Flow of a Beattie-Bridgeman Gas with Variable Specific Heats,
NAVAL ORDNANCE LAB WHITE OAK MD
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When missiles or aircraft travel at high speeds, several times greater than the speed of sound, the pressures and temperatures of the airflow around them vary over a wide range. In deriving the aerodynamic characteristics of such missiles, and in the design of hypersonic wind tunnels to measure their properties, it is necessary to take into account the fact that thermodynamic properties of air deviate appreciably from those of a perfect gas, over the range of pressures and temperatures encountered. There are many cases for which large deviations from perfect-gas calculations are indicated. For example, in free-and pressurized-air range problems involving hypersonic Mach numbers, the temperature behind a shock wave is appreciably less than that calculated from perfect gas formulas, the density appreciably more, and the pressure nearly the same. Here the differences result mainly from the increased specific heat due to vibration rather than the Beattie-Bridgeman equation of state. On the other hand, for hypersonic wind tunnels with supply pressures up to about 100 atmospheres and supply temperatures high enough to avoid air condensation, differences in static and pitot pressures from the corresponding perfect-gas values are of the order of a few percent and most values lie within present measuring accuracy. Graphs permitting rapid numerical evaluation of the resulting formulae are presented.
- Fluid Mechanics