Experimental study of numerical methods for the solution of gas dynamics problems with shock waves (original) (raw)
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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.
Numerical Simulation of Shock Wave Propagation n a Mixture of a Gas and Solid Particles
Combustion, Explosion, and Shock Waves, 2010
A numerical method based on the cubic interpolated polynomial (CIP) approach is applied for simulation of two-velocity two-temperature two-phase flow dynamics. Validation of the results is provided by numerical tests. A problem of shock wave propagation in a mixture of a viscous heat-conducting gas and solid particles of essential volume fractions is investigated as an application case. The influence of the particle size and drag coefficient formulation on the flow pattern, in particular, on the temperature behavior within the relaxation zone is revealed. A comparison with experimental dependences of the parameters behind the shock front on the Mach number is performed.
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31st International Symposium on Shock Waves 1, 2019
A structure of planar shock wave propagating through a helium-argon mixture is calculated applying the direct simulation Monte Carlo method based on ab initio interatomic potential for several values of the Mach number in the range between 1.5 and 10. To characterize the density and temperature variations along the shock wave, dimensionless slopes of these quantities, defined through their maximum derivative with respect to the spatial coordinate, are calculated. A comparison of the slopes and density distributions for different values of molar fraction shows that the chemical composition strongly affects the shock wave characteristics.
International Journal for Numerical Methods in Biomedical Engineering, 2010
This article employs an alternative procedure to treat a class of non-linear hyperbolic systems, using a preliminary model to describe pollutants motion in an atmosphere, accounting for the production or destruction of pollutants, described, as a first approximation, by a source term. The mathematical description consists of a non-linear hyperbolic system of m +2 partial differential equations representing mass and momentum conservation for the multicomponent mixture of air and gases and mass balance equations for the gases. After simplifying assumptions, the resulting one-dimensional system of m +2 equations is simulated in such a way that the simultaneous problem is treated sequentially: the operator is splitted into a non-homogeneous (time-dependent) ordinary part and a homogeneous associated hyperbolic one. This latter is simulated by a Glimm's scheme for evolution in time, employing an approximate Riemann solver for each two consecutive steps. The employed Riemann solver approximates the solution of the associated Riemann problem by piecewise constant functions always satisfying the jump condition-giving rise to an approximation easier to implement with lower computational cost. Comparison with the standard procedure, employing the complete solution of the associated Riemann problem for implementing Glimm's scheme, has shown good agreement.
Title: Gas Dynamics Equations: Computation
2016
Computation Shock waves, vorticity waves, and entropy waves are fundamental discontinuity waves in nature and arise in supersonic or transonic gas flow, or from a very sudden release (explosion) of chemical, nuclear, electrical, radiation, or mechanical energy in a limited space. Tracking these discontinuities and their interactions, especially when and where new waves arise and interact in the motion of gases, is one of the main motivations for numerical computation for the gas dynamics equations. The fundamental equations governing the dynamics of gases are the compressible Euler equations, consisting of conservation laws of mass, momentum, and energy:
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.
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.
Numerical simulations of interactions between shock wave and gas-liquid-air interfaces
Journal of Physics: Conference Series, 2010
A gas-liquid-air model and problems of interactions between the shock wave and the interfaces during the expansion process are rather familiar in the study of liquid explosive dispersal and underwater explosion near air-water surface. It involves large density discontinuity and large pressure gradient at the same time which brings difficulties for the numerical simulations. In this paper, we use the level-set methods to capture the interface and the modified ghost fluid method (MGFM) to treat the interface conditions. Strong shockinterface interactions and influences of the disturbance on the two interfaces are investigated. The initial fragmentation of the liquid is studied based on the analyses of the fluid pressure distribution and the variation of the interface, combining the conditions of the cavitations occurrence in the liquids.
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.