A study of shock waves in expanding flows on the basis of spectroscopic experiments and quasi-gasdynamic equations

Abstract

A comprehensive numerical and experimental study of normal shock waves in hypersonic axisymmetric jets of N 2 is presented. The numerical interpretation is based on the quasi-gasdynamic (QGD) approach, and its generalization (QGDR) for the breakdown of rotational-translational equilibrium. The experimental part, based on diagnostics by high-sensitivity Raman spectroscopy, provides absolute density and rotational temperatures along the expansion axis, including the wake beyond the shock. These quantities are used as a reference for the numerical work. The limits of applicability of the QGD approach in terms of the local Knudsen number, the influence of the computational grid on the numerical solution, the breakdown of rotation-translation equilibrium, and the possible formation of a recirculation vortex immediately downstream from the normal shock wave are the main topics considered.

Comparison of the numerical solutions of the full Boltzmann and S-model kinetic equations for gas flow through a slit

“…These parameters vary strongly along the x axis, the amplitudes of these variations damp downstream. The alternate presence of supersonic and subsonic areas demonstrates the existence of strong shock waves and the formation of the Mach disk like structure [17,24]. These structures are characterized by a sharp decrease of the density and the temperature along symmetry line and by the fast flow acceleration.…”

“…The accuracy of this computation tends to O(Dc 2 ), when the number of integration nodes in phase space tends to infinity. It should be noticed that in contrast to an explicit scheme, for which an additional to (17) restriction for the time step appears Dt < 1/max i, j (m i, j ), explicit-implicit scheme (18) allows us to use the same Dt as for transport step, according to condition (17).…”

Simulating Argon, Helium, and Nitrogen Shock Waves

“…To allow for possible nonequilibrium in translational and rotational degrees of freedom, we also used the QGDR system for a diatomic gas with two rotational degrees of freedom [10]. Previously QGDR equations had been successfully applied to compute the nitrogen shock wave structure, producing a good fit with the kinetic results [10] and experimental data in the modeling of underexpanded jets [11]. For one-dimensional flow, the QGDR system has the form Table 3 shows the dependence of the reciprocal front width on the Mach number.…”

Numerical modelling of rarefied gas flow through a slit at arbitrary pressure ratio based on the kinetic equation

“…A special attention should be paid to the case p 1 /p 0 = 0.1 and δ = 100 when all quantities n, u x and T have the sharp variations near the point x = 5. In the case of axisymmetrical flows, such sharp variations are also observed [3,31] and called Mach discs. For the two-dimensional flow considered here, the variations can be called as Mach belts.…”