Approved: Ernesto Gutierrez-Miravete, Engineering Project Adviser

Transcription

1 A Design Study of the Heat Removal System for the Propulsion Machinery of a Nuclear Powered Ship by Scott E. Misiaszek An Engineering Project Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the degree of MASTER OF ENGINEERING IN MECHANICAL ENGINEERING Approved: Ernesto Gutierrez-Miravete, Engineering Project Adviser Rensselaer Polytechnic Institute Hartford, CT December, 2010

2 CONTENTS LIST OF TABLES... iv LIST OF FIGURES... v NOMENCLATURE... vi SUBSCRIPT NOMENCLATURE... viii ABSTRACT... ix 1. Introduction Background System Design & Nuclear Heat Removal Systems Commercial vs. Naval Nuclear Power Mechanical Drive vs. Electric Drive Problem Methodology Results: System Design System Specifications Task Definition and Requirements Task Assumptions and Assessment Functional Design Detail Design Heat Generation Calculation Fresh Water Flow Calculation Heat Exchanger Baseline Calculation Heat Exchanger Design Calculation Pipe Sizing Calculation Pressure Drop Calculation Pump Design Calculation ii

3 3. Conclusions References Appendix A: Moody Diagrams Appendix B: Y-Strainer Flow Rate vs. Pressure Drop Chart [18] Appendix C: System Design Excel Spreadsheet Output iii

4 LIST OF TABLES Table 1 EDS Propulsion Information Table 2 Heat Generation Calculation Table 3 Fresh Water Flow Calculation Table 4 Vendor Provided HX Performance Specifications Table 5 HX Baseline Calculation Table 6 Known HX Information Table 7 HX Design Calculation Table 8 Pipe Sizing Calculation Table 9 Pressure Drop Calculation Table 10 Pump Specifications iv

5 LIST OF FIGURES Figure 1 Cooling Tower [15]... 2 Figure 2 Heat Exchanger [6]... 3 Figure 3 Mechanical Drive [2]... 4 Figure 4 Electric Drive [2]... 5 Figure 5 High Level System Diagram... 9 v

6 NOMENCLATURE A area (ft 2 ) a area of one plate of heat exchanger (ft 2 ) Cp specific heat (Btu/lbm- ºF) D diameter (ft) e absolute roughness (ft) ε efficiency F volumetric flow (ft 3 /hr) or (GPM) f friction factor g gravitational constant (32.2 ft/s 2 ) H head loss (ft) h heat transfer coefficient (Btu/hr-ft 2 -ºF) k thermal conductivity (Btu/hr-ft-ºF) K L valve loss coefficient L length (ft) m mass flow rate (lb/hr) n number of plates in heat exchanger P power (HP) p pressure drop (psi) ρ density (lb/ft 3 ) Pr Prandtl Number Q heat load (Btu/hr) R relative roughness r radius (ft) Re Reynolds Number R W plate wall thermal resistance (hr-ft 2 -ºF/Btu) T 1 fresh water inlet temperature (ºF) T 2 fresh water outlet temperature (ºF) t 1 seawater inlet temperature (ºF) t 2 seawater outlet temperature (ºF) vi

7 t plate plate wall thickness (ft) U heat exchanger overall heat transfer coefficient (Btu/hr-ft 2 - ºF) µ viscosity (lbm/ft-hr) v fluid velocity (ft/sec) Z viscosity at bulk temperature (lbm/ft-hr) Z W viscosity at plate wall temperature (lbm/ft-hr) vii

8 SUBSCRIPT NOMENCLATURE avg baseline drv FW in mtr new out plate R SW trans W average relating to the values for the baseline design of the heat exchanger in relation to the motor drive fresh water relating to inlet in relation to the propulsion motor relating to the values for the new design of the heat exchanger relating to outlet relating to the heat exchanger plates required seawater in relation to the transformer in relation to the wall of a component or pipe viii

9 ABSTRACT Throughout nuclear powered ships, massive quantities of heat are generated. This excess heat must be removed from the system that generated it for the ship to function properly. Cooling systems must be designed to remove all of the excess heat from the ship. Engineers must consider numerous factors when designing a heat removal system, including material and component selection, heat exchanger design strategy, safety and reliability issues. This engineering project provides a methodology that takes these factors into account when designing a heat removal system for the electric drive propulsion system for a nuclear powered ship. A real world situation is used to help set the scope for designing the heat removal system. The methodology includes the thought process of the design, including assumptions and calculations used to design the system. A tool was generated in the form of a spreadsheet that captures all assumptions and calculations. This tool can be used for instantaneous updates should any changes in the system need to be made. ix

10 1. Introduction 1.1. Background The removal of heat from propulsion machinery equipment of a nuclear powered ship is crucial for the ship to operate correctly. The design of these heat removal systems is complicated, requiring the incorporation of energy conservation principles and system design methods. To successfully design a effective system, a holistic design approach must be taken System Design & Nuclear Heat Removal Systems System Design is defined as: The activity of proceeding from an identified set of requirements for a system to a design that meets those requirements. A distinction is sometimes drawn between highlevel or architectural design, which is concerned with the main components of the system and their roles and interrelationships, and detailed design, which is concerned with the internal structure and operation of individual components. The term system design is sometimes used to cover just the high-level design activity. [19] System design is needed in all aspects of life. It is used to design the software used to write this document, to designing the air purification system on the International Space Station. System design helps meet system requirements in the most efficient ways using analytical means. Without system design, ad hoc approaches would be made to develop systems. These ad hoc systems would be less efficient, more costly, and potentially more dangerous than ones developed with the analytical means of system design. Heat removal systems are widely used throughout the world. They are seen everywhere from radiators in vehicles, to the huge cooling towers used at power generation stations. All of these systems are designed and built using the principles of heat transfer and thermodynamics. Heat transfer is defined as the transfer of thermal energy from one region of matter or a physical system to another [3]. This definition sums up the operation of all heat removal systems. There are two main laws that help engineers design heat transfer systems. They are the First and Second Law of 1

11 Thermodynamics. The First Law of Thermodynamics is an expression of the principle of conservation of energy, or simply put, energy can neither be created nor destroyed. Without this law, calculating how much thermal energy is entering and leaving a system would be impossible [4]. The Second Law of Thermodynamics expresses the principle that heat flows spontaneously and irreversibly from higher temperatures to lower temperatures [4]. Without this law, describing the flow of thermal energy would be impossible. These two laws are fundamental in designing a heat removal system Commercial vs. Naval Nuclear Power When designing heat removal systems for nuclear operations it must be recognized that for different nuclear uses, there are different heat removal methods. To emphasize this point for the purpose of this project, consider the following heat removal methods for nuclear power generation. Commercial nuclear power generation plants use cooling towers (Figure 1) for heat removal, whereas nuclear powered ships rely on heat exchangers (Figure 2). Figure 1 Cooling Tower [15] 2

12 Figure 2 Heat Exchanger [6] Cooling towers use the evaporation of water to remove excess heat to the atmosphere, while heat exchangers transfer excess heat from one medium to another that are separated by a solid barrier. Heat exchangers are use on ships because they are relatively compact, and more efficient compared to cooling towers. Another key reason for heat exchanger use for ships is the abundance of cooling media in the form of seawater. As long as the ship is at sea, it will be able use seawater to remove the excess heat back into the ocean Mechanical Drive vs. Electric Drive Besides creating a system design methodology, a secondary objective of this project was to shed more light on discussions taking place across the Navy hierarchy involving the application of the electric drive system (EDS). Currently, nuclear powered ships use mechanical drive systems (MDS) to propel them through the water. Mechanical drive propulsion systems (Figure 3) have a prime mover (steam turbine) that, through the use of reduction gears, powers the propulsor. A turbine generator uses the mechanical energy from an auxiliary mover to generate electric energy for ship use. While reactors on nuclear powered vessels provide vast amounts of energy for ship use, 75-80% of it is designated for mechanical drive use [2]. With this amount of energy tied 3

13 up for propulsion, other functions of the ship that require power lose operational flexibility. This has been an issue which the Navy has been looking to solve. Figure 3 Mechanical Drive [2] Investigations have been made into using a new propulsion system called the electric drive system. An electric drive system (Figure 4) would combine the propulsion generation and electrical generation of the mechanical drive into one system, which allows for greater operational flexibility. For EDS, main turbine generators (MTG) replace the prime and auxiliary movers of the MDS. All reactor power is converted to electric power through the use of the MTGs. All of the generated electric power is sent to a common electrical bus where is can be distributed to propulsion, navigation, weapons, or any other systems requiring electric power. The common electrical bus is also able to redistribute power across the ship as demands for electrical power change, so if the ship needs to run at full speed, power can be redistributed from other systems to operate the propulsion system. This project focuses on the operation of the propulsion aspect of the EDS, which is as follows. The common electrical bus sends power to a transformer that modifies the voltage and frequency of the electrical energy so it can be used by the drive and the motor. From the transformer, the electrical energy travels to the motor drive. The propulsion motor then takes the electrical energy from the motor drive and converts it into mechanical energy to drive the propulsor. 4

14 Figure 4 Electric Drive [2] Besides the ability to distribute the full power of the reactor, the EDS has other advantages over the MDS. By comparing the system layouts (Figure 3 and Figure 4), it can be seen that the MDS has a much more rigid layout of the reduction gears and the long shaft. The EDS has a much shorter shaft length, and uses cables to connect the components to allow for energy transfer. These cables allow for more flexibility for system arrangement. This will result in a smaller system that will make space available for other uses. The smaller EDS will also be easier to construct than the larger, more rigid MDS [2] Problem The above mentioned definition of system design is an excellent definition, but what is one supposed to use when a system must actually be designed? System design is complex and far reaching, however there is not much in the way of resources devoted to specific systems design. There are long definitions and high-level process maps which describe the process of systems design. These definitions and maps are general and apply to any system design, including database systems, mechanical systems, and numerous others. There is no specific methodology to design a specific system, which would be more useful than a generalized process map with a lack of focus on any specific discipline. Much of system design being done in industry is worked by using 5

15 tribal knowledge, or the accumulated knowledge and experience of the job over time. It is unreasonable to expect new and inexperienced engineers without tribal knowledge, to undertake system design tasks, and expect them to succeed in a timely and cost efficient manner. This project is meant to provide a methodology for the design of a heat removal system for an electric drive propulsion system. It is meant to serve as a useful guide and tool to be used should a request for a heat removal system be made. This methodology may not be perfectly applicable to every heat removal system design request, but it is the hope of this author that it will provide enough information to help and guide other fellow engineers Methodology This project uses a real world example as its foundation. A step by step methodology will be assembled as the real world example is analyzed. Assumptions and limits will be used to set the boundaries of the heat removal system. Design and engineering principles will be used to proceed, step by step, through the methodology of the design of the system. Three phases will be evaluated to proceed through the real world example. The first is System Specifications. This is a qualitative assessment of the customer request, requirements, and assumptions. Next is the Functional Design phase. This phase is a qualitative assessment of the system layout, including piping components, and needed system operating parameters. Lastly is the Detail Design phase. This is the most difficult phase because it is here where most of the quantitative analysis takes place. The system operating parameters will be defined numerically, as well as the component specifications by heat transfer, thermodynamic and fluid mechanic analyses. Excel will be used to perform and compile these analyses into easy to use spreadsheets. Process Model will be used to show the development of the system layout. 6

16 2. Results: System Design 2.1. System Specifications Task Definition and Requirements A customer has requested for a system to be designed to remove heat from Electric Drive Propulsion Machinery for a nuclear powered ship. The components requiring heat removal are the transformer, motor drive, propulsion motor. The task requirements are as follows: The system must be fresh water to seawater heat removal system. This is to maximize the ship s ability to remove heat to an almost endless heat sink (the ocean). Incorporate a 15% safety margin to the heat loads to allow for any extraordinary circumstances that may occur. Use components already tested and approved by the Navy to reduce the cost of testing and approving new components. The heat exchanger model to be used in the system is provided with baseline data (Table 4). Pumps and other system components will be selected off of the Navy s approved component list. The system components will be cooled in parallel. There will be a 20ºF temperature difference across each component. The maximum system fluid (fresh water or seawater) temperature is 130ºF Task Assumptions and Assessment The task assumptions, which the customer has approved, are as follows: The electric motor is a 30,000 HP motor. The motor output is operating at 100% power to provide an upper limit on the heat needed to be removed. The provided component efficiencies (Table 1) were calculated with the motor output operating at 100%. All components are assumed to be entirely fresh water cooled. Air cooling is not accounted for. 7

17 Assume pressure drop of 10 psig at design flow, across each electric drive components. This task must be researched to collect more data on the request to see if the task can realistically be achieved. For example, if the customer wanted a design for a system that is 101% efficient, the request would have to be declined since it is impossible to do. In the case of the fresh water to seawater heat removal system, there are already systems similar to it in existence, so the customer request is be feasible. After this stage, research was done to investigate if there are similar requests that have been done. Finding previously completed tasks would provide a road map and lessons learned to help complete this new task more efficiently. For the sake of the project, it shall be assumed that there are no previously completed tasks that would help, so that the full design and analyses may take place. Therefore, this system must be designed from scratch Functional Design Functional design develops the high level behavior and composition of the system. This is more of a qualitative design that lays the foundation for the detail design phase to add detailed quantitative values to the system. During the task assessment phase it was determined that the system would need to be designed from scratch. This means that a brainstorming session is needed to capture ideas for the high level system design. Form the brainstorming season, the best design should be created to help form the foundation of the detail design. Figure 5 depicts the results of the brainstorming session. 8

18 Transformer Motor Drive Motor Fresh Water Side Seawater Side FW Centrifugal Pump A FW Centrifugal Pump B (Cross Connect) Seawater Outlet (Cross Connect) Motor Operated Gate Valve Motor Operated Globe Valve Ball Valve Heat Exchanger Figure 5 High Level System Diagram 9 SW Centrifugal Pump A Y-Strainer A SW Centrifugal Pump B Y-Strainer B Seawater Inlet

19 The heat removal system was designed to have a fresh water closed loop to remove heat from the components, and another seawater loop to remove the heat from the fresh water and then be discharged to the ocean. The system was designed to have two operable sides with cross connects. This was to minimize risk should the system experience a casualty. Multi-speed centrifugal pumps were chosen to move the fluid through the system, because they are commonly used in fluid piping systems. Multispeed pumps were chosen to help regulate flow for varying heat demands. Y-strainers were put in on the seawater side to remove any particulate matter from the water to prevent fouling of the heat exchangers. The initial seawater inlet uses grating to remove large matter in the water, while the Y-strainers will remove the smaller matter. Numerous valves were put in to direct the flow of the system. Ball valves uses in this system are standard for fluid flow systems. Motor operated gate valves are used in this system to provide quick changes in flow direction as a result of system casualties. Motor operated globe valves were placed after the transformer, motor drive, and propulsion motor to regulate the flow through the components. With the multi-speed pumps, gate valves, and globe valves, the fluid flow through the components will be well regulated. Copper-nickel 70:30 (CuNi) piping will be used for the system. The material was selected because the material is strong yet flexible. The flexibility will make it easier for system construction when piping must be bent to fit the system layout. CuNi was also selected because of the natural property of copper to act as a biocide. This will help kill any organisms in the seawater side of the system, which will help prevent biofouling of the heat exchanger. The system calculations will be done based on half the system. This is because only one side of the system will be operating at a time, with the other side as backup Detail Design Detail design takes the high level overview of the system and starts to delve into the details of the system. This stage of the design is scientific and mathematical, requiring engineering knowledge and numerous analyses. The analyses provide the design guidelines of the system. 10

20 The setup to the detail design phase is very similar to the setup of any standard word problem. The known information, including assumptions, and what is trying to be found is written down. The know information includes the previously stated assumptions from the customer and the customer provided information on the component efficiencies (Table 1) and baseline heat exchanger data (Table 4). The customer is looking for a design for a heat removal system. The following list is what needs to be solved for to complete the system design. Fresh Water Flow Rate Seawater Flow Rate Fresh Water Pump Net Positive Suction Head (NPSH) Seawater Pump NPSH This may not seem like much to be solved for, but numerous other values will be needed to be solved for to find the previously mentioned values. Many of these values will also prove valuable to the overall system design. With the system laid out, and the knowns and unknowns validated, the system calculation and analysis may begin Heat Generation Calculation The following table is part of the information the customer supplied for the task. Motor Power Output EDS Propulsion Information Transformer Efficiency Motor Drive Efficiency Motor Efficiency Motor Output (HP) % 96.78% 96.34% 97.59% Table 1 EDS Propulsion Information Assuming that all losses due to efficiencies translate to heat loss then the heat generated by the components can be calculated as follows: 11

21 where: P in = Pout ( εtrans )( ε drv )( ε mtr ) (1) P in = input power (HP) P out = output power (HP) ε = efficiency 30,000 P in = = 32, 970HP (0.9678)(0.9634)(0.9759) Using the conversion 1 HP = 2,544.4 Btu/hr, the heat losses can be solved for, for each component as follows: Q trans = ( 1 ε trans )( Pin )(2,544.4) Q trans = ( )(32,970)(2,544.4) = 2,701, 251 Btu hr (2) Q drv = ( 1 ε drv )( Pin ε trans )(2,544.4) (3) Q drv = ( )(32, )(2,544.4) = 2,971, 500 Btu hr Q mtr ( Pout 1 ) = ε mtr (2,544.4) ε mtr (4) 30,000 Q mtr = ( ) (2,544.4) = 1,885, Btu hr Q= Q + Q + Q trans drv mtr = 7,557, 782 Btu hr (5) where: Q = total heat load (Btu/hr) 12

22 As a check to this math: Q= ( Pin Pout )(2,544.4) = (32,970 30,000)(2,544.4) = 7,557, 782 Btu hr (6) See Table 2 for the tabulated results of this section s calculations. With a total amount of heat that needs to be removed, the next step is to calculate how much fresh water it will take to remove the heat. 13

23 Heat Generation Calculation Transformer 96.78% Eff. Motor Drive 96.34% Eff. Motor 97.59% Eff. Motor Power Output Input Power (HP) Transformer Efficiency Transformer Loss (Btu/Hr) Motor Drive Efficiency Motor Drive Loss (Btu/Hr) Motor Efficiency Motor Output (HP) Motor Losses (Btu/Hr) Total Cooling Load (Btu/hr) % % 2,701, % 2,971, % ,885,030 7,557,782 Delta Power (HP) Total Cooling Load Check (Btu/hr) ,557,782 Table 2 Heat Generation Calculation 14

24 Fresh Water Flow Calculation One very important requirement is added here. As requested, a 15% safety margin was added to all heat loads to prepare for any extraordinary circumstances. Looking at the requirements also help set some conditions for the system. From the requirement that no fluid system operates higher than 130 F, it will be assumed that the fresh water temperature reaches a maximum of 120 F out of the components, to provide a safety margin of 10 F. With this assumption, the freshwater temperature into the components will be 100 F, from the requirement stating a 20 F temperature change across the components. Using the new safety margin heat loads, assumptions, and requirements, the fresh water flow rates for the system and each component can be found. Q m= ( C p, FW )( T1 T2 ) (7) where: m = mass flow rate (lb/hr) T 1 = fresh water inlet temperature ( F) T 2 = fresh water outlet temperature ( F) C p,fw = specific heat of fresh water (Btu/lbm-ºF) Fresh water specific heat (C p,fw ) is assumed to be 1 Btu/lbm-ºF since there is not a significant change in the specific heat of water from F. 3,106,439 m trans = = 155, 322 (1)( ) lb hr m 3,417,225 = = 170, 861 drv (1)( ) lb hr 2,167,785 m mtr = = 108, 389 (1)( ) lb hr 15

25 Converting the mass flow to a volumetric flow: F m = ρ FW (8) where: F = volumetric flow (ft 3 /hr) ρ FW = density of fresh water (lb/ft 3 ) Fresh water density is solved using: ρ FW = 2 T1 T (9) ρ FW = = lb 3 ft F trans m = ρ trans FW 155,322 = = ,519 3 ft hr This calculation is repeated for the motor drive and the propulsion motor. See Table 3 for values. The table also has a column that converts the volumetric flow in ft 3 /hr to GPM using the conversion of 1 ft 3 = 7.48 gallons. These values were summed up to find a total fresh water flow rate of 879 GPM. 16

26 Fresh Water Flow Calculation Component Heat Load (Btu/Hr) Design Margin Heat Load (Btu/Hr) Specific Heat H2O (Btu/lb- F) Density H2O (lb/ft^3) Tin ( F) Tout ( F) Delta T ( F) Mass Flow Rate (lb/hr) Volumetric Flow Rate (ft^3/hr) Volumetric Flow Rate (GPM) Transformer 2,701,251 3,106, ,322 2, Motor Drive 2,971,500 3,417, ,861 2, Motor 1,885,030 2,167, ,389 1, Total 7,557,782 8,691, ,572 7, Table 3 Fresh Water Flow Calculation 17

27 Heat Exchanger Baseline Calculation With a fresh water flow rate found, the seawater flow rate must be found. This can only be done by designing and analyzing the heat exchanger where the seawater will remove heat from the fresh water. Table 4 is the heat exchanger baseline information provided by the customer. The baseline information must be used to help design the heat exchanger used for the heat removal system being designed for this project. Vendor Provided HX Performance Specs Plate Surface Area (ft^2) Plate Thickness (ft) Number of Plates 165 Plate Thermal Conductivity (Btu/hr-ft- F) 12.1 Heat Load (Btu/Hr) 21,660,583 Fresh Water Inlet Temp ( F) Fresh Water Outlet Temp ( F) 110 Seawater Inlet Temp ( F) 95 Seawater Outlet Temp ( F) 112 Fresh Water Flow rate (GPM) 1,937 Seawater Flow rate (GPM) 2,909 Fouling Factor (%) 0 Freshwater Side Pressure Drop (PSI) 2.12 Seawater Side Pressure Drop (PSI) 3.45 Table 4 Vendor Provided HX Performance Specifications Based on this information, the baseline heat exchanger Log Mean Temperature Difference (LMTD) is calculated as follows [1]: where: T 1 = fresh water inlet temperature (ºF) T 2 = fresh water outlet temperature (ºF) t 1 = seawater inlet temperature (ºF) t 2 = seawater outlet temperature (ºF) ( T1 t2) ( T2 t1) LMTD = (10) ( T ) 1 t2 ln ( T2 t1) 18

28 ( ) (110 95) LMTD = = ºF ( ) ln (110 95) The overall heat exchanger performance is calculated using: Q = UA(LMTD) (11) where: Q = heat load (Btu/hr) U = heat exchanger overall heat transfer coefficient (Btu/hr-ft 2 - ºF) A = heat transfer area (ft 2 ) where: n = number of plates a = area of one plate (ft 2 ) A = na = ( 165)(6.025) = ft 2 (12) Q 21,660,583 U = = = Btu/hr-ft 2 -ºF (13) A( LMTD) (18.06) The heat exchanger heat transfer coefficients are calculated using the Nusselt equation [1] as follows: 19

29 0.14 x 0.33 Z k h= C(Re) (Pr) (14) ZW D where: h = heat transfer coefficient (Btu/hr-ft 2 -ºF) D = diameter (ft) k = seawater/fresh water thermal conductivity (Btu/hr-ft-ºF) C = constant provided by the heat exchanger vendor x = constant provided by heat exchanger vendor = 0.75 Re = Reynolds Number Pr = Prandtl Number Z = seawater/fresh water viscosity at bulk temperature (lbm/ft-hr) Z W = seawater/fresh water viscosity at plate wall temperature (lbm/ft-hr) For this calculation it was assumed that the viscosity at the bulk cooling temperature was equal to the viscosity at the plate wall temperature. Using this assumption enables the following equation to express the fresh water heat transfer coefficient in terms of the seawater heat transfer coefficient. h h FW SW k = k FW SW Re Re FW SW 0.75 Pr Pr FW SW 0.33 (15) where: C cancels due to the constant being equal for the heat exchanger fresh water and seawater side k FW = fresh water thermal conductivity (Btu/hr-ft-ºF) k SW = seawater thermal conductivity (Btu/hr-ft-ºF) Re FW = fresh water Reynolds Number Re SW = seawater Reynolds Number Pr FW = fresh water Prandtl Number Pr SW = seawater Prandtl Number 20

30 Fresh water thermal conductivity was found to be Btu/hr-ft- ºF by solving: k FW T = FW,avg T FW,avg 2 T FW,avg 3 (16) where: T FW,avg = average fresh water temperature between inlet and outlet (ºF) Seawater thermal conductivity was found to be Btu/hr-ft- ºF by solving: k SW 0.29 TSW,avg TSW,avg = 2 (17) where: T SW,avg = average seawater temperature between inlet and outlet (ºF) The following equation is used to calculate the Reynolds Number for both the fresh water and seawater [1]: Fρ Re= 50.6 Dµ where: F = flow rate (GPM) ρ = density (lbm/ft 3 ) D = internal diameter, equal on fresh water and seawater sides (in) µ = viscosity (lbm/ft-hr) (18) Fresh water density is solved using equation (9) from above. Seawater density is solved using the following equation and inlet seawater temperature: ρ SW = 2 t1 t (19) 21

31 Fresh water viscosity was found to be 1.34/ft-hr by solving: µ FW 4 TFW, avg TFW, avg TFW, avg = (20) Seawater viscosity was found to be 1.74/ft-hr by solving:: µ SW 5 TSW, avg TSW, avg = + 2 (21) Using equation (18) to solve for the ratio of fresh water to seawater Reynolds Numbers: Re Re FW SW ( F = ( F FW SW )( ρfw)( µ SW) = )( ρ )( µ ) SW FW (1,937)(61.44)(1.74) (2,909)(63.69)(1.34) = 0.84 (22) The following equation is used to solve for the Prandtl Number [1]: Pr = C p µ k (23) Fresh water specific heat (C p,fw ) is assumed to be 1 Btu/lbm-ºF since there is not a significant change in the specific heat of water from F. Seawater specific heat is solved using: 5 C p, = ( )( T, ) SW SW avg (24) Solving for the respective Prandtl Numbers: (1)(1.34) Pr FW = = 3.60 (0.371) (0.958)(1.74) Pr SW = = 4.67 (.357) 22

32 Equation (15) can now be solved using all of the previously calculated values: h h FW SW = ( 0.84) = (25) With this ratio, the fresh water / seawater heat transfer coefficients, and plate wall thermal resistance can be calculated as follows: 1 U = 1 1 R h + + SW h FW where: R W = plate wall thermal resistance (hr-ft 2 -ºF/Btu) W (26) Substituting the ratio of fresh water to seawater heat transfer coefficients into equation (26), to get: U = 1 + h SW h SW + R W (27) Solving for the plate wall thermal resistance is as follows: R = W t k plate plate (28) where: t plate = plate wall thickness (ft) k plate = plate thermal conductivity (Btu/hr-ft- ºF) R W = = hr ft F Btu Substituting all known values into equation (27) to get: 1,206.8= h SW h SW 23 4

33 Solving for h SW : h SW Btu 3,030.2 hr ft = 2 F Using the results from equation (25) to solve for h FW : h FW Btu 2,529.8 hr ft = 2 F Table 5 below gathers all of the results to the previous calculations: HX Baseline Calculation Log Mean Temp Difference ( F) Overall Heat Transfer Coefficient (Btu/Hr-ft^2- F) 1,206.8 Fresh Water Density ((lb/ft^3) Average Fresh Water Temp ( F) Fresh Water Viscosity (lbm/ft-hr) 1.34 Seawater Density ((lb/ft^3) Average Sea Water Temp ( F) Seawater Viscosity (lbm/ft-hr) 1.74 Reynolds Fresh Water / Reynolds Seawater 0.84 Fresh Water Specific Heat (Btu/lbm- F) 1 Seawater Specific Heat (Btu/lbm- F) Fresh Water Thermal Conductivity (Btu/Hr-ft- F) Seawater Thermal Conductivity (Btu/Hr-ft- F) Prandtl Fresh Water 3.60 Prandtl Seawater 4.67 Prandtl Fresh Water / Prandtl Seawater 0.77 Freshwater / Seawater Heat Transfer Coeff Plate Wall Thermal Resistance (Hr-ft^2- F/Btu) Seawater Heat Transfer Coefficient (Btu/Hr-ft^2- F) 3,030.2 Freshwater Heat Transfer Coeff (Btu/Hr-ft^2- F) 2,529.8 Table 5 HX Baseline Calculation With the baseline heat exchanger calculations complete, it is now possible to obtain design specifications from the heat exchanger for this project design. 24

34 Heat Exchanger Design Calculation The following table contains all of the known information gathered about the heat exchanger being used for this design: Known Information Plate Surface Area (ft^2) Plate Thickness (ft) Number of Plates 165 Plate Thermal Conductivity (Btu/hr-ft- F) 12.1 Heat Load (Btu/Hr) 8,691,449 Fresh Water Inlet Temp ( F) 120 Fresh Water Outlet Temp ( F) 100 Fresh Water Volumetric Flow (GPM) 879 Fresh Water Mass Flow (lb/hr) 434,572 Seawater Inlet Temp ( F) 90 Fouling Factor (%) 0 Table 6 Known HX Information A seawater inlet temperature of 90ºF was assumed. This assumption was based on research done to find the warmest ocean on the planet. It was found that the Indian Ocean was the warmest exceeding 82ºF [9]. The assumption adds in a safety margin of 8 ºF. The method to solve this design is to approach it from two paths. Two log mean temperature differences will be calculated using two different calculations. When the two log mean temperature differences are equal, that means that the values found are the correct ones for this design. Multiple iterations are needed until LMTD 1 = LMTD 2. Excel was used to make this iterative process quicker. Log Mean Temperature Difference 1 For this approach a seawater flow rate is guessed. This calculation will use the correct seawater flow rate, instead of one of the iterative guesses. The seawater outlet temperature (t 2 ) must be solved, to find LMTD 1. Using a seawater volumetric flow rate of 1,341 GPM, outlet seawater temperature is calculated as follows: 25

35 Q= m where: m SW = mass flow rate of seawater (lb/hr) FW C ( t ) 1 p, SW 2 t (29) Converting the mass flow rate to a volumetric flow rate using: m = ( )( ρ FW ) FW F FW (30) Seawater density is solved using equation (19), and using proper conversion units to find m SW = 685,732 lb/hr. The seawater heat capacity is solved using equation (24). Substituting values into equation (29): 8 1,691,449= (685,732)(0.957)( t 2 90 ) Solving the equation, t 2 = 103.2ºF. With t 2, the LMTD 1 can now be solved as follows: ( ) (100 90) LMTD = ( ) ln (100 90) 1 = Log Mean Temperature Difference 2 The approach to find LMTD 2 is very similar to the approach used for the baseline heat exchanger design. Some of the values from the baseline calculation will also be used to find LMTD 2. Expanding equation (15) and the assumptions that go with it, results in the following equation showing a relationship between the new values being calculated and the old values from the baseline calculations: h h new baseline k = k new baseline F F new baseline 0.75 Pr Pr new baseline 0.33 (31) Note that the Reynolds Numbers are substituted with the flow rates since a ratio is being used with the same fluid mediums. From here the thermal conductivities and Prandtl Numbers are calculated exactly as done in the heat exchanger baseline calculation, 26

36 except using values from Table 6. Any needed seawater values not in Table 6, come from the values calculated in Log Mean Temperature Difference 1. The results are as follows: h new, SW 3, ,341 = , Solving the equation you find h new,sw = 1,725.0 Btu/hr-ft 2 -ºF. h new, FW = 2, , Solving the equation you find h new,fw = 1,441.1 Btu/hr-ft 2 -ºF. The overall heat transfer coefficient is now solved using equation (26) and the previously calculated plate wall thermal resistance. U = , , Btu = hr ft F Rearranging equation (11) you get: LMTD LMTD = 2 Since the LMTDs match, that means that the calculated values are correct. In the case that the Log Mean Temperature Differences didn t match, the guess for the seawater flow rate would need to be changed, and the calculations repeated. Excel was used to make this process faster. Table 7 captures all of the values calculated in this section. Q UA 8,691,449 ( )(994.13) 2 = =

37 HX Design Calculation Seawater Volumetric Flow (GPM) 1,341 Seawater Density (lb/ft^3) Seawater Mass Flow (lb/hr) 685,732 Seawater Specific Heat (Btu/lbm- F) Seawater Outlet Temp ( F) Log Mean Temp Difference 1 ( F) Average Fresh Water Temp ( F) 110 Fresh Water Specific Heat (Btu/lbm- F) 1 Fresh Water Density (lb/ft^3) Fresh Water Viscosity (lbm/ft-hr) Fresh Water Thermal Conductivity (Btu/Hr-ft- F) Average Seawater Temp ( F) 96.6 Seawater Specific Heat (Btu/lbm- F) Seawater Density (lb/ft^3) Seawater Viscosity (lbm/ft-hr) Seawater Thermal Conductivity (Btu/Hr-ft- F) Prandtl Fresh Water 4.08 Prandtl Seawater 5.06 Seawater Side Heat Transfer Coeff (Btu/Hr-ft^2- F) 1,725.0 Fresh Water Side Heat Transfer Coeff (Btu/Hr-ft^2- F) 1,441.1 Plate Wall Thermal Resistance (Hr-ft^2- F/Btu) Overall Heat Transfer Coefficient (Btu/Hr-ft^2- F) Log Mean Temp Difference 2 ( F) Difference Between LMTD1 and LMTD Table 7 HX Design Calculation With the flow rates for both the fresh water and seawater, it is now possible to size pipes for the system. 28

38 Pipe Sizing Calculation Pipes will need to be sized for each EDS propulsion system component, along with fresh water and seawater headers. From the functional design we know that the pipe material will be CuNi 70:30. Using this material, an assumption can be made about the fluid velocity in the pipe. The assumption being made for the pipe sizing calculations is that the fluid velocity may not exceed 10 ft/sec. This assumption was made by researching CuNi pipe and finding that typical acceptable design velocities are around 13 ft/sec [5]. It was decided not to exceed 10 ft/sec to provide a safety margin for the piping design. Using this assumption the pipe sizing calculations are as follows: where: F = volumetric flow (ft 3 /sec) v = fluid velocity (ft/sec) A = cross sectional area of pipe (ft 2 ) F = va (32) Solving for pipe cross sectional area: A F = v = 10 trans trans = trans 0.07 ft 2 This process of solving for pipe area was repeated for the motor drive, propulsion motor, fresh water header, and seawater header. The results are tabulated in Table 8. To convert the pipe area into a pipe diameter: A= π 2 2 D ( )( r ) = ( ) π 2 (33) where: r = radius of pipe (ft) D = diameter of pipe (ft) A D = 2 π 29 (34)

39 D trans = 2 A trans π This calculation was again repeated for all components and headers. The final value of this equation comes out in feet. As shown in Table 8, there was also the inclusion of a conversion for feet to inches. The pipe diameter was rounded because most pipes are manufactured to the nearest whole inch. After this, the final true velocities of the fluid flowing in the pipe were found using equation (32). The final results are shown below. Pipe Sizing Calculation Component Volumetric Flow Rate (ft^3/sec) Max Allowable Velocity (ft/sec) Pipe Area (ft^2) Pipe Diameter (in) Rounded Pipe Diameter (in) Actual Velocity (ft/sec) Transformer Motor Drive Motor Fresh Water Headers Seawater Headers Table 8 Pipe Sizing Calculation 30

40 Pressure Drop Calculation Using the information during the functional design phase and all of the previous calculations, pressure drop calculations may begin. Since the system has not been through the arrangements phase, where this system would be designed to fit in the ship, assumptions will have to be made. It is unknown what the pipe lengths will be or how many bends will be in the system. A conservative estimate of straight pipe will be made for each component and header. This conservative estimate should capture the full pressure loss when the system is fully incorporated into arrangements. The pipe length assumptions can be seen in Table 9, which is at the end of this section. Head loss was calculated for the transformer, motor drive, and propulsion motor using the customer approved assumption that there is a 10 psig loss across each component, and using the following equation to convert psig to head loss. H = 144 p ρ (35) where: H = head loss (ft) p = pressure drop (psig) 144 H = 10 = ft The pressure loss associated with the heat exchanger is calculated using the equation: p 2 fl m D 2ρA = 2 (36) By applying this equation with the pressure loss values from the baseline heat exchanger calculation, the pressure loss for the new heat exchanger design can be found. Assuming that there is no great change in the density between the baseline and new values, then the only changing values in the above equation are the mass flow rate (m) and the heat transfer area (A). Since ratios are going to be used between the baseline and new values, volumetric flow rates can be used instead of mass flow rates. It is also recognized that 31

41 the only value affecting the heat transfer area is the number of plates. So the new equation is as follows: p = p F baseline, FW baseline,, new FW baseline FW Fnew, FW nnew 2 n 2 (37) p 2 2 1, new, FW = 2.12 = psi The head loss associated with this pressure loss was solved using equation (35) as follows: 144 H FW = = 24 ft The seawater side head loss was calculated exactly as the fresh water side was to find a head loss of feet. The head loss associated to the piping is calculated using the following equation: H = ( f ) L D 2 v 2g (38) where: f = friction factor L = length of pipe (ft) g = gravitational constant The friction factor is found using a Moody Diagram [11], by comparing the pipe relative roughness and Reynolds Number. The relative roughness is found using: where: R = relative roughness e = absolute roughness (ft) R= e D (39) 32

42 The absolute roughness of CuNi pipe was found to be 5*10-6 ft [12]. Using this value, the relative roughnesses for all pipes were found. See Table 9 for relative roughness values. The Reynolds Numbers were found using: ρvd Re= µ (40) All of these values were already calculated previously, so it was a simple matter of substituting them into the above equation. The Reynolds Numbers results can be found in Table 9. With the Reynolds Numbers and relative roughnesses, the friction factors can now be found. See Appendix A for the Moody Diagrams [11] with the method for finding the friction factors for each pipe and Table 9 for the friction factors. Substituting into (38) to get: H L ) D v trans 2g 2 2 trans trans = ( f trans = (0.0138) = trans This was repeated for all the components and headers to find the head loss. The values are shown in Table 9. With the head loss for the main components of the drive system and the piping calculated, the head loss for minor components of the system can be found. This includes the valves and Y-strainers. The following equation is used to solve for head loss for valves [12]: ft where: H = ( K L 2 v ) 2g (41) K L = valve loss coefficient Looking at Figure 5, it is seen that the system is composed of ball valves, gate valves, and globe valves. To calculate the head loss associated with these valves the valve loss coefficients must be investigated. It was found that: K Lball K L gate = 0.05 = 0.15 K L globe 33 =10

43 Because of the low values for the ball and gate valves, the assumption was made that the glove valves are the only valves which have a significant impact on the head loss of the system. Using this assumption the glove valve head loss is as follows: H trans = (10) ft 2(32.2) = H drv = (10) ft 2(32.2) = H mtr = (10) ft 2(32.2) = To solve for the head loss associated with the Y-strainer, design information is needed from the vendor. The Flow Rate vs. Pressure Drop chart [18] for the Y-strainer can be found in Appendix B. By using a seawater flow rate of 1,341 GPM and knowing that the strainer will be 8 inches, because it is part of the seawater header, a pressure drop of 9 psi is found. Using equation (35), the head loss is found: H strainer = pstrainer = 9 = ft ρsw Table 9 shows the tabulated data from the calculations. The green highlighted sections are meant to draw attention to the fact that these values won t update with the rest of the spreadsheet. The friction factors must be found anew, using the Moody Diagrams, after which the spreadsheet will continue to update. Now that the main contributors to head loss have been calculated, it is possible to calculate the pump requirements for both the seawater and freshwater pumps. 34

44 Pressure Drop Calculation Component Diameter (ft) # of feet of pipe Velocity (ft/sec) Density (lb/ft^3) Viscosity (lbm/ftsec) Reynolds Number Relative Roughness Friction Factor Loss Coefficient Pressure Loss (psig) Transformer Motor Drive Motor HX FW Side HX SW Side Transformer Pipe E E Motor Drive Pipe E E Motor Pipe E E Fresh Water Header Pipe E E Seawater Header Pipe E E Transformer Globe Valve Motor Drive Globe Valve Motor Globe Valve Y-Strainer Head Loss (ft) Table 9 Pressure Drop Calculation 35

45 Pump Design Calculation With the flow rates for both fresh water and seawater calculated, the last thing to calculate for the pumps is the required net positive suction head (NPSH R ). The NPSH R of a system must be exceeded by the pump or the pump will experience cavitations. The cavitations cause a loss in pump efficiency and could potentially damage the pump. To calculate the NPSH R for the fresh water pump, the head loss for each component and its respective piping and globe valves is summed. This is because the system is cooled in parallel. Since the system is cooled in parallel, the path with the largest head loss is used for the NPSH R calculation, since the other parallel paths with lower head losses will be handled by the larger head loss being taken into account. After summing the head losses from the different paths, it was found that propulsion motor pathway possessed the largest head loss. Summing this value with the head losses of the main fresh water header and the fresh water side of the heat exchanger the NPSH R for the fresh water side of the system comes to feet. Therefore, the fresh water pump should meet the minimum requirement of 879 GPM and provide a minimum of feet of net positive suction head. When the actual pump is selected it would be wise to select a pump with values that are larger than the ones afore mentioned to provide a buffer for any extraordinary circumstances. To calculate the NPSH R for the seawater side, all that needs to be done is sum the head losses of the main seawater header piping, the y-strainer, and the seawater side of the heat exchanger. This value comes out to be feet. Therefore, the seawater pump should provide a minimum of 1,341 GPM and feet of net positive suction head. As for the fresh water pump, the actual seawater pump should exceed these values for any extraordinary circumstances. Table 10 shows the tabulated data from the calculations. 36

46 Fresh Water Pump Specifications Head Loss (ft) Required Flow Rate (GPM) Required Net Positive Suction Head (ft) Component Transformer/Transformer Pipe/Transformer Globe Valve Drive/Drive Pipe/Drive Globe Valve Motor/Motor Pipe/Motor Glove Valve HX FW Side Fresh Water Header Pipe Seawater Pump Specifications Component Head Loss (ft) Required Flow Rate (GPM) Required Net Positive Suction Head (ft) HX SW Side , Seawater Header Pipe 4.27 Y-Strainer Table 10 Pump Specifications 37

47 3. Conclusions Numerous calculations were done to find values needed for the design of the system the customer requested. Fresh water and seawater flow rates and NPSH R were found, along with a plethora of values needed to find the overarching system design parameters. All of these values can be found in the System Design Excel spreadsheet portion of this project. The Excel spreadsheet outputs which are also the tables at the end of each section may also be found in Appendix C. After doing the analyses, the overall system design in Figure 5 will work with the values found during the detail design phase. Once the system is incorporated on the ship with all other ship systems, a more precise system design could be done. This more accurate system design would take the pipe length assumptions used in this analysis, and convert it to actual pipe lengths, with all the bends taken into account. With the new values for piping, the calculations can be redone and the new values applied. The goals of this project have been met. A methodology for the design of an electric drive propulsion machinery heat removal system for a nuclear powered ship was developed, with all actions and assumptions explained in a step by step fashion. An Excel spreadsheet was also developed for use by anyone possessing it. The spreadsheet allows for instantaneous updates of information when values are changed. This will hopefully be useful to the new and inexperienced engineers out in industry who deal with system design. 38

48 References 1) Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport Phenomena. New York: J. Wiley, Print. 2) Bowman, Frank. "An Integrated Electric Power System: the Next Step." GlobalSecurity.org - Reliable Security Information. Web. < 3) Cȩngel, Yunus A. Heat Transfer: a Practical Approach. Boston: McGraw-Hill, Print. 4) Cȩngel, Yunus A., and Michael A. Boles. Thermodynamics an Engineering Approach. Boston: McGraw-Hill, Print. 5) "Copper.org: Copper Nickel: Sea Water System Design." Copper.org: Copper Development Association - Information on Copper and Its Alloys. Web. < 6) "Exchanger Service - Plate Exchangers." HEAT EXCHANGER REPAIR. Web. < & Frame Heat Exchangers.htm>. 7) General Electric. "Handbook of Industrial Water Treatment." Water & Process Technologies: Water, Wastewater and Process Systems Solutions. Web. < 8) Hills, Peter D. Practical Heat Transfer. New York: Begell House, Print. 9) "Indian Ocean." Wikipedia, the Free Encyclopedia. Web. < 10) ITER Joint Central Team, ITER Heat Removal System: System & Process Control Design, December, Print 11) "Moody Diagram.jpg." Wikimedia Commons. Web. < 12) Munson, Bruce Roy, and T. H. Okiishi. Fundamentals of Fluid Mechanics. Hoboken, NJ: J. Wiley & Sons, Print. 13) "Nuclear-Powered Ships Nuclear Submarines." World Nuclear Association Nuclear Power - a Sustainable Energy Resource. Web. < 39

49 14) "Nuclear Propulsion." Federation of American Scientists. Web. < 15) "Oswego County Today»Oswego» Nine Mile 1 Shuts Down When Water System Fails." Oswego County Today. Web. < 16) Saline Water Conversion: Engineering Data Book. [Washington]: U.S. Dept. of the Interior, Print. 17) Smith, Joseph M., Hendrick C. VanNess, and Michael M. Abbott. Introduction to Chemical Engineering Thermodynamics. Boston: McGraw-Hill, Print. 18) Sure Flow Equipment. "Technical Information." Industrial Strainers. Web. < 19) System Design. Encyclopedia.com. Web. a. 40

50 Appendix A: Moody Diagrams see next page [11] 41

51 Transformer 42

52 Motor Drive 43

53 Propulsion Motor 44

54 Fresh Water Header 45

55 Seawater Header 46

56 Appendix B: Y-Strainer Flow Rate vs. Pressure Drop Chart [18] 47