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Non‐equilibrium hypersonic viscous flows with high enthalpy conditions have been computed with an implicit time‐dependent finite‐difference scheme. This scheme accounts for both chemical and vibrational non‐equilibrium processes in air flow around a hemispherical cylindrical body. The air was assumed to decompose into the following five species N, O, NO, N2 and O2 and only the two diatomic species N2 and O2 are taken in thermal non‐equilibrium. A range of Mach number from 14 to 18 has been investigated. The numerical results have been compared with those obtained by other workers and are in agreement with ballistic range data concerning the standoff shock distance at M= 15.3. The computed heat flux wall follows the trends of the experiments with an under prediction increasing with the Mach number. The influence of the thermal non‐equilibrium assumption on the computed standoff shock distance is investigated.

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