Abstract
In this paper, in order to accurately describe the high temperature and high pressure state of gas under detonation conditions, a new simplified form of the virial equation of state (EOS)—the Virial–Peng–Long (VPL) EOS—is proposed based on the theoretical calculation results of dimensionless virial coefficients based on the Lennard-Jones 6-12 (LJ 6-12) molecular potential. In this EOS, the virial coefficients of the third to the fifth order are expressed in the form of an empirical fitting formula. In order to more accurately describe the PVT state of gas at higher temperature than the Virial–Han–Long (VHL) EOS, we theoretically calculate the fourth-order dimensionless virial coefficient in a higher temperature range and apply it to the fourth-order term of the equation, and the fifth-order term of the equation is based on the theoretical calculation results by Kofke in the higher temperature range. Then, in order to verify and evaluate the accuracy of the VPL EOS in describing the PVT state of high temperature and high pressure gas, we refer to relevant molecular dynamics PVT data and NIST database PVT data of methane in the range of P = 0.028 19–187.2648 GPa and T = 623.7–4369.3 K, oxygen in the range of P = 0.01–111.4876 GPa and T = 519.9–4066.8 K, and nitrogen in the range of P = 0.1–2.2 GPa and T = 700–2000 K. The PVT data were calculated by the VPL EOS and compared with the reference values and the calculated values of the Virial Wu (VLW) EOS and VHL EOS. The mean absolute percentage deviation of the calculated values of the VPL EOS is less than 2.0%, which is better than that of the VLW EOS and VHL EOS.
Highlights
The equation of state (EOS) of fluids is usually applied to describe the PVT relationship of fluids, which is widely used in the fields of chemistry and fuel science, earth science, and explosion mechanics
In order to accurately describe the high temperature and high pressure state of gas under detonation conditions, a new simplified form of the virial equation of state (EOS)—the Virial–Peng–Long (VPL) EOS—is proposed based on the theoretical calculation results of dimensionless virial coefficients based on the Lennard-Jones 6-12 (LJ 6-12) molecular potential
The third and fourth order virial coefficients in the VHL EOS are fitted based on the theoretical calculation results of dimensionless virial coefficients recorded in relevant literature, and the fifth and sixth order terms are calibrated by using PVT parameters of methane in high temperature and high pressure regions
Summary
The equation of state (EOS) of fluids is usually applied to describe the PVT relationship of fluids, which is widely used in the fields of chemistry and fuel science, earth science, and explosion mechanics. The third and fourth order virial coefficients in the VHL EOS are fitted based on the theoretical calculation results of dimensionless virial coefficients recorded in relevant literature, and the fifth and sixth order terms are calibrated by using PVT parameters of methane in high temperature and high pressure regions. For the fifth order virial term, we fit the fifth order term based on the theoretical calculation results obtained by Kofke using the MSMC (Mayer Sampling Monte Carlo) method.[22] On this basis, in order to verify and evaluate the accuracy of the VPL EOS in describing the PVT relationship of high temperature and high pressure gas over a wide temperature range, using the VPL EOS, the PVT data of methane, oxygen, and nitrogen are calculated and compared with the calculation results of the other two virial EOSs for gaseous detonation products—the VLW EOS and VHL EOS—as well as the relevant MD data and NIST data
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