Molecular description of steady supersonic free jets

Abstract

A detailed analysis of the non-local thermal equilibrium (n-LTE) problem in the paraxial zone of silence of supersonic free jets is reported. The study is based on a hybrid approach that combines Navier-Stokes equations with a kinetic equation derived from the generalized Boltzmann (Waldmann-Snider) equation. The resulting system is solved for those flow quantities not easily amenable to experimental measure (translational temperature, flow velocity, and entropy) in terms of the quantities that can be measured accurately (distance, number density, population of rotational states, and their gradients). The reported solutions are essentially exact and are formulated in terms of macroscopic quantities, as well as in terms of elementary collision processes. Emphasis is made on the influence of dissipative effects onto the flow (viscous and diabatic) and of the breakdown of thermal equilibrium onto the evolution of entropy and translational temperature. The influence of inelastic collisions onto these effects is analysed in depth. The reported equations are aimed at optimizing the experimental knowledge of the n-LTE problem and its quantitative interpretation in terms of state-to-state rates for inelastic collisions.

Laboratory Study of Rate Coefficients for H2:H2 Inelastic Collisions between 295 and 20 K

“…For the paraxial region of the jet this solution provides a very good approximation. It is, however, subject to some uncertainty due to the dissipation function  (Montero 2013(Montero , 2017 associated with the large bulk viscosity of nH 2 . This effect is important in jets generated at low pressure.…”

Inelastic Collisions of O2 with He at Low Temperatures

“…Following the empirical finding of our previous work on pure O 2 jets, the translational temperatures have been first determined from the local number densities n ( z ) by means of the isentropic condition (Δ S = 0) along the jet for an ideal gas where n 0 is the stagnation number density. These T T temperatures were then checked against a more rigorous approach: for a real gas mixture of monatomic plus diatomic molecules, the Δ S = 0 condition leads to an isentropic ( i ) translational temperature but any Δ S ≠ 0 raises it to where R = 8.314 51 J mol –1 K –1 is the universal gas constant. For an inviscid-adiabatic (i.e., no dissipation) gas flow, the entropy due to T R ≠ T T nonequilibrium is given by …”