Non-linear analyses of temperature oscillations in a closed-loop pulsating heat pipe

In this paper, the chaotic behavior of wall temperature oscillations in a closed-loop pulsating heat pipe was investigated using non-linear analyses on temperature data. The tested heat pipe, consisting of 5 turns, was made of copper capillary tube and had an internal diameter of 2 mm. Ethanol was selected as the working fluid with filling ratios (FR) of 30%, 50% and 70%. Wall temperature fluctuations were recorded under three different heating power inputs of 37, 60, and 87 W. Various methods, including pseudo-phase-plane trajectories, correlation dimensions (DE), Lyapunov exponents, and recurrence plots, were used to analyze the non-linear dynamics characteristics of temperature oscillation data. Three types of attractors were identified under different power inputs. All of the calculated positive largest Lyapunov exponents were found to be less than 0.1, demonstrating the weak chaos characteristics of the pulsating heat pipe. The increase of the power input augments the correlation dimensions and contributes to the improvement of the thermal performance of the pulsating heat pipe. For each power input, the correlation dimensions have the trend of DE,FR=50% > DE,FR=70% > DE,FR=30%, and the best thermal performance was obtained at 50% filling ratio. At least four independent variables are required in order to describe the heat transfer characteristics of a PHP. The average time of the temperature oscillation stability loss, i.e., the inverse of the largest Lyapunov exponent, decreases as the power input increases. In the recurrence plots, chaotic states were observed. The Recurrence Quantification Analysis indicates larger values of the order-2 Renyi entropies K2 at the evaporation section than at the condensation section. Moreover, the trend that K2,Q=87W > K2,Q=60W > K2,Q=37W at each filling ratio both for Te4 and Tc4 collaborating with the positive, finite largest Lyapunov exponent gives a hint of the maximum entropy self-organization process of the temperature oscillations with the increase of power input.