Mathematical modelling and experimental study of non-equilibrium flows of gases with internal degrees of freedom

摘要

Experimental as well as theoretical studies related to rotational relaxation processes in free jet expansion of nitrogen have been done in the past for a wide range of stagnation conditions. When the Knudsen number is of order one, a continuum description of the fluid flow becomes invalid due to free drifting molecules, which lead to the thermal non-equilibrium. A recently developed interlaced system of a path-integral form of the kinetic equation and conservation equation has been used as unified solution for such problems where large variations in the Knudsen number takes place. Objective of this work was to develop a mathematical model of non-equilibrium flows of molecular gases with internal degree s of freedom using the interlaced system as well as experimental investigation of such flows using the Electron Beam Fluorescence Technique. The work was carried out in four main stages: 1. Molecular dynamics calculations of the binary collision between two nitrogen molecule using 2C-Lennard Jones potential model to calculate inelastic collision cross sections, 2. Modification in the path-integral form of the Boltzmann equation using the simplified expressions for the collision-cross section and transition probabilities, 3. Applying the interlaced system, initially on a problem of relaxation of a gas homogenous in space and later to free jet flow of nitrogen, and 4. Experimental investigation of free jet expansion of nitrogen in low-density wind tunnel using the Electron Beam Fluorescence Technique and comparing the experimental results with the numerical ones. Based on the observations made during MD simulations, a functional relationship was established between the collision diameter and the relative velocity of binary collision. Based on the R-R and R-T energy transfer, a model for the transition probability was developed. The simplified model of the total collision cross-section, where collision cross section and transition probability were separated, was used to transform the kinetic equation. For all calculations and measurements, rotational temperatures deviated from the equilibrium value at different locations along the jet axis and froze at different levels depending on the p0D0/T0 and stagnation temperature T0. For equal p0D0/T0 value, degree of rotational non-equilibrium was less where the stagnation temperature was high. The experiments and calculations were found to be in quite good agreement.