An analogy between the Van der Pol equation and the Greitzer model

Abstract

This paper presents the idea to exploit the similarity between the Van der Pol equation and the Greitzer lumped parameter model. The Greitzer model is a widely used nonlinear model to describe surge transients in turbocompressors. One of the difficulties in applying this model is the identification of the model parameters. Usually, a priori knowledge is combined with a tuning procedure for the model parameters to match simulation results with experimental data. In contrast to the Greitzer model, there are various analytical approximations available for the period time of the Van der Pol oscillator. We propose to use the similarity with the Van der Pol equation and apply the available approximations for the identification of the model parameters in the Greitzer model. In this paper we will focus on demonstrating the similarity between both models. For this purpose we will introduce a coordinate transformation for the Greitzer model. In the subsequent parameter study we show that the transformed model exhibits the same qualitative behavior as the original compression system model. Furthermore, the parameter study reveals a linear relation between the most important model parameter and the limit cycle period time. These results form a solid basis for further research into exploiting the similarity with the Van der Pol system.