Temperature dependence of shock wave structure in helium and neon

Abstract

Temperature dependence of a planar shock wave in helium and neon is studied by the direct simulation Monte Carlo method based on ab initio potentials. A quantum approach to interatomic interactions used here allows us to carry out calculations over a wide temperature range beginning from 1 K up to 5000 K. Moreover, for high temperatures, the quantum approach requires less computational effort than the classical one. Three gaseous species are considered: helium-3, helium-4, and neon. The problem is solved for three values of the Mach number Ma = 2, 5, 10. No influence of the quantum effects has been detected within the numerical error for the temperature of 300 K and higher. For temperatures lower than 300 K, the influence of the quantum effects in helium exceeds the numerical error and reaches 230%. In the case of neon, the quantum effect does not exceed 2% in the whole temperature range considered in the present work. A comparative analysis of flow-fields in shock waves at various temperatures points out a strong influence of the temperature ahead of a shock wave on its structure. The numerical data provided in the supplementary material can be used to model any flow of helium and neon in a wide range of temperatures.

Thermodynamic and kinetic investigation of the influence of external centrifugal field and the heat transfer on a confined neutral gas

“…That property gives the Boltzmann equation an excellent advantage and various modern applications rather than the Navier-Stokes equations [12,13]. Many papers were dealing with Boltzmann kinetic equation and its applications in many critical physical situations such as heat transfer between two parallel plates [14,15], shock waves [16], irreversible thermodynamics [17], sound propagation in a rarefied gases [18], oscillatory flow [19,20], thermal radiation [21][22][23], plasma [24], and other various amazing applications [25][26][27].…”

Shock Wave Driven Out by a Piston in a Mixture of a Non-ideal Gas and Small Solid Particles Under the Influence of Azimuthal or Axial Magnetic Field

“…For integrating numerically, fourth-order Runge-Kutta method is used. Parameters of the inert mixture (alumina Al 2 O 3 or glass) are within the following range: dust particle size is in the order of 1 μm − 10 μm (see Higashino and Suzuki [24], Fedrov and Kratova [51]), the material density of solid particles ρ sp = 2.5 g/cm 3 , mass fraction (concentration) of solid particles in the mixture is varied from K p = 0 to K p = 0.4. This case may be realized in an airflow with a suspension of alumina or glass particles.…”

“…Shock waves sharply raise the pressure and temperature of the medium. Shock waves are very thin, and the thickness of shock wave is about 10 −7 m for air at ambient conditions (see [1][2][3]). Shock wave studies are of great importance from the standpoint of both practical applications and fundamental research.…”

Numerical evaluation of novel kinetic models for binary gas mixture flows

“…The second proof is to compare the total macroscopic properties of the gas ρ, u 0 , T and validate the results against single species results. This test case is well-studied and there are suitable experimental, e.g 43 , and numerical results, e.g 30,31,44 . As described earlier, the power law for the…”

“…A benchmark test case for validation of new models is the profile of a normal shock wave, since it is the simplest form of high speed non-equilibrium flow. It is well-inspected for binary mixtures of monoatomic gases, e.g experimentally 26,27 and numerically 5,6,[28][29][30] , where all numerical papers validate their results against the results from the full Boltzmann equation 23 . Here, the mixture models are first shown to reduce to single species models and are validated with known results 31 .…”