Modified Marrone-Treanor dissociation model: formulation and benchmarking for diatom/atom mixtures

TL;DR

The Modified Marrone-Treanor (MMT) model provides a predictive two-temperature framework for diatomic dissociation in thermo-chemical nonequilibrium, grounded exclusively in quasi-classical trajectory data on ab initio PESs. It combines a corrected nonequilibrium rate $k_ ext{diss}^ ext{MMT-NB}(T,T_ ext{v})$, a vibrational energy removal term via a Knab-like formulation, and ab initio-derived vibrational relaxation times, with non-Boltzmann corrections that are later generalized to composition-dependent factors ensuring correct approach to equilibrium. The model is calibrated against QCT and DMS data for N$_2$ and O$_2$ and demonstrates high fidelity in both isothermal and adiabatic 0D CFD benchmarks, while remaining computationally efficient for CFD use. This work lays the groundwork for a 5-species extension and provides a physically grounded, scalable tool for hypersonic dissociation simulations with rigorous energy coupling, enabling improved predictive capability for downstream CFD analyses of shock-laden flows.

Abstract

We present a modified Marrone-Treanor model for dissociation with rate parameters derived exclusively from quasiclassical trajectory calculations on ab initio potential energy surfaces. Analysis of the trajectory dataset for reactant O2 and N2 diatoms sampled from Boltzmann internal energy distributions over a wide T,Tv range indicates that a modified version of the classical Marrone-Treanor two-temperature model captures the most relevant physics of shock-heated dissociating diatomic species very well. We find that simple correction factors account for non-Boltzmann depletion effects observed in direct molecular simulations employing the same potentials. The concentration-dependent functional form proposed for these correction factors ensures that depletion effects vanish at chemical equilibrium. Based on comparisons in isothermal and adiabatic heat baths we verify that the resulting two-temperature dissociation model accurately reproduces all major features observed in the direct molecular simulations, while remaining computationally inexpensive enough for large-scale computational fluid dynamics simulations.

Figures (17)

• Figure 1: Vibrational relaxation times for nitrogen and oxygen. DMS data torres24b and curve fits (blue), M&W correlation MillikanW1963 plus Park's high-temperature correction Park1993 (black).
• Figure 2: Average change in vibrational energy per dissociation normalized by $D_{0,s}$ for all 6 dissociation reactions, temperatures normalized by $T_{\mathrm{D},s}$.
• Figure 3: Support for single/simple dissociation for all dissociation reactions, at $T = T_\mathrm{v} = 10\,000 \, \mathrm{K}$.
• Figure 4: Effective diatomic potential for two rovibrational states with similar internal energies
• Figure 5: Probability of dissociation from a specific remainder energy $\varepsilon_\mathrm{rem}$