Speaker
Description
Hypersonic computational fluid dynamics (CFD) codes must account for chemical and thermodynamic changes in the flow that occur at timescales that are similar to the flow time. These include chemical reactions such as dissociation and ionization as well as thermal relaxation. The relaxation terms account for the finite time required to excite (usually vibrationally or electronically) the atoms and molecules in the flow. These two processes are modeled using two different parameterizations. In NASA codes for example, the chemical processes are modeled using modified Arrhenius reactions with detailed balance and the Park temperature model. Meanwhile, the relaxation processes are fit using a relaxation time parameterized by Landau and Teller and refit by Millikan and White (which added high temperature corrections from Park).
Modern CFD codes are slowly moving to new computational architectures generally characterized by the GPU. These are effectively large vector machines that gain performance by batching repetitive tasks into a single operation over a large array. This puts pressure on the software engineer to merge as many processes as possible into one general implementation. However, the physics as outlined above forces the software to calculate chemical source terms in two stages: the relaxation and then the chemistry.
This work begins with the relatively simple question of whether one can express the vibrational relaxation process as a chemical reaction. For example, consider a nitrogen molecule colliding with an atom. The reaction $$N_2 + N \leftrightarrow N_2 + N$$ clearly does not change the densities of either species. However, by evaluating the forward rate at one temperature and the backward at another, as is already typical for hypersonic codes, one can force an energy transfer to occur. Using some simple fitting one can arrive at reaction rate constants that capture the Millikan and White fits.
The reaction parameterization and the Millikan and White fits are different parameters and cannot result in the same average energy transfer at all combinations of translational and vibrational temperature. Notably, the reaction fit diverges from the Millikan and White fit at high translational and low vibrational temperature. At first glance, this suggests that using a reaction parameterization is impossible.
However, what has not been validated is the overall validity of the Millikan and White fit at these conditions. At present, state to state models and quantum chemistry solutions are available to calculate these reaction rates. Torres, for example, calculated vibrational relaxation times using the Direct Molecular Simulation (DMS) method. However, his results provide only an average value over vibrational temperature. Contours of instantaneous vibrational energy transfer rate as a function of translational and vibrational temperature are not available. In this work, QCT simulations of the N3 system are produced to compare against Millikan and White, a reaction parameterization, and the results of Torres.
Summary
This work discusses the parameterization of vibrational relaxation in modern CFD codes and compares the energy transfer to QCT data.