Dynamic Simulation of Turbine Engine used with Molten Carbonate Fuel Cell for Power Generation in the Megawatt Range

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1 Wright State University CORE Sholar Browse all Theses and Dissertations Theses and Dissertations 2013 Dynami Simulation of Turbine Engine used with Molten Carbonate Fuel Cell for Power Generation in the Megawatt Range Carlos Eduardo Gutierrez Wright State University Follow this and additional works at: Part of the Mehanial Engineering Commons Repository Citation Gutierrez, Carlos Eduardo, "Dynami Simulation of Turbine Engine used with Molten Carbonate Fuel Cell for Power Generation in the Megawatt Range" (2013) Browse all Theses and Dissertations Paper 1160 This Thesis is brought to you for free and open aess by the Theses and Dissertations at CORE Sholar It has been aepted for inlusion in Browse all Theses and Dissertations by an authorized administrator of CORE Sholar For more information, please ontat

2 DYNAMIC SIMULATION OF TURBINE ENGINE USED WITH MOLTEN CARBONATE FUEL CELL FOR POWER GENERATION IN THE MEGAWATT RANGE A thesis submitted in partial fulfillment of the requirements for the degree of Master of Siene in Engineering By CARLOS EDUARDO GUTIERREZ BS, Wright State University, Wright State University

3 WRIGHT STATE UNIVERSITY GRADUATE SCHOOL Deember 17, 2013 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Carlos Eduardo Gutierrez ENTITLED Dynami Simulation of Turbine Engine Used With Molten Carbonate Fuel Cell for Power Generation in the Megawatt Range BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Siene in Engineering Mith Wolff, PhD Thesis Diretor Committee on Final Examination George Huang, PhD, Chair Department of Mehanial and Materials Engineering Mith Wolff, PhD James Menart, PhD Sott Thomas, PhD R William Ayres, PhD Interim Dean, Graduate Shool

4 ABSTRACT Gutierrez, Carlos Eduardo MS Egr, Department of Mehanial and Materials Engineering, Wright State University, 2013 Dynami Simulation of Turbine Engine used with Molten Carbonate Fuel Cell for Power Generation in the Megawatt Range Molten arbonate fuel ells (MCFC) have a high operating temperature of approximately 650 C (1200 F) to ahieve suffiient ondutivity of its arbonate eletrolyte Therefore, a gas turbine engine oupled with a MCFC is desirable sine the turbine engine an be used to provide hot gas to the athode, and the athode gas residue an be used to raise the temperature of the natural gas and water vapor mixture (fuel) before it enters the MCFC at the anode Dynami models of a hybrid power plant onsisting of a gas turbine engine and a MCFC with their respetive omponents were developed in MATLAB/Simulink to apture in real time the hanges due to sudden flutuations on power loads, air flows, et, and to develop safe and effiient ontrol of this system The power plant is omposed by a ompressor, turbine, shaft, heat exhangers, heat reovery unit, an oxidizer and a molten arbonate fuel ell working synergistially able to ahieve high operating effiienies and power demands in the MW range The projet is a joint effort between Purdue University and Wright State University where the oxidizer and fuel ell models are developed by Purdue, and the rest of the omponents are developed by Wright State University iii

5 TABLE OF CONTENTS Page 1 INTRODUCTION 1 2 BACKGROUND 2 3 MODELING 6 31 GAS TURBINE ENGINE Compressor Turbine Shaft SHELL AND TUBE HEAT EXCHANGER Introdution General Equations Shell Side Flow Tube Side Flow MOLTEN CARBONATE FUEL CELL HEAT RECOVERY UNIT Heat exhangers Mixing Chamber CONTROL Flow Control Fuel Temperature Control 49 iv

6 353 Stak Temperature 50 4 MODEL VALIDATION Shell and Tube Heat Exhanger Mixing Chamber Simulation Run Parameters 60 5 APPLICATION 61 6 CONCLUSIONS 75 REFERENCES 77 APPENDIX A PI CONTROLLERS 79 APPENDIX B GAS PROPERTIES 82 v

7 LIST OF FIGURES Figure Page 21 Hybrid GT/MCFC System 2 21A Hybrid GT/MCFC System Gas Turbine Engine 6 31 Compressor Map 9 32 Turbine Map Pressure Ratio vs Correted Mass Flow Turbine Map Effiieny vs Pressure Ratio 13 21B Hybrid GT/MTFC System Shell and tube heat exhanger Single segmental shell and tube heat exhanger Leakage through baffles Shemati of ontrol volume applied to heat exhanger Corretion fator JL for leakage hart Corretion fator JB for bypass in the bundle-shell gap hart Corretion fator RB for pressure drop hart Corretion fator RL for pressure drop hart Moody diagram 33 21C Hybrid GT/MCFC System Molten Carbonate Fuel Cell Molten Carbonate Fuell Cell 37 21D Hybrid GT/MCFC System Heat Reovery Unit Shemati of Heat Reovery Unit Multi-tube heat exhanger axial disretization temperature response 43 vi

8 315 Shemati of o-flow and ounter-flow heat exhangers Shemati ontrol volume mixing hamber Molar flow rates of gas mixture going into tube side of STHX Air molar flow rate going into shell side of STHX Outlet temperature of gas mixture Outlet temperature of air Pressure loss of gas flowing in tube side Pressure loss of air flowing in shell side Current load applied to plant Flows subjeted to urrent load Total hybrid power in MW Gas Turbine Engine Power in kw Fuel Cell Power in kw Perentage of power ontributed by GT LHV plant effiieny subjeted to urrent load HHV effiieny subjeted to urrent load Fuel ell stak temperature Air flow going through turbine engine Temperature of air entering turbine Heat transfer rate from hot gas inside tubes to the wall tubes Heat transfer rate from wall tubes to ompressed air 71 vii

9 514 Variation of ompressor pressure ratio Compressor outlet temperature Surge margin Compressor orreted speed perentage Ratio of temperature of wall tubes and temperature of gas flowing inside tubes Temperature of natural gas for desulfurization Perentage of air flow passing from turbine to oxidizer through flow valve 74 viii

10 LIST OF TABLES Table Page 31 Correlation onstants for staggered and in-line tube banks 24 ix

11 1 INTRODUCTION In the past few years, a great deal of attention has been given to fuel ells oupled with gas turbine engines to reate systems for power generation These systems an ahieve very high effiienies There are a ouple of onfigurations that have been developed For instane, one of them has a gas turbine engine with a high temperature operating fuel ell plaed where the ombustor usually is Air is ompressed by the ompressor and then heated The pressurized flue gas then enters the athode side of the fuel ell where it would reat eletrohemially to reate eletriity with pressurized fuel provided at the anode The pressurized flue gas leaving the athode would then enter the turbine where it is expanded to reate even more eletriity This partiular system has the disadvantage that the fuel ell has to be operated within a pressure range, whih may not be the most suitable pressure ratio for the turbine engine Another disadvantage is that the fuel ell needs to be operated at pressures muh higher than ambient pressure inreasing the ost of the fuel ell for materials and impeding internal reforming of the fuel further inreasing the overall ost and affeting the effiieny of the system In addition, the fuel ell and turbine engine mutually rely on eah other for the system to funtion, in that way, affeting its reliability [2] The hybrid system being modeled was developed by FuelCell Energy, In In this system, the fuel ell and turbine engine run independently from eah other and the turbine engine is able to operate in a wide range of pressure ratios (from 3 to 15) This means that different power plant sizes an be ahieved where low pressure ratios are used for sub-mw power plants, and high pressure ratios (9 to 15) are used for MW plant sizes [1][24] The latter is the ase being modeled 1

12 2 BACKGROUND It is important to aknowledge that this projet is a joint effort between Wright State University and Purdue University Purdue University is responsible for the fuel ell model as well as some related omponents suh as the atalyti oxidizer, while Wright State University is in harge of the omponents in the gas engine inluding the heat exhangers that would be related to the gas turbine engine operation and fuel preparation Now, the hybrid system being modeled is shown in Fig 21 Turbine Compressor Fig 21 Hybrid GT/MCFC System Eah of the omponents of the plant will be disussed in detail in subsequent hapters, so for now the proess on how the plant operates and the main funtion of eah omponent is disussed The fuel ell is a molten arbonate fuel ell (MCFC) On the fuel ell side, water and natural gas are fed through a heat reovery unit, whih operates on waste heat from the athode exhaust After the water is evaporated in the HRU, it is then mixed with the 2

13 natural gas This mixture enters the anode of the MCFC as fuel The humidifiation proess provides the steam needed for the reforming of natural gas This natural gas/water-vapor mixture reats in the fuel ell with the gas provided at the athode produing eletriity Not all the fuel reats, so some of it just passes through the anode The anode exhaust is then fed to a atalyti oxidizer where it reats with the air that is being delivered by the turbine This oxidizer also serves to onvert any arbon monoxide leaving the anode to arbon dioxide whih is used in the athode side of MCFC The produt hot gas from the oxidizer is then fed through a shell-and-tube heat exhanger (STHX) to heat up the air oming from the ompressor The gas from the oxidizer is ooled down in this proess and leaves the heat exhanger at a temperature that is suitable for the MCFC to the athode side Finally, the athode exhaust gas is direted to the heat reovery unit (HRU) whih will prepare the natural gas/water-vapor mixture that is used in the anode On the turbine engine side, air is ompressed by the ompressor and is fed diretly to the STHX where it is heated using the oxidizer gas The ompressed hot air is now ready to enter the turbine where it is expanded to slightly above ambient pressure It is important to notie that the ompressed air an also be fed through the HRU before it enters the STHX As a matter of fat, that is how the original system was developed by FuelCell Energy, In However, sine the system modeled operates at a pressure ratio of ~10, the ompressed air leaves at a high enough temperature (about 350 C) from the ompressor where it an be diretly fed to the STHX There has been a lot of researh over the past years on the development and ommerialization of fuel ells There are different kinds and eah is suited better to 3

14 different types of appliations This researh will fous on molten arbonate fuel ells, whih is used for power generation and the type used for the power plant onfiguration There are several developments in the literature based on partiular assumptions for MCFC Lukas et al developed the modeling and ontrol aspets of an internal reforming MCFC power plant They developed a lumped-parameter MCFC model based on representation of both fast and slow dynamis by onsidering reforming reation kinetis, mass storage, and ell polarization losses [6, 25] Although their researh is foused on the fuel ell side only, a lot of it is appliable to the hybrid MCFC\Turbine engine power plant and the fuel flow ontrol used in this simulation as well as the dynamis in the MCFC are based on their work Gas turbine engines are widely used for different type of appliations in the aviation, maritime and power generation industries Even though turbine engines vary in sizes and types, they all share the same basi omponents suh as ompressors ombustors and turbines The gas turbine engine model used in this simulation was developed by Sientifi Monitoring In The engine model is based on a omponent approah for ease of modifiation and replaement of different engine omponents [3] Eah omponent is a losed funtional unit with its own set of inputs and outputs and if these are provided, the omponent an operate independently For example, the turbine module an be used as a stand-alone turbine omponent for a given set of flow and effiieny maps, and a given set of upstream and downstream boundary onditions Alternate onfigurations based on the system studied shown in Fig 21 have been onsidered using the same priniple of deoupling the gas turbine engine with the MCFC Ghezel-Ayagh et al [1] presented an approah for a 40MW plant design based on fuel 4

15 ell lusters of the existing MCFC by Fuel Cell Energy In and using a gas turbine engine with inter-stage ompressor ooling to obtain very high overall ompressor pressure ratios without the signifiant inrease of ompressor outlet temperature to ultimately inrease the overall fuel effiieny of the hybrid plant The same methods that will be illustrated in this researh an be used to extend to any other power plant onfiguration with multiple turbine engine spools, heat exhangers, molten arbonate fuel ells, et The purpose of this researh is to present a detailed modeling approah for eah of the omponents and sub-omponents of this MCFC/GT power plant to apture in real time the hanges due to sudden flutuations on power loads, air flows, et, and to develop safe and effiient ontrol of this system Eah of the omponents of the system was modeled using Matlab/Simulink whih is able to simulate linear and nonlinear systems in ontinuous or disrete time Moreover, the user is allowed to hange different parameters/inputs while the simulation is running and immediately see and analyze the results 5

16 3 SYSTEM MODELING 31 Gas turbine Engine Turbine Compressor Fig 21A Hybrid GT/MCFC System Gas Turbine Engine The turbine engine model was developed by Sientifi Monitoring, In A volume inertia method is applied in a lumped fashion for eah omponent (ompressor, turbine, et) Therefore, a multiple stage turbine or ompressor is simulated as one omponent For the ompressor and the turbine, the dynami modules are based on volume dynamis The dynamis for the shaft are based on moment of inertia Compressor and turbine maps and lumped volumes for eah omponent are required for its respetive modules to work Shaft speed and moment of inertia are the design parameters for this module to work The omponents are linked upstream to downstream, beause they were reated to simulate flow from inlet to exhaust For this ase, only the ompressor, turbine and shaft modules are used sine the ombustor is replaed by a shell-and-tube heat exhanger whih serves as the bridge 6

17 between the MCFC and the gas turbine engine 311 Compressor This model ontains a stati setion as well as a dynami setion Flow, effiieny, exit temperature, surge margin and required shaft torque are alulated in the stati setion The map values of orreted flow, effiieny and pressure ratio are funtions of orreted speed and Rline (arbitrary parameter) The transition volume dynamis omputes the exhaust pressure It is alulated by integrating over time the differene between airflow delivered downstream and airflow required downstream at exhaust temperature [3] Compressor - Stati Setion The inlet free stream temperature, T,, and pressure, P in,, are nondimensionalized in by dividing eah by its respetive standard sea level stati values T, in (31) T ref P, in (32) P ref where T ref R and P ref 14 7 psia for English units, whih is the ase here The orreted engine speed N is omputed N N (33) where N is the atual speed of the shaft in RPM 7

18 The perentage speed used to pull out values from the ompressor map is obtained omputing where N N % 100, (34) N Des N is the ompressor orreted speed at design point Des Fig 31 is the ompressor map used in this model showing the relationship between orreted mass flow, pressure ratio, orreted engine speed and ompressor effiieny The orreted mass flow m Corr, ompressor effiieny and pressure ratio PR map, are funtions of an arbitrary parameter (Rline) and N% m Corr f ( Rline, N %) (35) f ( Rline, N %) (36) PR map f ( Rline, N %) (37) 8

19 Fig 31 Compressor Map [3] The mass flow rate m Cin going into the ompressor is omputed using the definition of orreted mass flow one obtained from the map m Cin m Corr (38) The outlet temperature, T, out, is alulated using the relationship T, out T, in PR map (39) where γ is the speifi heat ratio evaluated at the average between inlet and exhaust temperature 9

20 respetively Two flow parameters FP and FP, are alulated using map vol PR and PR map FP map m PR Corr map PR 1 map 1 1 (310) FP vol m Corr PR PR 1 map 1 1 (311) Here PR is the pressure ratio alulated with the outlet pressure P, out, omputed in the dynami setion, and the inlet pressure P, in PR P, out (312) P, in The arbitrary parameter Rline is iterated until the following ondition is satisfied FP FP 0 (313) vol map Finally, the torque required by the ompressor is alulated in the following manner where E net E is the net energy, the torque required by the ompressor and is the angle net moved in radians The required torque for the ompressor is then alulated by m Cin h h out in 60 (314) N 2 10

21 where h in and h are the inlet and outlet enthalpies respetively and N is the speed of the out shaft in RPM Compressor - Dynami Setion The exhaust pressure P, is omputed by applying the ontinuity equation and out the ideal gas equation m in m out dm dt (315) P mrt (316) Substituting m from the ideal gas equation to the ontinuity equation we obtain P ( m in m out ) RT t P T T t (317) Finally, after simplifiations suggested by Horobin [8] ( m in m out ) RT P T T t The seond term an be dropped and P, is alulated by out dp ( m out in m, out ) dt R air T, out (318) 312 Turbine The orreted mass flow and turbine effiieny are read off the maps and are a funtion of orreted speed and pressure ratio P P turb in turb, out, / The transition volume dynamis omputes the exhaust pressure based on air thermodynami properties just as it is done in the ompressor module [3] 11

22 Turbine - Stati Setion The turbine map used in this model is divided into two, Fig 32 and Fig 33 Fig 32 shows the relationship between orreted mass flow m Torr, pressure ratio PR turb, and orreted turbine speed N%, while Fig 33 shows the relationship between turbine effiieny t, PR and turb N% Fig 32 Turbine map - Pressure Ratio vs orreted mass flow [3] Just as it was done in the ompressor, the pressure and temperature of the stream going into the turbine are nondimensionalized 12

23 T turb, in (319) turb T ref P turb, in (320) turb P ref where again T ref R and P ref 14 7 psia Fig 33 Turbine map Effiieny vs Pressure ratio [3] The orreted turbine speed N is omputed turb N turb N (321) turb 13

24 where again N is the speed in RPM of the shaft onneting the ompressor and turbine The perentage speed used to pull out values from the turbine map is similarly obtained by omputing where N turb N % 100, (322) N turbdes N is the turbine orreted speed at design point turbdes The pressure ratio is defined as PR turb P turb, in (323) P turb, out and PR turb The orreted mass flow m Torr is obtained from Fig 32 and is a funtion of N% and PR turb m Torr f ( PR, N %) (324) turb The turbine effiieny is obtained from Fig 33 and is also a funtion of N% t f ( PR, N %) (325) t turb The outlet temperature T, is then obtained by using the following relationship turb out T T turb, in turb, out 1 1 (1 PR t turb (1 ) / ) (326) The mass flow rate m Tin is omputed just as it was done with the ompressor using the definition of orreted mass flow 14

25 m Tin m Torr turb (327) turb Finally, the torque given by the turbine is alulated the same way as it was done with the ompressor turb m Tin h h out in 60 (328) N 2 Turbine - Dynami Setion The turbine exhaust pressure P,, is obtained the same way as it was done in the ompressor turb out dp ( m turb out in m, out ) dt R turb air T turb, out (329) 313 Shaft The differene between the turbine and ompressor torques is dynamially integrated to obtain the shaft speed This speed (N) is fed bak to the ompressor and turbine modules The relationship between torque and angular veloity is the following net d I dt (330) where ω is the angular veloity in rad/s This an also be written as the equation shown below solving for the shaft speed dn dt ( ) turb 60 (331) I 2 15

26 where and are the turbine and ompressor torques respetively, I is the moment turb of inertia of the shaft, and N is the speed of the shaft in RPM 32 Shell-and-tube heat exhanger Turbine Compressor Fig 21B Hybrid GT/MCFC System Shell-and-Tube Heat Exhanger 321 Introdution The shell-and-tube heat exhanger is one of the most versatile and used heat exhangers in the industry as it is suitable for many appliations It is omposed by a bundle of tubes enlosed in a shell The tubes are supported by baffles, whih in addition to provide mehanial stability to the tubes, they provide higher heat transfer oeffiients, but at the ost of pressure losses in the shell side fluid However, this penalization is more than ompensated with the heat transfer rates that an be ahieved There are different types of onfigurations, and the one being modeled is shown in Fig 34 In the power plant being modeled, the oxidizer gas exhaust flows inside the tubes while the air oming out of the ompressor flows inside the shell and outside the 16

27 tubes in a ross-ounterflow manner The type of baffle arrangement used in the shelland-tube heat exhanger is seen in Fig 34 This partiular arrangement is known as single segmental Important parameters regarding baffle onfiguration for overall performane are baffle spaing and baffle ut Fig 34 - Single segmental shell and tube heat exhanger [19] A lumped volume approah is used to determine the dynamis of the heat exhangers Control volumes are applied in the shell and tube side with their respetive energy and mass balane Both, the oxidizer exhaust gases and the air from turbine are assumed to be thermally perfet gases The heat transfer oeffiient and pressure losses in the shell are relatively omplex to alulate ompared to the tube side As an be seen in Fig 35, the shell side fluid would experiene leakage through the baffles that would affet the heat transfer oeffiient and pressure loss This is due to tube-to-baffle learanes The Bell- 17

28 Delaware method [4] is used for the shell side and onsists of orretion fators being applied to the ideal ross-flow heat transfer and pressure drop values Fig 35 Leakage through baffles [16] The software CHEMCAD has the apability of designing STHX Therefore, it was used to size/design a heat exhanger that would meet ertain temperature outlet requirements for eah flow given a ertain set of inlet mass flows and temperatures Many onfigurations (ie, number of tubes, shell and tube diameters, tube thikness, baffle ut, baffle spaing, et), an provide the same desired outlet temperatures However, the most effiient design is the one that provides the least pressure losses while providing the same heat transfer rate required 322 General Equations All properties are taken at average temperature between the inlet and outlet stream Shown below in Fig 36 is a lumped ontrol volume applied at the tube side, shell side, and the metal of the tubes of a ounter-flow heat exhanger 18

29 E st wall m T t, out t, out E st Fig 36 Shemati of ontrol volume applied to heat exhanger Assumptions (1) Thermally perfet gases (2) Radiation heat transfer negleted (3) Heat exhanger is isolated so no heat is lost to the surroundings (4) Inlet and exit pressure losses are not inluded Continuity m in m out m (332) Energy Balane From the 1 st law of thermodynamis, we have that energy an t be reated or destroyed It s onserved in E out E stored (333) E For thermally perfet gases, we have 19

30 E stored du dt mc v dt dt (334) Energy Balane: Tube Side Flow Applying an energy balane to the tube side and noting that no work is being done, and negleting kineti and potential energies of the streams oming in and out, we obtain the following: m C t dt t, out m C T T ), t v t p, t t, in t, out dt ( Q 1 (335) m t t t (336) From Newton s law of ooling we have Q 1 A h i ( T T i w ave, t ) (337) where h is the heat transfer oeffiient inside the tubes and A i i is the inner surfae area of the tubes and is defined as A i N D L (338) t i where Also, N is the number of tubes, t D the inner diameter of the tubes and L the length i T ave, t T t, out T 2 t, in (339) Energy Balane: Shell Side Flow Applying an energy balane to the shell side and noting that no work is being done, and negleting kineti and potential energies of the streams oming in and out, we obtain the following: 20

31 m s C dt s, out m C T T ), s v s p, s s, in s, out dt ( Q 2 (340) where m s s s (341) and Q 2 A o h ( T T o w ave, s ) (342) where h o is the shell heat transfer oeffiient and A o is the outer surfae area of the tubes defined as A o N D L (343) t o where D is the outer diameter of the tubes and o T ave, s T s, out T 2 s, in (344) Wall (tubes) Finally, applying an energy balane to the tubes m w Cp w dt dt w Q 1 Q 2 (345) m w w w (346) Energy Balane: General Putting all equations together we end up with a set of three equations with three 21

32 unknowns ( T t,, T out s, out, and T ) sine the inlet temperatures are known The following w equations are solved simultaneously taking all properties at average temperatures for the two streams dt t, out C m C ( T T ) A h ( T T ) (347) t t v, t p, t t, in t, out i i w ave, t dt dt s, out C m C ( T T ) A h ( T T ) (348) s s v, s p, s s, in s, out o o w ave, s dt dt w C A h ( T T ) A h ( T T ) (349) w w p, w i i w ave, t o o w ave, s dt 323 STHX - Shell Side flow STHX - Shell Side Flow- Heat Transfer Coeffiient The shell side heat transfer oeffiient,, is obtained using the Bell-Delaware method [4] where orretion fators are applied to the ideal ross-flow heat transfer and is expressed as h o h h o h J C J L J B (350) where J C = the orretion for baffle onfiguration J L = the orretion fator for leakage, and J B = the orretion for bypass in the bundle-shell gap oeffiient, The equation to obtain the Nusselt number and ultimately the heat transfer h, in ideal ross flow is given by Nu h D k o a Re m Pr 034 F F 1 2 (351) 22

33 where a and m=orrelation onstants F 1 =orretion fator for surfae-to-bulk physial properties variation F 2 orretion fator for the effet of number of tube rows in the array Pr= Prandtl number k= thermal ondutivity D o = external tube diameter Re= Reynolds number defined as Re V max D o (352) F 1 Pr Pr w 026 (353) where Pr w is the Prandtl number taken at the wall temperature F 2 10 when the number of tube rows ( N ) is 10 or greater The orrelation onstants depend on the geometries of the ross-flow tube banks These geometries an be lassified as in-line (square 90 ) or staggered arrays (triangular) and are shown below In-Line Banks Staggered Banks 23

34 The table shown is used to obtain the proper orrelation onstants for the type of tube banks and Reynolds number range Range of In-line banks Staggered banks Reynolds a m A m E Table 31 Correlation onstants for staggered and in-line tube banks [4] To alulate the Reynolds number, V max is defined as the maximum veloity between the tubes near the enterline and is given by V max m S m (354) where S m is the flow area near the enterline, and is defined for square tube arrays as S m D D OTL o L D D ( P D ) B s OTL T o PT (355) where L B D s = Baffle spaing =Shell Diameter D OTL = The tube bundle diameter P T = the tube pith D OTL is obtained using the following expression 24

35 D OTL D s b where is the bundle-to-shell diametral learane b The Reynolds number an then be expressed as Re m D S o m (356) oeffiient The next step is to alulate the orretion fators for the ideal heat transfer For the orretion for baffle onfiguration, J C, we first alulate the fration of tubes ( F C ) in ross flow This expression is given by F 2 D D 2 L sin os 2 L 2 os 1 S 1 S 1 OTL D D OTL D S D 2 L OTL (357) where L is the baffle ut and represents the distane from the inside surfae of the shell to the top of the baffle, and is expressed as L B D 100 s (358) where B is the perentage baffle ut Finally, a linear relationship to obtain the orretion for baffle onfiguration,, J C as a funtion of F C is given by J F for 15< B <45 (359) 25

36 The orretion fator for leakage J L is a funtion of the shell-to-baffle and tubeto-baffle leakage areas, S and S respetively They are alulated using the following expressions sb tb S sb D s sb os L D C s (360) S tb D o tb N T F / 2 1 (361) where and are the radial learane between baffle and shell and the tube and baffle, sb tb respetively Also, N T denotes the number of tubes J L S S S sb tb sb is a funtion of and S S S m sb tb Fig 37 Leakage heat transfer oeffiient orretion fator, JL [4] 26

37 Ultimately, the orretion for bypass in the bundle shell gap J B is related to the fration of the ross flow area available for bypass flow and is given by F bp D s D S m OTL L B (362) J B is also a funtion of the ratio of number of pairs of sealing strips ( N ss ) to the number of ross rows N The latter an be alulated from N D s 1 2 L P TP / D s (363) where P P TP T for square tube arrays An important note about sealing strips is that they are used to prevent exessive bypassing around or through the tube bundle Finally J is alulated from the hart given below as a funtion of F and N / N B bp ss 27

38 Fig 38 Bundle-to-shell gap heat transfer oeffiient orretion fator, JB [4] Now we have all oeffiients to obtain the shell side heat transfer oeffiient h h J J J Notie that the orretion fators J o C L B C, J, and J are only dependant on the geometry of the shell-and-tube heat exhanger and do not depend on the streams that are entering the heat exhanger STHX - Shell Side Flow- Pressure Drop The pressure drop alulation using the Bell-Delaware method is similar to that of the heat transfer oeffiient alulation That is, orretion values are applied to the pressure drop for ideal ross flow The pressure drop for ideal ross flow without inluding inlet fators is given by L B 28

39 P N K f 1 V 2 2 max (364) where V is the same from Eqn 354, and N is the same from Eqn 363 Here K is a max f parameter and is a funtion of Re based on V max, and the geometrial layout of the tube array For in-line square arrays and a pith-to-diameter ratio ( P / T D o ) of 125 (a typial value applied in shell-and-tube heat exhangers also used in this simulation) by K f is given K f Re Re Re for 3 Re 2 10 (365) K f Re Re Re 3 11 for Re Bell gives the pressure drop for ideal window zone as P w 26 m S m S w N w P D T o S m m 2 S w for Re 100 and P w 2 06 N 2 S m S w w m for Re >100 (366) where N and S are the number of effetive ross flow rows in the window and the w w window flow area respetively They are defined as N w 08 L P TP (367) 29

40 30 (368) The pressure drop in the shell an then be omputed using the following expression (369) where N is the number of baffles and and are orretion fators and are obtained using the following harts It is important to note that this pressure drop alulation doesn t inlude inlet and exit pressure drops Fig 39 Bundle-to-shell gap pressure drop orretion fator, RB [4] os 4 o T s s s s s s w D F N D L D D L D D L D D S w B L w B s N N R P R P N R P N P B R L R

41 Fig 310 Leakage pressure drop orretion fator, RL [4] 324 STHX - Tube Side flow In internal flows, an important parameter alled the Moody frition fator is used to determine the pressure drop It s a funtion of Reynold s number and pipe roughness and is obtained using the Moody diagram shown in Fig 311 There are many equations to determine the frition fator based on the diagram, and the one used for this simulation is Serghide s expliit equation [12], whih an be used throughout the entire Moody diagram for Re>

42 A B C f 2 log 2 log 2 log e / D 37 e / D 37 e / D 37 A ( B A) C 2 B A 2 i i i 2 12 Re 251 A Re 251 B Re (370) where the Reynolds number is defined as: u m i Re D (371) u m = mean veloity e=internal roughness of tubes (a value of 0001 was used in the simulation) D = Inner diameter of tubes i The total flow inner ross-setional area, A i, is defined as A i 2 N D t i (372) 4 Sine u m m A i, the Reynolds number an be rewritten as m D i Re (373) A i 32

43 Fig 311 Moody Diagram [10] STHX - Tube Side flow - Heat transfer oeffiient Turbulent Flow Sine entry lengths for turbulent flows are typially short, 10< (L/D) <60, it is often reasonable to assume that the average Nusselt number for the entire tube is equal to the value assoiated with the fully developed region Gnielinski [9] proposes the following equation for Nu and is valid for the limits shown with it (Re 1000 )( f / 8) Pr 1 / 2 2 / ( f / 8) (Pr 1) Nu turb (374) 05 Pr Re

44 Here, Pr is the Prandtl number defined as C p Pr where all properties are taken at average temperatures k Finally, one Nu is alulated then the inner heat transfer oeffiient, h, an turb i be alulated from the definition of the Nusselt number h D i i Nu (375) turb k t where k = thermal ondutivity of the fluid inside the tubes t Laminar Flow Sine the temperature at the wall varies along the tubes, the onstant wall heat flux for the ombined entry length equation is used Nu lam D i (Re Pr ) 4364 L (376) D i Pr(Re ) L whih is valid over the range 07 < Pr < 7 The Moody frition fator redues to f and h is alulated using the i definition of the Nusselt number 64 Re 34

45 STHX - Tube side flow - Pressure Drop Entry and exit pressure losses are not inluded, so the pressure drop is alulated using the definition of frition fator [23] f ( dp / dx ) D (377) / 2 2 u m Sine ( dp / dx ) is onstant in the fully developed region, the pressure drop p p 1 p 2 an be expressed as p p 2 p1 dp f u 2 D 2 x 2 m x1 dx f u 2 m 2 D ( x 2 x 1 ) i 2 m L u p f (378) D 2 where L x 2 x ) and is the total length of the tubes ( 1 35

46 33 Molten Carbonate fuel ell Turbine Compressor Fig 21C Hybrid GT/MCFC System Molten Carbonate Fuel Cell Fuel ells only need hydrogen as fuel to operate However, pure hydrogen is very diffiult to store and handle with our urrent infrastruture beause it has to be maintained at a very high pressure and very low temperatures Therefore, substanes rih in hydrogen suh as propane, methanol, ethanol, et an be used instead if the hydrogen moleules somehow are extrated from an outside mehanism and then fed to the fuel ell stak This mehanism is known as a reformer Due to its high operating temperatures ( C), MCFCs have the advantage for internal reforming That is, there is no need for an outside reformer and the hydrogen moleules are separated within the fuel ell [15] Its eletrolyte is typially a molten arbonate salt mixture suspended in a erami matrix, sandwihed between an anode and a athode The anodes are Ni based Ni-Al and Ni-Cr have been used before sine plain Ni is not stable enough due to the elevated temperatures [18] The athodes are usually made of NiO sine they are ative enough for oxygen redution 36

47 The disadvantages of MCFC are that this same high operating temperatures plaes severe demands on the orrosion stability and life ell of the omponents, espeially in the environment of the molten arbonate eletrolyte [17] Fig 312 Molten Carbonate Fuel Cell [6] As shown in Fig 312, hydrogen is supplied at the anode (after being reformed from the natural gas) Oxygen, arbon dioxide (these from the oxidizer), and hydrogen eletrons from the external iruit are being supplied at the athode These eletrons reat at the athode with the oxygen and arbon dioxide to form positive harged oxygen ions and negatively harged arbonate ions These arbonate ions will move through the eletrolyte to the anode and reat with the positively harged hydrogen ions to form water and arbon dioxide The reation taking plae at the anode is: 37

48 2 3 H CO H O CO 2e while the reation taking plae at the athode is: 1 O CO 2e CO 2 3 The model was developed assuming that stored energy is only in the large metal mass, gas mixtures are ideal, and exit stream temperatures are equal to the solid stak temperature This is beause time onstants for the fuel ell staks are quite large ompared to the gas mixtures As mentioned before, this projet is in onjuntion with Purdue University, so for a omprehensive and thorough model of the fuel ell the reader is enouraged to see referene 5 38

49 34 Heat Reovery Unit (HRU) Turbine Compressor Fig 21D Hybrid GT/MCFC System Heat Reovery Unit The HRU main omponents are a series of heat exhangers as shown in Fig 313 Fig Shemati of Heat Reovery Unit 39

50 Legend The heat exhangers onsist of a fuel superheater (HX1), a water vapor or steam heater (HX2), a natural gas heater (HX3), and a waste heat boiler (not shown) The purpose of these heat exhangers is to prepare the fuel mixture using the athode exhaust gas in a series of heat exhangers The hydrodesulfurizer removes sulfur impurities from the natural gas It has negligible effet on the temperature and gas omposition sine these impurities are found in amounts of parts per million [6] This desulfurization proess ours at 370ºC Similarly, the fuel pre-onverter removes higher impurities suh as propane and ethane and only a pressure drop is modeled This implies that the natural gas provided at the natural gas heater (HX3) for the simulation doesn t ontain any impurities and is made up of a mixture of mostly methane as well as hydrogen, arbon dioxide and arbon monoxide 341 Heat Exhangers In ontrast to the shell-and-tube heat exhanger (STHX) used to heat up the ompressed air with the exhaust gas from the oxidizer, these STHXs don t have any baffles Therefore, the flows are in pure ounterurrent flow in all of them Hene, a 40

51 different and muh simpler approah is used to alulate the heat transfer oeffiient and pressure losses in the shell side, but the same approahes shown in setion 324 are used for the tube side Also, to differentiate these heat exhangers to the one used for the ompressed air, they would be denoted as multi-tube heat exhangers (MTHXs) As done with the previous STHX for ompressed air and oxidizer gas, CHEMCAD was used to size/design the MTHXs The analysis of these MTHXs is also performed using the lumped apaitane method, whih implies that the radial temperature of the tubes is onstant For this to be valid Bi 0 1, whih ours for this ase Bi is the Biot number and is defined as Bi hl k, where L is the harateristi length defined as the ratio of the solids volume to surfae area L V / A What this means is that the resistane to ondution within the solid in the radial diretion is muh less than the resistane to onvetion aross the fluid boundary layer However, the same annot be said about the way the temperature of the tubes ats axially To aount for the hange in temperature in the longitudinal diretion, the heat exhanger is divided into setions So for example, a heat exhanger with tubes of 3 meters in length an be divided into 3 setions of 1 meter per setion and an be linked up depending on the type of flow (ounter-urrent or o-urrent) The number of setions depends on the type of auray that one wish to obtain and the omputational time willing to sarifie for it Show in Fig 314 is the tube side outlet temperature response between dividing one of the ounterurrent heat exhangers used in the HRU between 2 and 3 setions for a fuel mixture entering at ambient onditions in the tube side and using the MCFC athode exhaust gas residue in the shell side The inlet streams information as well as the 41 s

52 heat exhanger dimensions are given below IN(shell) IN(tubes) Stream Name MCFC Gas Residue Fuel Mixture Temp K Pres kpa Molar Flow Rate (mol/s) Perentage Composition of MCFC Gas Residue Carbon Dioxide (CO2) = 567% Water Vapor (H2O)= 2241% Nitrogen (N2) = 6561% Oxygen (O2)= 631% Perentage Composition of Fuel Mixture Hydrogen(H2) = 1168% Methane (CH4) = 2798% Carbon Monoxide (CO) = 005% Carbon Dioxide (CO2) = 346% Water Vapor (H2O)= 5683 Nitrogen (N2) = 00% Oxygen (O2)= 00% Heat Exhanger General Data: Shell ID 167 m Shell in Series/Parallel 1/1 Number of Tubes 3783 Tube Length 07 m Tube OD/ID 00191/00157 m Tube Pattern SQUARE(90 ) 42

53 Outlet Tubes Temperatures (deg C) Multitube Heat Exhanger Axial Disretization Setions 3 Setions Time (ses) Fig 314 Multi-tube heat exhanger axial disretization temperature response The transient temperature response is nearly idential between dividing the setions by 2 or 3 setions At steady state, the temperature differene is only by ~ 2 deg C For this reason, all MTHXs were divided by 2 setions for this simulation Shown below are the two possible onfigurations that the setions an be onneted 43

54 Counter-flow Co-flow Fig 315 Shemati Co-flow and ounter-flow heat exhangers Even though this same priniple applies to the STHX, the STHX wasn t divided into setions beause it ontains baffles, so the flow is not in pure ounterurrent flow, but rather ounter-ross flow Therefore, the STHX is left as one setion only Despite this, the results obtained ompare very well to other data as shown in setion 4 MODEL VALIDATION HRU - Heat Exhangers - Shell Side Flow HRU - Heat Exhanger - Shell Side Flow - Heat Transfer Coeffiient 44

55 For the flow in the shell side, the same equations and proedure desribed in STHX Tube side flow (see page 29) is used for both turbulent and laminar flow But the Nu, Re, and f equations are now obtained using D known as the hydrauli diameter, hy whih is defined as D A (379) P hy 4 where A = Cross-setional area P = wetted perimeter For the ase of shell side flow, this an be written as A A o ( D 4 2 s N t D 2 o ) (380) P D N D ) (381) ( s t o Also the mean veloity, u m, used to alulate Re now beomes u m m (382) A o HRU - Heat Exhanger - Shell Side Flow - Pressure Drop The pressure drop alulation is given by p f D L hy u 2 2 m As done in the previous setion, f is obtained using D while u hy m is obtained using A o 45

56 342 HRU - Mixing hamber The mixing hamber is modeled applying an energy and mass balane assuming that no energy is lost to the surroundings Fig 316 Shemati ontrol volume mixing hamber The mixing hamber is assumed to be well mixed, so the temperature and omposition of the mixture inside the hamber is the same as the one oming out of it Also, all streams in eah mixing hamber are treated as thermally perfet gases Continuity M 1 2 out M M (383) Energy E in E out E st dt out M h M h ( M M ) h C out m v (384) dt M is the total molar flow rate (mol/s) in eah stream and h denotes the molar enthalpy (J/mol) in this ase, not the heat transfer oeffiient as denoted before Molar enthalpy is found using the following expression h X h (385) i i i 46

57 where Also, X is the molar fration of eah speies in a stream i is known and represents the volume of the mixing hamber Finally ρ is m obtained using the ideal gas equation P (386) RT out 47

58 35 Control Before we get into speifi ontrols, it is important to mention that all ontrollers used are single loop and PI-type (proportional and integral gains) See Appendix A for more details 351 Flow Control Referring to Fig 313 in setion 34, we see a series of valves that ontrol the flow and temperature at different loations The flow valves ontrol the amount of natural gas and steam delivered to the system for a given power load Two important ontrol objetives are: 1 To maintain the fuel utilization of the fuel ell at 75% 2 To maintain the steam-to-arbon ratio entering the fuel ell at 20 The first objetive is a ompromise of high voltage versus effiient use of the hydrogen delivered The seond is to prevent arbon formation within the fuel ell staks Set-points for mass flow rates of natural gas and steam an be derived to aomplish the aforementioned objetives w set natgas KM M I / F CH 4 pr sys (387) ( M 2 M )( x 4 x x ) CH 4 H 2 O pr, H 2 pr, CH 4 pr, CO w set steam 2 M H 2 O meas w natgas (388) M CH 4 where K is a onstant, M and i x, are the moleular weights and the mole frations of pr i eah speies respetively, M is the average moleular weight, I is the system pr sys urrent, and w is a measured flow rate of natural gas [6] meas natgas 48

59 352 Fuel Temperature Control Again, referring to Fig 313 fuel temperature ontrol is aomplished by using two bypass valves One bypass valve bypasses natural gas from the natural gas heater (HX3) to a mixing hamber to maintain the temperature of the natural gas at about 370ºC This temperature is required so desulfurization an our in the hydrodesulfurizer After the desulfurizer, the natural gas is mixed with the heated steam oming from the steam heater (HX2) and is direted to the fuel preonverter Then, this mixture is direted to a seond bypass valve whih will ontrol the temperature of this fuel mixture before it enters the fuel ell Some fuel will bypass the fuel superheater (HX1) to a mixing hamber where it is mixed with fuel mixture going into HX1 The set temperature of the fuel will depend on the power load and ambient onditions More diretly, it depends on the temperature and flow rate of the gas entering the athode to be able to keep the fuel ell (stak) temperature onstant The athode exhaust gas leaves the fuel ell at about 676 C (949 K), same as stak temperature, and sine this same gas is used to heat up the fuel mixture, then the fuel mixture ould only be heated up to a ertain temperature less than 676 C and an never be greater than that However, when the gas entering the athode is very hot (hot ambient temperatures), the fuel mixture entering the anode needs to ool down to effetively maintain a onstant stak temperature In onlusion, the fuel mixture almost always goes diretly to HX1 without bypassing Only when the temperature of the gas entering the athode side inreases too muh, some of the fuel mixture bypasses HX1 to effetively maintain the fuel ell stak temperature onstant 49

60 353 Stak temperature Stak temperature needs to be maintained at 676 C to avoid arbon formation within the fuel ell Fuel mixture temperature helps to ontrol stak temperature However, the main ontrol is a flow valve whih will restrit the amount of air oming from the turbine going into the oxidizer Due to slow dynamis of stak temperature, feedbak alone is not suffiient to maintain a tight ontrol Therefore, feedforward ontrol is additionally applied using a hart of steady state eletrial power versus steady state air flow This predetermines the amount of air flow rate needed for a given power load Feedbak ontrol is then used to adjust this air flow rate set-point to obtain the desired stak temperature 50

61 4 MODEL VALIDATION The overall system annot be validated operating as a whole beause there is no experimental data for this partiular simulation to ompare However, eah omponent in the power plant an be isolated and validated for the type of appliations that they would be used for in this simulation The gas turbine engine and the molten arbonate fuel ell models were developed by Sientifi Monitoring In and Purdue University respetively The oxidizer model was also developed by Purdue University Therefore, the validation of the turbine engine an be enountered in ref 3, and the validation for the molten arbonate fuel ell and the oxidizer an be enountered in ref 7 In addition to the mixing hamber model used in HRU, what is left to validate from the system are the heat exhangers used to heat up the fuel, as well as the heat exhanger used to heat up the ompressed air Hene, in this setion only the mixing hamber and the heat exhangers models will be disussed Two types of validation are neessary to assure that the results obtained are aurate These are steady and unsteady state The unsteady state behavior of the heat exhanger is only shown in this setion, but annot be validated sine there is no experimental data However, when the heat exhanger reahes steady state, the outlet temperatures and pressures of both streams are ompared using the software CHEMCAD 51

62 41 Shell and tube heat exhanger Steady state values of the STHX from the model are ompared with steady state values given by CHEMCAD in rating mode for heat exhangers when the inlet streams are given at the tube side and the shell side Outlet temperatures and pressure losses of eah stream are the values to be ompared The omposition, pressures and temperatures of the initial streams are the atual values when the hybrid system reahes steady state at design point As a reminder, the air stream omes from the ompressor while the gas stream omes from the oxidizer For this validation, the heat exhanger starts at steady state and when it reahes 1000 seonds, the molar flow rate of the gas mixture is stepped down from 4071 mol/s to 200 mol/s The heat exhanger reahes steady state again, and at 6000 seonds the air flow rate is stepped down from 4839 mol/s to 200 mol/s where the system would reah a third steady state The inlet temperatures and pressures of both the tube and shell side streams are held onstant and are shown below along with the heat exhanger information Also, the perentages of the speies in the gas mixtures are held onstant Only the flow rates are varied, whih are shown in Fig 41 and Fig 42 IN(shell) IN(tubes) Stream Name Air Gas Temp K Pres kpa Perentage Composition of Gas Mixture Carbon Dioxide = 1810% Water Vapor = 1813% Nitrogen = 5215% Oxygen = 1161% 52

63 Heat Exhanger General Data: Shell ID 274 m Shell in Series/Parallel 1/1 Number of Tubes Tube Length 274 m Tube OD/ID 00191/00157 m Tube Pattern SQUARE(90 ) Tube Pith 002 m Number of Tube Passes 1 Number of Baffles 3 Baffle Spaing 057 m Baffle Cut % 23 Baffle Type SSEG Fig 41 Molar flow rates of gas mixture going into tube side of STHX 53