Effect of tube heat conduction on the single branch pulsating heat pipe start-up

• The imposed evaporator heat power and condenser temperature have been considered for the single branch PHP open to a reservoir.
• The start-up depends mainly on evaporator power, PHP tube parameters (heat conductivity and section), gas phase parameters and reservoir pressure.
• The dependence on evaporator and condenser length, parameters of liquid phase and condenser temperature is weak.
• The start-up threshold is independent of the parameters of the liquid film deposited by the receding meniscus at the internal tube walls.

The oscillation inception in the single-branch pulsating heat pipe (PHP, called also oscillating heat pipe) has been studied in the presence of the heat conduction along the PHP tube, with the imposed both evaporator heat power and condenser temperature. A start-up regime caused rather by the meniscus/film evaporation than boiling has been considered. The dynamic equilibrium system state has been analyzed, where the liquid film is absent and the meniscus is located at a position where the tube temperature corresponds to the saturation temperature. The temporal evolution of the system responding to an initial fluctuation shows a non-linear response even for small fluctuations. The stability of the equilibrium state has been analyzed. The stability threshold corresponds to the start-up criterion. The main result of the above analysis is the independence of the start-up criterion of the liquid film properties (film shape and thickness). This result applies to the multi-branch PHP too. Due to the large tube thermal inertia, influence of the temporal variation of the tube temperature on the threshold can be neglected; only the equilibrium spatial temperature distribution along the tube matters. The start-up threshold value is determined for the temperature gradient along the tube, more specifically, its equilibrium value at the equilibrium meniscus location. It depends only weakly on other system parameters like condenser temperature or adiabatic section length. An analytical expression for the threshold has been obtained. The start-up power scales like square root of the tube heat conductivity. The liquid viscous dissipation is found to be much less important than the energy dissipation via the fluid and solid heat transfer.