Shock Waves in Air at Very High Pressures

Abstract

The equations of the shock wave in air at n.t.p. are solved numerically for pressures on the high pressure side up to 1000 atmospheres. The solution enables all the physical entities, such as temperature, wave velocity, particle velocity, air density, etc., on the shock wave front to be expressed numerically as a function of the wave pressure. To solve these equations it is necessary to know the internal energy (E) and volume (ν) of one gramme of air over certain regions of the two-dimensional range 1<p<1000 atmospheres and 273<T<16000° K. Calculations are carried out to assess the numbers of the various types of molecules, atoms and ions present at any p and T. The only E values needed at high p are those for which T is also high, and the simple gas laws may therefore be assumed for the volume determinations. The resultant energy is obtained by summing the internal energies of the different groups of atoms and molecules present. Statistical mechanics furnishes equations whose solution fixes the composition. This set of equations is difficult to solve to any degree of accuracy if oxides of nitrogen are taken into account; of these only nitric oxide, NO, ever exceeds a concentration of 1% by weight, and its maximum concentration is less than 5% As a first approximation, the shock wave equations are worked out on the assumption that the species present are N2, O2, N and O. These calculations make full allowance for all quantum states apart from ionic states. They are refined later by taking into consideration the presence of NO and argon (1.3% by weight) and ionization possibilities.