Re-entry flow is a classical example of non-equilibrium high temperature gas dynamics. Such flows are characterized by complex physical phenomena, such as

- Ro-vibrational excitation of the molecular entities,
- Chemical and ionization reactions, and
- Electronic excitations of the atoms, molecules and ions.

These phenomena make the flow physics both interesting and complicated. Ro-vibrational excitation occurs at relatively lower temperature than the other two processes. Also, ro-vibrational excitation influences the flow chemistry and electronic excitation due to the highly coupled nature of these phenomena. Hence modelling and simulating ro-vibrational excitation becomes critical in the overall analysis of the flow. It is known that inelastic energy exchange among molecules during a high-energy collision has a finite relaxation time which is multiple factor greater than the mean collision time. Shock-tube experiments on vibrational relaxation by Landau-Teller provided a relation of the vibrational relaxation time as a function of temperature and pressure. Phenomenological models for modelling the inelastic energy exchange and vibrational excitation have been developed using these shock-tube experiments. However, in flows with high degree of non-equilibrium, such experiments and the computational models are grossly inaccurate. The overall objective of the present project is to improve our understanding of ro-vibrational excitation and inelastic energy exchange during a collision at a fundamental level using molecular dynamics algorithms.

State-to-state inelastic collision cross-sections is a measure of probability for a collision between a pair of molecules at one combination of ro-vibrational levels to transform in to another combination of ro-vibrational levels. The goal is to calculate the inelastic collision cross-sections for all combinations of pre and post-collision ro-vibrational states for all the possible collision pairs pertaining to five species air chemistry (N 2 , O 2 , N, O, NO). The cross-sections will be calculated using a statistical method known as Quasi-classical Trajectory (QCT) algorithm. A trajectory calculation comprises of tracking the interaction of two molecules (or atom-molecule) on a highly accurate computational chemistry based potential energy surface (PES) and identifying the end product of the interaction. A large number of such trajectories are repeated for a given input energy to calculate inelastic collision probability and subsequently the cross-sections. Although this procedure has been well established, it is not a widely used method due to its computational cost. The present proposal aims to improve the computational efficiency of the work by employing the machine learning algorithms. This is the novelty of the present work.

The second part of the project involves development of new improved models based on stronger theoretical principles for various simulation methodologies, such as, direct simulation Monte Carlo (DSMC) method and Navier-Stokes-Fourier (NSF) based Computational Fluid Dynamics (CFD) algorithms. In contrast to the partial differential equation based NSF based CFD algorithms, DSMC is a particle method widely used to simulate re-entry flows at rarefied ambient conditions where the continuum assumption is invalid. The traditional model for handling inelastic energy collisions in DSMC is highly phenomenological in nature and hence unreliable for simulating flows with high degree of non-equilibrium. In addition to this, current models for estimating the vibrational relaxation time in non-equilibrium NSF based CFD codes for simulating re-entry flows at lower altitude also suffer from similar issues. Finally, the impact of the new models on the re-entry flows in both rarefied and continuum ambient conditions will be analyzed using a comparative study with traditional models.