Strong Shock Waves Research Articles

Solutions of the imploding shock problem in a medium with varying density

We consider the solutions of the Guderley problem, consisting of an imploding strong shock wave in an ideal gas with a power law initial density profile. The self-similar solutions, and, specifically, the similarity exponent that determines the behavior of the accelerating shock, are studied in detail, for cylindrical and spherical symmetries and for a wide range of the adiabatic index and the spatial density exponent. We then demonstrate how the analytic solutions can be reproduced in Lagrangian hydrodynamic codes, thus demonstrating their usefulness as a code validation and verification test problem.

Implication of self-throttling on combustion performance in a strut-based scramjet combustor

The present work describes the numerical investigation on the implication of self-throttling on combustion performance of a strut-based scramjet combustor. Firstly, the mixing characteristics of a strut with and without self-throttling are compared and evaluated to portray the effect of self-throttling in a DLR based scramjet combustor. Later, a separate study is performed to investigate the influence of location of self-throttling on the combustion performance of a strut-based scramjet combustor. Our study reveals that the self-throttling increases the enthalpy of formation and the generates the strong shock waves which improves the mixing rate of fuel and air. Further, the mixing commences relatively earlier with reduced pressure losses when the self-throttling is employed. It is observed that the volume of core flame region and the thickness of a flame depends on the distance between the reflected shock and the self-throttling injection slot.Also, the combustion performance deteriorates with the increase in distance between the reflected shock and the injection slot of self-throttling. Further, the combustion and mixing efficiency is found to be optimalwhen self-throttling is employed at the distance of100 mm from the inlet of the combustor.

A simple FORCE-type centred scheme accurate for contact discontinuities: Application to compressible Euler flows

The FORCE-type centred schemes are simple and efficient and do not explicitly require the wave propagation information of the system to calculate the numerical flux. However, their poor resolution for contact discontinuities seriously affects their applications. In the present work, a simple FORCE-type centred scheme accurate for contact discontinuities is proposed and applied to calculations of compressible Euler flows. The missing contact wave of the original FORCE centred scheme is restored with an algebraic method and the resolution for contact discontinuities is further improved by using the boundary variation diminishing (BVD) algorithm to minimize the density jump in the numerical diffusion term of the original FORCE centred scheme. Numerical results of several one- and two-dimensional benchmark test problems fully demonstrate that the proposed centred scheme is capable of capturing contact discontinuities more sharply than the complete-wave HLLC upwind scheme. In addition, another advantage of the proposed centred scheme is that it is free from the carbuncle phenomenon which afflicts many contact-capturing upwind schemes (e.g. Roe and HLLC) in calculations of multidimensional flow problems involving strong shock waves.

Third order asynchronous time integration for gas dynamics

A third order Asynchronous Runge Kutta method is introduced. The method can handle strong shock waves using independent local time stepping at the cell level. This method is then coupled with a novel third order limiting strategy based on an artificial viscosity-like sensor. The limiter is then used in the framework of the multi-slope MUSCL method for unstructured meshes. This integration method can also advantageously be coupled with Asynchronous Adaptive Mesh Refinement to treat compressible, reacting, multi-component flow problems. The accuracy and acceleration properties of the method are shown on a wide range of numerical tests.

Revisiting the strong shock problem: Converging and diverging shocks in different geometries

Self-similar solutions to converging (implosions) and diverging (explosions) shocks have been studied before, in planar, cylindrical, or spherical symmetry. Here, we offer a unified treatment of these apparently disconnected problems. We study the flow of an ideal gas with adiabatic index γ with initial density ρ∼r−ω, containing a strong shock wave. We characterize the self-similar solutions in the entirety of the parameter space γ,ω and draw the connections between the different geometries. We find that only type II self-similar solutions are valid in converging shocks, and that in some cases, a converging shock might not create a reflected shock after its convergence. Finally, we derive analytical approximations for the similarity exponent in the entirety of parameter space.

RESEARCH ON THE AUSM SPLITTING DSMC-IP METHOD FOR HYPERSONIC RAREFIED FLOW FIELD

The Information Preservation (DSMC-IP) method is improved by using Advection Upstream Splitting Method (AUSM) splitting scheme, to solve the problems that the Direct Simulation of Monte Carlo (DSMC) method is effected by a large statistical dissipation, and that he traditional IP method cannot simulate the strong shock wave accurately. The fluxes of correlation terms in governing equations are reconstructed by local Mach numbers as the standard, so that the calculation is more accurate in accordance with the flow characteristics on both sides of the shock wave, thus forming a new DSMC-IP method with high statistical accuracy and hypersonic flow simulation ability. This method is utilized to simulate supersonic flow around the cylinder and hypersonic flow around the nozzle with divergent angle, the results of the AUSM splitting DSMC-IP method is basically consistent with the results of DSMC method, however the former has lower statistical scatter, and the flow characteristics are clearer. The surface characteristic coefficients differences between the results and the experiment or reference values are less than 5.5%. It is proved that the AUSM splitting DSMC-IP method is accurate and effective in the hypersonic flow simulation.

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.

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.

The influence of viscosity and turbulence on the supersonic flow compression and expansion corner

Super- and hypersonic flow around aircraft elements is accompanied by the formation of a complex flow structure, which is characterized by the presence of strong shock waves, rarefaction waves, contact discontinuities, separation and reattachment of the flow. For such problems, the interaction of shock waves with viscous boundary layers is characteristic. Such interaction is quite complex and largely determines the effectiveness of aircraft. When flowing around complex structures of aircraft and their power plants in the vicinity of convex corner points of the geometry, compression and expansion flows are locally realized. The calculation of oblique shock waves, formed when flowing around the compression angle, and simple expansion waves, formed around the flowing angle of expansion, is included as an element of solving many problems of constructing streamlines and finding the pressure distribution on the streamlined surface. Based on the technology of adaptive meshes, a numerical model is proposed for studying two-dimensional effects arising from supersonic flow around the angles of compression and expansion. Numerical simulation was performed using various models such as inviscid, laminar or turbulent. In the calculations, the Mach number of the incident shock wave varies from 2 to 15, and the flow angle varies from 5 to 15 degrees. The Reynolds number, calculated from the characteristics of the unperturbed flow, is equal to 105. The working gas is air (γ = 1.4). A qualitative picture of the flow during diffraction of a shock wave on steps of different geometry is considered. When the shock wave interacts with the compression angle, flow separation and the formation of a recirculation region are observed, and when the shock wave interacts with the expansion angle, the Prandtl–Mayer wave is misaligned. The results of calculations are compared with theoretical data on the parameters of the flow behind the shock front or fan of the rarefaction wave. Studies have shown the influence of the effects of viscosity and turbulence on the flow structure and distribution of flow characteristics when flowing around the angles of compression and expansion. The simulation results can find application in solving problems related to the design of air intakes of high-speed flying aircrafts, in particular, in parametric and optimization calculations of gas-dynamic flows that arise in the elements of propulsion systems of supersonic and hypersonic aircraft.

Isothermal Strong Spherical Shock Waves in Uniform Medium

Isothermal Strong Spherical Shock Waves in Uniform Medium

An integration method based on a novel combined flow for aerodynamic configuration of strutjet engine

In this paper a novel design method of aerodynamic configuration is proposed to integrate forebody, strut and inlet for strutjet engine, and a model at design point of Mach number 6 is generated to investigate the aerodynamic performance by both simulations and experiments. The basic flow field employed by proposed method is a combined flow named IBB, which is combined by Internal Conical Flow A (ICFA), truncated Busemann flow I (BI) for external section, and truncated Busemann flow II (BII) for internal section. The model configuration is generated by streamline tracing method from basic flow field, in which the forebody section is traced from ICFA and BI flows, and the inlet as well as strut section is traced from BII flow. The simulations in Mach number 4, 5, and 6 demonstrate uniform starting flow fields with relatively high total pressure recovery, which agree well with experiments in wind tunnel. Additionally, in low Mach number cases, this inlet could start at Mach number 3 while it is unstarted at Mach number 2.7; in high Mach number cases, a uniform flow could still exist in Mach number 6.5 while a relatively strong shock wave boundary layer interaction is found in cowl area of Mach number 7 case, indicating the inlet designed by proposed method works in a relatively wide Mach number range.

Aerodynamic Optimization Design of a Supersonic Compressor Rotor with High Pressure Ratio

Supersonic compressors have a high wheel speed and operational capability, which facilitate a high stage pressure ratio. However, the strong shock waves in the passage of a supersonic rotor and the interference between shock waves and boundary layers can lead to large flow loss and low efficiency. Moreover, the existing design of a high-load supersonic compressor has the problem of small stall margin. In this study, an automatic optimization method including 2D profile optimization and 3D blade optimization is proposed to achieve a high efficiency at the design point of a supersonic compressor rotor under the premise of reaching the desired mass flow rate and total pressure ratio. According to the analysis of flow near the stall point of the supersonic compressor rotor, the mechanism responsible for rotor tip stall is established, that is, the aerodynamic throat appeared inside the flow passage, reducing the ability of the blade tip to withstand back pressure, and the low-speed areas caused by the tip-leakage-vortex breakage and boundary layer separation reduced the flow capacity of the blade tip. Based on the reasons for rotor stall, three methods are proposed to improve the stall margin, which include increasing the exit radius of the upper meridian, forward sweep of the blade tip, and increasing the chord length of the blade tip. The above method is used to design a supersonic rotor with a total pressure ratio of 2.8, which exhibits an efficiency of 0.902 at the design point and a stall margin of 18.11%.

Creating plasma from foam using high-energy lasers

Studying the transition of foam into the plasma state can lead to applications such as charged particle acceleration with lasers and creating strong shock waves with radiation-controlled energy transport.

A third-order subcell finite volume gas-kinetic scheme for the Euler and Navier-Stokes equations on triangular meshes

A third-order gas-kinetic scheme (GKS) based on the subcell finite volume (SCFV) method is developed for the Euler and Navier-Stokes equations on triangular meshes, in which a computational cell is subdivided into four subcells. The scheme combines the compact high-order reconstruction of the SCFV method with the high-order flux evolution of the gas-kinetic solver. Different from the original SCFV method using weighted least-square reconstruction along with a conservation correction, a constrained least-square reconstruction is adopted in SCFV-GKS so that the correction is not necessary and continuous polynomials inside each main cell can be reconstructed. For flows with large gradients, a compact hierarchical WENO limiting is adopted. In the gas-kinetic flux solver, the inviscid and viscous flux are coupled and computed simultaneously. Moreover, the spatial and temporal evolution are coupled nonlinearly which enables the developed scheme to achieve third-order accuracy in both space and time within a single stage. As a result, no quadrature point is required for the flux evaluation and the multi-stage Runge-Kutta method is unnecessary as well. A third-order k-exact finite volume GKS is also constructed with the help of k-exact reconstruction. Compared to the k-exact GKS, SCFV-GKS is compact, and with less computational cost for the reconstruction which is based on the main cell. Besides, a continuous reconstruction can be adopted in SCFV-GKS among subcells in smooth flow regions, which results in less numerical dissipation and less computational cost for flux evolution. Thus the efficiency of SCFV-GKS is much higher. Numerical tests demonstrate the strong robustness, high accuracy and efficiency of SCFV-GKS in a wide range of flow problems from nearly incompressible to supersonic flows with strong shock waves.

The non-relativistic interiors of ultra-relativistic explosions: Extension to the Blandford–McKee solutions

The hydrodynamics of an ultrarelativistic flow, enclosed by a strong shock wave, are described by the well-known Blandford–McKee solutions in spherical geometry. These solutions, however, become inaccurate at a distance ∼R/2 behind the shock wave, where R is the shock radius, as the flow approaches Newtonian velocities. In this work, we find a new self-similar solution that is an extension to the Blandford–McKee solutions and that describes the interior part of the blast wave, where the flow reaches mildly relativistic to Newtonian velocities. We find that the velocity profile of the internal part of the flow does not depend on the value of the shock Lorentz factor, Γ, and is accurate from r = 0 down to a distance of R/Γ2 behind the shock. Despite the fact that the shock wave is in causal contact with the entire flow behind it, a singular point appears in the equations. Nevertheless, the solution is not required to pass through the singular point: for ambient density that decreases slowly enough, ρ ∝ r−k with k<12(5−10)≅0.92, a secondary shock wave forms with an inflow toward the origin.

Thermo-acoustic instability in the process of flame propagation and transition to detonation

The paper is devoted to the numerical analysis of the reactive mixture explosion during the accidents at a launch site. The particular scenario concerns the explosion in the unconfined volume after accidental fuel release into the atmosphere. It is shown that the development of intrinsic flame instability results in the generation of compression waves, which occur to be intensified via the mechanism of thermo-acoustic instability. In turn, intensification of the compression waves leads to the formation of strong shock waves and even detonation in the case of a highly reactive mixture. The leading role in this process belongs to the transversal waves generated in the folds of the developed flame surface and propagated along the flame surface. It is the localization of the compression wave inside the reaction zone that causes amplification of the compression wave due to energy release.

Influence of shock wave impinging region on supersonic film cooling

Shock waves can significantly affect the film cooling for supersonic flow and shock waves may have different influence when impinging in different regions. The present study numerically compared the results of shock wave impinging in three different regions and analyzed the effect of impinging region. The shock wave generators were located at x/s = 5, 25, 45 with 4°, 7° and 10° shock wave incidence. The mainstream Mach number was 3.2 and the coolant Mach number was 1.2 or 1.5. The numerical results illustrated that the shock wave impinged in the further upstream region led to a larger high-pressure region and a larger vortex in the boundary layer. Moreover, placing the shock wave generator upstream resulted in the lower mass fraction of coolant in the downstream region. The velocity in the upstream part of the cooling layer was lower than the midstream and downstream part, which resulted in the less ability to resist the shock wave impingement. Therefore, the upstream impingement deteriorated the cooling performance to a greater extent. The study also manifested that the stronger shock wave had a larger effect on supersonic film cooling. Increasing the coolant inlet Mach number can increase the blowing ratio and reduce the mixing, which was of benefit to improve cooling effect.

Characteristic unsteady pressure field on a civil aircraft wing related to the onset of transonic buffet

Unsteady pressure fields on a civil aircraft wing near the onset of transonic buffet have been investigated experimentally to identify flow unsteadiness that relates to the buffet onset determined by global criteria. An 80%-scale NASA Common Research Model was tested in the JAXA 2 m × 2 m Transonic Wind Tunnel at a Mach number of 0.85 and a chord Reynolds number of 2.27 × 106. The angle of attack was varied in small increments around the buffet onset angle determined by global criteria based on the lift curve and wing-root strain-gauge data. Unsteady pressure fields over the wing were measured using unsteady pressure-sensitive paint (PSP) with temperature-effect correction by temperature-sensitive paint (TSP). Characteristic pressure fluctuations, known as “buffet cells”, were observed under the off-design conditions at a bump Strouhal number of 0.2–0.5. The PSP results showed that the buffet cells arise at the mid-span wing at η ≈ 0.45, where a strong shock wave causes an initial boundary-layer separation. Phase shift distributions indicated that a pressure perturbation propagates from the inboard wing toward the outboard wing. The convection velocity and spanwise wavelength were approximately 0.5U∞ and 1.3cMAC, respectively. The angle of attack at which buffet cells first appear was found to be approximately equal to the buffet onset determined by the global criteria, indicating that the occurrence of the buffet cells is deeply related to the buffet onset for the present wing geometry.

Physical investigation of acoustic waves induced by the oscillation and collapse of the single bubble

The objective of this paper is to apply both experimental and numerical methods to investigate acoustic waves induced by the oscillation and collapse of a single bubble. In the experiments, the schlieren technique is used to capture the temporal evolution of the bubble shapes, and the corresponding acoustic waves. The results are presented for the single bubble generated by a low-voltage bubble generator in the free field of water. During the numerical simulations, a three-dimensional (3D) weakly compressible model is introduced to investigate the single bubble dynamics, including the generation and propagation of acoustic waves. The results show that (1) Compression wave, rarefaction wave and shock wave are generated during expansion stage, collapse stage and rebound stage of the bubble respectively. (2) Compression waves are induced by the rapid expansion of the bubble and eventually steepen into one shock wave propagating outward in the liquid, then another strong shock wave is emitted at the final collapse stage. The velocity and pressure of the liquid field increases after the shock wave. (3) Rarefaction waves are generated during the collapse stage due to the contraction of the bubble. The rarefaction wave reduces the liquid pressure and its spatial distribution is dispersive. The pressure of these acoustic waves and their effect on the liquid velocity attenuate with the increase of propagation distance.

Characterization of shock wave signatures at millimetre wavelengths from Bifrost simulations.

Observations at millimetre wavelengths provide a valuable tool to study the small-scale dynamics in the solar chromosphere. We evaluate the physical conditions of the atmosphere in the presence of a propagating shock wave and link that to the observable signatures in mm-wavelength radiation, providing valuable insights into the underlying physics of mm-wavelength observations. A realistic numerical simulation from the three-dimensional radiative magnetohydrodynamic code Bifrost is used to interpret changes in the atmosphere caused by shock wave propagation. High-cadence (1 s) time series of brightness temperature (Tb) maps are calculated with the Advanced Radiative Transfer code at the wavelengths 1.309 mm and 1.204 mm, which represents opposite sides of spectral band 6 of the Atacama Large Millimeter/submillimeter Array (ALMA). An example of shock wave propagation is presented. The brightness temperatures show a strong shock wave signature with large variation in formation height between approximately 0.7 and 1.4 Mm. The results demonstrate that millimetre brightness temperatures efficiently track upwardly propagating shock waves in the middle chromosphere. In addition, we show that the gradient of the brightness temperature between wavelengths within ALMA band 6 can potentially be used as a diagnostics tool in understanding the small-scale dynamics at the sampled layers. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.