Limitations of the bulk viscosity approach in modeling the expanding nitrogen flows

Abstract

The accuracy of application of the bulk viscosity approach in modeling the spherically-expanding flows of nitrogen has been evaluated in comparisons of distributions of translational and rotational energy calculated within the framework of the Chapman-Enskog method and solutions of the nonequilibrium gasdynamic equations and the relaxation equation. The calculations of the bulk viscosity, relaxation time, shear viscosity, thermal conductivity, and diffusion coefficients are carried out in the temperature range from 10 K to 1,000 K for nitrogen using the classical Parker’s model (at moderate temperatures) and the quantum-mechanics adiabatic energy-exchange approach (at temperatures T < 100 K). The numerical solutions of the Navier-Stokes equations are analyzed for both approaches under the conditions of nitrogen flow in underexpanded jets. It is found that the bulk viscosity approach predicts much thinner spherical shock-wave areas than those estimated by the relaxation-equation approximation. The use of large values of the bulk viscosity ratio (estimated using the quantum-mechanical model) in calculations leads to distributions of rotational temperature along the radial ray that do not have any physical meaning and do not match any known experimental data for expanding nitrogen flows.