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Modified Marrone-Treanor model: parameterization and benchmarking for five-species air

Erik Torres, Thomas Gross, Graham V. Candler, Thomas E. Schwartzentruber

TL;DR

This work delivers a comprehensive, first-principles–anchored parameterization of the Modified Marrone-Treanor model for five-species air, enabling efficient two-temperature CFD of nonequilibrium hypersonic flows. By deriving dissociation rates, vibrational-energy coupling, and vibrational relaxation times from QCT and DMS data on Minnesota PESs, the authors create PES-consistent thermodynamics and chemistry that closely reproduce direct molecular simulations in 0D benchmarks. The study provides two benchmarking paths (DMS-bench and Park comparison), discusses non-Boltzmann corrections, and outlines three practical parameter sets for real CFD use, including scenarios with and without multi-surface O_2 enhancement. The results demonstrate that MMT can reproduce key DMS features while remaining orders of magnitude faster than DMS, underscoring its utility for high-enthalpy, hypersonic flow simulations and guiding future work on electronic-excitation effects and reaction mechanisms. The framework advances predictive capabilities for nonequilibrium air chemistry, with direct implications for design and analysis of hypersonic vehicles and high-enthalpy facilities.

Abstract

We present updated parameters for five-species air (N2, O2, NO, N and O) reactions to be used with the Modified Marrone-Treanor two-temperature model. The vibrational relaxation and chemical reaction rates are derived from quasiclassical trajectory calculations and direct molecular simulations using ab initio potential energy surfaces. The resulting model enables efficient computational fluid dynamics simulations of nonequilibrium air chemistry in hypersonic flows. We show that the model reproduces direct molecular simulation benchmark solutions with high accuracy in zero-dimensional heat baths representative of strong nonequilibrium post-shock conditions. The model's analytical expressions for dissociation rate coefficient and vibrational energy change per reaction ensure that the correct amount of energy is transferred between the vibrational and trans-rotational modes. Detailed balance is imposed for three-body recombination reactions and our simulations exhibit quasi-steady-state dissociation rates and proper approach to thermochemical equilibrium. In direct comparison with the Park TTv model, the Modified Marrone-Treanor model predicts significantly slower conversion of N2 into N below 10000 K and significantly more NO production at all temperatures. This is likely due to its significantly higher Zeldovich reaction rates compared to Park.

Modified Marrone-Treanor model: parameterization and benchmarking for five-species air

TL;DR

This work delivers a comprehensive, first-principles–anchored parameterization of the Modified Marrone-Treanor model for five-species air, enabling efficient two-temperature CFD of nonequilibrium hypersonic flows. By deriving dissociation rates, vibrational-energy coupling, and vibrational relaxation times from QCT and DMS data on Minnesota PESs, the authors create PES-consistent thermodynamics and chemistry that closely reproduce direct molecular simulations in 0D benchmarks. The study provides two benchmarking paths (DMS-bench and Park comparison), discusses non-Boltzmann corrections, and outlines three practical parameter sets for real CFD use, including scenarios with and without multi-surface O_2 enhancement. The results demonstrate that MMT can reproduce key DMS features while remaining orders of magnitude faster than DMS, underscoring its utility for high-enthalpy, hypersonic flow simulations and guiding future work on electronic-excitation effects and reaction mechanisms. The framework advances predictive capabilities for nonequilibrium air chemistry, with direct implications for design and analysis of hypersonic vehicles and high-enthalpy facilities.

Abstract

We present updated parameters for five-species air (N2, O2, NO, N and O) reactions to be used with the Modified Marrone-Treanor two-temperature model. The vibrational relaxation and chemical reaction rates are derived from quasiclassical trajectory calculations and direct molecular simulations using ab initio potential energy surfaces. The resulting model enables efficient computational fluid dynamics simulations of nonequilibrium air chemistry in hypersonic flows. We show that the model reproduces direct molecular simulation benchmark solutions with high accuracy in zero-dimensional heat baths representative of strong nonequilibrium post-shock conditions. The model's analytical expressions for dissociation rate coefficient and vibrational energy change per reaction ensure that the correct amount of energy is transferred between the vibrational and trans-rotational modes. Detailed balance is imposed for three-body recombination reactions and our simulations exhibit quasi-steady-state dissociation rates and proper approach to thermochemical equilibrium. In direct comparison with the Park TTv model, the Modified Marrone-Treanor model predicts significantly slower conversion of N2 into N below 10000 K and significantly more NO production at all temperatures. This is likely due to its significantly higher Zeldovich reaction rates compared to Park.

Paper Structure

This paper contains 27 sections, 59 equations, 34 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Modified Marrone-Treanor model for air
  3. Governing fluid equations for a two-temperature chemistry model
  4. Formulation for dissociation rate coefficient in the MMT model
  5. Formulation of vibrational energy-chemistry coupling term in the MMT model
  6. Updated MMT parameters for air
  7. Model parameters for comparison against DMS results
  8. Model parameters proposed for full 5-species air simulations
  9. MMT-specific non-Boltzmann correction factors
  10. Characteristic behavior of rate coefficient and vibrational energy removal terms
  11. Vibrational relaxation times
  12. MMT model comparison against Direct Molecular Simulations
  13. Vibrational excitation and dissociation of 5-species air mixture in isothermal heat baths
  14. Vibrational excitation and dissociation of 5-species air mixture in adiabatic heat baths
  15. MMT model behavior when approaching chemical equilibrium
  16. ...and 12 more sections

Figures (34)

  • Figure 1: Example of an MMT dissociation-type reaction: $\boldsymbol{\mathrm{NO + O \rightleftharpoons 2O + N}}$
  • Figure 2: Example of an exchange-type reaction: $\boldsymbol{\mathrm{NO + O \rightleftharpoons O_2 + N}}$
  • Figure 3: Example of a mixed-type reaction: $\boldsymbol{\mathrm{2NO \rightleftharpoons 2O + N_2}}$
  • Figure 4: Vibrational relaxation times (1/3). DMS data torres24b and curve fits (blue), M&W correlation millikan63a (black) plus Park's high-temperature correction park93a (dotted black).
  • Figure 5: Vibrational relaxation times (2/3). Original (blue) / adjusted (red) DMS data torres24b and curve fits, M&W correlation millikan63a (black).
  • ...and 29 more figures