Shock wave interaction with area changes in ducts

This paper addresses nonlinear effects which result from the interaction of shock waves with vortices. A series of experiments are carried out, which involve the interaction of a strong shock wave with a single plane vorticity wave and a randomly distributed wave system. These experiments are first conducted in the linear regime to obtain a mutual verification of theory and computation. They are subsequently extended into the nonlinear regime. A systematic study of the interaction of a plane shock wave and a single vortex is then conducted. Specifically, we investigate the conditions under which nonlinear effects become important, both as a function of shock Mach number, M1, and incident vortex strength (characterized by its circulation Γ). The shock Mach number is varied from 2 to 8, while the circulation of the vortex is varied from infinitesimally small values (linear theory) to unity. Budgets of vorticity, dilatation, and pressure are obtained. They indicate that nonlinear effects become more significant as both the shock Mach number and the circulation increase. For Mach numbers equal to 5 and above, the dilatation in the vortex core grows quadratically with circulation. An acoustic wave propagates radially outward from the vortex center. As circulation increases, its upstream-facing front steepens at low Mach numbers, and its downstream-facing front steepens at high Mach numbers. A high Mach number asymptotic expansion of the Rankine--Hugoniot conditions reveals that nonlinear effects dominate both the shock motion and the downstream flow for ΓM1 > 1.

Recently, micro shock tubes have been widely used in various fields such as aerospace, combustion and medical science. Needle-free drug delivery device is a typical example of the application of the micro shock tube used in the field of medical science. Compared to the macro shock tube, the flow viscosity and micro scale effects considerably influence the shock wave propagation in the micro shock tube, which makes shock wave behaviors significant difference from the theoretical prediction. Boundary layers which develop behind the moving shock wave attenuate the shock wave propagation as well. Additionally, the gas-particle flows are also shown the different characteristics compared to the single gas flow in the micro shock tube. Particles are induced by the shock wave inside the micro shock tube and accelerated in the supersonic nozzle. Supersonic flows and particle velocity make experimental studies difficult to be performed in the micro shock tube. Even though micro shock tubes have been studied for decades, shock flow characteristics and particle dynamics inside the micro shock tube are not well known to date. For the present study, pressure measurements and optical visualization have been carried out in a micro shock tube. Static pressure measurements were used for investigating the shock wave propagation in the driven section, and Pitot pressure measurements were used for obtaining flow characteristics at the exit of nozzles. Two high sensitive pressure transducers were used for recording pressure changes as the shock wave moved through pressure transducers and the shock Mach number was calculated. Particle tracking velocimetry was conducted to analyze particle-gas two-phase flows. Particle distribution and velocity were obtained in the present experiment study.

When the shock wave propagating along the straight circular tube reaches at the open end, the spherical shock wave is generated by the emission of a shock wave from an open end and the unsteady jet is formed near the open end behind the spherical shock wave. The shock strength of spherical shock wave is dependent on the shock Mach number in the tube, and it attenuates with propagation distance from the open end. In this study, the flow induced by the emission of a comparatively strong shock wave from an open end of a tube with the infinity flange is analyzed numerically by the TVD method. As a result, it is concluded that the asymptotic position and diameter of Mack disk of unsteady jet are equal to the steady jet corresponding the pressure ratio. In addition, the relationship between strength of spherical shock wave and Mach number of incident shock wave is clarified from viewpoints of the characteristics of attenuation and directivity for the spherical shock wave.

The interaction of shock waves with a contact surface between gases of different densities has been studied experimentally and theoretically. The basic mechanism for the instability of perturbations at the interface is baroclinic vorticity generation resulting from the misalignment of the pressure gradient of the shock and the density gradient of the interface. In the present study, the effects of interface density contrast and initial thickness, and incident wave strength on the development of the instability at the interface are investigated. The experiments were performed in a new vertical shock tube facility where the interaction of a shock wave with either a discontinuous interface, formed by a thin (0.5 µm) plastic membrane, or a continuous interface, created by retracting a metal plate initially separating the two gases, was studied. Air was used on one side of the interface and either helium, carbon dioxide, refrigerant-22 or sulphur hexafluoride was used on the other side as the test gas. Experiments to study the time evolution of quasi-sinusoidal perturbations on a continuous interface have shown that the growth rates are reduced as the interface thickness is increased. It has been observed that growth rates of perturbations of wavelength λ ~ 25 mm on interfaces of thickness δ ~ 10 mm are about three times smaller than those predicted by the linear theory for the impulsive acceleration of discontinuous interfaces. A new model that accounts for the growth rate reduction caused by the presence of a finite density gradient on the interface has been proposed, and good agreement was obtained with the present experimental results. Experiments were also performed to observe the schlieren visual thickness of plane discontinuous or continuous interfaces with random small-scale perturbations after interaction with the incident shock wave and its reverberations. The interface was initially located near the end wall of the shock tube to permit the observation of the development of the interface phenomena after the arrival of the incident shock and its reverberations. It is found that the interaction of a shock wave with a discontinuous interface causes the appearance of a turbulent mixing zone between the two gases, whose growth rate slows down as time increases, owing to a decrease in turbulence intensity and the action of viscosity. Because of the large uncertainty associated with the measurements a short time after the interaction with the incident shock, the accurate determination of a possible universal power law governing the thickening of the interface is not feasible. Results for the interaction of the first reverberation of the primary wave with the already turbulent interface have demonstrated that this growth is sensitive to the initial pre-growth state of the interface. It also appears that the thickening of the turbulent mixing zone is accomplished by the merging of large structures within the interface. However, since the energy available for the turbulent motions at the impulsively accelerated interface remains constant after the interaction with the shock and also depends on the wavelength of the initial perturbation, it is not certain whether the development of mixing at the interface achieves an asymptotic stage of self-similar turbulence independent of initial conditions, as has been observed for the gravity-driven interfaces. Also, it has been found that the growth rates measured in the present experiments with discontinuous interfaces are nearly an order of magnitude lower than those reported by previous investigators. The continuous interfaces formed by the retracting plate are smoothed by molecular diffusion, and thus the combination of low density gradient and small initial perturbations is such that they exhibit growth only after being perturbed by acoustic noise introduced by the reverberation of waves between the interface, the side walls and the end of the shock tube. The development of viscous boundary layers on the side walls of the test section can cause the bifurcation of waves reflected from the end wall of the shock tube, and, thereafter, the formation of wall bubbles and interface contaminating jets. Moreover, the generation of vortical structures by the baroclinic instability excited by the interaction of reflected waves with the distorted interface within the boundary layer has been demonstrated. Significant contamination of the test gas can by achieved by these structures, even if reflected-wave bifurcation is absent. Moreover, the strain induced by the vorticity in these wall structures tends to thin the interface; the magnitude of this effect on the growth rates in the present plane interface experiments is estimated to be of order 10% for discontinuous interfaces and 50% for continuous interfaces.

We investigate interactions between a planar shock wave and homogeneous isotropic turbulence by employing direct numerical simulations. The shock wave at the shock Mach numbers 1.5 and 1.1 propagates through the turbulence without mean velocity. The interactions are studied for the statistical properties of turbulence and pressure increase of the shock wave. Fluid compression due to the shock wave causes velocity fluctuations to increase. This influence is more significant for the velocity component in the shock wave normal direction. The fluid compression in the shock wave normal direction also changes the spatial distribution of the vortical structures, resulting in the amplification of enstrophy. The characteristic length scales of turbulence, such as Taylor microscale, decrease by the interaction. The shock wave propagation in turbulence causes the fluctuation of pressure increase across the shock wave. We also show that the fluctuation of the pressure increase becomes stronger for the larger shock Mach number case.

An exact analytical model for the interaction between an isolated shock wave and an isotropic turbulent vorticity field is presented. The interaction with a single-mode two-dimensional (2D) divergence-free vorticity field is analyzed in detail, giving the time and space evolutions of the perturbed quantities downstream. The results are generalized to study the interaction of a planar shock wave with an isotropic three-dimensional (3D) or 2D preshock vorticity field. This field is decomposed into Fourier modes, and each mode is assumed to interact independently with the shock front. Averages of the downstream quantities are made by integrating over the angles that define the orientation of the upstream velocity field. The ratio of downstream/upstream kinetic energies is in good agreement with existing numerical and experimental results for both 3D and 2D preshock vorticity fields. The generation of sound and the sonic energy flux radiated downstream from the shock front is also discussed in detail, as well as the amplification of transverse vorticity across the shock front. The anisotropy is calculated for the far downstream fields of both velocity and vorticity. All the quantities characteristic of the shock-turbulence interaction are reduced to closed-form exact analytical expressions. They are presented as explicit functions of the two parameters that govern the dynamics of the interaction: the adiabatic exponent gamma and the shock Mach number M1 . These formulas are further reduced to simpler exact asymptotic expressions in the limits of weak and strong shock waves (M_{1}-11, M_{1}1) and high shock compressibility of the gas (gamma-->1) .

Due to their complexity, certain engineering problems like finding shock strength, Mach number etc. and the interaction of shock wave with a structure in free and restricted metal forming techniques cannot be achieved in a single experimentation, these can be obtained only through a number of trials and that leads to increase in cost and time. In such cases both cost and time can be reduced by adopting numerical simulations. In this projectcommercial software ANSYS is used to simulate the propagation shock wave through a shock tube, free and shape forming of metallic plates subjected to this shock wave. Shock Mach numbers up to 2.12 have been generated by varying the driver to driven pressure ratios. Thin copper plates of diameter 60mm and thickness of 0.5mm and 0.3mm are subjected to shock wave loadingin order to form into dies.These dies,madeof structural steel are modelled with pre-defined shapes. The plate peakoverpressures ranging from 9 to 20bar have been generated.The midpoint deflection, Von Mises stress and strain are calculated for free forming copper plates. The simulated results are compared with the experimental values available in literature. The simulated results match well with the experimental values.

The propagation of a spherical shock wave in a non‐ideal gas with or without gravitational effects is investigated under the action of monochromatic radiation. Similarity solutions are obtained for adiabatic flow between the shock and the piston. The numerical solutions are obtained using the Runge‐Kutta method of the fourth order. The density of the gas is assumed to be constant. The total energy of the shock wave is non‐constant and varies with time. The effects of change in values of non‐idealness parameter, gravitational parameter, shock Mach number, radiation parameter, and adiabatic exponent of the gas on shock strength and flow variables are worked out in detail. It is investigated that the presence of gravitational field increases the compressibility of the medium, due to which it is compressed and, therefore, the distance between the inner contact surface and the shock surface is reduced. A comparison is also made between the solutions in the cases of the gravitating and the non‐gravitating media. It is manifested that the gravitational parameter and the radiation parameter have in general opposite behaviour on the flow variables and the shock strength.

In this paper, we investigate the modified Kadomtsev–Petviashvili (mKP) equation for the nonlinear waves in fluid dynamics and plasma physics. By virtue of the rational transformation and auxiliary function, new bilinear form for the mKP equation is constructed, which is different from those in previous literatures. Based on the bilinear form, one- and two-soliton solutions are obtained with the Hirota method and symbolic computation. Propagation and interactions of shock and solitary waves are investigated analytically and graphically. Parametric conditions for the existence of the shock, elevation solitary, and depression solitary waves are given. From the two-soliton solutions, we find that the (i) parallel elastic interactions can exist between the (a) shock and solitary waves, and (b) two elevation/depression solitary waves; (ii) oblique elastic interactions can exist between the (a) shock and solitary waves, and (b) two solitary waves; (iii) oblique inelastic interactions can exist between the (a) two shock waves, (b) two elevation/depression solitary waves, and (c) shock and solitary waves.

Vorticity generation and flame distortion induced by shock flame interaction

In case of some accidents on railways there may be situations when the shock wave appears and interacts with different objects on the railway (wagons, cargo, buildings etc.). In these cases it is necessary to predict the possible effect of shock wave diffraction on the different objects. Study of these problems on the basis of physical experiments (laboratory experiment or field experiment) demand expensive and unique experimental facility. In some cases physical experiment can’t be set. That is why mathematical simulation plays the important role in solving problem connected with shock wave propagation. For practice it is necessary to have predictive quick computing mathematical models which allow to perform numerical experiment on the basis of non-powerful computers. Now, in Ukraine, there is a real deficit of mathematical models which allow to compute quickly shock wave interaction with different objects. The aim of this work was development of quick computing numerical model to simulate shock wave propagation and its interaction with the wagons. The model is based on the numerical integration of Euler equations which are written in integral form. To solve modeling equations difference scheme of splitting was used. Results of numerical modeling are presented.

Development of instability in the region of mixing of fast-moving gases of different densities is a topical problem for energy-commuting facilities. Conventionally, the mixing layer is considered as a surface of the continuity break, i.e., as the contact break. The interaction of the shock wave with a perturbed contact discontinuity generates the Richtmeyer‐Meshkov instability. At the final stage, in the region of the initial contact break, the region of turbulent mixing separating the flows of compressed gases is formed. Numerous works on numerical modeling of the development of the Richtmeyer‐Meshkov instability based on the Euler equations did not take into account the influence of processes of mutual penetration of gases. Therefore, it is of interest to investigate this problem based on the equations of the double-speed two-temperature gas mixture, where each component has its own velocity and temperature. This approach allows one to describe the development of instability at various stages allowing for mutual penetration of gases. The necessity of applying models of multicomponent systems to describe the destruction of the contact boundary and formation of the region of the mixture was, e.g., pointed out in [1]. In [2], a semiempirical model of turbulent mixing of a multicomponent medium based on the use of its own velocity for each component is constructed. In this model, it is assumed that turbulent mixing appears instantly. Below, based on the equations of the double-speed two-temperature gas dynamics of the mixtures, we investigate the processes at the initial stages of mixing. We previously [4] investigated the interaction of the mixing layer with the incident shock wave and compression wave [5]. In this work, on the basis of equations of the doublespeed two-temperature gas dynamics of the mixtures [3], we investigate the processes of development of the Richtmeyer‐Meshkov instability during the interaction of the incident shock wave with the perturbed mixing layer allowing for the further repeated interaction of the layer with the waves reflected from the end. The initial sinusoidally perturbed diffusion layer of mixing was formed on the basis of the solution suggested in [4] with the perturbation amplitude a 0 , the perturbation wavelength λ , and the initial layer width δ 0 . The interaction of the mixing layer with the incident shock wave, which transfers from the light gas into the heavy gas and from the heavy gas into the light gas, is considered. The parameters of the mixture in the layer are described by the equations of the double-speed two-temperature gas dynamics of the mixtures [3], which transform to the Euler equations for pure gas out of the layer. The method of calculation of the starting set of equations is described in [4, 5]. The shock wave moved from upward to downward. At the upper boundary, the condition that derivatives were equal to zero was given, and the lower boundary is a solid wall. Symmetry conditions were given at the side boundaries. We considered the incidence of the shock wave on the mixing layer with the reflection angle in a onedimensional approximation in the absence of perturbations in the initial mixing layer. The results of these investigations are in complete agreement with the conclusions of [6].

This study numerically and experimentally examines the resulting flow field of a shock wave passing through a pipe gap. The effects of gap geometry and shock Mach number variation are investigated. Incident shock Mach numbers of 1.3, 1.4, and 1.5 and gap widths of 25 and 50 mm were used, which correspond to 0.5 and 1.0 pipe inner diameters, respectively. For both cases, the incident shock wave propagated into the downstream pipe at much reduced strength. A strong expansion propagated into the upstream pipe causing a significant pressure drop from the initial post-shock pressure. Expansion waves at the outflow resulted in supersonic speeds as the flow entered the gap for Mach 1.4 and 1.5. A notable feature was the formation of a standing shock at the inlet to the downstream pipe for the higher two Mach numbers in both cases. Decreasing the gap width moved the standing shock closer to the downstream pipe. For the lowest Mach number of 1.3, no standing shock system was set up. The propagation conditions in the downstream pipe showed that the pressure is initially unsteady, but becomes more uniform, controlled by the developed wave system in the gap. For the flanged gap case, the flow within the gap is confined for much longer and hence produces more intense and complex flow feature interactions and an earlier transition to turbulence. The induced shock strength in the downstream pipe is independent of gap geometry and separation distance examined in this paper as verified by experimental pressure traces.

view Abstract Citations (46) References (45) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The effect of losses on acceleration of energetic particles by diffusive scattering through shock waves Voelk, H. J. ; Morfill, G. E. ; Forman, M. A. Abstract A discussion of the effect of local losses on the acceleration of energetic particles by shocks is presented, which considers the energy losses of individual particles and the damping processes for the scattering hydromagnetic waves by means of time asymptotic and steady-state calculations. For acceleration to be a local effect within the Galaxy, the local scattering mean free path must be small by comparison with the effective overall galactic mean free path deduced from the cosmic-ray escape time. Given the spatial extent of the layer for strong shocks propagating into neutral interstellar clouds, the possibility of localized diffusive acceleration is investigated. The estimated strength and extent of the scattering region is not large enough to confine acceleration within the layer, which will instead extend across the entire cloud. The integrated losses of the cloud will then determine the efficiency. Publication: The Astrophysical Journal Pub Date: October 1981 DOI: 10.1086/159272 Bibcode: 1981ApJ...249..161V Keywords: Energetic Particles; Energy Dissipation; Interstellar Matter; Molecular Clouds; Particle Acceleration; Shock Wave Propagation; Cosmic Rays; Gas Ionization; Gaseous Diffusion; Magnetohydrodynamic Waves; Shock Wave Interaction; Stellar Winds; Wave Scattering; Astrophysics full text sources ADS |

Context. We revisit the study of shocks interacting with molecular clouds, incorporating coupled gas-dust dynamics. Aims. We study the effect of different parameters on the shock-cloud interaction, such as the dust-to-gas ratio or the Mach number of the impinging shock. By solving self-consistently for drag-coupled gas and dust evolutions, we can assess the frequently made assumption that the dust is locked to the dynamics of the gas so that dust observations would result in direct information on the gas distribution. Methods. We used a multi-fluid model where the dust is represented by grain-size specific pressureless fluids. The dust and gas interact through a drag force, and we used four dust species with weighted representative sizes between 1 and 500 nm. We use the open source code MPI-AMRVAC for a parametric study of the effect of the gas-dust ratio and the Mach number of the shock. By using the radiative transfer code SKIRT, we create synthetic millimeter wavelength maps to connect to observations. Results. We find that the presence of dust does not significantly affect the dynamics of the gas for realistic dust-gas ratios, and this is the case throughout the range of Mach numbers explored (1.5−10). For high Mach numbers, we find a significant discrepancy between the distribution of the dust and gas after the cloud-shock interaction with the larger dust species clearly lagging the heavily mixed and accelerated gas (re)distribution. Conclusions. We conclude that observational studies of dusty environments may need to account for clearly separated spatial distributions of dust and gas, especially those studies that are representative of molecular clouds that have been interacting with high Mach number shock fronts.