Behavior Of Shocks Research Articles

Numerical Investigation of Two-Phase Shock Waves in CO2 Flows Using a Modified Hertz–Knudsen Model

Abstract Understanding the complex behavior of two-phase shocks in CO2 flows is essential for a variety of applications, including carbon capture and storage () and transcritical refrigeration cycles. This study presents a comprehensive numerical investigation of two-phase shock waves using the multispecies user-defined real gas model in Ansys Fluent. The simulations are performed for de-Laval nozzles, exploring the two-phase shock features for three-dimensional (3D), two-dimensional (2D), and two-dimensional axisymmetric geometries. The nonequilibrium condensation, subsequent evaporation, and denucleation occurring across the shock are modeled through a set of user-defined scalar transport equations implemented within Ansys Fluent. The two-phase computational fluid dynamics (CFD) simulations are carried out in proximity to the critical point where real gas effects are relevant. The CO2 real gas properties are computed using an in-house Python code and integrated into the solver via user-defined functions as external look-up tables. This study provides valuable insights into the physical processes underlying two-phase shocks in CO2 flows and their sensitivity to geometric variations and thermodynamic conditions. The findings contribute to the development and modification of predictive models and optimized designs for systems involving two-phase CO2 flows. The results highlight the influence of geometry configurations and thermodynamic conditions on shock location and intensity, providing comparisons for shock waves occurring in two-phase flows and supercritical single-phase flows.

Temperature-reducing shocks in optically thin radiative MHD—Analytical and numerical results

Shocks are often invoked as heating mechanisms in astrophysical systems, with both adiabatic compression and dissipative heating that leading to the increase in temperature. While shocks are reasonably well understood for ideal magnetohydrodynamic (MHD) systems, in many astrophysical plasmas, radiation is an important phenomena, which can allow energy to leave the system. As such, energy becomes non-conservative, which can fundamentally change the behavior of shocks. The energy emitted through optically thin radiation post-shock can exceed the thermal energy increase, resulting in shocks that reduce the temperature of the medium, i.e., cooling shocks that have a net decrease in temperature across the interface. In this paper, semi-analytical solutions for radiative shocks are derived to demonstrate that both cooling (temperature decreasing) and heating (temperature increasing) shock solutions are possible across the whole temperature range in optically thin radiative MHD. Numerical simulations of magnetic reconnection for solar-like temperatures and plasma-β with optically thin radiative losses also yield both heating and cooling shocks in roughly equal abundances. The detected cooling shocks feature a significantly lower pressure jump across the shock than their heating counterparts. The compression at the shock front leads to locally enhanced radiative losses, resulting in significant cooling within a few grid cells in the upstream and downstream directions. The presence of temperature-reducing (cooling) shocks is critical in determining the thermal evolution, and heating or cooling, across a wealth of radiative astrophysical plasmas including magnetic reconnection in the solar corona.

Oil shocks and currency behavior: A dual approach to digital and traditional currencies

Given the financial markets' growing preference for examining digital platforms, this study explores the dynamic relationship of oil shocks with both conventional and digital currencies. It provides a novel approach for evaluating the relationship between aggregate oil, demand, and supply shocks using three conventional currencies (Japanese Yen, Chinese Yuan, and Euro), cryptocurrencies (Bitcoin, Ethereum, Tether), and DeFi tokens (Maker, Chainlink, and Basic Attention Token). We use wavelet analysis to test the asymmetric association among variables from June 22, 2018, to July 11, 2023. The outcomes of continuous wavelet confirm the volatile behavior of oil shocks and studied currencies. In particular, a nonlinear wavelet coherence is observed between oil shocks and DeFi tokens, cryptocurrencies, and traditional currency in the short, medium, and long term. Moreover, crypto and conventional currencies are found to respond more strongly to external events than DeFi tokens. Given the empirical findings and the rapid transformation of digitalized finance with ongoing currency restructuring, this study plays a critical role by actively influencing the adaptation of regulatory frameworks to align with dynamic changes in associations, serving as a strategic guide for regulatory bodies to navigate the complexities of emerging financial paradigms.

Analysis of shock wave propagation in two-layered blood flow model via Lie symmetry

In this paper, we study the two-layered blood flow model within the framework of Lie symmetry analysis to investigate a range of closed-form solutions. Our investigation involves optimal classification, revealing the existence of six optimal subalgebras within the model. Further, we streamline the model by reducing it into a system of ordinary differential equations (ODEs), thereby deriving several exact solutions. Our analysis establishes the presence of the nonlinear self-adjointness property in the governing equation, leading to the development of various conservation laws. Furthermore, leveraging one of the exact solutions we obtained, we delve into the behaviour of characteristic shocks, C1 waves, and their interactions, providing a comprehensive understanding of their dynamics.

Relativistic spherical shocks in expanding media

ABSTRACT We investigate the propagation of spherically symmetric shocks in relativistic homologously expanding media with density distributions following a power-law profile in their Lorentz factor. That is, $\rho _{_{\rm {ej}}} \propto t^{-3}\gamma _{_{\rm {ej}}}(r,t)^{-\alpha }$, where $\rho _{_{\rm {ej}}}$ is the medium proper density, $\gamma _{_{\rm {ej}}}$ is its Lorentz factor, α > 0 is constant, and t, r are the time and radius from the centre. We find that the shocks behaviour can be characterized by their proper velocity, $U^{\prime }=\Gamma _s^{\prime }\beta _s^{\prime }$, where $\Gamma _s^{\prime }$ is the shock Lorentz factor as measured in the immediate upstream frame and $\beta _s^{\prime }$ is the corresponding three velocity. While generally, we do not expect the shock evolution to be self-similar, for every α > 0 we find a critical value $U^{\prime }_c$ for which a self-similar solution with constant U′ exists. We then use numerical simulations to investigate the behaviour of general shocks. We find that shocks with $U^{\prime }\gt U^{\prime }_c$ have a monotonously growing U′, while those with $U^{\prime }\lt U^{\prime }_c$ have a decreasing U′ and will eventually die out. Finally, we present an analytic approximation, based on our numerical results, for the evolution of general shocks in the regime where U′ is ultrarelativistic.

Employment and technology: Creative creation or creative destruction? An asymmetric analysis

AbstractTheoretical predictions of the effect of technological change on employment are ambiguous and depend on the extent to which new technology is embodied in new jobs. This paper separates positive and negative shocks and examines the extent to which technological shocks have an asymmetric effect on unemployment in nine European countries by using hidden cointegration analysis within a likelihood‐based panel framework. The findings are consistent with the hypothesis that technological changes have had an unequal effect on unemployment because negative and positive shocks have different impacts on unemployment in terms of sign and size. It is interesting to note that women appear to be the group most negatively impacted by technological shocks. The estimates also show that the results are inconsistent because technological advancement has resulted in ‘creative destruction’ in four countries while ‘creative creation’ has occurred in five of them. It is worth mentioning that the methodological framework utilized in this paper can be a useful tool for predicting the behaviour of technological shocks. Policy implications are discussed.

Partially ionized two-fluid shocks with collisional and radiative ionization and recombination – multilevel hydrogen model

ABSTRACT Explosive phenomena are known to trigger a wealth of shocks in warm plasma environments, including the solar chromosphere and molecular clouds where the medium consists of both ionized and neutral species. Partial ionization is critical in determining the behaviour of shocks, since the ions and neutrals locally decouple, allowing for substructure to exist within the shock. Accurately modelling partially ionized shocks requires careful treatment of the ionized and neutral species, and their interactions. Here we study a partially ionized switch-off slow-mode shock using a multilevel hydrogen model with both collisional and radiative ionization and recombination rates that are implemented into the two-fluid (PIP) code, and study physical parameters that are typical of the solar chromosphere. The multilevel hydrogen model differs significantly from magnetohydrodynamic (MHD) solutions due to the macroscopic thermal energy loss during collisional ionization. In particular, the plasma temperature both post-shock and within the finite-width is significantly cooler that the post-shock MHD temperature. Furthermore, in the mid to lower chromosphere, shocks feature far greater compression than their single-fluid MHD analogues. The decreased temperature and increased compression reveal the importance of non-equilibrium ionized in the thermal evolution of shocks in partially ionized media. Since partially ionized shocks are not accurately described by the Rankine-Hugoniot shock jump conditions, it may be incorrect to use these to infer properties of lower atmospheric shocks.

Calculations of Compression of a Spherical Layered System by Shock Waves Taking into Account the Transfer of Thermal Radiation in the Kinetic Model

At present, numerical simulation is the main, and often the only, tool for detailed description of some physical phenomena in the study of the processes of material compression by shock waves. The study of the behavior of shock and rarefaction waves on the simplest model tests helps in the analysis of more complex calculations, for example, problems of inertial thermonuclear fusion on laser facilities. The paper considers comparative calculations of a test problem that simulates compression of a spherical layered system consisting of two substances by shock waves.

Time-varying unobserved heterogeneity in earnings shocks

This paper considers the transitory-permanent model for the earnings process, and allows for time-varying individual-specific unobserved heterogeneity in each shock. The cross-sectional heterogeneity in each shock is drawn from an unknown distribution at each time period. Sufficient conditions for the nonparametric identification of the cross-sectional density functions of the heterogeneity are provided, under different assumptions on the time series behavior of the transitory shock. The method proposed is then applied to earnings data to document a high degree of cross-sectional heterogeneity in each shock.

Fiscal deficits and the socioeconomic consequences of rebalancing: Insights from a TVP‐VAR with stochastic volatility

AbstractThis article connects two salient economic features: (i) Fiscal shocks have asymmetric effects across business cycle phases (Gechert, Horn, & Paetz, 2019); (ii) the unemployment‐output trade‐off is time varying and may be unstable. The intertwined dynamic behaviour of fiscal deficit shocks and the unemployment‐output trade‐off is studied in this article using a time‐varying parameter (TVP) vector autoregression (VAR) with stochastic volatility techniques applied to the analysis of data from Canada, France, Germany, Japan, Spain, Sweden, United Kingdom and the United States of America. We confirm the trade‐off heterogeneity across country, and its time‐varying nature across time, showing in addition its fluctuation around a long‐run reference value. We document significant short‐run impacts of fiscal shocks on the unemployment‐output trade‐off which, based on the experience of the Global Financial Crisis, becomes larger in periods of economic turmoil. Policy‐wise, the rebalancing of public finances may have unexpected adverse effects on job creation if implemented during slumps, precisely when the labour market sensitivity with respect to the performance of the product market is likely to be more acute. This message is particularly relevant in the aftermath of the Covid‐19 pandemic.

Asymmetric behavior of oil price shocks and output performance in Africa

A comprehensive cross-country dataset is employed in this reseach to examine the impact of oil price shocks and its asymmetry on output in African oil exporting countries (AOECs). Using a panel-VAR model, the study accounted for impulse-response between output and oil price shocks. In addition, through the PVAR model, variance decomposition is performed to assess the importance of those effects and guidelines are offered for policy formation. The study revaled that oil price shocks create heterogeneously asymmetric effect on output. The study revealed the prevalence of Dutch Disease among the AOECs as apparent in the impact of negative oil price shocks on exchange rates and output. The study recommends that policies should be formulated to minimize the effect of oil price shocks on output, especially negative oil price shocks revealed to adversely affect oil revenue (policies aimed at strengthening economic activities through diversification, so as to enhance the export mix). This will reduce the AOECs’ on-going reliance on large revenues from oil, arising from positive oil price shocks which the literature has argued to have a negative and hindering impact on economy, mainly because it impacts the non-oil sector.

Asymmetric behavior of oil price shocks and output performance in Africa

A comprehensive cross-country dataset is employed in this reseach to examine the impact of oil price shocks and its asymmetry on output in African oil exporting countries (AOECs). Using a panel-VAR model, the study accounted for impulse-response between output and oil price shocks. In addition, through the PVAR model, variance decom-position is performed to assess the importance of those effects and guidelines are offered for policy formation. The study revaled that oil price shocks create heterogeneously asymmetric effect on output. The study revealed the prevalence of Dutch Disease among the AOECs as apparent in the impact of negative oil price shocks on exchange rates and output. The study recommends that policies should be formulated to minimize the effect of oil price shocks on output, especially negative oil price shocks revealed to adversely affect oil revenue (policies aimed at strengthening economic activities through diversification, so as to enhance the export mix). This will reduce the AOECs’ on-going reliance on large revenues from oil, arising from positive oil price shocks which the literature has argued to have a negative and hindering impact on economy, mainly because it impacts the non-oil sector.

Interaction of multiple shocks in planar targets with a ramp-pulse ablation

Interaction of multiple shocks plays a critical role in setting up an adiabatic compression of megabar pressure in nanosecond timescale in inertial confinement fusion. In this paper, we present observations of dynamic behavior and interaction of multiple shocks in polystyrene (CH) planar targets driven by a single-ramp pulse of 2.5 ns at the SG-II laser facility with a specially designed velocity interferometer system for any reflector (VISAR). A maximum pressure of 7.65 Mbar and a mass density of 3.46 g/cm3 are measured, respectively. Radiation-hydrodynamic simulations reveal the interaction process of the multiple shocks and are in good agreement with the measurements. A theoretical model is proposed to invert the space-time history of the shock generation with the VISAR data. Moreover, an optimized double-slope ramp pulse is proposed for further compression experiments. The improved multiple-shock coalescence is expected to effectively enhance both density and velocity for an initial compression of the CH target.

Modelling oil price shocks and exchange rate behaviour in Nigeria – A regime‐switching approach

AbstractConsequent upon the intermittent variations in the global oil prices over the years and its attendant effects on exchange rate dynamics of oil‐rich economies, the study investigates the regime‐switching behaviour of oil price shocks and exchange rate behaviour in Nigeria. The period of investigation spans 1980q1 – 2020q4 and the technique of analysis is the Markov‐Switching Dynamic Regression. Predicated on an extended portfolio balancing theory, the unit‐root test with structural break confirms break points in the data. The Markov‐Switching Dynamic Regression shows the presence of two regimes of low and high global oil price shocks in the data. Additional results show that expectation plays a huge role in the oil price and exchange rate nexus in Nigeria and that the regime of low global oil price comes with more shock effects than that of high global price of oil. With short memory property, both the low and high global prices of oil exhibit high persistence level above 70 percent but the duration of persistence for the latter is half‐life the former. The study recommends that the monetary authority should introduce exchange rate policy surprise and further diversify the economy from oil dependence.

Optimal Triggering Policy of Protective Devices Considering Self-Exciting Mechanism of Shocks

Safety-critical systems are commonly required to complete specific missions in shock environments, and their failures may lead to severe economic losses and significant safety hazards. To enhance system reliability, protective devices are commonly equipped to resist external shocks. The existing literature focuses mainly on the maintenance policy of safety-critical systems, ignoring the system reliability analysis considering the effect of protective devices and the self-exciting mechanism of shocks. This paper considers multi-state systems equipped with a protective device in shock environments where valid shocks and invalid shocks occur stochastically. The system state degenerates due to valid shocks or the self-exciting behavior of invalid shocks. The self-exciting mechanism is triggered when the number of cumulative or consecutive invalid shocks suffered by the system exceeds a certain threshold, leading the system to a worse state. The protective device can be triggered to protect the system from the damage of external shocks when the state is worse than a predetermined threshold. The protective effect is characterized by reducing the probability of valid shocks. A finite Markov chain embedding approach is used to evaluate the system reliability index. In addition, an optimization model is constructed to determine the optimal triggering threshold of the protective device. The numerical results indicate that protective devices can significantly improve the reliability of the system and incorporating the self-exciting mechanism of shocks into reliability modeling contributes to accurate reliability evaluation.

Weak discontinuities in one-dimensional compressible nonideal gas dynamics

Abstract This article concerns the study of various parameter effects on the propagation of weak discontinuities by using the method of characteristics. Analytical solutions of the quasi-linear system of hyperbolic partial differential equations (PDEs) are obtained and examined the evolutionary behavior of shock in the characteristic plane. The general behavior of solutions to the Bernoulli equation, which determines the evolution of weak discontinuity in a nonlinear system, is studied in detail. Also, we discuss the formation and distortion of compressive and expansive discontinuities under the van der Waals parameter effect and small particles for planar and cylindrical symmetric flow. The comparison between planar flow and cylindrical symmetric flow is studied under the influence of nonidealness and mass fraction of dust particles. It is found that the compressive waves become shock after a certain lapse of time. The medium considered here is the mixture of van der Waals gas with small dust particles.

Analysis on the asymptotic behavior of transonic shocks for steady Euler flows with gravity in a flat nozzle as the gravity vanishes

This paper concerns the asymptotic behavior of transonic shocks for steady Euler flows with gravity in a flat nozzle as the gravity vanishes. One of the key points is to quantitatively determine the position of the shock front as the gravity is small. To this end, a free boundary problem for the linearized Euler system with small gravity will be proposed. Then one can obtain the information of the approximating position of the shock front. Once the initial approximation of the shock solution is obtained, a nonlinear iteration scheme can be constructed to show that the position of the shock front is a small perturbation of the initial approximation, which establishes a quantitative expression for the shock solution. Such an expression shows the asymptotic behavior as the gravity goes to zero.

Study of shocks in a nonideal dusty gas using Maslov, Guderley, and CCW methods for shock exponents

Abstract In this work, we consider the system of partial differential equations describing one-dimensional (1D) radially symmetric (i.e., cylindrical or spherical) flow of a nonideal gas with small solid dust particles. We analyze the implosion of cylindrical and spherical symmetric strong shock waves in a mixture of a nonideal gas with small solid dust particles. An evolution equation for the strong cylindrical and spherical shock waves is derived by using the Maslov technique based on the kinematics of 1D motion. The approximate value of the similarity exponent describing the behavior of strong shocks is calculated by applying a first-order truncation approximation. The obtained approximate values of similarity exponent are compared with the values of the similarity exponent obtained from Whitham’s rule and Guderley’s method. All the above computations are performed for the different values of mass fraction of dust particles, relative specific heat, and the ratio of the density of dust particle to the density of the mixture and van der Waals excluded volume.

A Sub-element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods

In this paper, a new strategy for a sub-element-based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to interpret a DG element as a collection of data and construct a hierarchy of low-to-high-order discretizations on this set of data, including a first-order finite volume scheme up to the full-order DG scheme. The different DG discretizations are then blended according to sub-element troubled cell indicators, resulting in a final discretization that adaptively blends from low to high order within a single DG element. The goal is to retain as much high-order accuracy as possible, even in simulations with very strong shocks, as, e.g., presented in the Sedov test. The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing. The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.

Propagation of one-dimensional planar and nonplanar shock waves in nonideal radiating gas

The present study seeks to investigate a quasilinear hyperbolic system of partial differential equations which describes the unsteady one-dimensional motion of a shock wave of arbitrary strength propagating through a nonideal radiating gas. We have derived an infinite hierarchy of the transport equation which is based on the kinematics of one-dimensional motion of shock front. By using the truncation approximation method, an infinite hierarchy of transport equations, which governs the shock strength and the induced discontinuities behind it, is derived to study the kinematics of the shock front. The first three transport equations (i.e., first, second, and third-orders) are used to study the growth and decay behavior of shocks in van der Waals radiating gas. The decay laws for weak shock waves in nonradiating gas are entirely recovered in the second-order truncation approximation. The results obtained by the first three approximations for shock waves of arbitrary strength are compared with the results predicted by the characteristic rule. Also, the effect of nonideal parameters and radiation on the evolutionary behavior of shock waves are discussed and depicted pictorially.