Piston motion mathematical model in the tube influenced by burning gas

Abstract

The article deals with mathematical models of the pneumatic system with piston moving under the influence of the pressure of the compressed gas under heating. To determine the piston motion parameter, the mathematical model of the system has been built in several ways: by means of ordinary differential equations and using the gas dynamic equations. Both cases under consideration allow obtaining the approximate value of the piston motion parameters when the piston reaches the open end of the tube or peak velocity. The first method provides quite simple and much faster solution in comparison with the second method, but the second one takes into consideration gas molecular characteristics which makes it more accurate. The purpose of the study is to compare the results obtained by using both methods on performance and accuracy criteria, and to make recommendations on each method feasibility.