Simplified Mathematical Model of a novel ‘Closed Loop Two-Phase Wicked Thermosyphon (CLTPWT)’

A novel “Closed Loop Two-Phase Wicked Thermosyphon (CLTPWT)” was designed, fabricated, and tested by a California-based start-up company for thermal management of overhead light emitting diodes (LEDs). This device is comprised of a central evaporator and a circular heat exchanger coil connected by transport lines. Despite the presence of a porous wick structure in the evaporator, gravity provides the necessary driving potential for circulation of the working fluid in this device and therefore the name CLTPWT. A thermal model of this device was previously developed (by the authors) to predict its thermal performance. The evaporator model employed in the previous study assumed constant thermal resistances that were obtained from one specific ‘size’ of the evaporator. This paper simplifies this existing model by mathematically decoupling the evaporator from the coil of the device. The primary objective of the model is to obtain temperature predictions that are not based on an evaporator package geometry (size) which permits investigation of a wider operating power range. In addition, this model accounts for the mass flow rate of the working fluid based on a steady state pressure balance, as opposed to the previous model which estimates this based on the thermal solution. The model predicts thermal performance of the device in terms of the evaporator (and condenser) saturation temperature (Tsat), sub-cooler temperature (Tsc), and two-phase mixture quality (x evp) leaving the evaporator package. These predictions are compared with both experiments performed in a limited operating power range and with the predictions based on the previous model. The predictions of the current model are found to be in good agreement with both. In addition, this paper also reports the effect of independent variables such as the air temperature (Tair) and fill volume (V fill) on the performance of the CLTPWT.