Mars Surface Missions Require Light, Efficient and Robust Passive Bulk Insulation to Survive the Harsh and Dynamic Thermal Environment

PLEASE TYPE THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet

Surname or Family name: PANDEY

First name: SIDDHARTH Other name/s:

Abbreviation for degree as given in the University calendar:

School: SCHOOL OF ENGINEERING AND INFORMATION Faculty: AEROSPACE ENGINEERING TECHNOLOGY

Title: NATURAL CONVECTION IN STEP PROFILE GAS GAPS WITHIN MARS ROVERS

Abstract 350 words maximum: (PLEASE TYPE) Mars surface missions require light, efficient and robust passive bulk insulation to survive the harsh and dynamic thermal environment. Gas gap insulations potentially offer a clear benefit over other existing solutions given their light and robust setup. However, onset and establishment of thermal convection within these enclosures poses a risk to deteriorating performance of the thermal control. Natural thermal convection within the gas gap enclosure is strongly dependent on the gap configuration and boundary conditions and has not been sufficiently investigated for relevant geometries by ongoing Mars rover thermal tests. The problem of convection in gas gaps is even more critical for rover teams dependent only on passive and electrical heating for their gas gap insulation maintenance. A cylindrical single step enclosure problem is selected for the investigation. Thermal convection onset and stabilisation is measured using T-type thermocouples in a Mars environment setting. The variation of Rayleigh number by adjusting bulk fluid temperature, gas pressure, heating arrangement and rover tilt is shown on the overall local and average Nusselt numbers with numerical and experimental tests. Finally, numerical modelling is used to show the impact of three dimensional flow patterns on the localised and average Nusselt numbers. The work leads to generation of heat transfer correlations for Rayleigh number variations, temperature and velocity predictions for the benefit of Mars rover thermal teams and adds to the limited understanding of natural convection within cylindrical enclosures for low Rayleigh number problems.

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‘I hereby grant the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstract International (this is applicable to doctoral theses only). I have either used no substantial portions of copyright material in my thesis or I have obtained permission to use copyright material; where permission has not been granted I have applied/will apply for a partial restriction of the digital copy of my thesis or dissertation.'

AUTHENTICITY STATEMENT

‘I certify that the Library deposit digital copy is a direct equivalent of the final officially approved version of my thesis. No emendation of content has occurred and if there are any minor variations in formatting, they are the result of the conversion to digital format.’ ORIGINALITY STATEMENT

‘I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.’ Natural Convection in Step Proﬁle Gas Gaps within Mars Rovers

Siddharth Pandey

A thesis submitted in fulﬁlment of the requirements for the degree of Doctor of Philosophy

School of Engineering and Information Technology

March 2018 i Statement of Originality

I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project’s design and conception or in style, presentation and linguistic expression is acknowledged.

ii Natural convection in rover gas gaps can lead to thermal losses critical to the power budget, if the combined eﬀects of speciﬁc gap geometry, gap orientation and boundary conditions are not completely accounted for.

iii Acknowledgements

I would like to thank UNSW Canberra for the award of the Research Training Scholarship to support my doctoral research in Canberra, Australia. I would like to express my sincere gratitude to my supervisors, Dr. Sean Tuttle and Dr. John Young, for giving me the opportunity to study at UNSW Canberra and work on this exciting topic of research. Their friendly and understanding nature along with years of combined experience in experimental testing and numerical modelling helped me tremendously throughout the doctoral process. I would like to thank the staff members of the Technical Support Group at the School of Engineering and Information Technology (Daniel Korab, Darryl Budarick, Doug Collier, Marcus Almeida, James Baxter), GridPro Technical consultant Mr. Samuel Ebenezer and the Research Staff members at UNSW Canberra Space (Dr. Philippe Lorrain, Dr. Michael Petkovic) for their invaluable support towards the completion of my experiments. This research project was undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government. Acknowledgements are in order to all my colleagues and friends in Can- berra, Lorin, Courtney, David J, Jonathan C, Amin, Anna, George, Kami, Paris, Claire, Firdaus, Rounak, Alex, Ern, Carol, Ali, Jai, Steve and Amna for their support and feedback. My friends back home in India and elsewhere who supported me through crucial times, Ram, Subho, Adhiraj, Ujjwal, Varun, Lavanya, Ankit, Ashna, Shekhar, Siddharth, Kavya, Rachel and Preeti. I would like to thank Wing Cdr (Retd.) Ram Swaroop Tarnacha for inspiring me to take up the challenge of a doctoral research in Aerospace Engineering. My sincere gratitude and respect for my parents, Commodore (Retd.) Ajay Kumar Pandey and Amita Pandey, my brother Aditya Pandey, without their sacrifices and continuous belief in me, I would never be able to achieve my goals. Finally, to my wife, Aarti Subhedar, without whom I would never finish this work, I love you.

iv Publications

• Pandey, S., Tuttle, S., Young, J. ‘Tackling Convective Heat Losses within Mars Surface Mission Systems.’ 68th International Astronauti- cal Congress, Sep 25-29 2017, Adelaide, Australia.

• Pandey, S., Tuttle, S., Young, J. ‘Designing an Experiment to Improve the Understanding of Thermal Convection to aid Gas Gap Design of Mars Rovers.’ 16th Australian Space Research Conference, Sep 26-28 2016, Melbourne, Australia. 1 Contents

1 Abstract 11

2 Introduction 12 2.1 Why explore Mars? ...... 12 2.2 Mars: A challenging thermal environment ...... 13 2.2.1 Overview ...... 13 2.2.2 Mission-speciﬁc Thermal Challenges ...... 13 2.2.3 Passive Thermal Control Solutions ...... 16 2.2.4 Testing Gas Gap Insulation for Bulk Insulation . . . . 16 2.3 Fundamental complexities in modelling Enclosure-bound Nat- ural Convection ...... 18 2.3.1 Overview ...... 18 2.3.2 Relevant Geometry Selection ...... 18 2.3.3 Relevant Boundary Condition Deﬁnition ...... 19 2.4 Summary of Motivations ...... 20 2.5 Research Questions and Objectives ...... 20 2.5.1 Research Questions ...... 20 2.5.2 Research Objectives ...... 21 2.6 Thesis Outline ...... 21

3 Literature Review 23 3.1 Fundamental Natural Convection ...... 23 3.1.1 Introduction ...... 23 3.1.2 Internal Natural Convection ...... 28 3.1.3 Natural Convection in Low Ra regimes ...... 34 3.1.4 Natural Convection in Non-Conventional Enclosures Geometries ...... 36 3.1.5 Summary of Observations ...... 37 3.2 Thermal Management in Mars Rovers and Landers ...... 38 3.2.1 NASA Jet Propulsion Laboratory Mars Rover Thermal Team ...... 38 3.2.2 Airbus Defence and Space: ExoMars 2020 Rover Ther- mal Design and Analysis ...... 40 3.2.3 JAXA Mars Rover Thermal Design Analysis ...... 42 3.2.4 Summary of Observations ...... 43 3.3 Review Summary ...... 44

2 4 Research Methodology and Problem Setup 46 4.1 Research Path ...... 46 4.1.1 Identiﬁed Gaps in Literature Review ...... 46 4.1.2 Requirements Based on the Gaps ...... 47 4.1.3 Conducted Sub-Investigations ...... 47 4.1.4 Targeted Contributions to the Body of Knowledge . . . 48 4.2 Problem Formulation ...... 48 4.2.1 Axisymmetric Internal Enclosure ...... 48 4.2.2 Boundary Conditions and Assumptions ...... 49 4.3 Numerical Modelling Setup and Validation ...... 50 4.3.1 Geometry Selection ...... 50 4.3.2 Geometry Discretization ...... 51 4.3.3 Numerical Setup Description ...... 54 4.3.4 Numerical Model Validation ...... 59 4.3.5 Computational Resource Utilization ...... 60 4.3.6 Numerical Data Generation ...... 60 4.4 Experimental Setup and Validation ...... 60 4.4.1 Heater and Control Surface Design ...... 61 4.4.2 Measurement Methods ...... 68 4.4.3 Setup: Thermal Vacuum Reconﬁguration ...... 72 4.4.4 Test Operations ...... 75 4.4.5 Data Processing ...... 79

5 Measuring Onset and Formulation of Thermal Convection within Thermal Vacuum Chamber Setup 80 5.1 Research Gaps for Experimental Gas Gap Testing for Mars Rovers ...... 80 5.2 Setup Limitations ...... 80 5.3 Solution Strategy ...... 82 5.4 Eﬀect of Shroud Thermocouple Conﬁguration on Gas Gap Heat Transfer Analysis ...... 82 5.4.1 Test Objectives ...... 82 5.4.2 Setup Description ...... 83 5.4.3 Findings ...... 85 5.4.4 Inferences ...... 87 5.5 Fluid-Induced Temperature Fluctuations ...... 90 5.5.1 Test Objectives ...... 91 5.5.2 Setup Description ...... 91 5.5.3 Findings ...... 92 5.6 Chapter Summary ...... 93

3 6 Heat Transfer around Step Profile for Low-Medium Rayleigh number Flow Regimes 96 6.1 Effect of Cold Plate Temperature ...... 97 6.1.1 Findings ...... 99 6.1.2 Inferences ...... 101 6.2 Effect of Aspect Ratio on Step Profile ...... 119 6.2.1 Findings ...... 119 6.2.2 Inferences ...... 120 6.3 Effect of Gas Pressure ...... 120 6.3.1 Findings ...... 130 6.3.2 Inferences ...... 155 6.4 Effect of Ring Heater on Heat Transfer within Short Gap . . . 155 6.4.1 Findings ...... 155 6.4.2 Inferences ...... 157 6.5 Effect of Rover tilt on established convection in Mars systems 159 6.5.1 Findings ...... 161 6.5.2 Inferences ...... 175 6.6 Chapter Summary ...... 178

7 Three Dimensional Eﬀects of Thermal Convection in Mars systems 191 7.1 Test Objectives ...... 193 7.2 Flow Structures and Localized Heat Transfer Variations . . . . 193 7.2.1 Tall Gap Aspect Ratio ...... 193 7.2.2 Cold Plate Temperature ...... 197 7.2.3 Enclosure Fluid Pressure ...... 204 7.2.4 Enclosure Tilt ...... 204 7.3 Chapter Summary ...... 210

8 Conclusions and Recommendations 215 8.1 Conclusions ...... 215 8.2 Recommendations for Future Work ...... 219

A Working Fluid Thermal Properties 235

B Engineering Drawings of Test Articles 236

4 List of Figures

1 Cylindrical geometry with phase angle φ to define heating direction, as used by Weinbaum [1]...... 30 2 Research Path ...... 46 3 Side Cut Section of Geometry ...... 49 4 Computational Model ...... 50 5 Horizontal Flat Surface Gap Geometry for Mesh Independence and Numerical Model Validation Study ...... 52 6 Richardson’s Extrapolation for Defined Working Parameter at Grid Spacing h=0 for 2D Geometry Cases 1 and 2...... 54 7 Richardson’s Extrapolation for Defined Working Parameter at Grid Spacing h=0 for 2D Geometry Case 3 and 3D Geometry Case 1...... 54 8 Richardson’s Extrapolation for Defined Working Parameter at Grid Spacing h=0 for 3D Geometry Cases 2 and 3...... 55 9 Two-Dimensional Computational Mesh (mirrored along axis of symmetry) for Case H=160mm, h=100mm...... 56 10 Two-Dimensional Computational Mesh (mirrored along axis of symmetry) for Case H=160mm, h=100mm, Zoomed in to show meshing scheme near step...... 57 11 Isometric View of Three-Dimensional Computational Mesh (mirrored along axis of symmetry) for Case H=160mm, h=100mm 58 12 Thermal Conductance versus Horizontal Gap Thickness for Flat Gap with Constant Plate Temperatures ...... 61 13 Screenshot from ANSYS Transient Heating Module (FEA) showing Heater Surface Temperature Predictions For Desired Plate Thickness ...... 65 14 Temperature versus Time Comparison between FEA prediction and lab-based measurement for Vacuum Case for Heater Surface...... 66 15 Heater Plate with Ceramic Resistors ...... 67 16 Heater Plates with Electrical Heater Tape ...... 67 17 Measuring thermal emissivity of plate surface using TIR 100-2. 69 18 Multipurpose Space Science Exploration (MUS2E) facility at Space Research Laboratory, UNSW Canberra...... 73 19 Multipurpose Space Science Exploration (MUS2E) Schematic . 74 20 Thermal Conductance Values from Subcampaign 1 as compared to CFD and Literature ...... 76

5 21 DC Power Supply Unit with RMS Benchtop Multimeter used to monitor voltage fluctuations ...... 77 22 Prevention of Condensation and Frost buildup during Tests . . 78 23 Experimental Setup for SubCampaign 1 and 2 ...... 84 24 Top View of Shroud Showing Thermocouple Junctions 1 to 4 for SubCampaign 1 and 2 ...... 85 25 Comparison of Heat Transfer Analysis for Three Different Shroud Thermocouple Configurations (Type B protrudes 2-3 mm into the gap) ...... 85 26 Variation of Average Shroud Temperature, Standard Devia- tions of Shroud Temperature and Heat Transfer Coefficient Standard Deviation plotted over the Experiment Duration. . . 88 27 Average Shroud Temperature for different Thermocouple Con- figurations around the Shroud...... 89 28 Experimental Setup for SubCampaign 3 ...... 92 29 Temperature Fluctuations for Aspect Ratio 1 and 2 ...... 94 30 Temperature fluctuations with oscillation termination upon switching off ring heater power...... 95 31 Non-dimensionalised Bulk Fluid Temperature Across Enclo- sure Half Width for Different Cold Plate Temperatures.(Note h1,h2 are length units while h is heat transfer coefficient) . . . 98 32 Bulk Fluid Temperature (normalised by heater-cold plate temperature difference) Across Enclosure Half Width for Different Cold Plate Temperatures...... 102 33 Local Nusselt Number Across Enclosure Half-Width for Dif- ferent Cold Plate Temperatures ...... 103 34 Average Nusselt Number v/s Average Rayleigh Number for Short Gap (varied by Cold Plate Temperature) ...... 104 35 Average Nusselt Number v/s Average Rayleigh Number for Tall Gap (varied by Cold Plate Temperature)...... 105 36 Isotherm Contours for Aspect Ratio 1 for Set of Cold Plate Temperatures ...... 107 37 Isotherm Contours for Aspect Ratio 2 for Set of Cold Plate Temperatures...... 109 38 Isotherm Contours for Aspect Ratio 3 for Set of Cold Plate Temperatures...... 111 39 Velocity Contours for Aspect Ratio 1 for Set of Cold Plate Temperatures...... 113 40 Velocity Contours for Aspect Ratio 2 for Set of Cold Plate Temperatures...... 115

6 41 Velocity Contours for Aspect Ratio 3 for Set of Cold Plate Temperatures...... 117 42 Non-dimensionalised Bulk Fluid Temperature Across Enclo- sure Half Width for Different Aspect Ratio Cases...... 122 43 Local Nusselt Number Across Enclosure Half Width for Dif- ferent Aspect Ratio Cases...... 124 44 Average Nusselt Number v/s Average Rayleigh Number for Short Gap (varied by Aspect Ratio) ...... 126 45 Average Nusselt Number v/s Average Rayleigh Number for Tall Gap (varied by Aspect Ratio)...... 128 ◦ 46 Isotherm Contours for Tc= -35 C for a set of Aspect Ratios. . 130 ◦ 47 Velocity Contours for Tc= -35 C for a set of Aspect Ratios. . 132 48 Non-dimensionalised Bulk Fluid Temperature for a set of fluid pressures...... 135 49 Local Nusselt Number Across Enclosure Half Width for a set of fluid pressures...... 137 50 Average Nusselt Number v/s Average Rayleigh Number (varied by fluid pressure) for Short and Tall Gaps...... 138 ◦ 51 Isotherm Contours for set of fluid pressures, Tc= -35 C, AR3. 140 ◦ 52 Isotherm Contours for set of fluid pressures, Tc= -15 C, AR3. 142 ◦ 53 Isotherm Contours for set of fluid pressures, Tc= 5 C, AR3. . 144 ◦ 54 Isotherm Contours for set of fluid pressures, Tc= 25 C, AR3. . 146 ◦ 55 Velocity Contours for set of fluid pressures, Tc= -35 C, AR3. . 148 ◦ 56 Velocity Contours for set of fluid pressures, Tc= -15 C, AR3. . 150 ◦ 57 Velocity Contours for set of fluid pressures, Tc= 5 C, AR3. . . 152 ◦ 58 Velocity Contours for set of fluid pressures, Tc= 25 C, AR3. . 154 59 Non-dimensionalised bulk fluid temperature across Short Gap for Ring Heater ON and OFF setting for a set of Aspect Ratios.159 60 Local Nusselt Number across Short Gap for Ring Heater ON and OFF setting for a set of Aspect Ratios...... 161 61 Average Nusselt Number v/s Ra (varying pressure) for Ring Heater On and OFF...... 162 62 Isotherm Contours for set of fluid pressures, AR1, Ring Heater ◦ Off, Tc=25 C...... 164 63 Isotherm Contours for set of fluid pressures, AR2, Ring Heater ◦ Off, Tc=25 C...... 166 64 Isotherm Contours for set of fluid pressures, AR3, Ring Heater ◦ Off, Tc=25 C...... 168 65 Velocity Contours for set of fluid pressures, AR1, Ring Heater ◦ Off, Tc=25 C...... 170

7 66 Velocity Contours for set of fluid pressures, AR2, Ring Heater ◦ Off, Tc=25 C...... 172 67 Velocity Contours for set of fluid pressures, AR3, Ring Heater ◦ Off, Tc=25 C...... 174 68 Non-dimensionalised Bulk Fluid Temperature Across Enclo- sure Half Width for Enclosure Tilt Study...... 176 69 Local Nusselt Number Across Enclosure Half Width for En- closure Tilt Study...... 177 70 Average Nusselt Number v/s Average Rayleigh Number (varying tilt angle)...... 178 ◦ 71 Isotherm Contour for AR1, Tc=-35 C for a range of Tilt Angles.180 ◦ 72 Isotherm Contour for AR2, Tc=-35 C for a range of Tilt Angles.182 ◦ 73 Isotherm Contour for AR3, Tc=-35 C for a range of Tilt Angles.184 ◦ 74 Isotherm Contour for AR1, Tc=-35 C for a range of Tilt Angles.186 ◦ 75 Isotherm Contour for AR2, Tc=-35 C for a range of Tilt Angles.188 ◦ 76 Isotherm Contour for AR3, Tc=-35 C for a range of Tilt Angles.190 77 Top View of 3D Cylindrical Step Profile showing the Ring Heater and Inner Heater (solid lines) with circumferential path with each (dashed lines) along which the local Nusselt numbers are to be calculated...... 192 78 Isometric View Plan for Isotherm Contour for Set of Tall Gap Aspect Ratios, Enclosure Fluid Pressure of 30 mbar...... 195 79 Isometric View Plan for Velocity Contour for Set of Tall Gap Aspect Ratios, Enclosure Fluid Pressure of 30 mbar...... 197 80 Line Averaged Local Nusselt Number Values Around Ring and Inner Heater Plate for Range of Aspect Ratios ...... 198 81 Isometric View Plan for Isotherm Contour for A Set of Cold Plate Temperatures...... 200 82 Isometric View Plan for Isotherm Contour for A Set of Cold Plate Temperatures...... 202 83 Line Averaged Local Nusselt Number Values Around Ring and Inner Heater Plate for set of cold plate temperatures...... 203 84 Isometric View Plan for Isotherm Contour for A Set of Enclo- sure Fluid Pressures...... 206 85 Isometric View Plan for Velocity Contour for A Set of Enclo- sure Fluid Pressures...... 208 86 Line Averaged Local Nusselt Number Values Around Ring and Inner Heater Plate for set of enclosure fluid pressures...... 209 87 Isometric View Plan for Isotherm Contour for Enclosures with Tilt (along X axis) and No-tilt Angle...... 211

8 88 Isometric View Plan for Velocity Contour for Enclosures with Tilt (along X axis) and No-tilt Angle...... 212 89 Line Averaged Local Nusselt Number Values Around Ring and Inner Heater Plate for tilt and no tilt cases...... 213 90 Summary of Results and Implications for Mars Rover Gas Gap Designers ...... 216 91 Thermal Conductivity of Carbon Dioxide gas at 10 mbar for Mars Temperature Window ...... 235 92 Thermal Conductivity of Nitrogen gas at 10 mbar for Mars Temperature Window ...... 235 93 Drawing for Heater Plate Assembly 1: Recess plate ...... 236 94 Drawing for Heater Plate Assembly 1: Supporting plate . . . . 237 95 Drawing for Heater Plate Assembly 2: Inner heater plate . . . 238 96 Drawing for Heater Plate Assembly 2: Ring heater plate . . . 239 97 Drawing for Inner Shroud ...... 240 98 Drawing for Heater Plate Assembly 2: Inner heater plate . . . 241 99 Drawing for Heater Plate Stands ...... 242 100 Drawing for Thermal Plate Cap ...... 243

9 List of Tables

1 Comparison of Sweep-based and Blocking Topology Grid Schemes for a Sample Internal Natural Convection Problem for a Hor- izontal Gap Enclosure...... 52 2 Richardson’s Extrapolation Value f0 and Asymptotic Range of Convergence for the 2D Grids...... 53 3 Richardson’s Extrapolation Value f0 and Asymptotic Range of Convergence for the 3D Grids...... 54 4 2D Grid Size and Quality Details ...... 55 5 3D Grid Size and Quality Details ...... 55 6 Average Emissivity Values for Working Surfaces ...... 68 7 Heat Transfer Balance for AR1 Cold Plate Temperature -35◦C 118 8 Percentage Difference Between Experimental and CFD Re- sults for Average Nusselt Number for Cold Plate Temperature Case Solutions for Short Gap ...... 118 9 Percentage Difference Between Experimental and CFD Re- sults for Average Nusselt Number for Cold Plate Temperature Case Solutions for Tall Gap ...... 119 10 Percentage Difference Between Experimental and CFD Re- sults for Average Nusselt Number for Four Fluid Pressure Case Solutions for Short Gap ...... 133 11 Percentage Difference Between Experimental and CFD Re- sults for Average Nusselt Number for Four Fluid Pressure Case Solutions for Tall Gap ...... 133 12 Percentage Difference Between Experimental and CFD Re- sults for Average Nusselt Number for Ring Heater Effect Study on Short Gap ...... 157

10 1 Abstract

Mars surface missions require light, efficient and robust passive bulk insulation to survive the harsh and dynamic thermal environment. Gas gap insulations potentially offer a clear benefit over other existing solutions given their light and robust setup. However, onset and establishment of thermal convection within these enclosures poses a risk to deteriorating performance of the thermal control. Natural thermal convection within the gas gap enclosure is strongly dependent on the gap configuration and boundary conditions and has not been sufficiently investigated for relevant geometries by ongoing Mars rover thermal tests.The problem of convection in gas gaps is even more critical for rover teams dependent only on passive and electrical heating for their gas gap insulation maintenance. A cylindrical single step enclosure problem is selected for the investigation. Thermal convection onset and sta- blisation is measured using T-type thermocouples in a Mars environment setting. The variation of Rayleigh number by adjusting bulk fluid temperature, gas pressure, heating arrangement and rover tilt is shown on the overall local and average Nusselt numbers with numerical and experimental tests. Finally, numerical modelling is used to show the impact of three dimensional flow patterns on the localised and average Nusselt numbers. The work leads to generation of heat transfer correlations for Rayleigh number variations, temperature and velocity predictions for the benefit of Mars rover thermal teams and adds to the limited understanding of natural convection within cylindrical enclosures for low Raleigh number problems.

11 2 Introduction

This chapter introduces the high level and problem-speciﬁc research questions that drive this doctoral thesis, to help the reader better understand the motivation behind the work. The exploration of Mars and the associated thermal control challenges faced by Mars rover design teams are presented. Gas gaps are presented as the most promising passive bulk thermal insulation strategy. The unique challenges faced while numerically and experimentally studying relevant gas gap enclosures is brought out. This results in the chosen research motivations, imminent research questions and chosen research objectives to arrive at useful information both for the ﬂuid dynamics and the Mars rover teams. The chapter concludes with an outline of the thesis.

2.1 Why explore Mars?

Mars has fascinated humans over generations and across civilizations. Some of the earliest records were made by the ancient Egyptian astronomers, who in the second millenium BCE recorded its retrograde motion [2]. With the first telescopic observations by Galileo Galilei in 1610, surface maps produced in the late 19th to early 20th century showed an Earth-like planet with cloud cover, polar caps and permanent surface features. Some scientists such as Perciwal Lowell reportedly observed canals on its surface, speculated to be constructed artificially to transport water from the poles to drier parts [3].In fact, it was widely believed for a few years that Mars was inhabitated by intelligent life [4]. However, in the 1920s, with better telescopes and observations, these canals were found to be optical illusions and very small concentrations of water vapour and oxygen on the planet were reported [5]. Nonetheless, it had a tremendous impact on popular culture at the time and scientific interest in the red planet grew in the first half of the 20th century [3].It was realized that Mars, our nearest neighbour, would help humans achieve several goals: help answer whether it ever supported life in the past; offer us a well-preserved Earth-like evolution record; and be a testing ground for human habitation off Earth [6]. Since the 1960s, multiple orbiting and surface spacecraft have explored Mars, sent by the Soviet Union/Russia (Roscosmos), the United States (NASA), the Europeans (ESA) and lately the Indian Space Agency (ISRO). The prime objectives for all these agencies can be appropriately described as: to determine if Mars ever supported life, to understand the present and past climate of Mars, the origin and evolution of Mars geology and finally to prepare for human exploration of the planet [7].

12 2.2 Mars: A challenging thermal environment 2.2.1 Overview Exploration of the Martian surface requires roving or stationary spacecraft subsystems to operate within their allowable flight temperatures (AFT), which are set by the hardware operable ranges and driven by the external local environment, ground surface properties and internal heat dissipation during the various modes of operation. Mars has a dynamic thermal environment for surface exploration. A rarefied atmosphere, diverse surface topology (with varying soil properties and elevations), dynamic cloud system, dust laden winds and temperature cycles due to global seasons lead to a multitude of possible exposed local thermal environments on the surface [8]. Global scale climate models, such as the NASA Ames General Circulation Model [9] are used to maintain statistical databases [10] of Mars environment based on physical models and observations from orbit and surface missions, beginning with Mariner 9 orbiter (1971) and Viking 1 and 2 orbiter and lander missions (1975) and are regularly supported by measurements retrieved from the ongoing orbit and surface missions on Mars [11]. Based on the time of year and the location on Mars, the ground level atmospheric temperatures can vary anywhere between -15◦C and 25◦C in the day and drop to about - 100◦C at night [11]. The Martian surface atmospheric pressure is about 0.7% of Earth’s surface atmospheric pressure, mainly consisting of carbon dioxide (96%), nitrogen (1.9%) and traces of free oxygen, carbon monoxide, water and methane, among other gases [12]. Local wind speeds were recorded by the Viking 1 and 2 mission instruments to reach up to 20 m/sec [8]. Depending on the scientific objectives, the mission could be targeted at any particular site on Mars, which would have its own unique thermal environment, based on its location (latitude, longitude and elevation), time of year (Ls) and atmospheric depth (Tau, a measurement of dust concentration in the surface atmosphere), surface albedo and ground thermal inertia [13]. From now on within this report, the discussion shall be limited to Mars rovers (and by doing this, it shall be assumed we are covering most, if not all of the thermal design scenarios for Mars landers as well).

2.2.2 Mission-speciﬁc Thermal Challenges The thermal challenges of every Mars surface mission increase with its in- tended life on Mars, number of components (and their temperature requirements) and strongly depend on the targeted location for operation [14]. ’Shorter’, ’simpler’ missions are relatively ’light’ on thermal control requirements, e.g. the Sojourner rover ( ∼ 10.5 kg, landed in 1997) planned for

13 7 Martian days (sols) (but lasted for 85 sols) had only one major science instrument- Alpha Particule X-ray Spectrometer (APXS) and some external engineering systems (e.g. motors, cameras, etc.) [15]. The major thermal requirements were for its primary battery pack -40◦C to +55◦C with no more than 5 hours above +40◦C [15]. Eventually, the failure of the electrical battery resulted in colder than normal temperatures causing vital electrical connections to break and eventually loss of communications [16]. Based on the success of the thermal control strategy employed in Sojourner (Warm Electronics Box (WEB) enclosure, discussed in detail in Chapter 2), NASA launched Mars Exploration Rovers (MER) Spirit and Opportunity ( ∼ 175 kg) with longer planned missions (90 sols) and a larger number of electronic components and scientific instruments [17]. NASA’s Phoenix mission ( ∼ 300 kg) landed in the colder, northern plains of Mars in 2008 [18]. The mission was chosen to be a stationary lander to keep the mission costs and power requirements low, especially as solar insolation was lower than the previous equatorial sites and colder ambient temperatures required higher thermal maintenance [19]. A unique subsystem thermal challenge with this mission was its robotic arm, which had a number of actuators that had specific operational windows due to the bearing lubricant [20]. As the mission designs grew complex, the thermal challenges went up. NASA’s Mars Science Labo- ratory (Curiosity, ∼ 899 kg), by far the largest, heaviest and most complex rover, landed at Gale Crater near the Martian equator in 2012 with a planned mission life of 1 Martian year ( 2 Earth years). It has a suite of 10 scientific instruments, robotic arm, mast cam and a large number of electronic components, which all create a unique challenging thermal environment to operate in [21]. Most of the external hardware has AFT limits of -128◦C to +50◦C, except a camera unit (CCMU: ChemCam Mast Unit) and a pyro firing assembly (which are kept warm using survival heaters) have AFT limits of -40◦C to +50◦C [22]. The rover internal hardware mounted on the Rover Avionics Mounting Plate (RAMP) has temperature (AFT) limits of -40◦C to +50◦C and mounted science modules are qualified to operated over a wider temperature range of -50◦C to +70◦C [22]. Thus we see a clear requirement to ensure some of the internal components are to be kept warmer by as much as 50◦C as compared to the ambient on cold Martian nights. Their thermal team also reported an underprediction of local ambient temperatures by as much as 25◦C due to the local heating effects of the rover’s nuclear power source, which required the analytical thermal models to be adjusted [22]. Further, disagreements in the modeled and measured temperature variations due to dust deposition, unexpected Martian night winds and changes in soil properties in various locations all have resulted in continuous adjustments to the thermal models [22]. Despite all these complexities, MSL has had sufficient

14 waste heat from its nuclear power source to compensate for any unexpected thermal losses and maintaining the desired stable internal temperatures for its components. For long duration missions, small Radioisotope Power systems (RPS) are used (also used on the Viking missions, which were planned to operate for 90 sols and lasted 2-3 Martian years [19]) and have been shown to successfully achieve their thermal control objectives and prolong mission durations [22, 23]. However, RPS use Plutonium-238 as fuel, which being in very short supply, signiﬁcantly drives up the mission cost and development timeline (oweing to the government clearances sought and hazard mitigation tests required) [24]. Therefore, for MER size and duration missions, it has been found to be optimal to operate with solar electric propulsion [25]. The European ExoMars Rover mission (slated to launch in 2020) [26] will look for signs of extinct life, having an expected mission duration of 1 Martian year [27]. Like the MER missions, the ExoMars Rover mission will be solar- electric powered, [19] but some of its thermal control objectives are far more complex. The rover chassis consists of the Analytical Laboratory Drawer (ALD) and the Service Module (SVM) which have electronic components and science instruments that need to be simultaneously maintained at different and stringent temperature ranges [28]. The team has reported the biggest challenge will be maintaining the collected sample temperature below -5◦C (for the astrobiology experiments) inside an enclosure where nearby instruments and electronics are dissipating heat [28]. The rover utilizes ambient Martian atmosphere (primarily carbon dioxide) for bulk insulation by maintaining a gap between the rover chassis and the compartments [28]. A cluster of radioisotope heater units are used to individually heat sensitive components, as has been done in previous missions [19,29]. In terms of thermal control strategy, the ExoMars rover would be by far the most ambitious mission till date. This is because of several reasons: the gas gap concept has been used previously but for single units with much smaller dimensions [30] and its performance, along with those of thermal electric coolers and thermal capacitors is still not completely well understood in Mars conditions of temperature, pressure and gravity (more on this in the next subsubsection) [28]. Thus, as future missions get more complex and are designed to survive for longer durations on the Mars surface without the support of nuclear waste heat for thermal management, the mass, volume and power allocations for thermal control systems all need to be further optimized. It is deemed crucial to understand the performance of available passive thermal control solutions in order to ensure mission objectives are achieved.

15 2.2.3 Passive Thermal Control Solutions

The earliest surface missions to Mars (Viking landers) utilized Dacron enclosed fibreglass blankets and multiple layers of double metallized radiation shileds separated by Dacron netting around the thermally isolated compartments [23]. In the early 90s, thermal engineers at NASA JPL tested foam insulations, being inexpensive, machinable, and having low thermal conductivity and low density-ideal for thermal insulation in atmospheric environments [14]. These solid passive bulk insulants are required to have strong cohesize mechanical integrity to withstand depressurization rates to vacuum during the launch phase of a mission [14]. Some samples that have been tested are Eccofoam, an open cell polyuerthane foam insulation and Roha- cell, a closed cell polymethacryimide and Silica aerogel. Silica aerogel has the lowest thermal conductivity of these (∼ 0.015 W/m-k), it has a ultra- low density (∼ 16 kg/m3) and therefore also has low mechanical strength. Hence, it requires a lightweight supporting structure to hold it in place to withstand launch and landing loads for a mission [14]. This led to the development of two thermal structures for the Mars Pathfinder mission, the Integrated Structural Assembly (ISA) (using Eccofoam bounded in graphite- cyanate facesheets within Nomex core) for the lander and aerogel bounded by glass epoxy facesheets for the Warm Electronic Box (WEB) for the So- journer rover [31]. The next iteration of passive thermal insulation was the utilization of in-situ Martian atmosphere, i.e. gas gap insulation by standing off the radiation shield enclosure from the hardware using Mylar spacers. This proved to be lighter, less expensive and faster to fabricate and install than the previous scheme of solid bulk insulants [30]. The gas gap also does not require structural support, only a containment barrier around the components requiring thermal isolation [30]. It was however recognized that the gas, even at 6-10 mbar Mars ambient pressure, could lead to heat loss due to gas movement between the hot and cold surfaces, i.e. thermal convection, if the gap was large enough to instigate it.

2.2.4 Testing Gas Gap Insulation for Bulk Insulation

Using theory of free convection for enclosures, (explained in Chapter 2), for a temperature diﬀerence of 43◦C, (electronic box at -50◦C and night time ambient at -93◦C), the ’safe’ gap width below which the convective heat transfer component was near zero was determined to be 6 cm [30]. The total amount of heat loss through the gas gap insulation (without any convection related losses) was determined to be about 3.2 W as compared to 4.5 W for a similar ﬁberglass batt insulation [30]. The MSL team has calculated

16 that natural convection can drive these values up by about 40-50% based on horizontal gap empirical relations, if the gap size exceeds the critical amount. The overall total heat loss (conduction based) via the gas gap for MSL was attributed to about 25% of the overall heat loss, which was deemed a significant factor for thermal control, and would be even more so for the solar-electric thermal designs [32]. Subsequent gas gap insulation design studies done at NASA JPL utilized computational fluid dynamics software, but continued to use critical gap thickness criteria based on uniform gap spacings, either horizontal or vertical with respect to the gravity vector [32]. Based on the test results, different gas gap thicknesses were allocated for the top, bottom and side portions of MSL’s RAMP. However, this calculation was done assuming uniform gas gap spacing around the electronic box with radiation emissivity estimation based on infinite parallel plate theory. The ExoMars Rover mission team has conducted several experimental tests under Mars conditions using nitrogen and carbon dioxide gases [33–36] and have arrived at similar unispaced dimensional critical gap lengths, i.e. 6-11 cm. The ExoMars team have avoided time intensive CFD modelling and have used node-based thermal models to estimate thermal convection contribution. Work published as recently as in 2016 by one of these teams reports high modelling error resulting from these single and multiple node models for parallel plane and free space convection assumptions [36]. This indicates there is a clear requirement to adequately model the heat transfer based on realistic simulation of the geometry, the boundary and operating conditions for the cases. The Japanese (Japan Exploration Agency JAXA) 2020 Mars rover design also accounts for a 6 cm thick gap based on similar estimates as those used by the NASA and ExoMars teams [37]. The estimation of worst case assumptions can easily lead to usage of more than required allocation of insulation material (which adds to overall mass and volume usage), and an over-estimation of thermal convection loss which affects the efficiency of the on-board thermal power compensation system in place. The tests studied the horizontal or vertical gap thicknesses in isolation, without taking into account any adjacent gap volumes, effects of corner or edges that might have an impact on the heat transfer set up. In addition, the temperature difference between the hot and cold surfaces was assumed to have a constant effect for the entire range of possible average bulk fluid temperatures within the gaps. Furthermore, the effect of tilting of the rover, (i.e. changing the gravity vector relative to the effective geometry and its effect on the overall heat transfer performance of gas gap) remains ot be seen. Such scenarios, though not overly critical for a rover with sufficient nuclear waste heat to maintain desired temperatures, are much more important for smaller, conservative rovers (such as the 2020 ExoMars and the 2020 Japanese rover) that need

17 to have a complete understanding of the gas gap performance under such conditions.

2.3 Fundamental complexities in modelling Enclosure- bound Natural Convection

2.3.1 Overview Buoyancy-induced flows involve a unique coupling between fluid motion and transport processes that make them a complex, though a widely relevant topic of study since the early 1940s [38]. The problems are fundamentally classified as either external (free) convection or the more complex internal (natural) convection [39]. The reason the internal cases are deemed more complex is that for external convection, classical boundary layer theories result in simplifications that help predict the main flow parameters which are independent of the boundary layer flow [38]. But for confined natural convection, a core region is surrounded by boundary layers that form near the wall and cannot be determined directly from the boundary conditions and geometry due to this interdependence between the core and boundary layer flows [40]. Further, in many cases, multiple core regions in the form of ’cells’ and ’layers’ can form, making it a intrinsically complex problem to solve [38]. This is an important point to note here, as it is this extreme sensitivity of the core flow formation on the particular geometry and boundary conditions that prevent usage or direct comparison of results from previously conducted ’seemingly similar’ problems [38]. It has been well reported by Simon Os- trach’s group during 1972-1985 [41–43] that several studies in the past have wrongly assumed the core flow similarities for similar geometry and boundary condition cases, causing incorrect reporting of velocity and temperature distributions. Hence there is a need to deal with such problems not just numerically but with closely guided control experiments [38].

2.3.2 Relevant Geometry Selection Based on applications of interest, multiple geometries, ranging from rectangular, square, cylindrical and annuli shaped have been studied to understand the development of convection flow within such enclosures [38]. Cooling of electronic equipement is a common motivation for enclosure based convection studies, that deal with ’non-basic’ geometry configurations that involve steps and walls subjected to abrupt temperature nonuniformities, as they occur in such applications [44]. As it has been established that the core flow that develops is extremely sensitive to the geometric condition and boundary

18 conditions, most numerical studies have focused on starting with solving sim- plified two-dimensional sections with a minimal number of heated surfaces, and then building complexity of the problem to achieve desired heat transfer and flow predictions [38]. To understand the effect of profiled heated surface geometry, the first step commonly is to look at a single step profile, characterize the parameter space and understand the sensitivy of each variable term to the overall heat transfer (described by Local and Average Nusselt Numbers, explained in next chapter) for a range of convection fluid regimes (described by Average Rayleigh number, also explained in next chapter) [44]. Further, it is important to ensure no other ’corners’ or ’edge’ effects influence the boundary layer establishment when trying to derive flow and heat patterns for a particular single step profile. This can be difficult in a rectangular enclosure but can be achieved with a cylindrical step profile geometry.

2.3.3 Relevant Boundary Condition Definition Natural convection in enclosures is influenced not just by the temperature gradients but also by the bulk fluid temperature within the core flow [45]. As Martian surface ambient temperature cycles throughout a sol, the bulk fluid temperature of Martian atmosphere within the gas gap would change, thereby leading to varying conditions, even if the temperature gradient was maintained at a constant value using electrical or nuclear heating. Previous studies have shown a general trend of an increasing rate of heat transfer for higher bulk fluid temperatures [46–49]. Mars presents an environment with almost a third of the Earth’s gravity. Natural convection in reduced gravity adds to the existing complexity in accurately modelling the flow and heat transfer parameters [38,50]. Convection for crystal growth in near-zero gravity environments was studied on board NASA’s space shuttle, and it was evident that the reduced (but not zero) gravitational effects led to complex fluid motions that were not seen in Earth’s gravity environment [50]. The onset of natural convection in enclosures is strongly dependent on the boundary conditions and confining boundaries requiring detailed information on the magnitude and direction of accelerations, geometric configurations, imposed boundary conditions and material properties [41, 50]. Most available literature lacks complete information to give useful insights of reduced gravity effects on natural convection. A part of this is due to insufficient experiments conducted in reduced gravity environments [41, 50]. For the crystal growthEarth based experiments, a range of flow patterns were reported upon scaling the Rayleigh numbers to achieve desired simulations for low gravity, in some cases leading to heat transfer measurements that diverged from actual measured values in the spacecraft environment [50]. This brings forward the

19 difficulties in simulating reduced gravity natural convection experiments in Earth gravity. Finally, the importance of knowing the exact gravitational acceleration direction with reference to the enclosure is required is reiterated for accurate assessment of heat transfer. Previous studies [45,50,51] have shown a drop in heat transfer due to convection with the increase in tilt of a horizontal gap enclosure, a pertinent scenario having thermal design implications for a rover traversing uneven surfaces. The Mars rover thermal engineering teams have been simulating Mars environment and relevant boundary conditions by adjusting and scaling parameters (for e.g. for Mars gravitational acceleration), however, the exact effect of varying the individual parameters (surface temperature differences, bulk fluid temperature, gas pressure, tilt) for arriving at relevant Mars enclosure heat transfer simulations remains to be studied.

2.4 Summary of Motivations Thermal losses via gas gaps can be as high as 25% of total heat loss for Mars rovers [32] and a clear requirement is identified to further understand the performance criteria for relevant geometry and boundary conditions. Further, several leading authors in the field of natural convection in enclosures have reported on the extreme sensitivity of the established convective heat transfer on the particular enclosure geometry and boundary conditions. This indicates a unique problem that calls for specific numerical-experimental studies of a set of cases. Investigating the thermal performance of gas gaps for step geometries under a range of boundary and operating conditions is an important open problem to be addressed for the benefit of future Mars rover designs, particularly the solar-electric powered configurations.

2.5 Research Questions and Objectives 2.5.1 Research Questions Identifying the challenges of experimentally measuring thermal convection in reduced pressure environments from surface temperature measurements, achieving Mars relevant heat transfer conditions by individually varying bulk fluid temperature, gas pressure, configuration tilt for a single step geometry and numerically studying the three dimensional fluid patterns are deemed as the three main lines of investigation for this doctoral investigation. To this end, the following research questions are formulated. • With what accuracy can convective heat transfer coefficients be measured using thermocouples within a Mars chamber setup for step gap

20 geometries with constant wall heat ﬂux problem under Mars relevant Rayleigh numbers?

• How does an adjacent heated surface (at a lower hight) impact the heat transfer across a horizontal gap?

• Does changing the Rayleigh number via adjusting bulk ﬂuid temperature, gas pressure, tilt or heated surface have same eﬀect on Nu as adjusting aspect ratio?

• What are the three dimensional eﬀects on the global and local Nusselt number across a step proﬁle geometry?

2.5.2 Research Objectives In addressing the research questions, the following research objectives will be targeted:

• Develop understanding of fundamental natural convection-in relevant geometry and boundary conditions

• Study past and current thermal analysis studies employed by Mars rover teams: identify research gaps and cases that can be used for model validation.

• Identify gap volume and control surface geometry, which can be tested experimentally and numerically.

• Measurement of thermal convection onset and stability within liimited instrumentation with thermal vacuum chamber

• Test and validate heat transfer around step proﬁle for range of low Ra, varied by temp, pressure, AR and ring heater toggle.

• Conduct detailed numerical modelling for temperature and ﬂow feature within gaps, tilt case

• 3D eﬀects of gap volume: implications for future work.

2.6 Thesis Outline The chapters in this report are laid out as following. Chapter 3 covers the literature review of fundamental natural convection and Mars rover internal thermal analysis. Chapter 4 covers the development of problem, research

21 methodology and assumptions for the cases. Novel experimental technique to capture onset and set in of thermal convection is presented in Chapter 5. Variation of Ra via toggling temperature, gas pressure, AR, ring heater toggle and rover tilt and effect on Nu is presented in Chapter 6. The 3D effects of convection around step profile is presented in Chapter 7. Finally, the findings, summaries and recommendations are presented in Chapter 8.

22 3 Literature Review

This chapter covers a brief history of natural convection investigations with emphasis on the several complexities faced and assumptions made in numerical and experimental studies. Geometry nomenclature and relevant non- dimensional parameters used to describe fluid states are defined. With relevance to the problem of natural convection inside Mars rover configurations, an overview of previous work for relevant boundary conditions (low Rayleigh number, varied by temperature, pressure and gravity) and geometry configurations (step geometries) is presented. Finally, the specific shortcomings and most critical problems to be addressed are identified and summarised. These helped in formulating the problem setup and research path of this thesis and are reported in the following chapter.

3.1 Fundamental Natural Convection

3.1.1 Introduction

Most of the early fluid dynamics research was led by aeronautical development, a field that was initially associated with internal stress-related fluid pressure or viscous forces [39]. However, fluids with body forces, (i.e. forces independent of inter-fluid stresses and arising from distant vector forces such as gravity and magnetic fields) received less attention due to their complex coupling with thermodynamics and having little to do with early aeronautics research [39]. From around the late 1930s, with development of gas turbine engines, nuclear power and high speed flight, thermal fluids started receiving more attention and were identified as an important practical area requiring further analysis [52]. Thermal natural convection, understood to be primarily affected by gravitational forces, volumetric expansion and density or concentration differences in fluids, continues to date to be the most widely studied body force problem, finding applications in aeronautics, astrophysics, geophysics, nuclear power, electronics and chemical engineering [39]. To describe the velocity and temperature distributions of fluids with body forces, the basic equations for conservation of mass, momentum, energy and equation of state for a compressible, viscous, heat-conducting fluid, derived in Section B of reference [39] are presented in Cartesian tensor notation as:

∂ρ ∂(ρU ) + j = 0 (1) ∂t ∂Xj

23 ∂[µ( ∂Ui + ∂Uj )] ∂(µ ∂Uj ) ∂Ui ∂Ui ∂Xj ∂Xi 2 ∂Xj ∂P ρ + Uj = ρfi + − − (2) ∂t ∂Xj |{z} ∂Xj 3 ∂Xi ∂Xi | {z } body | {z } |{z} inertia viscous pressure ∂(k ∂t ) ∂T ∂T ∂P ∂Xj ∂Ui ∂Ui ∂Uj 2 ∂Uj 2 ρcp + Uj = Uj + + µ[( )( + ) − ( ) ] ∂t ∂Xj ∂Xj ∂Xj ∂Xj ∂Xj ∂Xi 3 ∂Xj | {z } | {z } | {z } | {z } thermalconvection compression thermalconduction viscousdissipation (3) ρ = ρ(P,T ) (4)

Where Ui refers to the velocity components in Xi direction, ρ is density, th t denotes time, fi is the i component of the body force per unit mass, µ is the absolute viscosity coefficient, P is the pressure, cp is the specific heat at constant pressure, T is temperature and k is the coefficient of thermal conductivity. Non-dimensionalising the involved parameters helps understand their individual significance on the overall dynamics of the system, thus a simplification can be brought in by assuming the body forces are mainly due to temperature effects, flow is steady and the viscosity and thermal conductivity coefficients are constant. The state equation shall be assumed to be independent of pressure to obtain:

ρ = ρr[1 − β(T − Tr)] (5) ∂T where β = ρ[ ∂ρ ]P is the volumetric expansion coefficient of the fluid and the subscript r indicates the unheated no-flow state. Introducing the above assumptions and Eq. 5 in Eq. 2 and Eq. 3 and non dimensionalising the following quantities:

U θ X P u = i , v = , x = i , p = (6) i i 2 U¯ θw d ρU¯ The steady-state momentum and energy equations can then be written as:

∂u ∂( ∂ui + j ) ∂ ∂uj ∂ui Gr 1 ∂xj ∂xi 2 ∂xi ∂p uj = 2 v + [ − ] − (7) ∂xj Re Re ∂xj 3 ∂xi ∂xi

2 ∂v 1 ∂ v ∂p E ∂ui 2 ∂uj 2 uj = + Euj + [ − ( ) ] (8) ∂xj P rRe ∂xj∂xj ∂xj Re ∂xj 3 ∂xj Where the dimensionless quantities are denoted by lower case and dimensional by upper case; θ = T-Tr is a temperature diﬀerence, d is the chrac- teristic length dimension with w as subscript denoting quantity measured at

24 ¯ wall. U is taken to be the freestream velocity (U∞ in combined forced and natural convection ﬂows. The solution to the body force induced convection problems depends on the following four parameters, Reynolds number (Re), Grashof Number (Gr), Prandtl Number (Pr) and Eckhert Number (E) deﬁned as:

3 2 Ud βfiθwd cpµ U Re = ; Gr = 2 ; P r = ; E = (9) ν ν k cpθw However, for natural convection cases involving density-induced fluid movement, where the flow is generated solely by the body force, the freestream velocity is zero. The parameters governed by inertial forces, i.e. Reynolds and Eckhert number, are not considered for such cases. A new characteristic velocity is defined as:

¯ p U = βfiθwd (10) The non-dimensional steady-state momentum and energy equations for natural convection are derived to:

∂( ∂ui + ∂uj ) ∂ ∂ui ∂ui 1 ∂xj ∂xi 2 ∂xj ∂p uj = v + √ [ − ] − (11) ∂xj Gr ∂xj 3 ∂xi ∂xi

2 ∂v 1 ∂ v ∂p K ∂ui 2 ∂uj 2 uj = √ + Kuj + √ [ − ( ) ] (12) ∂xj P r Gr ∂xj∂xj ∂xj Gr ∂xj 3 ∂xj

Here a new dimensionless term K is defined as βfid , which determines the cp work done by frictional heating and due to compression. This term is an important term for natural convection studies in rotational machinery, (e.g. gas turbine engine blade cooling) where these two types of work can significantly influence the natural convection flow and heat transfer [39]. However, it shall be seen that this term is close to zero for the general natural convection case considered for this thesis. Hence, for flows solely generated by density differences caused by changes in temperatures in the flow, there is a strong coupling between density and velocity components. Density differences due to temperature differences within an otherwise static fluid results in buoyancy forces due to gravity, which cause the fluid particles to shift, thereby changing the initial density and temperature distribution. This tells us that the velocity and density distributions cannot be treated separately. In addition, the nonlinearity of the basic governing equations make it a complex problem to solve [39].

25 Given the complexities arising from the high order of the governing partial differential equations and non linearity, two boundary layer theory approaches have conventionally been used to attain solutions for specific problems. The first approach involves transforming the partial differential equations into ordinary equations, and the second requires satisfying integrated equations away from surfaces after they along with boundary conditions have been satisfied at the surface. These techniques have been successfully used to solve several free convection cases for vertical plate, inclined plate, horizontal and vertical cylinders [39]. However, the problem of thermal instability is idenitified for a simple flat horizontal plate where the density gradient due to temperature is parallel to the body force direction (in most cases, the gravity vector). To understand this case, let us consider pouring a higher density fluid into a container with a lower density fluid. Due to gravity, the fluids will move and stabilize such that the lower density fluid will form a stable layer on top of the denser fluid medium. The final state will be that of stable equilibrium. Continuing the analogy, if we consider a single fluid with uniform density within a container with the bottom horizontal surface heated, the fluid near this surface shall be stable until a critical point after which the density will drop low enough to cause the heated fluid to move upwards. The conditions in which this sets in has been shown to be dependent on the container’s specific configuration and the fluid’s physical properties [39]. The heat input will result in a continuous motion where the colder fluid above will continue to descend, get heated and rise. Hence, the final state here would be a state of steady motion, but not equilibrium.

Bénardwas the first researcher to perform controlled laboratory experiments on thermally unstable liquid layers in 1900 [53]. Assuming uniform temperatures away from walls and negligible density variation, he worked with very thin (few millimetres) liquid layers on a heated metallic plate, with the upper liqid surface exposed to cool ambient air. The resulting fluid motion caused a temporary semi-regular structure of cells that eventually phased into stable hexagonal cells with vertical boundaries. The liquid was seen to rise within the cell core, spread out towards the top and descend down along the vertical side boundaries [53]. These cells were referred to as Bénardcells. The theoretical investigation of the problem was first done by Lord Rayleigh [54] and validated by several authors in the subsequent years [55, 56]. The analysis mainly reported on the (i) geometry of the convection cell and (ii) determining the criteria for the convection onset within a finite depth fluid layer [39]. The stability of the flow was found to be related to the product of the Prandtl and Grashof numbers, i.e. the Rayleigh number (Ra). The number was found to be independent of the cell shape, given

26 βgh34T by κν with h, 4T, κ being the fluid layer depth, temperature difference between bounding surface and thermal diffusivity, among previously defined parameters. The critical Ra was found to be around 1700, at which the fluid just started to move [39]. Pellew and Southwell [57] did rigorous experiments to relate the Rayleigh number to the cell wavelength (defined as the spatial distance between two adjacent cell edges) and calculating the wavelength for specific cell shapes. They showed that for an infinitely long horizontal gap, any symmetrical pattern could be formed, but eventually the cell shape for the smallest Rayleigh number materializes. They were also the first to show that in order to maintain a constant fluid motion in an enclosure with two insulated boundaries, the other two surfaces were to act as a constant heat source and a heat sink, to ensure a continuous upward-downward cyclic motion. Finally, it was shown that cells formed between layers of indefinite horizontal fluid layers (within enclosures with vertical side walls set apart by much larger distances than the distance between the layers) and those within flows bounded by rigid vertical boundaries were not identical. An interdependence between inter-wall spacing and shape of the wall boundaries on the horizontal surface temperature difference was brought out [58] that needed to be further understood. Up until the point where the fluid was more likely to move due to instability caused by heat addition, the linear theory yielded a definitive stability criterion and defined a qualitative understanding of the fluid motion. Beyond the critical Rayleigh number, the cell wavelengths amplified in a non-linear nature that would require a non-linear theory to determine the heat transfer and fluid flow. A non-linear solution based on boundary layer theory, involving constant vorticity and temperature within cell interior and viscosity and heat conduction effects near the wall was reported [59] and verified with experiments conducted by Schmidt and Saunders [60]. Another non-linear study was conducted by Morton [61] based on quasi-steady non-linear temperature distribution showed that departures from linear temperature distributions resulted in a higher critical Rayleigh number. Goldstein [62] conducted unsteady heating of fluid within parallel rigid planes, to simulate a deceleration (e.g. cooling system within an atmospheric reentry vehicle) and showed a much higher critical Rayleigh number than for static cases, due to constant disruption of convective heat transfer due to operating conditions. Beyond studies done on convection onset and cell development, it was shown by Schmidt and Milverton [63] that once the motion started, the heat transfer rate suddenly increased. They also experi- mented with increasing the Rayleigh number beyond the critical value, which lead to negligible temperature gradients at the midway plane. Transition to turbulence was reported at a sudden rate for denser fluids (water, about Ra = 45, 000) and much more gradual for gases (air, about Ra = 5, 000).

27 Chandrashekhar [64] reported coriolis force and magnetic fields having a stabilizing effect on thermal instabilities by delaying cellular motion in as- trophysical problems (such as energy convection within central and surface layers of stars). During these initial times, cases where the fluid was heated from below were described as a ’thermal instability’, and were commonly encountered in the fields of aeronautics, propulsion, atomic power, electronics and chemical engineering [65]. Thermal instabilities were also found and described in astrophysics and meteorological areas of investigation [66, 67] with a comprehensive mathematical review of the problem done by Lin [68]. Similarities in thermal instabilities between different kinds of geomtries were first pointed out by Low [69] who compared flows between parallel horizontal surfaces (heated from the bottom) with flow between coaxial cylinders rotating at different speeds [70]. The boundary conditions were identical but the system of differential equations were quite different. However, a qualitative analogy was brought out and discussed in a few supporting studies [55, 56]. Boundary layer profiles for cases with horizontal fluid flow and flow over slightly undulated walls were shown to be similar [71].

3.1.2 Internal Natural Convection Early work on internal natural convection flows was mainly experimental or semi-empirical in nature. Elenbaas studied natural convection heat transfer between two parallel plates heated to the same temperature, giving semi- empirical Nusselt numbers for the medium of air for different vertical tube cross sections [72–74]. Using dimensional analysis, functional equations were derived and correlated with experimental or semi-accurate numerical studies to give semi-empirical formulae for Nusselt numbers. However, no information was given on the velocity and temperature distributions and in several cases there was significant disagreement between the formulae and experimental data [39]. Interest in internal natural convection heightened around 1945 when heat extraction from fluids with internal heat sources, (e.g. atomic piles within nuclear powerplants) were being developed. Schmidt studied the natural convection heat transfer within turbine rotor blade spacing and showed its application to heat extraction in nuclear facilities [75]. Adding to the already existing complexity of interdependence between hydrodynamics and thermodynamics for natural convection problems, internal flows involve boundary surface interaction with the core flow rendering them difficult to analyze [39]. Thus conventionally, a limited range of simple configurations was investigated that could be applied to a wide range of problems in science and industry. Some of the earlier ones studied were vertical channels with fully and nearly fully developed flows, (e.g. chimneys) [76], closed-end

28 tubes [77], rotating cylinders (relevant to turbine blade cooling and cooling of high-speed atmospheric re-entering vehicles) [78]. Flows between rotating cylinders, though enclosed, have a predominant rotational flow where the solution parameters (ReΩ) were readily obtained. However, for generic enclosed internal natural convection flows with high Grashof numbers, these are driven by a coupling between the boundary layer flow and the interior (or core) flow, rendering them difficult to solve [39]. This cyclical dependence of the core on the boundary layer and vice-versa for enclosed flows is further complicated by the formation of multiple cores and subregions [38, 41, 79]. Ostrach [38] reports most literature seems to overlook this critical aspect of enclosed natural convection which causes final temperature and velocity distributions to be extremely sensitive to the enclosure configuration and boundary conditions and incomparable with other seemingly ’similar’ problems. The coupling leads to a spatial effect of the driving force that needs to be properly accounted for before properly studying the results, calling for experimental validation of numerical studies. Completely confined configurations with internal natural convection were first studied by Lewis [80] for gas filled spaces within commercial insulation foam material. Though due to the small cell spaces, Lewis only considered cases with Rayleigh number less than 1, leading to flows without boundary layer phenomena. Similar works on low Rayleigh number flows were sur- veyed and compiled by Ostroumov [81] and Drakhlin (for spherical cavity configurations) [82] in 1952. Batchelor [66] studied the rectangular enclosures with height to width (Aspect Ratio) ratios of 5 to 200 for rectangular enclosures and determined that a range of different flow regimes could occur depending on the aspect ratios and the Rayleigh number Ra. For low Rayleigh number cases, convection was found to be insignificant as compared to conduction [83]. For rectangular enclosures with very large aspect ratios, a linear temperature distribution in the middle was reported with convection limited near the top and bottom walls, which later spread throughout the volume as the Rayleigh number was increased enough to cause boundary layer flows [52]. Horizontal cylinder configurations were popular among analytical researchers of the problem, since they had only two parameters associated with the configuration (radii and length), there were no corner effects (and no resulting mixed boundary conditions), and varying just the heating phase angle covered heating from side and bottom directions [84]. Ostrach was the first to deal with steady laminar flows within horizontal cylinders [52, 67] working with the assumption that the core was isothermal and underwent solid body rotation (this helped satisfy most of the boundary layer equations and was was used for a few years from then). In 1960, Martini and Churchill [85] repeated Ostrach’s tests but observed a rotating

29 fluid band near the walls but a stagnant central core, with a bottom heavy core resisting rotation. Further investigations by Ostrach and others [1,86,87] showed both core configurations could be theoretically explained. Weinbaum used a phase angle φ , (see Figure 1) to define the heating location, (φ = 0 π for heating from side and φ = 2 for heating from below) with a higher Ra achieved by using a high Pr and a Gr value of 1. This was a useful methodology as it used a linearization theory that allowed solving the equations without involving non-linear terms and boundary layer solutions while still mathematically satisfying all conditions to arrive at physically relevant solutions [83]. Further experimental investigation [41, 79, 86, 88, 89] showed that

Figure 1: Cylindrical geometry with phase angle φ to define heating direction, as used by Weinbaum [1]. the temperature and velocity distributions in the core were heavily dependent on the configuration and the imposed boundary conditions. Further broad conclusions could be drawn that flows heated from below [60] within horizontal cylinders resulted in closed Velocitys within a rotating isothermal core

30 whereas those heated from the side [85,89–91] showed a thermally stratified core with isotherms and Velocitys coinciding. Analytical solutions based on numerical modelling [85, 92] gave good agreements with experimental data, mainly because they were closely guided by experiments. The numerical solutions have the advantage of requiring less information at the start of equation solving, mainly a one point boundary value problem, instead of a complete description of core configuration [38]. However, limitations in computational technology and numerical techniques of the 1960s constrained the amount of numerical modelling that could be carried out to solve the coupled higher order equations [38]. Batchelor [93] studied high aspect rectangular and square enclosures, assuming an isothermal core with constant vorticity while Pillow [59] solved problems in a similar configuration heated from below with unstable convection. This goes to show that the importance of adequate core and thermal boundary condition descriptions was not realized during the initial days of solving natural convection within high aspect ratio rectangular and square enclosures [38]. Batchelor conducted more work [94, 95] with non-stagnant cores and interior flow boundaries outside the viscous boundary region and it was until a few years later when stagnant core assumptions were further studied as a valid alternate possibility [42, 86, 87]. Batchelor’s analytical predictions [66] were validated by experiments conducted by Eck- ert [90] for air layers within vertical isothermal walls to show a domination of thermal conduction for below critical Rayleigh numbers and above critical aspect ratios, with convection being limited nearer to walls [38]. The core was shown to be non-isothermal and uniform only in horizontal direction. Since then, most publications on the topic seem to reflect numerical solution results that are closely guided by experimental work for medium to high Rayleigh numbers (up to Ra = 3e5) [38]. Temperature distributions within the core, formation of secondary cells and convection patterns near the walls were some of the points of observation that varied between the findings of the different groups, most likely due to the different setup and measurement techniques. Gill was able to formulate the first theoretical model for laminar flow experiments in rectangular high aspect enclosures that gave really good agreements [84, 91, 96]. A compilation of the numerical solutions for the vertical gap problem was presented by Vahl Davis, Newell-Schmidt and Ostrach [41, 97–99]. Incorrect physial assumptions for the core and thermal boundary conditions were shown to be the main reasons for moderate to large scale disagreements between analytical and experimental work. Lin- ear theories that operated on the assumptions of a decoupling between the core and the boundary could no longer be used to solve laminar flows with viscous boundary layers interacting with the internal flows. The need for experimental guidance and verification of analytical and numerical solutions

31 was reiterated constantly for all cases [38]. Some of the early investigations of special boundary condition cases brought out further complexities in the flow patterns. Chu et al. [100] studied the impact of varying the size and location of a heating element within the flow, along with those of enclosure aspect ratio and thermal boundary conditions. Using an (alternating-direction-implicit) model that allowed nonconservative finite difference solutions of the coupled equations, good agreements were seen between experiments and numerical solutions. A complex interdependence of the rate of circulation on the rate of heat transfer was reported [100]. Although conduction dominated for the flows with Rayleigh number less than 1000, there was always a small amount of fluid circulation for all of Rayleigh number above zero. Vertical boundary layer theory was shown to not be useful in predicting the results. Cooling of electronic enclosures using windows, solar collection systems and room fires were some motivations for the first set of studies of partial enclosures, i.e. small openings with an interaction of an external fluid stream with internal natural convection [101]. A detailed investigation of flows through circular apertures within the top and bottom of a vertical cylindrical enclosure was carried out by Sparrow and Samie [102]. Complex interactions between flow recirculations and wall boundary layers were reported, and the impact on the overall heat transfer from the cylinder walls was highlighted as an important area requiring further consideration [102]. Another relevant geometry configuration studied is the annulus between concentric, off center and eccentric cylinders, one placed within the other. Several combinations of cylinder height ratios, diameter ratios and relative axial positions were investigated numerically and experimentally [103–105]. Solutions were presented in the form of Velocity, isotherm maps, velocity profiles, surface and overall heat transfer rates and local and average Nusselt numbers [38]. Experimental work was limited to temperature measurements [104] that only allowed the calculation of average heat transfer coefficients and Nusselt numbers. These were shown to be in good agreement with numerical results, correlated with the Rayleigh number and cylinder geometries, but were almost independent of positioning of the internal cylinder within. However, the internal stream functions from the numerical work [103] showed variations in flow patterns for different internal cylinder positions, hinting at the need to have intrusive measurement techniques to be able to capture accurate velocity and temperature distributions, to bring out the appropriate heat transfer coefficients. Sun and Zhang [106] conducted interferometer based intrusive experiments while Fusegi and Farouk carried out three dimensional numerical simulations of concentric cylinder enclosures [107]. Difficulties in experimentally simulating such theoretical problems, i.e. accounting for the interaction of bounded walls with external boundary layer flows was realized

32 and considered by Sparrow and Prakash [108]. Heat transfer correlations with the developed flow system were presented as Nu = f(Gr) equations for several ranges of Gr [38]. It was shown that the heat transfer rates were reduced and a thermally stabilizing gradient was achieved due to external flows [38, 108]. Another ’conjugate’ problem such as the one just reviewed was based on the thermal conduction in the walls and its disruptive effect on the setting in thermal convection [109]. Both interferometer based temperature measurement experiments along with Alternative Direction Implicit (ADI) method-based finite difference schemes were used to report temperature distributions and heat transfer coefficients. The effect of wall heat conduction was shown to destabilize the thermal convection within the core flow, while also support the local thermal convection near the walls [109,110]. The effects of radiation exchange between the bounded surfaces was considered and its dependence on local wall temperatures was brought out in an extended publication [111]. Yang conducted comprehensive numerical work on the radiation contribution for multidimensional enclosures [112]. Low aspect ratio enclosures with side heating were studied as they were relevant to solar collectors or gas cooling of nuclear reactors [38, 43, 113, 114]. Bound- ary layer and core flow structures were studied for various aspect ratio and Grashof number regimes, the significance of secondary flow structures and their impact on heat transfer were brought out. Three dimensional natural convection in liquid metal filled rectangular enclosure was studied both numerically and experimentally [115] and low Prandtl number flows were shown to give similar average Nusselt number predictions as numerical two dimensional studies. The flow was seen to develop both within the core and near the boundaries. Overall, the studies of different configurations, application of various boundary conditions, different measurement and numerical techniques, three dimensional and two dimensional studies, all seem to bring out the sheer complexities within enclosure driven natural convection problems. Radiation heat exchange within enclosures can be a significant influence on the overall natural convection for particular geometries, fluids and boundary conditions. In most test cases, radiation was isolated or minimized. A proper understanding of the boundary and core flows, temperature and velocity distributions, effects of external environments and relevant boundary conditions was critical while theoretically solving the flow equations. The numerical findings required supporting experiments to arrive at accurate heat transfer and flow formation predictions.

33 3.1.3 Natural Convection in Low Ra regimes

Natural convection flow structures and heat transfer performances are char- acteristically distinct across the range of Rayleigh numbers. For flows within the Mars rover configuration, we are particularly interested in the behaviour of low Rayleigh numbers, from around 100 to about 10,000. For achieving these numbers to simulate such flow conditions for experiments on Earth, it is important to understand the effect of a few of the individual parameters of the βgh34T Rayleigh number (presented in the previous section as κν ) on the overall flow and heat transfer development, mainly the gravitational acceleration, fluid pressures and temperatures. For low gravity flows, early motivations were born out of the need to understand the effect of reduced gravity on fuel storage system designs and crystal growth experiments onboard in space [50]. Liquid and vaporized fuel movement inside tanks in reduced gravity led to fuel draining away from engine feed lines leading to failed starts. Also, fuel sloshing (pogo sloshing, combustion instability, spacecraft jitter) were discov- ered as serious engineering problems caused by gravity affected fluids [50]. Crystal growths involved mass transfer processes guided by concentration and temperature gradients, and the unusual action of reduced gravity natural convection affected the crystal morphology and growth rate [50]. It is important to understand it is not so much the gravity induced buoyancy, but the ratio of the gravity to the other forces acting on the fluid (pressure, viscous, inertial) that determines the overall effect [50]. For higher number of acting forces on a configuration, it was found to be harder to simulate the reduced gravity flows in Earth conditions. Another consideration, not so significant for Mars surface conditions but more for space environments was a non- uniform gravity field environment, that presented a range of accelerations depending on the proximity to a celestial body and orientation, (NASA’s −3 −5 Space Shuttle faced steady state accelerations of 10 go to 10 go) [50]. This reduced gravity environment should not be confused with zero gravity (an ideal theoretical situation), and even slight variations in gravity can lead to slight but not insignificant disturbances in the flow velocities which over time 3 βfiθwd can impact the heat transfer [50]. From Grashof number Gr = ν2 , we know that velocity varies directly or as a square root of it, thus, a reduced −3 −5 gravity of 10 go to 10 go for a characteristic length of 10 cm, temperature difference of 10 K, which normally gives a Gr of 106 at Earth surface gravity, would give a velocity of about 0.1 mm per second [50]. Significant alteration of flow patterns, transition criteria from laminar to turbulent convection can affect heat transfer designs, if the simulated reduced gravity thermal experiments do not give the correct solution [116]. The critical Rayleigh number was seen to vary from less than 1708 [117] to higher than 106. Overall,

34 the rate of thermal convection would be low, but any change in orientation could easily result in momentum balance getting disrupted, leading to difficulties in finding accurate heat transfer solutions [50]. Further, a serious lack of experiments conducted in altered gravity environments has resulted in several open questions on thermal convection behaviour. Several discrep- ancies have been noted by Kostogloue et al. [118] on the variation of Nusselt numbers with Rayleigh numbers for reduced gravity experiments conducted onboard parabolic flights conducted by the European Space Agency. Lack of external natural convection is consistently measured for subcritical Rayleigh numbers, which went against the predictions made based on existing empirical data for similar Rayleigh number tests conducted on Earth surface. This highlighted an important point that at least for some configurations and boundary conditions, simply adjusting the Rayleigh number for lower gravity cannot correctly replicate the effect of conducting the tests in low gravity environments [118, 119]. Studies for low Rayleigh numbers achieved by adjusting temperature and pressure have been continuously reported over the years for a variety of industrial applications (e.g. evacuated spaces used as gas gaps for microelectromechancal systems) and fundamental physics development. As the dependence of the results on the specific configurations and boundary conditions makes it difficult to seek out and compare findings from different independent groups, most of the studies are numerical in nature, with pressure or the gas density parameter or the gravity vector input being adjusted to achieve the low Rayleigh number [120–126]. These studies provide insights into fluid movement behavior for different boundary conditions. Direct Simulation Monte Carlo (DSMC) methods for rarefied gas flow in rectangular enclosures have been used to generate fluid movement directions for linearly heated side-walls for a range of Knudsen numbers [127]. The transition from the slip flow to the transition flow regime has been investigated using both Navier Stokes-Fourier and Direct Simulation Monte Carlo methods to reveal combined effects of wall temperature ratios and Knudsen number regimes on heat transfer and flow structure [128]. Overall heat transfer and wall temperature estimates are made by varying the geometry and boundary condition parameters (individually or as combinations) to identify the strongest influencing parameters on rarefied confined flows in rectangular enclosures [129]. The effect of enclosure inclination with respect to horizontal on the overall heat transfer is shown to be considerable for higher Rayleigh numbers (106) as compared to lower values [130]. Average Nusselt number correlations for inclined rarefied gas cavities have been reported, emphasizing on the complex impact of gravitational accleration on the heat transfer and flow structure [131].

35 3.1.4 Natural Convection in Non-Conventional Enclosures Ge- ometries

Natural convection in non-conventional geometric enclosures were the subject of investigation and periodically reported upon in relevant journals and proceedings in the last three decades. Lee conducted computational and experimental studies of a trapezoid shaped enclosure set at different incli- nations [45]. De and Dalal [47] pursued numerical modelling of two different thermal boundary conditions (uniform wall temperature versus uniform wall heating) for a heated square suspended within a larger square enclosure. They showed variation in fluid isotherms and Velocitys, heat transfer rates for varying aspect ratios and boundary conditions. Several case and condition specific conclusions were noted in several works, however, the review shall continue to focus on the generic learnings from these studies that would help formulate the problem setup and achieve the research goals set out for this thesis. While most problems discussed so far focused on geometries with smooth and flat surfaces, the problem of protrusions and cavities within confined enclosures is of immense relevance for heat dissipation from electronic boards and lies relatively unexplored [38]. One of the main motivations for studying this configuration stemmed about 30 years back from a thermal control solution to cool micro-electric components for terrestrial applications [112,132], a goal quite opposite to ours with gap insulation within Mars rovers. Limited data exists on the effect of geometric factors on the heat transfer, since geometries, material properties and boundary conditions vary from case to case basis and complicate the compilation of a generic empirical database for direct comparisons useful to a wider range of applications [133]. Keyhani conducted experiments to study the effect of aspect ratio of protruding heat sources on natural convection and showed the local Nusselt number correlation with local Rayleigh number (based on heater length as its characteristic length scale) was independent of number of heaters, heater configuration and cavity-protrusion ratio [133]. Chang and Tsay studied a single heated step geometry using numerical model based on commercially available FLUENT software to see the effect on flow structure and heat transfer characteristics by varying the Rayleigh number, Prandtl number and geomet- rical size of the step [44]. Dagtekin et a. [48] used FLUENT CFD software to attain entropy generation for backward shaped enclosures for a range of Rayleigh numbers varying from 103 to 106. Kalidasan et a. conducted similar numerical analysis for a forward facing stepped enclosure with a sinusoidal time variant temperature boundary condition [46].

36 3.1.5 Summary of Observations Some of the important observations that have been made so far from the review of fundamental enclosure natural convection investigations have been listed below:

• Rayleigh number, Grashof number, Prandtl number and Nusselt number are the main non-dimensional parameters derived to study the problem of natural convection.

• Even for subcritical Rayleigh number ﬂows, while thermal conduction dominates the heat transfer within the enclosure, there are ﬂuid circulations either near the walls, within the core or both.

• Internal convection is far more complex than external convection, due to a cyclic interdependency between the boundary layer flow and core flow within the region. This complexity is significantly distinct for completely confined flows. Problems of interaction with an external fluid as well as partial enclosures also affect the overall thermal stabilization.

• The inherently unstable thermal convection problem (i.e. enclosure with heating from below) requires proper knowledge of boundary conditions, refinement of results of all flow patterns within the fluid in order to arrive at accurate heat transfer rates.

• As a rule, ﬂow structures and local and average heat transfer rates are extremely sensitive to geometry and boundary conditions, requiring ex- clusive investigation of most enclosure driven problems. In most cases, experiments have guided numerical investigations to give a complete description of the solution. Strong inconsistencies between experimental measurements of Nusselt number for variety of heat transfer cases (geometry and boundary conditions) throughout the past 5 decades of work indicate the inherently complex problem and inapplicability of linear scaling using Buckingham pi theorem

• Experiments depending solely on temperature measurements are limited to the calculation of the system’s average Nusselt number, and do not show the sensitivity of the heat transfer rate to the positioning of heaters or axial location of the inner cylinder in case of annuli problem. Hence, either intrusive measurement techniques such as interferometry or numerical modelling of the ﬂow needs to be carried out to capture these eﬀects.

37 • Reduced gravity environments lead to lower yet still non-zero ﬂuid velocity ﬂuctuations that need to be accurately accounted for. Experi- mentation with natural convection in reducred gravity remains an open problem. The adjustment of other parameters within the Rayleigh number to simulate a lower gravity does not give the same results as those while conducting the tests in a low gravity environment.

• Step geometry natural convection results are heavily dependent on the calculation of the modiﬁed local Rayleigh number for the ﬂow.

3.2 Thermal Management in Mars Rovers and Landers The utilisation of gas-gaps for insulation of temperature sensitive hardware within Mars rovers has been tested and in some cases already implemented by several Mars rover thermal teams around the world. A review of strategies utilized are presented here, with a focus on experimental challenges, material and test strategies used and the most relevant open questions to be addressed.

3.2.1 NASA Jet Propulsion Laboratory Mars Rover Thermal Team Tsuyuki et al. [134] were the first to propose the utilisation of ambient Mars atmosphere as an efficient thermal insulation medium within a lightweight multiple layer radiation shield enclosure. The insulation layers were held off using Mylar spacers. Thermal conductivity of the atmosphere (mainly CO2 0.006 W/m-K to 0.02 W/m-K) was shown to be less than that of other solid passive thermal insulants such as Aerogel or Fibreglass batt material (0.01 W/m-K to 0.028 W/m-K) for the entire range of possible temperatures on the surface (-100◦C to 30◦C) and Mars pressure of 8 torr [134]. Another advantage offered was that the MLI blanket used to provide the gap spacing was a flexible material that could be tailored and wrapped efficiently around hardware of different shapes, making efficient use of internal spacing. The candidate geometry was based on the canceled Mars Surveyor Program’s Payload Electronics Box (PEB) design, (which was later modified to form the Warm Electronics Box). The critical gap spacings were calculated to 2.4 cm for the sides and 2.3 cm for the top and bottom, based on critical Rayleigh number of 1700 and 2000 (from free convection theory) for horizontal and vertical gaps respectively [134]. Experiments were performed within a thermal vacuum chamber using gaseous N2 instead of CO2 (since CO2 is unstable and prone to freezing below -90◦C). By keeping the gap spacing lower than the earlier mentioned critical values, free convection was assumed to be absent and the effective heat transfer was based on conduction and

38 radiation modes. The radiation heat flow per face was approximated using infinite parallel plate theory. The results showed a total insulation heat loss of 2.4 W for the CO2 gas gap and 5.3 W for N2 as compared to 3.9 W for Fiberglass for tests done at -50◦C. For tests at 0◦C, they recorded total loss of 3.9 W for the CO2 gas gap and 7.1 W for N2. In addition, the team also reported improvements in respective masses, fabrication costs and delivery times for the CO2 gas gap ( 0.2˜ kg, US$ 6,000 , around 1 week) as compared to for fibreglass batt insulation ( 0.5˜ kg, US$ 9,000, 1 month) [134]. Gas gap insulation was tested for use on NASA’s Mar Science Laboratory (MSL) to insulate its Rover Avionics Mounting Platform (RAMP)- an arrangement of flight hardware and internal payload arranged on a suspended electronics board held off from the rover chassis [32]. Around 25% of the overall heat loss (around 150 W) was attributed to losses through the gas gaps. A three step approach of analytical, numerical and experimental solution of relevant horizontal and vertical gas gaps was followed. Even though the RAMP had a combination of various profiled features, the empirical for- mula for Nu = f(Ra) based on a single horizontal flat surface [135] was used. This was used to derive analytical predictions of variation of heat transfer coefficient versus gap thicknesses to arrive at critical gap spacings. The trends seemed to show a drop in conductance values with increasing gap thicknesses, upto a critical point where convection starts and the conductance shoots up, only to again drop as the gap thickness was further increased. Computational fluid dynamics was used to simulate the experimental test articles, mainly a horizontal gap using circular Aluminium plates enclosed by a shroud. Thermal conductance was calculated with the top plate held at a constant temperature of -80◦C and the bottom at fixed heat input to maintain a constant temperature of -30 ◦C. (where thermal conductance, Q G = hA = δT ). Not many details of the developed model (problem setup, whether domain was 2D axisymmetric or 3D) were provided and upon email inquiry, it was informed over email that a lot of the test information was restricted from being publicly shared, under a United States International Traffic in Arms Regulations (ITAR) license, which prevented further discussions with the team on the topic. The experiments were conducted in a bell jar using parallel plates made of Aluminium, enclosed within a shroud with Goldized-Kapton used to cover gaps between plate edges and walls. Low emissivity gold plating was used on the surfaces to minimize radiation losses. The bell jar was filled to 8 torr with CO2 and N2 to simulate Mars conditions. Further details on number of runs, temperatures achieved were not reported. Tests were conducted for horizontal gap thicknesses of 3.8 cm, 5 cm, 7.6 cm, 10 cm and 12.7 cm. The main results were that the experiments recorded a greater heat transfer loss than the pure conduction case, but were

39 signiﬁcantly lower than those predicted by the CFD. The onset of thermal convection was predicted to occur at 7.6 cm rather than 6.4 cm which was predicted by the CFD. No thermal convection scenario was found at larger gap thicknesses which produced more heat transfer than simple conservative assumptions of pure gas conduction through gap thicknesses of 3.8 cm. Sev- eral questions regarding the CFD and test setup remained, as to whether the team had considered modelling the protrusions and cavities on the RAMP, how had they tackled the challenge of maintaining CO2 within the bell jar at lower than -30◦C for long durations of time to achieve stable temperatures. In any case, thermal convection loss magnitudes were not a huge concern given the nuclear-waste heat rejection system (HRS) that could easily compensate the heat lost during cold Mars nights and has been able to maintain steady itnernal temperatures over long periods of time [22]. The main concern though is for the solar-electric powered rovers being designed by the Europeans and the Japanese which do not have such reserves of waste heat and need to characterize the losses via gas gap to mW scale.

3.2.2 Airbus Defence and Space: ExoMars 2020 Rover Thermal Design and Analysis The thermal design and performance evaluation of the European Space Agency’s ExoMars Rover is currently being carried out by Airbus Defence and Space. The rover consists of two compartments, the service module and the analytical lab drawyer, each housed within the internal structure, held off via a gas gap of 3 cm [33]. Gas gap insulation is preferred over alternative solid insulants based on its low effective thermal conductivity, lightweight gap enclosure requirements. Also, melamine foam (basotect) (thermal conductivity of 0.25 W/m-K), an alternative insulant contains Silicon that could cause interference with the onboard organic tracers on the rover (which are looking for proof of past or extant life on Mars). Another option, silica aerogel has a low thermal conductivity of 0.016 W/m-K but is only produced by NASA for its applications and is therefore proven to be difficult to procure. The team uses natural convection theory to arrive at an effective Rayleigh numbers of 90 for Mars environment, for a maximum worst case temperature difference of 50◦C, ambient pressure of 7 torr, characteristic gap length of 3 cm. It is expected thermal conduction to dominate the heat transfer at this low Rayleigh number, however the team aims to confirm this via experimental testing and also investigate the effect of corners, tilt of enclosure and non-uniform heating of the interior surface. The test setup within thermal vacuum facility includes two concentric Aluminium boxes spaced by 2.9 cm, coated with vacuum deposited aluminium and supported with glass rein-

40 forced plastic studs to reduce the conductive heat transfer. Thermocouples were suspended between the gaps to record the temperatures. The setup was cycled through a range of surface temperatures and chamber pressures. The main findings were that gas even in absence of convection instigated a higher heat transfer across surfaces as compared to vacuum. The two boxes eventually maintained equilibrium and were within a standard deviation off each other. The position of the thermocouples was not fixed and led to inconsistent measurements since there was little control over their positions. All temperature differences could be attributed to conductive couplings and radiation heat losses due to given number of exposed surfaces. The numerical model used to compare the results was built as a thermal mathematical model (TMM), created using ThermXL, a thermal modelling tool developed by ITP Engines [33]. Conductive couplings between the boxes were done by hand whereas radiative couplings were calculated from ESARAD software. All surface temperatures were used from the test results. The onset of thermal convection was based on the average temperature difference between the plates, with the Earth ambient pressure giving the lowest difference of around 19◦C. Overall, temperature differences were reported to be large enough to prove from heat transfer balance that no convection was occuring. In 2015, the team carried out further tests [35] to check if baffles were needed to break up the gas gap cavity into smaller sections to prevent convection. Setup modifications to work around the earlier faced challenges included a computer controlled valve that regulated the gas pressure during low temperature cycles and guard heaters to prevent conductive coupling. Several baffle test configurations were tested for a range of temperatures and CO2 and N2 to achieve Rayleigh number of 90. The baffles showed a significant improve- ment in the insulation performance for gaps greater than 3 cm but tended to reduce the performance for shorter gaps. Also, a higher heat loss for N2 was recorded as compared to CO2 which was expected based on the different gas densities. However, the challenges with assembly and robustness of these lightweight baffles remains a concern. In the following year [36], the team decided to conduct an evaluation of modelling techniques based on different gas coupling models for three different configurations. The approaches used were:

• Pure conduction with multiple gas nodes. This technique considers the heat ﬂow through gas to be purely conductive, with the entire volume divided into nodes that are conductively coupled to each other and eventually to the walls.

• Convection into free space with one gas node per gap. This technique

41 considers all heat transfers through ’small’ gaps ( 3 cm) via conductive coupling and the remaining gas (not in those gaps) as a single isothermal node of heat transfer

• Convection into free space with multiple gas nodes. Here the ’large’ gaps are discretized into one node per face and convection to free space equations are applied on all the other gas gaps. Each of the large gas nodes are coupled to each other via conductive couplings.

• Limited parallel plates without gas nodes. This method was used by the JPL team [32] and applies a conductive coupling for gaps smaller than 3.8 cm and a conductive coupling of 3.8 cm for gaps larger than 3.8 cm as it has been shown that the decrease in conductive coupling due to increased path length is compensated by the increase in the coupling due to convection.

• Temperature dependent limited parallel plates without gas nodes. Like the previous method, this one uses a similar technique, except instead of a ﬁxed path length, it has a temperature dependent path length.

The results indicated that there was significant convection and gas coupling for cases above 60 mm gap spacing. Standard gas equations were adequate for Earth pressures but overpredicted couplings for Mars pressures. There was insignificant distinction between choosing single or multiple gas node for standard gas equations for free space convections. The limited parallel plate technique underestimated the gas coupling for Earth pressures but was accurate for Mars pressures, although it showed inconsistencies for plate temperature differences higher than 60◦C. The temperature dependent limited parallel plate technique did not correctly predict heat transfer for any of the cases, requiring deeper insight into the heat transfer mechanisms. Over- all, this over-simplification of the complex natural convection based problem is inadequately approached by any of these 5 methods.

3.2.3 JAXA Mars Rover Thermal Design Analysis The Japanese Aerospace Agency (JAXA) is planning to launch its ﬁrst rover to Mars to search for living organisms in the Martian soil. The rover is a 150 kg class spacecraft that shall be solar electric powered [37]. The thermal team presented a preliminary design of the thermal conﬁguration that does not utilize nuclear heat sources, unline the recent NASA and ESA rovers,

42 but has a Mars Exploration Rover (MER) type philosophy of packing all electronics in one single insulated box. The insulation material was set to gas gaps as with previous studies, it was found to be the most robust and give the best performance out of all possible options. Vacuum insulation was considered but the heavy Vacuum panel would add to mass budget and affect the rover’s mobility. Their gas gap involves a separation layer that holds close to the protected surface due to volume constraints during Mars entry and gets released to be held at 6 cm thicknesses upon landing in a hold and release mechanism [37]. The team uses Thermal Desktop/ SINDA Fluint (CRtech INC.) to build a thermal mathematical model for th rover. The model builds a heating rate calculation for given solar direction variation versus time, diffuse solar flux, diffuse sky IR, ground IR and ground albeedo for given latitude, longitude, data and value of heat sources. Convective heat transfer to the ambient from the panels and conductive heat transfer within the gas gap is included as well. A single node analysis is carried out. Without a nuclear heat source, the greatest risk to the mission is seen as to survive a dust storm. This is mainly a factor of power consumption and generation and optical depth τ. If τ increases to 5.0 on the coldest day, the heater power consumption reaches 629 Wh and drives the battery levels below 90% per day [37].

3.2.4 Summary of Observations Some of the main observations from this section are listed below:

• Use of theoretical convection theory equations for horizontal, vertical or external gaps are only suﬃcient to give initial estimates of the heat transfer, in order to understand the accurate heat transfer rates, it is important to deﬁne the relevant geometry, boundary conditions and conduct numerical and experimental tests of the problem.

• Baseline CFD data exists for the MSL Curiosity mission to validate the rate of change of heat transfer with varying gap thicknesses. This shall be a good place to start with testing and validating horizontal gap ﬂows in thermal vacuum chambers.

• Maintaining chamber pressure and measuring surface and ﬂuid temperatures are quite challenging. It is important to use substitute gas for CO2 (i.e. N2) and use pump and gas feed to allow for stable chamber pressures. Conducting gas gap thermal tests with a single gas as compared to actual Mars atmosphere gas mix (i.e. without the trace

43 gas elements) is a good assumption towards simulating the thermal properties of the working ﬂuid within the natural convection enclosure.

• None of the teams have investigated the effect of protruding, caving pattern of the heated electronic boards, most have assumed flat surfaces in both numerical as well as experimental tests, which is far from reality. The study of enclosures with even a single step, for Mars relevant boundary conditions is by itself an important first step that needs to be completely resolved.

• An eﬀective methodology to predict the onset and stabilization of thermal convection within a thermal vacuum chamber, with limited measurement capabilities needs to be realized.

• Single and multiple node models have been shown to be inadequate to predict thermal convection for the ExoMars rover. A continuum based numerical model needs to be developed to solve for heat transfer rates, strongly supported with experimental tests.

• The eﬀect of rover tilt needs to be seen on the heat transfer rate.

• The variation of Rayleigh number by adjusting temperature, pressure and geometry need to be studied and results to be compared.

• A convenient way could be to simplify the CFD results as a set of parameters which could be applied to an industry standard thermal modelling tool for predicting the thermal performance of a set of gas gap conﬁgurations for a range of boundary conditions.

3.3 Review Summary The literature review started with covering the unique aspects of fundamental natural convection and the complexities in partially and completely confined configurations. Important high level conclusions based on decades of tackling this common but unique problem were highlighted. The strong dependence on geometry configuration and boundary conditions on the final flow structures and heat transfer balances were repeatedly stressed. Follow- ing from this, prior and ongoing thermal management gas gap configuration studies conducted by NASA JPL, ExoMars thermal team and JAXA were studied. The shortcomings with using flat gas gap theories and heat transfer correlations to arrive at critical gap thickness criteria are presented. While other industries have relied on using numerical modelling for predicting gap performances for their applications, the Mars thermal teams have focused

44 on experimental work and limited/no use of adequate numerical modelling (except JPL team) for their conﬁgurations. Challenges with conducting natural convection experiments within thermal vacuum chambers are reported, mainly towards the measurement of heat transfer as well as maintaining realistic Mars temperature and pressure conditions. Hence, there are some distinct open problems both from experimental measurement as well as a numerical prediction of heat transfer within natural convection enclosures formed by ’step’ shaped surfaces for Mars relevant Rayleigh number regimes. The following chapter shall build on the main requirements to formulate the problem and the details on the numerical and experimental setup shall be presented.

45 4 Research Methodology and Problem Setup

4.1 Research Path The research path for the thesis consisted of four main steps as shown in Figure 2.

Figure 2: Research Path

4.1.1 Identiﬁed Gaps in Literature Review These have been detailed in the previous chapter, however, a concise list is included here for the beneﬁt of the reader.

1. Study of internal natural convection is a complex problem, solutions are sensitive to geometries and boundary conditions.

2. Fundamental concentric cylinder enclosure for low Ra (∼ 1000) is still an open problem.

3. Guidance of experiments for CFD modelling is crucial to arrive at accurate local heat transport and ﬂow details.

4. Subcritical Ra flows (flows with only gas conduction) can also have fluid movement which influences the final flow structure and heat transport. This phenomenon is not well studied for low Rayleigh number problems.

5. Theoretical achievement of desired Ra number for flow by adjusting parameters does not result in similar flow structure and heat transport. Effect of each parameter on overall flow needs to be further studied.

46 6. Use of ﬂat surface gap based heat transfer correlations are good only for generic estimates, there is a need to derive accurate correlations based on the geometry.

7. Mars rover thermal management teams have reported challenges with conducting gas gap tests in vacuum chambers. Problems mainly with maintaining stable temperature and pressures and positioning the temperature sensors

8. Flight avionic boards have cavities and protrusions into gas gaps, need to study step proﬁle geometries for Mars case pressures.

9. Eﬀect of tilt of rover with respect to gravity vector on heat transfer and ﬂow structure within the gas gap.

10. Asymmetric and axisymmetric temperature distributions (spatial and temporal) for cylindrical step proﬁle cases need to be investigated.

4.1.2 Requirements Based on the Gaps After identifying the main research gaps within the literature for fundamental natural convection and Mars rover thermal testing, a limited set of research requirements were deﬁned to be tackled within the allotted 3.5 years for the doctoral candidature.

1. Experimental and CFD investigation of Concentric cylinder enclosure for relevant boundary and operating conditions.

2. Conﬁguring a concentric cylinder gas gap test within existing Thermal Vacuum Chamber Facility.

3. Comparing heater conﬁguration and thermocouple positoning for predicting onset and capture of natural convection.

4. Conduct CFD analysis (2D axisymmetric and 3D) to study Ra change eﬀect on ﬂow structure and heat transfer.

4.1.3 Conducted Sub-Investigations To address these requirements, a set of sub-investigations were carried out with a coupled numerical and experimental approach.

1. Measuring onset and formulation of natural convection within thermal vacuum chamber setup.

47 2. Heat Transfer around Step Proﬁle fow low-medium Ra cases.

3. Three Dimensional eﬀects of Thermal Convection in Mars Systems.

4.1.4 Targeted Contributions to the Body of Knowledge Finally a list of research contributions to the existing body of knowledge were set to be achieved.

1. Gas gap measurement techniques for spatial and temporal variation of temperature.

2. Qualitative ﬂow description and quantitative heat transfer correlations for range of Ra variation cases.

3. Three dimensional CFD data showing eﬀect of ﬂow rotation on heat transfer balances.

4.2 Problem Formulation In order to conduct the sub-investigations both numerically and experimentally, the relevant geometry, boundary conditions and initial assumptions are ﬁrst deﬁned.

4.2.1 Axisymmetric Internal Enclosure As has been reported in the reviewed published work on fully enclosed natural convection problems, the solutions are heavily dependent on the geometric configurations. The real-world problem under consideration consists of gas gaps around heat-dissipating contoured profiles. To study a single step profile problem, a cylindrical enclosure is chosen over a cartesian (square or rectangular) enclosure to reduce the number of corners and therefore the edge input parameters, which allows to single out the effect around one step edge. A side cut section of the selected geometry is illustrated in Figure 3. An axisymmetric internal concentric volume, enclosed by an overhanging horizontal circular cold surface with diameter D over two horizontal heated surfaces, differently leveled by h2 and surrounded by cylindrical wall with height h1. One of the heated surface is circular with diameter d while the other is a ring that sits around it with outer diameter D and inner diameter d. The axis of symmetry is represented with a vertical dashed line through the centre of the geometry. It shall be later discussed that the 2D axisymmetric CFD model is limited to one half of this geometry. The direction of the gravity vector g is normal to the heated surfaces.

48 Figure 3: Side Cut Section of Geometry

4.2.2 Boundary Conditions and Assumptions The control volume serves to simulate the free space between a section of heat-dissipating horizontal surface within a Mars rover within a range of distances from a cold wall (thermally coupled with Martian ambient environment). The volume is enclosed by an adiabatic cylindrical shroud (physically decoupled from both hot and cold surfaces). Isothermal temperature with no-slip boundary condition is applied at the cold wall surface. Constant heat ﬂux no-slip boundary condition is applied at the two uniformly heated surfaces into the enclosure. The sidewalls are set to adiabatic no-slip boundary conditions with zero temperature gradient in the x direction. The non dimensional steady state momentum and energy equations 11 and 12 (derived in Section 3.1.1) are solved. The following assumptions were made:

1. Gas properties vary according to Kinetic Theory of Gases. 2. Radiative emissivities are uniform across all the surfaces.

49 Figure 4: Computational Model

3. Cold surface always maintains uniform temperature throughout its area.

4. Gas density variation within the control volume is governed by the Boussinesq approximation, which is valid when β(T − To) << 1.

4.3 Numerical Modelling Setup and Validation 4.3.1 Geometry Selection The purpose of the numerical model is to complement the planned experimental tests by providing the temperature and velocity distributions within the enclosure (since we are limited to surface or near-surface measurements in our experiments within the thermal vacuum chamber) and conduct a larger set of parametric analysis studies to help bring out the most relevant cases which were then carried out experimentally (to save time and operation costs). A wide range of cylindrical gas gap volumes are achievable within the available thermal vacuum chamber testing facilities, (Hmax=400 mm, Dmax=375mm),

50 and the computational geometry is scaled within these limits. Both two dimensional (axisymmetric) and three dimensional domains representing the enclosure volume were prepared (in millimetre scale) using ANSYS Geom- etry Modeler and Autodesk Inventor 2015 in order to support the planned sub-investigations.

4.3.2 Geometry Discretization Three main priorities drove the selection of grid generation scheme for the subsequent numerical work, namely: the initial setup and subsequent modi- fication time; solution accuracy and the convergence criteria rates for CFD solution. For this comparison study, a flat surface horizontal gap geometry with boundary conditions (constant top and bottom surface temperatures, adiabatic walls) based on a well understood problem [136] was meshed using a sweep based mesher (ANSYS meshing tool [137]) and a blocking topology scheme (GridPro v6.6 [138]) for same grid densities. The average setup time was calculated from geometry import to final mesh file generation. Calcu- lation of average internal flow velocities along a horizontal line equidistant from top and bottom surfaces was compared with published data from [136] to arrive at solution accuracies. Solution accuracy was calculated based on value differences as a percentage of published data value, reported in Table 1 graded between 0 and 1, where 0.9 indicated less than 5% error and 0.1 indicated above 70% difference. ANSYS Fluent CFD solver was used and convergence criteria was set to 0.00001, monitored for energy, momentum and velocity equations. The results described in Table 1 showed the blocking topology scheme with GridPro gave a better performance and was more suited for the planned numerical work. The GridPro grids were smoother and orthogonal throughout (this was later observed to be a critical requirement for regions near the corner edges in the step enclosures, where notable fluid accelerations were leading to delayed convergence in the initial few runs). Solution accuracy grading for the two meshes also showed the GridPro mesh to give accurate mesh solutions. Grid resolutions and errors due to discretization were calculated both for two dimensional and three dimensional grids based on Grid Convergence Index (GCI) estimations [139, 140]. Final GCI values were ensured to be within the asymptotic range of convergence. A refinement ratio of 2 was selected to prepare three grids of increasing grid densities per case, first for 2-D then 3-D geometries. Area averaged non-dimensional velocity (scaled by bulk fluid velocity) along horizontal centreline equidistant from the top and bottom surfaces was chosen as the working parameter to check for grid independency. From [139], the following steps were followed:

51 Figure 5: Horizontal Flat Surface Gap Geometry for Mesh Independence and Numerical Model Validation Study

Table 1: Comparison of Sweep-based and Blocking Topology Grid Schemes for a Sample Internal Natural Convection Problem for a Horizontal Gap Enclosure.

Guiding Criteria ANSYS 17.0 Mesher GridPro 6.6 Average Setup Time 4 hours 2.5 hours Solution Accuracy 0.3 0.404 Iterations to Convergence ∼ 60000 iterations ∼ 20000 iterations

For each of a case’s three grid levels, the working parameter values were recorded as f1, f2 and f3. The order of convergence ’p’ is then determined, where r is the ratio of reﬁnement:

ln( f3−f2 ) p = f2−f1 (13) ln(r)

The grid convergence index (GCI) is calculated based on the error e in working parameter value between grid levels and Fs, the safety factor, here taken as 1.25:

F |e| GCI = s (14) rP − 1 To check if GCI is within asymptotic range of convergence:

52 GCI2,3 P ≈ 1 (15) r × GCI1,2

Complimenting the GCI method, Richardson’s extrapolation was also carried out to check for grid independence based on working parameter value error convergence:

f − f f = f + 1 2 (16) h=0 fine rP − 1 A total of six geometry case grids (three each for 2D and 3D), for varying h length values of 5 mm, 10 mm and 20 mm were tested for grid independency using the GCI and Richardson’s extrapolation method. Asymptotic range of convergence values of close to 1 were achieved (presented in Tables 2 and 3) along with plottings for Richardson’s extrapolation value for working parameter values at normalized grid spacing of 0 (Figures 6, 7 and 8) which quantified the discretion errors. The grid cell numbers and maximum orthogonal skew (values between 0 and 1 in increasing order of grid quality) are presented in Table 4 and Table 5. The grid development is done ensur- ing y+ values (non-dimensional distance from boundary walls) close to 1, as recommended for internal natural convection CFD studies [48,137]. First cell wall height value was 1e-5m. Multiblock structured scheme is used for grid generation, a representative cut section for 2-D Case 1 can be seen in Figure 9. The image is mirrored to show the entire cross section whereas in reality, only half of the domain is meshed and solved to save computational memory and time. Maintaining consistent cell inflation and shape near the region near the step corner (as shown in Figure 10) proved to be challenging but was critical to capture higher fluid accelerations. This was remarkably better achieved in GridPro as compared to previous grids generated using ANSYS Meshing tool.

Table 2: Richardson’s Extrapolation Value f0 and Asymptotic Range of Con- vergence for the 2D Grids.

2D Geometry f0 GCI Asymptotic Check Case 1 0.9959 1.0018 Case 2 0.9871 1.0019 Case 3 1.0031 1.0024

53 (a) 2D Geometry Case 1. (b) 2D Geometry Case 2.

Figure 6: Richardson’s Extrapolation for Deﬁned Working Parameter at Grid Spacing h=0 for 2D Geometry Cases 1 and 2.

(a) 2D Geometry Case 3. (b) 3D Geometry Case 1.

Figure 7: Richardson’s Extrapolation for Deﬁned Working Parameter at Grid Spacing h=0 for 2D Geometry Case 3 and 3D Geometry Case 1.

Table 3: Richardson’s Extrapolation Value f0 and Asymptotic Range of Con- vergence for the 3D Grids.

3D Geometry f0 GCI Asymptotic Check Case 1 0.9704 1.0059 Case 2 0.9772 1.0031 Case 3 0.9926 1.0011

4.3.3 Numerical Setup Description The ﬂow regime (for the range of internal natural convection problems to be considered) is assessed to be continuum or molecular ﬂow based on the

54 (a) 3D Geometry Case 2. (b) 3D Geometry Case 3.

Figure 8: Richardson’s Extrapolation for Deﬁned Working Parameter at Grid Spacing h=0 for 3D Geometry Cases 2 and 3.

Table 4: 2D Grid Size and Quality Details

2D Case Cell Number Max. Orthogonal Skew Case 1 893819 0.542 Case 2 957294 0.626 Case 3 1025965 0.631

Table 5: 3D Grid Size and Quality Details

3D Case Cell Number Max. Orthogonal Skew Case 1 642480 0.643 Case 2 646400 0.681 Case 3 662000 0.671

Knudsen number Kn and the mean free path.

k T K = √ B (17) n 2πd2pL

λ = KnL (18)

where kB is Boltzmann Constant, T is the bulk ﬂuid temperature(260 K), d is the particle diameter (232 picometre for CO2), p is the total pressure (6 mbar) and L is a length scale (in this case the scale of the gap width, around 0.05 m). This gives a Knudsen number of 3.2e-4 and a λ of 1.6e-5, which indicates the regime is well within the continuum ﬂow regime. The coupling

55 Figure 9: Two-Dimensional Computational Mesh (mirrored along axis of symmetry) for Case H=160mm, h=100mm. between flow and heat transfer has several implications on the solution strategy for natural convection modelling within closed domains. The main thing is to ensure efficient solution of equations over the set number of iterations. Selecting a pressure based solver allows solving the isothermal flow for convergence and then solving flow and energy equations to complete the simulation. ANSYS Fluent 17.0 solver recommends a lower under-relaxation factor for temperature dependent flows, hence a value of 0.8 was adopted. Closed domain temperature dependent flows require stringent near-wall treatments. Therefore, realizable k- model was selected with enhanced wall treatment, full buoyancy treatment and thermal effects included. The solution depends on the mass value within the volume, which is determined by the density estimation for the problem. Based on ANSYS Help guidelines, S2S Radiation Model was selected, being the most suited model for radiative transfer with non-participating media within enclosures [137]. By trial and error, a total of 100 iterations per timestep were found to be sufficient for convergence. For small temperature differences within the domain and domain density

56 Figure 10: Two-Dimensional Computational Mesh (mirrored along axis of symmetry) for Case H=160mm, h=100mm, Zoomed in to show meshing scheme near step. variations within 20%, the Boussinesq calculation is the recommended option by ANSYS for accurate density calculation. However, upon selecting this option, the initial estimates of density for the relevant temperature and heating boundary conditions resulted in diverging solutions. Subsequently, density estimations were based on ”Ideal Gas” laws with the Kinetic The- ory Option selected to solve for temperature dependent properties of specific heat, thermal conductivity and viscosity. Nitrogen gas is selected (this is because nitrogen gas is the preferred working fluid for experimental testing, since it is relatively cheap, inert, prevents atmospheric condensation at low temperatures within vacuum chambers, a well documented problem faced by most Mars rover teams [32,33,35]). Based on the requirements of the particular computational campaign, both steady and transient runs were carried out, to investigate flow structure, heat transfer properties within the domain as well as the time dependencies of the solution. Boundary conditions on the walls were set based on campaign requirements, mainly involving fixed

57 Figure 11: Isometric View of Three-Dimensional Computational Mesh (mirrored along axis of symmetry) for Case H=160mm, h=100mm

temperature and heat ﬂux settings at the working surfaces and adiabatic heating on other surfaces. Emissivity values for all the surface materials were used from conducted measurements using radiation based emissivity measurement apparatus. The Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm is used to discretize the pressure velocity coupling, as recommended by Fluent Guidelines for natural convection wall- bounded problems [137]. Cases were solved for steady and transient settings, with solution timestep values (based on ANSYS Help Guidelines for solving √ L internal natural convection ﬂows) determined as 4 gβδT L where L and U are length and velocity scales, respectively. A convergence criteria of 1e-6 was set for monitors of all the solved equations and surface monitors for internal average temperature and velocity magnitudes were logged to check for time

58 independence of solutions. Postprocessing of results was carried out ﬁrst in ANSYS CFD Post to determine local and average Nusselt Numbers along with heat transfer coeﬃcients. Contour and data plotting was then done in Tecplot 360 EX.

4.3.4 Numerical Model Validation The numerical solver was tested and compared against a CFD study undertaken by the NASA JPL MSL team(Bhandari et al.) [32] for a three dimensional axisymmetric horizontal gas gap between two circular aluminium disks surrounded by a thermally decoupled shroud. The main objective of their work was to study the behaviour of convective heat transfer for a range of gas gap thicknesses for a constant temperature-adiabatic side wall boundary condition. Solution acceptance criteria was to match thermal conductance values within 0.01 W/K (or a difference from JPL study calculations within 0.1%), which correlated to heat inputs of within approximately 1 W. The heated wall at the bottom was maintained at -30◦C and the top wall cooled to -70◦C. The side walls were set to be adiabatic. Solutions from the solver were compared with JPL’s work for heat transfer coefficient (HTC) times unit area A, in terms of thermal conductance G = (HTC)A versus horizontal gap thickness h as presented in Figure 12. Theoretical estimations for the same were calculated based on horizontal gap Nusselt number correlation from [141] and for pure conduction case [32] and presented in the same figure. Thermal conductance tends to drop steeply as gas thickness is increased (mainly since heat transfer due to conduction is inversely propor- tional to conduction path length) until a point, after which convection sets in, leading to a short spike in thermal convection, which tends to gradually reduce for larger gap thicknesses. The JPL model tended to show a thermal conductance value of 0.026 W/K, which stabilized around 0.025 W/K for larger gap thicknesses. The results from the conducted numerical validation indicated good agreement with the JPL readings, a convection onset peak thermal conductance of 0.0256 W/K, which drops gradually to around 0.022 W/K for larger gap thicknesses. Both the JPL and our flat gap validation model showed higher thermal conductance values than those calculated using existing Nusselt number correlations for horizontal gap configurations for constant temperature wall boundary conditions. This is expected given the incapability of the theoretical models to capture the transient fluid circulation effects, which lead to higher rates of thermal convection and are dealt with more accurately with numerical discretization. The convection onset peak also was shown to occur at a slightly smaller gap thickness of 70 mm as compared to theoretical estimation of 90 mm. Numerical solution time inde-

59 pendence criteria (less than 0.01% residual diﬀerence per 100 seconds) and working parameter (thermal conductance diﬀerence from JPL study within 0.1%) magnitude were achieved with the developed numerical setup.

4.3.5 Computational Resource Utilization Preliminary grid and model validation studies were conducted on a single processor workstation, Intel Core i7-4770 CPU utilizing 16 GB of installed memory to run on an ANSYS 17.0 Solver Serial License owned by University of New South Wales. Batches of test runs which took longer than 4 weeks of physical run time were prepared and run on the Raijin High Peformance Computing Cluster of the National Computational Infrastructure Facility, supported by the Australian Government. Depending on individual cases, the runs were speciﬁed to utilize anywhere between 16-128 CPUs, memory of 16- 64 GB for a desired computational wall time of 48 hours for job completion.

4.3.6 Numerical Data Generation After achieving grid and model validation based on the prepared CFD case setup, the objective of the numerical investigation was to study first a two dimensional axisymmetric and then a full three dimensional step profile, formed with a protruding cylindrical heated surface co-axially placed within a simple cylindrical enclosure with constant heating from below and a fixed cold temperature on top. The main objectives were to characterize the effect of Rayleigh number variation by toggling different parameters and capture the effect on local and average heat transfer coefficients. The model based results would compliment the findings from the experiments conducted for the same boundary conditions and configuration. The goal of the three dimensional modelling was to capture the three-dimensional structure of velocity and temperature distribution around the annulus, to ensure no significant features were left out while conducting 2D axisymmetric simulations. In addition, the objective was to check its effect on local and average heat transfer coefficients between the heated surfaces and the cold wall sinks. The findings and contributions to the body of knowledge from this segment are covered in Chapters 6 and 7.

4.4 Experimental Setup and Validation This section covers a description of the preparation of test articles for the three experimental subcampaigns conducted to support the numerical solutions, as part of this thesis work. Several constraints on material selection

60 Figure 12: Thermal Conductance versus Horizontal Gap Thickness for Flat Gap with Constant Plate Temperatures and operating practice have to be taken into account to meet the low outgassing requirements while working with vacuum chambers and pumps. A summary of the diﬀerent measurement techniques used are presented, while the comparison of the generated results is covered in the next chapter. Steps for reconﬁguring a thermal vacuum chamber facility for enclosure driven heat transfer testing and associated operational challenges are covered.

4.4.1 Heater and Control Surface Design • Material Selection and Sizing: A total of 3 subcampaigns were carried out, the first two focusing on horizontal gas gaps and the third one on step profile gaps. Experimental components were either built from scratch or procured commercial off the shelf (COTS) to create a hori-

61 zontal and step profiled gas gap, for testing within a thermal vacuum chamber. The entire test setup had to fit in within the available working volume of the research group’s thermal vacuum chamber, i.e. a cylinder of 400 mm diameter and 600 mm length. Materials were constrained to those with low or acceptable outgassing properties (mainly total mass loss (TML) values and collected volatile condensable materials (CVCM) counts), as per NASA’s Outgassing Data Report [142] and discussions with the laboratory supervisor and staff. Aluminium 6060 and Stainless Steel 304 were the preferred metals used to fabricate sheets and shrouds for the tests, based on ease to procure, machine and mainly their low outgassing properties. A cylindrical gas gap was created between a constantly heated circular surface plate and a constant temperature cold plate directly above it, surrounded by a shroud to minimize any fluid influences from the plate edges. Heating methods and plate thicknesses were selected based on desired thermal mass and heating efficiency values (discussed in the following subsection). For the first and second set of tests, the heater surface plate was heated using a circuit of 40 1W rated ceramic heaters [143] placed within machined recesses on the underside of the heater plate. The heater plate was designed with dimensions of 375 mm diameter (to match the chamber’s cold plate temperature and coincidentally also replicate the plate surface area used in JPL’s gas gap tests for MSL [32]) and a thickness of 9 mm with 5 mm recesses to fit the ceramic heaters, which were clamped in place with a 2 mm stainless steel plate to ensure maximum heating efficiency into the Aluminium plate. Based on the learnings from the first two sets of tests, the third and final set of tests were conducted using two heater plates, heated with electrical heater tape [144]. The thermal vacuum chamber had an actively cooled plate attached on its baseplate, which was normally used to bolt spacecraft components on to, to conduct standard thermal cycling tests as part of environment testing. The setup was reconfigured to have the cold plate repositioned and attached to the lid of the thermal vacuum chamber, suspended above the heated surface, to simulate the constant temperature cold boundary condition. Galden HT-110 thermal fluid (-60◦C to +100 ◦C) was pumped in and circulated along a spiral scroll using a Huber Uni- stat 815w thermal control unit. The first two set of experiments used an aluminium 6060 sheet metal shroud (thickness defined by desired thermal mass value) 385 mm internal diameter and 400 mm length while the final experiment set used an additional smaller stainless steel (190 mm internal diameter and 300 mm length) to support the inner heater. Thermal conductive decoupling was maintained between shrouds and

62 surfaces using empty gaps and teﬂon spacers throughout the setup. Crumpled aluminium coated sheet blankets were wrapped around the aluminium shroud to minimize losses due to radiation. T-type thermocouples were positioned throughout the enclosure and on relevant surfaces using aluminium and Kapton tape. Vacuum compatible wiring was used to power the heaters.

• Heating Methods: Temperature variations across the heated surface were aimed to be kept within 4◦C to prevent thermal fluid influences caused by spatial non uniformity of heating in horizontal gap enclosures [133]. Since the thermal vacuum facility was a shared resource with another spacecraft testing group, it was important to efficiently utilize the available test time, placing a requirement to ensure quick temperature stabilizations and heat transfer balances for the gas gaps, in order to complete all the planned test objectives for the subcampaigns. This required the working surfaces, mainly the heated plates, to have a low enough thermal mass (component mass times the isobaric specific heat capacity) to allow quick heat up and cool down periods between tests but also high enough to ensure temperature fluctuations from the lab environment did not seep in to negatively affect the test objectives. However, since the laboratory did not have an actively controlled temperature environment, the tests had to be run for atleast 1.5-2 times longer at times to capture the daily temperature cycles. This was more significant for the non-vacuum cases, since the inside of the chamber was better coupled to the exterior (the lab environment). Times during mid-noon to late afternoon during spring and autumn months were blocked out to ensure the laboratory temperature variation was minimal, with the best achieved being within 2◦C per 3 hours window cycle. For most surfaces, diameters and lengths were defined by desired geometry configurations but the thicknesses were based on desired thermal mass values. Some initial finite element analysis simulations led to stability time predictions for heat up and cool down phases for vacuum cases for cylindrical enclosures. As a starting point based on available test time, a time criteria of 1 hour for heat up and cool down for tests with gas and 3 hour for heat up and cool down for tests in vacuum were selected to calculate desired thermal mass values. Desired plate surface temperatures T, initial temperature Ti, and gap temperature T∞ were set to arrive at required mass values based on Equation 17 below. Plate and shroud thicknesses were calculated from the derived component mass values. For the ceramic heater based heater, a plate thickness of 9 mm was defined as optimum to

63 achieve desired surface temperature uniformity and stabilized heating within 1 hour period. Tests conducted during the first subcampaign confirmed the acceptable performance of the heater surface. Desired temperature surface predictions from the FEA with variations within 3K were predicted for the derived plate thickness, as shown in Figure 13. Figure 14 reflects a close match between predicted and measured temperature-time curves for the vacuum case. The vacuum case was considered the ‘worse case scenario’ for determining the plate thickness as the cases with gas were expected to stabilize quicker and more uniformly, with the expected assistance from gas conduction and convection. To further reduce the temperature stabilization time and also number of components that would affect thermal contact resistance values in the subsequent modelling, a decision was made to switch to using heater tape for the step profile heater tests and conducted in the third subcampaign. Since this negated the need for recesses for optimum heat transfer to the working surface of the plate, plate thickness was reduced to 3 mm. This allowed faster temperature stabilization times and the heater tape performed satisfactorily to maintain spatial variation of temperature to be within 3 K. Comparison of these two heating mechanisms is covered in the next chapter. The required power input was calculated using Equation 20 for the derived component mass and specific heat values.

T − T∞ −hAt = e mCp (19) Ti − T∞

dT Q = −mC (20) out p dt

• Fabrication Process: Heater plates and a cover plate for the chamber’s cold plate (to cover the set of screw holes to ensure a smooth flat surface) were machined using a CNC Tormach machine by staff from the Technical Support Group (TSG) of the School of Engineering and In- formation Technology of the University. The shrouds were prepared by cutting to size and rolling 3 mm sheet metal pieces. The ends were riv- eted for the larger shroud and spot welded for the smaller one. Round- ness check was carried out with an objective to remain within 98% as a standard for rolling Aluminium and Stainless Steel metals. Ce- ramic heat resistors were procured from the Technical Support Group and arranged in series configuration in a quadrant formation around the heater plate as seen in Figure 15. Each of the quadrant could be

64 Figure 13: Screenshot from ANSYS Transient Heating Module (FEA) showing Heater Surface Temperature Predictions For Desired Plate Thickness

heated individually to enable partial heating of surface plates. Electri- cal heater tape rolls were procured from the Space Group Lab at the University and tested on sample aluminium pieces for their heating effi- ciencies (more on this in the next chapter). After meeting the required surface uniformity and temperature stability criteria, it was applied to the two heater surfaces (ring and inner heater) for the step profile tests. Figure 16 shows the tape layout and the ring heater propped in place on the thermal vacuum chamber during test installation. Rods made out of Delrin (material with very low thermal conductivity and low outgassing properties) were procured from the TSG and machined to prop up the ring heater for the step profile tests. 1 mm Teflon sheet material was procured from the Hypersonics Research Group of the School of Engineering and Information Technology and cut to size to use as spacers between the working surfaces to ensure thermal conductance decoupling.

• Low Outgassing Requirements and Constraints: Conductive and radiative heat transfer in vacuum environments asymptotically reduces to get aﬀected by vacuum pressures below 1e-3 mbar [142]. For all relevant purposes, the thermal vacuum chamber and its components were accordingly used to maintain a lower limit vacuum of one magnitude lower, i.e. 1e-4 mbar. Commonly used materials with low outgassing rates in vacuum were therefore chosen to build the test setups. Alu- minium 6060 and Stainless Steel 304 were used to fabricate the sur-

65 Figure 14: Temperature versus Time Comparison between FEA prediction and lab-based measurement for Vacuum Case for Heater Surface.

faces that enclosed the gaps. Initial plans of using an electric motor driven actuator system to vary the height of the gap were dropped as it turned out to be beyond the budget scope and time duration of the research project to procure vacuum compatible motors. Similarly, all other materials and connectors were selected after referring to NASA’s Outgassing Data Report and consultations with the Space Lab supervisor and staff. The low temperature maintenance requirements under near-vacuum or low pressure environment also had implications on the choice of working gas for the tests, Nitrogen was preferred over Carbon dioxide, given its stability at those temperature and pressures (Car- bon dioxide has been reported to freeze at temperatures lower than -70◦C [32,33]. Some initial CFD work indicated that using a substitute gas did not have a significant effect on the rate of heat transfer but

66 (a) Heater Plate with Ceramic (b) Stress Clamped with Sup- Resistor Layout porting Plate (Bottom Side Up)

Figure 15: Heater Plate with Ceramic Resistors

(a) Heater Tape Layout with (b) Inner heater and Ring Heater Teﬂon spacers taped with Kap- Surfaces Propped on Stands ton made of Delrin

Figure 16: Heater Plates with Electrical Heater Tape

displayed a slightly different velocity distribution pattern. The differences between the performance of the two gases for gas gap studies was limited to their similar heat transfer performance, any small-scale fluid movement variations did not immediately contribute to the set thesis objective and were left aside for future investigations.

• Test Article Preparation: The design dimensions were set within 0.2

67 mm tolerance criteria. Fabricated test articles were made to undergo a ﬁt check before test preparation. Gap clearances of 3 mm were placed between shroud and plate edges for the 1 mm Teﬂon sheet. Test articles were then cleaned with lint-free cloth using Isopropyl Alcohol (IPA) and then Acetone to remove dust, dirt, oil, pen marks while wearing rubber gloves. Thermocouples were also cleaned and attached using aluminium and kapton tape at required positions on the shrouds and plate surfaces. The test articles were then placed in an oven at 60◦C for 48 hours before installation to outgas water and any remaining contam- inants on them. Test installation plans were pre-planned and shared with test operators before beginning installation. Test articles were placed upon the chamber’s base plate and thermocouple and electrical heater connector ends were connected to data ports and checked for functionality.

4.4.2 Measurement Methods • Thermal Emissivity Measurement: To minimize heat transfer due to radiation, the working surfaces were hand polished and visually inspected to ensure a uniform surface finish and low thermal emissivity. Thermal emissivities of the plates and shroud surfaces were measured using the TIR 100-2 emissivity meter as shown in Figure 17. Instrument precision setting for ± 0.005 was noted while 9 measurements were made in a 3 by 3 matrix across the plate surfaces and 16 measurements in a 4 by 4 matrix were made for the shrouds. Once it was ascertained that the emissivity values for each surface were within a 0.1 variation, an arithmetic average of the numbers was taken to arrive at final values. These were input values for the CFD modelling of radiation conducted after the experiment testing. It is acknowledged that the measurements were done at 15◦C lab temperature, which is higher than some of the surface temperatures during the tests. Potentially, a small difference in emissivity is expected but still not significant enough for the temperature range of the planned experiments.

Table 6: Average Emissivity Values for Working Surfaces

Material Working Surface Thermal Emissivity Al 6060 Hot Plate 0.048 Al 6060 Cold Plate 0.079 SS 304 Shroud 0.035

68 Figure 17: Measuring thermal emissivity of plate surface using TIR 100-2.

• Temperature Measurement and Sensor Placement: Upto 40 Omega T- type thermocouples with limits of error of ± 1 ◦C were used to gather temperature data for the experiments. T type thermocouples were chosen given their favorable temperature range of -200 ◦C to +350 ◦C. However, the upper limits on the allowed temperature was set by the upper allowable limits of the acrylic adhesive of the aluminium tape used to attach them in place, while the lower limit by the Galden ﬂuid circulated within the cold plate. The thermocouples were taped to predecided positions on the working surfaces based on initial estimations of where the thermal history log would be relevant for subsequent ﬂow-temperature comparisons with the CFD solutions. Shroud ther-

69 mocouple positions were tested by trying three placements, i.e. on the shroud side surfaces facing the enclosure, on the external surfaces and ﬁnally positioning them to sit protruding 3 mm into the enclosure through the shroud. The results are discussed in the next chapter, the thermal mass of the shroud was shown to be low enough to allow for continuing to place the thermocouples on the shroud’s internal surface for the step proﬁle tests.

• Heat Transfer Coefficient and Nusselt Number Estimation: Heat transfer balance equation was set up to estimate the heat transfer coefficient and eventually the average Nusselt number for the system. Thermal conductivity values were measured for Aluminium 6060 (205.4 W/m-K) and Delrin stock (0.38 W/m-K) by measuring temperature gradients over fixed thicknesses. Electrical heat power and cold plate temperatures were fixed input values for the tests. From equation 20 and 21, the heat transfer coefficient ‘h’ and Nusselt number Nu were derived respectively for the various test cases. The conduction components were mainly from the heat lost via the thermal stand of the heater plate and the interface between the plate and the shroud. The radiation heat component comprised of a multisurface circuit with heat being exchanged between both surfaces of the plates, shrouds and the inner walls of the chamber wall.

Qheatinput = Qconductionlosses + Qconvection + Qradiation (21)

dT Q = (k ) +h(T −T )+σ(T 4 −T 4 ) input dx acrossconductionpaths hotplate coldplate source sink (22)

hL Nu = (23) k • Uncertainty in Measurement: Uncertainities in Heat transfer coeﬃcient and Nusselt number derivations are calculated based on their result functions ‘R’ which are a product of primary independent variables ‘x’ in their equations based on the product function relation expressed as [145]:

a1 a2 an R = x1 x2 ...xn (24)

70 Performing partial diﬀerentiation:

∂R a1 a2 ai−1 an = x1 x2 (aix1 )...xn (25) ∂xi Dividing the terms by R in equation 22 [145]:

1 ∂R a = i (26) R ∂xi xi

Uncertainty wR is calculated as [145]:

1 2 ∂R 2 ∂R 2 ∂R 2 wR = [( w1) + ( w2) + ... + ( wn) ] (27) ∂x1 ∂x2 ∂xn Inserting the relation in equation 24 in equation 25 [145]:

1 wR X aiwx 2 2 = [ ( i ) ] (28) R xi The additive terms are similarly expressed as [145]:

X R = a1x1 + a2x2 + ... + anxn = aixi (29) with the partial derivatives as [145]: ∂R = ai (30) ∂xi with the uncertainty expressed as [145]:

2 X ∂R 1 2 2 wr = [ [( )wxi ]] (31) ∂xi or X 1 2 2 wr = [ [aiwxi ]] (32) Individual parameter uncertainities were noted for thermal conductivities for aluminium, delrin, stainless steel; surface temperature, length measurements, surface emissivities, heater voltage and circuit current as ± 0.01 W/m-K, ± 0.00001 W/m-K, ± 0.01 W/m-K, ± 0.65 K, ± 0.0002 m, ± 0.005, ± 0.05 V and ± 0.001 A respectively. Accordingly, equations 26 and 30 were used to calculate the derived measurement uncertainty values for heat transfer coeﬃcient ‘h’ (± 0.00001W/m2-K), Nusselt number ‘Nu’ (± 0.001).

71 4.4.3 Setup: Thermal Vacuum Reconﬁguration

• Experimental Facility: The Multipurpose Space Science Exploration (MUS2E) facility located in the Space Research Laboratory at UNSW Canberra was used to conduct the planned experiments. MUS2E is a small scale thermal vacuum chamber configured within a vertically oriented cylindrical vessel, as shown in Figure 18. The internal diameter and height of the vacuum vessel are 415 mm and 400 mm respectively. This height can be increased using a cylindrical extension by 200 mm. A combination of a scroll (Edwards nXDS10i) and a turbo- molecular (Pfeiffer Adixen ATH500M-magnetically levitated) vacuum pump is employed to achieve an ultimate vacuum level of 1e-4 mbar. The confoiguration schematic of MUSE is presented in Figure 19. The pumping system is dry which eliminates the risk of oil/hydrocarbon contamination of the vacuum environment and any test article placed within. A Huber Unistat 815w thermal control unit is connected to a circular thermal plate (referred to as ‘cold plate’) within the chamber. Galden HT110 is used as the thermal fluid to allow for temperature control between -55 ◦C and 100 ◦C. The pressure within the vacuum chamber is measured using a Pfeiffer PKR251 vacuum gauge (Pirani and Cold Cathode measurement system) with a measurement range of 5 e-9 mbar to 1 bar. The pressure within the backing line of the turbo- molecular pump is measured using an InstruTech CVM211 convection vacuum gauge with a measurement range of 1.3e-4 mbar to 1.33 bar. The chamber is configured with a single dataport with connections for 40 thermocouples and a set of 1 USB-A, 2 DB9, 4 SMA and 3 DB25 electrical feedthroughs. Data acquisition and digital control of the equipment is carried out via a National Instruments NI c-DAQ (8 slots) system, consisting of three 16-channel NI-9214 thermocouple modules and one 8-channel NI-9178 digital output module. The computer interface is provided via a Python Graphic User Interface (GUI) which can alternatively be run via a Windows command terminal.

• Setting up Natural Convection Experiments: The default configuration of MUS2E consisted of the cold plate attached to the baseplate on which the chamber wall was placed. For the planned set of experiments, the cold plate was positioned to hang down, fixed to the chamber lid above the heater plates placed on the baseplate. Thermal fluid feedthroughs on the baseplate were blanked off and new connections and supporting bellows were fabricated by the Technical Support Group (TSG) for the required connections from the lid. The reconfigured system was

72 Figure 18: Multipurpose Space Science Exploration (MUS2E) facility at Space Research Laboratory, UNSW Canberra.

73 Figure 19: Multipurpose Space Science Exploration (MUS2E) Schematic

leak tested and recomissioned before any experimental testing was conducted. Nominal chamber vacuum pressure values of around 1 e-4 mbar were achieved as in the default configuration. Thermal fluid pressure setting and temperature control was also not affected by the chamber reconfiguration.

• Setup Constraints due to Laboratory Temperature and Gas Pressure Control: Since the experimental facility was not placed in a temperature controlled laboratory, the laboratory temperature was continuously logged over 60 second periods for the test duration using two Thermochron iButtons that were placed near the chamber, while away

74 from any fans or heat sources. This was done to monitor the effect of laboratory temperature diurnal cycling on the temperature stabilization rates of the test articles. The chamber was back-filled with Nitrogen gas which over a test duration period had a finite leak rate. The chamber pressure was continuously logged every 1 second to check the effect of this leak rate on temperature stabilization rates and to support subsequent CFD modelling. These constraints were identified during the test designing phase. The quantified impact of temperature and chamber pressure on the test objectives are covered in the next chapter.

4.4.4 Test Operations • Experimental Subcampaigns: A total of three experimental subcampaigns were planned and undertaken in the duration of this thesis in November 2015, July 2016 and October 2017. The first subcampaign was a proof of concept run, aimed at generating Thermal Conductance Measurements for a set of horizontal gas gap thicknesses for comparison and model validation with the JPL tests. Heat transfer measurements resulted in satisfactory agreement with CFD solution and results from literature [32, 141] with per case variation from compared values to be within 0.1 W/K, as shown in Figure 20. Heat transfer is seen to kick in around 70 mm - 80 mm gap thickness for our model and for JPL(Bhandari et al) study. This first subcampaign resulted in realistic time estimations for the entire phase: test article preparation, installation, operation and strip down. Lower than expected temperature stabilization rates for heater plate led to design modifications that were tested in the second subcampaign. A set of forty 5 mm recesses were made on the bottom side of the heater plate to improve thermal contact between the ceramic resistors and the plate. Thermocouple placement on the shroud was tested and compared by placing them externally and protruding through the shroud into the enclosure. The number of thermocouples placed on the shroud were increased from 4 in subcampaign 1 to 16 in subcampaign 2, to capture any variations along the tangential direction, which would not be observed in the two dimensional numerical studies. The final subcampaign was aimed to study the step profile enclosure geometry with two new heater plates, a new internal shroud. This was an elaborate test campaign aimed to study the effect of Rayleigh number variation by individually varying the cold plate temperature, gas pressure and gap thickness on the overall heat transfer within the enclosure. The findings from the last two

75 subcampaigns will be presented in the next chapter.

Figure 20: Thermal Conductance Values from Subcampaign 1 as compared to CFD and Literature

• Voltage Supply and Monitoring: An RSR Triple Linear DC Power Sup- ply Unit was used to supply power to the heater plates. Voltage input was monitored using a Uni-T True RMS Benchtop Multimeter. Voltage ﬂuctuations for the entire test duration were ensured to be within 1e-4 V.

• Condensation Monitoring: For test cases requiring cold plate temperatures to drop below 0◦C, it was important to monitor condensation and frost build up on the external surface of the thermal ﬂuid pipes and chamber walls, which were exposed to the warmer laboratory temperature. Upon subsequently driving the thermal ﬂuid temperature above

76 Figure 21: DC Power Supply Unit with RMS Benchtop Multimeter used to monitor voltage ﬂuctuations

0◦C, there was signiﬁcant risk of the melt water pooling around the chamber-base plate juntion and falling into the pumps. Such an event occured during the beginning of the third subcampaign, resulting in chamber contamination and water entering the turbo-molecular pump. Subsequently, the test was restarted, this time with foam insulation taped on the thermal ﬂuid pipes to prevent any condensation/frost build up and industrial sponges attached around the pipes to absorb any water. Frost build up and foam insulation around the pipes are shown in Figure 22. This is a serious concern and needs to be appropriately dealt with before conducting any long duration low temperature tests within a thermal vacuum facility.

• Laboratory Temperature Monitoring: Laboratory temperature was continuously monitored over the test duration using Thermochron iBut- tons with a 60 second sampling period and 0.1 ◦C precision, placed near

77 (a) Heavy Frost Build Up upon (b) Thermal Fluid Pipes insu- Running Thermal Fluid at -35◦C lated with Foam Material and for 24 hours Sponges

Figure 22: Prevention of Condensation and Frost buildup during Tests

the chamber, away from any exhausts or ducts. Movement of persons and opening and shutting of laboratory door was minimized to prevent unneccessary ﬂuid movement near the vacuum chamber.

• Temperature Stability Criteria: The desired temperature stability criteria was set based on conventional spacecraft thermal cycling standard adopted by Airbus team and NASA JPL of 0.5 ◦over 4 hour period [32,35].

• Operational Constraints: The first two subcampaigns were planned to be conducted in two week windows while the final subcampaign was conducted over a six week window. Test article preparation, chamber reconfiguration and strip down accounted for a week before and after the planned tests. The chamber operation guidelines required the pres- ence of a test operator during the tests. The role of the test operator was to assist in chamber reconfiguration, test article installation, system start up, operation of pump valves and general safekeeping of the facility.

• Data Archiving: Data generated during the test was first saved on the Laboratory computer accessed by the test operator and eventually stored on the shared cloud storage folder maintained by the Space group. Backup files were made on two separate external hard disks, a laptop and a work desktop. Eventually, the files were uploaded on UNSW Data Archive Facility.

78 4.4.5 Data Processing • Rayleigh Number Calculation: The calculation of Rayleigh number for the experiments was based on the length scale parameter (horizontal gas gap distance) and fluid properties for bulk fluid temperature and gas pressure, as determined from the NIST Chemistry WebBook maintained by the National Institute of Standards and Technology, U.S. Department of Commerce [146]. Final stabilized average temperature readings were logged and heat transfer balances were calculated based on equation 20. Heat transfer coefficients, thermal conductance and Nusselt number values were then generated for the different cases.

• Stabilized spatial and temporal temperature estimation: Both spatial and temporal variations in surface temperatures were logged and col- lated for the diﬀerent cases during the second and third subcampaigns. The ﬁndings from these are presented in the following chapter.

79 5 Measuring Onset and Formulation of Ther- mal Convection within Thermal Vacuum Chamber Setup

5.1 Research Gaps for Experimental Gas Gap Testing for Mars Rovers The main list of observations based on the review of work of previous and ongoing Mars thermal teams has been covered in Chapter 3 under section 3.2.4. For the beneﬁt of the reader, the main research gaps pertaining to the experimental investigations have been restated as below, based on which the solution strategy and test objectives were deﬁned, within the constraints of the test setup.

• Mars thermal management teams have investigated gas gaps for smooth and flat horizontal surfaces to simulate heat sources within Mars rover enclosures. The effect of corners formed by protruding profiles within the gas gap enclosure on the overall heat transfer and flow structure remains to be characterised.

• The eﬀect of temperature sensor positioning on the accurate temperature measurement and eventually the calculation of overall heat transfer within the gap has not been studied in detail.

• The thermal vacuum chamber by itself with gas inside is not a perfectly insulated closed system. Without it being located in a temperature controlled environment, the eﬀect of laboratory temperature on the gas gap temperature has not been discussed and reported.

• The prediction of the onset and formation of thermal ﬂuid movement within three dimensional gaps for low Rayleigh numbers within thermal vacuum chambers has not been studied and reported by the involved engineering groups.

5.2 Setup Limitations Conducting low Rayleigh number gas gap tests within thermal vacuum chambers involve a number of limitations, both with respect to measurement and operational capabilities. Over the years, most internal natural convection studies (both fundamental ﬂuid physics or application based) have been conducted using bespoke experimental setups, based on the speciﬁc objectives

80 of the tests. Most of these involved testing within clear tanks with thermally insulated walls, filled with liquids as working fluids. Thus, for fluids with higher densities, optics and interferometry based non-intrusive measurement techniques could be utilized to quantify velocity and density measurements. Since for 6-10 mbar fluid pressure cases for Mars, the low Rayleigh number regime requires conducting tests within a pressure vessel with active temperature control, all Mars rover teams are faced with the design and operating constraints of working in a thermal vacuum chamber. This ruled out the usage of several density based measurement techniques or made their inte- gration within the thermal vacuum configuration significantly complicated, requiring major overhauling of the chamber. Some of the main limitations that informed the design of test objectives for this thesis were:

• Since the gas gap tests were conducted within a closed opaque thermal vacuum chamber, the measurement capability was limited to surface and near surface temperatures and chamber pressure measurements. Non-intrusive flow measurement techniques were complicated, expensive to incorporate and left out by the teams. Measurements were mostly limited to surface temperature and chamber pressure, from which average Nusselt number was calculated without a complete understanding of the flow structure and temperature distribution within the gaps. Long term three dimensional effects of the gas on the surface temperature were not studied in-depth.

• Maintaining stable chamber pressures at gas temperatures below -50◦C for CO2 gas was signiﬁcantly cumbersome given the unstable phase state at those temperature and pressures. For this reason, N2 gas was used for the tests and scaling assumptions were executed to arrive at heat transfer estimations and overall analysis conclusions.

• The thermal vacuum chamber is not completely thermally insulated, located in a laboratory environment that does not have active temperature control. Hence, the eﬀect of the temperature changes in the laboratory on the gas gap temperatures remains to be studied.

• The thermal vacuum chamber is back-filled with gaseous N2 upto desired chamber pressures and is susceptible to leaks (ambient air leaking into the chamber). The effect of the leak rate on the final heat balance needs to be accounted for.

• For conducting gas gap tests within a thermal vacuum system, it is required to ensure that only low outgasing materials are used for the

81 tests and test article cleaning and bakeout is carried out before each installation and test run.

5.3 Solution Strategy Based on the observed research gaps in gas gap testing, a strategy was sought to investigate thermal fluid movement and assisted heat transfer within a relevant gap configuration within the constraints of standard thermal vacuum chamber facility. First, a simple horizontal gap cylindrical enclosure was prepared to test the effect of thermocouple placement on measured heat transfer (from a constantly heated flat surface into a cold plate directly above it) and log the spatial distribution of temperature around the central axis, as part of the first two experimental subcampaigns. The effects of ambient laboratory temperature and chamber leak on the effective heat transfer within the gas gap and the test objectives were quantified. The third subcampaign tested a step profile enclosure for the onset and stabilization of temperature while en- forcing a range of Rayleigh number regimes. The experimental results from these objectives are discussed below, while the supporting numerical work and flow structure related findings are covered in the next two chapters.

5.4 Effect of Shroud Thermocouple Configuration on Gas Gap Heat Transfer Analysis Heat transfer analysis for gas gap tests within thermal vacuum chambers is solely based on the plate and wall surface temperature measurements for provided heat into the gap, sinked by colder wall surfaces. It is critical to understand the effect of practical considerations such as alternative thermocouple configurations, ambient laboratory temperature and chamber leak rates on the surface temperature distributions and to quantify the influence (if any) on the final heat transfer analysis.

5.4.1 Test Objectives The main objective of this test was to compare shroud temperature measurements obtained by three alternative thermocouple configurations, i.e. Inter- nal Position (A), Through Position (B) and External Position (C) (described in the following subsection) and quantify the impact on the overall average heat transfer coefficient within the gap. Cold plate temperature, heat flux input and chamber pressure were the primary variables and hot plate temperature, shroud temperature were the measured variables. Average heat

82 transfer coefficient and final stabilized average shroud temperatures were defined as the required final data. Control ranges were set for heat flux input, cold plate temperature, chamber pressure setting, gas gap height (constant) and test phase duration time intervals. Based on the standard deviation from the mean for the measured temperature using each shroud thermocouple configuration, the influence would be concluded to be ‘Insignificant’ if within 1 standard deviation, ‘Minimal’ if within 1.5 standard deviation or ‘Significant’ if within 2 standard deviation, as per guidelines for temperature measurement technique comparisons defined in a standard experiment planning textbook [145]. The spatial and temporal distribution of the shroud temperature would shed light on any asymmetricity in the temperature distribution around the shroud. The average heat transfer coefficient values for the gap are calculated and compared by deriving their standard deviation from the arithmetic mean value. A description of this novel measurement technique is given to enable ongoing and future Mars rover teams to further the understanding of thermocouple placement and to help investigate the onset and stabilization of low Rayleigh number regime fluid movement based on shroud temperature spatial and temporal distributions.

5.4.2 Setup Description The experiment was conducted in the second subcampaign, as described in section 4.4.4 and illustrated in Figure 23. The setup consists of a gas gap created by a constantly heated plate, an overhanging temperature controlled plate and a surrounding shroud installed within the MUS2E facility. A fixed electrical heat input of 5 W±1% is provided to the ceramic resistor heater plate resulting in a constant 40 W/m2 on the gap facing surface (representative of typical RAMP segment heat flux values [32]). The cold plate is maintained at a Mars relevant ambient average summer time evening temperature of 250 K [147]. The gap height between the two plates was set to 12 mm ±0.001%. The chamber is back-filled with N2 gas at 10 mbar±10%. A total of 28 Type T thermocouples are used, with 4 each on the plates and 12 on the shroud. The shroud thermocouple locations are configured in 4 junctions around the shroud, labelled 0.25, 0.5, 0.75 and 1.0, as illustrated in Figure 24. At each junction leveled midheight between the two plates, three thermocouples are configured to ‘internal’, ‘through’ and ‘external’ settings as illustrated in Figure 25. The ‘internal’ and ‘external’ configurations involve using Kapton and Aluminium tape to fix the thermocouples on either side of the shroud (internal configuration facing into the gap). The ‘through’ configuration involved first attaching a vacuum compatible heat shrink onto the thermocouple joint end with only the bi-metal Copper/Constantan tip

83 exposed by about 3-5 mm. Four 1.6 mm through holes were drilled at the junction locations and EC-2216 B/A (Vacuum rated thermal epoxy adhesive [148]) was used to fix the heat shrunk points to the shroud to hold the thermocouple ends in place, with the bimetal joints probing in 2-3mm from the shroud internal surface, into the gap. The adhesive was allowed to cure over 24 hour before being cleaned and baked out for the testing. Before tests, each set of thermocouples were calibrated and measurement differences within 0.65 K were digitally recorded to ensure no measurement discrepancy creeped into the results. A total of 4 tests were run to check for data repro- ducibility and ‘end-of-test’ for each case was dictated by heater plate surface temperature stabilization rates (averaged over 10 minute windows) of within 0.5◦C over 4 hour periods, as used in NASA and Airbus Mars Rover Thermal Gas Gap tests [32, 35]. The 4 tests took 1 hour, 1.25 hours, 1.3 hours and 1 hour to reach the prescribed stability after which the experiment was conducted for a 5 hour test period. Laboratory temperature was measured with a thermocouple attached to the chamber’s baseplate exposed and thermally coupled with the laboratory ambient environment. Measurement uncertainty for temperature measurements, voltage input and chamber pressure were defined as per Equations 26 and 30 (section 4.4.2) for heat balance equations 20 (section 4.4.2).

Figure 23: Experimental Setup for SubCampaign 1 and 2

84 Figure 24: Top View of Shroud Showing Thermocouple Junctions 1 to 4 for SubCampaign 1 and 2

Figure 25: Comparison of Heat Transfer Analysis for Three Diﬀerent Shroud Thermocouple Conﬁgurations (Type B protrudes 2-3 mm into the gap)

5.4.3 Findings

The main ﬁndings were:

85 • Time taken to achieve the temperature stabilization criteria (as defined in Section 5.4.2) for each of the 4 test cases was approximately 1.15 hours, slightly longer than that achieved for vacuum based experiments in the previous subcampaign (as illustrated in Figure 14 in Sec- tion 4.4.1). Though slightly counter-intuitive as one would expect the gas to expedite heater surface cooling, but as was later seen during the numerical work (discussed and reported in the next chapter) the fluid disturbance would instigate temperature variations on the heater and shroud surfaces thereby delaying temperature stabilization by about 30 minutes. In addition, a stronger coupling with the laboratory’s cycling thermal environment (via the gas in the chamber) lead to longer stabilization times. This resulted in improving thermal insulation between gas gap and the chamber, with the tests being conducted at a time during the day when the laboratory temperature shift was minimal. Subsequent laboratory temperature measurements during the experiment duration recorded less than 2K ±0.65K variation (as illustrated in Figure 26(a)), an ideal scenario with minimized effect of ambient temperature dirunal cycling on the gas gap temperature measurements. Thus an estimation of test time durations was achieved which would be helpful for ongoing and future testing, in the absence of accurate FEA models (with realistic convection and enclosure radiation models) for gas gaps.

• Temperature measurements from the three thermocouple configurations were compared by calculating the standard deviation from the arithmetic mean of the finalized stable temperatures for 600 second periods after 2 hour, 3 hour, 4 hour and 5 hour marks over the experiment duration. As illustrated in Figure 26 (b), the standard deviation values were consistently within 0.5 for all the junctions around the shroud, throughout the test duration. This indicated that the thermocouple configuration had insignificant impact on the measured temperatures. The low thermal mass of the aluminium shroud on which the thermocouples were configured is attributed to such close temperature measurements made by all the three configurations. The average heat transfer coefficient was calculated from Equation 20 (Section 4.4.2) based on shroud temperature measurements from each configuration and the standard deviation of the set of three values was plotted over the experiment duration, illustrated in Figure 26 (c). The difference in the calculated values was shown to be within a standard deviation value of 0.006 K, with the variance dropping after about 3 hours into the test. The overall average heat transfer coefficient value

86 was estimated to be 1.103±0.47% W/m2-K. • The finalised stable temperature distributions for 600 second periods for the three thermocouple configurations around the shroud were plotted at t=2 hour, 3 hour, 4 hour and 5 hour intervals, as illustrated in Figure 27. These spatial temperature distributions reveal a shift in the temperature distribution over time. These were validated from three independent temperature measurements at each junction and were consistently shown in all the four test case runs. The magnitude and time duration of the temperature shift varied although by a small amount, chaotically for all the four cases. However, the temperature magnitudes were significant enough to indicate that an asymmetric temperature distribution existed around the shroud over the test duration. The temperature difference was consistent between 4K to 6K and could be seen to shift between diametrically opposite junctions (e.g. 1 and 3, 2 and 4) to adjacent junctions (e.g. 1 and 2, 2 and 3) quite erratically for the different test periods. Such an asymmetricity was not recorded while running the tests under vacuum. This hints towards the action of the gas on the internal temperatures to vary over time. This was consistent with reports of fluid rotation over similar test time periods for horizontal cylindrical gaps reported, although for higher Ra flow numbers [86, 103, 106]. Although unlike the reported observations, the direction of rotation was not constant and changed aperiodically after random full or semi cycles around the enclosure. Another observation was the difference in measured temperature values for the three configuration were always consistent in that the external thermocouple logged a value (insignificant albeit a non zero amount) higher than the through-hole and internal thermocouples. This was attributed to direct radiative effect of the internal surfaces exposed to the heated surface.

5.4.4 Inferences The inferences made from the reported findings and results are as under: • Heat transfer estimates for gas gaps heavily rely on final stabilized surface temperature measurements which depend on several parameters driven by each setup and laboratory environment (unless the gas gap system is completely thermally isolated from the ambient, which for vacuum chamber experiments is almost never the case). The laboratory temperature variation (within 2K ±0.65K) on the test objectives (which aimed to realize the difference in heat transfer estimates between three thermocouple configurations and to find the asymmetry

87 (a) Average Shroud Temperature (b) Standard Deviation of Variations Across the 4 Junc- Shroud Temperature Readings tions over the Experiment Dura- from Three Conﬁgurations over tion the Experiment Duration

(c) Standard Deviation of Aver- age Heat Transfer Calculations for Temperature measurements from three conﬁgurations over Experiment Duration

Figure 26: Variation of Average Shroud Temperature, Standard Deviations of Shroud Temperature and Heat Transfer Coeﬃcient Standard Deviation plotted over the Experiment Duration.

88 (a) Average Shroud Temperature (b) Average Shroud Tempera- for different Thermocouple Con- ture for different Thermocou- figurations around the Shroud at ple Configurations around the T=2 hours Shroud at T=3 hours

(c) Average Shroud Temperature (d) Average Shroud Tempera- for different Thermocouple Con- ture for different Thermocou- figurations around the Shroud at ple Configurations around the T=4 hours Shroud at T=5 hours

Figure 27: Average Shroud Temperature for diﬀerent Thermocouple Conﬁg- urations around the Shroud.

89 in temperature distribution within the gap) was found to be minimal. Temperature stabilization took a few minutes longer than the stabilization during vacuum based tests, indicating initial ﬂuid disturbances delaying heater surface temperature stability and coupling with the external environment via the gas in the chamber.

• Thermocouple mounting configuration was found to have an insignificant impact on the measured average shroud surface temperatures and the calculated heat transfer coefficient values for given thermal mass value of the shroud. Higher thermal mass based shroud surfaces could potentially lead to minimal or significant estimate differences. This kind of sensor configuration based heat transfer analysis comparison has not been reported so far and is useful for Mars rover teams with several options for measuring temperature and heat transfer for gaps within thermal vacuum chamber setups. Thermocouple configuration ‘A’ (internal configuration) was adopted (for ease of installation and test assembly) for the following tests conducted as part of the third subcampaign.

• A temperature shift of 4-6K was recorded around the shroud over the test duration of 5 hours indicating an asymmetric temperature distribution. Such asymmetry was not recorded for the vacuum cases and therefore was attributed to gas-assisted heat transfer. The distribution shift was erratic for the 4 test runs and although not immediately useful information for thermal design engineers (as overall heat transfer coefficient values were not affected), compliments the findings for fundamental investigations of horizontal cylindrical enclosures for low Rayleigh number regimes.

5.5 Fluid-Induced Temperature Fluctuations The first and second subcampaigns helped achieve accurate heat transfer estimates (thermal conductance estimates, heat transfer coefficient values), qualitative fluid-temperature interactions based on asymmetric temperature shifts over time for a simple horizontal gap configuration with relevant boundary conditions for Mars case systems. The next step was to study a relevant configuration problem that would influence heat transfer and flow structures within a gas gap. A step profile cylindrical enclosure setup was configured for tests in the third and final subcampaign. The main objective of this subcampaign was to study the effect of varying several parameters to change the Rayleigh number and quantify the change in heat transfer coefficients

90 and flow structure. This is discussed in the next two chapters. However, an interesting observation of temperature fluctuations on the inner heater plate was observed during the tests and is reported here. The fluctuations were not reported on any other plate or shroud surfaces. The magnitude of fluctuations were within temperature measurement uncertainities thereby not allowing robust inferences. However, they were periodic and consistently observed upon test repetition for a particular set of test cases. A list of factors potentially causing these fluctuations was made and were individually isolated to check for the source. These factors were the DC voltage supply, thermal control unit for circulating Galden fluid, scroll pump, ring heater power and laboratory ambient temperature. Since the fluctuations were of an insignificant magnitude and did not indicate to have strong characteristic frequencies based on conducted Fourier analysis, no indications on heat transfer could be inferred. However, given the highly limited amount of published literature on low Rayleigh number step profile based gas gap configurations, these observations are documented for further investigation by a future study.

5.5.1 Test Objectives The main objective for this test was to record temperature fluctuations by plotting time series distribution of temperature data for finalized average heater plate surface temperatures for three different gap aspect ratios. Po- tential sources of the fluctuations were identified. Source of fluctuation was to be established.

5.5.2 Setup Description Some of the test articles and operation procedure were changed based on the learnings from the previous steps and the test objectives for this subcampaign. The circular heater plate was replaced with a thinner (3 mm) ring heater (of identical external diameter) and a 3mm inner disc heater (with similar external diameter as the the diﬀerence between external and internal diameters of the ring). A new heating method (as described in Section 4.4.1) using electrical heating tape was used to heat the two heater surfaces. This allowed for faster heat transfer stabilization rates and also reduced the number of components and thermal contact conductance to be accounted for during Finite Element Analysis (FEA) for the same. The setup has been illustrated in Figure 28. Teﬂon spacers were used to decouple the thermal conductance between plates and shrouds, shrouds and chamber baseplate. The heater circuits on both the heater plates could be controlled independently. The

91 inner disc was placed on a new inner shroud placed within the hollow of the ring heater. The height between the inner disc heater plate and the thermal (cold) plate was kept constant while the height between ring heater and thermal plate was varied to arrive at a set of three aspect ratios. Tests were conducted for four cold plate constant temperatures (-240.15 K, 260.15 K, 280.15 K and 300.15 K), four gas chamber pressures (10 mbar, 30 mbar, 60 mbar and 100 mbar), and three diﬀerent aspect ratios (gap height between ring heater plate and thermal plate varied by 160 mm (Aspect Ratio 1), 210 mm (Aspect Ratio 2) and 260 mm (Aspect Ratio 3)). Electrical power was supplied independently to the ring heater upto 25% max test ratings to keep the upper temperature limit on the heater surfaces within 400 K (which was the upper temperature range for the adhesive on the Aluminium tape used to ﬁx the thermocouples). The power settings for the ring heater and disc heater were 9.107 W and 2.94 W respectively. Temperature stabilization and operation procedure was identical as for previous two subcampaigns.

Figure 28: Experimental Setup for SubCampaign 3

5.5.3 Findings The following are the main ﬁndings from this study:

• Tests conducted for all the three aspect ratios did not show any temperature ﬂuctuations until testing was carried out for cold plate temperature of 300.15 K and chamber pressure of 60 mbar and above. Also

92 they only set in once the temperatures and heat transfer balances were allowed to stabilize after about 2 hours from start of test. A change in laboratory temperature by over 1 K per hour upset the fluctuations, which then seemed to step in once the laboratory temperature settled within less than a change of 1 K per hour. For higher than 100 mbar, the fluctuations lost their periodicity and became erratic. Amplitudes of the fluctuations were within 0.2 K - 0.4 K, well within the calculated measurement uncertainity of 0.65 K for the used Type T thermocouples. This is illustrated in Figure 29. The period of oscillation was estimated to be about 100 seconds per cycle for AR 1 and 3 cases. AR 2, a longer temperature cylce of 220 s was recorded. • Aspect Ratio 3 recorded similar fluctuation amplitude and frequency as for Aspect Ratio 1 as seen in Figure 30 (a). A list of potential sources of the temperature fluctuations was made. The list included DC voltage supply, thermal control unit for circulating Galden fluid, scroll pump, ring heater power and laboratory ambient temperature. One by one, each of these potential sources was isolated and the temperature over the inner disc plate was monitored. Out of all these, only upon switching off the ring heater did the temperature fluctuations seem to die out. The ring heater was switched off after 6800 seconds from ‘beginning of test’ and the temperature fluctuations died out at 7030 s. This is illustrated in Figure 30 (b) and (c). Fourier Function Transform Analysis did not seem to indicate any strong amplitude peaks over a range of frequencies, indicating that the fluctuations seem to cancel themselves out. Since the fluctuations were well within the measurement uncertainity window, further analysis was held off as beyond the scope of the carried out work. But it was important to point out that the initial suspects (mainly the scroll pump, temperature control unit or the voltage supply) were not leading them to occur). A possible electrical interference caused due to the heater tape circuitry within the ring heater could be the cause for this interference. The fact that the fluctuations were not recorded on the shroud or other surfaces hinted that they were not flow induced, being localised to the inner heater plate.

5.6 Chapter Summary The observations, procedures and inferences from the conducted experiments during the three subcampaigns have been presented in this chapter. A description of the two experimental setups in subcampaigns 1-2 and 3 are presented along with thermocouple conﬁguration preparation for the beneﬁt of

93 (a) Time series plot for average (b) Time series plot for average heater plate temperature (over heater plate temperature (over last 10 minutes) at T=2 hours for last 10 minutes) at T=2 hours for aspect ratio 1 aspect ratio 2

Figure 29: Temperature Fluctuations for Aspect Ratio 1 and 2 the experimenter of gas gap tests within thermal vacuum facilities. A comparison of the temperature measurements made by three different thermocouple configurations is shown to have an insignificant effect on heat transfer analysis estimation. Temperature asymmetry is shown for three dimensional gas gaps which are not reported for most two dimensional numerical or three dimensional cartesian geometry configuration studies. Minor temperature fluctuations are reported for particular cold plate temperature and chamber pressure conditions and the source of the fluctuations is derived to be one of the heater configurations. Although the fluctuations are well within the measurement uncertainity of the Type T thermocouple, the observed con- sistencies and periodicity of the fluctuations are reported which could be relevant to a future study focused on these micro-instabilities of temperature. The next two chapters shall discuss the main findings of subcampaign 3 with supporting numerical work focusing on velocity and temperature flow structures and three dimensional fluid distributions for variations of Ralyeigh number based on toggling cold plate temperature, gas pressure, configuration tilt, ring heater ON/OFF and gap aspect ratio.

94 (a) Average heater plate temper- (b) Complete time history for as- ature (over 10 minutes) at T=2 pect ratio 3 with oscillation ter- hour for aspect ratio 3 mination encircled

Figure 30: Temperature ﬂuctuations with oscillation termination upon switching oﬀ ring heater power.

95 6 Heat Transfer around Step Proﬁle for Low- Medium Rayleigh number Flow Regimes

Based on the findings from the literature review, a summary of which is reported in Chapter 3 (3.3), a combined experimental-numerical investigation of cylindrical step profile enclosure for Mars rover gas gap-relevant boundary and operating conditions was carried out. Experiments conducted in the third experimental subcampaign are supported with two dimensional axisymmetric and three dimensional numerical solutions that cover heat transfer coefficient and Nusselt number calculations across the gas gaps along with temperature and velocity distributions. The main objective, as described in 4.3.6, is to study the variation of the Rayleigh number of the flow within the enclosure by adjusting different variable parameters and investigating three dimensional flow distributions around the annulus and check for any influence on the local and average heat transfer coefficients. Since the study was aimed to contribute both towards applied research (heat transfer correlations for Mars rover gas gaps) as well as to fundamental fluid physics (provide quantitative and qualitative solutions to natural convection problems for step profile in low-medium Rayleigh flow regimes), the parameters to vary the Rayleigh number were a combination of realistic design control input parameters for Mars rover gas gap design (cold plate temperature, heating ratio, enclosure tilt) as well as physical boundary condition varying parameters (gas pressure, gap aspect ratio). The latter of the two sets might not vary during rover operations but the investigation would contribute to a fundamental investigation of the problem, perhaps directly useful to future applications with the same or similar geometries and boundary conditions. The control ranges for these variable parameters were defined individually based on rover design, operation and laboratory test constraints. The descriptions for each of these are presented in the following subsections as they are examined individually. Each test case for the variable parameter is introduced, the impact on non-dimensional temperature, local and average Nusselt numbers is discussed along the width of the gaps and over the corresponding Rayleigh number range. The deviation of the numerical solution for heat transfer variation from experimental measurements is presented as a percentage difference and the reasons for this are discussed. A brief description of the velocity and isotherm contours adds to the understanding of the effect of the parameter variation. The overall implications on heat transfer balances for Mars rover gas gaps is brought out for each test parameter. We refer to the experimental setup illustrated in Figure 28 in Chapter 5 (5.5.3) while describing the variable parameters

96 within the configuration. Therml conduction is minimised between the inner and outer shroud surfaces to ensure minimal conductive heat transfer. The heater plates are heated with constant power based on 25% maximum power setting (this was deduced based on the generated maximum allowable heater surface temperature, 140◦C which the aluminium tape adhesive holding down the thermocouples could withstand before evaporating). The heat flux ratio of 1:2 between the inner heater plate and ring heater plate was a fixed value throughout the subcampaign of tests, in proportion to their surface areas. Due to time limitations, the influence of heat flux ratio as a variable parameter on the heat transfer is not covered in this thesis and should be a part of the continuation of this work. For description purposes, the gap between the ring heater and cold plate is referred to as the ‘tall gap’ and between inner heater plate and cold plate as ‘short gap’. For all the cases within the subcampaign, the short gap was fixed to a constant value, while the tall gap was varied to give 3 different aspect ratios. Since it is assumed that the heat transfer properties will be axisymmetrically distributed, the results are plotted and contoured for half of the width of the cut section of the geometry, i.e. a radius length measured from one end of the outer shroud to the centre annulus axis (as was illustrated earlier in Figure 4 in Chapter 4 (4.2.2)) to help draw comparisons between temperature, heat transfer and velocity variations between the short and tall gaps. To help interprete the results, Figure 31 illustrates the geometry domain sized for the enclosure half width equalling the cylindrical volume’s radius R. The gap heights are denoted h1 and h2 for short and tall gaps respectively while h is the heat transfer coefficient (W/m-K). As per standard practice for natural convection problems, the bulk fluid temperature and the line aver aged output parameters are measured at the defined mean depths for the two gap heights. Dimensionless temperature θ (non-dimensionalised by bulk fluid temperature), average heat transfer coefficient h¯ and average Nusselt number Nu¯ are calculated across the individual widths (0.5 R) of each gap.

6.1 Effect of Cold Plate Temperature The overhanging flat plate is maintained at a constant temperature, cooler than the heated inner and ring plate surfaces. This overhanging plate represents the heat sink within the closed internal convection system, also for our case the rover wall is a surface thermally coupled with the external Mars ambient temperatures. Natural internal convection within enclosures has been seen to change variably for different cold plate temperatures and cannot be assigned to set temperature difference values between the cold and hot surfaces [32,35]. To cover the range of possible ambient Mars temperatures that

97 (a) Geometry Domain with Position and Parameter Deﬁnition

(b) Tilt angle θ location (around z axis normal to plane) and speciﬁcation.

Figure 31: Non-dimensionalised Bulk Fluid Temperature Across Enclosure Half Width for Diﬀerent Cold Plate Temperatures.(Note h1,h2 are length units while h is heat transfer coeﬃcient)

98 a rover could potentially be exposed to and staying above the lower operational temperature limit for our experiment chamber (i.e. -40◦C is the lower limit of Galden ﬂuid used to actively control cold plate temperature), four ◦ ◦ ◦ speciﬁc cold plate temperatures (Tc) are tested for, -35 C, -15 C, 5 C and 25◦C.

6.1.1 Findings Since the bulk fluid temperature distribution across the heater surface is driven by the temperature difference between the heater plate and cold plate, it is calculated across a line equidistant from both the plates at the gap mid- heights for each of the gaps (as illustrated in Figure 31) and was plotted (Figure 32) as the dimensionless quantity θ (difference between measured temperature and cold plate temperature, normalized by the temperature gradient between the heater and cold plate) for the four different cold plate temperatures for the three different aspect ratios: AR1 (2.67), AR2 (3.5) and AR3 (4.33) based on tall gap height (160 mm, 210 mm and 260 mm) to short gap height (60 mm). Higher bulk fluid temperatures were measured for higher cold plate temperatures. The temperature peak seemed to be larger and more distinct at the interface zone between the two gaps for AR3, especially at lower cold plate temperatures. The increment of temperatures in the bulk fluid seemed to increase a lot more gradually as the gap aspect ratio was increased. This could be explained given the marginally reducing effect of increasing the tall gap aspect ratio on the cold plate influence on bulk fluid temperatures. The local Nusselt number calculations (Figure 33), averaged at mid-height also showed larger values for higher cold plate temperatures. These values were also higher within the tall gap as compared to short gap for each case by as much as 2.5 times and as little as 1.3 times. The average Nusselt number for the average Rayleigh number (calculated individually for short and tall gaps, with the gap height as the characteristic length parameter) indicated that even though the lower cold plate temperature cases had a higher temperature gradient, the thermal expansion coefficient values were lower which led to a lower Rayleigh number value, as compared to the higher cold plate temperature cases. This was counter-intuitive initially but later understood when a significantly consistent trend of dropping Nusselt number with increasing Rayleigh number was derived from the temperature readings taken during the experiments. Both for short and tall gaps, the colder plate temperature cases showed lower heat transfers due to the gas as compared to the higher cold plate temperature cases. This was expected since the thermal conductivity of the gas was higher by 17% for the higher bulk fluid temperature. In addition, it could be concluded that the impact of the bulk fluid

99 density on the gap was seen to be significant and overpowering than individual surface temperature differences between hot and cold plate. Higher rates of convective heat transfer in the numerical model were attributed to higher levels of heat lost through the gas in the CFD solver due to under-prediction of radiation heat input from the surfaces using the Surface to Surface (S2S) model for enclosures. In addition, despite accounting for expected conductive and radiative losses, the experimental cases showed on an average 8% lower heat dissipation from the heater plates, as compared to the numerical solution. Therefore, the difference between experimental and numerical calculations for heat transfer are a combination of higher than measured experimental heat losses and underprediction of radiation heat input into the gap in the numerical solution. The radiation underprediction by 96.9% (listed in Table 7) is expected due to two possible reasons. Currently, the solver only allows the user to define single emissivity values per boundary surface, whereas emissivity measurements taken of the working surfaces for the experiments showed variation of 20% to 50% of surface averaged mean values across the surface. The variation due to measurement repeatability was within 5%-10%, therefore an actual physical variation across the surface was measured but could not be defined accurately in the numerical model. Secondly, S2S model efficiency for unstable heat transfer problems has been reported to calculate lower than expected radiation contribution numbers [149]. The radiation contribution estimations for higher Rayleigh number cases involving stronger convection currents and enhanced flow instability were even lower than those for low Rayleigh number cases. Total heat input was calculated for experiments based on the heater resistance per unit length of the heater tape. Conduction losses were estimated through the thermal contact surfaces with the heater plate-thermal leg and the heater plate-shroud interface. Radiation losses from the external surfaces (facing the chamber walls and chamber baseplate) were approximated to 20% of the overall radiation heat transfer within the gap enclosure, calculated from initial vacuum based FEA transient heating solutions for the configuration enclosed within the chamber volume. For the CFD, this derived total heat input value was defined as a boundary condition and conduction paths were set, again based on the realistic values estimated from the experiments. As a reference, the heat power input per heat transfer mode is illustrated for one case (Aspect Ratio 1, Cold Plate Temperature -35◦C) in Table 7. The solver was then run to give the balance combination of convection and radiation. The model predicts higher heat transfer rate due to natural convection by 11.9%. Therefore, for all the cases, it was seen that more heat was available for gas-assisted loss in CFD as compared to the actual case as seen in the experiments. In other words, higher than expected heat losses reduced the

100 heat dissipation from the heater plates in the experiments. The summary of average Nusselt number Nu¯ calculations for the experiments and the CFD and the percentage difference between these are presented for the short and tall gap in Tables 8 and 9. Thus, it was seen that the difference in values between experiments and CFD was higher for cases with higher Rayleigh number as the solver underpredicted the radiation components. An overpre- diction of heat transfer due to convection by 11.9% brought about a 3.11% higher numerical prediction of the average Nusselt number for the short gap and a 7.8% higher prediction of the same for the tall gap. Studying the isotherm contours illustrated in Figures 36 to 38 helps us understand the temperature distribution within the gap. Two distinct plumes are recorded over each of the representative heater surfaces. The contour lines were closer packed for higher cold plate temperature cases, indicating a stronger density gradient as compared to the lower cold plate temperature cases. The velocity contours (Figure 39) showed as the fluid flowed from the ring heater gap upwards across the interface point, reached the cold plate wall and dropped back down the outer shroud wall, a single cell was formed at the interface point. Formation of other slightly weaker cells are seen closer to the cold plate and outer shroud. The main inferences from these findings will be presented in the next subsection.

6.1.2 Inferences The main inferences drawn for study of eﬀect of cold plate temperature on natural convection heat transfer for step proﬁle and low-medium Ra are as under:

• Higher cold plate temperatures lead to warming of the bulk fluid temperatures, with this increase being more gradual for higher aspect ratio enclosures. This is an expected finding since the larger gap enhances the heat inflow from the lower plate.

• A higher rate of convection heat transfer was recorded for higher cold plate temperatures with larger Nusselt numbers logged for all aspect ratio cases. This was attributed to higher thermal conductivity for the warmer gas, which had a stronger eﬀect than the temperature gradient between the heater and cold plate. Thus the average Nusselt number decreased due to lower thermal conductivity (linked with lower cold plate temperature) having a stronger impact on the heat transfer even though the Rayleigh number increased due to a larger plate temperature diﬀerence.

101 (a) Non-dimensionalised Bulk (b) Non-dimensionalised Bulk Fluid Temperature Across En- Fluid Temperature Across En- closure Half-Width for Aspect closure Half-Width for Aspect Ratio 1 Ratio 2

Figure 32: Bulk Fluid Temperature (normalised by heater-cold plate temperature diﬀerence) Across Enclosure Half Width for Diﬀerent Cold Plate Temperatures.

102 (a) Local Nusselt Number Across (b) Local Nusselt Number Across Enclosure Half-Width for Aspect Enclosure Half-Width for Aspect Ratio 1 Ratio 2

Figure 33: Local Nusselt Number Across Enclosure Half-Width for Diﬀerent Cold Plate Temperatures

103 (a) Average Nusselt Number v/s (b) Average Nusselt Number v/s Average Rayleigh Number for Average Rayleigh Number for Short Gap for Aspect Ratio 1 Short Gap for Aspect Ratio 2

Figure 34: Average Nusselt Number v/s Average Rayleigh Number for Short Gap (varied by Cold Plate Temperature)

104 (a) Average Nusselt Number v/s (b) Average Nusselt Number v/s Average Rayleigh Number for Average Rayleigh Number for Tall Gap for Aspect Ratio 1 Tall Gap for Aspect Ratio 2

Figure 35: Average Nusselt Number v/s Average Rayleigh Number for Tall Gap (varied by Cold Plate Temperature).

105 (a) Isotherm Contours for Aspect Ratio 1, Tc = -35◦C

(b) Isotherm Contours for Aspect Ratio 1, Tc = -15◦C

106 (c) Isotherm Contours for Aspect Ratio 1, Tc = 5◦C

(d) Isotherm Contours for Aspect Ratio 1, Tc = 25◦C

Figure 36: Isotherm Contours for Aspect Ratio 1 for Set of Cold Plate Tem- peratures

107 (a) Isotherm Contours for Aspect Ratio 2, Tc = -35◦C

(b) Isotherm Contours for Aspect Ratio 2, Tc = -15◦C

108 (c) Isotherm Contours for Aspect Ratio 2, Tc = 5◦C

(d) Isotherm Contours for Aspect Ratio 2, Tc = 25◦C

Figure 37: Isotherm Contours for Aspect Ratio 2 for Set of Cold Plate Tem- peratures.

109 (a) Isotherm Contours for Aspect Ratio 3, Tc = -35◦C

(b) Isotherm Contours for Aspect Ratio 3, Tc = -15◦C

110 (c) Isotherm Contours for Aspect Ratio 3, Tc = 5◦C

(d) Isotherm Contours for Aspect Ratio 3, Tc = 25◦C

Figure 38: Isotherm Contours for Aspect Ratio 3 for Set of Cold Plate Tem- peratures.

111 (a) Velocity Contours for Aspect Ratio 1, Tc = -35◦C

(b) Velocity Contours for Aspect Ratio 1, Tc = -15◦C

112 (c) Velocity Contours for Aspect Ratio 1, Tc = 5◦C

(d) Velocity Contours for Aspect Ratio 1, Tc = 25◦C

Figure 39: Velocity Contours for Aspect Ratio 1 for Set of Cold Plate Tem- peratures.

113 (a) Velocity Contours for Aspect Ratio 2, Tc = -35◦C

(b) Velocity Contours for Aspect Ratio 2, Tc = -15◦C

114 (c) Velocity Contours for Aspect Ratio 2, Tc = 5◦C

(d) Velocity Contours for Aspect Ratio 2, Tc = 25◦C

Figure 40: Velocity Contours for Aspect Ratio 2 for Set of Cold Plate Tem- peratures.

115 (a) Velocity Contours for Aspect Ratio 3, Tc = -35◦C

(b) Velocity Contours for Aspect Ratio 3, Tc = -15◦C

116 (c) Velocity Contours for Aspect Ratio 3, Tc = 5◦C

(d) Velocity Contours for Aspect Ratio 3, Tc = 25◦C

Figure 41: Velocity Contours for Aspect Ratio 3 for Set of Cold Plate Tem- peratures.

117 • The interface point or the edge of the inner heater plate is a critical region to understand the interaction of developed fluid movements due to heating from the ring heater and the inner heater. Velocity contours indicate the formation of a ‘fluid circulation zone’ (fcz), a single rotation cell near this point. This point, or rather the circumferential edge of the inner heater (in 3D) is where the maximum heat is lost from the inner heater surface, and can be seen in the local Nuseelt number plots near r/R=0.5 in Figure 33 (a) and figure 33 (b). This indicates that the edges of corners should be provided with better thermal contact decoupling and insulation to reduce heat lost due to convection. It is to be noted that this is a particular feature of the geometry that has implications for Mars rover gas gaps and needs to be further studied, rather than an issue with the setup.

Table 7: Heat Transfer Balance for AR1 Cold Plate Temperature -35◦C

Heat Input Experiments(W) CFD Solution(W) % Deviation Heat Conduction 2.595 (28.83%) 2.595 (28.83%) 0 Natural Convection 5.031 (55.89%) 5.706 (63.39%) +11.9 Heat Radiation 1.374 (15.26%) 0.698 (7.75%) -96.9 Total 9.001(100%) 9.001(100%) 0

Table 8: Percentage Diﬀerence Between Experimental and CFD Results for Average Nusselt Number for Cold Plate Temperature Case Solutions for Short Gap

Nu¯ Values -35◦C -15◦C 5◦C 25◦C AR1 EXP 2.181 1.876 2.667 2.549 AR1 CFD 2.251 2.068 2.862 2.661 % Diff 3.109 9.284 6.813 4.208 AR2 EXP 2.153 2.164 2.186 2.393 AR2 CFD 2.183 2.239 2.251 2.481 % Diff 1.374 3.349 2.844 3.546 AR3 EXP 2.183 2.287 2.326 2.365 AR3 CFD 2.224 2.322 2.365 2.413 % Diff 1.843 1.507 1.649 1.989

AR1 (2.67), AR2 (3.5) and AR3 (4.33) based on tall gap height (160 mm, 210 mm and 260 mm) to short gap height (60 mm).

118 Table 9: Percentage Diﬀerence Between Experimental and CFD Results for Average Nusselt Number for Cold Plate Temperature Case Solutions for Tall Gap

Nu¯ Values -35◦C -15◦C 5◦C 25◦C AR1 EXP 2.756 2.256 3.365 3.281 AR1 CFD 2.989 2.465 4.009 3.854 % Diff 7.795 8.478 16.063 14.867 AR2 EXP 3.083 3.196 3.585 4.055 AR2 CFD 3.632 3.851 3.976 4.517 % Diff 15.115 17.008 9.834 10.228 AR3 EXP 3.431 3.706 4.374 4.856 AR3 CFD 4.465 4.834 5.061 5.352 % Diff 23.157 23.334 13.574 9.267

6.2 Effect of Aspect Ratio on Step Profile As brought out during the discussion in the previous section 6.1 for cold plate temperature, three different aspect ratios for the step profile configuration were selected based on rover gas gap aspect ratios for MSL Rover configuration [32] and the useful volume constraints of the vacuum chamber (as described in Chapter 4 (4.4.3)) used for the tests. The aspect ratios were based on the ratio of the tall gap (160 mm, 210 mm and 260 mm) heights to short gap height (60 mm) to give AR1 (2.67), AR2 (3.5) and AR3 (4.33). The rest of the configuration and scheme of calculations was same as described for the cold plate temperature case in section 6.1 earlier. Some of the same result files have been rearranged and replotted to bring out the effect of aspect ratio on the heat transfer and flow distribution. Dimensionless temperature and local Nusselt number were plotted using the CFD solution for the different aspect ratio cases. Average Nusselt number along the midheight plane was plotted against average Rayleigh number (calculated for changing aspect ratios).

6.2.1 Findings

The dimensionless temperature proﬁles along the short and tall gap heights, across the enclosure half width show a peak at the interface point for all the three aspect ratio test cases as illustrated in Figure 42. Aspect Ratio AR2 and AR3 showed higher temperature values through their mid gaps, signifying slightly higher rate of heat transfer, as compared to that in AR1.

119 However, the variation was relatively inconsistent across the cold plate temperatures to formulate a strong inference. The local Nusselt number values were highest for AR3 and the values increased for increasing cold plate temperatures, as seen in Figure 43. The average Nusselt number for short gaps (Figure 44) did not give a clear correlation for average Rayleigh number (calculated for varying aspect ratio) at cold plate temperatures lower than 25◦C, possibly since the Rayleigh regime within this gap values were still too small (within Ra=400). The average Nusselt number, however, consistently increased for increasing Rayleigh number values from 6,000 to 40,000 for the tall gap cases, as seen in Figure 45. The isotherm contours over the heater surfaces (Figure 46) indicate a stronger magnitude band over the heater plates for AR3. Velocity Velocitys and multiple cells were seen closer to the cold plate wall, mainly because of stronger inﬂuence from the closer inner heater plate. The surface area of the velocity cell around the interface point seemed to be larger for the lower AR cases. The percentage diﬀerence values for average Nusselt number are covered in Tables 8 and 9 for the short and tall gaps respectively, as discussed in the previous cold plate temperature test case.

6.2.2 Inferences Some of the main inferences drawn from the Aspect ratio study case are listed below:

• Local Nusselt number values along tall gaps increase by around 1.5-2 times for AR3 as compared to AR1, resulting in a higher heat loss for enclosures with higher aspect ratios. The eﬀect is less pronounced for the short gaps for the diﬀerent aspect ratios,

• Test cases with higher cold plate temperatures resulted in heat transfer rates being more sensitive to the change in aspect ratios. Hence, warmer nights or daytime ambient conditions on Mars would be more prone to heat losses from higher aspect ratio enclosures.

6.3 Effect of Gas Pressure Local surface atmospheric pressures on Mars does not vary more than 10% of their mean diurnal values. However, from a fundamental thermofluid physics standpoint based on the conducted literature review, the behaviour of internal natural convection influenced by a range of fluid pressures (still less than Earth ambient pressures) within step profile enclosures is an open problem that has not been investigated to date. The objective of this case study was

120 (a) Non-dimensionalised Bulk Fluid Temperature ◦ Across Enclosure Half Width for Tc= -35 C

(b) Non-dimensionalised Bulk Fluid Temperature ◦ Across Enclosure Half Width for Tc= -15 C

121 (c) Non-dimensionalised Bulk Fluid Temperature ◦ Across Enclosure Half Width for Tc= 5 C

(d) Non-dimensionalised Bulk Fluid Temperature ◦ Across Enclosure Half Width for Tc= 25 C Figure 42: Non-dimensionalised Bulk Fluid Temperature Across Enclosure Half Width for Diﬀerent Aspect Ratio Cases.

122 (a) Local Nusselt Number Across Enclosure Half ◦ Width for Tc= -35 C

(b) Local Nusselt Number Across Enclosure Half ◦ Width for Tc= -15 C

123 (c) Local Nusselt Number Across Enclosure Half ◦ Width for Tc= 5 C

(d) Local Nusselt Number Across Enclosure Half ◦ Width for Tc= 25 C Figure 43: Local Nusselt Number Across Enclosure Half Width for Diﬀerent Aspect Ratio Cases.

124 (a) Average Nusselt Number v/s Average ◦ Rayleigh Number for Short Gap for Tc= -35 C

(b) Average Nusselt Number v/s Average ◦ Rayleigh Number for Short Gap for Tc= -15 C

125 (c) Average Nusselt Number v/s Average ◦ Rayleigh Number for Short Gap for Tc= 5 C

(d) Average Nusselt Number v/s Average ◦ Rayleigh Number for Short Gap for Tc= 25 C Figure 44: Average Nusselt Number v/s Average Rayleigh Number for Short Gap (varied by Aspect Ratio)

126 (a) Average Nusselt Number v/s Average ◦ Rayleigh Number for Tall Gap for Tc= -35 C

(b) Average Nusselt Number v/s Average ◦ Rayleigh Number for Tall Gap for Tc= -15 C

127 (c) Average Nusselt Number v/s Average ◦ Rayleigh Number for Tall Gap for Tc= 5 C

(d) Average Nusselt Number v/s Average ◦ Rayleigh Number for Tall Gap for Tc= 25 C Figure 45: Average Nusselt Number v/s Average Rayleigh Number for Tall Gap (varied by Aspect Ratio).

128 (a) Isotherm Contours for Aspect Ratio AR1 for ◦ Tc= -35 C.

(b) Isotherm Contours for Aspect Ratio AR2 for ◦ Tc= -35 C.

129 (c) Isotherm Contours for Aspect Ratio AR3 for ◦ Tc= -35 C.

◦ Figure 46: Isotherm Contours for Tc= -35 C for a set of Aspect Ratios. to vary the fluid pressure through four settings: 10 mbar, 30 mbar, 60 mbar and 100 mbar resulting in four distinct Rayleigh regimes and observing the impact on the dimensionless temperature, local and average Nusselt number. The AR3 enclosure configuration was chosen for this problem to study the density-driven fluid movement.

6.3.1 Findings The non-dimensionalised bulk fluid temperatures consistently showed (Figure 48) higher values for higher fluid pressures across all the cold plate temperatures. The values peaked at the interface point. The difference in values across fluid pressures reduced for higher cold plate temperatures. Similarly, local Nusselt number values were higher for higher fluid pressures, the difference being upto 5 times for 100 mbar cases as compared to 10 mbar cases, as seen in Figure 49. The difference in values between short and tall gap also was larger for higher cold plate temperatures. The average Nusselt number for the colder plate temperature cases recorded higher values, indicating higher degree of convection versus conduction, illustrated in Figure 50. The average Nusselt number values increased up to 2.5 times for fluid pressure levels of 100 mbar for short gap and 4 times for levels of 100 mbar for tall gaps. The slope was also larger for short gap cases, indicating a higher rate

130 (a) Velocity Contours for Aspect Ratio AR1 for ◦ Tc= -35 C.

(b) Velocity Contours for Aspect Ratio AR2 for ◦ Tc= -35 C.

131 (c) Velocity Contours for Aspect Ratio AR3 for ◦ Tc= -35 C.

◦ Figure 47: Velocity Contours for Tc= -35 C for a set of Aspect Ratios. of Rayleigh number increase, as compared to the tall gap cases. Isotherm contours (Figure 51) tend to indicate the number of bands reduces for higher fluid pressures, indicating a more uniform bulk fluid temperature, as can be seen in the temperature plot too. The number of bands also tend to increase (higher gradient) for each fluid pressure case for higher cold plate temperature settings. This is attributed to higher rate of heat transfer for high fluid pressure settings for lower cold plate temperatures (Figure 52-54). The intensity of the circulation zone also tends to weaken for higher fluid pressure cases, possibly due to more uniform bulk fluid temperature smooth out the density differences that normally sustain the distinct cell around that zone. The intensity also is seen to get stronger for higher cold plate temperatures. Thus, from both the quantitative plotting of Nusselt number and the flow contours, we can infer that lower cold plate temperatures for higher fluid pressures lead to higher heat transfer values and more uniform bulk fluid temperatures. The percentage difference between experimental and CFD estimations of average Nusselt number for short and tall gaps is listed in Tables 10 and 11. The observation of higher estimation of average Nusselt number in CFD as compared to experiments follows the same reasoning as explained earlier in this chapter for the cold plate temperature(i.e. higher than measured experimental heat losses and underprediction of numerical radiative heat input). It is interesting to note that the percentage difference values

132 through out the cases are within 7% for short gap and within 25% for tall gaps. Roughly, higher percentage diﬀerence values are logged for lower cold plate temperatures with tall gap cases.

Table 10: Percentage Diﬀerence Between Experimental and CFD Results for Average Nusselt Number for Four Fluid Pressure Case Solutions for Short Gap

Nu¯ Values -35◦C -15◦C 5◦C 25◦C P1 EXP 2.183 2.287 2.326 2.365 P1 CFD 2.224 2.322 2.365 2.413 % Diff 1.843 1.507 1.649 1.989 P2 EXP 2.865 3.056 2.528 2.789 P2 CFD 3.068 3.176 2.706 2.869 % Diff 6.616 3.778 6.577 2.788 P3 EXP 4.235 4.369 3.403 3.569 P3 CFD 4.412 4.517 3.534 3.746 % Diff 4.011 3.276 3.706 4.725 P4 EXP 6.754 5.649 4.723 4.065 P4 CFD 6.789 5.901 5.011 4.208 % Diff 0.515 4.271 5.747 3.398

Table 11: Percentage Diﬀerence Between Experimental and CFD Results for Average Nusselt Number for Four Fluid Pressure Case Solutions for Tall Gap

Nu¯ Values -35◦C -15◦C 5◦C 25◦C P1 EXP 3.431 3.706 4.374 4.856 P1 CFD 4.465 4.834 5.061 5.352 % Diff 23.157 23.334 13.574 9.267 P2 EXP 5.856 6.542 5.657 5.996 P2 CFD 6.404 6.811 5.813 6.359 % Diff 8.557 3.949 2.683 5.708 P3 EXP 9.651 10.589 7.365 8.023 P3 CFD 10.464 10.828 7.771 8.443 % Diff 7.741 2.207 5.224 4.974 P4 EXP 16.365 15.236 12.005 9.146 P4 CFD 18.451 15.591 12.503 9.596 % Diff 11.305 2.276 3.983 4.689

133 (a) Non-dimensionalised Bulk Fluid Temperature ◦ Across Enclosure Half Width for Tc= -35 C

(b) Non-dimensionalised Bulk Fluid Temperature ◦ Across Enclosure Half Width for Tc= -15 C

134 (c) Non-dimensionalised Bulk Fluid Temperature ◦ Across Enclosure Half Width for Tc= 5 C

(d) Non-dimensionalised Bulk Fluid Temperature ◦ Across Enclosure Half Width for Tc= 25 C Figure 48: Non-dimensionalised Bulk Fluid Temperature for a set of ﬂuid pressures.

135 (a) Local Nusselt Number Across Enclosure Half ◦ Width for Tc= -35 C

(b) Local Nusselt Number Across Enclosure Half ◦ Width for Tc= -15 C

136 (c) Local Nusselt Number Across Enclosure Half ◦ Width for Tc= 5 C

(d) Local Nusselt Number Across Enclosure Half ◦ Width for Tc= 25 C Figure 49: Local Nusselt Number Across Enclosure Half Width for a set of ﬂuid pressures.

137 (a) Average Nusselt Number v/s Average Rayleigh Number (varied by ﬂuid pressure) for Short Gap

(b) Average Nusselt Number v/s Average Rayleigh Number (varied by ﬂuid pressure) for Tall Gap

Figure 50: Average Nusselt Number v/s Average Rayleigh Number (varied by ﬂuid pressure) for Short and Tall Gaps.

138 (a) Isotherm Contours for P=10 mbar, Tc= - 35◦C, AR3

(b) Isotherm Contours for P=30 mbar, Tc= - 35◦C, AR3

139 (c) Isotherm Contours for P=60 mbar, Tc= - 35◦C, AR3

(d) Isotherm Contours for P=100 mbar, Tc= - 35◦C, AR3

◦ Figure 51: Isotherm Contours for set of ﬂuid pressures, Tc= -35 C, AR3.

140 (a) Isotherm Contours for P=10 mbar, Tc= - 15◦C, AR3

(b) Isotherm Contours for P=30 mbar, Tc= - 15◦C, AR3

141 (c) Isotherm Contours for P=60 mbar, Tc= - 15◦C, AR3

(d) Isotherm Contours for P=100 mbar, Tc= - 15◦C, AR3

◦ Figure 52: Isotherm Contours for set of ﬂuid pressures, Tc= -15 C, AR3.

142 ◦ (a) Isotherm Contours for P=10 mbar, Tc= 5 C, AR3

◦ (b) Isotherm Contours for P=30 mbar, Tc= 5 C, AR3

143 ◦ (c) Isotherm Contours for P=60 mbar, Tc= 5 C, AR3

◦ (d) Isotherm Contours for P=100 mbar, Tc= 5 C, AR3

◦ Figure 53: Isotherm Contours for set of ﬂuid pressures, Tc= 5 C, AR3.

144 ◦ (a) Isotherm Contours for P=10 mbar, Tc= 25 C, AR3

◦ (b) Isotherm Contours for P=30 mbar, Tc= 25 C, AR3

145 ◦ (c) Isotherm Contours for P=60 mbar, Tc= 25 C, AR3

(d) Isotherm Contours for P=100 mbar, Tc= 25◦C, AR3

◦ Figure 54: Isotherm Contours for set of ﬂuid pressures, Tc= 25 C, AR3.

146 ◦ (a) Velocity Contours for P=10 mbar, Tc= -35 C, AR3

◦ (b) Velocity Contours for P=30 mbar, Tc= -35 C, AR3

147 ◦ (c) Velocity Contours for P=60 mbar, Tc= -35 C, AR3

(d) Velocity Contours for P=100 mbar, Tc= - 35◦C, AR3

◦ Figure 55: Velocity Contours for set of ﬂuid pressures, Tc= -35 C, AR3.

148 ◦ (a) Velocity Contours for P=10 mbar, Tc= -15 C, AR3

◦ (b) Velocity Contours for P=30 mbar, Tc= -15 C, AR3

149 ◦ (c) Velocity Contours for P=60 mbar, Tc= -15 C, AR3

(d) Velocity Contours for P=100 mbar, Tc= - 15◦C, AR3

◦ Figure 56: Velocity Contours for set of ﬂuid pressures, Tc= -15 C, AR3.

150 ◦ (a) Velocity Contours for P=10 mbar, Tc= 5 C, AR3

◦ (b) Velocity Contours for P=30 mbar, Tc= 5 C, AR3

151 ◦ (c) Velocity Contours for P=60 mbar, Tc= 5 C, AR3

◦ (d) Velocity Contours for P=100 mbar, Tc= 5 C, AR3

◦ Figure 57: Velocity Contours for set of ﬂuid pressures, Tc= 5 C, AR3.

152 ◦ (a) Velocity Contours for P=10 mbar, Tc= 25 C, AR3

◦ (b) Velocity Contours for P=30 mbar, Tc= 25 C, AR3

153 ◦ (c) Velocity Contours for P=60 mbar, Tc= 25 C, AR3

(d) Velocity Contours for P=100 mbar, Tc= 25◦C, AR3

◦ Figure 58: Velocity Contours for set of ﬂuid pressures, Tc= 25 C, AR3.

154 6.3.2 Inferences Since the change in fluid pressures from 10 mbar to 100 mbar is not a realistic operating scenario for Mars rover case, the main inferences are listed as takeaway points from a fundamental thermofluid physics understanding perspective: • For the range of gas pressures evaulated, the heat transfer within short gaps was more sensitive to an increase in fluid pressures as compared to that within tall gaps. This could be explained as thermal conductivity increased with gas pressure, whereas for the tall gap, the transition from convection was not as distinct and nothing much was happening on the convection front yet. • Cases with lower cold plate temperatures showed a stronger potential/driving gradient, leading to higher rates of heat transfer for rising fluid pressures. • High rate of heat transfer in denser fluid indicated significantly more uniform isotherm contours and weaker velocity single cell near the interface point of the two gaps.

6.4 Effect of Ring Heater on Heat Transfer within Short Gap For the step profile enclosure with two heated surfaces at different levels below the overhanging cold plate, it was important to understand the influence of the heat input from the ring heater and its density driven flow disturbances on the heat transfer within the short gap. The influence was checked by comparing two cases, one with both heater surfaces operating at 25% operating power and the other with only the inner heater surface operating at 25% operating power and the ring heater switched off. The ring heater surface would then assume surface temperature based on its radiation exposure and contact with the enclosure fluid. Tests were conducted at 10 mbar fluid ◦ pressure and cold plate fixed temperature of Tc=25 C. Non-dimensionalised bulk fluid temperature, local Nusselt number and average Nusselt number were estimated from conducted experiments and CFD, illustrated in Figures 62-67.

6.4.1 Findings The bulk ﬂuid non-dimensionalised temperatures were consistently higher across the short gap enclosure width for the case with ring heater on, for all

155 three aspect ratio configurations as illustrated in Figure 59. This indicated that after reaching stability, the influence of the heat from the ring heater was uniform across the short gap, with highest values near the interface point. A similar trend was observed for the local Nusselt number (Figure 60) for all the three aspect ratios. This leads to the understanding that the ring heater assists in the convection heat transfer across the short gap, by increasing local Nusselt Number values by 16%-25% between the short gap. Figure 60 (a) shows the comparison of experimental and numerical estimations of average Nusselt number with Rayleigh number (varied by gas pressure). It is important to note here that even though the Rayleigh number is within Ra=800, the short gap experiences average Nusselt number enhancement by about 10% for fluid pressure of 10 mbar (representative of Mars atmospheric case) due to the adjacent ring heater plate. This is an important observation for subcritical Rayleigh number regimes that can have enhanced heat losses due to interaction with adjacent and differently leveled heating surfaces. Figure 60 (b) shows the variation of average Nusselt number with Rayleigh number across short gap for the three different aspect ratio cases. It is observed that the highest heat transfer rate in the short gap is oberved for the case with shortest adjacent ‘tall’ gap height, i.e. for the smallest aspect ratio case, AR1. The further the ring heater plate is from the short gap, the weaker is the influence on the heat transfer within it. A study of the isotherm contours indicates (Figure 62) that the bands are a lot more closely spaced near the inner heater plate for higher fluid pressure cases than those in lower fluid pressures. The higher fluid pressure leads to uniform density distribution throughout the enclosure, leading to further evenly spaced contours. The number of bands is also higher for higher aspect ratio test cases. As has been seen previously for higher fluid pressure case study, the cell strength near the interface point diminishes for higher fluid pressure cases, owing to more uniform bulk fluid temperatures which smoothen out any fluid movements near this zone. An interaction between the boundary layer zone and the core flow zone can be seen with two main cells, each near the cold plate and the inner heater plate. The coupling is seen to get stronger given larger overlap between the circulation zones for higher fluid pressure cases. The percentage difference between experimental and CFD solutions for average Nusselt number between ring heater on and off for a set of fluid pressures within the short gap is listed in Table 12. Under-prediction of radiation component leading to higher than actual fluid convective heat transfer estimates lead to around 1%-5% higher values for average Nusselt number along the short gap. The percentage difference values are slightly higher when ring heater is off (varying between 2%-17%) possibly due to further constraining of the radiation convergence algorithm of the Surface to Surface (S2S) model

156 caused by transient surface temperatures on the ring heater and its adjacent shroud wall surfaces as opposed to when ring heater is on which leads to higher temporal stability in these temperature values. Table 12: Percentage Diﬀerence Between Experimental and CFD Results for Average Nusselt Number for Ring Heater Eﬀect Study on Short Gap

Nu¯ Values Ring Heater ON Ring Heater OFF P1 EXP 2.365 2.576 P1 CFD 2.413 2.839 % Diff 1.989 9.263 P2 EXP 2.789 2.819 P2 CFD 2.869 3.373 % Diff 2.788 16.424 P3 EXP 3.569 3.845 P3 CFD 3.746 4.431 % Diff 4.725 13.225 P4 EXP 4.065 4.395 P4 CFD 4.208 4.996 % Diff 3.398 12.029

6.4.2 Inferences The main inferences drawn from studying the effect of ring heater on the heat transfer across the short gap are listed as under: • Even for Rayleigh number flows less than Ra=1700 (value determined as critical for horizontal gaps), an adjacent ring heater (placed within a tall gap with higher rate of heat transfer) can lead to an increase of heat transfer within a short gap by as much as 10% for Mars relevant cold plate temperature and fluid pressures. This is an important observation which would be a useful indication to Mars rover teams to conduct detailed experiments with supporting CFD to study heat transfer around step profile geometries for their gas gap problems. A difference of 10% is quite significant in the power constrained operations scenario of a Mars rover, it represents 10% of onboard resources which is unavailable to the payload and if not mitigated, can impact mobility of the rover. • Size of the tall gap aspect ratio can directly influence the heat transfer across the short gap. The closer the tall gap is from the short gap, the

157 (a) Non-dimensionalised bulk ﬂuid temperature across Short Gap for AR1.

(b) Non-dimensionalised bulk ﬂuid temperature across Short Gap for AR2.

158 (c) Non-dimensionalised bulk ﬂuid temperature across Short Gap for AR3

Figure 59: Non-dimensionalised bulk ﬂuid temperature across Short Gap for Ring Heater ON and OFF setting for a set of Aspect Ratios.

higher is the impact on the convection driven heat losses within the system. Reducing the aspect ratio from AR3 to AR1 (reduced by 40%) leads to about a 26% increase in the natural convection heat transfer (average Nusselt number) for the system.

• Even for cases with ring heater off, a peak in the fluid pressure results in the bulk fluid temperature to be more uniform, leading to weakening of circulation cell near the interface point.

6.5 Effect of Rover tilt on established convection in Mars systems The Mars rovers are designed to traverse uneven terrain over their mission duration on the surface of the red planet, with maximum permissible rover tilt for NASA’s MSL and ExoMars Rover ranging from 25◦-30◦ [7, 36]. The ExoMars team has carried out preliminary experiments and reported insignificant influences of rover tilt on the heat transfer. The objective for this work is to conduct a numerical heat transfer comparison study with 3 different tilt angles (15◦, 30◦and 45◦) along the z axis (third axis normal to the plane, illustration in Figure 31(b)(Section 6.1)) about the interface point

159 (a) Local Nusselt Number across Short Gap for AR1

(b) Local Nusselt Number across Short Gap for AR2

160 (c) Local Nusselt Number across Short Gap for AR3

Figure 60: Local Nusselt Number across Short Gap for Ring Heater ON and OFF setting for a set of Aspect Ratios. and compare it with the no tilt case to provide a definitive answer to the expected heat transfer rate. Given time and resource constraints, no experiments could be conducted to validate these solutions. The dimensionless bulk fluid temperature, local and average Nusselt number were estimated, as done for the previous study cases in this chapter. Cold plate temperature and fluid pressure were fixed at -35◦C and 10 mbar respectively.

6.5.1 Findings An increase in tilt angle resulted in consistently lower dimensionless bulk fluid temperatures, as illustrated in Figure 68. Temperature distributions for the tilt cases were only lower in magnitude but similarly uniform as the no-tilt case. Similar trends were seen for the local Nusselt number cases for higher tilt angles, as seen in Figure 69. The main reason behind this is the gravity vector normal to the heating surfaces, which for tilted enclosures was smaller in magnitude than that in no-tilt case. This lead to weaker buoyancy forces reducing the resulting fluid velocity and weakening the natural convection.The drop in local Nusselt number values ranged from about 25% in short gap cases to about 30% in tall gap cases. The percentage difference in value could be as high as 42% for AR3. This indicated that local

161 (a) Experimental and CFD results for Average Nusselt Number v/s Ra (varying pressure) for Ring Heater On and OFF

(b) Average Nusselt Number v/s Ra (varying pressure) for Ring Heater OFF for a set of As- pect Ratios

Figure 61: Average Nusselt Number v/s Ra (varying pressure) for Ring Heater On and OFF.

162 (a) Isotherm Contours for AR1, P=10 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(b) Isotherm Contours for AR1, P=30 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

163 (c) Isotherm Contours for AR1, P=60 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(d) Isotherm Contours for AR1, P=100 mbar, ◦ Ring Heater Off, Tc=25 C Figure 62: Isotherm Contours for set of fluid pressures, AR1, Ring Heater ◦ Off, Tc=25 C.

164 (a) Isotherm Contours for AR2, P=10 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(b) Isotherm Contours for AR2, P=30 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

165 (c) Isotherm Contours for AR2, P=60 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(d) Isotherm Contours for AR2, P=100 mbar, ◦ Ring Heater Off, Tc=25 C Figure 63: Isotherm Contours for set of fluid pressures, AR2, Ring Heater ◦ Off, Tc=25 C.

166 (a) Isotherm Contours for AR3, P=10 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(b) Isotherm Contours for AR3, P=30 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

167 (c) Isotherm Contours for AR3, P=60 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(d) Isotherm Contours for AR3, P=100 mbar, ◦ Ring Heater Off, Tc=25 C Figure 64: Isotherm Contours for set of fluid pressures, AR3, Ring Heater ◦ Off, Tc=25 C.

168 (a) Velocity Contours for AR1, P=10 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(b) Velocity Contours for AR1, P=30 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

169 (c) Velocity Contours for AR1, P=60 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(d) Velocity Contours for AR1, P=100 mbar, ◦ Ring Heater Off, Tc=25 C Figure 65: Velocity Contours for set of fluid pressures, AR1, Ring Heater ◦ Off, Tc=25 C.

170 (a) Velocity Contours for AR2, P=10 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(b) Velocity Contours for AR2, P=30 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

171 (c) Velocity Contours for AR2, P=60 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(d) Velocity Contours for AR2, P=100 mbar, ◦ Ring Heater Off, Tc=25 C Figure 66: Velocity Contours for set of fluid pressures, AR2, Ring Heater ◦ Off, Tc=25 C.

172 (a) Velocity Contours for AR3, P=10 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(b) Velocity Contours for AR3, P=30 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

173 (c) Velocity Contours for AR3, P=60 mbar, Ring ◦ Heater Oﬀ, Tc=25 C

(d) Velocity Contours for AR3, P=100 mbar, ◦ Ring Heater Off, Tc=25 C Figure 67: Velocity Contours for set of fluid pressures, AR3, Ring Heater ◦ Off, Tc=25 C.

174 heat transfer rates for higher aspect ratio enclosures were more significantly affected by rover tilt, given the larger contribution of fluid velocity driven energy transport as compared to for smaller aspect ratio enclosures. Figure 70 showed the drop in average Nusselt number values for average Rayleigh numbers, as varied by tilt angle (gravity vector). The overall impact on these values was seen to be higher in tall gaps as compared to the short gaps, as clearly the former had higher Rayleigh numbers (5,000-40,000) as compared to the latter (300-500). The isotherm contours for the study (Figure 71-73) did not reveal significant differences for the tilted enclosures, with the tilt induced distortion in the contour bands only seeming visibly obvious for the 45◦case. The tilt was seen to be a lot more prominent for AR3, where the heat transfer rate was also relatively the most affected. The Velocity contours however gave a deeper insight into the effect of the tilted enclosures, with a comprehensive change in the Velocity contouring even for the smallest tilt angle case of 15◦. Two distinct circulation zones were observed to form within the short and tall gap heights, spreading across the width. The skewed orientation of the zones (mainly the one in the tall gap) led to formation of multiple small weak circulation zones near the cold plate and shroud boundary walls. The circulation zone normally observed near the interface point was seen to elongate and transition towards the ring heater surface for tilt angle 15◦but then move back up for higher tilt angles. These were interesting flow structure observations recorded to contribute to the body of knowledge of fundamental thermofluid flow movement for tilted enclosures, but did not seem to have direct bearing on the Mars rover gas gap design, other than highlighting the need for doing more non intrusive optical flow diagnostics for relevant enclosures and boundary conditions for Mars rover gas gap experiments. A complete understanding of flow structure and local and average Nusselt number is paramount towards understanding and predicting the impact of geometry tilt on the internal natural convection for Mars relevant fluid regimes and boundary conditions.

6.5.2 Inferences The main inferences from the enclosure tilt study are listed as under:

• A drop in local Nusselt number as high as 42% by tilting the enclosure about the interface point by 45◦for tall gaps is reported. Rovers utilizing gas gap technology and without access to radiogenic heating to maintain stable internal temperatures could be positioned on a slope overnight to prevent it from losing heat, as the magnitude of the gravitational vector normal to the heated surfaces would weaken

175 (a) Non-dimensionalised Bulk (b) Non-dimensionalised Bulk Fluid Temperature Across En- Fluid Temperature Across En- closure Half Width for AR1 closure Half Width for AR2

Figure 68: Non-dimensionalised Bulk Fluid Temperature Across Enclosure Half Width for Enclosure Tilt Study.

the buoyancy induced natural convection heat loss. It is acknowledged this would not work for regions with flat and even surfaces, however, in the interest of the observations, the recommendation is put forward to the rover thermal management teams to consider whenever an uneven stretch is met. The final decision would be a tradeoff between stability risks( due to the tilt) and predicted values of saved heating power.

• The velocity contours indicate the internal ﬂow velocity structure is extremely sensitive to even a 15◦tilt to the enclosure. As has been reported in literature, internal natural convection is strongly coupled to ﬂuid velocity and temperature distribution at the boundary and core

176 (a) Local Nusselt Number Across (b) Local Nusselt Number Across Enclosure Half Width for AR1 Enclosure Half Width for AR2

Figure 69: Local Nusselt Number Across Enclosure Half Width for Enclosure Tilt Study.

flow and requires further experimental analysis to validate some of the made observations. For example, the circulation zone seen to exist for the no-tilt case near the interface point seems to relocate closer to the ring heater for 15◦tilt only to lift back up to the interface point for higher tilt angles. This can have implications on the local heat transfer rates near the interface point, as has been reported in this section. Further work is recommended, involving optical non-intrusive flow visualization for relevant step profile and boundary conditions, to help validate the CFD results.

177 (a) Average Nusselt Number v/s (b) Average Nusselt Number v/s Average Rayleigh Number (vary- Average Rayleigh Number (varying tilt angle) for Short Gap ing tilt angle) for Tall Gap

Figure 70: Average Nusselt Number v/s Average Rayleigh Number (varying tilt angle).

6.6 Chapter Summary

A cylindrical step profile geometry was studied for boundary and operating conditions relevant to Mars rover gas gap testing work. The Rayleigh number of the system was scaled by toggling a set of variable parameters: cold plate temperature, tall gap aspect ratio, fluid pressure and tilt angle. The effect of the ring heater on the heat transfer along the short gap height was studied. The main inferences were drawn to inform Mars rover thermal design teams as well as to contribute to the limited understanding of internal natural convection around step profile enclosures in low-medium Rayleigh number regimes. Higher cold plate temperatures (representative of warmer external ambient temperatures around the rover) were likely to have higher rates of convection losses from the heated surfaces due to higher gas thermal conductivity resulting in stronger effect of bulk fluid temperature than the actual temperature difference between the plates. The interface point, or the corner edge (in a three dimensional cylindrical geometry) was a critical region that almost always maintained a high level of heat loss into the gap. Cases with colder plate temperatures (representative of cold Mars nights) were more susceptible to heat losses from higher aspect ratio gaps. Even for Rayleigh number regimes lower than Ra=1700, a tall gap adjacent to a short or ‘safe’ gap led to about 10% increase in Nusselt number. Higher tilt angles lead to reduced heat transfer rates within the short and tall gaps. Flow structures are extremely sensitive to enclosure tilt and result in transition of circulation zone near interface point, affecting the heat transfer rate of the

178 ◦ (a) Isotherm Contour for AR1, Tc=-35 C, Tilt Angle=0◦

◦ (b) Isotherm Contour for AR1, Tc=-35 C, Tilt Angle=15◦ system. The next chapter will investigate some of the three dimensional observations for the ﬂow and will check for its impact on the local and average heat transfer of the system.

179 ◦ (c) Isotherm Contour for AR1, Tc=-35 C, Tilt Angle=30◦

◦ (d) Isotherm Contour for AR1, Tc=-35 C, Tilt Angle=45◦

◦ Figure 71: Isotherm Contour for AR1, Tc=-35 C for a range of Tilt Angles.

180 ◦ (a) Isotherm Contour for AR2, Tc=-35 C, Tilt Angle=0◦

◦ (b) Isotherm Contour for AR2, Tc=-35 C, Tilt Angle=15◦

181 ◦ (c) Isotherm Contour for AR2, Tc=-35 C, Tilt Angle=30◦

◦ (d) Isotherm Contour for AR2, Tc=-35 C, Tilt Angle=45◦

◦ Figure 72: Isotherm Contour for AR2, Tc=-35 C for a range of Tilt Angles.

182 ◦ (a) Isotherm Contour for AR3, Tc=-35 C, Tilt Angle=0◦

◦ (b) Isotherm Contour for AR3, Tc=-35 C, Tilt Angle=15◦

183 ◦ (c) Isotherm Contour for AR3, Tc=-35 C, Tilt Angle=30◦

◦ (d) Isotherm Contour for AR3, Tc=-35 C, Tilt Angle=45◦

◦ Figure 73: Isotherm Contour for AR3, Tc=-35 C for a range of Tilt Angles.

184 ◦ (a) Velocity Contour for AR1, Tc=-35 C, Tilt Angle=0◦

◦ (b) Velocity Contour for AR1, Tc=-35 C, Tilt Angle=15◦

185 ◦ (c) Velocity Contour for AR1, Tc=-35 C, Tilt Angle=30◦

◦ (d) Velocity Contour for AR1, Tc=-35 C, Tilt Angle=45◦

◦ Figure 74: Isotherm Contour for AR1, Tc=-35 C for a range of Tilt Angles.

186 ◦ (a) Velocity Contour for AR2, Tc=-35 C, Tilt Angle=0◦

◦ (b) Velocity Contour for AR2, Tc=-35 C, Tilt Angle=15◦

187 ◦ (c) Velocity Contour for AR2, Tc=-35 C, Tilt Angle=30◦

◦ (d) Velocity Contour for AR2, Tc=-35 C, Tilt Angle=45◦

◦ Figure 75: Isotherm Contour for AR2, Tc=-35 C for a range of Tilt Angles.

188 ◦ (a) Velocity Contour for AR3, Tc=-35 C, Tilt Angle=0◦

◦ (b) Velocity Contour for AR3, Tc=-35 C, Tilt Angle=15◦

189 ◦ (c) Velocity Contour for AR3, Tc=-35 C, Tilt Angle=30◦

◦ (d) Velocity Contour for AR3, Tc=-35 C, Tilt Angle=45◦

◦ Figure 76: Isotherm Contour for AR3, Tc=-35 C for a range of Tilt Angles.

190 7 Three Dimensional Eﬀects of Thermal Con- vection in Mars systems

The test configuration chosen to study the effect of a step profile on heat and flow distribution within a cylindrical enclosure was analysed by conducting experiments and supporting two dimensional axisymmetric CFD runs. In addition, to capture any three dimensional aspects of the temperature and flow within the domain volume (which were not captured in the 2D study), a limited set of 3D CFD runs was conducted. The results from these runs help understand the change in temperature and flow distribution upon varying a set of parameters and also quantify the effect on the local and average heat transfer contribution from natural convection. The objective is to check if there is any information loss by forcing the behaviour simulation to be 2D axisymmetric. As discussed earlier, the cylindrical step profile configuration is not a direct representation of Mars rover gas gaps but an important initial step to conduct a fundamental investigation for this opem problem, for relevant boundary and operating conditions. A cylindrical enclosure does not have many corners and edges (which is the case for rectangular enclosures, seen in almost all gas gaps in rovers) and helps study the behavior of temperature and fluid velocity around a single edge. The three dimensional geometry is prepared and discretized, with same settings as for the 2D axisymmetric case as discussed in chapter 4 (section 4.3) to allow direct comparisons with experiment and 2D CFD results. As in Chapter 6, a set of design input and boundary condition parameters was solved for to achieve a range of Rayleigh number fluid regimes and generate fluid and velocity distributions within the domain volume. Solutions were derived when flow residual monitors within 1e-6 were achieved for continuity, momentum and energy equations and the overall heat transfer balance net imbalance was within 1%. For cases with well-established fluid movement (Velocity magnitudes of 0.05 and higher), the cells seem to move around the annulus at tangential velocities ranging from 0.0001 m/s to 0.001 m/s. No consistent rotation pattern was seen as the cells seemed to move clockwise and anti- clockwise irregularly over long periods of time, without completing a cycle. A strong coupling was observed between the circumferential temperature nonuniformities and tangential velocity strengths. Since the overall heat transfer was not seen to be affected by the temporal fluctuations, single timestep cap- tures were studied, with finalised time points determined based on the heat transfer balance and residual criteria for natural convection. On an average, each case took close to two-three hours of flow time before the desired ‘sta- biltiy’ was reached. An iterative timestepping scheme was adopted to solve

191 the flow and energy equations for 0.05% variation in property per timestep. The local Nusselt number for the short and tall gap was calculated along sixteen imaginary vertical lines circumferentially placed, the first set of eight placed around the cylindrical step profile (above the ring heater) and the second arranged circumferentially above the inner heater (shown as dashes in Figure 77). Figure 77 gives the top view of the cylindrical enclosure, with the measurement lines (normal to the viewing plane) seen as squares and marked IH1 to IH8 for the inner heater points and RH1 to RH8 for the ring heater points. The isotherm and velocity contours are studied for each test case and significant visible asymmetries in temperature plumes or velocity cell structures are described. Heat transfer coefficient calculations are used to derive the local Nusselt number and its % variation (relative to mean values taken for all 8 positions). Inferences are drawn from these qualitative and quantitate estimations, highlighting the three dimensional nature of the natural convection and its impact on Mars rover gas gap designs.

Figure 77: Top View of 3D Cylindrical Step Proﬁle showing the Ring Heater and Inner Heater (solid lines) with circumferential path with each (dashed lines) along which the local Nusselt numbers are to be calculated.

192 7.1 Test Objectives The objective of the 3D CFD modelling of the cylindrical step profile configuration is to highlight the important three dimensional observations, which are not captured in the conducted thermal vacuum chamber experiments and the 2D axisymmetric CFD modelling. The temperature and velocity structure as well as the effect of such variations on the local and average Nusselt number are derived, with a 10% or greater variation in these values as compared to the 2D calculations being deemed significant enough to require 3D CFD runs for all gas gap cases relevant to Mars rover designs. Transient behavior of the flow and effect on overall heat transfer within gap due to the internal natural convection is discussed.

7.2 Flow Structures and Localized Heat Transfer Vari- ations A range of ﬂuid regimes are achieved by individually varying the control parameters, tall gap aspect ratio (AR1:2.67, AR2:3.5, AR3:4.33), enclosure ﬂuid pressure (10 mbar to 100 mbar), cold plate temperature (-35◦C to 25◦C) and enclosure tilt (30◦). The range and magnitude of these parameters are the same as considered for the 2D axisymmetric study, based upon Mars rover gas gap design operating and boundary conditions. Surface contours from the heater surfaces and a set of viewing planes, normal and parallel to the heater surfaces are generated. The local Nusselt number is derived across the short and tall gaps along circumferentially placed vertical lines between the heated and cold plates (as illustrated in Figure 77).

7.2.1 Tall Gap Aspect Ratio The tall gap height was varied to generate a set of three aspect ratios. Con- stant heat flux with ratio 1:2 was provided via the inner and ring heater, scaled to their individual surface area ratios. Based on the observations made in the 2D axisymmetric case, the cases showing significant fluid movement were picked: the cold plate was kept at a constant 25◦C and enclosure fluid pressure was set to 30 mbar. A symmetrical distribution of fluid temperature around the annulus is observed for AR1, the shortest tall gap height (Figure 78(a). The asymmetry is limited to specific axes for higher aspect ratios, slowly disappearing eventually. Figure 79(a) shows the fluid movement is isolated to within the 2D cut plane normal to the heating surface, rising from the ring heater surface, around the interface point, reaching the cold plate and then dropping as the fluid cools and becomes dense. AR2 case,

193 ◦ (a) Isotherm Contour for AR1, Tc=-25 C, 30 mbar

with a taller gap height shows the beginning of circumferential movement in the flow, with a total of three equally distant circulation zones forming around the annulus. The velocity magnitudes also increase from 0.008 to 0.035 around the gap, at the same height as the inner heater from the ring heater. Figure 78(b) and 79(b) show the distinct temperature zones and circulation zones. Compared to that, the temperature distribution is different and is quite aperiodic for AR3, as Velocity magnitudes increase to about 0.14 around the inner heater. A symmetric but three dimensionally varying temperature and velocity distribution for this case can be seen in Figure 78(c) and 79(c). Line averaged local Nusselt number values are plotted (Figure 80) and indicate mean percentage variations in their values around the annulus vary from 0.05% around the ring heater for AR1, to 3.49% for AR2 and 4.51% for AR3. The variations for all three aspect ratio cases over the inner heater remain within 0.051%. Higher rates of heat transfer were thus seeming to initiate circumferential fluid movement with only the higher aspect ratio cases recording a finite yet not having a significant influence on the bulk heat transfer. The average Nusselt number variation from the 2D axisymmetric calculations for the enclosure volume was less than 1%, indicating that the fluctuations in local Nusselt number nullifed each other.

194 ◦ (b) Isotherm Contour for AR2, Tc=-25 C, 30 mbar

◦ (c) Isotherm Contour for AR3, Tc=-25 C, 30 mbar

Figure 78: Isometric View Plan for Isotherm Contour for Set of Tall Gap Aspect Ratios, Enclosure Fluid Pressure of 30 mbar.

195 ◦ (a) Velocity Contour for AR1, Tc=-25 C, 30 mbar

◦ (b) Velocity Contour for AR2, Tc=-25 C, 30 mbar

196 ◦ (c) Velocity Contour for AR3, Tc=-25 C, 30 mbar Figure 79: Isometric View Plan for Velocity Contour for Set of Tall Gap Aspect Ratios, Enclosure Fluid Pressure of 30 mbar.

7.2.2 Cold Plate Temperature

Four different fluid regimes were generated by fixing the cold plate temperature to -35◦C, -15◦C, 5◦C and 25◦C. Enclosure fluid pressure and tall gap aspect ratio were fixed to 30 mbar and AR3 respectively. An asymmetric temperature distribution was seen around the ring heater for the lower cold plate temperatures of -35◦C and -15◦C, while for warmer cold plates, the distribution seemed symmetric and even radially uniform for 25◦C, as seen in Figure 81. The Velocity contours showed multiple circulation zones (roughly diametrically opposite) with circumferential movement for the lower temperatures (Figure 82). Plots for local Nusselt number around the ring heater showed percentage variations of 2.79% and 3.23% for cold plate temperatures of -35◦C and -15◦C respectively. The values were lesser than 0.001% for the higher cold plate temperature cases. The overall deviation from 2D axisymmetric CFD solution for the problem was less than 1%. The observation of fluid movement at lower cold plate temperature can be attributed to the higher plate temperature differences leading to stronger lateral fluid movement.

197 (a) Line Averaged Local Nusselt Number Values Around Ring Heater Plate for Range of Aspect Ratios

(b) Line Averaged Local Nusselt Number Values Around Inner Heater Plate for Range of Aspect Ratios

Figure 80: Line Averaged Local Nusselt Number Values Around Ring and Inner Heater Plate for Range of Aspect Ratios

198 ◦ (a) Isotherm Contour for Tc= -35 C

◦ (b) Isotherm Contour for Tc= -15 C

199 ◦ (c) Isotherm Contour for Tc= 5 C

◦ (d) Isotherm Contour for Tc= 25 C Figure 81: Isometric View Plan for Isotherm Contour for A Set of Cold Plate Temperatures.

200 ◦ (a) Velocity Contour for AR3, Tc=-35 C, Tilt Angle=0◦

◦ (b) Velocity Contour for AR3, Tc=-35 C, Tilt Angle=15◦

201 ◦ (c) Velocity Contour for AR3, Tc=-35 C, Tilt Angle=15◦

◦ (d) Velocity Contour for AR3, Tc=-35 C, Tilt Angle=15◦

Figure 82: Isometric View Plan for Isotherm Contour for A Set of Cold Plate Temperatures.

202 (a) Line Averaged Local Nusselt Number Values Around Ring Heater Plate for set of cold plate temperatures

(b) Line Averaged Local Nusselt Number Values Around Inner Heater Plate for set of cold plate temperatures

Figure 83: Line Averaged Local Nusselt Number Values Around Ring and Inner Heater Plate for set of cold plate temperatures.

203 7.2.3 Enclosure Fluid Pressure

Any increase in pressure within the enclosure volume was seen in the 2D axisymmetric cases (discussed in Chapter 6 (section 6.3)) to significantly drive up the heat transfer rates. To check spatial distributions around the centre annulus, four enclosure fluid pressure volumes were tested in 3D: 10 mbar (Mars relevant), 30 mbar, 60 mbar and 100 mbar. Even though enclosure fluid pressure variation does not have a direct line of contribution to Mars rover gas gap tests (as local surface Mars atmosphere pressure variations are within 10% of the mean diurnal value, throughout the year), it is critical to understand how the fluid behaves from a fundamental research point of view for step profile internal enclosures. N2 gas was chosen for the CFD run to help compare results against conducted experiments and 2D axi-symmetric cases. Enclosures with pressures of 10 mbar and 30 mbar did not show any temperature asymmetry in the circumferential direction, as illustrated in Fig- ure 84(a) and 84(b). Velocity magnitudes were quite weak and within 0.01 in both cases (Figure 85(a) and 85(b)). However, for the higher pressure setting of 60 mbar, the isotherm bands lose their uniformity around the annulus (Figure 84(c)) and two wide fluid circulation zones are formed, each covering half the circumference section, maintaining a symmetry along YZ plane (as per orientation defined here in Figure 85(c). For the pressure setting of 100 mbar, this symmetry is lost as these two circulation zones shrink and multiple smaller zones are formed, as seen in Figure 84(d) and 85 (d). From these observations, it can be inferred that a rise in fluid pressure causes an increase in the bulk fluid density, which leads to stronger buoyant forces. These forces result in the formation of equally spaced fluid circulation zones around the annulus, which break into smaller, irregular zones as the fluid pressure is increased. The percentage variation in local Nusselt number is below 0.001% for pressures upto 30 mbar, 1.02% for 60 mbar and 3.69% for 100 mbar (Figure 86). The deviation in the overall average Nusselt number from the 2D solutions for all the tested pressure cases was below 1%.

7.2.4 Enclosure Tilt

Enclosure tilt cases were first solved with 2D axisymmetric grids (discussed in previous Chapter 6 (Section 6.5)) to reveal slightly rotated or distorted temperature plumes and significantly different velocity circulation zones as compared to no-tilt case. To study the variations in the 3D domain, a comparison was drawn between tilt of angle 0◦(no tilt) and tilt angle of 30 degree (tilted along X axis in 3D domain, as seen in Figure 87). Fluid Pressure was fixed at 10 mbar and cold plate temperature at 25◦C. AR3 was chosen

204 (a) Isotherm Contour for Enclosure Fluid Pres- sure= 10 mbar

(b) Isotherm Contour for Enclosure Fluid Pres- sure= 30 mbar

205 (c) Isotherm Contour for Enclosure Fluid Pres- sure= 60 mbar

(d) Isotherm Contour for Enclosure Fluid Pres- sure= 100 mbar

Figure 84: Isometric View Plan for Isotherm Contour for A Set of Enclosure Fluid Pressures.

206 (a) Velocity Contour for Enclosure Fluid Pres- sure= 10 mbar

(b) Velocity Contour for Enclosure Fluid Pres- sure= 30 mbar

207 (c) Velocity Contour for Enclosure Fluid Pres- sure= 60 mbar

(d) Velocity Contour for Enclosure Fluid Pres- sure= 100 mbar

Figure 85: Isometric View Plan for Velocity Contour for A Set of Enclosure Fluid Pressures.

208 (a) Line Averaged Local Nusselt Number Values Around Ring Heater Plate for set of enclosure ﬂuid pressures

(b) Line Averaged Local Nusselt Number Values Around Inner Heater Plate for set of enclosure ﬂuid pressures

Figure 86: Line Averaged Local Nusselt Number Values Around Ring and Inner Heater Plate for set of enclosure ﬂuid pressures.

209 for this comparison study. Figures 87(a) and 88(a) show the symmetrical distribution of temperature around the annulus for the no-tilt case. This symmetry is disrupted upon tilting the enclosure by 30◦about the X axis, leading to the formation of two irregular circulation zones seen on either side of the ring heater (Figures 87(b) and 88(b). The velocity magnitude also increases from 0.001 to 0.04 for the tilt case. However, the overall local Nu is seen to drop, with percentage fluctuations of 3.336% in the tilt case(Figure 89). However, the overall average Nusselt number deviation from 2D CFD solution is less than 1%. The reason behind the formation of this asymmetric temperature distribution is that upon tilting the enclosure, the gravity vector force is unequally distributed on the bulk fluid particles around the annulus. This creates a gravitationally induced density distribution gradient which leads to the circumferential movement of the fluid around the annulus. Even though the overall heat transfer rates are reduced due to the tilt, the fluid velocities increase and the temperatures distribution themselves faster. This is indicative of the fact that fluid movement does not always corelate with rates of heat transfer.

7.3 Chapter Summary 3D CFD solutions of cylindrical step profile gas gap geometries are able to capture tangential fluid movement around the annulus and formation of multiple flow circulations also around the annulus, something which the 2D axisymmetric solutions do not. These have implications on the prediction of localized heat transfer parameters and the overall heat transfer analysis within the configuration. Almost all gas gap studies for rover configurations have conducted 2D CFD work to estimate heat transfer due to natural convection. This chapter covers the 3D CFD solution of the cylindrical step profile configuration, to highlight the influence on the spatial distribution of natural convection heat transfer, both as a percentage variation of local Nus- selt numbers from the mean values and as a deviation from average Nusselt number estimations made with 2D grids. For comparison purposes, the fluid regime is varied by individually varying the configuration (tall gap aspect ratio, configuration tilt) and specific boundary conditions (cold plate temperature, enclosure fluid pressure). Temporal variations in the 3D domain are observed to show finite tangential velocities in the circumferential direction around the annulus but no periodic rotations. Experiment results also indicate aperiodic changes in spatial asymmetries of temperatures around the annulus which shift with time. The tangential velocity components are driven by the circulation zone size and strength. Higher tall gap aspect ratios result in distinct temperature plumes and multiple circulation zones around

210 ◦ (a) Isotherm Contour for AR3, Tc=25 C, Tilt Angle=0◦

◦ (b) Isotherm Contour for AR3, Tc=25 C, Tilt Angle=30◦

Figure 87: Isometric View Plan for Isotherm Contour for Enclosures with Tilt (along X axis) and No-tilt Angle.

211 ◦ (a) Velocity Contour for AR3, Tc=25 C, Tilt Angle=0◦

◦ (b) Velocity Contour for AR3, Tc=25 C, Tilt Angle=30◦

Figure 88: Isometric View Plan for Velocity Contour for Enclosures with Tilt (along X axis) and No-tilt Angle.

212 (a) Line Averaged Local Nus- (b) Line Averaged Local Nus- selt Number Values Around Ring selt Number Values Around In- Heater Plate for tilt and no tilt ner Heater Plate for tilt and no cases tilt cases

Figure 89: Line Averaged Local Nusselt Number Values Around Ring and Inner Heater Plate for tilt and no tilt cases. the annulus. The overall variation from the mean value of the local Nusselt numbers is highest for the largest aspect ratio case. However, a negligible change in the overall average Nusselt number value is found. Thus, a higher Rayleigh flow regime caused by large aspect ratio results in higher velocity magnitudes, formation of circulation zones and asymmetric circumferential temperature distributions. On the other hand, lower cold plate temperature cases reflect a higher rate of fluid movement circumferentially, even though the local and average Nusselt number values are smaller than those for higher cold plate temperature cases. The average Nusselt number for the system calculated for the 3D domain does not deviate more than 1% from the volume averaged value estimated from the 2D axisymmetric solution of the problem. An important observation made is that higher temperature gradients result in stronger circumferential fluid movements and circulation zone formations around the annulus, and are not dependent on the overall heat transfer rate, which in fact is higher for higher cold plate temperatures. While the cylindrical enclosure gap geometry is studied here as a starting point to understand flows with axisymmetric geometries (minimizing number of corners and edges) and is not a directly applicable gap configuration for Mars rovers, it is clear that the variation of parameters that influence the Rayleigh number have implications on the 3D nature of the developed flow, potentially even for cartesian or rectangular geometries that are designed for rover internal layouts. Higher enclosure fluid pressure case solutions reveal the formation of stronger circulation zones, mainly as a result of higher density gradients,

213 strengthening the circumferential velocity magnitudes. Upon further increasing the fluid pressure, the equally spaced circulation zones break into smaller irregular zones. Tilting the enclosure about an axis results in a unbalance in the gravitational vector load distribution, affecting the density gradient, and leading to circumferential movement of the fluid around the annulus. Just as in the cold plate temperature condition, the case with a lower heat transfer (tilt case) reflects a stronger tangential velocity as compared to the no-tilt case. Thus we observe that circumferential movement of flow caused by the formation of multiple circulation zones does not influence the overall heat transfer within the configuration (neglible (0.001%) deviation from volume integral estimates from the 2D axisymmetric solutions) but results in a 3%-4% variation in local Nusselt numbers within tall gaps. Localized heat dissipation rates from heated surfaces on flight hardware exposed to gas gaps could be differently affected because of any three dimensional fluid circulation (that are not captured in 2D studies). Also, the variation of Rayleigh number over different fluid regimes by changing individual parameters lead to either strong correlations between lateral fluid movement and heat transfer or no dependence. For cases with well established circulation zones, the fluid patterns vary from case to case, indicating a close dependency on boundary conditions and thermal energy induced by the flow.

214 8 Conclusions and Recommendations

Even the loss of a few watts of energy on-board a Mars rover (mainly for solar electric powered ones) has serious implications on the energy saving, payload capability and the mobility aspects of the mission. Losses due to natural convection via gas gaps (account for up to almost 25% of overall losses for the MSL rover) are complex mechanisms that are not very well understood. Most teams have used simplistic gap geometries (uniform spacing between heated surfaces and cold rover walls) that have been well studied in literature (though for different applications and under different boundary conditions) to arrive at dimensional length scales within which the gap width is prescribed to be kept. Adjustments for testing on Earth are made by scaling temperature and gas pressure to account for lower Martian gravity. However, the variation of each individual parameter of the Rayleigh number (while others are fixed) on the overall heat transfer and flow distribution has not been studied yet. The use of gas gaps for passive thermal insulation in Mars rovers requires a proper understanding of heat dissipation from step- profile heated surfaces within enclosures in Martian surface gravity, pressure and ambient temperature conditions. The thesis was aimed towards identifying and characterising the enclosure driven heat transfer around a step profile gap for a range of Rayleigh numbers, arrived at by individually varying a set of parameters. Steps to augment gas assisted heat transfer analysis during thermal vacuum testing and three dimensional numerical analysis led to findings useful for Mars rover thermal designers and added to the limited understanding of the general case of Rayleigh number flows around step profiles.

8.1 Conclusions

In Chapter 3, the conducted literature review is presented in two parts. In the first part, the inherent complexities of enclosure-bound natural convection flows were highlighted, the coupling between the core and boundary flows resulted in a complex problem where the solution was heavily dependent on the enclosure configuration and boundary conditions. A complete understanding of the flow structure was critical to accurately describe the heat transfer across the enclosure, (not just the calculation of average heat transfer coefficients), thus requiring numerical modelling, closely guided by experiments. Focusing on special cases relevant to gas gap configurations for Mars rovers, the review revealed that natural convection in non-conventional enclosure geometries in low Rayleigh number regimes were an open prob-

215 Figure 90: Summary of Results and Implications for Mars Rover Gas Gap Designers lem that had not been tackled directly by anyone so far. The influence of low gravity on fluid movement and overall effect on heat transfer balance within enclosures remained largely unexplored. Given the challenges to test for effect of gravity, research groups scale the Rayleigh number by adjusting other parameters such as gas pressure and bulk fluid temperature. Although theoretical, the desired Rayleigh number is achieved, physically, the problem is not replicated. Given the strong dependence of final heat transfer balance on the fluid velocity and temperature distributions, there was a requirement to study the effect of varying a set of individual parameters while keeping others fixed to attain a range of Rayleigh numbers. In the second part of the chapter, a review of gas gap modelling and testing work undertaken by Mars rover thermal management teams around the world to help refine the research questions for this thesis. The review of this part highlighted some of the main challenges faced during gas gap testing: maintaining a stable low gas temperature and pressure within the enclosure; thermocouple placement and measurement of gas-assisted heat transfer and insufficient data on heat

216 transfer characteristics of typical geometry profiles of Mars rover internal hardware. In Chapter 4, a critical open problem of characterising a less studied but commonly encountered enclosure geometry feature (step profile) for relevant boundary and operating conditions is identified. The CFD modelling and experimental test setup design capabilities and limitations are discussed. The main objective of the CFD work is to overcome some of the limitations of thermal vacuum system based experiments, i.e. running an extended set of test cases, solving for reduced gravity environments and allowing a detailed investigation of fluid flow and temperature distribution within the enclosure. In Chapter 5, three different thermocouple placement configurations are compared during the first two experiment subcampaigns for temperature measurement of the gas and exposed shroud surface around the enclosure core flow for heating power and temperature boundary conditions based on the JPL Gas Gap tests for the Curiosity rover. Tests revealed the low thermal mass of the shroud material resulted in insignificant differences between the temperature measurements attained from the three configurations, all within standard deviation of 0.5 K. The average heat transfer coefficient values calculated was also shown to not be affected by the different configurations, with calculated values within a standard deviation of 0.0006 W/m2-K, with the variance dropping asymptotically 3 hours into the tests. The tests also revealed a shifting asymmetricity in the temperature distribution around the shroud with differences of 4 K to 6 K at diametrically opposite locations, hinting towards a time dependent action of the internal gas temperature on the shroud, consistent with published reports of fluid rotation within cylindrical enclosures. The final experiment subcampaign configuration consisted of a cylindrical step profile gap geometry where tests carried out for cold plate temperature of 300.15 K and chamber pressure of 60 mbar and above revealed temperature fluctuations with 0.2 K to 0.4 K with oscillation period of 100-220 seconds per cycle. A list of potential sources for these temperature fluctuations was made, consisting of DC voltage supply, thermal control unit, scroll pump, ring heater power and the laboratory ambient temperature. The tests were repeated with each potential source isolated, only to reveal that the ring heater caused these fluctuations. Thus, the effect of thermocouple placement and heater components on gas gap performance testing brought out the micro-instabilities of temperature within such enclosures for low Rayleigh number regimes. In Chapter 6, the effect of individually varying a set of design input and boundary value parameters (cold plate temperature, gas pressure, tall gap aspect ratio, heater ratio and geometry tilt) on natural convection within the cylindrical step profile for Rayleigh number of 400-40,000 are discussed. A

217 higher cold plate temperature setting is shown to increase bulk fluid temperature, leading to enhanced heat transfer within the enclosed gas. The corner edge between the two heaters, referred to as the ’interface point’ in most of the test cases showed a higher surface heat loss than the rest of the heated surfaces on the two heaters. This was attributed to the higher localised fluid velocities near the corner, leading to enhanced rates of convection transport. Cases with colder plate temperatures were more susceptible to heat losses from higher aspect ratio gaps. The tests also revealed that for subcritical Rayleigh number regimes (Ra less than 1700) within the short gap between the inner heater and cold plate, an adjacent tall gap with established convection (generated by a lower ring heater plate) can result in about a 10% increase in average Nusselt number values. The size of the tall gap was seen to directly influence the heat transfer across the short gap, with the shorter aspect ratio tall gaps leading to a higher rate of loss from the short gap. This was an interesting observation, counter-intuitive to what would be expected, with higher aspect ratios leading to higher rates of heat transfer. Varying the gas pressure in the enclosure lead to an increase in average Nusselt number by 2.5 times for pressure levels of 100 mbar for short gaps and 4 times for tall gaps. The Nusselt number vs Rayleigh number slope was consistently higher across aspect ratios for short gaps, indicating a stronger effect of gas pressure on heat transfer across short gaps. Tilting the enclosure by as little as 15◦was shown to result in changes in fluid and temperature distributions within the enclosure. An increase in the tilt angle resulted in lower bulk temperatures, leading to a drop in overall heat transfer losses, about 25% for short gaps and about 30% for tall gaps. Higher aspect ratio tall gaps were significantly affected by the rover tilt, mainly due to the stronger fluid driven energy transport. In Chapter 7, the three-dimensional fluid flow and temperature distribution around the cylindrical step profile enclosure is studied along with its impact on the local and average Nusselt number values. The solutions for a cylindrical step shape though not directly applicable to Mars rover gas gap performance tests (which are mainly box-like and aren’t axisimmetric), are a critical first step to analyze the internal flow for a configuration with the least number of corners to influence the established natural convection. Just as in Chapter 6, the fluid regime conditions are varied by toggling the tall gap aspect ratio, configuration tilt, cold plate temperature and enclosure fluid pressure. Results reveal a periodic tangential movement of flow around the annulus, driven by the circulation zone size and strength of the cell. The local Nusselt number shows a 3%-4% variation from two-dimensional studies while the average Nusselt number is not seen to be significantly different, varying only by about 0.001%. A higher Rayleigh flow regime caused by

218 larger aspect ratio configurations results in the formation of multiple circulation zones, asymmetric circumferential temperature distributions and higher velocity magnitudes. On the other hand, lower rates of heat transfer for lower cold plate temperatures and higher tilt angles reflect stronger tangential velocity magnitudes. The strength and direction of velocity magnitude (i.e. up-down or tangential) is seen to have an impact on the overall heat transfer for a three dimensional problem. The variation of Rayleigh number by adjusting individual parameters is seen to either cause strong correlations between lateral fluid movement and heat transfer or have no dependence. Thus, the inconsistent response of the heat transfer to the established fluid movement for the different parameter variables indicate a strong coupling between the boundary conditions and the flow’s thermal instabilities.

8.2 Recommendations for Future Work There are a number of ways in which the work in this thesis could be extended. Gas gap testing for Rayleigh number regimes of 100-40,000 requires tests in thermal vacuum chambers, under vacuum (1e-4) and reduced gas pressures of 10 mbar to 100 mbar. Normally, the gas gap experimenter has to work within the existing constraints around pre-existing test installations. The au- thor conducted this work only during times in the day when lab temperature was within 2K±0.65K variation to reduce the delay in plate temperature stabilisation. To further minimize the impact of laboratory temperature effects on the experiments and maximise the time for experimentation, it is recommended to have an active control over the laboratory temperature around the thermal vacuum chamber to ideally within 1 K for the entire duration of a test run. The microscale temperature fluctuations recorded for specific cold plate temperature and gas pressure settings (although within the measurement uncertainity of the type T thermocouple with insignificant impact on the measured heat transfer balance) could be a relevant topic for investigation for another application focused on their occurance. Studying the extent of the impact of fluid flow and temperature distribution on the overall heat transfer balance could heavily benefit from low density non-intrusive flow visualization techniques during the experiments. The main obstacle here is having viewing access through the shroud which can be achieved by redesigning the shroud to have viewing ports allowing measurements to be taken without physically disrupting the flow. It would be critical to account for variations in radiation emissivity and thermal mass values due to the transparent window material for accurate heat transfer estimations. The thermal emissivity value definition for the working surfaces in the ANSYS

219 Fluent module currently only allows specifying a single value per surface, for the Surface to Surface (S2S) model to calculate radiation contribution. However, emissivity measurements taken for hand polished surfaces indicated emissivity value variations by over 30% throughout the surface . For coupled convection-radiation simulations in enclosures, it would be important to accurately define the emissivity values to reduce the difference in experimental and numerical predictions of natural convection heat transfer coefficients. Detailed tests for specific geometry and boundary conditions (heat dissipation rates, cold plate temperature, gas pressure) for Mars rover gas gaps and mission profiles, based on the developed CFD and experimental procedure need to be conducted in order to provide direct feedback regarding their performance. Just like for fundamental internal natural convection problems, the Mars rover gas gap tests cannot completely rely on existing heat transfer correlations for simplistic gaps and require closely coupled numerical (2D and 3D) and experimental studies for specific gas gap geometries for relevant operating and boundary conditions. Natural convection in rover gas gaps can lead to thermal losses critical to the power budget, if the effect of specific geometry, orientation and boundary conditions are not completely accounted for.

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234 A Working Fluid Thermal Properties

Thermal conductivities values for the working ﬂuids for the numerical and experimental analyses were imported from the National Institutes of Stan- dards and Technology (NIST) database for 10 mbar isobaric conditions for Mars surface temperature range.

Figure 91: Thermal Conductivity of Carbon Dioxide gas at 10 mbar for Mars Temperature Window

Figure 92: Thermal Conductivity of Nitrogen gas at 10 mbar for Mars Tem- perature Window

235 B Engineering Drawings of Test Articles

The test articles used in the experiments within the thermal vacuum chamber were designed and fabricated with support of the Technical Support Group at the School of Engineering and Information Technology, UNSW Canberra. Two heater plate assemblies were conﬁgured for the tests, one involving ceramic heat resisors sandwiched between metal plates, the other a two part (inner and ring heater plate) system with Aluminium heat tape used for heating.

Figure 93: Drawing for Heater Plate Assembly 1: Recess plate

236 Figure 94: Drawing for Heater Plate Assembly 1: Supporting plate

237 Figure 95: Drawing for Heater Plate Assembly 2: Inner heater plate

238 Figure 96: Drawing for Heater Plate Assembly 2: Ring heater plate

239 Figure 97: Drawing for Inner Shroud

240 Figure 98: Drawing for Heater Plate Assembly 2: Inner heater plate

241 Figure 99: Drawing for Heater Plate Stands

242 Figure 100: Drawing for Thermal Plate Cap

243