Temperature and entropy in supersonic free jets

Abstract

Translational temperature (Tt), flow velocity (v), and entropy increment (ΔS) along the paraxial zone of silence of supersonic free jets are studied in the frame of the Navier-Stokes (NS) equations. Expressions for the experimentally non-accessible quantities Tt, v, and ΔS are formulated in terms of the experimentally accessible number density (n) and rotational temperature (Tr). The scope of the inviscid-adiabatic and isentropic flow approximations is discussed with emphasis in the dissipative effects onto the flow variables. The influence of dissipative contributions due to viscosity and heat conductivity onto the translational temperature and entropy of pure helium supersonic jets is illustrated. Two sources of entropy increment in the jets have been identified and formulated quantitatively, namely, the dissipative effects, and the Tr ≠ Tt non-equilibrium in gases including molecular species. As far as the rarefaction of the jet allows for the use of the NS-equations, a number of “exact” expressions relating the flow variables n, Tt, Tr, v, and ΔS along mixed supersonic jets of atoms and molecules are reported. These expressions are aimed at an optimal experimental diagnostics of the jets.