Shock Waves

, Volume 22, Issue 6, pp 647–651 | Cite as

Revised model coefficients for vibrational relaxation in a nitrogen–oxygen gas mixture

  • R. M. GehreEmail author
  • V. Wheatley
  • R. R. Boyce
Technical Note


A numerical investigation of thermal non-equilibrium flows requires species specific relaxation rates, which are often calculated using the Landau–Teller model. This model requires the determination of collision specific relaxation times, which can be computed using Millikan and White’s empirical formula. The coefficients used in this formula for each specific collision pair form a set of coefficients, which are assessed here. The focus of the investigation lies on their performance in hypersonic low-temperature (300–2,500 K) flows that occur at shock-tunnel nozzle exits or in supersonic combustion ramjets (scramjets) before combustion. Two experimental validation cases are chosen; a shock-tunnel nozzle and a sharp cone in hypersonic cross-flow experiment. A comparison of the experimentally measured vibrational temperatures at the nozzle exit against numerical data shows large discrepancies for two commonly used coefficient sets. A revised set of coefficients is proposed that greatly improves the agreement between the numerical and experimental results. Furthermore, the numerically generated shock shape over the sharp cone using the revised set of coefficients correlates well with the experimental measurements.


Thermal non-equilibrium Relaxation rates Hypersonic flows Computational fluid dynamics  Thermal modeling and analysis 



The authors would like to thank Professor Graham Candler’s research group for providing their CFD research code. The research is funded by the Australian Space Research Program. Furthermore, thanks go to Professor Chul Park for his helpful discussions regarding thermal non-equilibrium.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Centre for HypersonicsUniversity of QueenslandBrisbaneAustralia

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