The Effect of Working Fluid Inventory on the Performance of Revolving Helically-Grooved Heat Pipes

1. The Effect of Working Fluid Inventory on the Performance of Revolving Helically-Grooved Heat Pipes Presenter: Dr. Scott K. Thomas, Wright State University Co-authors: R. Michael Castle, Graduate Research Assistant (Currently with Belcan Corp.) Dr. Kirk L. Yerkes, AFRL/PRPG

2. Objectives • Determine • Capillary Limit • Thermal Resistance • Evaporative Heat Transfer Coefficient • Vary • Heat Input • Radial Acceleration • Fluid Inventory

3. Applications of Revolving Heat Pipes • Thermal Management of Rotating Devices • Aircraft Generators • Large-Scale Industrial Electric Motors • Rotating Satellites Curved Heat Pipe Straight Heat Pipe ω R R ω

4. Previous Research Klasing, K., Thomas, S., and Yerkes, K., 1999, “Prediction of the Operating Limits of Revolving Helically-Grooved Heat Pipes,” ASME Journal of Heat Transfer, Vol. 121, pp. 213-217. Thomas, S., Klasing, K., and Yerkes, K., 1998, “The Effects of Transverse Acceleration-Induced Body Forces on the Capillary Limit of Helically-Grooved Heat Pipes,” ASME Journal of Heat Transfer, Vol. 120, pp. 441-451. Findings: • Capillary limit increased significantly with radial acceleration • Straight axial grooves showed no improvement with radial acceleration Shortcomings: • Effect of liquid fill not examined • Helical groove geometry not rigorously determined

5. Working Fluid Inventory mt = mv + ml = Vvs/vv + GVgr/vl Total Inventory Mass Vvs = πDvs2Lt/4 + Vgr(1 - G) Vapor Space Volume Vgr = LgrNgrAgr Groove Volume Agr = wh + h2(tan θ1 + tan θ2) /2 Groove Area Lgr = Lt[(2πrh/p)2 + 1]1/2 Groove Length p = 2π(s - s1)/(φ - φ1) Groove Pitch G = Vl/Vg Ratio of Liquid Volume to Total Groove Volume

6. Working Fluid Inventory • Measure groove height and width • Bitmap image from microscope • Microscope scale • Adobe Illustrator θ1 θ2 h w

7. Working Fluid Inventory • Measure helical groove pitch • Angular transducer • High precision voltmeter • Vertical milling machine

8. Working Fluid Inventory Agr h w p rh θ1 Lgr θ2 Vgr V - V1 s - s1 Dvs Lt mt(g) G

9. Heat Pipe Fill Station • No horizontal lines • Short runs of large diameter tubing • Detect and remove trapped vapor by cycling valves • Fully calibrated Δmt (g) Δmd (g) G

10. Experimental Setup • 8 ft dia Centrifuge Table • 20 HP DC motor • Separate instrumentation and power slip rings • On-board TC signal conditioning • Double-pass hydraulic rotary coupling • Copper-ethanol heat pipe bent to outer radius of centrifuge table

11. Experimental Setup Thermocouple placement: • Unheated/uncooled sections for thermal resistance • Circumferential and axial distributions in evaporator section for evaporative heat transfer coefficient

12. Experimental Results Temperature distributions: • Uniform temps for low input power levels • Evaporator temps increase with input power: Partial dryout of evaporator Inboard

13. Experimental Results Thermal resistance vs transported heat: • For G = 0.5, partial dryout even for low power, Rth decreased with ar • For G = 1.0 and 1.5, Rth decreased and then increased when dryout commenced • For G = 1.5, dryout was not reached for ar > 2.0-g G = 0.5 G = 1.5 G = 1.0 Qt(W)

14. Experimental Results x = 54 mm x = 130 mm Evaporator temperature vs transported heat for ar = 0.01-g: • Temperature increased with Qt • For G = 1.0, grooves were full near adiabatic section, dry near evaporator end cap • Temps converge to the same value around the circumference during dryout x = 92 mm x = 168 mm Qt(W)

15. Experimental Results Evaporator temperature vs transported heat for ar = 10.0-g: • Dryout was delayed due to improved pumping of helical grooves • Temperature variation around circumference was greater than ar = 0.01-g x = 54 mm x = 130 mm x = 168 mm x = 92 mm Qt(W) Qt(W)

16. Experimental Results x = 54 mm x = 130 mm Evaporative heat transfer coefficient vs transported heat for ar = 0.01-g: • he was very low for G = 0.5 due to dryout • he increased and then decreased as dryout was approached • For G = 1.0, partial dryout along the axis occurred (he converged around circumference) x = 92 mm x = 168 mm Qt(W) Qt(W)

17. Experimental Results x = 130 mm Evaporative heat transfer coefficient vs transported heat for ar = 10.0-g: • he was more uniform around the circumference and along the axial direction for G = 1.0 • he was more constant with respect to Qtcompared with ar = 0.01-g x = 54 mm x = 92 mm x = 168 mm Qt(W) Qt(W)

18. Comparison of Analytical Capillary Limit Model and Experimental Data Maximum heat transport vs radial acceleration: • Qcapincreased significantly with ar • For G = 0.5, heat pipe operated only for ar 8.0-g • For G = 1.5, capillary limit could not be reached for ar 4.0-g • Analytical model agrees well with data for G = 1.0 • Assumed full grooves, no liquid communication G = 0.5 G = 1.5 ar (g) G = 1.0 ar (g)

19. Conclusions • Capillary limit increased, thermal resistance decreased significantly with working fluid inventory • Evaporative heat transfer coefficient was a strong function of working fluid inventory • Analytical model prediction was good for G = 1.0, but unsatisfactory for underfilled and overfilled heat pipes

20. Current Research • Thomas, S., Lykins, R., and Yerkes, K., 2000, "Fully-Developed Laminar Flow in Trapezoidal Grooves with Shear Stress at the Liquid-Vapor Interface," submitted to the International Journal of Heat and Mass Transfer. • Thomas, S., Lykins, R., and Yerkes, K., 2000, "Fully-Developed Laminar Flow in Sinusoidal Grooves," submitted to the ASME Journal of Fluids Engineering. • Use results of numerical model to improve analytical capillary limit model for revolving helically-grooved heat pipes • Numerical model accounts for countercurrent liquid-vapor shear stress and working fluid inventory