A theoretical model based on a quasi-one-dimensional formulation is developed which allows determination of the shock stand-off distance at the stagnation point of blunt bodies in hypersonic non-equilibrium flows. Despite the simple ideal dissociating gas model implemented in the theoretical approach, it gives insight into the main physics governing the shock stand-off problem. More detailed and precise data are obtained by a numerical simulation where vibrational and chemical relaxation processes as well as their interactions are taken into account. The physical modelling of these processes is based on a kinetic approach and on a generalized Chapman–Enskog method of solving the Boltzmann equation. Explicit formulae for rate constants and vibrational energy consumption are derived and incorporated into the general conservation equations. Good agreement between theoretical, numerical and experimental results is achieved which ensures a reliable and mutual validation of the different methods.

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Nomenclature A = chemical symbol e = total energy per mass unit e A , e D = activation, dissociation energy e Vp = vibrational energy of species p _ e Vp = vibrational energy production of species p due to TV and VV collisions e Vps = vibrational energy gained (lost) by species p due to reaction s f = distribution function J = collisional term in Boltzmann equation K = rate constant k = Boltzmann constant p = pressure Q = quantity Q at equilibrium q = total heat flux q v = vibrational heat flux R = hemispherical body radius T = translation-rotation temperature T V = vibration temperature V = mean velocity (components u and v) V p = mean velocity of component p _ w p = mass production of species p due to chemical reactions _ w Vp = vibrational energy production due to chemical reactions X = longitudinal coordinate in the nozzle x, y = coordinates in the physical plane Y = transverse coordinate in the nozzle = shock standoff distance =R = normalized shock standoff distance = density Subscripts a, b = upstream, downstream from the detached shock b = backward reaction C = chemical f = forward reaction i = internal level p, q = species p, q R = rotation s = reaction s T = translation TV = translation-vibration exchange V = vibration VV = vibration-vibration exchange 0 , 00 = stoichiometric coefficients 1, 2, 3, 4, 5 = associated to species N 2 , O 2 , NO, N, O

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