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LUND UNIVERSITY LIBRARIES

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

Hallstadius, Peter LU (2021) MVKM01 20202
Department of Energy Sciences
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
Hallstadius, Peter LU
supervisor
organization
course
MVKM01 20202
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Equation of state, exp-6, Monte Carlo, detonation, shock wave, thermochemical code
report number
LUTMDN/TMHP-21/5468-SE
ISSN
0282-1990
language
English
id
9041784
date added to LUP
2021-03-15 13:36:23
date last changed
2021-03-15 13:36:23
@misc{9041784,
  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.}},
  author       = {{Hallstadius, Peter}},
  issn         = {{0282-1990}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Analytical Exponential-6 Equation of State Based on Monte Carlo Simulations}},
  year         = {{2021}},
}