by

R. Michael Castle and Scott K. Thomas, Department of Mechanical and Materials Engineering, Wright State University, Dayton, OH 45435

and

Kirk L. Yerkes, Air Force Research Laboratory (PRPG), Wright-Patterson AFB, OH 45433-7251

The results of a recently completed experimental and analytical study showed that the capillary limit of a helically-grooved heat pipe (HGHP) was increased significantly when the transverse body force field was increased. This was due to the geometry of the helical groove wick structure. The objective of the present research was to experimentally determine the performance of revolving helically-grooved heat pipes when the working fluid inventory was varied. This thesis describes the measurement of the geometry of the heat pipe wick structure and the construction and testing of a heat pipe filling station. In addition, an extensive analysis of the uncertainty involved in the filling procedure and working fluid inventory has been outlined. Experimental measurements include the maximum heat transport, thermal resistance and evaporative heat transfer coefficient of the revolving helically--grooved heat pipe for radial accelerations of a_r = 0.0, 2.0, 4.0, 6.0, 8.0, and 10.0-g and working fluid fills of G = 0.5, 1.0 and 1.5. A previous capillary limit code has been updated and improved, and comparisons are made to the present experimental data.

Helically-grooved heat pipes (HGHPs) have potential applications in the thermal management of rotating equipment such as aircraft alternators, large-scale industrial electric motors, and spinning satellites. In two recent studies (Klasing et al., 1999; Thomas et al., 1998), the performance of revolving HGHPs was investigated. It was found that the capillary limit increased with the strength of the acceleration field perpendicular to the heat pipe axis. In order to move HGHPs closer to application, knowledge must be gained concerning the sensitivity of the capillary limit to working fluid fill amount, since variations in the fill amount are inevitable during the manufacture of these devices. Very few studies were available concerning the effect of working fluid fill on the performance of axially--grooved heat pipes, but those found have been outlined below. In addition, synopses of the two aforementioned studies on revolving HGHPs have also been provided.

Brennan et al. (1977) developed a mathematical model to determine the performance of an axially-grooved heat pipe which accounts for liquid recession, liquid-vapor shear interaction and puddle flow in a 1-g acceleration environment. The model considered three distinct flow zones: the grooves unaffected by the puddle, the grooves that emerge from the puddle, and the grooves that are submerged by the puddle. The model for the puddle consisted of satisfying the equation of motion for the puddle and the continuity equation at the puddle-groove interface, and was solved by a fourth-order Runge-Kutta integration method with self-adjusting step sizes. The assumptions made by the model for the puddle were uniform heat addition and removal with a single evaporator and a single condenser section, and one-dimensional laminar flow in the puddle. The transport capability of the grooves unaffected by the puddle and the grooves extending beyond the puddle were approximated by a closed-form solution with laminar liquid and vapor flow. The working fluids used for the experiment were methane, ethane and ammonia. Brennan et al. (1977) stated that the mathematical model agreed well with the experimental data for ideally filled and overfilled heat pipes, but some differences were noted for underfilled heat pipes. In general, it was found for ideally filled heat pipes the predicted transported heat was higher than that measured. Also, this discrepancy was more significant for lower operating temperatures. In addition, it was found during the experiments that the maximum transported heat increased with fill volume.

Vasiliev et al. (1981) performed a series of experiments on an aluminum axially-grooved heat pipe which was overfilled and ideally filled. The width and height of the grooves were w = 0.123 mm and h = 0.7 mm, respectively, with an overall heat pipe length of L_t = 80.0 cm. The working fluids were acetone and ammonia. Vasiliev et al. showed that the temperature difference from the evaporator to the adiabatic regions increased at a much slower rate with increasing overfills. This was attributed to a thin film of liquid emerging from the overfill pool wetting the upper grooves. Vasiliev et al. stated that this thin film was lifted over the grooves by capillary forces due to microroughness on the groove surface. A mathematical model was developed for low temperature axially-grooved heat pipes to estimate heat pipe performance for 0-g and 1-g applications. The mathematical model was a set of boundary-value problems applied to each groove and was solved by a numerical iteration method. The model was based on pressure balance equations and mass continuity written for a single groove. The temperature of the vapor in the adiabatic region was an input parameter, and the vapor pressure gradient was assumed to be one-dimensional. In addition, the liquid-vapor shear stress was assumed to be constant, and the starting liquid film thickness was of the same order of magnitude as the groove microughness. Very good agreement was reported between the mathematical model and experimental transported heat results for ideally filled and overfilled heat pipes under gravity.

Thomas et al. (1998) presented experimental data obtained from a helically-grooved copper heat pipe which was tested on a centrifuge table. The heat pipe was bent to match the radius of curvature of the table so that a uniform transverse (perpendicular to the axis of the heat pipe) body force field could be applied along the entire length of the pipe. The steady-state performance of the curved heat pipe was determined by varying the heat input (Q_in = 25 to 250 W) and centrifuge table velocity (radial acceleration a_r = 0.01 to 10-g). It was found that the capillary limit increased by a factor of five when the radial acceleration increased from a_r = 0.01 to 6-g due to the geometry of the helical grooves. A model was developed to calculate the capillary limit of each groove in terms of centrifuge table angular velocity, the geometry of the heat pipe and the grooves, and the temperature-dependent working fluid properties. The agreement between the model and the experimental data was satisfactory.

Klasing et al. (1999) developed a mathematical model to determine the operating limits of a revolving helically-grooved straight heat pipe. The capillary limit calculation required an analysis of the total body force imposed by rotation and gravity on the liquid along the length of the helical grooves. The boiling and entrainment limits were calculated using methods described by Faghri (1995). It was found that the capillary limit increased significantly with rotational speed due to the helical geometry of the heat pipe wick structure. The maximum heat transport was found to be a function of angular velocity and tilt angle from horizontal. In addition, a minimum value of angular velocity was required to obtain the benefits of the helical groove geometry.

The first objective of the present study was to determine the sensitivity of the performance of revolving HGHPs to the working fluid fill amount. This required a precise knowledge of the geometry of the heat pipe and helical grooves. In addition, a precision filling station was constructed and calibrated to determine the uncertainties involved in the filling procedure. The copper-ethanol heat pipe was tested on a centrifuge table at Wright-Patterson AFB (AFRL/PRPG) to determine the capillary limit, thermal resistance and evaporative heat transfer coefficient for fill ratios of G = 0.5, 1.0 and 1.5, and radial accelerations of a_r = 0.01, 2.0, 4.0, 6.0, 8.0 and 10.0-g. The second objective of the present study was to improve the existing analytical capillary limit model developed by Thomas et al. (1998) using the above-mentioned geometric measurements and by using improved equations for the working fluid properties.