Bifurcation analysis of a pulsating heat pipe

Abstract

Heat pipes are being used for transferring a very high amount of heat in electronic devices. The Pulsating Heat Pipe has the advantage of not having a wick structure and, therefore, is a promising candidate for both terrestrial and space applications. However, understanding Pulsating Heat Pipe's operation is somewhat limited due to the multi-physics involved in the process. The presence of self-sustained oscillations can be understood by non-linear dynamics. In order to understand these oscillations, recently a simple phenomenological model is developed. This model explains all the thermodynamic processes of the system. Moreover, the oscillatory behavior of the liquid slug is modeled in a similar way to the spring-mass system. The system of non-linear ordinary differential equations, containing the conservation equations for the liquid slug and vapor bubble separately, has been solved numerically and the bifurcation analysis has been performed using MATCONT. The oscillatory behavior of the position of the liquid slug is identified through Hopf bifurcation. For self-sustained oscillations, the Pulsating Heat Pipe must operate in the region where limit cycles exist, the so-called unstable side of the Hopf bifurcation line. It is observed that the Hopf bifurcation is subcritical throughout the parametric range of operation. The existence of subcritical Hopf bifurcation indicates that limit cycles may exist even in the linearly stable region. However, further analysis reveals that such regions in the parameter space are negligibly small and, hence, may not be of any practical consequence. It is also important to note that heat transfer enhances as one operates in a chaotic regime. Although the presence of the chaotic feature is confirmed by experimental data, the onset of this regime is an important aspect of analysis that has not been addressed in previous works. In the present work, Period-doubling bifurcation and Neimark–Sacker bifurcations have been identified to analyze the onset of chaotic regimes. Therefore, there is a possibility of two different routes to chaos. Further studies with improved models may shed more light on the chaotic regimes.