Nonlinear Analysis of Chaotic Flow in a Three-Dimensional Closed-Loop Pulsating Heat Pipe

Abstract

Numerical simulation has been conducted for the chaotic flow in a 3D closed-loop pulsating heat pipe (PHP). Heat flux and constant temperature boundary conditions were applied for evaporator and condenser sections, respectively. Water and ethanol were used as working fluids. Volume of Fluid (VOF) method has been employed for two-phase flow simulation. Spectral analysis of temperature time series was carried out using Power Spectrum Density (PSD) method. Existence of dominant peak in PSD diagram indicated periodic or quasi-periodic behavior in temperature oscillations at particular frequencies. Correlation dimension values for ethanol as working fluid was found to be higher than that for water under the same operating conditions. Similar range of Lyapunov exponent values for the PHP with water and ethanol as working fluids indicated strong dependency of Lyapunov exponent to the structure and dimensions of the PHP. An O-ring structure pattern was obtained for reconstructed 3D attractor at periodic or quasi-periodic behavior of temperature oscillations. Minimum thermal resistance of 0.85 ˚C/W and 0.88 ˚C/W were obtained for PHP with water and ethanol, respectively. Simulation results showed good agreement with experimental results from other work under the same operating conditions.

Physical principles and state-of-the-art of modeling of the pulsating heat pipe: A review

“…Pouryoussefi and Zhang [149,150,151] performed an extensive study of 2,4, and 5-turn PHP configurations in 2D and 3D by VOF. Dry area appearance is described.…”

Thermal Performance of Micro-Pulsating Heat Pipe

“…Because of this, the velocity calculated near the interface is not accurate and leads to large velocity difference between the interacting phases. (6) The momentum equation, shown above is dependent on the volume fractions of all phases through the properties and μ. (7) In VOF, energy and temperature are considered as mass-averaged variable in the domain.…”

“…(11) Surface tension dominated study has a significant effect on the element type. According to Zhang et al [6], hexahedral and quadrilateral mesh is preferred in case of two dimensional and three-dimensional domains for surface tension dominated problem. Therefore, proper mesh with all quadrilateral elements should be chosen for simulation shown in figure 2.…”

“…Zhao et al [5] studied the influence of initial vacuum pressure condition for different pressure values of PHP and found that variation of oscillating pressure difference is very less. Zhang et al [6] Studied the chaotic behavior of PHP with two turns and depicted the temperature profile at evaporator and discussed about bubble generation. Zhang et al [7] studied the behavior of PHP computationally with constant temperature boundary condition in both evaporator and condenser.…”

Chaotic Diagnostics in a Biodiesel Combustion System Using PLIF and Nonlinear Time Series Analysis▴

“…Through data analysis of combustion process information, the combustion state can be accurately identified and classified, thus providing useful judgment strategies and accurate prediction for industrial production [19]. For many years, researchers have characterized the properties of chaotic behaviors and distinguished between the different types of chaos by plenty of methods and criterias, including power spectrum [20,21], features of a trajectory in the phase space such as strange attractor [22], Lorenz map [23], Poincare map [24], Hurst index [25,26] and Lyapunov stability [27,28]. The identification of chaos by these methods is complicated and tedious.…”