New relations between macroparameters in shock wave

Abstract

The profiles of macroparameters in a strong shock wave in one-component monatomic gas are investigated. It is found out that the heat flux is changed approximately as the second power polynomial, and the velocity gradient is changed as the third power polynomial of the gas velocity in the shock wave. Three independent coefficients of these polynomials are the functions of Mach number of the undisturbed flow. These dependencies allow us to describe the velocity and temperature profiles in strong shock waves in elementary functions. With these relations we can describe the stress and heat flux through the velocity and temperature gradients. The relations generalize the Newton-Fourier linear laws which are true for the infinitely weak shock wave.

Constitutive Relations for Stresses and Heat Flux. Non-Newtonian Gasdynamics

“…Moreover, it was proved that this function is the solution of the model kinetic equation for Couette problem. The general results of paper [6] are valid not only for BGK equation, but also for Boltzmann equation with Maxwell molecular model, as it was shown by DSMC method in papers [7,8].…”

“…Present investigation is the extension to previous research of impulse and energy transport processes in two onedimensional flows under special molecular model [5][6][7][8][9]. In paper [5] the structure of asymptotic series of Hilbert normal solution for shear flow corresponding to the plane Couette problem was obtained.…”

“…Statements of Couette problem differ in [7,8] by the boundary conditions for Boltzmann equation. In paper [9] it was N xy p shown, that it is possible to describe the strong shock wave flow by the macroscopic equations that are the generalization of Navier-Stokes equations.…”

“…In paper [9] it was N xy p shown, that it is possible to describe the strong shock wave flow by the macroscopic equations that are the generalization of Navier-Stokes equations. One of the purposes of this research is the determination of the applicability the results of papers [7][8][9] to the gas with another molecular models. Basic hypothesis assumed in this paper is the generalization of dependences established for shear flow problem.…”

Macroscopic Equations for High-Speed Rarefied Monatomic Gas Flows past Cold Bodies

“…It was shown the structure of normal Hilbert solution of Boltzmann equation for Maxwell molecules at arbitrary nonequilibrium [6].Than the constitutive relations for stress and heat flux were determined for BGK model kinetic equation [7] by analytical approach and for Boltzmann equation [8,9] by DSMC solution. The possibility of construction the constitutive relations similar to relations in Couette flow was shown for shock wave flow [10] and for spherical expansion flow into vacuum [11]. The first attempt to construct the more general equations for arbitrary flow was made in [11].…”