SOLUBILITY, SEA PROPERTIES, EFFERVESCENCE AND BALLAST DESIGN FOR AN EXTRATERRESTRIAL SUBMARINE by PETER MEYERHOFER Submitted in partial fulfillment of the requirements for the degree of Master of Science Mechanical Engineering CASE WESTERN RESERVE UNIVERSITY January 2019 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis of Peter Meyerhofer candidate for the degree of Master of Science. Committee Chair Prof. Yasuhiro Kamotani Committee Member Prof. Paul Barnhart Committee Member Prof. Joseph Prahl Date of Defense October 24th, 2017 *We also certify that written approval has been obtained for any proprietary material contained therein. 1 Table of Contents 1 Introduction ........................................................................................................ 14 2 Literature Review ............................................................................................... 18 3 Solubility Model ................................................................................................. 21 3.1 Background ................................................................................................. 21 3.2 Analysis and Filtering ................................................................................. 26 3.3 Analytical Model ........................................................................................ 30 3.3.1 Functional Form .................................................................................. 30 3.3.2 Curve Fit to Data ................................................................................. 31 4 Titan Sea Properties ........................................................................................... 37 4.1 Solubility at Titan Temperatures ................................................................ 37 4.2 Assumptions ................................................................................................ 38 4.3 Governing Equations .................................................................................. 39 4.4 Chemical Potential Model........................................................................... 44 4.4.1 Imposed Temperature .......................................................................... 44 4.4.2 Constant Enthalpy................................................................................ 46 4.4.3 Constant Entropy ................................................................................. 49 4.4.4 Constant Mole Ratio ............................................................................ 49 4.5 Imposed Solubility ...................................................................................... 50 4.5.1 Surface Solubility (SS) ........................................................................ 50 4.5.2 Full Solubility (FS) .............................................................................. 50 4.6 Assessment .................................................................................................. 52 4.7 Properties .................................................................................................... 54 4.8 Uncertainty .................................................................................................. 56 5 Effervescence ..................................................................................................... 60 5.1 Problem Statement ...................................................................................... 60 5.2 Effervescence Model .................................................................................. 62 5.2.1 Skin Temperature ................................................................................ 62 5.2.2 Applied Solubility................................................................................ 64 5.2.3 General Bubble Nucleation ................................................................. 65 5.2.4 Bubble Incipience and Nucleation Site Density .................................. 66 5.2.5 Bubble Growth .................................................................................... 67 5.2.6 Volume and Area Coverage ................................................................ 70 5.2.7 Pressure Drop in Propellers ................................................................. 82 5.2.8 Solution Method .................................................................................. 85 5.3 Numerical Results ....................................................................................... 86 6 Ballast Trade Study ............................................................................................ 95 6.1 Submarine Literature Review ..................................................................... 95 6.2 General Considerations ............................................................................... 96 6.2.1 Tank Size and Sink Rate ...................................................................... 97 6.2.2 Uncertainty ........................................................................................ 100 6.2.3 Parts ................................................................................................... 103 6.3 Pump System ............................................................................................ 104 6.3.1 Analysis ............................................................................................. 105 6.3.2 Operations .......................................................................................... 106 6.3.3 Parts ................................................................................................... 108 2 6.4 Bladder Only ............................................................................................. 109 6.4.1 Analysis ............................................................................................. 109 6.4.2 Operations .......................................................................................... 110 6.4.3 Parts ................................................................................................... 111 6.5 Noncondensible Gas without Separator .................................................... 112 6.5.1 Analysis ............................................................................................. 112 6.5.2 Operations .......................................................................................... 116 6.5.3 Parts ................................................................................................... 118 6.6 Noncondensible Gas with Separator ......................................................... 119 6.6.1 Analysis ............................................................................................. 119 6.6.1.2 CVs and Equations ................................................................................ 121 6.6.1.2.1 Ramp Stage ........................................................................................ 121 6.6.1.2.2 Expansion Stage ................................................................................. 123 6.6.1.3 Solution Method.................................................................................... 124 6.6.1.3.1 Ramp Stage ........................................................................................ 124 6.6.1.3.2 Expansion Stage ................................................................................. 126 6.6.1.4 Numerical Results and Discussion........................................................ 127 6.6.2 Operations .......................................................................................... 133 6.6.3 Parts ................................................................................................... 134 6.7 Gas Purification ........................................................................................ 135 6.7.1 Refrigeration ...................................................................................... 137 6.7.2 Distillation ......................................................................................... 139 6.7.3 Membrane .......................................................................................... 142 6.7.4 Adsorbent........................................................................................... 144 6.7.5 Mass Comparison .............................................................................. 146 6.8 Nitrogen Gas with Separator ..................................................................... 148 6.8.1 Unmodified Vapor System ................................................................ 148 6.8.2. Vapor System with Heater ...................................................................... 149 6.8.3. Liquid Storage ......................................................................................... 151 6.8.4. Liquid Actuator ....................................................................................... 154 6.8.5 Parts.......................................................................................................... 155 6.9 Nitrogen Pump System ............................................................................. 157 6.9.1 Assessment ........................................................................................ 158 6.10 Sea Boiling System ................................................................................... 159 6.10.1 Assessment ........................................................................................ 160 6.11 Comparison ..............................................................................................