Johnston. The Noble-Abel Equation of State: thermodynamic derivations for ballistics modeling

(Ян А. Джонстон. Уравнение состояния Нобля-Абеля: термодинамические производные для баллистического моделирования). Report. Defense science and technology organization. 2005. -28 p. Accurate modeling of gun interior ballistics promotes more effecient gun and propelling charge design. In order to simulate interior ballistic flowfields, such models require a description of the thermodynamic behavior of the propellant gas. The Noble-Abel equation provides a simple and reasonably accurate equation of state for propellant gases at the high densities and temperatures experienced in guns. Most computational fluid dynamics-based ballistics models, however, require additional thermodynamic functions which must be derived from the equation of state. This note presents the derivation of such thermodynamic functions for Noble-Abel gases. Although the derivations are geared toward the functional requirements of the commercial Fluent code, the results are equally applicable to all computational fluid dynamics solvers. Also presented is a brief numerical example for a typical propellant, highlighting the different thermodynamics of the Noble-Abel and ideal gas equations. Contents: Introduction. Ihermodynamic Functions. Equation of State. Specific Heats. The Specific Gas Constant. Entropy. The Isentropic Process. Sound Speed. Partial Derivatives of State Variables. Example.