On the nonlinear characteristics of two-phase flow system as modified Fitzhugh-Nagumo model

Abstract

Two-phase flow systems are used in many industries for high heat transfer because these systems utilize latent heat of vaporization. However, these systems are susceptible to two-phase flow instabilities, which have been studied for the last several decades, mainly using numerical simulations and, to some extent, nonlinear stability analysis. These instabilities lead to flow excursions or flow oscillations and have recently been related to various nonlinear phenomena obtained by numerical continuation software. Further research of the instabilities shows that such systems’ behavior is like the FitzHugh-Nagumo (FHN) model. Therefore, the existing two-phase flow model (with some reasonable approximations) is modified into a form identical to the FHN model. It is demonstrated that the modified model reasonably captures the physical attributes of the existing model. Moreover, it is shown that the phenomena described in the FHN model are the same as predicted by earlier models. Since FHN models and their various attributes are relatively well established, they can control the instabilities or operate the two-phase system at desired conditions. The characteristics of the system dynamics with various types of disturbance (instantaneous and periodic) have been investigated. The system provides an unattainable periodicity for periodic perturbation. In comparison, it responds with a single large amplitude or spike dynamics for instantaneous perturbation.