Axially Grooved and Arterial Heat Pipe Testing and Numerical Analysis by Michel Garcia B.Eng., Carleton University A Thesis submitted to the Faculty of Graduate Studies and Research in partial fulfilment of the requirements for the degree of Master of Applied Science Ottawa-Carleton Institute for Mechanical and Aerospace Engineering Department of Mechanical and Aerospace Engineering Carleton University Ottawa, Ontario, Canada April 2006 Copyright © 2006 - Michel Garcia Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 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A bstract Testing of an axially grooved and an arterial heat pipe was performed under ambient conditions. Steady-state axial temperature distribution as a function of heat input and sink temperature was determined. Variable inclination testing with 5 W input power was performed to determine the dryout angle. Horizontal testing with variable power input was performed to determine the capillary limit. The effective thermal conductivity of each heat pipe as a function of heat input and sink temperature was determined. Numerical modelling of the axially grooved heat pipe tested was performed. Poiseuille number as a function of contact angle and attachment point was deter­ mined. A capillary limit model was developed based on the groove geometry and external heat pipe dimensions. The parametric study of attachment point and con­ tact angle variation led to the prediction of maximum heat transfer. Satisfactory agreement was found between the experiment and numerical model. iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgment s I would like to thank my supervisor, Professor Tarik Kaya for being there to an­ swer my many questions. Funding provided by CRESTech, MMO, and NSERC was appreciated. I am grateful to the Carleton Mechanical and Aerospace Engineering machine shop and administrative staff who gave me much of their time. I am also thankful to my family and friends for their support. iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents Abstract iii Acknowledgments iv Table of Contents v List of Tables viii List of Figures ix 1 Introduction 1 1.1 Origins............................................................................................................. 1 1.2 Thermodynamic Cycle ................................................................................ 2 1.3 Effective Thermal Conductivity ................................................................ 3 1.4 T esting............................................................................................................. 4 1.4.1 Gravitational Tilt Testing ............................................................. 5 1.5 Importance of the Poiseuille N u m b e r...................................................... 6 1.6 Liquid-Vapour Counterflow.......................................................................... 7 1.7 Modelling of Re-Entrant Grooves ............................................................. 8 1.8 Heat Transfer Lim its................................................................................... 9 1.8.1 Capillary Lim it................................................................................. 10 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.9 Arterial Heat P ip e s ........................................................................................ 11 2 Experimental Investigation 13 2.1 Test Setup Summary.................................................................................... 13 2.2 Experimental Equipment.............................................................................. 14 2.2.1 General S e tu p..................................................................................... 14 2.2.2 Heat P ipes........................................................................................... 15 2.2.3 H e a tin g ............................................................................................... 19 2.2.4 Cooling ............................................................................................... 21 2.2.5 Insulation and S u p p o rt..................................................................... 22 2.2.6 Tilting M echanism ........................................................................... 23 2.2.7 Data A cq u isitio n ............................................................................... 26 2.3 Experimental Process.................................................................................... 30 2.3.1 Steady-State Response..................................................................... 30 2.3.2 Transient R esponse........................................................................... 30 2.3.3 Testing Performed ............................................................................ 30 2.4 Experimental R esu lts.................................................................................... 32 2.4.1 Temporal Temperature Variation................................................... 32 2.4.2 Spatial Temperature V ariation........................................................ 42 2.4.3 Effective Thermal C onductivity ..................................................... 51 2.4.4 Heat B a la n c e ..................................................................................... 53 2.4.5 Inclination T e s tin g ............................................................................ 57 2.4.6 Horizontal Dryout ............................................................................ 59 2.4.7 AHP Heater Location V ariatio n ..................................................... 59 3 Numerical Modelling 68 3.1 Axially Grooved Heat Pipe Capillary Limit T heory ............................. 68 vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2 Liquid G roove .................................................................................................. 69 3.2.1 Global Pressure L osses ..................................................................... 69 3.2.2 Groove M odelling ............................................................................... 72 3.3 Governing Equation ....................................................................................... 78 3.3.1 Boundary C onditions......................................................................... 82 3.4 Solving the Governing E q u atio n ................................................................. 85 3.4.1 Finite Difference M odel................................................................... 85 3.4.2 Finite Element Model ................................................................... 90 3.5 Vapour Flow.................................................................................................... 92 3.6 Combining Liquid and Vapour Flow s ....................................................... 93 3.7 Capillary Limit Code S tru c tu re ................................................................ 96 3.8 Numerical R esults......................................................................................... 97 3.8.1 Velocity Fields Resulting from Different Boundary Conditions 98 3.8.2 Contact Angle V ariatio n....................................................................100 3.8.3 Attachment