# Calculating the Time of Adiabatic Flow of an Ideal Gas from a Constant Volume Reservoir Using Relative Parameters

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy

Release:

2018, Vol. 4. №2

Title:
Calculating the Time of Adiabatic Flow of an Ideal Gas from a Constant Volume Reservoir Using Relative Parameters

For citation: Tarasov V. V. 2018. “Calculating the Time of Adiabatic Flow of an Ideal Gas from a Constant Volume Reservoir Using Relative Parameters”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 4, no 2, pp. 94-104. DOI: 10.21684/2411-7978-2018-4-2-94-104

Vadim V. Tarasov, Cand. Sci. (Tech.), Associate Professor, Department of Engineering Graphics, Bauman Moscow State Technical University; midav-5491@mail.ru

Abstract:

This work continues the computational and analytical study of the adiabatic process of the ideal gas outflow from the constant volume reservoir. The author’s previous works considered two main tasks: 1) determining the total time of the gas outflow from the tank; and 2) finding the analytical expression to engineer the methods of calculation for determining the amount of gas pressure in the tank depending on the outflow time.

The results of these works (with some assumptions) allow solving the tasks for each specific case determined by the absolute values of the initial parameters with a sufficient degree of accuracy.

At the preliminary stage of the development of new units, it is possible to employ a more general computational and analytical study using relative parameters, excluding some initial values, and thus, to the identify parameters that directly affect the nature of the process under study.

Since this paper considers the process of gas flow depending on time, when showing the output of the calculated ratios for the argument, the relative time is used. Given that the thermo- dynamic parameters of an ideal gas are related by the equation of state, the relative value of one of the three gas parameters a can be considered s a function: pressure, temperature, and density.

This paper considers the temperature of the gas at the outlet from the tank and the total time of the gas discharge as the parameters of the reduction in the output of the calculated ratios. In each specific task, both of these parameters are constant values, the values of which can be determined from the source data. The casting parameters are taken in the output section because they are the result of the entire expiration process.

The use of relative values has shown that the nature of the flow of the process of expiration, in the adopted formulation of the problem, depends only on two constant values: the total differential pressure (a parameter that determines the potential energy of the gas enclosed in the tank) and the adiabatic index (a parameter, which characterizes the working body).

In this paper, exact analytical dependences are obtained for the calculation of two possible modes of gas flow: critical and subcritical. However, if the direct dependence of the relative temperature on the relative time is obtained for the subcritical regime, then the opposite is obtained for the subcritical regime (time on temperature). To obtain the most popular in the practice of engineering calculations of direct dependence (temperature on time), the author has used the approximation function. The obtained approximate ratio allows to determine the value of the relative temperature at a given value of relative time with a sufficiently high degree of accuracy.

Keywords:

References:

1. Tarasov V. V.2016. “Withdrawal of the Calculated Dependence to Determine the Pressure of the Ideal Gas in the Tank of a Constant Volume during Its Adiabatic Outflow”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 2, no 4, pp. 80-88. DOI: 10.21684/2411-7978-2016-2-4-80-88
2. Tarasov V. V. 2016. “Calculation of the Ideal Gas Outflow Time from the Reservoir of Constant Volume into the Environment with a Constant Pressure at an Adiabatic Process”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 2, no 2, pp. 84–95. DOI: 10.21684/2411-7978-2016-2-2-84-95
3. Krutov V. I. (ed.). 1981. Tekhnicheskaya termodinamika [Technical Thermodynamics]. Мoscow: Vysshaya shkola.
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