Analysis of Fluid Flow in Axial Re-entrant Grooves with Application to Heat Pipes

by

Scott K. Thomas and Vikrant Damle

Department of Mechanical and Materials Engineering

Wright State University, Dayton, OH 45435-0001

Abstract

The fully developed laminar flow within a re-entrant groove has been analyzed using a finite element model. Re-entrant grooves have been used in both axially-grooved heat pipes and in monogroove heat pipes. The main benefit to using this type of wick structure is the reduction of the liquid pressure drop along the length of the groove due to countercurrent liquid-vapor interaction at the meniscus. All previous researchers assumed that the pressure drop within the liquid could be modelled as flow within a smooth tube, but the results of the current analysis show that this assumption can lead to significant errors in the pressure drop prediction. An extensive literature survey was completed and the results of five previous studies were used to validate the current numerical model. It was found that the present finite element model is both more accurate and consumes less computer resources than a finite difference based model developed previously by one of the authors of the current manuscript. A parametric analysis was carried out to determine the Poiseuille number, Po = $f$Re, the dimensionless mean velocity, $\overline {v^*}$, and the dimensionless volumetric flow rate, $\dot {V^*}$, as functions of the geometry of the re-entrant groove (groove height $1.0 \le H^* \le 4.0$, slot half-width $0.05 \le W^*/2 \le 0.9$, fillet radius $0.0 \le R^*_f \le 1.0$), and the liquid-vapor shear stress ($0.0 \le -\tau^*_{lv} \le 2.5$). It was determined that the flow variables were strongly affected by the groove height, slot half-width and liquid-vapor shear stress, but were relatively unaffected by the fillet radius. The case in which the meniscus recedes into the re-entrant groove was examined, which could be a result of evaporator dry-out or insufficient liquid fill amount. The cross-sectional area of the liquid in the groove, $A^*_l$, the meniscus radius, $R_m^*$, and the above-mentioned flow variables were calculated as functions of the meniscus contact angle ($0^\circ \le \phi \le 40^\circ$) and meniscus attachment point ($0.0 \le H^*_l \le 2.75$). In general, the flow variables were more strongly affected by the meniscus attachment point than the meniscus contact angle. Finally, the results of the numerical model were used to determine the capillary limit of a low-temperature heat pipe with two different working fluids, water and ethanol, for a range of meniscus contact angles. The capillary limit heat transfer was found to attain a maximum value in the slot region and then decreased dramatically when the meniscus receded into the circular region of the re-entrant groove.