First-Principle-Inspired Reduced-Order Models of Chemical-Kinetics in $\text{H}_2\left(\text{X}^1Σ_g^+\right)$+$\text{H}\left({}^2\text{S}\right)$ System

TL;DR

This work addresses nonequilibrium chemistries in the H2+H system relevant to hypersonic entry into giant-planet atmospheres by building a full rovibrational state-to-state database from first-principles quasi-classical trajectory calculations on the BH potential energy surface and solving rovibrational master equations. It then develops two reduced-order models: a Modified Two-Temperature model that embeds master-equation-derived parameters for vibrational-translational coupling and dissociation, and a Hybrid Coarse-Graining scheme that combines graph-based and centrifugal-barrier groupings optimized across wide temperature ranges via maximum likelihood estimation. The models are validated against full state-to-state solutions in 0-D and 2-D hypersonic flow scenarios, showing substantially improved accuracy in predicting energy transfer and dissociation dynamics, with the Hybrid Coarse-Graining capturing low-lying state behavior and the Modified 2T model accurately representing RVT coupling and QSS dissociation rates. Applying these models to Uranus-entry conditions reveals a 16.5% difference in predicted convective heat flux at the stagnation point between the Modified 2T and conventional 2T approaches, underscoring the practical impact of accurate nonequilibrium chemical-kinetics modeling on TPS design and hypersonic aerothermodynamics.

Abstract

In the present study, two-different reduced-order models are proposed for $\text{H}_2\left(\text{X}^1Σ_g^+\right)$+$\text{H}\left({}^2\text{S}\right)$ system by leveraging first-principle quasi-classical trajectory simulations and in-depth master equation analyses. The most recent available ab-initio potential energy surface is adopted to construct a new set of rovibrational state-to-state kinetic database valid over a wide range of temperatures. Firstly, a modified two-temperature model is proposed by incorporating the master equation-informed model parameters, enabling the advanced treatment of the internal energy coupling and the nonequilibrium dissociation predictions. Secondly, a hybrid coarse-graining model is proposed by combining a graph-based approach optimized globally for a wide range of temperatures with a centrifugal-barrier-based coarse-graining method. The proposed reduced-order models offer significantly improved accuracy in predicting the nonequilibrium energy transfer and dissociation dynamics compared to the existing coarse-graining and 2T models in previous studies. In addition, aerothermal heating prediction relevant to Uranus planetary entry reveals 16.5% of convective heat flux discrepancy compared to the present modified 2T approach with the existing 2T, demonstrating the importance of accurate modeling of the chemical-kinetics in the $\text{H}_2\left(\text{X}^1Σ_g^+\right)$+$\text{H}\left({}^2\text{S}\right)$ system.

Figures (17)

• Figure 1: Comparisons of the (a) bound-bound transition cross sections and (b) thermal dissociation rate coefficients with the literature data kim2009mastervargas2024stateESPOSITO1999636.
• Figure 2: Flowchart summarizing the procedure for constructing the HCG model, in which the centrifugal-barrier-based (CB) method is applied to the high-energy states region, while the graph-based (GB) method is employed for the low-energy states region with the optimization via MLE.
• Figure 3: Contour of the determined HCG group indices overlayed on the effective diatomic potential of $\text{H}_2\left(\text{X}^1 \Sigma_g^+\right)$. Each dot represents a rovibrational state, and the groups are labeled with assigned colors.
• Figure 4: Temporal evolutions of the rotational and vibrational temperatures at different heat-bath temperatures (dissociation mechanisms excluded).
• Figure 5: Contour plots of the rovibrational StS inelastic rate coefficients at 10,000 K are shown for the initial target state with vibrational quantum number ($v$, $J$), transitioning to ($v'$, $J'$). The top row displays values within two orders of magnitude of the largest rate coefficient on the states. The bottom row presents the rate coefficient magnitude as a function of $\Delta v$ and $\Delta J$.