TY - JOUR

T1 - Evaluation of the Vibrational Relaxation Time for Air Components Based on the FHO and FHO-FR Models

AU - Исаков, Андрей Алексеевич

AU - Летова, Анна Юрьевна

AU - Кустова, Елена Владимировна

PY - 2026/6/1

Y1 - 2026/6/1

N2 - Abstract: Various theoretical methods for calculating the vibrational relaxation time of air components are proposed. An accurate forced harmonic oscillator (FHO) model, as well as its advanced modification taking into account free molecular rotations (FHO-FR) are implemented to calculate the state-to-state vibrational energy transition rate coefficients. Due to the high computational complexity of the FHO-FR model, its direct use in nonequilibrium gas dynamic problems is prohibitively expensive. Therefore, an effective regression model, FHO-FR-reg, is proposed. It accurately approximates the energy exchange rate coefficients calculated using the original FHO-FR model, with a maximum error of less than 2%. The high computational efficiency of the FHO-FR-reg regression model is demonstrated. For N2–N, N2–O, N2–N2, O2–N, O2–O, O2–O2, NO–N, NO–O, NO–NO, O2–N2, and N2–O2 collisions, the relaxation times are calculated using three methods: the Landau–Teller formula; formulas of the kinetic theory of gases based on averaging the vibrational transition energy excess with the cross sections of the corresponding vibrational energy exchanges; and by solving the zero-dimensional isothermal bath relaxation problem. The results are compared with the available experimental data and the results of direct molecular simulations (DMS). Analysis of the results shows that the optimal model for all considered collision types is a simple analytical Landau–Teller formula in combination with the deactivation rate coefficient calculated using the FHO model. The necessity of taking into account the coupled vibrational-rotational relaxation at high temperatures is discussed.

AB - Abstract: Various theoretical methods for calculating the vibrational relaxation time of air components are proposed. An accurate forced harmonic oscillator (FHO) model, as well as its advanced modification taking into account free molecular rotations (FHO-FR) are implemented to calculate the state-to-state vibrational energy transition rate coefficients. Due to the high computational complexity of the FHO-FR model, its direct use in nonequilibrium gas dynamic problems is prohibitively expensive. Therefore, an effective regression model, FHO-FR-reg, is proposed. It accurately approximates the energy exchange rate coefficients calculated using the original FHO-FR model, with a maximum error of less than 2%. The high computational efficiency of the FHO-FR-reg regression model is demonstrated. For N2–N, N2–O, N2–N2, O2–N, O2–O, O2–O2, NO–N, NO–O, NO–NO, O2–N2, and N2–O2 collisions, the relaxation times are calculated using three methods: the Landau–Teller formula; formulas of the kinetic theory of gases based on averaging the vibrational transition energy excess with the cross sections of the corresponding vibrational energy exchanges; and by solving the zero-dimensional isothermal bath relaxation problem. The results are compared with the available experimental data and the results of direct molecular simulations (DMS). Analysis of the results shows that the optimal model for all considered collision types is a simple analytical Landau–Teller formula in combination with the deactivation rate coefficient calculated using the FHO model. The necessity of taking into account the coupled vibrational-rotational relaxation at high temperatures is discussed.

KW - vibrational relaxation time

KW - state-to-state kinetics

KW - forced harmonic oscillator model

KW - optimization of numerical calculations

KW - nonlinear regression

KW - forced harmonic oscillator model

KW - nonlinear regression

KW - optimization of numerical calculations

KW - state-to-state kinetics

KW - vibrational relaxation time

UR - https://www.mendeley.com/catalogue/c76f7f92-1bdf-307a-96be-cc63e98ec411/

U2 - 10.1134/S1063454126700093

DO - 10.1134/S1063454126700093

M3 - Article

VL - 59

SP - 195

EP - 207

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -