Comparative analysis of numerical and approximate analytical solutions to the problem of piston acceleration in a pipe by compressed gas
Authors: Bykov N.V.
Published in issue: #2(86)/2019
DOI: 10.18698/2308-6033-2019-2-1852
Category: Mechanics | Chapter: Mechanics of Liquid, Gas, and Plasma
The paper focuses on mathematical and numerical simulation of piston acceleration by compressed gas in a guide pipe, also known as Lagrange ballistic problem. We consider two approaches to an approximate analytical solution of the problem: the uniform deformation approximation, within which a new exact dimensionless solution for the piston trajectory is obtained, and a solution in the simple wave region, for which new estimates of applicability limits are obtained. The wave motion of a gas is described with the numerical solution of gas dynamics dimensionless equations on a moving mesh. We analyze the working areas of approximate analytical solutions comparing the latter with the numerical solutions. Furthermore, we demonstrate the calculation of a model example, which compares the results of calculations for various models and estimates the variation range in dimensionless parameters from the point of view of practical application. The dimensionless representation of the solutions allows us to summarize the results obtained. Based on the efficiency analysis, we deal with the issue of energy performance of piston acceleration by compressed gas. Findings of research show that with an increase in the length of the pipe and the ratio between the mass of compressed gas and the mass of the piston, the efficiency decreases
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