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    • When the virial coefficients of propellant gas at high tempe

    2018-10-25

    When the virial coefficients of propellant gas at high temperature and pressure are calculated, the second virial coefficients of CO, H2 and N2 can be obtained by Eqs. (4) ~ (6); the second virial coefficients of H2O and CO2 can be obtained by Eq. (7)[17] and Eq. (8)[18]; the third virial coefficients of the five elementary gases can be obtained by Eqs. (9) ~ (10) and Table 1[19]. Although an error will be brought by using the revised third virial coefficient CSP equations to calculate in the third virial coefficient at a higher temperature, the effect of extrapolation error on the maximum pressure of the propellant gas could be ignored at such a high temperature. The second and the third virial coefficients of the propellant gas can be obtained by calculating the second and the third virial coefficients of the main component elementary gases according to Eqs. (2) ~ (3), and approximately taking other small component gases as ideal gases of which B and C are zero. Then the comparative factor Z of propellant gas can be calculated. Finally, the maximum pressure of the propellant gas can be calculated by the equation pV = nZRT. Table 2 lists the maximum pressures of closed bomb tests of a gun propellant, whose formula is C24.86H32.27O33.46N9.54, under different loading conditions. The maximum pressures calculated by different theoretical virial coefficients calculation methods are also listed in Table 2. These theoretical virial coefficients calculation methods include the revised SE-CSP virial coefficient purchase EPZ015666 proposed in this article, the function of a simplified intermolecular force model [5] and a polarity modified function based on Lennard-Jones (6–12) potential function [6]. The calculations are completed under the same conditions, such as gas composition, content of elementary component gas, explosive temperature, and other component gasses as ideal gasses except the main component gasses and so on. The experimental results in Table 2 were corrected with heat loss, and the influence of ignition powder on pressure was eliminated. From Table 2 it can be seen that the maximum pressure values calculated through the revised SE-CSP expression are closer to the experimental results at different loading conditions compared to the values calculated in Refs. [5,6], and the calculated errors from modified SE-CSP are obviously smaller than those from the other methods with the increase in loading density. The comparative results indicate that the revised SE-CSP equation is suitable for maximum pressure calculation of propellant gas at high temperature and pressure, and its calculation accuracy is higher than those in Refs. [5,6]. All the pressures calculated by the three methods in Table 2 are lower than the experimental values, and the calculated errors present a slightly increasing trend with the increase in loading density. This phenomenon is probably caused by the approximation calculation, in which the main component gases are taken as real gases, and the small quantity of other dissociated gases are taken as ideal gases. This approximation leads to the result that the calculated value is lower than the experimental data. When the loading density increases, the degree of dissociation grows higher. If the dissociated gases are taken as ideal gasses at that time, the error brought by deletion approximation grows. But this error is still in the acceptable range in engineering calculation. Therefore, some amendments, such as managing dissociated gas components, could be made to improve the pressure calculation accuracy of propellant gas in calculation.
    Conclusion For the limited temperature range of the simple extended corresponding state principle (SE-CSP) and the difficulty in calculating the virial coefficients, the second virial coefficient SE-CSP expressions for the main component gases of propellant gas were amended by fitting and extrapolating the corresponding experimental data of the gases. The amendment in the present paper makes the SE-CSP expressions suitable for calculating the main component gases of propellant gas at high temperature and pressure. The second virial coefficients calculated by the revised SE-CSP expressions are in good agreement with the experimental data at low temperature. Then these revised SE-CSP expressions are extrapolated; the second virial coefficients calculated by these extrapolated expressions agree with the values in Refs. [5,6] at high temperature. The extrapolated revised SE-CSP virial expressions were used to calculate the maximum pressure of propellant gas in constant volume. The calculated error presented in the paper is smaller than those in Refs. [5,6], which indicates that the extrapolated revised SE-CSP virial expressions are appropriate for the maximum pressure calculation of propellant gas in constant volume at high temperature and pressure, and have better calculation accuracy. The revised SE-CSP expressions, which avoid establishing the complicated molecular model for virial coefficient calculation, provide a simple way to calculate the virial coefficient of propellant gas at high temperature and pressure, and have practical significance in theoretical calculation.