Interaction between a shock and an acceleration wave in a perfect gas for increasing shock strength (original) (raw)
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Interaction of an acceleration wave with a strong shock in reacting polytropic gases
Applied Mathematics and Computation, 2013
Interaction of an acceleration wave with a strong shock in reacting polytropic gases 4.1 Introduction This chapter is concerned with the problem of interaction of an acceleration wave with a strong shock wave in reacting gases. The general theory of wave interaction problem has its origin from the works of Jeffrey [35] and Boillat & Ruggeri [36, 40]. Radha, Sharma & Jeffrey [23] have shown that the general theory of wave interaction problem which originated from the work of Jeffrey [35] leads to the results obtained by Brun [42] and Boillat & Ruggeri [36, 40]. In continuum Mechanics, weak discontinuity waves are also known as acceleration waves and is an important kind of solutions of nonlinear hyperbolic systems. These waves are characterized by a discontinuity in a normal derivative of the field but not in the field itself [34]. The problem of the interaction of an acoustic wave with a shock has been studied by Swan & Fowles [37] and Van Moorhen & George [38]. The evolution of a weak discontinuity for a hyperbolic quasi-linear system of equations satisfying the Bernoulli's law has been studied quite extensively in the literatures [39,
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Central European Journal of Engineering, 2011
This paper investigates the problem of propagation of planar and non-planar weak shock waves in a non-ideal medium. The mathematical formulation developed in this work leads to a closed system of coupled transport equations which efficiently describes the strength of a shock wave and the first order discontinuities induced behind it. The influence of the parameter of non-idealness and the non planar configuration of the wavefront on the nonlinear distortion, attenuation and shock formation of pulses, are discussed in detail. An analytical expression for the shock formation distance is obtained and a direct comparison between the ideal versus the non ideal gas flow is established. Also, the usual asymptotic decay laws for weak shock are recovered.
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Journal of Applied Mechanics and Technical Physics, 1975
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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.
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.
Diffusive shock acceleration: a method based on integral equation
Advances in Space Research, 2000
The structure of a strong shock, slgmficantly modified by cosmic rays (CRs) 1s studied on the level of a kinetic description, assummg Bohm-type diffusion The original problem that 1s commonly formulated m terms of the diffusion-convection equation for the dlstrlbutlon function of CRs, coupled with the thermal plasma through the momentum flux contmulty equation, 1s reduced to a nonhnear integral equation m one variable
On the Mutual Penetrations of Two Fluids Whose Interface is Accelerated by a Shock Wave
Shock Waves, 2006
A shock tube experimental investigation and numerical simulations are undertaken to study the evolution of a perturbed interface of two different gases accelerated by a shock wave. The experimental method is based on a high-speed camera laser sheet diagnostic technique, and simulations are provided by our code CARBUR based on a finite volume discretization of Navier-Stokes's equations. Two gas pairs are used to illustrate both the heavy/light (air/He) and the light/ heavy (air/SF 6 ) cases. Two simultaneous large initial perturbations, one positive and one negative, are tested for an incident shock wave Mach number in air of about 1.3. The thin membrane (less than 1 μ) which materializes the initial interface between the two test gases presents 2D perturbations whose wave number is close to 1 in order to rapidly reach the non-linear regime. The development of the perturbations is captured at a frequency of 10 kHz after the interface acceleration, and the experiments are complemented with a numerical simulation to validate the interface deformations. Results show an asymmetric mutual gas penetration increasing with the absolute value of the Atwood's number. Furthermore, they confirm that the heavier gas penetrates the lighter as thin spikes and the lighter gas penetrates the heavier as large bubbles. Moreover, we show that the spike moves faster than the bubble in the heavy/light case and slightly faster in the light/heavy one. Finally, numerical and experimental results are in agreement.
Numerical study of unsteady shock wave interaction in a rarefied gas
2018
Unsteady interactions of shock waves are simulated numerically and analyzed taking into account viscosity and heat conductivity effects. Both a symmetric head-on collision of two shock waves of an equal strength and an asymmetric interaction of two shock waves propagating with different velocities are considered. In comparison with the classical inviscid case new effects connected with a finite width of the interacting shock waves have been observed. An increase in temperature and entropy is observed in the wake trailing behind a viscous spot formed by the intersecting symmetric finitewidth shock waves. An expanding viscous contact wave formed as a result of the asymmetric interaction generates weak pressure and disturbances in the space between two reflected shock waves.
Precursor shock waves at a slow—fast gas interface
Journal of Fluid Mechanics, 1976
This paper presents experimental data obtained for the refraction of a plane shock wave at a carbon dioxide-helium interface. The gases were separated initially by a delicate polymer membrane. Both regular and irregular wave systems were studied, and a feature of the latter system was the appearance of bound and free precursor shocks. Agreement between theory and experiment is good for regular systems, but for irregular ones it is sometimes necessary to fake into account the effect of the membrane inertia to obtain good agreement. The basis for the analysis of irregular systems is one-dimensional piston theory and Snell's law.