Numerical and theoretical study of the shock stand-off distance in non-equilibrium flows

Abstract

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.

Experimental and Numerical Investigation of Hypervelocity Carbon Dioxide Flow over Blunt Bodies

“…Inger et al presented a hypersonic shock standoff theory, incorporating nonequilibrium gas mixtures with freestream dissociation, based upon a compressibility coordinate transformation [39]. A theoretical model for the nonequilibrium shock standoff distance was also introduced by Belouaggadia et al [40], following an analytical solution proposed by Olivier [41]. The Olivier solution was confined to frozen and equilibrium flows, while the numerical model of Belouaggadia et al [40] implemented calculated density profiles.…”

“…A theoretical model for the nonequilibrium shock standoff distance was also introduced by Belouaggadia et al [40], following an analytical solution proposed by Olivier [41]. The Olivier solution was confined to frozen and equilibrium flows, while the numerical model of Belouaggadia et al [40] implemented calculated density profiles. At the postshock-toequilibrium density ratios in the present experiments, we find there is very little difference between density profiles calculated by the Wen and Hornung [4] and Belouaggadia et al [40] methods.…”

“…The Olivier solution was confined to frozen and equilibrium flows, while the numerical model of Belouaggadia et al [40] implemented calculated density profiles. At the postshock-toequilibrium density ratios in the present experiments, we find there is very little difference between density profiles calculated by the Wen and Hornung [4] and Belouaggadia et al [40] methods. As a result, the theory of Wen and Hornung [4] is used in this study.…”

Evaluation of Hypervelocity Carbon Dioxide Blunt Body Experiments in an Expansion Tube Facility

“…1 Inger et al presented a hypersonic shock stand-off theory, incorporating nonequilibrium gas mixtures with freestream dissociation, based upon a compressibility co-ordinate transformation. 32 A theoretical model for the non-equilibrium shock stand-off distance was also introduced by Belouggadia et al, 33 following an analytical solution proposed by Olivier. 34 The Olivier solution was confined to frozen and equilibrium flows, while the numerical model of Belouggadia et al implemented calculated density profiles.…”

Expansion Tube Investigation of Shock Stand-Off Distances in High-Enthalpy CO2 Flow Over Blunt Bodies

“…35 Their model approximated the density profile as linear. A theoretical model for the non-equilibrium shock stand-off distance was also introduced by Belouggadia et al, 36 following an analytical solution proposed by Olivier. 37 The Olivier solution was confined to frozen and equilibrium flows, while the numerical model of Belouggadia et al implemented calculated density profiles.…”