Analytical Exponential-6 Equation of State Based on Monte Carlo Simulations

Abstract: The exponential-6 (exp-6) potential is an intermolecular pair potential that is widely used to model fluids at high densities. The path from molecular interaction to equation of state (EOS) for a gas is not straightforward however. Monte Carlo methods and molecular dynamics give accurate results but are too slow for demanding applications like detonation modelling or numerical simulations of reactive flows. In this thesis, I propose a new equation of state in the form of an analytical expression for the excess Helmholtz free energy of an exp-6 fluid. All other thermodynamic properties are obtained as derivatives of this expression and gas mixtures are treated as an effective simple fluid. The equation of state is based on extensive Monte Carlo simulations and therefore combines the excellent accuracy of the simulations with the numerical efficiency of a polynomial expression. The average relative error in compressibility factor and internal energy is 0.14% and 0.25% respectively, which is a significant improvement over statistical mechanical theories. The number of polynomial coefficients was also significantly reduced compared to previous equations of state, through the use of a new variable transformation. The EOS was implemented into a thermochemical code in order to optimise gas parameters and evaluate its performance on pure gas data, shock compression and detonation properties. Gas densities were typically predicted to within 1.5% at pressures below 1 GPa and temperatures above 300 K. Calculated shock Hugoniots showed excellent agreement with experimental values up to 150 GPa and 15 000 K, and the detonation performance was accurately predicted for a number of different types explosives.