Binary scaling is a similitude law that facilitates the study of hypersonic flows around blunt bodies. It conserves the Reynolds number and the binary (two-body) reaction rates, which are mainly present in the nonequilibrium layer, and scales properly the convective heat transfer. It requires duplication of the product of density and a length scale of the flow, ρL, as well as the free-stream enthalpy, H. Its use for ground-to-flight extrapolation depends on the fractional extent of regions of the flow where higher order reactions become important. It is known to be useful for creating partial similarity between laboratory flow and hypersonic flight.
Flow conditions of different free-stream density but almost constant free-stream enthalpy were designed for the X2 super-orbital expansion tube. Therefore, if the dimensions of the test model are scaled so as to keep the product ρL constant, the flows should be similar from the perspective of binary scaling.
The test gas of interest is a mixture of 97% CO2 and 3% N2 , which corresponds to the high altitude atmosphere of Venus, and is close to that of Mars. The strategy adopted to produce different free-stream density is to vary the thickness of the steel plates used as diaphragm to separate the driver from the shock tube. The fill pressure in the rest of the tube is then adapted so as to retrieve a similar flight equivalent velocity.
The results are depicted in figure 1. Two sets were obtained, set A for medium enthalpy and set B for high enthalpy. It was demonstrated with numerical simulations that the match between the scaled temperature, density, and concentration profiles was satisfying, despite small variations in free-stream temperature and enthalpy.
Those conditions were then used to identify the effect of binary scaling on important features of the flow such as spectral radiation and species concentration profile. This paper focuses on shock standoff distance. Flows were obtained over cylindrical and spherical models, so as to identify possible variation between two-dimensional and three-dimensional problems.
As foreseen in the numerical simulations, the nondimensional shock standoff distance is smaller over scaled models. This is due to the post-shock equilibrium density being smaller than what it should be as predicted by experimental correlations, such as Van Dyke`s [3]. That effect is even more visible for spheres than for cylinders.
[1] H.G. Hornung. Experimental real-gas hypersonics. Aeronautical Journal, 92:379-389, 1988.
[2] F.K, Lu and D.E. Marren. Advances in Hypersonics Test Facilities, progress in Astronautics and Aeronautics 198, chapter Principles of Hypersonic Test Facility Development p. 17-25. Zarchan, P., 2002.
[3] M. D. Van Dyke. The supersonic blunt-body problem review and extension. Journal of Aeronautical Sciences, 25:485-495, 1958.
