, for a two-dimensional layer of charged microspheres levitated in a plasma. In this strongly coupled dusty plasma, a shock was launched as a blast wave by moving an exciter wire at a supersonic speed and then bringing it to a halt. Runs were repeated with the layer of microspheres prepared two ways: a crystallinelike solid and a liquid. The liquid was sustained using laser heating, with conditions that were otherwise the same as in the solid. The shock width was found to be less in a liquid than in a solid, where it was four to six lattice constants. These measurements were based on the high-gradient region of density profiles. The profiles were obtained from particle coordinates, measured by high-speed video imaging. The spatial resolution was improved by combining particle coordinates, in the shock's frame of reference, from a sequence of images.

To Predict a Shock Pulse using Non Linear Dynamic Model of Rubber Waveform Generator

Drop test produces a variety of shock pulses, these shock pulses can accurately be predicted using polynomial based nonlinear empirical relations. The aim of this study is to monitor and improve the reliability of such systems/structures/equipment that might face critical installations or unlikely shocks during transportation, otherwise catastrophic failure is difficult to avoid. Rubber Wave Generators (RWGs) in Drop Test Machines (DTMs) are generally used for producing sinusoidal shock pulse of specific time and height. Three types of RWGs are used for analyzing the behavior of the generated shock pulse. The nonlinear equation expressing the restoring and damping forces through cubic and quadratic nonlinear terms is formulated. Harmonic Balance Method (HBM) is used to solve the nonlinear equation. Each RWG is excited harmonically through its base. The nonlinear stiffness and damping terms are obtained experimentally by the use of suitable curve fitting techniques. The nonlinear equation is reformulated to predict the shock pulse during drop test. Drop tests ranges from low g to 156g are performed at different heights and weights. Results of both experimental and nonlinear equation waveforms are within prescribed range defined in JEDEC and MIL standards for all three RWGs. The results also show that the presented method has the ability to accurately predict the shock pulse shape, time and width at a range of heights and weights.

Numerical Simulations of Shock Waves in Viscous Carbon Dioxide Flows Using Finite Volume Method

An efficient numerical tool for studying shock waves in viscous carbon dioxide flows is proposed. The developed theoretical model is based on the kinetic theory formalism and is free of common limitations such as constant specific heat ratio, approximate analytical expressions for thermodynamic functions and transport coefficients. The thermal conductivity, viscosity and bulk viscosity coefficients are expressed in terms of temperature, collision integrals and internal energy relaxation times. Precomputed in the wide temperature range thermodynamic functions and transport coefficients are implemented to the numerical code which is used for the simulations of the shock wave structure. Including the bulk viscosity to the kinetic model results in the increasing shock width and improves the agreement with experimental data.

Numerical simulations of shock waves in viscous carbon dioxide flows using finite volume method

An efficient numerical tool for studying shock waves in viscous carbon dioxide flows is proposed. The developed theoretical model is based on the kinetic theory formalism and is free of common limitations such as constant specific heat ratio, approximate analytical expressions for thermodynamic functions and transport coefficients. The thermal conductivity, viscosity and bulk viscosity coefficients are expressed in terms of temperature, collision integrals and internal energy relaxation times. Precomputed in the wide temperature range thermodynamic functions and transport coefficients are implemented to the numerical code which is used for the simulations of the shock wave structure. Including the bulk viscosity to the kinetic model results in the increasing shock width and improves the agreement with experimental data.

A finite scale model for shock structure

In this paper we explore the use of a finite scale model of fluid dynamics to predict the finite structure of a shock wave in a perfect gas. We begin by documenting the history and issues that have arisen when Navier–Stokes theory is applied to the shock structure problem, and continue by motivating the improvement that finite scale theory might provide from its representation of inviscid (anomalous) dissipation. Our primary results include the formulation of a traveling wave equation from finite scale theory, an analysis of the solutions of that equation as regards shock width and monotonicity properties, and an estimation of the critical parameter of the theory from experimental data.