Withdrawal of the Calculated Dependence to Determine the Pressure of the Ideal Gas in the Tank of a Constant Volume during Its Adiabatic Outflow

About the author:

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

Abstract:

The calculation of the gases outflow from the tank of finite volume is an essential engineering problem. In general, when one considers the outflow of a real gas accounting for external heat exchange and the variability of the output nozzle flow rate, solving this problem is rather difficult — the development of complex mathematical models is required. In some special cases (close to the real conditions), the solution is simplified, e. g., if one considers the adiabatic outflow of an ideal gas at a constant flow rate. Furthermore, the resulting in such cases solution can be used in certain mathematical models as a first approximation.

This article continues the author’s work published in the 2^nd issue of the journal “TSU Herald. Physical and Mathematical Modeling. Oil, Gas, Energy” in 2016. The article reviewed the solution to the problem, allowing to determine the outflow time of an ideal gas from a reservoir of constant volume during the adiabatic process. It was noted that the main difficulties in this task arise during the consideration of the subcritical regime expiration. Therefore, for this region an approximate, though a rather accurate formula was proposed to determine both the total time of expiry gas from the tank and the functional dependence between the outflow time and the pressure in the tank — t(p). To find the most demanded among engineers functional dependence p(t), the obtained inverse conversion formula was proposed to be used. Naturally, this approach complicates the whole calculation process, and, in addition, it leads to more errors. Therefore, this work’s task was formulated as the retrieval of the direct dependencies p(t). In this task, the author used as an intermediate parameter the values of Mach number (determined by the gas velocity at the outlet of the tank). The analytical research led to obtaining the formula for determining the approximate, but rather accurate value of the pressure in the tank depending on the outflow time.

References:

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