Real gas effects on the prediction of ram accelerator performance

The analysis of ram accelerator performance is based on one-dimensional modelling of the flow process that propels the projectile. The conservation equations are applied to a control volume travelling with the projectile, and quasi-steady flow is assumed. To date the solution obtained, namely the generalized thrust equation, has been based on the ideal gas assumption. At the high level of pressure that is encountered during the ram accelerator process, this assumption cannot be regarded as adequate. Thus, a more appropriate equation of state (EOS) should be used instead. Depending upon the level of pressure, several equations of state are available for dense gaseous energetic materials. The virial type of EOS can be more or less sophisticated, depending upon the extent of complexity of the intermolecular modelling, and turns out to be totally appropriate for most gaseous explosive mixtures that have been investigated at moderate initial pressures, i.e., less than 10MPa. In the present case the Boltzmann EOS was applied. It is based on very simplified molecular interactions, which makes it relatively easy to use in calculations. Moreover, the energetic EOS needs to be taken into account. This concerns all the calorimetric coefficients, as well as the thermodynamic parameters, which can no longer be expressed as only a function of temperature. The higher the pressure level, the more sophisticated these corrections become, but the main relationships that account for real gas effects are basically the same. These include the use of a general form of analytical operators applied to correct the thermodynamic functions and coefficients. The equations governing the one-dimensional model were taken as a basis for the real gas corrections and were solved analytically. The parameters which play the most crucial roles in this correction can thus be highlighted. A complete set of equations involving the real gas effects are presented in this paper. The QUARTET code was used in this investigation, especially for determining chemical equilibrium compositions. This more accurate model can better predict the projectile acceleration of the thermally choked propulsive mode. Although the present analysis is applied to the fuel-rich methane-oxygen-nitrogen mixture currently used in the ram accelerator experiments, its general formulation makes it readily applicable to any other mixture. The projectile velocity and acceleration histories determined by the Hugoniot analysis for the thermally choked ram accelerator mode, assuming the Boltzmann EOS, turn out to be in much better agreement with experimental observations up to the CJ detonation velocity than that when based on the ideal gas assumption. Received 9 August 1996 / Accepted 23 May 1997