Propagation of Shocks through Nonuniformly Heated Gases (original) (raw)
Related papers
Shock bowing and vorticity dynamics during propagation into different transverse density profiles
Physica D: Nonlinear Phenomena, 2002
A 2D numerical investigation is presented of shock wave propagation into a gas whose density is modulated in the transverse direction across the width of a shock tube. These density modulations represent temperature distributions in which low density corresponds to high temperature gas and high density corresponds to low temperature gas. This work is motivated by recent shock-plasma experiments, and mechanisms to explain the experimentally observed shock "splitting" signatures are investigated. It is found that the shock splitting signatures are more pronounced when the shock wave is more strongly curved or bowed. This occurs as the depth of the initial density profile is increased. The gross features of the shock splitting signatures are relatively insensitive to variations in the shape of the initial density profile (into which the shock propagates). Several interesting features of vorticity production and evolution are also indicated.
In this paper, the generalized analytical solution for one dimensional adiabatic flow behind the strong imploding shock waves propagating in a non-ideal gas is obtained by using Whitham's geometrical shock dynamics theory. Landau and Lifshitz's equation of state for non-ideal gas and Anand's generalized shock jump relations are taken into consideration to explore the effects due to an increase in (i) the propagation distance from the centre of convergence, (ii) the non-idealness parameter and, (iii) the adiabatic index, on the shock velocity, pressure, density, particle velocity, sound speed, adiabatic compressibility and the change in entropy across the shock front. The findings provided a clear picture of whether and how the non-idealness parameter and the adiabatic index affect the flow field behind the strong imploding shock front.
Propagation of strong shock waves in a non-ideal gas
Acta Astronautica, 2019
We studied the problem of converging cylindrical and spherical strong shock waves collapsing at the axis/center of symmetry for a non-ideal gas with constant density. We have applied the perturbation series technique which provides us a global solution to the implosion shock wave problem yielding the results of Guderley's local self-similar solution, which is valid only in the vicinity of the axis/center of implosion. We analyzed the flow parameters by expanding the solution in powers of time and found the similarity exponents as well as the corresponding amplitudes in the vicinity of the shock-collapse. The flow parameters and the shock trajectory have been drawn in the region extending from the piston to the center of collapse for different values of adiabatic coefficient and the non-ideal parameter.
A Full Evaluation of Accurate Constitutive Relations for Shock Wave Structures in Monatomic Gases
2021
We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range 1.0 − 11.0. Compared to previous studies that focussed mainly on the density profile across the shock, here we also include temperature profiles as well as non-negativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bi-velocity hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.
Passage of a shock wave through inhomogeneous media and its impact on gas-bubble deformation
Physical Review E, 2015
The paper investigates shock-induced vortical flows within inhomogeneous media of nonuniform thermodynamic properties. Numerical simulations are performed using an Eularian type mathematical model for compressible multi-component flow problems. The model, which accounts for pressure non-equilibrium and applies different equations of state for individual flow components, shows excellent capabilities for the resolution of interfaces separating compressible fluids as well as for capturing the baroclinic source of vorticity generation. The developed finite volume Godunov type computational approach is equipped with an approximate Riemann solver for calculating fluxes and handles numerically diffused zones at flow component interfaces. The computations are performed for various initial conditions and are compared with available experimental data. The initial conditions promoting a shock-bubble interaction process include: weak to high planar shock waves with a Mach number ranging from 1.2 to 3 and isolated cylindrical bubble inhomogeneities of helium, argon, nitrogen, krypton and sulphur hexafluoride. The numerical results reveal the characteristic features of the evolving flow topology. The impulsively generated flow perturbations are dominated by the reflection and refraction of the shock, the compression and acceleration as well as the vorticity generation within the medium. The study is further extended to investigate the influence of the ratio of the heat capacities on the interface deformation.
Evolution of Weak Shock Waves in Perfectly Conducting Gases
Applied Mathematics, 2011
This article aims at studying one dimensional unsteady planar and cylindrically symmetric flow involving shocks under the influence of magnetic field. The method of generalized wavefront expansion (GWE) is employed to derive a coupled system of nonlinear transport equations for the jump of field variables and of its spatial derivatives across the shock, which, in turn determine the evolution of wave amplitude and admit a solution that agrees with the classical decay laws of weak shocks. A closed form solution exhibiting the features of nonlinear steepening of the wave front. A general criterion for a compression wave to steepen into a shock is derived. An analytic expression elucidating how the shock formation distance is influenced by the magnetic field strength is obtained. Also, the effects of geometrical spreading and nonlinear convection on the distortion of the waveform are investigated in the presence of magnetic field.
Stretching of material lines in shock-accelerated gaseous flows
Physics of Fluids, 2005
A Mach 1.2 planar shock wave impulsively accelerates one of five different configurations of heavy-gas ͑SF 6 ͒ cylinders surrounded by lighter gas ͑air͒, producing one or more pairs of interacting vortex columns. The interaction of the columns is investigated with planar laser-induced fluorescence in the plane normal to the axes of the cylinders. For the first time, we experimentally measure the early time stretching rate ͑in the first 220 s after shock interaction before the development of secondary instabilities͒ of material lines in shock-accelerated gaseous flows resulting from the Richtmyer-Meshkov instability at Reynolds number ϳ25 000 and Schmidt number ϳ1. The early time specific stretching rate exponent associated with the stretching of material lines is measured in these five configurations and compared with the numerical computations of Yang et al. ͓AIAA J. 31, 854 ͑1993͔͒ in some similar configurations and time range. The stretching rate is found to depend on the configuration and orientation of the gaseous cylinders, as these affect the refraction of the shock and thus vorticity deposition. Integral scale measurements fail to discriminate between the various configurations over the same time range, however, suggesting that integral measures are insufficient to characterize early time mixing in these flows.
Propagation characteristics of shock waves driven by gaseous detonation waves
2010
We experimentally investigated propagation characteristics of the shock wave driven by a gaseous detonation wave emerging from the open end of a cylindrical detonation tube. In the present study, we visualized the shock wave and exhaust flowfields using a shadowgraph optical system and we obtained peak overpressure in the tube axial direction and the continuous shape transformation of shock waves around the tube open end. We also obtained overpressure histories of the shock wave using piezo-pressure transducers within 201 m from the open end of the tube. We normalized and classified these results by four regions using non-dimensional pressure and distance which are independent of variety of mixture and tube diameter. In the vicinity of the open end of the tube, the shock wave is nearly planar and does not significantly attenuate, and the peak overpressure maintains approximately C-J pressure. Subsequently, the shock wave attenuates rapidly, transforming from quasi-spherical to spherical. Farther from the tube open end, the shock wave propagates with approximately sound characteristic so This paper is based on work that was presented at the 22nd International Colloquium on the Dynamics of Explosions and Reactive Systems, Minsk, Belarus, July 27-31, 2009. J. Kasahara and A. Matsuo are Senior Member AIAA. that the peak overpressure decreases proportional to 1/r . Eventually, the shock wave begins to attenuate more rapidly than ideal sound attenuation, which may be due to the viscous effect.
Effects of molecular diffusivity on shock-wave structures in monatomic gases
Physical Review E, 2021
We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the prediction of shock structure in a monatomic gas in the Mach number range 1.0 − 11.0. The constitutive equations are extracted from a previously derived thermomechanically consistent Burnett regime continuum flow model. The numerical computations of the resulting hydrodynamic equations along with classical ones are performed using a finite difference global solution (FDGS) scheme. Compared to previous studies that focussed mainly on the density profile across the shock, here we also include temperature profiles as well as nonnegativity of entropy production throughout the shock. The results obtained show an improvement upon those obtained previously in the bi-velocity (or volume/mass diffusion) hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.