Determination of gas parameters in resonant pipes and channels of engines with a periodic workflow using the piston analogy method

Abstract

This paper investigates a process of gas flow in the resonant tube of an engine with a periodic workflow. Analysis of various flow models and comparison of known data have shown that the problems of constructing closed 0-dimensional models of the operating cycle for some types of engines remain unresolved. Given this, the question arises about the dimensionality of models of individual engine elements, including the resonant pipe model, which must be included in the general model of the cycle, especially at the initial stage of its development. To solve the identified problems, a mathematical model of air flow has been improved, built on the basis of an analogy with a '"liquid" piston. Unlike existing ones, the piston analogy model allows one to calculate the instantaneous velocity averaged over the length of the pipe using a numerical solution of the differential equation for velocity. To test the model built, an alternative finite-difference 1-dimensional gas-dynamic model was selected, with the help of which a test simulation of air flow in a pipe was performed. It has been established that the piston model allows one to find the flow velocity with an accuracy of 5 % for a pressure drop varying according to a sinusoidal law. The permissible limits for changes in the oscillation frequency and pipe length were found, at which the piston model has a minimum error. Based on the results of the study, it was concluded that with a small mass and inertia of the liquid piston, the proposed model gives results close to those provided by more complex models with higher dimensionality. This indicates the possibility of using a piston model for elements such as pipes as part of a 0-dimensional thermodynamic model of engines with a periodic operating process as an approximate alternative to traditional 1-dimensional flow models