Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Chanduri, Sai Ram
Master of Applied Science - MASc
University of British Columbia
Although geothermal energy is widely used for residential and commercial air-conditioning, there has not been much research done to employ geothermal energy and for data center (DC) cooling. Due to the absence of heating loop and a continuous need for cooling the servers, it has proven difficult to develop a DC cooling system which operates solely on geothermal heat exchange. The primary objective of this research was to investigate the thermal feasibility of developing an environment friendly geo-exchange cooling solution for data centers with smaller capacities. The cooling system detailed in this thesis discusses the underground as a heat sink, and the transfer of heat from the data server room to the underground by means of air-water heat exchange. After developing a few geothermal well designs, a numerical model was designed to examine the heat transfer between the rejected hot DC water and the cold well water. The thermal performance of the geothermal well is then analyzed under steady-state and transient conditions. An analytical approach was used to investigate the thermal behavior of the well under steady-state conditions, whereas both analytical and numerical approaches were used to study the heat transfer characteristics under transient conditions. Numerical simulations and heat transfer calculations were done to establish the trends of heat transfer rate with various sizing parameters of the well. These analyses suggest that the well can be operated only under transient conditions and hence, a multiple-well model is devised and the heat transfer calculations are performed for the same using analytical approach. The theoretical and numerical analyses thus conducted were used to infer the feasibility of the developed cooling solution.
GEOTHERMAL COOLING FOR DATA CENTERS bySai Ram Chanduri B.E. in Mechanical Engineering, Osmania University, 2017A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE inTHE COLLEGE OF GRADUATE STUDIES(Mechanical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan)December 2020 © Sai Ram Chanduri, 2020 The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis/dissertation entitled: Geothermal Cooling for Data Centers submitted by Sai Ram Chanduri in partial fulfillment of the requirements for the degree of Master of Applied Science in Mechanical Engineering Examining Committee: Dr. Sunny Li, Faculty of Applied Science Supervisor Dr. Sumi Siddiqua, Faculty of Applied Science Supervisory Committee Member Dr. Ernest Goh, Faculty of Applied Science Supervisory Committee Member Dr. Kasun Hewage, Faculty of Applied Science University Examiner i Abstract Although geothermal energy is widely used for residential and commercial air-conditioning, there has not been much research done to employ geothermal energy and for data center (DC) cooling. Due to the absence of heating loop and a continuous need for cooling the servers, it has proven difficult to develop a DC cooling system which operates solely on geothermal heat exchange. The primary objective of this research was to investigate the thermal feasibility of developing an environment friendly geo-exchange cooling solution for data centers with smaller capacities. The cooling system detailed in this thesis discusses the underground as a heat sink, and the transfer of heat from the data server room to the underground by means of air-water heat exchange. After developing a few geothermal well designs, a numerical model was designed to examine the heat transfer between the rejected hot DC water and the cold well water. The thermal performance of the geothermal well is then analyzed under steady-state and transient conditions. An analytical approach was used to investigate the thermal behavior of the well under steady-state conditions, whereas both analytical and numerical approaches were used to study the heat transfer characteristics under transient conditions. Numerical simulations and heat transfer calculations were done to establish the trends of heat transfer rate with various sizing parameters of the well. These analyses suggest that the well can be operated only under transient conditions and hence, a multiple-well model is devised and the heat transfer calculations are performed for the same using analytical approach. The theoretical and numerical analyses thus conducted were used to infer the feasibility of the developed cooling solution.ii Lay Summary The demand to increase the number of data centers (DCs) is rapidly growing throughout the world to accommodate the explosion of digital content, big data, e-commerce, and internet traffic. During their course of operation, data centers emit enormous amounts of heat and traditionally, air-conditioning is used to cool the servers. The energy thus consumed for cooling is one of the major contributors to the increased carbon footprint and global pollution, as the cooling system accounts for 40% of the energy needs of the data center. Over the recent years, data center industry has been striving hard to reduce the carbon emissions. The most effective way to cut down these emissions is by reducing the power requirement for data center cooling, as the energy needs for server cooling can be achieved by means of green and eco-friendly strategies.Even though the recent innovations in DC cooling industry has enabled us to employ renewable energy dependent cooling systems (wind energy, solar energy-based cooling systems) and passive cooling strategies like open atmospheric cooling, these are highly sensitive to geographical locations and seasonal fluctuations. On the other hand, as the underground temperature fluctuates minimally throughout the year at a certain depth, the heat generated in the servers can be rejected underground without interruption. Though the geo-exchange and the geothermal energy are widely used in residential and commercial cooling and heating, there has not been much work done in utilizing the underground thermal sinking for DC cooling. This work aims at investigating the feasibility of employing geo-exchange as an active cooling solution for small-scale data centers, by developing a geo-exchange-based DC cooling system. iii Preface The material presented in this thesis, including the literature review, design and development of the geothermal well for data center cooling, CFD and numerical analysis, was completed by Sai Ram Chanduri, under the supervision of Professor Sunny Li from the department of Mechanical Engineering. Mr. Mojtaba Zabihi and Dr.Xuan Gao have given their valuable inputs and suggestions in the design improvements, gaining technical knowledge and organizing the research structure. The revision and organizing the dissertation has been completed with the inputs from Professor Sunny Li. The idea of this research has been accepted for Microsoft CSME 2020 conference under the proceedings: âM. Zabihi, R. Li, S. R. Chanduri, and A. R. H. Nezhad, âGeothermal Cooling for Data Centersâ, Progress in Canadian Mechanical Engineering. Volume 3, Jun. 2020, doi: 10.32393/csme.2020.98.â iv Table of Contents Abstract ............................................................................................................................................ i Lay Summary .................................................................................................................................. ii Preface............................................................................................................................................ iii Table of Contents ........................................................................................................................... iv List of Tables ................................................................................................................................ vii List of Figures .............................................................................................................................. viii List of Abbreviations ..................................................................................................................... xi List of Symbols ............................................................................................................................. xii Acknowledgements ...................................................................................................................... xiv Dedication ......................................................................................................................................xv Chapter 1: Introduction ................................................................................................................1 1.1 Data Center Cooling ....................................................................................................... 3 1.1.1 Strategies for data center cooling ........................................................................... 4 1.1.2 Data Center cooling guidelines & standards .......................................................... 9 1.2 Literature Review ........................................................................................................ 10 1.3 Summary ..................................................................................................................... 12 Chapter 2: Research objectives and methodology ....................................................................14 2.1 Motivation ..................................................................................................................... 14 2.2 Research idea ................................................................................................................ 15 2.3 Objectives ..................................................................................................................... 21 2.4 Methodology ................................................................................................................. 22 v 2.5 Thesis layout ................................................................................................................. 27 Chapter 3: Numerical setup ........................................................................................................29 3.1 Governing equations ..................................................................................................... 29 3.2 Geothermal well design ................................................................................................ 31 Chapter 4: Data server room ......................................................................................................41 4.1 Assumptions .................................................................................................................. 41 4.2 CFD simulation of data server room ............................................................................. 42 Chapter 5: Results........................................................................................................................49 Section-I: Steady-state analysis ................................................................................................. 49 I.1 Numerical approach ...................................................................................................... 51 I.2 Design Modifications .................................................................................................... 56 I.3 Analytical approach ...................................................................................................... 61 I.4 Comparison of thermal resistances of wells at steady state .......................................... 64 Section-II: Transient Analysis ...................................................................................................... 67 II.1 Numerical model ........................................................................................................... 69 II.2 Analytical approach ...................................................................................................... 75 II.3 Effect of physical dimensions on rate of heat transfer (TS) ......................................... 77 Chapter 6: Multiple well model ..................................................................................................80 6.1 Analytical approach ...................................................................................................... 80 6.2 Results and discussion .................................................................................................. 84 Chapter 7: Conclusions ...............................................................................................................93 7.1 Research conclusions .................................................................................................... 93 7.2 Limitations of the research ............................................................................................ 94 vi 7.3 Contributions of the research ........................................................................................ 96 7.4 Future scope for the research ........................................................................................ 96 Bibliography .................................................................................................................................98 Appendix A ................................................................................................................................. 107 Appendix B ................................................................................................................................. 112 vii List of TablesTable 1.1 Summary of thermal guidelines, ASHRAE, 2011 .......................................................... 9 Table 3.1 Pipe sizes and the maximum volumetric flow rates ..................................................... 36 Table 5.1 Properties of the gravel used for the numerical simulation .......................................... 51 Table 5.2 Properties of the soil used for the numerical simulation .............................................. 51 Table 5.3 Thermal conductivity ranges of various soil types ....................................................... 52 Table 5.4 Obtained heat transferred values from the analytical method (cylinder) ...................... 63 Table 5.5 Thermal resistances of the geothermal well at a soil domain volume of 1000 m3 ....... 65 Table 5.6 Effect of mesh size on the rate of heat transferred for a various geo-well sizes .......... 67 Table 5.7 Rate of heat transfer with the depth of pipe buried in TS of the geothermal well ........ 77 Table 5.8 Change in heat transfer per length with the domain area at transient state of the geothermal well ............................................................................................................................. 78 Table 5.9 Change in heat transfer per length with the diameter at transient state of the cylindrical geothermal well ............................................................................................................................. 78 Table 6.1 Variation of maximum heat transferred with depth of well in multiple-well system ... 90 Table 6.2 Variation of thermal conductivity with increasing soil thermal conductivity .............. 91 viii List of Figures Figure 1.1 An inside view of a data server room ............................................................................ 2 Figure 1.2 Energy consumption by various sub-systems in DC ..................................................... 4 Figure 2.1 Thermal network of the geo-exchange heat transfer system .................................... 16 Figure 2.2 a Server cabinet equipped with heat exchanger .......................................................... 18 Figure 2.2 b Each heat exchanger is composed tube coil and electrical fan ................................. 18 Figure 2.3 Schematic diagram showing geothermal cooling of data centers ............................... 20 Figure 2.4 Schematic diagram of a multiple-well based geothermal cooling system .................. 21 Figure 2.5 Flowchart of the research methodology ...................................................................... 23 Figure 3.1 Schematic diagram detailing the concept of geothermal well ..................................... 32 Figure 3.2 Schematic of a multiple well geothermal heat exchange system ................................ 36 Figure 3.3 3D CAD model of the geothermal well in ANSYS Design Modeller ........................ 38 Figure 3.4 a Developed mesh at the interfaces for the 3D CAD model of geothermal well- Mesh at the inlet pipe-porous medium interface ................................................................................... 38 Figure 3.4 b Developed mesh at the interfaces for the 3D CAD model of geothermal well- Mesh at the porous medium-soil interface .............................................................................................. 39 Figure 4.1 3D ICEM model of the data server rack ...................................................................... 43 Figure 4.2 Velocity pathlines inside the server rack at steady state ............................................. 44 Figure 4.3 Velocity vectors around the cabinets at steady state ................................................... 45 Figure 4.4 Cabinet-wise temperature distribution at steady state (temperature in 0C) ................. 46 Figure 4.5 3D ICEM model of the proposed cabinet layout ......................................................... 47 Figure 4.6 Cabinet-wise temperature distribution at steady state (temperature in 0C) ................. 47 Figure 5.1 Pressure contour of the designed geothermal well at steady state ............................... 54 ix Figure 5.2 Velocity contour of the designed geothermal well at steady state .............................. 55 Figure 5.3 Temperature contour of the designed geothermal well at steady state ........................ 56 Figure 5.4 2D CAD model of the modified geothermal well ....................................................... 58 Figure 5.5 2D CAD model mesh of the modified geothermal well .............................................. 59 Figure 5.6 Temperature contour of the designed geothermal well (2) at steady state .................. 60 Figure 5.7 Variation of heat transferred to the L/d ratio of the geothermal well at steady state .. 64 Figure 5.8 Variation of thermal resistance with the heat transfer surface area of three wells ...... 66 Figure 5.9 Schematic showing the proposed geothermal cooling solution for transient analysis. 68 Figure 5.10 Axisymmetric CAD model of the cylindrical geothermal well................................. 69 Figure 5.11 Geometrical mesh of the CAD model of the axisymmetric geothermal well ........... 70 Figure 5.12 Total heat transfer rate change with time during transient operating phase of the geothermal well ............................................................................................................................. 72 Figure 5.13 Area-weighted average of temperature change with time during transient operating phase of the geothermal well ........................................................................................................ 73 Figure 5.14 Temperature contour of the transient analysis of the axisymmetric geothermal well74 Figure 5.15 Temperature contour change during the transient operating stage of the geothermal well................................................................................................................................................ 74Figure 5.16 Graph showing heat recovery stage of the geothermal well during the transient analysis ....................................................................................................................................... 75 Figure 5.17 Variation of heat transfer rate with heat transfer surface area ................................... 79 Figure 6.1 Schematic showing multiple geo-exchange wells connected together ........................ 81 Figure 6.2 Schematic showing the idea of a multi- geothermal well system ............................... 82 Figure 6.3 a Schematic showing switching between wells in a multi-well model â 1st step ....... 83 x Figure 6.3 b Schematic showing switching between wells in a multi-well model â 2nd step...... 83 Figure 6.4 Temperature contour of the 2D cylindrical well at transient state (after 3655 s) ........ 85 Figure 6.5 Results of maximum heat transfer (W) obtained from a single well (with convection).89 Figure 6.6 Maximum heat transferred with the increase in depth of the well ............................. 90 Figure 6.7 Variation of maximum heat transfer rate with the increasing soil thermal conductivity .................................................................................................................................. 92 Figure A.1 3D CAD model with metal rods bridged between the soil and the geothermal well 107 Figure A.2 A detailed view of the metal rods bridging soil and the geothermal well ................ 108 Figure A.3 A detailed view of the metal rods bridging soil and the geothermal well ................ 108 Figure A.4 3D CAD model of the fin geothermal well model (top-view) ................................. 109 Figure A.5 3D CAD model of the fin geothermal well model ................................................... 109 Figure A.6 Geometric mesh of the fin geothermal well model .................................................. 110 Figure A.7 Geometric mesh of the fin geothermal well model at interfaces .............................. 110 Figure A.8 Temperature contour of the fin geothermal well system at steady state .................. 111 Figure A.9 Temperature contour of the well in fin geothermal system at steady state .............. 111 Figure B.1 Sequence of selection and operation in a well cycle of 1125 minutes ..................... 112 xi List of AbbreviationsASHP â Air Source Heat Pump ASHRAE â American Society of Heating, Refrigeration and Air-Conditioning Engineers CAD â Computer Aided Design CFD- Computational Fluid Dynamics COP â Coefficient of Performance CPU â Central Processing Unit CRAC â Computer Room Air Conditioning DC â Data Center GSHP- Ground Source Heat Pump ISO â International Standards Organization IT â Information Technology NDRC- National Defense Research Council PUE â Power Usage Effectiveness xii List of Symbols ð½?Ì ? - diffusion flux of species jâðð½?Ì ? - species diffusionðððð. ?â? - viscous dissipation â - Sphericity of the medium µ - Dynamic Viscosity D - Diameter of particles making the medium v - Average velocity Keff - effective conductivity Keffâð - conduction heat transferredRi - Inertial resistance Rv - Viscous resistance Sh - heat content in the chemical reaction (zero in this case) ð - Density â - Porosity of the medium ?Ì? - mass flow rate (kg/s) ð¶ð - Specific heat (J/kg-K) ð¥ð - temperature difference (K) â - thermal diffusion length, K - thermal conductivity ð0 â ðâ - the temperature difference between the geothermal well and the ambient medium. Rth - thermal resistance xiii ðððð- Rate of change of flux in the normal directionâ - Characteristic lengthS - Shape factor xiv AcknowledgmentsFirstly, I would like to present my sincere thanks to my supervisor, Dr. Sunny Li, for giving me an opportunity to pursue this research and providing me boundless support and motivation throughout my research phase by providing me knowledge, insight and motivation. I sincerely thank Prof.Li for changing my writing and presentation skills. I would like to extend my gratitude towards Mr. Mojtaba Zabihi, who has provided me a continuous support in learning FLUENT and other technical inputs. With his support, the results mentioned in the chapter 4 are obtained. My appreciation to Dr. Xuan Gao for helping me to shape my research scope and focus. My sincerest thanks to all my professors at University of British Columbia, who have helped me in gaining invaluable knowledge. I would also like to thank my dearest friend Ms. Anusha Kankanala, whom I had the opportunity to study with. I would like to provide my deepest gratitude to my parents, brother and sister, for constantly motivating me never to give up. xv DedicationâTo my parents, my brother and my sister, who have always stood with me at all stages of my life. I thank you for your strongest affection and continuous support throughout my life.â 1 Chapter 1: Introduction Data Centers (DCs) are essential for the existence of almost every sector â from the small server rooms to the enterprise data centers. Without those, IT and communications sector would not even withstand a day [1]. With the information market expanding day by day, the energy consumption inside the data centers is rising exponentially. Data Center industry accounts for nearly 1-2% of global energy consumption, and it is expected to increase exponentially in the coming years [2,3]. With the exponentially increasing storage, processing and transfer of data, the global carbon footprint has been surging every year. According to Natural Resource Defense Council (NRDC), since 2014, data centers have been adversely affecting the environment by releasing 200 million metric tons of CO2 every year. And these numbers continue to upsurge with time. This leads the need to bring in greener strategies to decrease the carbon emissionsby DCs [4,5]. The energy demand in the DCs is more than 100 times that of a typical office space and it is significantly increasing with the expansion of server capabilities [6]. It is estimated that nearly 1.5-3 % of the total energy consumption in the developed countries accounts to the use of data centers. With the explosion of data usage, the carbon footprint of data centers is expected to reach 259 Mt CO2 emissions by 2020, even with the advancements in green energy [7]. The lack of access to elite energy-efficient infrastructure is limiting the DC market in emerging countries. In a commercial perspective, reducing the energy consumption in data centers even by a small extent will give a competitive edge to the companies. Also, in the recent years, there has been an increase in regulations and corporate responsibility to adopt greener technologies to reduce the increasing global carbon footprint. Hence, due to limited available space and competitiveness, data center companies are forced to work on innovative 2 technologies which reduce the processing server sizes and increase the cabinet density. This can be done by imbibing various strategies, including the reduction of the DC Power Usage Effectiveness (PUE) or by stacking the data chips into three-dimensional arrangement, thereby reducing the distance of interconnection between chips [7]. An inside view of the modern server room in a DC is shown below in the figure 1.1. In a data server room, major portion of the energy is consumed primarily for data processing and cooling systems. Though server virtualization has enabled DC industry to cut down power requirements significantly, the rate of growth in this aspect is slowing down quickly. Keeping this in mind, the most efficient way to reduce the energy consumption is by reducing the power required for cooling the data servers. Hence, if the cooling can be achieved through passive and eco-friendly strategies, the carbon emissions can be shorteddrastically. Figure 1.1 An inside view of a data server room [8] 3 1.1. Data Center Cooling:Over the years, the major proportion of total energy consumption in data centers can be attributed to cooling, which will be eventually converted into heat, a lower grade form of energy. As this heat is at low temperature, it is difficult to use this heat energy for any direct use. Hence, the best method to avoid this would be to reduce the heat emitted at the source level. With effective hardware, this can be achieved. In the aspect of heat dissipation, one of the most effective ways to reduce DC energy consumption is to reduce the power requirement of DC cooling [9,10,11]. The DC design has been experiencing the decrease in floor space and the increase in the quantity of computing and storage capacity, and the trend results in a continuous increase of heat load footprint per square meter [12], which is up to ~10 kW/m2. To effectively deal with the high heat density so that servers operate within safe temperature limits, high-capacity cooling must be provided and requires a significant amount of electrical power [13,14,15]. The cooling system alone may account for up to 40% in average of the energy demand of a data center [16,17]. Typically, in a data center, the refrigerated fluid (generally water) from the evaporator is circulated into the DC server cabinets through Computer-Room Air Conditioning (CRAC) units. The ceiling of the server room is built in a raised portion to accommodate space for cooling the air, which is circulated inside the room. This circulation of chilled air throughout the data center room involves consumption of energy. A typical split of energy consumption by various data center sub-systems (in CRAC cooling) is detailed in Figure 1.1 & Figure 1.2. Figure 1.2 elucidates the power consumption by various components of a data center [18]. Analysis reveals that servers consume most of the energy in a DC and in the cooling systems, chiller & CRAC units consume the most. Hence, the benefits of reducing energy 4 consumption in DCs depends on highly-reliable systems and at the same time, reducing the energy consumption in these components by the development of suitable effective and efficient measures is imperative [19]. Figure.1.2 Energy consumption by various sub-systems in DC (modified from [18]) 1.1.1 Strategies for Data Center Cooling:Practically, the electric energy utilized by various components in the Data Center must get converted to heat, and this heat needs a kind of heat rejection system to be extracted. The cooling system has to be designed in such a way that the continuous full-load operation should not affect the server components, operating well under the worst-possible scenario. Over the years, the data center cooling industry has employed various techniques and methods of heat rejection. Ranging from the simple air cooling to the sophisticated immersion cooling, there has been an immense progress in the data center cooling technology to reduce the PUE, a ratio which measures the energy usage effectiveness in a DC, to the proximity of 1. The various cooling solutions used in a DC server room are as follows: 5 a. Air Cooling:As the name indicates, it involves the extraction of heat from the servers by utilizing air as a medium. Chilled air is produced with a refrigerant and circulated through the server room. This refrigerant extracts heat from the server components through heat exchange and then passes on heat further to the refrigeration chiller evaporator. The fluid inside the chiller undergoes the refrigeration cycle, where the fluid undergoes compression, followed by the condensation inside the condenser. The heat which is obtained in the condenser is discharged into the atmosphere via a cooling tower. In a conventional data center, an air-cooled system has a Computer Room Air Conditioner (CRAC) unit, which cools the server cabinets by extracting the hot air from the server room and cooling it. In order to aid the cooling process, there are other components like fans, chillers and cooling towers. It is like a conventional air-conditioning in a residential building, except that CRAC units can handle high fluctuations in server load, without any human intervention. The cold under-floor air enters the above-floor space through perforated tiles that are placed at the foot of the server racks. The racks, in turn, draw in this air through their front face and exhaust hot air from the rear face. The hot air finally returns to the top of the air-conditioning unit (CRAC). Sullivan [20] has proposed an arrangement where the cold and hot streams of air are separated and are contained. This is called hot/cold aisle arrangement. This arrangement has become common design for the data server room layout. However, it is not necessary to contain both hot and cold streams of the air, as containing one of the streams is enough in most of the cases. The cold air is supplied to the cabinet room through fin perforated tiles located on the floor of the server room. 6 b. Liquid Cooling: Liquid cooling is gaining popularity over the years due to its ability to extract a large amount of heat when compared to the traditional air-cooling. In the direct liquid cooling, the central processing units are cooled by the cold plate, while rest of the components use the cold air flow to reject heat. The efficiency in direct cooling is achieved by two primary heat transfer processes â one between the sink and the chilled air, and the one between the rejected hot air and the chilled water. Aquasar, the supercomputer based on water cooling, was studied extensively by Zimmermann et al. [21] to analyze its energy performance. The in-rack cooling, in combination with the liquid cooling is much more effective than the traditional air-cooling systems. The rack-level cooling can be equipped at the back door of the cabinet and the heat from the server is extracted through a mini heat exchanger. By using this technique, the need to separate hot and cold aisles can be avoided. In order to study such system, Almoli et.al. [22] has developed a CFD code which analyzes the liquid cooling performance of the heat exchanger . Garimella et al. [23] has performed a study to analyze the similar system. According to him, the Power Usage Effectiveness (PUE) of such system can go as low as 1.3. However, with the recent advancements in liquid cooling, it is estimated that PUE can reach 1. c. Immersion Cooling:This is one of the emerging technologies in the data center cooling industry. As water has high specific heat, it can absorb a lot more heat than air. In traditional liquid cooling, the water flow is limited. However, if the data center is immersed directly in a permanent aquatic body like a river or ocean, the fluid does not need to be pumped and there will be an infinite supply of water. Haywood et al. [24] proved that the efficiency of the immersive cooling system comprising of high 7 density cabinets has reduced the source-discharge line temperature drop by 81 %. The resulted calculations revealed that the immersion cooling technology can save more than 50% of the cooling costs when compared to the traditional air-cooling technology. d. Free Cooling: In colder climates, the open atmospheric air can be used for cooling the data centers. As this air is openly available and free to use, these cooling systems are called open-cooling or free-cooling systems. In order to monitor the temperature of the atmospheric air in the surroundings, temperature, flow and humidity sensors are used [25]. It is estimated that the data centers in the North America can utilize more than 8500 hours of these air-side economizers per year [26]. Often, these free-cooling systems are used in combination with dry cooling systems or cold pond systems for enhancing their reliability. e. Geothermal Cooling:Green technologies are being applied to the cooling of data centers. Most data center cooling systems use the atmosphere as the heat sink. For example, the CRAC-based cooling systems pumps heat to the air outside the data center. However, the air temperature varies with seasons. Microsoft has immersed one of its data centers at sea [27], using the sea, large waterbody, as the heat sink. The drowned data center has very effective cooling with very low energy consumption. However, the cost involved in establishing such a data center is prohibitive. In addition to waterbody, another type of heat sink is land. Using underground as the heat source or heat sink, geothermal heating and cooling have been widely used for buildings [28, 29]. Geothermal energy is becoming increasingly popular in the world to cater the needs of space heating and cooling. The word âgeothermalâ refers to the heat in the underground. 8 Underground, unlike air, is less sensitive to the temperature fluctuations. Moreover, the soil is abundantly available and can be considered as an infinite medium. As the ground acts as an infinite sink and source of heat, enormous amounts of heat can be extracted from and discharged to it for heating and cooling purposes. Unlike residential spaces, data centers do not need energy for heating purposes, as they continuously reject heat only. In the conventional cooling of data centers, Air Source Heat Pumps (ASHPs) are used. These are inefficient when compared to Ground Source Heat Pumps (GSHPs) or free cooling pumps. Also, relative to GSHPs, ASHPs have a high Power Usage Effectiveness (PUE), which is the amount of power utilized by the data center equipment to the amount of power delivered. PUE is a critical metric in deciding the energy efficiency of the DC and thus, data center companies are striving to bring it closer to 1 (ideal maximum). Moreover, lower PUE indicates lower carbon footprint. As a result, more DCs are replacing ASHPs with GSHPs, despite the high initial investment costs for better energy savings over long run. The findings approve that the temperature of the soil fairly remains constant throughout the year at a shallow depths in most of the regions without geographical complexities. This little fluctuation in the underground temperature enables us to cool the data servers, which operate at the same temperature range [30, 31]. Also, as the server load in the data centers remains almost in the same range with minor fluctuations, geothermal well can be designed with a maximum constant capacity. In case of geothermal cooling for data centers, as the underground acts as the infinite sink, the heat generated in the server cabinets of a DC is rejected to the underground geothermal well with the help of air-water heat exchange. The details of this are discussed in the further chapters. 9 1.1.2 Data Center Cooling Guidelines & Standards: The IT components need to be highly reliable, as they are sensitive to fluctuations in IT load. Because of the same reason, there have been control regulations laid out to prevent the malfunctioning or failure of IT equipment. American Society of Heating, Refrigeration and Air Conditioning Engineers (ASHRAE), under ISO 14644-1 class 8 standard proposes the various thermal regulations required inside a data server room [32]. These regulations are listed in the Table 1 shown below. The regulations primarily identify humidity and temperature as the major parameters. ASHRAE identifies data center IT equipment in 4 classes â A1, A2, A3 and A4, which operate in the respective temperature and humidity conditions as mentioned (see Table 1). Failure of DC components need not be always related to temperature and humidity, as sometimes, it can occur due to other factors like improper load regulation and dust in the electronic components. Hence, it is important to keep in mind that if the IT equipment is well-regulated and effective, energy consumption will significantly come down [33]. Table.1.1 Summary of thermal guidelines, ASHRAE, 2011 (modified from [32,33]) Dry-bulb temperature Humidity range Maximum dew point Recommended Class A1 and A4 18 â 270C 5.50C DP to 60%RH And 150C DP - Allowable Class A1 15 - 320C 20% - 80% 170C Class A2 10 - 350C 20% - 80% 210C Class A3 5 - 400C 8% - 85% 240C Class A4 5 - 450C 8% - 90% 240C 10 1.2 Literature Review: Keyword search is extensively used in identifying the relevant research papers and journal articles [34-37]. âGoogle scholarâ and âEngineering villageâ are used for searching the papers by using the keywords âdata centersâ, âgeothermal data center coolingâ, âsustainability in data centersâ, âdata center energy efficiencyâ and âdata center energy managementâ. Papers from various journals, research publications and articles are studied and the information is processed by meticulously analyzing the technicalities involved. As the research information needed to be identified should be latest, the reviewed research should be up to date. Because of the same, the period of 2000-2020 (except [84] from 1969 and [81] from 1984) is selected for the research study. Based on the same, 84 research papers, journal articles and conference papers are studied. The concept of utilizing the underground as a sink has existed since many years and in fact, geothermal energy is one of the most popular renewable energy sources used in homes, office spaces, other buildings etc. [38]. From the performance, it can be concluded that the geothermal energy is highly reliable, resilient, eco-friendly and sustainable. Soltani et.al. 2019 has illustrated the idea that the underground can be used as a source to store heat like a battery, calling it as âthermal batteriesâ [39]. Though the idea of geothermal cooling is not new, the process of cooling is often interlinked with the heating loop [40, 41, 42]. However, for applications like data centers where only cooling is required, and that too in a relatively much larger capacities, the concept of geothermal cooling is facing a few serious challenges. Moreover, the initial investment costs of the geothermal cooling systems are highly discouraging to many firms. 11 In order to study the ground-source heat pumps, extensive studies have been performed to analyze if they are suited to cooling applications. The performance of these ground source heat pumps are deeply studied when there is thermal imbalance due to the seasonal fluctuations in a chiller-based GSHP system. These studies include residential buildings [43], office spaces [44], research facilities [38] and various commercial spaces [45-48]. These studies are done across various regions of the world including Hong Kong, Greece, USA, China, Korea [49] etc. The addition of a cooling tower to the existing chiller system has been researched by Zhou et al. [50]. There were also studies done on open cooling system added to the ground source heat pumps for residential buildings [51]. There are other studies which studied the incorporation of commercial cooling technologies in the combination with the cold ponds [52], hot pavement systems [53], pavement dry coolers [54, 55] etc. Along with the numerical analyses, there have been experimental studies conducted on the GHSPs to understand the thermal performance of the building under GHSP, when compared to the AHSP system. A couple of studies that fall under this category are two residential buildings in Spain [56, 57]. It is evident that the primary research focus of the geothermal cooling applications has been the residential systems (in tropical or hot regions). The cooling load required for a general residential system is of the range 12-15 kW [58], whereas for data centers, it is in MW. This huge difference in cooling requirements incur new challenges in the geothermal data center cooling industry. The dominant setback can be attributed to the high thermal resistance of the soil, which curbs the rate of heat transfer to a large extent. However, there have been a few attempts made to incorporate geothermal cooling in data centers. The Cornell university data center set up in Ithaca has a capacity of 51 MW and it operates on water-based geothermal cooling system [59]. Zurmuhl et.al. [60] details about an experimental 12 data center setup in Ithaca, NY installed for Verizon telecommunications, based on an innovative GHSP (Ground Source Heat Pump) design, aided by a dry cooler technology. The idea has produced successful results, but it is limited to lower capacity cooling applications (12-15 kW). The implementation of geothermal cooling using various technologies like liquid cooling, free cooling etc. are elucidated in the literature [61-64]. Most of the proposed geothermal cooling systems for data centers utilize large volumes of water, which is often catered by large water bodies. Though this is effective, there are certain environmental concerns like changing the water body temperature, thus affecting the aquatic life residing in them. Also, it is a highly expensive investment and the construction process is laborious. Various strategies can be employed to improve the heat transfer into the ground. One of the most effective methods is to increase the heat transfer surface area which can done by using strategies like extended surfaces, porous materials etc. (discussed in the chapter 3 and chapter 5). Porous medium is used as an energy storing material for a long time. Also, it has been known that the rate of heat transfer increases with the increase in the heat transfer area, which can be done with the help of a porous medium. Chen et.al., 2018 [65] details the use of porous material to store the ground heat and utilizing this heat for pipeline applications. Hooman et.al., 2010 [66] illustrates the use of porous material in the cooling towers as a condenser. 1.3 Summary: Data centers emit massive amounts of heat during their operation and cooling systems are used to reject this heat to atmosphere, water, ground etc. by using various sophisticated strategies. Most of the conventional methods used for DC cooling are one of the major contributors to the 13 rise in carbon footprint. With the increasing awareness and regulations to promote environment-friendly cooling, the DC industry has been moving towards green strategies. Geothermal systems, which are known for their reliability, have the potential to overcome the limitations of solar, wind and open-cooling based systems. Yet the use of geo-exchange in DC cooling has been understudied. Hence, with the knowledge gained from the above cited literature, a novel geo-exchange well model has been developed by employing various strategies and the possibility of utilizing geothermal heat rejection for data centers has been evaluated by a detailed thermal analysis. 14 Chapter 2: Research Objectives and Methodology This chapter of the thesis outlines the importance of this research, the detailed idea of the geo-exchange well systems, objectives and expectations of the research, the methodology used in the research conduct and the structure of how the thesis is laid down. The primary objective of this research is to investigate the feasibility of applying geo-exchange by using various designs, in terms of heat transfer performance. The model is aimed to serve as a cooling solution for a small to medium capacity data center ranging between 200 KW and 1 MW, without using a water body. 2.1 Motivation: Even though the research on geo-exchange DC cooling has progressed over the years, much of the work related to geothermal cooling has its emphasis on using water bodies for rejecting the server heat. For the data centers located far from water bodies or the ones which cannot utilize water from the rivers or the lakes due to environmental regulations, this system poses strong hindrances. Hence, this highlights the importance of developing a simple geothermal-based DC heat rejecter system which can operate in multiple locations and weather situations along with bring eco-friendly. The high impedance of soil has hindered the researchers from progressing the geo-exchange cooling research. Though the inherent property of the soil cannot be changed, the heat transfer area of the ground-coupled well with the soil can be enhanced to increase the rate of heat transfer. Porous media can increase the rate of heat transfer surface area by multiple times and with the decrease in porosity the heat absorbing ability per envelope increases [67]. This has paved a way for the development of a porous-medium based geothermal well system discussed in the next section. The amount of heat transferred can also be increased by using multiple geothermal 15 wells instead of using a single one. And, this stood as the basis for the multiple-well model, which has been detailed in chapter 6. With respect to these two ideas, the possibility of utilizing underground for DC cooling has been analyzed in this research. The details of the research idea and the methodology of developing this idea has been discussed in the sections below. For this research, the liquid used for cooling purposes in water. 2.2 Research Idea: In the entire heat transfer process from the cabinets to the soil, there are multiple exchanges of heat energy between various components of the cooling system. Cold air enters the cabinets to extract away heat from the servers and this heat is transferred to the cold water from the underground. This heats up the geothermal well and after a continuos heat exchange, it reaches a saturation temperature (or unsteady temperature after operating for a certain time). This heat is dumped to the underground sink surrounding the well. During every stage of heat transfer, due to factors like materialistic properties, component design, fluid circulation rate etc. there will be a resistance for the free flow of heat. Thermal resistance (Rth) between two bodies or systems A and B is the ratio of the temperature difference between the them and the amount of heat flux between them [68]. Rth = ðð´âððµð(2.1) Here, ðð´ and ðð´ are the temperatures of the systems A and B respectively and q is the heat flux transferred between the system. These entire exchanges of heat and the thermal resistances involved can be illustrated in the form of a thermal network as shown in the figure 2.1. The focus of this research rests on the last resistance in the network i.e. the resistance to sink the DC heat into the underground. 16 Figure 2.1 Thermal network of the geo-exchange heat transfer system This entire cooling system can be divided into two sections â data server room and the geothermal system. The focus of this research is on the latter section. However, it is important to understand the technicalities involved on both the sides. a. Data Server Room: The heat generated from the servers can be removed with the help of either air cooing or liquid cooling. Air-cooling is a more popular and easy-to-implement technology than liquid cooling, whereas the liquid cooling is a lot more efficient cooling technology than air-cooling with respect to high-density server cabinets. However, it is quite sophisticated. Hence, for the sake of simplicity, it is assumed that the air-cooling technology is used in the server room. in the cabinet thecabinetiqehoiehoefehw17 The air-cooling techniques are evolving with the need to cool higher density cabinets. Though the use of CRAC units seem to go well on paper, the use of CRAC units is outdated and emphasizes some serious problems. Depending on the air flow and the layout of the servers, these CRAC units can possibly create localized hot-spots and turbulence zones within the server room. The localized hot-spots thus formed will result in large temperature gradients in the region and cut downs the cooling efficiency by a large extent. Moreover, they consume a lot of cooling power. The Power Usage Effectiveness (PUE) of a conventional CRAC-cooled system is very high (almost closer to 2). In the last decade, air-cooling techniques have improved and have involved containing the hot and cold air zones separately, to increase the localized cooling, thus increasing the energy efficiency, However, this has not eliminated the problem of high-power utilization of CRAC units. Temperatures in the hot spots reach 37.8 0C and the temperatures in the cold spots till 15.5 0C, which is not in the desirable temperature range of 18-27 0C [18]. In the recent years, efforts have been made to bring the cooling procedure closer to the heat source. This has resulted in the concept of In-rack cooling, which inherently means that the cooling system is designed at a rack-level. The in-rack cabinet cooling used for this research involves cooling and heat exchange for individual server cabinet. Figure 2.2 shows a server cabinet equipped with heat exchangers on its back panel. The front of the cabinet is open to the ambient air to maximize the airflow. To ensure the involvement of the entire airflow in the air-water heat exchange, the right, left, top, and bottom sides of the cabinet are closed, and the rear panel is open only to the heat exchangers. Each heat exchanger is composed of a finned tube coil and an electrical cooling fan. The coil is installed between servers and the fan. The fan is installed with its intake facing inside and its exhaust facing outside. Hence, airflow is pulled into the cabinet from front and passes through servers to take the heat, and then 18 warm air passes through the finned tube coil to release the heat to the water flow, and then exits through the fan. If the fan rotation can be reversed by switching the power, the air flow can be reversed. The major difference is the air temperature inside the data center. The reversed mode might be suitable for winter as air inside data center is warmer than the normal mode. The server cabinet cooling shown in Fig. 2.2 has multiple benefits as follows. 1. Proximity to the heat source.2. Ability to retrofit different cabinets/no interference with servers and existing electricalequipment.3. Ability to scale design depending on heat load.4. Each cabinet becomes a self-contained cooling unit.5. Redundancy can be built into the cooling solution, with multiple fans and heat exchangers.6. No requirement to cool the entire room e.g. no investment in large and inefficient CRACunits.Figure 2.2 (a) Server cabinet equipped with heat exchanger (b) Each heat exchanger is composed tube coil and electrical fan 19 b. Geothermal System:To achieve high cooling effectiveness, high cooling COP, and high reliability, a geo-exchangecooling system as shown in the figure 2.3 is conceptualized. In this system, underground is used as the heat sink, as data center heat is removed by water circulation and then dumped into water wells, called geothermal wells hereinafter. This system has three major advantages. 1. It has a low and steady heat sink temperature. Usually, the underground soil temperatureremains relatively constant during the year, making a constant heat sink. For most of theregions, the soil temperature at a depth of 5-15 m ranges from 10-15 â throughout the year[30,31].2. This geo-exchange cooling system has high heat transfer performance, which is based oneffective air cooling on servers, effective heat exchange from air flow to water flow, andeffective heat exchange in geothermal wells. These are the major research tasks in theproposed project.3. Another advantage is that the high system reliability due to three redundant components:redundant pump, redundant water source (utility water), and redundant geothermal well.The system is connected to utility water through the control valve #1. There are three benefits from having the utility water (in figure 2.3 and figure 2.4). 1. Utility water is used to adjust the water inside the wells.2. It enables to harvest the data center heat by getting warm water from valve#7 forcommercial or residential use.3. If both the wells fail, utility water feed connected to the system would be used for coolingthe data center with valves #1 and #7 open.20 Figure 2.3 Schematic diagram of a single-well geothermal cooling system The redundant geothermal well is necessary if one well fails or is in maintenance. Additionally, having two geothermal wells will enhance the data center cooling. The cooling can switch between the two wells by controlling the shut off valves #3-#6 so that none of them reaches the saturation temperature. Details about this geothermal cooling system will be explained in the next chapter. Similarly, instead of using a single well, multiple wells can be used as detailed in the figure 2.4. A network of hot and cold pipes is connected centrally, and each of the well is equipped with a hot and a cold pipe. Each well operates for a definite amount of time i.e., only a single well remains active at that particular time during the operating phase. The details of this idea are discussed in chapter 6 in detail. 21 Figure 2.4 Schematic diagram of multiple-well based geothermal cooling system 2.3 Objectives: As mentioned previously, though the concept of geo-exchange has an immense potential to work as a DC cooling system, there has not been enough focus on it, especially the non-aquatic (river or lake) systems. It arises the need to develop a geo-exchange cooling system which can be operated in multiple topographical conditions. It has been possible to develop only a 12-15 kW DC cooling system based purely on non-river geo-exchange system till date. Hence, this research aims at investigating the possibility of developing such geo-exchange heat rejection system in terms of thermal performance. The specific objectives are detailed below. 1. To investigate the feasibility of developing an eco-friendly geothermal cooling solution interms of heat rejection performance, for DCs of the range 200 kW-1 MW. The thermalanalysis is based on the finalized well design.22 2. To investigate the heat transfer performance of various geothermal well designs developed,based on enhancing the heat transfer area or by multiplying the number of wells.3. To analyze and optimize the heat transfer surface area required for the geothermal wellsystem.4. To identify the limitations in the thermal performance of the developed well and push thisgeo-exchange concept further.Though this research involves an entire geothermal cooling system, the scope of this research is pertained only to the geo-exchange part and the details mentioned about the data server room are used for the sake of validating the input temperature used for the geothermal well. Also, the focus of this research is entirely on the thermal aspects of the well. The costs and lifecycle performance of the well are out of scope for this research. For the sake of simplicity, there are a few reasonable assumptions considered for this research. 2.4 Methodology: The entire research is performed in various steps as highlighted in the flowchart below (figure 2.5). In this section, the methodology used in the approach of this research is detailed. i. Research Objectives:This phase involves the identification of research needs and setting up the one of the initialsteps in the research. During this stage, after brainstorming, an initial idea of the research was developed to fix the framework and the scope of the research. Using this as a basis of understanding needs, research objectives were framed. The objectives thus fixed are mentioned in the section 2.3. 23 Figure 2.5 Flowchart of the research methodology 24 ii. Literature Review:Using the developed idea as a foundation, an extensive study of research papers, journalsand other research works was performed. It involved the investigation of current and emerging trend on the data center cooling in an inverted pyramid way, starting with the study of emerging trends of DC cooling, the use of renewable and passive cooling technoligies in DC cooling andnarrowing the focus onto the geothermal cooling technologies. Then, various literature sources involving the technologies to implement geothermal cooling in data centers (like lake cooling, river cooling, immersive cooling etc.) were studied. Further, the feasibility of utilizing the geo-exchange by using various strategies has been studied. iii. Methodology Development:After a detailed study of literature, a research methodology was developed to work on theconceptualized idea. A flowchart has been devised with the aim of smoothening the work flow. iv. Study of Data Server Room:This step is not directly linked to the main tree, but this is a necessary step to validate theassumption of hot water temperature entering the geothermal well. Additionally, the numerical simulation performed gives an insight of the flow management inside the server room. v. 3D Modeling of Geothermal Well:Parameters like the pressure drop inherent properties of the medium like in porous medium,porosity, permeability, viscous resistance, inertial resistance are critical, as they decide if the considered porous medium serves the purpose of DC cooling. During this stage, a vigorous study 25 has been done to identify the values of porosity, permeability, and sphericity of gravel (considered porous medium). Using these values, the above-mentioned critical parameters are calculated. These values are used later as the inputs for the numerical simulation performed to understand the feasibility of the research idea. As there is no existing literature source which mentions about the use of porous medium model in data center cooling in the purview of the literary search performed, the 3D modeling of the geothermal well involved multiple modifications. The three-dimensional modeling of the geothermal well has been done using ANSYS Design Modeler. Based on the literature involving the general pipe sizes used in geothermal heating and cooling applications, the pipes used in this geothermal well are designed. Regarding the porous medium based design, the values obtained from the calculations of critical parameters of the geothermal well are used as inputs for the numerical simulation. vi. Steady-state Analysis:In this stage, the designed geothermal well is tested under steady-state conditions byanalytical approach, as the infinite domain scenario cannot be setup on ANSYS FLUENT. However, numerical simulation of the geothermal well is performed using the same, and the obtained results are analyzed to understand the influence of mesh, physical dimensions of the well and the domain dimensions on the rate of heat transfer. The obtained design is evaluated after the steady-state analysis and it was followed transient analysis as the results obtained in this state are unsatisfactory. 26 vii. Transient Analysis:Transient analysis is one of the most crucial stages of the research, as it aids to investigatethe time up to which the designed well can be operated effectively under given conditions. The single well performance of the designed well under time dependent and unsteady conditions can be analyzed using transient analysis. ANSYS FLUENT has been used for testing the geothermal well under time constraints and similar to the steady-state analysis, the variation of heat transfer rate with respect to the physical dimensions of the well and domain are studied under transient conditions. viii. Evaluation of the Design:This is the second evaluation of the designed well. Once the modeled geothermal well wassubjected to transient analysis, the design was evaluated to see if it is efficient with respective to the considered objectives. The obtained results from the numerical simulation were validated with the help of analytical methods and other cited literature. When the design failed to meet the expected criteria, the design has been subjected to modifications and was tested again in steady-state and transient analyses. This method had been repeated till the final conclusions have been drawn. ix. Multiple-well Model:If the transient performance of a single well is not satisfactory, a multiple-well model isdesigned, after considering the results obtained from the transient analysis. These wells are analyzed with the help of analytical methods, and the final conclusions on the application of multiple-well model for the considered DC capacity are drawn. 27 x. Verify and Conclude:In the final stage, the feasibility of implementing the proposed geo-exchange design wasevaluated, along with the possibility of developing the idea into a commercial technological solution. The pros and cons of the research are identified and the potential room for improvement in the future is suggested. 2.5 Thesis Layout: The thesis consists of eight chapters. The layout of each of the chapters is detailed below. Chapter 1 presents the introductory part of the research. It details the need to adopt cleaner and sustainable technologies in data center cooling. This chapter includes information on the current and emerging strategies on utilizing the underground as a heat sink. Also, the literature review of the research is propounded in this chapter. Chapter 2 gives an insight of the motivation, idea conceptualization, research objectives, the methodology used in conducting the research and the thesis layout. Chapter 3 explains about the numerical background of the thermal analysis involved. The governing equations and the solver details are explained. Also, it highlights the details of the soil parameters and the various calculations involved in the design of a geothermal well. It also shows the necessary assumptions taken for the analysis of the designed geothermal well. The designed models of the geothermal well are shown. Chapter 4 provides a view of cooling in a data center server room. A sample simulation of an in-rack cabinet cooling solution is done by modelling a rack and then CFD simulation is performed at a rack, cabinet, and the server room level to validate the water temperature entering the geothermal well. The results are backed up by the values obtained from the literature. 28 Chapter 5 consists of two sections â the results obtained from the steady-state and transient analyses. Section I presents about the steady-state analysis of the geothermal well. Numerical simulation of the modeled geothermal well is performed under steady state to prove the domain influence and the results are explained through analytical calculations. The effect of various well parameters on the rate of heat transfer is determined and the trends are noted. Section II gives and insight of the transient analysis or the time-response analysis of the modeled single geothermal well. The background of the analysis and further calculations are explained using the analytical approach. The effect of various well parameters on the rate of heat transfer is determined and the trends are noted. Chapter 6 highlights the innovative multiple well model proposed in this research. Time-response analysis of the thermal performance of geothermal well is presented using the analytical approach. Chapter 8 explains about the results and conclusions of the entire research. This chapter constitutes the positive outcomes and drawbacks of the conducted research. It also includes the future work that is proposed to push this research forward. 29 Chapter 3: Numerical Setup FLUENT 19.2 is used to solve the energy equation for this study. The pressure-based solver is used to solve the continuity, momentum equations, instead of the density-based solver. As the working medium considered is water, which is mildly incompressible, pressure-based solver is suitable for the process. Moreover, when the flow conditions are nearly laminar, this solver is highly accurate. For the spatial discretization and pressure-velocity coupling, SIMPLE algorithm is used for its relatively simplistic approach. Also, it results in a faster convergence for laminar flows. For every time step, the relative stopping criteria is set under the limit of 0.05. Realizable ðâð turbulence model is used to solve the turbulence in the water flow, as it provides an enhanced wall treatment when compared to the general ðâð model. It has been widely used in the numerical screening of pressure. The simplification of the wall treatment offered has resulted in reducing the computational cost by a large extent, without sacrificing the accuracy [69-72]. It is a two-layer model that fits aptly to resolve near-wall boundary problems [73]. The error for convergence is set under the order of 10-6 for the numerical simulation, except for the energy. For energy, the error threshold has been set to be under the order of 10-12. The mesh has been divided to finer elements near the boundaries and it is coarse in the domain where the heat transfer process is not significant. 3.1 Governing Equations: Geo-exchange in data centers involve the transfer of energy (heat) from the hot air of the data center servers to the cold water in the geothermal reservoir. Hence, when a numerical simulation is conducted, FLUENT involves the use of energy equation to solve for the rate of heat transferred. ANSYS FLUENT solves the energy equation [74], 30 ððð¡(ðð¸) + â. (?â?(ðð¸ + ð) = ( â. (Keffâð â â âðð½?Ì ? + (ðððð. ?â?)) +ð Sh (3.1) where Keff is the effective conductivity, ð½?Ì ? is the diffusion flux of species j, Sh is the heat contentin the chemical reaction (zero in this case), Keffâð term describes conduction, âðð½?Ì ? is the speciesdiffusion, ðððð. ?â? gives viscous dissipation. Similarly, the energy in above equation is given by ð¸ = â â ðð+ð22(3.2) where h is the sensible heat enthalpy. For ideal gases, h is given by h = â âðð?Ì ?ð(3.3) And for incompressible flows, it is h = â âðð?Ì ?ð+ðð(3.4) where ð?Ì ? is the mass fraction of species j andhj = â« ðð,ðððððððð (3.5) where Tref is the reference temperature in K. With regards to the heat transfer, conduction is the dominant mode of heat transfer in the geothermal well, and all other modes of heat transfer can be neglected. Equation 3.1 can be further simplified to ððð¡(ðâ) + â. (?â?â) = â. (keffâð) + Sh (3.6) where ð is the density, h is the sensible enthalpy, keff is the effective conductivity, T denotes temperature and Sh denotes volumetric heat source. When there is a solid-liquid interface, the increase in heat transfer due to liquid medium can be compensated by calculating the effective conductivity [75]. keff = k*fs + A*k*(1-fs) (3.7) 31 where fs is the solid fraction, k is the thermal conductivity of soil, A is a constant which depends on the solid-liquid combination. For a porous medium, the equation 3.7 changes to keff = â ðð + (1ââ)ðð (3.8)where â is the porosity, ks and kf are the thermal conductivities of the solid and fluid media respectively. Hence, from the energy equation, it is evident that the increase in heat transfer surface area will increase the total heat transferred. In one of the designs discussed in this research, a porous medium is used to enhance the heat transfer, as it increases the heat transfer surface area by multiple times. In simplistic term, a porous medium is defined as the material which have void or spaces in it for flow [29]. A porous medium is characterized by its most critical parameter porosity. Porosity represents the amount of void spaces in the material. All other properties of the porous material can be derived from its material through the value of porosity. 3.2 Geothermal Well Design: A geothermal well design involves the consideration of the objectives to be achieved with the geothermal well, consideration of soil properties and subsurface conditions, sizing of the pipe and the well. This section reviews the sequential steps involved in the modeling of the geothermal well. Considering the soil conditions at shallow depths, a couple of conceptual ideas are developed and subsequently, 3D CAD models are designed in accordance, with the help of ANSYS design modeler module. The primary objective is to reject the hot water from the data center to the underground, by using geothermal exchange. Initially, the hot water enters from the data center to the geothermal well. Gravity drives the water from inlet to the geothermal well. During this process, heat is transferred from hot water to the water in the reservoir, and 32 eventually, to the underground. This process is detailed in the form of a thermal network as shown previously in the figure 2.1. Thus, the hot water is cooled and reaches a thermal equilibrium and the well reaches a saturation temperature. The idea of utilizing the porous medium to enhance the active heat transfer area to improve the amount of heat transferred to the underground is investigated by developing a conceptual model as shown in the figure 3.1. The schematic diagram of the designed geothermal well with porous medium is shown in the figure below. Figure 3.1 Schematic diagram detailing the concept of the geothermal well A porous material can be defined as the one which is perforated or has voids and holes in it. The solid portion of the material is termed as âmatrixâ and the porous portion is called âvoidâ. Typically, fluids like water or air are filled in the voids. In this case, the solid portion of the porous medium used is gravel and the void portion is covered by water when it flows through it. The rejected heat fluid from the data center i.e. the fluid which has extracted heat from the server room, flows down the geothermal well, driven by gravity. Hence, if a porous section is added to 33 the geothermal well before reaching the water reservoir, the water has to seep into the reservoir via the porous medium. This porous section will not allow the water to seep in a straight line. The water would have to pass through the voids present in the porous medium. Depending on the porosity of the material, this increases the heat transfer area by tens and hundreds of times. The heat-absorbing capacity of the porous medium will increase exponentially. Gravel is the most widely used porous material for geothermal applications. The rate of heat transferred from the water to the soil depends primarily on the physical properties of the same. Hence, it is vital to estimate a few important properties of the porous medium. The CFD simulation of the geothermal well is performed in ANSYS FLUENT. Hence, while performing the calculations of the porous medium, FLUENT manual is used a reference guide. A porous medium model in ANSYS operates based on evaluating the flow resistances of the specific medium and inducting them to the material which is defined as âporousâ during the simulation. In short, the software treats a porous medium as a material wherein there will be a drop in momentum of the fluid due to viscous and inertial resistances. That being said, based on the thermal properties of the porous medium, it can also absorb or transfer heat to the fluid flowing through its voids. However, there are a few assumptions and limitations in modeling the porous medium in FLUENT. They are: 1. ANSYS FLUENT, by default, does not consider the porous medium to be void. It just sinksthe velocity of the fluid based on the volumetric flow rate of the fluid and the fluidresistances. Hence, the velocity calculated is superficial. However, there is an option tocalculate the physical velocity of the fluid instead of the former. In the present case, for thesake of simplicity, superficial velocity is considered.34 2. In this simulation, the porous medium considered is assumed to be isotropic. However, thereis a provision in FLUENT to vary the thermal properties of the porous medium with spaceand time. For the research case here, the flow is assumed to enter uniformly from the inletand with regards to the variation in temperature between the inlet and outlet, it is less than40 degrees Celsius. The thermal properties of gravel do not vary much in this temperaturerange; hence, it is assumed that the thermal properties of the porous medium remain thesame during the operation of the geothermal well.3. There are certain approximations taken in the calculation of superficial velocity, which arediscussed in the formulation part of this section.4. There is no consideration of the influence or interaction of the shock waves on porous partof gravel. This is quite reasonable for this simulation, as the velocity of water entering thewell is extremely low (less than 10 m/s in all cases).5. FLUENT assumes that there exists thermal equilibrium inside the porous material, bydefault. For the present case, this has not been changed.The calculations required for calculating the viscous and inertial fluid resistances in theporous medium are shown in the appendix A. Using the Ergunâs equation [74], we have the pressure drop given by equation 3.9 as the summation of viscous loss and inertial loss. ðððð= 150*µâ 2ð·2â(1ââ)2â3* v + ð*1.75â âð·â(1ââ)â3* v2 (3.9)where Rv is the viscous resistance, Ri is the inertial resistance, µ is the dynamic viscosity, ð is the density, â is the porosity of the medium, â is the sphericity of the medium, D is the diameter of particles making the medium, v is the average velocity. The first term on the right-hand side of the equation 3.9 gives viscous loss, and the second 35 term on the right-hand side gives the inertial resistance. When a laminar flow is considered, then, from the equation 3.9, second term can be dropped. Hence, the resulting Blake-Konezy equation is given by ðððð= 150*µð·2â(1ââ)2â3* v (3.10) Comparing equation 3.6 and equation 3.7 to the general fluid flow equation in porous medium, we have that the viscous loss is proportional to velocity and inertial loss is proportional to velocity squared. ðððð= Rv * µ * v + (Ri/2) * ð * v2 (3.11) The sphericity of a medium measures the tendency of the particles to be spherical in shape. This can be generally assumed as 0.75. Therefore, the equation (3.8) can be further reduced to equation 3.9.Rv = 150â âð·2â(1ââ)2â3Ri = 2*1.75â âð·â(1ââ)â3(3.12)The value of porosity varies, and it entirely depends on the type of gravel used. Based on the literature, in this case, the porosity is assumed to be 0.4. Also, the value of sphericity can be assumed to be 0.75. And the diameter of the gravel particle is 1 cm or 0.01 m. By substituting these values in the equation 3.9, obtain the values of viscous and inertial resistances are 15000000 (1/m2) and 2916.6 (1/m) respectively. These values are used as inputs for the CFD simulation of the geothermal well. Similarly, another conceptual model of utilizing multiple wells to increase the heat transfer is discussed in the chapter 6. Water is filled and extracted out of the wells by using a 36 network of pipes interconnected to each other. The primary concept of this multiple well model is shown in the schematic figure 3.2. Figure 3.2 Schematic of a multiple-well geothermal heat exchange system For the well design, the dimensions of the well and the pipe sizing is crucial, as the maximum volume of water entering the well is based on the same. In order to decide on the pipe size used in the design of geothermal well, commonly used pipe sizes are considered. The table shown below highlights the common pipe sizes and the maximum flow rates that can be allowed through them. Table 3.1 Various pipe sizes and the maximum volumetric flow rates (modified from [76]) Pipe size (inches) Maximum flow rates (lpm) 0.5 7.5708 0.75 15.1416 37 1 30.2832 1.25 45.4248 1.5 83.2788 2 151.416 2.5 264.978 3 454.248 4 984.204 6 2081.97 Hence, as per the data, the pipe size considered is 1 inch, and the volumetric flow rate considered under the maximum limit of 30 lpm. With regards to the size of the geothermal well, as a preliminary estimation, a box-shaped geothermal well is considered. A soil domain is modeled as an enclosure around the geothermal well, where the heat transfer takes place. The properties of the soil considered are from Hopmans et. al., 2002 [77]. And the soil considered is of 0.2 m3 m-3 volumetric water content. Coming back to the porous medium based model, a 3 x 3 m x 5 m box-shaped well was designed with the idea as mentioned above in the figure 3.1. The well is surrounded with a large soil domain of of the size 20 m x 20 m x 10 m (very large when compared to the size of the well), except the top, which is exposed to the atmospheric air. In order to understand the sole thermal performance of this well, the top part is assumed to be adiabatic, implying that the heat is transferred solely to the soil. Though the soil domain is infinitely large, a finite domain size is considered for the sake of simulation (which does not represent the actual heat transfer conditions). The 3D CAD model (box), and the mesh details are shown below (in the figure 3.3 and figure 3.4). 38 Figure 3.3. 3D CAD model of the geothermal well in ANSYS Design Modeler (a)39 (b) Figure 3.4 Developed mesh at the interfaces for the 3D CAD model of geothermal well a. Mesh at the inlet pipe-porous medium interface b. Mesh at the porous medium-soilinterface Figure 3.4 illustrates the mesh that has been generated for the developed 3D CAD model. A linear mesh of size of 0.1 m is generated for the entire model and the mesh is refined at the pipe surfaces to a size of 0.01 m, so that the solution is mesh independent. It can be observed from the figure 3.4 (a and b) that the element ends at the pipe-porous medium interface and porous medium-soil interface match and hence, the scope of error due to meshing is minimal. In order to perform the numerical simulation of the geothermal well, it is foremost to understand the heat transfer that takes place inside the data server room. The heat extracted from the servers characterize the temperature of the water entering the geothermal well. 40 ?Ì? = ?Ì?ð¶ðð¥ðserver room (3.13) where ?Ì? is the mass flow rate of the water entering the geothermal well (kg/s), ð¶ð is the Specific heat (J/kg-K) and ð¥ð is the temperature difference (K). And, equation 3.13 can be implied as ð¥ðwell = (Tin âTâ) server room = ?Ì??Ì?ð¶ð(3.14) And ?Ì? = KA ð¥ðwell (3.15) Hence, in order to obtain the value of the temperature of the water entering the geothermal well, it is important to know the temperature of the hot water leaving the data server room, before entering the geothermal well. In the next chapter, a numerical simulation of the data server room is performed to check if the water leaving the data center carries a temperature of around 50 0C is reasonable. 41 Chapter 4: Data Server Room Data sever rooms are the confined spaces which are responsible for the continuous functioning of the server cabinets. As discussed before, it is pivotal to understand the heat transfer process in the server room, as the temperature of the water leaving the data server room forms the basis for the geothermal well analysis .Though there are many types of cooling methods employed to cool the server cabinets, in-rack cooling is considered to be the most efficient method after immersive cooling. Thus, as discussed in the section 2.2, an in-rack cabinet cooling system is considered for understanding the thermal transactions involved inside the data server room. The details of the numerical simulation are discussed below. 4.1 Assumptions: This chapter involves a high-level view of the in-rack cooling system in a DC. During the conduct of the server room numerical simulation, there are a few reasonable assumptions made and simplifications considered in terms of the conditions inside the cabinet, boundary conditions and flow behaviour, eliminate the uncertainty. i. The boundaries of the server room are adiabatic with no-slip boundary conditions i.e. itis assumed that there is no heat leakage to the surroundings from the server room and theheat transfer involved is strictly between the cold air entering the server room and the hotserver racks.ii. A segregated pressure-based solver has been used to calculate the changes in three-dimensional changes in velocity, pressure, temperature, kinematic energy, dissipation ofkinetic energy etc. because it is more memory-efficient and simple to use.iii. CFD tools are used for data server rooms to determine the localized hot spots, predict42 temperature distributions and flow patterns. As the objective of this chapter is to understand the temperature distribution in the in-rack cooling system and obtain a valid assumption for temperature of the water leaving the server room and entering the geothermal well, the focus rests only on the heat transfer in racks and the dominance of other factors are neglected. iv. K-â method is used for solving the turbulence of air flow, which means that theturbulence is assumed to be isotropic. Also, the drawback of this model is that it assumesthat the flow is always and completely turbulent, which might not be the case for lowvelocity flows at certain regions. Yet this method is considered for faster convergence.4.2 CFD Simulation of Data Server Room: To monitor the temperature and flow distribution, numerical analysis has been performed in a pyramid way, starting at the rack-level, and then, the cabinet level. ANSYS ICEM has been used for the modelling, and FLUENT has been used for the numerical simulation. The details of the rack are shown in the figure 4.1. For the rack, the dimensions of 50 x 35 x 10 cm are considered. The cold air enters from the perforated holes at the entry of the cabinet, and extract the heat generated inside the rack, as the fans (blowers) suck the air from exit. The fluid velocity and the flow pattern is managed efficiently to maintain the rack temperature in an optimal range of 18-25 0C (as mentioned in the section 1.1.1). For the purpose of simulation, an inlet temperature of 15 0C is considered [78]. The server rack design considered in this research is a simplified rack design and is not a direct design of any commercially fabricated server rack. Variable speed fans are used to deal with the fluctuations in the load. Thus, they are used to control temperature swings due around 43 the server components. The load fluctuations, which dominate the changes in temperature, are dealt by varying the air-flow velocity using fans. A free flow of air enters through the fine grilled perforations of the heat exchanger, to exchange the heat to the cold water from the geothermal well via the mini-heat exchanger. The slightly cold air is further cooled down, due to the hot air being absorbed by the multiple finned heat sink. Once this air flows through the heat source and gets heated up, this heated air is extracted away by the fan to the server room, which in turn flows back to the rack and the cycle continues. Figure 4.1 3D ICEM model of the data server rack The generated mesh for this is shown in the figure 4.2. Given a 3D ICEM geometry, various CAD packages could be used to encode it and store it in a file. Encoding the geometry using an approximate mesh is one of the most common methods adopted to store a surface geometry. A linear mesh with varying fineness is created by covering the surface 44 geometry with a series of polygons, so that the encoded surface mesh can be stored in a file for sharing and future reference purposes. These files store the nodes of the polygons as well as the outward normal directions to the nodes. A refined mesh is created closer to the heat source and heat sink, when compared to the non-heat generating sections of the rack. Figure 4.2 ICEM generated mesh for the proposed server rack Firstly, the numerical simulation is started at a rack level. It is assumed that the average heat flux across from the source is 15 kW, which is quite a reasonable assumption [79]. The air flows naturally, hence the velocity magnitude of the air at inlet of the in-rack cooling system is 1 m/s. The ambient temperature is assumed to be 288 K and is applied at the server rack wall. This ambient temperature is not same that of the temperature of the ground water. Hot air leaves the server racks and heat up the server room. Though this air re-enters the server racks, due to the realistic efficiency of heat exchanger and the flow patterns developed around the server racks due to turbulence, the temperatures of the underground water and the ambient server room air will not be the same. The perforated grills are used as the flow inlets, fans act as the pressure 45 outlet. Apart from the heat source and the server walls, other walls involved in the numerical setup are assumed to be adiabatic. As detailed before, the temperature inside the data server room is fixed to 288 K and the temperature of the water entering the data server room is assumed to be 283 K. The mass flow rates of the water and air are adjusted in accordance to the desired outlet temperatures. Under ideal effectiveness conditions, in order to reject heat from a small DC, say of 250 kW capacity, the mass flow rate of the air is adjusted to 8.204 m3/s and the mass flow rate of the water is set to 1.495 m3/s. The flow rates are adjusted to match the varying load capacities. Results and Discussion:The obtained velocity path lines of the air particles during the entry and exit are captured. The details are shown in the figure 4.3 below. From the obtained results, it can be observed that the air particles enter freely from the perforated holes and are sucked by the fans from the other end, in the regions not obstructed by the heat sink. The flow velocity around this region falls to a low of 0.00268 m/s. The change in color from green to blue depicts the increase in velocity from entry to exit from 1 m/s to a maximum of 3.2 m/s. Figure 4.3 Velocity path lines inside the server rack at steady state 46 The temperature contour of the rack depicts that the maximum temperature obtained is 328 K. It can be observed from the temperature contour that the rack base has a temperature range of 308 K â 328 K (Figure 4.4). Without a surprise, the hottest zones are located around the heat transfer zones i.e. near the electronic components. Figure 4.4 Temperature contour inside the rack at steady state In the next stage, the CFD simulation is performed for multiple cabinets in a sample server room. As shown in the figure 4.5, six cabinets, which in turn comprised of four racks each were considered. Each cabinet of four racks has carried three perforation grills for the air to flow into the server racks. The heat flux is applied to each rack and the numerical simulation is performed. A single rack emits a heat of 15 kW, which makes the entire server room considered to be rejecting a load of 360 kW. The flow entry (cold) area and the flow exit (hot) area are marked down with blue and red colors respectively. 47 Figure 4.5 3D ICEM model of the proposed cabinet layout The contours of the static temperature at steady state is shown below (figure 4.6). The temperature contour reveal that the maximum temperature obtained is 57.5 0C and the least temperature is 22.5 0C. The high-temperature zones can be identified near the source and sink areas and most of the zones lie at a temperature around 45 0C. Figure 4.6 Cabinet-wise temperature distribution at steady state (temperature in 0C) 48 In this chapter, the temperature and flow distributions in an in-rack cooling system is understood at a rack and cabinet level. The maximum temperature of 57.5 0C obtained is well under the maximum allowed temperature on server racks. A server rack needs at least 120 CFM to cool a server rack of 1 kW [80]. When this is translated to the air flow required for a 15 kW server rack, it falls fairly short of 1 m/s. Hence, the assumption of flow velocity entering the server rack is valid. As the multiple-well system is used (discussed in the chapter 6) and every single cabinet is supplied with cold water, the pump power required for the continuous circulation is high. The pump power can be reduced by decreasing the mass flow rate of the cold fluid i.e. water. Also, in the multiple-well model, convective mode of heat transfer is considered. Hence, this passive strategy is employed to enhance the rate of open cooling, thereby reducing the pump power greatly. Hence, in order to assume the worst case scenario in terms of thermal performance, and best-case scenario in terms of conservation of energy, it has been roughly estimated that the water carrying the heat from the server room enters the geothermal well at around 50 0C [80]. In the next chapter, the thermal performance of the geothermal well is studied under steady-state and time-dependent conditions. 49 Chapter 5: Results In the last chapter, the numerical simulation of a data server room is performed and the results gathered indicate that it is reasonable to assume that the temperature of the water leaving the data server room and entering the geothermal well as 50 0C. In this chapter, the analysis is made for the designed geothermal model detailed in the section 3.2. The design is subjected to a comprehensive steady and unsteady analyses and based on the results, the design is modified to obtain a satisfactory conclusion. Section-I discusses the thermal behaviour of the well under steady state conditions. As the numerical simulation is dependent on the size of the domain, the emphasis in this section is on the analytical approach. For analyzing the transient behaviour of the well, numerical approach is preferred to the analytical one, as the transient behaviour is complicated and highly unpredictable. These details are detailed in the section-II. Section-I: Steady-state Analysis: Steady state thermal analysis of the geothermal well is used to calculate the thermal response to the heat loads depending on the given boundary conditions and assumptions which do not change with time. ANSYS FLUENT is used to perform the thermal analysis of the well under steady-state. This section includes the numerical simulation of the well, followed by the analytical comparison of the obtained results. Firstly, the assumptions involved in the numerical simulation are: 1. As the volume of water transferred to the soil is negligible when compared to the circulation within the well, the soil is assumed that it is a solid medium rather than a porous medium. It50 implies that there is only heat transfer between the geothermal well and the soil, but no mass transfer. 2. The soil domain considered for the simulation is finite, as modeling an infinite medium understeady-state conditions is limited by the software used.3. The water flow at the entry of the well is laminar. For the porous medium based design, thewater flow through the porous medium is laminar.4. The soil is assumed to be isotropic and hence, the properties of soil remain same in all thedirections.5. A segregated pressure-based solver has been used for memory efficiency and simplicity.6. The turbulence is assumed to be isotropic. This simplifies the minimal velocity regions withapproximations. Yet this method is employed for memory efficiency, faster convergence andsimplicity.7. The volume of water that enters the geothermal well is exactly equal to the volume of waterthat leaves the well and there are no volumetric losses. Hence, an outflow boundary conditionwith the flow factor one is imposed at the velocity outlet.8. The properties of the porous medium (gravel) and the soil remain constant independent of thefluctuations in the temperature.9. There is no friction near the pipe walls i.e. the friction factor of the pipe is zero and the no-slipcondition is applied at the pipe walls.10. The soil is assumed to be saturated. Though this is not the case for all the soils, this soil isconsidered for the preliminary analysis.51 I.1 Numerical Approach:A numerical analysis is performed for the geo- exchange well shown in the figure 3.3. Water enters from the inlet with a velocity of 3 m/s and seeps through the porous medium with the aid of gravity. During this process, momentum is lost due to the inertial and viscous resistances of the gravel. In order to set up the numerical simulation, the density, thermal conductivity and specific heat values of soil and gravel are gathered from the literature. The values of viscous resistance and inertial resistance are calculated from the Ergunâs equation (equation 3.11). The porosity of the gravel is assumed to be 0.4 and the diameter of the particles making the bed as 0.1 mm. The water-saturated porous medium (gravel) properties considered for this simulation are listed in the table 5.1 [81]. And the properties of the soil considered are detailed in the table 5.2 [82]. Table 5.1 Properties of the gravel used for the numerical simulation (modified from [81]) Input property of gravel Value Density (kg/m3) 2650Thermal conductivity (W/m-K) 2.4 Specific heat (J/kg K) 800 Inertial resistance (1/m) 15000000 Viscous resistance (1/m2) 2916.6 Porosity 0.4 Table 5.2 Properties of soil considered for the numerical simulation (modified from [82]) Input property of the soil Value Density 2400 Thermal conductivity (W/m-K) 1.9 Specific heat (J/kg K) 717 52 The type of soil considered here is saturated in nature. Practically, the nature of soil will be completely different in the respective regions. Thermal conductivity of the soil is highly sensitive to the moisture content, dry density of the soil and the mineral composition of the soil. Hence, before building a geothermal well system, it is crucial to investigate the properties of the soil, as the resultant thermal conductivity will change the heat transfer performance and sizing of the geothermal well system. The value of thermal conductivity of the soil can reach up to 7 W/m-K for the rocky soils and can drop as low as 0.15 W/m-K for soils containing clay content. Hence, the rocky-soil regions are the desired soils for the obvious reasons. Table 5.3 highlights the thermal conductivity ranges of various soil types [83]. Table 5.3 Thermal conductivity ranges of various soil types (modified from [83]) Soil type Thermal conductivity (W/m-K) Saturated soil 0.6 â 4 Sand perfectly dry 0.15 â 0.25 Sand moist 0.25 â 2 Sand saturated 2 â 4 Clay dry to moist 0.15 â 1.8 Clay saturated 0.6 â 2.5 Soil with organic matter 0.15 â 2 Solid rocks 2 â 7 Tuff (porous volcanic rock) 0.5 â 2.5 Initially, for the sake of simplicity, the thermal analysis of the geothermal well system has been performed by considering the soil thermal conductivity to be 1.9 W/m-K, which is the average value for most of the soils. The thermal performance of the developed geothermal well system under various soil conditions has been detailed in the chapter 6. 53 The real-time steady state simulation cannot be done, as the infinite domain cannot be modeled at steady-state. Yet, the steady-state analysis has been done to capture the parameters which affect the rate of well-soil heat transfer. The steady-state model used for the numerical simulation is mentioned in the figure 3.2. At the inlet, as the fluid enters from the inlet, velocity-inlet condition is chosen. The fluid (water) is assumed to be incompressible, the selection is justified. Velocity inlet boundary condition enables to define the relevant properties of the flow like flow velocity and direction, initial temperature and pressure. The total stagnation pressure in velocity-inlet boundary condition is not fixed, but rather it rises in accordance with the variation in velocity. Water enters the inlet pipe with a laminar flow velocity of 3 m/s and the initial temperature of 323 K. Outflow condition is selected for the outlet pipe with a factor 1, as it is assumed that the volumetric flow rate of water entering the inlet is equal to that of the volume of water leaving the outlet pipe and there is no leakage of water from the well to the underground. Regarding the wall conditions, the temperature of all the walls in the soil domain are at uniform temperature of 283 K and it is assumed that there is no heat transfer between the well and the atmospheric air i.e. the top layer of the well is insulated. This is to evaluate the thermal performance of the well under pure conduction. Also, it is assumed that there is no heat leakage from the pipes carrying water. Heat transfer from all other walls are ignored, as they tend to be zero at steady state. For the simulation, a box-shaped well is considered. The obtained results of the numerical simulation are shown below. From the pressure contour at the mid-section of the box-shaped well (figure 5.1) depicts that the pressure loss from the inlet to the outlet is extremely high. The initial pressure of the flow at the inlet is 118200 Pa and it becomes -30050 Pa, accounting to a net pressure loss of 148250 Pa. This implies that porous medium is too dense for the water to flow through 54 quickly. This can also state that the flow rate might be too little for the water to penetrate through the porous medium. Hence, in order to overcome the enormous pressure drop, either the porosity has to be increased or the pump power has to be increased. As the outlet is defined for the simulation, a low pressure is observed near the outlet, which indicates that the water is ready to be sucked from the well to the outlet. As the water rises above, pressure drops gradually. Figure 5.1 Pressure contour of the designed geothermal well at steady state This can be observed further in the velocity distribution contour (as depicted in the figure 5.2). Figure 5.2 shows the velocity contour of the geometric well, indicating the stream speeds at both the inlet and the outlet. We can observe that the velocity remains the same in the pipe due to 55 minimal friction and as soon as the water leaves the pipe, the stream becomes divergent and the velocity of the fluid greatly goes down at the boundaries when compared to the center. It becomes zero when it mixes with the underground water stream. Due to the low pressure created at the entrance of the outlet, the water has a higher velocity and it reaches a maximum velocity of 6.47 m/s at the inner mouth of the outlet pipe. Figure 5.2 Velocity contour of the designed geothermal well at steady state The temperature contour across the mid-section of the geothermal well is detailed in the figure 5.3. The distribution of temperature reveals that the maximum temperature of 323 K is uniformly distributed inside the well, and the temperature slowly decreases with the increase in distance from the well-soil boundary. This indicates that the rate of heat transfer from the hot water 56 to the geo-exchange well is slower than the heat transfer from well to the soil. In other words, the designed well completely ineffective in dissipating the heat to the underground from the data center. Figure 5.3 Temperature contour of the designed geothermal well at steady state I-2: Design Modifications:The above results indicate that the rate of heat that is being transferred from the hot water from the DC to the underground soil is very slow. The high impedance of soil has resulted in higher impedance and thus, the rate of heat transfer is slow. As the heat transfer depends on the surface area of the well, the surface area of the well must be increased to enhance the conductive heat transfer. With respect to these, there are certain limitations associated with the model 1. From the simulation, it is clear from the designed model that it has no capacity to transfer heatto the soil. Gravel is great at absorbing heat, but it does not dissipate it efficiently.57 2. The heat transfer from porous medium to walls was nearly 30000 W, which was no whereclose to the target, 1 MW.3. The pressure loss obtained was too high, which means that it needs a high pump power topump the water to leave from the outlet (which is uneconomical).4. Moreover, this simulation is dependent on the size of the domain. Hence, if the domain sizeincreases, the rate of heat transfer decreases and the domain size decreases, it increases. Inreality, this is not the situation.From the temperature contour, it is evident that the initially designed geo-exchange model is inefficient at the steady state, indicating that there is a need to enhance the rate of heat transfer to the soil. Decrease in porosity of the gravel results in the increase in water-gravel heat transfer area. However, given the pressure drop due to the use of highly porous gravel, this idea is impractical, and the use of porous medium can be eliminated. In order to increase the surface area of the geothermal well and to counter the low heat rejection to the soil, multiple fins made of high thermal conductivity (aluminum) are pierced into the well. These fins, which are also buried in the soil, act as a bridge to enhance the heat transfer to the soil. Numerical simulation is performed for this well and the temperature distribution examined for this well indicate that this design is inefficient, as it fails to overcome the design flaw of the previous model. This design is slightly modified by bridging copper rods bridged in between the geothermal well and the soil. Due to high thermal conductivity, these rods enable the gravel to transfer its heat extracted from the hot water to the underground, thus multiplying the rate the heat transfer. The design details of these models and the results obtained from them are discussed in Appendix A. 58 As discussed before, the real-time steady state conditions cannot be simulated using FLUENT. In order to understand the pattern of heat diffusion, this well of maximum heat that can be transferred from the geothermal well through pure conduction, a design shown below is considered (shown in the figure 5.4). Figure 5.4 2D CAD model of the modified geothermal well A simple geothermal well of dimensions 3 m x 3 m is designed with a soil domain of 20 m x 20 m surrounding the geo-exchange well. As the soil is assumed to be isotropic, a 2D CAD model can give an insight of the heat dissipation at steady state. The well is not physically modeled, but the walls of the well are represented as illustrated in the figure 5.4. The boundary conditions involved in this numerical simulation are quite similar to that of above-mentioned simulation 59 (figure 5.2), except for that there is no flow involved here and the CAD model is two-dimensional. The well-soil boundary is represented as one boundary and the walls of this boundary are at 323 K. A boundary condition of 283 K is applied at the soil wall (this boundary condition is not theaccurate representation of the real-time heat transfer condition, but this is the closest boundary condition that can be imposed in FLUENT). The variation of heat transfer with the physical dimensions of the well can be analyzed through the steady-state analysis and thus, the geo-exchange well design can be optimized for the transient state. A fine, quadrilateral mesh of 0.01 m is generated for the geothermal well system and the mesh is refined at the wall-soil boundary, as the heat transfer takes place at that interface. The ends of the mesh on the well side and the ends on the soil side coincide, indicating that the mesh is smooth. The details of the generated mesh are represented in the figure 5.5. Figure 5.5 2D CAD model mesh of the modified geothermal well 60 The temperature of the outside walls of the well (as shown in the figure 5.6) are at 323 K, which represents that the well is already at steady state and the outside walls of the soil domain are at 283 K. Though this does not represent the realistic heat transfer involved, this is the closest condition to the actual scenario that can be simulated in FLUENT. However, this numerical simulation helps to understand the pattern of heat propagation. Figure 5.6 Temperature contour of the simplified design of the geothermal well (2) at steady state Due to the dependency of domain size with the with regards to the results of heat transfer obtained in the numerical simulation, steady-state analysis through numerical simulation does not make much sense. However, this section is important, as it gives an insight of the pattern of heat dissipation from the well. Also, the influence of thermal resistances on the rate of heat transfer, well shape and mesh size, can be elucidated with the help of this steady state simulation (this is discussed in the section I-4). 61 I-3 Analytical Approach:As the numerical simulation is limited due to the inability of modeling an infinite-sized soil domain and to eliminate the dependence of domain size on the rate of heat transfer, analytical approach seems to be more suitable for the steady-state analysis. In case of pure conduction between solids or within the solids, dimensionless shape factors are used to evaluate the amount of heat transfer. Shape factors are the nothing but the dimensionless quantities which are used to represent the curvature of the heat flows in a linear relationship. While the shape factors are proved to be extremely useful in understanding the conductive heat transfer from the solids, the derivation of the shape factors are often sophisticated. For the analytical approach, shape factors are used to calculate the heat transfer in an infinite medium at steady state. At steady state, as the temperature of well reaches 50 °C, the entire well can be considered as a single shape. By calculating the shape factor, heat transfer from the well at steady state can be estimated. For the ellipsoid family geometries such as the spheroids, there are analytical solutions of shape factors available. The calculation of shape factors for the customized shapes is extremely complex and a knowledge of calculus is required to simplify the expressions. However, the calculation procedure of shape factors it is out of scope for this research. Yovanovich [84], with the help of analytical and numerical approaches, has derived a general expression for the shape factor (S) by comparing the shape factor with capacitance. When the cross-sectional area of the conducting system is kept constant along the heat direction of heat diffusion, this capacitance is a function proportional to the shape of the conductor and the calculated characteristic length of the conductor shape. Shape factor relates the thermal conductivity, the difference in temperature and the thermal diffusion length. According to Yovonowich, it is defined as 62 S = 1ðð =ð´â= ðð(ð0âðâ)= â¬ âðððððð´ð´ (5.1) where â is thermal diffusion length, k is thermal conductivity, ð0 â ðâ indicates the temperature difference between the geothermal well and the soil and R is the thermal resistance of the soil. The value of ððððrepresents the rate of change of flux in the normal direction of the heat dissipation. The dimensionless shape factor is given by ðâð´â = ðâð´= âð´â¬ âðððððð´ð´ (5.2) where â is the characteristic length, S is the shape factor. And, â is defined asâ = Volume of the bodySurface area (5.3) From the available literature, for the cylindrical well flushed by an infinite domain, the dimensionless shape factor is given by ðâð´â = âð´â= 3.1915+2.7726(ð¿ð)0.76â1+2ð¿ð , 0â¤ð¿ðâ¤ 8 (5.4) where L is the length and d is the diameter of the cylinder. And, the overall heat transferred is given by q = ðâð´â * K * (ð0 â ðâ) (5.5) The dimensionless shape factor represented in the equation 5.4 can be used to calculate the shape factors and thus, the heat transferred by the cylindrical geothermal well to the underground. By using these relations, when the L/d is decreased from 7 to 1.167, the variation of heat transfer is evaluated. The length of the cylindrical well (L) is kept constant and the diameter is varied to 63 maintain the ratio of length to the diameter in the range of 0 and 8. The results obtained are listed in the table 5.4. Table 5.4. Obtained heat transferred values from the analytical method for the cylindrical geothermal well L (m) Diameter (m) dimensionless shape factor Characteristic length (m) Heat transfer rate (W) 7 1 4.15 0.24 1435 7 2 3.92 0.46 1925 7 3 3.86 0.67 2331 7 4 3.84 0.87 2712 7 5 3.84 1.06 3071 7 6 3.85 1.23 3412 The obtained trend is shown below in the figure 5.7. It can be observed that the amount of heat transferred decreases with the increase in L/d ratio, implying that the rate of heat transfer increases as the cylinder tends to become long. The heat transfer rate, when the well has an L/d ratio of 1.23 is 3.412 kW, and it decreases non-linearly to 1.435 kW, as the length to diameter ratio of the cylindrical well tends to 7. Hence, in order to increase the rate of heat transfer, the geothermal well should have lesser L/d ratio. Considering the general space constraints, this is certainly advantageous, as going deeper into the underground is far more economical that increasing the surficial diameter of the well. 64 Figure 5.7. The variation of heat transferred to the L/d ratio of the geothermal well at steady state I-4 Comparison of Thermal Resistances of Wells at Steady State:The effect of different well dimensions on the rate of heat transfer of the geothermal well at the steady state are analyzed. Based on the simplified well design, three well shapes are considered â box, cylindrical and spherical. Multiple numerical simulations have been performed and the effect of thermal resistances on the rate of heat transferred is investigated, when the volume of the geothermal wells is constant. By keeping the domain volumes of the three geothermal wells the same. When Rb, Rc, Rs are the thermal resistances and Ab, Ac, As are the heat transfer surface areas of the of the box-shaped, cylindrical or spherical geothermal wells respectively, the variation of thermal resistance with respect to the change to the shape is shown in the table 5.5. The overall volume of the geothermal well is kept constant at each reading for all the three wells, and the 65 surface areas and depths are varied. For this analysis, the volume of the soil domain considered is 8000 m3. Table 5.5 Thermal resistances of the geothermal well at a soil domain volume of 1000 m3 Ab (m2) Ac(m2) As(m2) Rb (K/W) Rc (K/W) Rs (K/W) 24 23.4 7.7 0.105 0.085 0.055 54 132.9 17.3 0.044 0.023 0.032 96 236.3 30.7 0.015 0.014 0.021 150 369.2 48.0 0.009 0.009 0.014 216 531.6 69.1 0.006 0.006 0.010 294 723.6 94.1 0.004 0.003 0.007 384 945.1 122.9 0.002 0.001 0.004 486 1196.1 155.5 0.001 0.0002 0.002 The trend of the variation of thermal contact resistances with the surface area is shown below in the figure 5.8. It can be observed that the rate of decrease in thermal resistance with the increase in surface area is sharp in the box-shaped geothermal well, when compared to the other two wells. A maximum of 0.105 K/W is seen in the box-shaped geothermal well at an area of 24 m2, while the corresponding values of 0.085 K/W and 0.055 K/W in the cylindrical and spherical shaped wells. Even though the initial thermal resistance value of the spherical shaped well is the least at the first reading point, as the heat transfer surface area increases, the cylindrical well showed the least thermal contact resistance, implying that it performs well for heat rejection when compared to the other wells. From these results, it can be implied that the shape of the geo-exchange wells considered has a significant influence on the results of thermal resistances, which in turn affect the heat transferred between the well and the soil. The thermal resistance is low for the cylindrical shape when compared to the other shapes. Hence, it can be inferred that the cylindrical shaped well offers the best heat transfer in comparison to a box-shaped and a spherical shaped well. 66 Figure 5.8 Variation of thermal resistance with the heat transfer surface area of three wells Similarly, when a cylindrical well is considered, the effect of mesh size on the rate of heat transfer is studied and the obtained variation of the rate of heat transferred with the mesh size is detailed in the table 5.6. The mesh size considered at the boundaries for the coarse, fine, finer and finest meshes are 0.1 m, 0.07 m, 0.01 m and 0.005 m respectively. The effect of mesh size refinement is more evident when the length to diameter ratio is equal to 7 and it decreases as the ratio drops closer to 1, simply stating that the error would be maximum as the rate of heat transfer 67 increases. The variation of heat transfer rate for finer and finest meshes is negligible. Hence, in order to save computational time, the mesh selected for the numerical simulation was 0.01 m. Table 5.6 Effect of mesh size on the rate of heat transferred for a various cylindrical geothermal well sizes L/d ratio Coarse mesh (0.1 m) Fine mesh (0.07 m) Finer mesh (0.01 m) Finest mesh (0.005 m) 7 1419 1428 1433 1431 3.5 1901 1915 1924 1923 2.33 2303 2313 2332 2330 1.75 2663 2684 2710 2711 1.4 3024 3049 3070 3069 1.17 3299 3321 3411 3412 Section â II: Transient State Analysis: From the steady state analysis, it has been seen that one geothermal well cannot be used to transfer all the heat from the data center to the underground due to the high thermal resistance of the soil. However, a single well can be used for a specific amount of time, till it reaches the maximum allowable temperature. Later, the heat load is removed from the well to dissipate all the heat to the underground freely. In other words, there is a need to use multiple wells to reject the heat into the underground efficiently. Hence, the transient analysis of the geothermal well becomes crucial. The results of the steady state analysis imply that the pressure loss of the water is very high, implicating that the use of the porous medium in cooling the geothermal well is impractical. In order to overcome this difficulty of pressure loss, the pump power required is large, resulting in increasing the investment and operating costs. It is for the same reason, porous wells are not preferred. Moreover, the construction costs for that system would be far higher than the simple geothermal well design detailed in the previous section. 68 A simple geothermal model is designed as shown in the figure 5.6. The hot water from the data center is discharged to the empty geothermal well, and once the temperature reaches 293K, the heat load is removed from the well and the other geothermal well is put into use. Hence, similarly to the CAD model represented in the figure 5.4, the actual region of the well is not modeled. During the operating phase, the temperature of the well rises from the initial ground temperature (283 K) to the maximum allowed temperature (a threshold of 293 K has been set). And once the maximum allowable temperature is achieved, the geothermal well will undergo cooling process and the temperature recovers backs to the original initial temperature. Meanwhile, the responsibility of dissipating heat from the data center will be shifted to the alternative well available. The details of this multiple well system and the time-dependent operation of the wells are discussed further in the chapter 6. Figure 5.9 Schematic showing the proposed geothermal cooling solution for transient analysis69 II.1 Numerical Model:For the analysis, an axi-symmetric model of the geothermal well is modeled (as shown in the figure 5.10). An axisymmetric model is a two-dimensional representation of a three-dimensional model, in which the two-dimensional object is symmetric around the axis to complete the three-dimensional model. Axi-symmetric models are used to reduce the number of computations, thereby reducing the time for convergence by a large extent. Figure 5.10 Axisymmetric CAD model of the cylindrical geothermal well The CAD model of the axi-symmetric geothermal well is depicted in the figure 5.10. From the results obtained in steady state analysis, it is evident that the heat transferred to the underground will be in a range of few kW, there must be a few wells constructed to serve the purpose of rejecting 70 a few hundred kW. In other words, the steady-state geothermal well model is designed to work as a single well, whereas a transient well model is designed to work as a system of wells. Thus, the depth and radius of the geothermal well are considered to be 1.5 m each. A 9 m x 5 m block of soil domain is considered for this simulation, while the walls of the geothermal well are positioned centrally. A linear mesh of 0.01 m is generated for this CAD model. It is shown in the figure 5.11 Figure 5.11 Geometrical mesh of the CAD model of the axisymmetric geothermal well 71 The working of this system can be categorized into two phases â operation phase and recovery phase. During the operation phase of the geothermal well, the temperature of the well gradually increases and the rate of heat transfer decreases slowly, which indicates that the heat dissipating capacity of the geothermal well becomes exhausted with time. The walls of the geothermal well (as shown in the figure 5.7) are at 323 K throughout the operating phase, indicating that the well is absorbing the heat rejected from the data center. The walls of the soil domain considered are at a temperature of 283 K. The top layer of the geothermal well is exposed to the atmospheric air, but in order to analyze the conduction performance of the well, the top part of the well is assumed to be adiabatic i.e. there is no heat between the atmospheric air and the geothermal well. The maximum temperature to which the well can be operated is set to 200C. The transient heat analysis is performed by solving the transient heat conduction equation. The details of the trend depicting the change in heat transfer rate with time is shown in the figure 5.12. From the graph, it can be observed that the initial heat transfer rate is 210 kW and after 7500 seconds, it gets reduced to around 50 kW. The temperature rose from 283 K to 293 K during this time. This indicates the fact the heat rejecting capacity of the well gradually decreases with time and as soon as the threshold temperature (293 K) is reached, the well becomes non-operational. A redundant well is used to continue the heat transfer process and the hot well becomes non-operational and is allowed to recover (these details are explained in the chapter 6). 72 Figure 5.12 Total heat transfer rate change with time during transient operating phase of the geothermal well The area-weighted average of the temperature of the geothermal well is shown in the figure 5.13. For the well to reach the set threshold of 293 K, it takes around 40,600 seconds or around 11.28 hours i.e. the well can be operated only for 11.28 hours and it must undergo recovery after this. Also, the rise in temperature is in a decreasingly increasing fashion, validated by the Fourierâs law of conduction. 73 Figure 5.13. Area-weighted average of temperature change with time during transient operating phase of the geothermal well The temperature contour of the axisymmetric model is depicted in the figure 5.14. As illustrated in the figure, the temperature contour (after 360 s) at the walls of the geothermal well can be seen in red color, indicating that the temperature is maximum there, and it gradually reduces to 283 K in the soil domain (indicated by blue). It is evident that the hot region expands with time and a considerable change in the heat dissipation can be observed. Also, the temperature contours of the geothermal well during the operational phase can be seen in the figure 5.15 from the time 3 seconds to 360 seconds. 74 Figure 5.14. Temperature contour of the transient analysis of the axisymmetric geothermal well Figure 5.15 Temperature contours during the transient operating stage of geothermal well a. after 3 s b. after 6 s c. after 12 s d. after 60 s e. after 150 s f. after 360 sOnce the geothermal well reaches maximum temperature, the well is out of operation and the heat load is transferred to the other well. The recovery phase of the geothermal well is shown in the figure 5.16. The evaluated value of Fourierâs number indicates that the heat dissipation capacity of the soil. Under the given case, it takes an hour for the heat to impact the soil particles 75 at a distance of 1 m (discussed in the chapter 6). This implies that the heated geothermal well needs to stay out of operation for at least 11.28 hours and should undergo recovery. During this phase, the geothermal well will dissipate all the heat into the underground, and eventually reaches a thermal equilibrium with the infinite medium surrounding the soil after 98,000 seconds. Figure 5.16. A graph showing heat recovery stage of the geothermal well during transient analysis II.2 Analytical Approach: Transient heat conduction is a complex phenomenon, which is dependent primarily on two factors â dimensionless position and dimensionless time. By evaluating these two factors and by applying either the Dirichlet, Nuemann or Robin boundary conditions, the expressions for the heat conduction can be derived. 76 The geometric well considered is of cylindrical shape. It is assumed that the cylinder is long when compared to the diameter. Transient conduction external to the long circular cylinders is considered in this section. Yovonovich has detailed a way to derive the temperature changes for long cylinders by applying Nuemann and Dirichlet boundary conditions after deriving the two dimensionless parameters (dimensionless position and dimensionless time). When a long circular cylinder of radius a is considered and r represents the radius in the cylindrical coordinate system, the transient conduction equation is written as a function of the instantaneous rise in temperature as ð2ððð2+1ððððð¾=1ð¼ðððð¡(5.6) where ð¼ is the thermal diffusivity. And, ð¼ is given by ð¼ = K/ðð¶ (5.7) where K is the thermal conductivity, ð is the density, C is specific heat at constant pressure. From the properties of soil taken from the table 5.2 , the value of thermal diffusivity can be obtained as 1 x 10â6 m2/s. Carslaw and Jaeger [84] have used these equations and thus have derived the expressions for the rise in temperature for short term and the instantaneous heat flux. The instantaneous rise in temperature of the long circular cylinder is given by Î¸Î¸i=1âÏerfc [Ïâ12âF0] + (Ïâ1)âF04Ï3/2irefc [Ïâ12âF0] + (9â2Ïâ7Ï2)32Ï5/2i2erfc [Ïâ12âF0] (5.8) with Ï â¡ r/a > 1. The special functions ierfc (x) and ð2erfc (x) are integrals of the complementaryerror function. And similarly, the instantaneous surface heat flux is derived to aq(t)kÎ¸i=1âÏâF0+12â 14(F0Ï)12+ 18 F0 (5.9) 77 where θ i = Twell â Tsoil. These equations are used to calculate the instantaneous heat flux in the next section. II-3 Effect of Well Dimensions on the Transient Heat Transfer:In order to examine the effect of the dimensions of the geothermal well on the rate of heat transfer, a 2D geothermal well is considered and the maximum heat transfer from the well is investigated with various changes in parameters. When a domain of depth 10 m and a well diameter is considered, equipped with a pipe of diameter 0.25 m, the rate of heat transfer is analyzed in variation with the depth of the buried pipe. The details of the obtained results are shown below (table 5.7). Table 5.7 Rate of heat transfer with the depth of pipe buried in transient state of the geothermal well Depth of pipe buried (m) qâ (W/m)- instantaneous 1 11000 1.5 11000 2 11000 2.5 11000 3 11000 3.5 11000 4 11000 From the results, it is evident that the depth of the buried pipe does not affect the rate of heat transfer rate. In this case, in order to maximize the rate of heat transfer, we have considered that there is a convective heat transfer between the geothermal well and atmospheric air. Therefore, as the heat transfer rate does not depend on the depth of pipe buried, this factor can be conveniently ignored and thus, there need not be any changes made in this regard. 78 Similarly, the effect of domain area on the rate of heat transfer is checked from the results obtained through numerical simulation as shown in the table 5.7. The obtained results indicate that the considered domain size of the soil does not influence the results of the transient analysis. This is due to the fact that the initial temperature condition given in the numerical simulation is same as that of the soil (during the operating phase) and hence, at the initial time, the temperature remains 293 K throughout the domain. When the domain size of the soil is fixed as 20 m on all sides, the variation of rate of heat transfer with respect to the diameter of the cylindrical well is shown in the table 5.8. Table 5.8. Change in heat transfer per length with the domain area in transient state of the geothermal well Domain area (m2) qâ(W/m)- instantaneous 36 14000 81 14000 100 14000 144 14000 225 14000 Table 5.9. Change in heat transfer rate per length with the diameter in transient state of the cylindrical geothermal well Diameter (m) qâ (W/m)- instantaneous 2 14000 4 29000 5 34500 6 42500 10 56000 79 It can be observed that the rate of heat transfer increases non-linearly with the increase in the diameter of the cylindrical geothermal well (as shown in the figure 5.17). This can be attributed to the fact that the rate of heat transfer increases with the increase in heat transfer surface area. Figure 5.17 Variation of heat transfer rate with heat transfer surface area The results obtained from the transient analysis show that the transient heat conduction is highly sensitive to the heat transfer surface area when compared to the change in diameter or the depth of the pipe buried. Also, as it is evident that a single transient well cannot reject 1 MW, or at least 0.25 MW continuously. Each well can be operated only for a fixed time and hence, the need for the use of multiple wells arise. The details of a multiple well geothermal model are discussed in the next chapter. 80 Chapter 6: Multiple well model The results obtained from the transient analysis indicate that the given heat rejection rate of 1 MW, a single well can be operated for a span of few minutes. The average temperature of the single well reaches the set threshold of 20 0C in 11.28 hours, which means that the well is ineffective thereafter. Moreover, as the heat absorption rate of the soil decreases with time due to the increase in the local soil temperature at the well-soil boundary. These points iterate the fact that a single well is not sufficient to dissipate all the heat from the data center, making the single-well geothermal system obsolete. Hence, multiple wells, which operate at transient conditions are devised to serve the heat rejection, in place of a single well. 6.1 Design: Multiple cylindrical wells, each of the well with a diameter 3 m and a depth of 1.5 m (same as the finalized design), are arranged in the designated geo-exchange well system space, and are filled with water. It is assumed that the temperature of the water in the well remains steady and it is same as the underground soil temperature. A thin, high-thermal conductivity layer (preferably of copper or aluminum) is draped around the soil-well boundary to prevent the water seeping into the soil. It is assumed that the metal layer is completely efficient, and there is no delay in heat transmission from the well to the underground during the recovery process. It is also assumed that the performance of every single well is equal i.e. every well operates and recovers at same rate and the delay in performance due to switching wells is negligible. These water-filled geothermal wells are arranged in an array, separated by a uniform distance from the other well (a schematic for three wells is shown in the figures 6.1 and 6.2). All the wells are filled with equal volume of water, except for one empty well. For example, there are 81 ânâ number of wells in the multiple geothermal well system. Of those, ân-1â wells are filled with water and remaining well is empty. The cold water pumped from one of the water-filled wells is used to cool the hot air in DC, and once the heat is extracted, the water will be transferred to the empty well, filling it eventually and emptying the first well. Thus, at the end of this process, this leaves ân-1â filled wells and one empty well. During this process, the hot water in the newly filled well rejects heat to the underground (which is an infinite sink) and eventually reaches the initial temperature and this is later transferred to the empty well. The heat in this well is recovered by the soil after a certain time. Thereafter, the next well (one with cold water) is used to cool the DC, and this rejected hot water is filled in the newly emptied well. Every single well is equipped with two pipes, one to receive the hot water from the data server room, and the other, to pump the recovered water to the data center. These network of pipes are controlled centrally to switch the wells ON and OFF. These distance between wells is selected after the numerical simulation, which is based on the heat dissipation. Figure 6.1 Schematic showing multiple geo-exchange wells connected together 82 Figure 6.2 Schematic showing the idea of a multi-geothermal well system Switching Process:The switching process of the wells is illustrated with a 16-well system as shown in the figure 6.3. The empty well, filled well and the hot wells are marked with orange, blue and red colors respectively. The pair of wells between which there is a transfer of water volume is indicated as shown below. Initially, the water from one of the water-filled wells (blue) is pumped to the data center, and once the water from this well is emptied (indicated by orange), next well is turned ON. Meanwhile, during this process, the hot water rejected from the DC fills an empty well, turning it hot (red). And then, in the next step, the newly filled well (red) undergoes recovery process and the heat transfer takes place between the newly emptied well and the next well indicated. These steps are shown in the figure 6.3. 83 Figure 6.3 Schematic showing switching between wells in a multi-well model The process of switching shown above is not the ideal sequencing of operation, as there will be an influence of heat dissipation between wells. The optimal sequencing procedure is decided on the time taken for the heat to dissipate along a given length. From the transient analysis of Fourierâs number, when isotropic conditions are considered, it is evident that the influence of a well to the nearby geothermal well is likely. Hence, it is important to select the sequence in which the wells need to be operated. Four points are proposed to optimize the entire operation procedure of the multiple well geo-exchange system. 84 1. At any given sequence, 1xn will be the ideal sequence and a symmetric array would be theworst. 2. Always start with the corner wells, so that they can least affect the next order of wells beingselected and there will be least interaction. 3. Diagonal wells will be more distant when compared to adjacent wells. So, in case of making achoice, select diagonal ones for least interaction. 4. If the number of sides of array are increased, it increases the number of diagonal elements, but also, the area required will be more. The sequence in which the wells need to operate are selected by using these points. The detailed sequencing of a 16-well system is illustrated in appendix B. In the next section, the results obtained for this multiple geo-exchange wells by using analytical approach are discussed. 6.2 Results and Discussion: Analytical approach has been used to examine the thermal behaviour of this multiple-well system. The results interpreted from the transient analysis can be directly applied to the multiple wells, as only a single well is operated at a specific time and it is assumed that there is no effect of inter-well thermal dissipation due to the sequencing procedure followed. The mode of heat transfer to the soil is governed purely by conduction between the geothermal well and the underground. Pure conduction process is governed by Fourierâs law, which states that the rate in which the heat is conducted is proportional to the temperature gradient change across the three directions and the surface area involved in heat transfer. It can be calculated as shown below. The 3D heat conduction equation in general coordinates, when there is no heat source is given by ðððð¡= ð¼(ð2ððð¥2+ð2ððð¦2+ð2ððð§2) (6.1) 85 where ð¼ is the thermal diffusivity, given by k/ðð¶. From the properties of the soil mentioned in the chapter 3, the value of thermal diffusivity calculated is 1 x 10â6 m2/s. Thermal diffusivity indicatesthe rate in which the heat is diffused across the direction of heat propagation. This value, ð¼, is used to calculate Fourierâs number, which is the dimensionless ratio of conductive heat transfer and the heat content stored in the solid. Fourier number (F0) can be calculated by ð¹0 = ð¶t/ð¿2 (6.2)where t is the characteristic timescale in seconds and L is the conduction length in meters. Fourier number is constant only at that instant, and it varies with time and length. The transient simulation of a 2D well has been performed to check the time taken for the heat to affect a region of 1 m. The temperature is probed for an at least a difference of 1 degree, and the obtained results reveal that the time taken for the heat to dissipate heat through a distance of 1 m conduction length is a little more than one hour (indicated in figure 6.4). This indicates that if a single well is operated for one hour, and the wells are separated by less than 0.5 m, there will be a significant heat transfer influence between the wells. Figure 6.4 Temperature contour of the 2D cylindrical well at transient state (after 3655 sec) 86 A geothermal cylindrical well of diameter 3 m and a depth of 1.5 m is considered. The volume of this geothermal well is 10.6 m3. For a data center of capacity 0.25 MW, the temperature of water entering the well be 323 K and the ambient temperature (soil) is 283 K. Under these conditions, using the equation 3.13, the value of mass flow rate of the water calculated is 1.495 kg/s. Thermal resistance of the system can be calculated by using the conduction heat transfer equation 5.1. ð ð¡â is determined from the calculation of shape factor and the dimensionless heat transfer rate. The numerical simulation at steady-state for the single well of given dimensions is 0.03255 K/W. For enhancing the heat transfer, due to space constraints, it is optimal to have more depth to the well than the side. All the wells in this model are arranged in the form of an array and together, all the wells are assumed to spread over an area of 60 m x 60 m. Each well is assumed to have a diameter of 3 m. t = Volume of the wellVolume of well being filled in 1 second(6.3 a)The time taken to fill up one well of the given volume thus obtained is 7114 sec or 118.5 minutes. The total number of wells (n) required can be calculated by using the equation 6.3 briefed below. n = Time taken to recover a well completely to initial temperatureTime taken to fill a single well+ 1 empty well (6.3 b) From the results obtained through transient analysis, the time taken for a single well to recover from 323 K to 293 K (threshold temperature for operation) is around 98000 s (1635 min). Therefore, n = (1635/118.5) +1 ~ 15. This indicates that at least 15 wells are required for the multiple well system to work efficiently. To compensate the delay of heat recovery in the well due to the thin metal layer and the simplifications taken, an extra well is designed. These 16 wells are 87 arranged in the form of an array of 4 x 4, each separated by a distance of 2 m. This system of wells reach a common temperature after many hours or days of operation. As the steady state is not achieved in any well permanently, yet the temperature of the system tend a constant value, the system of wells tend to reach a quasi-static steady state. The transient performance of the single well is analysed as a case of pure conduction. This was done to check the heat rejection capacity of the geothermal well without any external aid. To reduce the load on the well system, the top part of the well is exposed to the atmospheric air. In such case, there are two modes of heat transfer involved â convection between the well and the atmospheric air & conduction between the geothermal well and the soil. The heat transferred from each of the modes are calculated subsequently as shown below. The heat transferred through convection is given by the Newtonâs law of cooling (equation 6.4) as ððððð£ = âð´(ððð£ð â ðððð) (6.4) where h is the convective heat transfer coefficient (W/m2K), A is the heat transfer surface area (m2), Tavg is the average temperature (K), Tair is the temperature of the atmospheric air (K). And, the convective heat transfer coefficient is given by h = Nu.k/L (6.5) where Nu is the Nusselt number, k is the thermal conductivity of the fluid (W/m-K) and L is the characteristic length in meters. Reynoldâs number can be calculated by using mean velocity (um) and characteristic length (L) by using the co-relation Re = ð¢ðð¿/Î½ (6.6) For Kelowna, the weather statistics [85] show that the measured average value of the wind speed is 12.39 kmph i.e. 3.442 m/s. And the properties of air reveal that the kinematic viscosity (ν) is 1.426*10-5 m2/s and Prandtl number (Pr) is 0.7336. Thermal conductivity (k) of the air at 88 film temperature of 300C is 0.02558 [86]. The value of thus calculated Reynoldâs number is 7241234, indicating that the flow is turbulent in nature. Under turbulent conditions, Nusselt number can be calculated by using the correlation Nu = 0.0296 ð ð0.8ðð0.33 when 0 â¤ Pr â¤ 60 (6.7)where Nu = hL/k. Nusselt number value of 8209 is obtained by using equation 6.7 and further, the value of convection heat transfer coefficient obtained from the above is approximately 7 W/ (m2K). The average temperature of the well system can be calculated by using the energy balance, which indicates that the total heat transfer to the atmosphere and the underground in this process is the sum total of the heat transferred due to convection and conduction. ðð¡ðð¡ðð = qconv + qcond (6.8)where qconv is the heat transferred due to convection, qcond is the conduction heat transferred and ðð¡ðð¡ðð is the total heat transferred. By using equations 5.1 and 6.4, the total heat transferred can be written as ðð¡ðð¡ðð = âð´(ððð£ð â ðððð) + ððð£ðâðâð ð¡â(6.9) where Tavg is the average temperature of the well system after the constant temperature is attained. As mentioned before in this section, the value of a single thermal resistance is 0.03255 K/W. As the heat diffuses in three dimensions, the maximum possible thermal resistance of the system is more that of a single well. It gives the maximum total thermal resistance of the system as 0.5208 K/W. By using equation 6.9, this totals out the value of the average temperature of the well system to approximately 11 0C. This indicates that the designed system of well work with in an expected manner. However, given the space constraints, it is not possible to spread the well over an area of 3600 m2 practically. If the conditions remains same and the array of wells are arranged in a 30 m 89 x 30 m dimensional square and the system is used to reject 0.25 MW heat, the obtained average temperature of the system is same i.e. 11 0C. The obtained calculations can be validated by using numerical simulation results of a single well. As mentioned earlier, a single well can be operated for 11.28 hours. Assuming that the there is no inter-thermal influence between the wells, if a single well can reject heat at a rate of 0.25 MW during the operation phase, it can be verified that the multiple-well system is functioning to expectations. For a single well, when the conduction and convection modes of heat transfer are considered, the numerical simulation results indicate that the maximum heat transfer rate is closer to 0.25 MW. Figure 6.5 Results of maximum heat transfer (W) obtained from a single well (with convection) In order to enhance the heat transfer rate, the wells have to be dug deep. For the wells from depth 1 m to 2.5 m, the increase in heat transfer rate with the depth is depicted in the table 6.1 and the trend of rise in heat transfer rate with depth is shown in the figure 6.6. The heat transfer rate 90 surges non-linearly from 0.22 MW to 0.47 MW, as the depth of each well in a multiple-well system is increased from 1 m to 2.5 m. Table 6.1 Variation of maximum heat transferred with depth of well in multiple-well system Depth of the well (m) Maximum heat transfer rate, q (W) 1 0.22 1.25 0.23 1.5 0.25 2 0.33 2.25 0.4 2.5 0.47 For the entire numerical analysis of the well, it has been assumed that the wall temperature of the well reaches 323 K instantly. It might not be true, as there will be intermixing of the fluid particles during the operation. In reality, there is no strict operating phase for the well, as the heat is continuously transferred to the soil. This will result in a slight deviation from the actual values. Figure 6.6 Maximum heat transferred with the increase in depth of the well Also, as discussed in the chapter 5, the thermal conductivity of soil is not constant in all regions and the heat transfer performance varies significantly with the thermal conductivity of the soil. When the thermal conductivity value is varied in the range of 0.15-7 with all other parameters 91 unchanged, the higher thermal conductivity soils showed larger heat capacities when compared to the lower thermal conductivity soils. However, the variation in the maximum heat transfer rate is not significant, adhering to the fact that the convection heat transfer overcomes the conduction heat transfer by a large extent. The obtained results are listed in the table 6.2 and the variation is plotted as shown in the figure 6.7. Table 6.2 Variation of thermal conductivity with increasing soil thermal conductivity Thermal conductivity (W/m-K) Heat transfer rate (kW) 0.15 245 0.5 245.9 1.2 248.2 1.9 250 2.5 251.4 4 255 5.5 258.6 7 263.2 The obtained trend of increasing heat transfer almost follows a linear relationship, when the whole geothermal system is considered. The heat transfer rate surges from 245 kW for a lower soil thermal conductivity to around 263 kW for soils with thermal conductivity of 7 W/m-K. However, this does not establish that there is a linear relationship between the conduction heat transfer rate and the thermal conductivity of the soil. 92 Figure 6.7 Variation of maximum heat transfer rate with the increasing soil thermal conductivity Thus, from the above results, it can be concluded that the multiple geo-exchange well system is efficient only for a small-scale data center. Moreover, the obtained results are based on the values of heat transfer coefficient and the atmospheric air temperature, which are averaged over the year. Canadian winters experience sub-zero temperatures (in most of the regions), while the summers are hot. Hence, the designed geothermal system performs well in winters, whereas it is a bit inefficient in summers. Also, for the best performance, the geothermal well system must be constructed in the rocky soil. However, it is recommended to combine this multiple-well system with an alternate source of cooling to compensate these limitations. In the next chapter, the final conclusions obtained from this research are detailed. 93 Chapter 7: Conclusions From the results obtained from the above analyses of the geo-exchange well under steady state, transient state of single and multiple wells, it can be concluded that the developed multiple-well model is suitable only for low capacity data centers, provided the convection heat transfer is considered. This chapter details the primary conclusions of the research, the limitations involved, the contributions of this research and the future work that can be done using this research. 7.1 Research Conclusions: 1. Due to the high thermal resistance of the soil, a single geothermal well cannot becontinuously operated to extract 1 MW.2. In such case, a single geothermal well can be used as a data center cooling solution onlyfor a limited time i.e., until the geothermal well reaches the threshold temperature.Hence, the developed geothermal well system is suitable to be operated only undertransient conditions.3. In order to serve the data centers with larger capacities, either the surface area in whichthe well array is spread must be relatively huge, which is impractical in most of thecases. In order to serve a DC of 250 kW, a 30 m x 30 m geothermal well system isrequired. This implicates that the size of the geothermal cooling system would beseveral times to that of the actual server room.4. The active heat transfer area in each of the wells must be enhanced greatly, which willincrease the conduction heat transfer rate. From the equation 6.10 and from the resultsobtained through numerical simulation, it is evident that the conductive heat transferrate is relatively meagre when compared to the convective heat transfer rate. This94 proves that the key in implementing the multiple well model lies in enhancing the conductive heat transfer rate. 5. A porous medium-based geothermal well increases the surface area of the heat transferto a great extent, but the performance of thus developed well is highly limited due tothe high thermal resistance barrier of the soil. The multiple porous medium basedgeothermal model will have higher efficiency than the developed simple multiple-wellmodel, it is not feasible to implement, as the investment & installation costs might bea lot more than the expenses saved during the course of its operation.6. From the numerical simulation results obtained from the two-dimensional transientanalysis (mentioned in the appendix B), it can be concluded that it takes nearly onehour for the heat to reach a distance of 1 m. Hence, this stands as an evidence for thepossibility of the wells thermally affecting one another even near the beginning of theirrespective operating cycles (This can be further cleared by understanding the sequenceof steps in a cooling cycle, as explained in the appendix B)7.2 Limitations of the Research: 1. The proposed geothermal cooling solution will be far more efficient and practical inthe colder climatic conditions than tropical conditions. Especially, during the winterseason when the temperatures fall below 00C, this geothermal cooling solution worksefficiently. Indirectly, it acts a hybrid system of free (open) cooling and geo-exchangecooling system.2. Due to the inconsistent soil properties across regions, the heat rejection capacity of thedeveloped geothermal well system will vary with the nature of soil. The geothermal95 well systems constructed on the rocky soils are relatively efficient than the ones constructed on the clay soils. 3. The maximum share of heat is transferred through the mode of convection thanconduction. Practically, when the wells are left open to the atmosphere, there will be aloss of water due to evaporation and diffusion. In such case, the volume of waterutilized for the DC cooling process increases multi-fold. If the wells are closed, the heattransfer rate due to convection must be sacrificed.4. In order to prevent the seepage of well water into the underground, a thermallyconductive layer is wrapped around the well. In a realistic scenario, this increases thematerial costs significantly and not to mention, the efficiency of such provision wouldbe low.5. If the wells are arranged in the form of arrays, the wells must be separated by a largedistance to prevent the thermal interference of the wells with each other. This will beimpractical in most of the cases, as it might need an area multiple times to that of thesize of the data center.6. When the wells are arranged in the form of an array, the sequence in which the wellsmust be operated is crucial to dictate the least thermal interference. The higher thenumber of wells used for cooling, the more difficult will be their sequencing. Also,switching the wells randomly will incur additional piping and control costs. In order toprevent this, the wells must be arranged far away from each other, say, along theperimeter of the data center or a random and distant fashion from each other.96 7.3 Contributions of the Research: Despite the limitations of this research, the conclusions of this research can accord the following contributions with respect to the geothermal cooling of data centers: 1. Prior to this research, maximum heat rejection capacity of a geothermal-based DCcooling system was 12-15 kW. The DC cooling system developed through thisresearch can reject heat at a rate of 250 kW, if implemented.2. The research conducted gives a thorough knowledge on the conduction performanceof the developed geothermal cooling system, various strategies that can be employedto enhance the heat transfer rate and the effect of various dimensional parameters onthe heat transfer performance.3. This research provides the important output that the geothermal cooling would besuitable only for DCs with heat rejection rates of a few hundred kW. The capacity ofthe geo-exchange well system cannot be enhanced significantly, no matter how muchthe depth of the single well is increased.7.4 Future Scope for the Research: Though the developed geo-exchange system cannot be extended to serve mega and giga scale DCs, this system has the potential to be implemented for small DCs, if the mentioned limitations are traversed. 1. From the results obtained, it can be concluded that the proposed geothermal coolingsolution is efficient only for the small capacity data centers (upto 0.25 MW). Giventhe advantages of low cost for implementation and simplistic approach, this modelcan be further developed to serve the university and school data centers.97 2. In order to reduce the load on the geothermal wells, further research has to be doneto develop the system so as to utilize the heat energy for domestic heat needs. Thiswill reduce the load on the multiple-well system and thus, its overall sizing.If the shortcomings of the research are crossed, the developed geo-exchange well system has the potential to cater the needs of a small-scale data center. Hence, further research has to be made by hybridizing this cooling solution with other cooling systems. 98 Bibliography 1. The Insight Research Corporation, The 2009 Telecommunications Industry Review: An Anthology of Market Facts and Forecasts, Boonton, NJ, USA, Nov 2008.2. Koomey, Jonathan G. "Worldwide electricity used in data centers." Environmental research letters 3, no. 3 (2008): 034008.3. Koomey, J., 2011. Growth in data center electricity use 2005 to 2010. A report by Analytical Press, completed at the request of The New York Times, 9.4. Natural Resources Defense Council (NRdata center) Annual Energy Report, 2014.5. Carbon Footprint Ltd, ISO14001:2015 certified for environmental management.6. Joshi, Y. and Kumar, P. eds., 2012. 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To increase the heat transfer, area of heat transfer has been increased, by developing fin type of metal rods protruding from soil. This design is not considered, as the conduction heat transfer is low and cannot cater the objective of extracting 1 MW from the data center. Figure A.1 3D CAD model with metal rods bridged between the soil and the geothermal well 108 Figure A.2. A detailed view of the metal rods bridging soil and the geothermal well Figure A.3 Geometric mesh of the metal rod-geothermal well model 109 Figure A.4 3D CAD model of the fin geothermal well model (top-view) Figure A.5 3D CAD model of the fin geothermal well model 110 Figure A.6 Geometric mesh of the fin geothermal well model Figure A.7 Geometric mesh of the fin geothermal well model at interfaces 111 Figure A.8 Temperature contour of the fin geothermal well system at steady state Figure A.9 Temperature contour of the well in fin geothermal system at steady state 112 Appendix B For a multiple-well system which has a recovery time of 1125 minutes (say) for one well i.e. for the completion of one entire cycle, the optimum order of selection is as follows: 113 114 115 Figure B.1 Sequence of selection and operation in a well cycle of 1125 minutes (step after the step)
Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Geothermal cooling for data centers
Text