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Technical Notes

1. oooonoccnoccnoncnonononconnonononnncnnncnnnons 3 22 3 3 4 Calculations and te ALON ia 3 26 3 4 MCECC and SOFC fuel cell ype Li 3 32 3 4 1 TRO GUC OM sti cases a accay sane caiees A Oestaaearesseedercavees S 3 32 3 4 2 MISS EUA niente a Sescaeeamnene Aton eauatadeedt 3 32 3 4 3 Modelling of the process in the fuel cell ooonoccnnoconicacincnconncnononnnos 3 34 3 4 4 Relations for calculating the cell voltage ooooonnnccinnccnoccconcnnonccnnnonnnos 3 36 3 5 Mortie separator YPE 22 lt cisc cscs cancescnctaxcec cnc ansataes RIRs 3 40 Sul The operation Of a moisture SeparatOT ooooooccnocnconcnononcnnncnoncnnnnncnnnnnnnccnnncnnnos 3 40 Cycle Tempo Manual Technical Notes 332 Ass mptons ofthe TO GE seiisscccsocsacvarsosdestesennedosvausenscexsnrndcncedeursuccunuedssateasess 3 40 3 5 3 Options in the calculations issisessccsecvonvevancssnnncndsiesaccvonsssaasesnenssseeestexassaereaestnas 3 40 3 5 4 II A o po ENT EA E 3 40 3 6 General sep arator Ype 20 sreski kod erasini ASEEN eee Ea ENARE 3 43 3 6 1 A O 3 43 3 6 2 Calculatio nio POMS orador iia 3 43 3 7 Chemical Tead or EVO 20 rotonda 3 45 3 7 1 Equilibria of individual reactions ooooonoccnococonccnnnnconnncnnncnonaconnnconnconcncnnnannnos 3 45 3 1 2 Thermodynamic calculati0DsS ooocnnccnooccnonnconnnnonacnonnconnononnconnnonnncnnnnnonncnnnos 3 48 3 8 SMA A ro E o A 3 49 3 8 1 Functioning of the model of the saturatOT ocooonnccnioccnocnconnnnnnnn
2. Ex Ex tm steam Ex feed 39 productgas It is assumed that the chemical composition of the flue gas during cooling in the reformer does not change The change in thermo mechanical exergy is then identical to the change in total exergy The functional efficiency then becomes ch ch ch Ex EX ec feed n productgas steam Ex f reforme tm tm tm Ex Ex E a Ey EX seed NG ep ase in fluegas out 40 Fuel cell In a fuel cell electricity is produced by making a fuel react combust with an oxidant Both flows are individually fed to the anode and the cathode of the fuel cell respectively In practice usually the fuel and oxidant also contain components that do not take part in the reactions in the cell these must be removed together with the reaction products Anode flow and cathode flow leave the cell separately The fuel cell produces electricity in the form of direct current The electrical energy produced can be regarded as the product of the fuel cell The change in chemical exergy of fuel and oxidant is available as an exergy source The thermo mechanical exergy of the fuel and oxidant flow however also changes as a result of the heating in the cell The thermo mechanical exergy absorbed by these flows can be utilized elsewhere in the systemand may therefore be deducted from the change in chemical exergy of the flows 1 e Ex Ex Ex J TS Ex Ex Je 41 Soure E E a
3. Computer program for calculating properties of the Freon refrigerants MIEDEMA J A LIEFHEBBER F and OP DEN BROUW El User manual of the CYCLE IM program Report EV 1157 2 1986 Delft University of Technology Laboratory for Thermal Power Engineering WESTER W Rekenprogramma voor brandstofcels ystemen Computer program for fuel cell systems Report EV 1464 1987 Delft University of Technology Laboratory for Thermal Power Engineering 10 11 Cycle Tem po Manual Technical Notes HARTMAN M and WESTER W Berekenen van de stoomtabellen Calculation of steam tables Report EV 1444 1987 Delft University of Technology Laboratory for Thermal Power Engineering TRA UPEL W Thermische Turbomaschinen Band 1 Auflage 2 Thermal turbo machines Volume 1 Edition 2 Springer Berlin 1966 KOTAS TJ Exergy Criteria of Performance for Thermal Plant Int J Heat amp Fluid Flow Vol 2 No 4 TSATSARONIS G Thermoeconomic analysis and optimization of energy systems Prog Energy Combust Sci 1993 Vol 19 BRODYANSKY V M SORIN M V LE GOFF P The efficiency of industrial processes exergy analysis and optimization Elsevier Science B V 1994
4. 3 50 E80S 11 out gas Subsequently the molar fractions of the other components can be calculated 1 x y ee forall i H O 3 51 kasa Nin wei o Xin gas H 0 3 8 3 Calculation of the mass flows The saturatoradds two mass equations to the systemmatrix mass balance of the apparatus ratio of the mass flows in the inlet and outlet pipes of the gas That ratio from the last equation GRATIO is determined by the amount of water absorbed in the gas M out as in gas l X in gas H 0 3 52 l X out gas H O in which M is the average mole mass The second mass equation will then be D 0 3 53 m in gas m out gas GRATIO In this form the equation is added to the systemmatrix 3 50 Apparatus models 3 8 4 Calculation of temperatures and use ofthe energy balance As far as the temperatures in the connected pipes are not already determined by data of other apparatus they can be specified by the user It is also possible to specify the differences in temperature between the pipes The energy balance of the saturatorcan if desired be used to determine one of the temperatures by specifying the energy exchange with the environment with DELE The mass flows that are used in this energy equation are determined as follows Because of the fact that the composition of the gas for the current iteration is already known in this stage of the calculation the ratio between the inlet and outlet mass
5. a Parameters which determine the size of the system such as number of apparatuses pipes turbines etc b Apparatus data Data may be specified which may differ for each apparatus The apparatus number and apparatus type are compulsory C Topology of the system It is made clear to the program how the pipes are linked between the apparatuses d Medium data per pipe e Reading in the optional data In each step the input data are where possible checked for accuracy For each error which is discovered an error messageis given The program stops in that case after the whole input phase has been completed Step 2 Creation of system matrix The calculation starts with the creation of the system matrix for the mass flow calculation A check is made that the number of equations corresponds with the number of pipes If this is not the case then an error message follows and the program stops Step 3 Calculating compositions In this step the medium types and gas compositions in the pipes are determined There are several apparatus routines for this depending on the apparatus types used 2 4 Basicconceptof Cycle Tempo Step 4 Diffe rence in compositions If the main iteration has been carried outa mmimum of twice and medium types occurin the systemwhich consist of a mixture then it is determined in which pipe the largest molar fraction change occurs in the succeeding main iterations It is also determined how many pipes do
6. dealt with in more detail in the next paragraph 3 2 Apparatus models 3 1 2 The calculation of the isentropic efficiency As stated in the previous chapter the isentropic efficiency of a turbine can either be specified by the user or calculated by the program For a limited number of types of steam turbines the isentropic efficiency can be calculated from data which are incorporated in the turbine code TUCODE possibly supplemented with data which relate to the geometry of the last stage DIAOUT and SLENG The turbine code TUCODE is a numeric code consisting of five numerals t1 to t3 t4 and ts The first numeral tl typifies the turbine as set outin Table 3 1 the other numerals are explained in Table 2 2 of part Reference Guide of the manual Tabel 3 1 The available turbine types Turbine Turbine type Basic value code isentr efficiency t ETHAID general type turbine gas turbine etc turbine to drive feed pump intermediate pressure turbine section between two reheaters with double reheating high pressure section HP with one row governing stage high pressure section HP with two row governing stage non reheatturbine combined HP MP LP with two row governing stage condensing section withoutgoverning stage to be used as MP LP or as LP back pressure section constantback pressure governed by the pressure back pressure section constantback pressure governed by the mass flow Co
7. and to choose the reactions in a better way It can also help to choose another order in which the equilibria for the different reactions are calculated in sucha way that one reaction does not steer the otherin the wrong direction at first starting value problem If three or more reactions have to be brought to equilibrium the above does apply all the more the less shifts compared to the original gas composition the better As a temporary solution the mixture can be brought to equilibrium with a gasifier at first type 23 Other possible problems with reactions programmed by the user Message NO GOOD POLYNOM EF The routine from the NAG library that solves polynomes from the equilibrium equations of the reactions comes across a mistake IFAIL gt 0 see manual of the library This does not have to mean that the polynome has not been described properly 3 47 Cycle Tem po Manual Technical Notes Message ERROR NUMBER OF SOLUTIONS FOUND xx The routine that selects the root which has to be the reaction coordinate does not find a or an univocal solution Check whether or not the polynome has been described properly 3 7 2 Thermodynamic calculations In the apparatus routine an unknown temperature is calculated out of the energy balance in many cases this will be the outlet temperature A temperature is calculated out of the pressure the enthalpy and the gas composition The reactor only influences the gas composi
8. 240 260 250 inlet volume flow E ns AA eee Figure 3 8 Isentropic efficiency with design conditions From the data supplied by the manufacturer the design conditions are determined for a number of compressors of different sizes Subsequently an univocal relation is determined by means of a weighted average The influence of the pressure ratio is ignored in this In reality the isentropic efficiency will not be completely independent of the pressure ratio higher final pressures will make the volume flow smaller in the last stages through which leakage and clearance losses will increase However from the available datano univocal relation with the pressure ratio could be derived 3 9 4 Calculation isentropic efficiency with off design conditions SULZER compressors For the calculation of the isentropic efficiency in an off design calculation the starting point is dimensionless characteristics Figure 3 9 shows the characteristic for type A Point NP in Figure 3 9 indicates the design point All conditions in the characteristic are relative values which means values expressed in percentages of the design point Figure 3 10 shows a similar characteristic for type AV In both figures a new operating point can be determined by means of a volume flow and a pressure ratio percentage This results in an efficiency percentage Moreover this results in a speed percentage for type A and an angular position percentage for type AV Bo
9. T z y o x EX in A EX out x Pn s 2 EX in Z EX out x Pn s The functional exergy efficiency then becomes Pn x CX out EX in Mex f de a DEX in o EXour x D Pns eo Note The de aerator is usually connected with the storage tank of the boiler feed pump The function of the storage tank is of no significance in considering stationary conditions In the top of the de aerator the non condensable gases are sucked off along with a small amount of steam If the discharge of this quantity of steam is included in the process calculation then according to comparison 15 the exergy of this flow is part of the exergy loss of the de aerator assuming that the discharged steam is not utilized elsewhere Compressor fan In a compressor or fan by means of shaft power a compressible medium is increased in pressure Functional efficiency for compressors is specified in the same way as for pumps L e EX out EX MES compressor Pegs 25 5 21 Cycle Tem po Manual Technical Notes Mixer splitter valve Mixers splitters and valves are tools that are frequently used in energy conversion systems but are not intended for energy conversion or energy transfer They may causeloss of exergy but it is impossible to speak of it in terms of a product Therefore it is not possible to define their exergy efficiency Note In system calculations it occurs that one uses splitters to separate components In that case th
10. Tempo for a water cooled steam condenser 3 2 2 Assumptions For the model for design calculations The condenser model is suitable for condensing both superheated and wet vapor of any medium The vapor can be condensed to saturation and if necessary the saturated liquid can be aftercooled It is possible to connect up to 3 inlet pipes for the secondary medium to the condenser outlet pipe for the condensate must be connected For the primary medium 1 inlet pipe and 1 outlet pipe must be connected With regard to the use of the condensermodel two mass equations and possibly 1 energy equation are added to the set of the systemequations see praragraph 3 2 3 For the model for off design calculations The condenser model for off design is suitable for describing condensation of saturated or wet steam The heat of condensation must be absorbed by cooling water In addition the flow on the secondary side must be without pressure drop In addition to the two mass equations and the energy equation the overall heat transfer equation is now also available to calculate an extra unknown The overall heat transfer equation is as follows Q UXAXATin 3 9 3 15 Cycle Tem po Manual Technical Notes where Q heat transferred kW U overall heat transfer coefficient kW m K A overall heat transfer coefficient m ATi log mean temperature difference K The heat transfer relations The overall heat transfer coefficient k is c
11. V For the GENERAL compressor there are no specific calculation methods and no facilities for off design calculations present In fact the calculational rules for the GENERAL compressor are equal to those for the pump type 8 The GENERAL compressor can be used for each type of compressor The SULZER compressors can be applied in a less general way For these types isentropic efficiencies can be calculated for design as well as off design conditions However the field of application is limited to the medium air pressures between 2 and 7 bar and inlet volume flows between 20 and 350 m s There are two types of SULZER compressors available L type A SULZR A An axial compressor without adjustable guide vanes Regulation takes place by changing the number of revolutions 2 type AV SULZR AV An axial compressor with adjustable guide vanes Regulation takes place by turning the vanes at a constant speed 3 9 2 Calculation procedure Establishing pressures temperatures and enthalpies at inlet and outlet of the compressor can take place by specification of data for apparatuses upstreamand downstream in the process or by specification of data for the compressor involved The mass flow through the compressor can be calculated out of the energy balance The energy balance can be 3 52 Apparatus models determined in a production function or in a turbine pump compressor combination It is standard to add 1 mass balance to the sys
12. account for the moment there are 3 mass flows in the combustor model oxidant fuel and flue gas Since in Cycle Tempo a total mass balance is prepared for each apparatus this means that in order to establish the mass flows 2 further equations are necessary For this 3 different relations are used 1 Where a mass flow is calculated in another apparatus an equation is automatically added to the system matrix 2 With the specification of the temperature at the outlet the mass ratio oxidant fuel is established Since the inlet temperatures are known this ratio follows from the energ y equation over the combustor 3 Finally an air factor can also be specified On the basis of the composition of oxidant and fuel the program in this case determines the mass ratio and again adds this relation to the system matrix The specification of both the outlet temperature and A is not possible as these both determine the mass ratio oxidant fuel This means that 1 mass flow must always be specified using the total mass balance so that there are three options with regard to the mass flows Option 1 Specify or calculate elsewhere 2 mass flows The third mass flow can now be calculated with the help of the total mass balance The energy balance can be used to calculate the flue gas temperature 3 22 Apparatus models Option 2 Specify or calculate elsewhere 1 mass flow and the flue gas temperature The 2 unknown mass flows can then be s
13. air natural gas flue gas coal and a large number of refrig erant mixtures are also available Cycle Tem po Manual Technical Notes 2 1 Principle of the calculation method The principle ofthe calculation method of Cycle Tempo is explained in the light of a simple example see Figure 2 1 For the water cycle process mass and energy balances can be prepared for the systemmatrix see Figure 2 2 With the systemmatrix the mass flows are calculated simultaneously The equations prepared are Equation p lt Mass balance of the boiler Mass balance of the turbine Total mass balance of the condenser Mass balance of cooling water side of the condenser Mass balance of the deaerator Mass balance of the feedwater pump Mass balance of the cooling water pump Energy balance of the deaerator So Y SM PA Ye eS 1 Energy balance of the condenser 10 Energy balance of the turbine For each closed cycle a mass balance must be eliminated in order to obtain an independent set of equations This is the reason why the mass balance of the pump with apparatus number 4 and the mass balance of the cooling water sink with apparatus number 7 are missing The program itself determines which mass balances are eliminated The systemmatrix is solved and the mass flows of the system are calculated With equation 9 the cooling water mass flow is fixed With equation 10 the size of the mass flows is established by the specified power of
14. each pipe Medium type Mass flow Molar flow Volume flow at inlet and outlet Pressure atinlet and outlet 2 6 Basicconceptof Cycle Tempo Temperature at inlet and outlet Enthalpy at inlet and outlet Entropy at inlet and outlet Vapor fraction at inlet and outlet if fluids are present for which 2 phase states are allowed Exergy at inlet and outlet Gf an exergy calculation is made Mass fraction if binary mixtures are present Step 11 Output As a control for each apparatus the energy balance is calculated with tt Apparatus Figure 2 3 Energy balance ofan apparatus D Drin hn 2 Omou i houd Q W For apparatuses with streams exchanging heat the internal heat transfer is also calculated The values are printed out in the table Heat exchanging equipment and give an idea of the accuracy ofthe solution Step 12 Exergy analysis In this step which is optional an exergy analysis is given for each apparatus and for the whole system 2 7 Cycle Tem po Manual Technical Notes app routines compositions app routines p T h app routines compositions app routines p T h Figure 2 4 Calculation run Cycle Tempo 2 8 A NS set up system matrix calculate compositions 4 differences in compositions calculate p T h 5 solwe system matrix r differences in mass flows G break off criterion composition
15. efficiency 9 10 11 A complete overview of the published definitions anda discussion ofthe pros and cons of the various definitions fall outside the scope of this manual Figure 5 2 which presents arough division is further elucidated below Generally efficiencies and thus also exergy efficiencies for practical use must meet a number of conditions 1 The sensitivity for changes in the systeminvolved must be large Efficiencies must be defined in sucha way that all values between 0 and 1 are possible and no other values 2 Preferably the definition of efficiency must be applicable in practice This means that the definition without additions must be practicable to a large number of different systems 3 It must be possible to calculate efficiency values quickly using available data Preferably one should avoid the necessity of making very detailed additional calculations 4 Efficiencies are a measure for a system s quality Such a standard is only reliable if based on data that amply take into account the influence of all relevant variables The quality of the process calculation performed determines whether this condition is satis fied As stated above an efficiency definition not only concerns a theoretically sound choice but also how to calculate without over exerting the exergy values needed for the efficiencies 9 11 Cycle Tem po Manual Technical Notes The preference for a specific efficiency defin
16. experience with these efficiencies A more obvious application is to use them for assessing analyzing and optimizing processes and systems We can think here of processes and systems for converting material balances in chemical process plants and of processes and systems for converting energy Below we will specifically deal with their application in energy conversion systems Exergy efficiencies have only minor importance for a rough evaluation of electricity production units the electricity produced is also the efficiently produced exergy while usually the exergy of common fuels for electricity production differs only a few percentages from the LHV For that reason a power plant s exergy efficiency will differ only slightly from its thermal efficiency and will therefore not provide additional information The situation is completely different for combined heat and power CHP plants An exergy efficiency there also visualizes the thermodynamic significance of the heat produced Since the exergy of heat depends on the temperature and is for finite temperatures always smaller than the energy quantity exergy efficiencies of combined heat and power plants will usually be lower than comparable thermal efficiencies The difference is determined specifically by the temperature level of the heat produced The exergy efficiency may provide additional information about the quality of the conversion in the CHP plant the interpretation of exergy effic
17. flow ratio at the inlet for part load calculations figure 3 the losses overthe inlet valves depending on the mass flow ratio figure 5 0 965 m for 60 Hz For 50 Hz 1 158 m 3 6 Apparatus models 3 i e_ El 600 i 500 400 i l pi l Pmax 137 89 bar 300 es a Pmin 1 32 bar 1 l y 0 20 40 60 80 100 120 140 gt p har Figure 3 2 Inlet steam conditions for which no efficiency corrections are necessary see also Table 3 2 Turbine codet 5 condensing section 3000 or 3600 rpm the volume flow underdesign conditions the inlet conditions of the steam with a view to the final moisture content figure 14 Turbine codet 8 twin speed condensing section 3000 1500 rpm or 3600 1800 rpm the volume flow underdesign conditions the inlet conditions of the steam with a view to the final moisture content figure 14 the expansion in the low speed part of the section Turbine codet 9 condensing section for 1500 rpm or 1800 rpm the volume flow underdesign conditions the inlet conditions of the steam with a view to the final moisture content figure 14 Cycle Tem po Manual Technical Notes The outlet losses for turbine types 5 8 and 9 are included in the isentropic efficiency which is printed out by the program and are also printed out separately immediately after the isentropic efficiency Where the basic
18. flows of the gas GRATIO is also known With this ratio the matching outlet mass flow of gas is calculated out of the old inlet mass flow and the outlet mass flow water is then calculated out of the inlet mass flow from the mass balance that occurred These mass flows are used in the energy balance to calculate the unknown enthalpy and the temperature that belongs to that If the inlet mass flows are the same for every iteration this will result in the fact that the energy balance is used for the current iteration During the first iteration mass flows are not yet known and therefore the energy balance cannot be used That is the reason why an estimation of the unknown temperature has to be given with parameter ESTTEM for this iteration If the energy balance is not used for the calculation of an unknown temperature or enthalpy it is available to calculate an unknown mass flow For this purpose a production function amp PROFUN has to be specified Generally the energy exchange with the environment will be negligible which means that POWER has to be specified as 0 0 If no enthalpy or mass flow is calculated out of the energy equation then the energy exchange with the environment will result However in practice this situation will hardly occur 3 51 Cycle Tem po Manual Technical Notes 3 9 Compressor type 29 3 9 1 Fields ofapplication There are three types of compressors 1 GENERAL 2 SULZER A 3 SULZER A
19. models the active cell area the cell voltage V the cell flow I and the electrical output power P are calculated It is supposed that the processes occurat a constant temperature and pressure the average cell temperature and pressure Prel Teen specified by the user If all fuel components in the fuel cell are converted the flow through the fuel cell is equal to 1 H CO and CH are considered to be fuel components the contribution ofhigher hydrocarbons is neglected 3 34 Apparatus models D y PE eae x2Fx y y 4y2 F M H CO CH mol a 3 29 in which yo are the concentrations at the inlet and M mola 18 the mole mass of the anode gas In reality only part of the fuel in the fuel cell is converted the ratio between the real and the maximum conversion is specified by the utilisation level Up The real cell flow I follows from l lex Ur 3 30 The relations that are used to calculate the cell voltage will be dealt with in section 3 The electrical output power of the fuel cell stack is identical to Pe V x x npcac 3 31 Apart from cell voltage and cell flow the composition at the anode outlet is also calculated in this block The quantities of H and CO that are converted on the cell area are calculated from the cell flow I using Faraday s law It is assumed that the shift reaction and at internal reforming IR also the reforming reaction always occurs at equilibrium on the electrode area at
20. not meet the break off criterion The break off criterion is Gi G amp D I lt e The result of this testis always printed out in the Text Output and during the calculation process on the screen Step 5 Calculating p T h The pressures temperatures and enthalpies are calculated with the help of apparatus routines The next order is followed 1 Turbines type 3 in order of increasing apparatus number Condensers type 4 in order of increasing apparatus number Flashed heaters type 5 in order of increasing apparatus number Heat exchangers EEQCOD 2 type 6 in order of increasing apparatus number Heat exchangers EEQCOD 1 type 12 in order of increasing apparatus number Moisture separators type 22 in order of increasing apparatus number DL Dy LY ae oe a Other apparatus types in order of increasing apparatus number If after such a passage not all properties are known the apparatus routines are called again but then in reversed order This procedure is repeated until the number of known properties doesn t increase any more Either the properties in all pipes are known or not enough input data are specified by the user to calculate these properties Step 6 Solving system matrix In the systemmatrix the enthalpies calculated in step 5 are substituted in the relevant energy equations The solving of this systemusing the Gauss elimination method gives the mass flows for the system 2 5 Cycle Tem
21. pressure or temperature of the gas is not specified by the user then the usermust give an estimate of these parameters with ESTPGS or ESTTGS in order to calculate the quantity of moisture separated in the first iteration For other iterations the pressure and the temperature from the previous iteration are used for this In addition for both the cooling medium and gas the pressure drops and temperature increases are specified For the gas these are always between the gas inlet and outlet pipe For the condensate discharge pipe no thermodynamic parameters can be specified since these are always related to the gas outlet pipe see part Reference Guide ofthe manual 3 5 4 Formulae used The three mass equations mass balance secondary equation of the cooling medium and the equation for the quantity of condensate separated 1 e the specified mass equation and the energy equation of the cooler are all used in the systemmatrix to calculate mass flows 3 40 Apparatus models The mass equation which relates to the quantity of condensate separated looks like the following XC x mgas in p mcondensate sep 0 3 40 where XC ratio between the incoming mass flow gas and the mass flow of condensate separated D mgas in incoming mass flow of gas p mass flow of condensate separated m condensate sep and is also included as such in the system matrix The coefficient XC is calculated in accordance with XC M ey eee C gasin
22. sensitivity to changes in the system A general definition of functional efficiency is 9 13 Cycle Tem po Manual Technical Notes L EX product 4 Mex y Y Ex source In which 2 Exproducr 18 the exergy of that part of the outgoing process and energy flows that can be considered to be a product of the system DEX ource is the exergy of that part of the ingoing process and energy flows that can be considered necessary for making the product in the present process Basically gt Ex ource must be identical to the supplied exergy minus the exergy of the ballast flows or 2 Ex 2 EX E a 5 source Similarly we can write for 2EXproduct A ad DEX sup a 2G alas 6 Since by definition the exergy of ingoing and outgoing ballast flows is the s ame the difference in exergy value between source and product must also be identical to the sum of the exergy losses in the system Le D Ex oae Ex gt Ex 7 source product The comparisons 4 through 7 are insufficiently clear about how to calculate the functional efficiency of a specific system First we will have to establish which flows or sub flows are part of Exproduct EXsource OF EXpatiast In addition to the definition given we also need a more detailed elaboration specification see also Figure 5 2 of the functional efficiency It appears however that it is not possible to provide a generally valid specification Of Exproduct E
23. the gas flow and discharged separately In order for the gas flow to be cooled another flow must be heated A moisture separatorcan be regarded as a heat exchanger provided that vapor is condensed from the secondary cooling flow and individually discharged The exergy change in the primary flow as a result of the heating is to be regarded as the product The source for this exergy changeis in principle the exergy change in the secondary flow The heat in the condensate can possibly still be utilized The condensate flow is therefore regarded as an outgoing secondary flow In that case several outgoing flows are concerned and the functional efficiency 1s EX out 7 EX in Il ef moisturacnaraioy 34 Ex in EX 34 s out Gasifier In a gasifier a solid fuel usually at elevated temperature and elevated pressure is converted into a gaseous fuel For this use is made of an oxidant air or oxygen and possibly steam as a gasification means Usually the product gas leaves the gasifier at an elevated temperature It may be necessary to cool the gasifier forexample in the form of jacket cooling Ashand slag can also be discharged at an elevated temperature It is possible to utilize the thermo mechanical exergy of these flows elsewhere in the system Analogous to the thermal cold gas and hot gas efficiency we can think of two ways to formulate functional exergy efficiency a The gasifier is regarded as a device that suppl
24. the turbine Where the coefficients in the energy equation of the system matrix are dependent on the mass flows an iterative calculation is necessary In the example the turbine efficiency may be dependent on the mass flow through the turbine In this way the enthalpies of pipes 2 and 7 which occur in the energy balance of equation 10 are also dependent on the mass flow The calculation with Cycle Tempo is included as example 1 in part Examples ofthe manual 2 2 Basicconceptof Cycle Tempo E 6 de A a C6 a I SE V Figure 2 1 example of a simple Cycle Tempo scheme pipe numbers component nr 1 2 3 4 5 6 7 8 9 10 boiler 1 1 1 m 0 turbine 2 1 1 1 Mo 0 condenser 3 1 A 1 1 m 0 condenser cooling 3 f 1 m 0 deaerator 5 1 1 1 Ms _ 0 feedpump 6 1 t Me 0 coolwater pump 8 1 m 0 deaerator 5 ha h5 h Ms 0 condenser 3 ho h h ho m 0 Figure 2 2 system matrix of the Cycle Tempo scheme 2 3 Cycle Tem po Manual Technical Notes 2 2 Calculation run of Cycle Tempo The process scheme may consist of a closed or an open system or of a combination of these systems For preparing the input data for a process scheme all the pipes apparatuses and cycles must be numbered for the purposes of the identification The calculation procedure is broken down into twelve steps The calculation run for Cycle Tempo is set outin Figure 2 4 Step 1 Reading in The order for reading in is
25. AS i M Es T 0 T E Advanced S Mulation Programs for TOTal Energy systems Cycle Tempo A ASIMPTOTE ADVANCED SIMULATION CAPABILITIES FOR THE ENERGY MARKET Release 5 Technical Notes A program for thermodynamic modeling and optimization of energy conversion systems Cycle Tempo Manual Technical Notes Table of contents Table of contents Chapter 1 Introduciendo icleda 1 1 Chapter 2 Basic concept of Cycle Tempo oooocoooncoocnnoncconncnonononnnononononncon nono nconononon nono nncnnonnnnos 2 1 2 1 Principle of the calculation Method indi dada 2 2 22 Calculation runot Cyce Tempor issiron na S 2 4 2 3 Creatina the SYS EMail id 2 9 PAS COSTA DIO COSS CS asalta add 2 10 232 Open PTOCESS CS dla 2 11 Chapter 3 Apparatus Models caida dit 3 1 3 1 Torone YDE ias 3 1 All INTO AO CO ad 3 1 E I The calculation of the isentropic efficiency ooooccnocconcnnonnconnnnonacnnnnconcnnnnnonos 3 3 3 1 3 Enthalpies at the xiractiOns vae 3 9 3 1 4 BE INAS O 3 10 3 2 Condenser UY ers ie caters ose ase ac ee a aes 3 15 321 irod CHo y APN NS 3 15 a PRS SUPT ON e a cs aac ss oe I 3 15 325 Calculation options for the design calculationN ooonccioconocononcnnonnannnoos 3 16 3 2 4 Calculation options for the off design calculation ooooocnnoccnonccnonanonos 3 18 3 3 Combustor DL ais 3 20 3 3 1 PPI CAUTION Sars ese vacteee restates eee o 3 20 3 3 2 ASUS ias 3 20 3 3 3 Calculation options for the mass flOWS
26. Also with condensers we may haveto deal with various ingoing process flows on the secondary level For the condenser s functional efficiency we will have to write EX out a EX in lles T icondensa 2 EX in E EX out 21 Note Usually in condensers non condensable gases are sucked off along with a certain vapor quantity If this discharge is considered in the process calculation the exergy of the discharged steam in the above comparison is attributed to the condenser s exergy loss Feedwater preheater For feedwater preheaters we can use the same specifications as for heat exchangers and condensers 5 20 Processing the results De aerator In a de aerator condensate is heated and de aerated using steam Usually in steam turbine circuits other relatively small condensate flows are fed to the de aerator After de aeration the liquid mixture is discharged to the boiler feed pump The de aerator can be regarded as a contact heater The condensate flow is regarded as the primary heat absorbing flow This flow is heated by mixing it with steam and condensate of higher temperatures these warmer flows can be regarded as the secondary heat producing medium flows Analogous to the heat exchanger we can write for the product N EX en re z Pnp x o CX in gt Pn x CX out z EN in 22 in which mpis the mass flow condensate heated in the de aerator Similarly we can write for the source s 23 PX
27. CO H2 with equation OPco X OPH X OPco X OPH 0 X KPS 3 46 De CH3 reforming reaction CH4 H20 lt CO 3H2 with equation 3 OPco Y 0PH Y KM 3 47 OPcH Y OPH 0 Y in which Opx the partial pressure of component x 3 45 Cycle Tem po Manual Technical Notes X the reaction coordinate of the watergas shift reaction y the reaction coordinate of the CH reforming reaction KPS the reaction constant of the watergas shift reaction KM the reaction constant of the CH reforming reaction If PREACT is specified it is taken as prot If it is not specified the lowest of the inlet pressures 1s taken Equations 3 46 and 3 47 are polynomes in x andy respectively By calculating the roots the new gas composition can be calculated Equation 3 46 is a second degree polynome equation 3 47 a fourth degree which means that both have several roots In order to select the right root an algorithm is used that requires the following the root must be real no more can react of a chemical than there is present If there is no or no univocal solution an error message occurs and the programme will be stopped The iteration process Because of the fact that more reactions can take place at different temperatures the total equilibrium cannot be calculated in one go Therefore an iterative process is needed For every reaction the new gas composition is calculat
28. H 0 gt AMLO M 1 C 3 41 gas in gas out H O where mean molar mass of the condensate separated condensatesep M mean molar mass ofthe incoming gas gas in Cana molar fraction water vapour in the inlet pipe of the gas Cae molar fraction water vapour in outlet pipe of the gas The only unknown in relation 3 41 is the molar fraction of water in the gas outlet pipe This is calculated with p Psat TETT gas out H O 3 42 P sasout where Tgas ot outlet temperature ofthe gas Peas out Outlet pressure of the gas Psat T the saturation pressure of water at a certain temperature T In order to calculate the molar fractions of the othercomponents in the outlet pipe of the gas the following relation is used 3 41 Cycle Tem po Manual Technical Notes iC C C E i H O 3 43 as out i as in i C gas in H O waarin Cyas out i the molar fraction of component i in the gas outlet pipe Cyas in i the molar fraction of component 1 in the gas inlet pipe The ratio between the mass flows of gas and cooling water follows from the energy balance For part load situations no additional relations are present The consequence of this 1s that even at part load the mass flow of the cooling medium 1s calculated such that the temperatures laid down are met 3 42 Apparatus models 3 6 General separator type 26 3 6 1 Starting points The general separator has the physical meaning of a separator o
29. SUMPTION ceceeessccesscsseceseeesecesecssecssecesecssecneeceecssecsecuecaseseeseeeaes 5 6 5 1 5 AN NS ce O O o O E 5 8 5 2 Calculation OF exergy efficiencies erat 5 9 5 2 1 MEO 01 i EEE E ctecsctss SU o 5 9 D 2 2 Possibilities for using exergy efficiencies oooonnoccnoccnocnnoonconnoconnnconncnnnanonncons 5 9 323 General definition of exergy efficiency seseessseessessseseesesessersreseeeereseesee 5 11 Table of contents 5 2 4 Explanation of efficiency definitions nr 5 15 5 2 5 Specification of functional exergy efficiencies of apparatuses 5 16 Literature Appendix A Figures for turbine efficiency calculations vi Cycle Tempo Manual Technical Notes Introduction Chapter 1 Introduction Energy production processes are becoming more and more complex because of the increase in the size of the power of production units and an increasing need for a higher overall efficiency in order to save primary energy Combinations of processes STAG and processes in which chemical reactions play an important part fuel cells and fuel gasification also result in complex calculations For such calculations where the process variables are considered in detail a computer program is required In the Laboratory for Thermal Power Engineering of the Delft University of Technology the computer program Cycle Tempo has been developed to calculate mass flows thermodynamic variables chemical equilibrium and compositions
30. The functional efficiency then becomes Ex productgas ash Ex t t t Ex Ex E id pa TEX AER Mex f gasifien steam ia 37 ch ch ch ch steam oxidant ash cooling Reformer A reformer can be seen as a device that aims at bringing abouta change in the chemical composition of a process flow In order to make the conversion into the desired product gas possible steam is fed to the feed while heatis supplied conversion takes place The heat required is usually obtained by placing the reformer pipes in a furnace where a certain amount of fuel is combusted In the calculation the reformer and combustion chamber are regarded as individual apparatuses where the heat required for the reforming process is supplied by cooling down the flue gas flow It is assumed that the change in chemical exergy of the product gas forms the product of the reforming process Le Ex 9 26 product T EX am EX ed 38 productgas steam Processing the results The change in the thermo mechanical exergy of the flue gas is considered to be the source However not only the chemical exergy of the product gas flow changes but also the thermo mechanical exergy as a result of the heating of the product gas As it is assumed that this thermo mechanical exergy can be beneficially utilized it may be deducted from the exergy produced by the flue gas 1 e Ex Ex ey Os see source fluegas in fluegas out
31. Xsource OF EXpallast Thus we must establish for each individual systemhow to specify the exergy of productand source The various authors do not use uniform methods and names to specify functional efficiencies The fundamental approach as supported by Brodyansky 11 is preferred but 5 14 Processing the results produces large practical problems since it requires a drastic breakdown of exergy values For this reason we chose for a more pragmatic approach that is closely linked to the propositions made by Kotas 9 and Tsatsaronis 10 In paragraph 5 2 5 the functional efficiency of a large number of apparatuses has been specified Considering the limited breakdown of exergy values required here this specification is generally workable The size of exergy values and thus of exergy efficiencies is dependent on the environment definition chosen Strictly speaking exergy efficiencies can only be mutually compared if the same environment definition is assumed 5 2 4 Explanation of efficiency definitions The difference between universal efficiency and functional efficiency can be illustrated with a simple example the process of heat transfer in a heat exchanger Asa given the purpose of the heat exchanger is to heat a process flow called primary flow by withdrawing heat from another process flow called secondary flow The exergy of the primary flow will increase as a result of the absorbed heat and the exerg
32. a C c gt a 43 7 o gt Apparatus models mole mass kg mole pressure bar power kW heat loss kW universal gas constant kJ moleK cell resistance ohm em temperature K cell voltage V fuel utilis ation distance from inlet m oxidant fuel ratio mole fraction component mole fraction component j at the inlet change in Gibbs energy kJ mole change in Gibbs energy at standard pressure 1 bar kJ mole voltage loss V efficiency of DC AC conversion anode cathode from cathode to anode direct current electric fuel mean at given temperature T cross section at distance x x 3 39 Cycle Tem po Manual Technical Notes 3 5 Moisture separator type 22 3 5 1 The operation ofa moisture separator Apparatus type 22 is a moisture separator The incoming gas is cooled by a cooling medium flowing in the opposite direction as a result of which water vapourcondenses The condensate formed is collected and discharged via a separate pipe 3 5 2 Assumptions ofthe model In the model it is assumed that the pressures ofthe moisture separated and the outgoing gas are equal and that the temperature of the moisture separated is 1 C lower than that of the outgoing gas The gas leaves the separatorsaturated 3 5 3 Options in the calculations Pressures and temperatures can be specified both by the user or obtained from apparatus located upstream or downstream If the outlet
33. a EA a ios oxidant oxidant This comparison shows that the source is formed by the change in total exergy of fuel and oxidant flows The functional efficiency then becomes electricdirectcurrent 42 Mex f fuelcell EX selin EX melour P EX csi EN ius 5 27 Cycle Tem po Manual Technical Notes Note Inthe fuel cell the chemical exergy suppliedis converted partly into electricity and partly into thermo mechanical exergy heat In the above comparison the part converted into thermo mechanical exergy can be regarded as ballast flow The larger the ballast flow the smaller the quantity of exergy that can be converted into electricity With the fuel cell one tries to convert the largest possible part of the chemical exergy into electricity Comparison 33 does not directly indicate the extent to which the fuel cell has succeeded in this Scrubber separator saturator Considering exergy we cannot speak of a product when dealing with scrubbers separators and saturators Therefore it is impossible to give a meaningful specification of functional efficiency Reactor As for reactors we can only specify functional efficiency after establishing the function of the reactor For specific designs of reactors for example a combustion chamber and a reformer strongly varying specifications have been given For the specifications given we distinguish on the basis of how heat is fed to the process and how the ou
34. alculate how 3 13 Cycle Tem po Manual Technical Notes high the annulus velocity is at this low pressure one can then quickly calculate how much one must enlarge the passage at the turbine exhaust to obtain subsonic velocities The printed value of the exhaust loss is applicabie for the volume flow corrected for the increased pressure and hence for the corrected velocity To calculate the isentropic efficiency the increased pressure is assumed for the actual enthalpy drop for the isentropic enthalpy drop the condenser pressure is assumed One thus gets a correct picture in the equation of isentropie efficiencies with a turbine with a bigger outlet which does not have a Supersonic annulus velocity The calculated exhaust losses are applicable for the outlet geometries of General Electric For other exhaust areas interpolation is carried out between the areas given This does not result in an exact solution butis satisfactory 3 14 Apparatus models 3 2 Condenser type 4 3 2 1 Introduction The condenser model in accordance with type 4 is carried out as a two media apparatus Both media can be chosen at random for a limited design calculation where the physical data of the media are in the material library of Cycle Tempo For the extended design calculation and the off design calculation the overall beat transfer coefficient k value is calculated The overall beat transfer equations required for this are available in Cycle
35. alculated using the instructions as stated in the V D L Warmeatlas edition 1988 Sth impression parts Gb and Ja This takes into account the heat transfer of condensing steamto the pipe wall the thermal conduction through the pipe wall the fouling onthe cooling water side of the pipe wall and the convective heat transfer from pipe wall to cooling water The log mean temperature diffe rence The log mean temperature difference is defined as AT AT AT _ Peona mou H eona Fewin _ Fowin Fono In 7 7 In AT In Lond 7 Toul In O cont 7 mou 3 10 AT Tona E Lenin Tona o Tonin When more than 4 pipes are connected to the condenserone looks at the temperatures in the main steam pipe and the temperatures in the cooling water pipes The effects of other incoming flows on the temperatures in the condenser are ignored 3 2 3 Calculation options for the design calculation For the design calculation only the mass balances are used included in the set of system equations and the energy equation 3 16 Apparatus models 2 D min X Nin D mout X Nour AE 3 11 The energy equation of the condensercan be used in two ways in the calculation The first option which can be selected by making the EEQCOD Energy EQuation CODe 1 uses the energy equation to calculate an unknown mass flow This possibility can for example be chosen when one wants to calculate the required quantity of cooling water Th
36. ange in total exergy of the working fluid We may suppose EX ae EK EX Ex MEX 13 source out The turbine s functional efficiency is then E nafi 14 Mex f turbina E EX iy y Pos Heat exchanger In a heat exchanger a process flow the primary flow is generally heated by withdrawing heat from anotherprocess flow the secondary flow 5 18 Processing the results It is assumed that the purpose of the heat exchanger is to heat the primary flow The increase in thermo mechanical exergy of the primary flow is then the product of the heat transfer process If the chemical composition of the working fluid remains unchanged the increase in thermo mechanical exergy is identical to the total exergy Ex Ex Ex 15 product pout pin The secondary flow supplies the exergy The exergy produced by this flow is identical to the exergy change of the secondary fluid in the heat exchanger For the secondary fluid it also applies that the chemical composition and thus the chemical exergy remains unchanged Ex SEX EX 16 source s in s out The functional exergy efficiency of the heat exchanger is then as follows Ex Ex p out p in EX in EX ex f heatexchangen 17 s out It occurs for example in the case of feedwater preheaters that various ingoing flows are involved at the secondary level these flows are mixed in the heat exchanger and leave the apparatus as one secondary pr
37. cal exergy of the fuel and oxidant flows is then larger than 5 22 Processing the results zero This thermo mechanical exergy cannot be regarded as a product of the combustion process and must therefore be deducted from the thermo mechanical exergy of the flue gas Therefore the increase in thermo mechanical exergy is chosen as the product tm product EX suegas tm tm Ex EX puel Ex 27 oxidant As the source for the production of this exergy the chemical exergy of the fuel and oxidant is used The chemical exergy of the flue gas flow is discharged to the environment and thus does not become available as a product As an exergy source the net availability is ch ch ch ica EX nel L aia EX tuevas 28 The functional exergy efficiency ofthe combustion chamber is then specified as follows n Ger a Exa a S i ex f combustiowhamben ch ch ch EX uel Ex ia EX tuegas 29 The above does not account for the presence of non combustible components in the fuel that are separated in the combustion chamber in the form of ash or slag The chemical exergy of these substances is not utilized for heat production and must therefore be deducted from the chemical exergy of the fuel In general ash and slag are discharged from the combustion chamber at high temperature It is possible to still utilize the thermo mechanical exergy ofthese substances the thermo mechanical exergy of ash and slag is therefore regarded as the pro
38. cal power PH i X Nm 1 If the turbine drives a generator Electric power PH i X Nm i X Ngen 1 Turbine driven pumps compressors type 8 ortype 29 in combination with one or more turbines on a shaft Blade power pump compressor PH i PH I lt 0 Mechanical power pump compressor PH i Mm 1 pump compressor Blade power turbine PH j PH j gt 0 Mechanical power turbine PH j X Nm j turbine Surplus mechanical PH j X Nm j turbine power turbine pump PH i Mm i pump compressor compressor combination If the turbine pump compressor combination drives a generator Electric power PH j x nm J turbine E PH i Mm i pump compressor X Ngen ij Processing the results Fuel cell type 21 If DELE the energy loss to the environment is specified HEATLOSS i DELE i If DELEP relative energy loss to the environment with respect to the power input is specified HEATLOSS i a If both DELE and DELEP are not specified then HEATLOSS i 0 DC power generated PH l HEATLOSS i AC power generated PH l HEATLOSS i x DCAC i DCAC is efficiency of conversion of DC power in AC power of apparatus 1 Sink source type 10 only heat production If for a sink source SUBTYP 1 is specified the energy exchange with the environment is considered as usefulheat The number of connected pipes determines the way how the amount of exchanged energy is defi
39. can be calculated Qioss is either specified or has a default value of 0 If the temperature in the ash pipe is known hy can now be determined Where the temperature of the ash is not specified this is taken as equal to the flue gas temperature If this must be calculated then to calculate the term O ashas the flue gas temperature is taken from the previous iteration D mig X hig Tio O mox x Nox O mtu x htu D mas Xx had Tio Qross 3 20 To determine the temperature of a gas mix at a given enthalpy pressure and composition functions are presentin Cycle Tempo With these the flue gas temrperature can now be determined 3 29 Cycle Tem po Manual Technical Notes Calculation of the chemical equilibrium In Cycle Tempo the following functions are present to calculate the chemical equilibrium where Treset Hreact Preact Yreact Y cec Mreact Dcec Ycee fi Treact Preact Yreact Nreact Nr Ycec fo Hreact Preact Yreact Nreact Nr Ncec f3 Treact Preact Yreact Nreact Nr Ncec fa Hreact Preact Yreact N react Ner Tcec fs Hreact Preact Yreact Nreact reaction temperature reaction enthalpy partial reaction pressure composition of the reactants composition at chemical equilibrium number mole reactants number mole at chemical equilibrium The partial reaction pressure follows from where Ncec Nncec cec n cec ncec Prac Pree x number mole gas
40. diffusor working properly 3 11 Cycle Tem po Manual Technical Notes The printed value of the enthalpy must be regarded as the total enthalpy which means that the velocity term is included in the enthalpy hio Asta Ya 3 6 Where Dtot the total enthalpy kJ kg Dstat the stationary enthalpy kJ kg v the velocity of the steam m s The value of the enthalpies for the pipe between the turbine and condenser are equal to each other for this reason the total enthalpy does not change in the pipe not even by friction loss or pressure increase in the diffusor The value of the specific enthalpy at the expansion line end point ELEP is thus not printed but can if required be calculated from ELEP UEEP EXHAUST LOSS 3 7 EXHAUST LOSS has a value lt 0 The vapor quality x at the exhaust from the lastrow of blades is given at the condenser pressure The value is hence virtual but corresponds to the value which Spencer et alia use to calculate the exhaust loss The printed steam quality in the outlet pipe has a different value for inlet and outlet of the pipe at the inlet the value of x corresponds with the specific enthalpy at the expansion line end point ELEP at the outlet the value of x corresponds with the specific enthalpy at the outlet of the turbine UEEP see for example the calculation results of example 6 in part Examples ofthe manual As a result the userdoes get a real picture of the steam qualit
41. duct of the process in the combustion chamber In that case the functional efficiency is tm tm tm tm 7 EX iia F EX ash EX ruel T EX doni ex f combustiouhamben ch ch ch ch EX tel EX ia EX gsh 7 EX icra 30 Note In practice not all of the fuel is converted in the combustion chamber If the non converted fuel also in modeling is discharged in the ash or the flue gas the chemical exergy of this quantity of fuel is regarded as a ballast flow according to the comparisons 18 and 19 5 23 Cycle Tem po Manual Technical Notes Boiler Usually a boiler is a complex installation consisting ofvarious apparatuses such as a combustion chamber several heat exchangers pumps and fans In a detailed analysis of a boiler we deal with each individual part and use the exergy efficiencies for the apparatuses involved In some situations a rough consideration of the boiler suffices the boiler is then regarded as just an apparatus in which a process flow absorbs heat The quantity of fuel required can then be determined using a stated thermal efficiency This makes a complete system calculation possible without detailed boiler calculations In such a consideration the flue gas flow to the stack is not calculated individually the heat discharged with the flue gases is included in the thermal efficiency of the boiler in which case the exergy of the flue gas when leaving the boiler is also unknown The purpose of boiler and optio
42. e energy equation is in this case added to the set of systemequations The unknown mass flow is then calculated when solving the set In the second option for which the EEQCOD must be 2 the energy equation is used to calculate an unknown enthalpy When a second state variable e g the pressure in the relevant pipe is known the unknown temperature can be calculated Calculation of a unknown mass flow EEQCOD 1 Before the set of systemequations can be solved first the coefficients of the energy equation the enthalpies are determined The enthalpies can be calculated when two state variables in the relevant pipe are known These two state variables can be specified in the apparatus data calculated in the light of the differences specified in the apparatus data e g a pressure difference over the apparatus specified in or calculated from the apparatus data of adjacent apparatus and transmitted via the connecting pipe taking into account any pipe losses In addition the right hand side of the equation the energy exchange with the environment must be known This must be specified in the apparatus data The set of systemequations can now be solved so that the mass flows can be determined Calculation of an unknown temperature KEQCOD 2 When the energy equation is used to calculate an unknown temperature the mass flows must be known from the energy equation For the first iteration run an initial value is ch
43. e in which the condenser discharges heat to the environment only becomes clear if we look at the combination of turbine condenser in which case the condenser must be assessed based on the exergy efficiency of this combination Considering the specific character of such combinations of apparatuses and the many possibilities we confine ourselves here to efficiencies for individual 9 17 Cycle Tem po Manual Technical Notes apparatuses We expect that with the given examples the userwill be able to specify functional efficiencies in an analogous manner for combinations of apparatuses which have a joint function On the following pages in stating the functional efficiency of each apparatus we will also briefly describe the process and elucidate the choice of exergy product and source Turbine In a turbine a working fluid is expanded so as to deliver mechanical energy via a shaft During the expansion process part of the process medium is sometimes extracted in the case of steam turbines for example extraction steam is used to pre heat boiler feedwater We may have to deal here with various outgoing flows The shaft power produced is regarded as the product of the process in the turbine so A P nafi 12 The thermo mechanical exergy produced by the working fluid is available as an exergy source Since the chemical exergy of the working fluid does not change the change in thermo mechanical exergy is identical to the ch
44. ed separately in sucha way that the result of the first reaction is the input of the second and so on At the end of the series the result is compared to the gas composition from the previous iteration If convergence did not yet occur and the maximum number of iterations has not yet been reached the calculation process 1s repeated 3 46 Apparatus models Convergence problems There will beno convergence problems if only one reaction takes place or the reactions are independent which means that they do not have any components in common If the reactions are dependent the occurrence of convergence problems depends on the original composition and the specified reaction temperatures There can be problems if a large shift occurs in the equilibrium of one of the reactions compared to the original composition of the gas This can take place by the reaction itself or forced by anotherreaction the equilibrium of which is too much to one side already Such a large shift that nfluences various reactions again and again will be considered by the iterative process as a number of shifts that gradually becomes smaller However this iteration process converges very slowly Solutions depend on the problem Enlarging the maximum number of iterations is only attractive in very small systems because of the long calculation time choose MAXIT with a size of 200 or more It is recommended to balance the original gas mixture in a better way
45. eous reaction product number mole non reacting gas C kJ bar mole mole mole mole mole mole 3 21 The number mole released in the reaction is not yet known when computing Pyeact An iterative process is then necessary For this the main iteration process of Cycle Tempo is taken This means that for neec the value from the previous iteration is used 3 30 ni O cec Presa E Preact x i 1 n n cec ncec 3 22 Apparatus models The reaction enthalpy follows from Hreact P mig x hig D mncec X Ancec 3 23 Here hg can be determined from the energy balance over the combustor see above To calculate the enthalpy of the non reacting gases the flue gas temperature must be known This does however depend on the equilibrium composition and is hence not yet known For this reason the flue gas temperature from the previous iteration is used Hreact Q mfg X hig E mncec x hele 2 3 24 If the reaction temperature is specified the equilibrium composition on the basis of this value is known If this is not the case then the reaction enthalpy is used In addition to the composition the reaction temperature is then also calculated 3 31 6 Cycle Tempo Manual Technical Notes 3 4 MCFC and SOFC fuel cell type 21 3 4 1 Introduction Cycle Tempo includes models for five types of fuel cells among which molten carbonate fuel cells MCFC and solid oxide fuel cells SOFC Fi
46. ere is in fact a separator involved It is not possible to give a meaningful definition for the functional exergy efficiency of a separator Drum A circulation evaporator consists ofa heat exchanger anda drum Heating and partial evaporation of the medium occur in the heat exchanger In the drum liquid and vaporare separated and the recirculated liquid is mixed with the feed If drum and heat exchanger are distinguished as individual apparatuses the drum can be regarded as an apparatus in which a liquid flow is evaporated using heat withdrawn from the heat exchanger The exergy absorbed during heating and evaporation of the feed is then regarded as the product The exergy produced by the flow circulating in the heat exchanger is the source of this product It then holds for the functional efficiency that S EX reou 7 arta 26 Mex f drum Ex Ex evaporatorout o evaporatorin Combustion chamber In a combustion chamber fuel is combusted using an oxidant The flue gases formed durmg the combustion are discharged Aside from heat losses as aresult of imperfect isolation the process is adiabatic The purpose of the combustion is to produce a gas flue gas of which only the thermo mechanical exergy 1s utilized The thermo mechanical exergy produced can thus be regarded as the product of the combustion chamber The fuel and oxidant are fed to the combustion chamber often at elevated temperature and pressure the thermo mechani
47. expansion line e 1 curved expansion line The expansion line is fixed when in addition to the pressures at the inlet and outlet of the turbine anothertwo of the following three variables are known the specific enthalpy at the inlet the specific enthalpy at the outlet the isentropic efficiency Cycle Tem po Manual Technical Notes N B The specific enthalpies themselves cannot be specified for turbines in general the enthalpies will be determined from the pressures and temperatures specified for various apparatuses 3 1 4 Exhaust losses Exhaust losses are calculated for the condensing sections t 5 8 and 9 using the procedure of General Electric The exhaust loss of the non reheat turbine type 4 is wrongly not calculated by the program the calculated power of the turbine is hence too great as the exhaust loss is not deducted from the enthalpy drop over the turbine For all the otherturbine types the exhaust loss is processed in the internal efficiency as it is a less essential part of the efficiency and because it is not very dependent on the load of the turbine The exhaust losses are deduced from the axial speed of the steam at the exhaust of the last row of blades This speed is calculated from the volume flow and the exhaust area Dy A 3 3 N TT Dout ling Van The exhaust loss follows from this with figure 16 3000 3600 rpm or 17 150011800 rpm The calculation of the exhaust loss The value
48. f solid parts With a view to strongly simplified calculations it is possible to separate arbitrary components from a gas or coal flow physically this looks like a separation by means of membranes as far as gases are concerned The model is set up in order to give the user a flexibility as large as possible for defining what and how much has to be separated Because of this flexibility no protection 1s built in against physically impossible processes only aright mole balance is taken care of without chemical reactions The energy losses that occur during the separation process will have to appear from the energy balance or they have to be specified by the user For the separation of water vapourfrom a gas flow by means of condensation a moisture separator has to be used type 22 or type 25 For the separation of moisture from steam according to medium type WATERSTM a node type 9 with EEQCOD 1 has to be used 3 6 2 Calculation options From the chemicals to be separated it can be defined which fractions have to be separated with button Separate components see Reaction data in paragraph 4 2 of part Cycle Tempo Operation of the manual and or which concentrations may remain in the main outlet pipe with button Bypass components see Reaction data in paragraph 4 2 of part Cycle Tempo Operation of the manual Also the complete composition of the medium in the main outlet pipe can be specified Pressures can be spec
49. from the air factor calculation of the flue gas temperature calculation of the equilibrium composition calculation of the pressures The following notations are used h specific enthalpy kJ kg n mass flow kg s Q heat transmitted kW y concentration mole mole Calculation of the oxidant fuel ratio from the flue gas temperature To calculate the oxidant fuel ratio the energy equation is used for the calculation In order to solve this the enthalpy of the flue gases is determined This enthalpy is apart from the temperature also dependent on the composition This composition is in turn very much dependent on the mass ratio oxidant fuel OF This means that this ratio cannot be solved explicitly from the energy equation In order to determine OF an iterative procedure is necessary The program therefore calculates for each main iteration a correction to the oxidant fuel ratio and uses this to calculate a new composition in the following iteration OF OF AOF 3 12 where AOF calculated correction in i iteration 3 26 Apparatus models If in the i iteration a flue gas temperature Tp is calculated which differs from the required flue gas temperature Teq then an extra quantity of oxidant must be added where Te Treg is positive while with a negative temperature difference the oxidant fuel ratio must fall One can regard AOF as the extra quantity of oxidant which must be mixed wit
50. gure 3 4 presents the principles of both types diagrammatically Various types of design can be modelled for both fuel cell types reforming external or internal reforming flow type co flow or counter flow Solid Oxide Fuel Cell Molten Carbonate Fuel Cell molten solid carbonate electrolyte Ea electrolyte ES os cathode hO 2e anode E OS Hz CO3 E da 1 202 CO3 2e H O CO 2E me CO anode H O7 HO 2e Figure 3 4 Principle of the SOFC and MCFC 3 4 2 Mass equations The fuel cell model adds two three or four equations to the systemmatrix depending on the number of mass flows thatis established by the processes in the fuel cell The mass balance over the apparatus is added automatically Dm a int Pm c in Pm a out Pm c out 9 3 25 3 32 Apparatus models The second equation which is automatically added to the systemmatrix is the equation that describes the mass exchange between cathode and anode Om c gt a Dm a in Dm a out Dm c gt a 3 26 If the mass flow fuel Pm fue has not been calculated elsewhere it is determined from the generated electrical power the fuel utilisation and the efficiency of the DC AC conversion In this case the following equation is added to the systemmatrix Dm a in Dm fuel 3 27 If the mass flow oxidant is not calculated in another apparatus it can be established by specifying l the outlet temperatu
51. gy input the following apparatuses are considered a Boiler reheater type 1 type 2 For the energy input in a boiler or reheater the following formula is used Energy input 2 PH i ETHAB i for all the apparatuses iof the type boiler reheater b Source type 10 For a source there are three possibilities I In case of medium type GASMIX the lower heating value LHV is calculated see paragraph 5 1 1 Energy input LHV i x Dmou i Processing the results for all the apparatuses 10f the type 10 with one connected pipe which is outgoing and for which a LHV greater than 0 is calculated I In case of medium type FUEL the lower heating value is specified by the user parameter LHV Energy input LHV i x Dmou i for all the apparatuses 10f the type 10 with one connected pipe which is outgoing and which is of medium type FUEL M If LHV is specified for a source with one connected pipe which is outgoing this value will be used A calculated LHV for medium type GASMIX or a specified LHV for medium type FUEL will be overwritten The total energy input is now Total energy input a b Remark Energy input other than above will not be taken into account in the calculation of the systemefficiency Cycle Tem po Manual Technical Notes 5 1 3 Energy output For the energy output the following apparatuses are considered a Turbines type 3 Blade power PH i Mechani
52. h closed cycle 1 mass balance of an apparatus must be eliminated The reason is that 1 mass balance for an apparatus can always be deduced from the other mass balances This is explained by the example in Figure 2 1 If we leave out the cooling water cycle equations 1 2 3 5 and 6 can also be written as Equation m1 m6 Equation m1 m2 m7 Equation m2 m3 Equation m4 m5 m Equation m5 m6 m4 m3 The resulting equation is the same as the mass balance of pump number 4 Thus adding this mass balance would cause a dependent matrix For the same reason the mass balance of sink number 7 is left out of the matrix The program itself eliminates 1 mass balance per closed cycle The user is free to specify the energy equations with a right hand side These are the so called production functions It is important to choose these equations such that they are not dependent on the mass balances 2 10 Basicconceptof Cycle Tempo 2 3 2 Open processes For an open process several possibilities are available for selecting mass balances This is illustrated from an example see Figure 2 6 Possible spsiant matrices for open process method Figure 2 6 Example open process method For an open process no mass balance of an apparatus is eliminated in the chain All the mass balances are necessary in the system matrix so that the solution for the systemwill meet the boundary conditions for the apparatuses The follo
53. h the flue gases to obtain the required flue gas temperature Both for and after the correction the energy balance must apply In the situation as this is calculated the following applies Rod Tox X OF Hal T tu hig Ti x 1 OF has Tas x AF Qioss 3 13 Including the extra quantity of oxidant the energy equation Nox T ox x OF AOF Hal T tu hi Tg x 1 OF AOF has Tas x AF Qioss 3 14 where hg hox enthalpies belonging to the calculated compositions he is the enthalpy of the mixture of flue gas and extra oxidant As the composition is altered by mixing in oxidant the thermal capacity of the flue gases has obtained a different value As aresult the enthalpy at the same temperature of the diluted flue gases differs from the first value calculated The corrected enthalpy can be calculated from the oxidant and flue gas enthalpy since for an ideal gas mix the following applies ne xh J where x mass fraction of component j If we apply this to he we find AOF x h T 1 OF x h Treg 3 15 A oo e a pe aes 1 OF AOF 3 27 Cycle Tem po Manual Technical Notes Combining equ 3 13 and 3 14 gives hox Tox x AOF hig Treg x 1 OF AOF he Ti 2 x 1 OFox 3 16 Filling in here equation 3 15 and making AOF explicit gives In the ith iteration the temperature T is now calculated as flue gas temperature On basis
54. he design of the combustor so that a general model for the incomplete course of the reactions within Cycle Tempo is meaningless In the combustor model in Cycle Tempo the equilibrium composition is taken into account It is however possible to allow the flue gas composition to differ from the equilibrium composition by not letting part of the reactants take part in the reaction For each component or for a pipe as a whole oxidant or fuel pipe a molar or mass fraction is specified which does not react but is passed directly to the flue gas pipe where this bypass flow is mixed with the reaction products see Reaction data in paragraph 4 2 of part Cycle Tempo Operation of the manual In addition it is possible to specify the equilibrium pressure and temperature entirely independently of the outlet conditions Data on the inlet side One last assumption is that temperatures and compositions on the inlet side must always be specified or calculated in the previous apparatus 3 21 Cycle Tem po Manual Technical Notes 3 3 3 Calculation options for the mass flows As remarked different applications impose different requirements with regard to the available input data and required output The most important variables which can be both calculated and specified are outlet temperatures ash flue gas mass flows oxidant fuel flue gas ash pressures and pressure drops air factor A If we leave the ash pipe out of
55. hile in comparison 4 the exergy loss is related to the exergy change in the secondary medium AEx Since AEx is always smaller than Ex in Exp in the functional efficiency 9 is more sensitive to changes in exergy loss than the universal efficiency 8 5 2 5 Specification of functional exergy efficiencies of apparatuses In general functional exergy efficiency is defined as 2 Ex roduc Mex Tz 10 source In order to be able to apply this efficiency to specific systems a further specification of 2Exproduct and 2Esource 18 required We must then establish for all ingoing and outgoing 9 16 Processing the results process flows which part of the exergy of the process flow must be attributed to product or source If only part of the exergy of a process flow is attributed to a source or product a breakdown is required into an active part source or product and a passive part ballast How to make sucha breakdown depends on the desired accuracy with which exergy efficiencies must be determined In practical situations it is usually allowed to neglect the kinetic and potential energy of process flows Initially we also started from this assumption to specify exergy efficiencies In a reversible process kinetic and potential energies can be fully converted into power if not insignificant they can be added to the relative exergy values Below we have chosen for a limited breakdown of exergy values for process flows
56. iencies however is still ambiguous Exergy efficiencies are particularly valuable in analyzing and optimizing systems An exergy analysis is usually composed of a detailed calculation of the exergy values of the process flows and the exergy losses in the system Such a calculation shows the places in the system where losses occurand the seriousness of these losses In the analysis an answer must be found to the question of how to limit exergy losses Based on the absolute value of exergy loss it is usually difficult to assess whether an exergy loss in an apparatus is unnecessarily large An exergy efficiency in which the exergy loss is judged from the added or transferred exergy gives a better picture of the quality of the processes in the apparatus and thus also 9 10 Processing the results gives a betterimpression of whether exergy losses can be reduced Exergy efficiencies of apparatuses or parts of installations can also be valuable in checking process calculations Unusual efficiencies can point to the calculation being based on unreal data or incorrect assumptions Obviously only frequently occurring apparatuses are eligible for sucha checking Since exergy efficiencies are important in analyzing and optimizing energy conversion systems we looked initially at the efficiencies of frequently occurring apparatuses in such systems 5 2 3 General definition of exergy efliciency Several authors have provided definitions for exergy
57. iency efficiency with transiting exergy etc 5 12 Processing the results definition of efficiencies universal functional definition pragmatic fundamental T J Kotas 9 G Tsatsaronis 10 V M Brodyansky et al 11 O 3 O o Q Y Figure 5 2 rough division of exergy efficiencies The difference in exergy between the ingomg and outgoing process and energy flows is identical to the exergy loss Le pa EX Si 2 EX out 2 EXioss 2 For 1 we can also write es 2 EX out ms EXjoss 3 Neu Dee The universal efficiency offers a clear definition for a variety of systems A disadvantage of this definition however is that the efficiency values obtained can be insensitive to changes in the system This occurs for example when only part of the flows undergo a change or when the flows undergo only minor changes The exergy loss is then small compared to the exergy of the ingoing process and energy flows We then deal with comparatively large ballast flows exergy flows that are actually fed to the process but not directly involved in the intended conversion As a result of these ballast flows the universal efficiency may be insensitive to changes in exergy loss This is the reason for defining functional efficiency in addition to universal efficiency With functional efficiency we try to eliminate the influence of ballast flows as much as possible in order to achieve the best possible
58. ies only fuel The thermal energy is notutilized elsewhere and is considered a loss The installation will then be assessed as to its cold gas efficiency In that case the chemical exergy of the gas produced can be regarded as the product of the gasifier The chemical exergies of the ingoing flows function as a source the chemical exergy of the discharged ash or slag is regarded as a ballast flow and must be deducted from the chemical exergy of the fuel The functional efficiency becomes then 9 25 Cycle Tem po Manual Technical Notes Ex productgas 35 Ex un Ex oxidant Taaa H ana T Exs steam The gasifier is part of a systemin which also the thermo mechanical exergy in the product gas can be utilized as can the thermo mechanical exergy of other process flows that are part of the gasification process The product of the gasification process in that case becomes the total exergy of the product gas with the addition of the thermo mechanical exergy of discharged ash or slag flows and the exergy increase in the cooling agent the thermo mechanical exergy of the supplied process flows solid fuel steam and oxidant must be deducted from this We then have the following formula Ex productgas ash Ex SEN aj E out a EX 7 EX cad EX am k Ex idan 36 product cooling Also in this case the chemical exergy of the ingoing process flows minus the chemical exergy of the ash or slag is the source
59. ified or calculated through pressure drops of the apparatus or obtained by otherapparatuses The same applies to temperatures with an additional option the calculation of one or in some cases two temperatures out of the energy balance if the energy exchange with the environment DELE is specified If all pressures are known and of all temperatures only the inlet temperature is known the relation Touts Toute TEMDIF 3 44 3 43 Cycle Tem po Manual Technical Notes occurs if TEMDIF is specified default TEMDIF unknown which means that also temperatures of downstream apparatuses can be taken and both temperatures will be calculated with an iterative procedure from the energy balance The decomposing criterion 1s 0 01 K Also coal can be processed in the separatorin order to abstract water for instance However the medium type ofthe separation pipe will always be GASMIX 3 44 Apparatus models 3 7 Chemical reactor type 27 3 7 1 Equilibria of individual reactions In the reactor chemical equilibrium reactions take place The equilibria are calculated by means of equilibrium constants These constants are a function of the temperature Kreaction f T reaction 3 45 in which Kreaction equilibrium constant dimension depends on reaction Treaction temperature at which the equilibrium is calculated K In the reactor the following reactions are standard The CO shift or watergas shift reaction CO H20 amp
60. into thermo mechanical exergy and chemical exergy Thermo mechanical exergy is the power produced if the process flow is brought in thermo mechanical balance with the environment in the prescribed manner The chemical composition remains unchanged in this process Chemical exergy is the power delivered if the process flow is brought in chemical equilibrium with the environment in the prescribed manner Chemical equilibrium with the environment means that the components composing the process flow are converted into environment components and expand to the partial pressure of the relative component in the environment The sum of the two exergy terms is identical to the exergy of the process flow 1 e ch a tm Ex Ex processflow 11 ot ai Ex Breaking down the exergy of a process flow into a thermo mechanical and a chemical component offers ample opportunity to distinguish between the active part source product and the non active part ballast On the basis of practical applications we will have to establish the adequacy of such a breakdown for different situations Below we have specified functional exergy efficiencies for a number of frequently occurring apparatuses these efficiencies can be used in analysing varying processes In this specification we have found that sometimes arbitrary choices cannot be avoided and that functional efficiencies cannot be stated for each apparatus For example the function of a condenserin a steam cycl
61. ions with turbine code t 2 3 4 5 8 and 9 correction formulae from General Electric are used to supplement the basic value of the isentropic efficiency ETHAID tothe final value ETHAI These corrections are read off from the figures in 1 The correction formula looks like the following ETHAI ETHAID x 1 A x 1 B x 1 C etc 3 1 3 4 Apparatus models Here ETHAI the calculated isentropic efficiency ETHAID basic value of the isentropic efficiency uncorrected A B C etc correction functions The basic values for the isentropic efficiency are also the ultimate isentropic efficiency for the conditions as mentioned in Table 3 2 as no corrections are carried out For each type of turbine except for types tl 0 and 1 the basic efficiency is corrected for conditions which deviate from the conditions mentioned in Table 3 1 for the figure numbers refer to the figures in 1 Turbine code t 2 high pressure section with single row governing stage the volume flow under design conditions the average diameter at half blade height of the row of blades of the governing stage figure 7 the ratio between the outlet pressure in the design situation and the inlet pressure figure 6 the mass flow ratio at the inlet for part load calculations figures 8 and 9 the number of inlet valves figure 12 Turbine codet 3 high pressure section with two row governing stage the volume flo
62. is unfortunately gives an inaccurate value for the enthalpy In general this inaccuracy will result in a negligible error for the total system but is marked for extremely low part load fractions N B Error messages from the programme relating to turbines which refer to a figure number refer to the figures from 1 see annex A Corrections for supersonic annulus velocities The exhaust loss are calculated on the basis of the exhaust velocity of the steam If this velocity is above the velocity of sound approx 425 m s then the pressure at the turbine exhaust is adjusted such that the velocities occurrin g are subsonic This method is also described by Spencer et alia 1 and means that the pressure at the outlet from the last row of blades must be increased by the following method PD p 3 8 Vs Where Dis pressure at the exhaust of the last row of blades bar Pk condenser pressure bar Van exhaust velocity of the steam annulus velocity m s Vs velocity of sound m s Where the annulus velocity even at this higher pressure is still above the velocity of sound 3 8 is again applied but then with the previous value of p instead of px and this is repeated where necessary until Van lt Vs This higher value of the pressure is not however expressed in the output the value of the condenser pressure specified is retained and the volume flow is based on this condenser pressure so that it is simple to later c
63. ition is thus also determined by the way in which exergy values are available The evidence shows that it is not possible to simultaneously satisfy all conditions stated Depending on the significance attached to the various conditions it is possible to define exergy efficiencies in various ways Figure 5 2 distinguishes two different definitions of efficiencies 1 e universal efficiency and functional efficiency Universal efficiency is based on a generally workable definition for exergy efficiency Due to the relative insensitivity to changes in the system it is rejected as insufficient in the publications stated Functional efficiency is preferred but requires further specification depending on the type of system For certain systems relevant specifications are difficult or completely inconceivable Both definitions of efficiency are introduced here in order to emphasize the significance of functional efficiency and to show the impossibility of specifying functional efficiency for certain systems We can define universal efficiency as follows Y Ex 1 n out Exu 2 EX In which gt EXout is the exergy of the outgoing process and energy flows gt EXin is the exergy of the ingoing process and energy flows The name exergy efficiency is not derived from literature In the literature stated we did not find aname for universal efficiency various names however are used for functional efficiency rational effic
64. lsoasa result of energy degradation caused by irreversible processes at the energy conversion level In many cases the losses prevail as a result of degradation Both energy drainage external losses and energy degradation internal losses involve loss of exergy The seriousness of these losses can be determined by using exergy efficiencies for processes apparatuses or systems In general the use of efficiencies is accompanied by interpretation problems Specifically in the case of complex systems it is not always clear how efficiencies have been defined which effects have been considered and which not In energy conversion systems it is quite often unclear whether an efficiency is based on the lower heating value LHV or on the higher heating value HHV of the fuel and whether the plant s own electricity consumption 9 9 Cycle Tem po Manual Technical Notes has been deducted from the power produced The use of efficiencies only makes sense if such interpretation problems can be solved and prevented Exergy efficiencies can be used for varying purposes For example it is conceivable that the authorities use exergy efficiencies in granting permits or levying taxes e g by requiring specific conversion efficiencies to be achieved at plant construction or operation Such an application however requires a thorough understanding ofthe potentials and limitations of exergy efficiencies and can only be realized if there is sufficient
65. nal reheater is to supply thermo mechanical exergy to the medium in the circuit The change in thermo mechanical exergy ofthe circuit medium can therefore be regarded as the product of the processes in the boiler The chemical composition of the circuit medium in the boiler remains unchanged the change in thermo mechanical exergy 1s identical to the change in total exergy or EX product EX an 7 ae EX steam 7 EX water 31 Exergy is supplied to the boiler in the form of fuel The chemical exergy of the fuel actually functions as a source In fact the chemical exergy of the oxidant and flue gas must be considered in the same way as with the combustion chamber Since these flows are not considered in modeling they are also neglected here in the exergy efficiency The chemical exergy of the oxidant and flue gas however is small compared to the chemical exergy of fuel Roughly we can say EX ource EX Ss We can write for the functional efficiency of boiler or reheater EX ream 7 EX ater Mex f boiler Ex 33 Note When speaking of fuel exergy we generally mean chemical exergy We implicitly assume that the fuel is available at ambient temperature and pressure 5 24 Processing the results Moisture separator flue gas condenser In a moisture separator or flue gas condenser a flue gas flow is cooled down to below the water dewpoint causing part of the vaporpresent in the gas to condense The condensate is separated from
66. ndensing section cross compound MP with 3000 rpm and LP with 1500 rpm Condensing section cross compound MP LP with 1500 rpm 1 A correction for the volume flow dy volume flow in m s N number parallel flow s for HP turbines mostly 1 for MP 1 or 2 LP mostly several For the program maximum 9 practical maximum 6 in exceptionalcases 8 2 3000 rem for 50 Hz and 3600 rpm for 60 Hz installations 2 1500 rem for 50 Hz and 1800 rpm for 60 Hz installations Factor A N A 0 0790669 N Dy 0 106188 N Dy 0 0338434 N Dy 0 0998955 N Dy N A N A 0 0998955 N Dy 0 0998955 N Dy Cycle Tem po Manual Technical Notes The efficiencies for the turbine types t1 1 2 3 4 5 8 and 9 are based on data from General Electric 1 The efficiencies of the turbine types tl 6 and 7 are based on data from Stork nowadays Stork Energy from Hengelo the Netherlands In order to run through the procedures correctly the required data in accordance with Table 2 2 of the input description are necessary A summary and brief description ofthe different turbine types with the relevant turbine code is given in Table 3 1 The basic values given in the table for the isentropic efficiency ETHAID are default values in the program the user can where necessary specify another value so that developments in the turbine efficiency can be followed or one can work towards a known internal efficiency For turbi
67. nditions These corrections are of the form 3 2 ETHAl ETHAID xf MN_ POUTDS FMND PINDS Here FMIN the mass flow at the inlet kg s FMIND the mass flow at the inlet under design conditions kg s POUTDS the outlet pres sure under design conditions bar PINDS the inlet pressure under design conditions bar This relates to different functions for turbines which are governed with the inlet pressure for t 6 and turbines which are governed with the mass flow at the inlet for t 7 3 8 Apparatus models 3 1 3 Enthalpies at the extractions In Figure 3 3 the possible expansion lines for the turbine are set out in the Moller diagram h s diagram The specific enthalpies at the extractions are determined by assuming a straight line in the Mollier diagram between inlet conditions and outlet conditions as in the left hand figure For condensing sections with TUCODE 5mdLe 8mdLe and 9mdLe a curved expansion line can be selected by specifying e 1 t5 in the input data This gives a more absolute value for the specific enthalpy at the extractions start and end point of the expansion is only affected by the isentropic efficiency not by the curve of the expansion line If necessary one can obtain a straight expansion line by specifying e 0 For the other turbine types the expansion line is always straight Figure 3 3 expansion lines for condensing sections in the h s diagram e 0 straight
68. ned I A Heat Sink or a smk source with one connected pipe and with subtype 1 specified the energy exchange with the environment equals the mass flow multiplied by the difference between the actual enthalpy and the enthalpy at ambient conditions In case of medium types GASMIX and WATERSTM the water component is considered as liquid at ambient conditions JI A Heat Sink or a sink source with two connected pipes and with subtype 1 specified the energy exchange with the environment equals PH i see paragraph 5 1 Cycle Tem po Manual Technical Notes The total energy production is now Total power production a b c Total heat production d 5 1 4 Own consumption For the energy consumption two different cases are considered Firstly the electricity driven pumps compressors not turbine driven pumps compressors and secondly values specified via the namelist amp AUXPOW a Electricity driven pumps or compressors type 8 or type 29 Power absorbed by medium PH i for an apparatus 1 of the type 8 or 29 which is not turbine driven Electrical power PH i Nariveli The efficiency of the pump compressor drive Ngrive 1 is built up by two efficiencies the mechanical efficiency nm 1 and the electric efficiency n 1 The total efficiency is then determined as follows I If both efficiencies are specified then Narive i Nm i X Nel I If one of the efficiencies i
69. nes or turbine sections with turbine code tl O the user can himself specify the isentropic efficiency This can be specified by the user or must be calculated from the inlet and outlet conditions found A specified internal efficiency ETHAI can if necessary be amended with usersubroutine APSUB The parameter in the header of this subroutine RESULT corresponds forturbines with the internal efficiency see example 1 in part Examples ofthe manual as a simple example Data of General Electric For turbine sections with turbine code t the isentropic efficiency is calculated from the geometry of the turbine using an expression from General Electric set out graphically in Figure 13 of 1 Copies ofthese and otherfigures used are included in this part of the manual as annex A In the expression which serves as a basis for Figure 13 the isentropic efficiency is a function of the volume flow in the design situation and of the pressure ratio between inlet and outlet of the section Any value specified for the isentropic efficiency ETHAD or of the basic value for the isentropic efficiency ETHAID in the input data is ignored The value of the isentropic efficiency in the output of the program includes a pressure drop of 2 over the valves at the inlet of the turbine In Figure 13 this pressure drop is regarded as external so that the value printed by the program is somewhat lower than the value found in Figure 13 For turbines and turbine sect
70. o Manual Technical Notes voad Di y AP roa AP pa X oe bar with Ona mass flow in the pipe at design kg s Va average specific volume in the pipe at design m kg Apea pressure loss in the pipe by flow resistance at design bar Omod actual mass flow in the pipe kg s Vod actual average specific volume in the pipe m kg APtod pressure loss in the pipe by flow resistance bar The total pressure loss Ap both at design and off design can be determined according to Ap Ap Ap bar Processing the results Chapter 5 Processing the results 5 1 Calculation of the system efficiency In the calculation of systemefficiencies four steps can be distinguished 1 Determination of the total energy input 2 Determination of the total energy production 3 Determination of the total own energy consumption 4 Calculation of system efficiencies In the program the variable PH is used to determine the energy exchange with the environment PH abbreviation of Power Heat of an apparatus 1 which has n inlet pipes and m outlet pipes is defined as follows PH gt hin J X min J gt hour 1 X Din our 1 j 1 ial Here h is the enthalpy kJ kg of the medium in a pipe at the side connected to apparatus 1 and the mass flow kg s in the pipe A positive value of PHG means that apparatus irejects energy to the environment 5 1 1 Calculation of the heating value The lower and higher hea
71. ocess flow In this case it holds true for the functional efficiency EX out EX yin Mex F heatexchangen z DEED y E Ex s out 18 Note If heat losses are considered in process calculations these are automatically taken into account in the above efficiency Pump In a pump a medium considered incompressible is increased in pressure using shaft power The exergy increase in the medium is regarded as the product Shaft power is available as a source for this exergy increase The pump s functional efficiency is then EX out EX TEx f pump aa P 19 shaft 9 19 Cycle Tem po Manual Technical Notes Flectromotors are often used for driving pumps If the losses with respect to driving are also taken into account it applies EX ous EX 2 Mex pump 0 electric Condenser There are various ways to consider the exergy efficiency of condensers In the case of a condenserthat is intended to discharge heat to the environment it is difficult to speak of a product since it is impossible to specify a functional efficiency However there are also situations in which the exergy absorbed by the primary medium in a condensercan be utilized elsewhere in the system This for example applies to warm condensers forthe heating of district heating water and to circuits connected in series We can then use the same wording for functional exergy efficiency as in the case of heat exchangers
72. of this a correction is calculated for the oxidant fuel ratio AOF and a new estimate made for the mass ratio oxidant fuel OF This is used in the i 1 iteration to calculate the new compositions and temperatures Calculation of OF from the air factor A Between the air factor A and the mass ratio oxidant fuel OF there is the following relation OF X x OF st where OFs stoichiometric mass ratio oxidant fuel OF is the oxidant fuel ratio where there are just enough oxygen atoms present to let all the fuel react completely This does not include those reactions with oxygen which are the side effects of combustion formation of sulphur oxides nitrogen oxides etc Decisive for the required O molecules is then the number of H andC molecules Say VH n number H atoms in component n VCn number C atoms in component n Von number O atoms in component n Then the following applies ya C M Vyn io e OF f 3 18 l gt Co K Vyn VOR oxid Use of equation 3 18 now supplies the oxidant fuel ratio 3 28 Apparatus models Calculation of the flue gas temperature When the energy equation is not used to calculate a mass flow then this can be used to determine the temperature of the flue gas The energy equation over the combustoris P mox x Nox B mtu x Nu O mas x Nas D mfg x hig Qross 3 19 The temperatures and compositions of oxidant and fuel are known so that the terms in the right hand side
73. of mixed flows for the following processes orcombinations of processes l Stean water cycles Gas turbine cycles Potassium topping cycles Fuel cell systems Coal gasification systems Vapor compression refrigeration machines and heat pumps FL AA AA Absorption refrigeration machines and heat pumps The computer program can be used for a variety of purposes Firstly process variables for new units can be calculated and optimised Secondly for existing production units the consequences ofa change in operation for example relating to the thermal efficiency can be easily calculated Finally the computer program can be used for the evaluation and testing of results 1 1 Cycle Tempo Manual Technical Notes Basicconceptof Cycle Tempo Chapter 2 Basic concept of Cycle Tempo Cycle Tempo was developed for computing thermodynamic properties gas compositions and mass flows in energy systems for the production of electricity heat and refrigeration These can be calculated with mass balances molar balances energy balances relations for thermodynamic properties In Cycle Tempo relations are available for computing thermodynamic properties for steamand water in accordance with the IFC equations of 1967 7 asetof 50 gases which may occur as an ideal mixture in a pipe also for chemical equilibrium calculations refrigerants potassium ammonia water mixtures Predefined compositions for
74. of the exhaust loss is shown in the output under EXHAUST LOSSES in kJ kg after the isentropic efficiency of the turbine The exhaust loss can be read off from figure 16 or 17 depending on the revolutions of the turbine and must be corrected for turbine efficiency and moisture content as indicated by Spencer et alia in figure 16 and 17 11 UEEP ELEP EL x0 87 x 1 y x 1 0 65y 3 4 Here UEEP Used Energy End Point the total enthalpy at the turbine exhaust also the enthalpy at the inlet of the condenser kJ kg ELEP Expansion Lime End Point the virtual value of the enthalpy at the end of expansion see Figure 3 3 kJ kg Apparatus models EL Exhaust Loss the exhaust loss as read off in figure 16 or 17 kJ kg y The mass fraction of moisture in the steam N B in the figures Y is the percentage moisture kg kg The relation with the printed exhaust loss EXHAUST LOSS is now EXHAUST LOSS EL x 0 87 x 1 y x 1 0 65y kJ kg 3 5 In Figure 3 3 the calculation is explained further the calculated exhaust loss Ahjoss EXHAUST LOSS is added up at the expansion line end point ELEP of the condensing section In this way the specific enthalpy at the turbine exhaust UEEP is obtained N B To calculate the turbine power the specific enthalpy at the turbine exh aust UEEP is usedin the energy balance This specific enthalpy is printed as the enthalpy in the pipe at the turbine outlet The calculated exhaust l
75. olved from the total mass balance and the oxidant fuel ratio calculated from the energy equation Option 3 Specify or calculate elsewhere 1 mass flow and specify the air factor A To solve the 2 unknown mass flows the mass balance and the calculated oxidant fuel ratio is used In the above the ash pipe is not taken into account Where the user does not define an ash pipe all the components are discharged to the flue gas pipe If however an ash pipe is specified then the substances which are discharged to the ash pipe are determined in the following way The non gaseous components Al0x s ALOx Fe203 Si02 s and S1020 are automatically discharged to the ash pipe The same happens for the solid carbon formed during the reaction In order to discharge a solid component or a part of this to the flue gas pipe any way the Bypass components button can be used see Reaction data in paragraph 4 2 of part Cycle Tempo Operation of the manual Via the Separate components button one can specify for each component that a particular fraction of the substances supplied via the oxidant or fuel pipe without taking part in the reaction is discharged directly to the fuel pipe see Reaction data in paragraph 4 2 of part Cycle Tempo Operation of the manual If the ash pipe is connected the program calculates an ash fuel ratio and adds this ratio to the systemmatrix For the 3 options we can now prepare the system ma
76. ononconcnnnnnonnss 3 49 3 8 2 Calculation of the gas composition in the gas outlet pipe 3 49 3 8 3 Calculation Of the mass OWS wsssccsscssscisssswsteventesnssonesdbewecavievecsianasanennscarsesienes 3 50 3 8 4 Calculation of temperatures and use of the energy balance 3 51 3 9 Compressor CYC ZO lios ico opio 3 52 3 9 1 Fields Of application ooooconoconoconocononnonononononononononononononononcnnnnnn non nononcnnncnnncnnnos 3 52 3 9 2 Calculation procedure ooocooccnoccnoncconncconnconnononononnnonnncnonnconno nono cnnnoconncnnnn con nannnnos 3 52 3 9 3 Calculation isentropic efficiency with design conditions SULZER COMIPTES SOLS nca2sncsccccsavnaessectacteastseiqenaueasconsenetadneioiechavagnientbeuidtaadidendandansqsaquniadeal 3 53 3 9 4 Calculation isentropic efficiency with off design conditions SULZER COMIPTES S OFS A 3 54 Chapter 4 Pressure losses in pipes 0 0 0 0 ccc cccccsccessecesecesecceseccseeceseeesceeeseeceseeeseeceseeesseseseeeaees 4 1 Chapter 5 Processing the results o oooonooconocnnocncooncoonnononcconnononnconnconnncnnnconn nono nncnn nono nnnnnnnos 5 1 5 1 Calculation of the system efficiency oocoooccnoconoconononnonnnonncconncnn nono nonnnnnnnon ono nnnnncninannncnss 5 1 5 1 1 Calculation of the heating Value oooooonoccnoocccocnconncnoncnonnnconncnonoconncnonnconcnnnnncons 5 1 5 12 A eee ene reer eer en ren ier ere 5 2 5 1 3 PPM TOG eese EE 5 4 5 1 4 OWN CON
77. opic efficiency with off design conditions Mp ofrdes With 201 1 p off des 7 x7 3 57 Finally the isentropic efficiency with off design conditions Ni offdes 18 determined as follows hz off des l OS k 1 4 i off des 3 58 In 1 Topas 71 ll oides For SULZER type A it is also possible to specify a speed percentage in stead of the design pressure ratio The calculation method is the same as above RS Y Pressure losses in pipes Chapter 4 Pressure losses in pipes Pressure losses in pipes may arise from differences in height flow resistances Pressure losses caused by height differences are calculated with the following relation Ap e x 107 bar With Ap pressure changein the pipe as a result of a height difference bar v average specific volume of the fluid in the pipe m kg g gravitation constant 9 80665 m s m s7 Ah height difference between inlet and outlet of the pipe m The average specific volume is the average of the specific volume at the inlet vin and the outlet Vout of the pipe y Vix Vomi mk 3 g At design the pressure loss as a result of flow resistance Ap is specified in the input At off design it is assumed that the flow in the pipe is always turbulent Furthermore it is assumed that the friction factor is independent of the velocity in the pipe These assumptions lead to the following relation 4 1 Cycle Tem p
78. osen for 3 17 6 Cycle Tempo Manual Technical Notes the mass flow ratio For the following iteration runs the mass flows are used which are calculated in the previous iteration run The energy exchange with the environment must be specified in the apparatus data The enthalpies from the energy equation can be determined in the same way as described in paragraph 3 2 4 except for the pipe for which the temperature must be calculated The unknown enthalpy can now be solved from the energy equation The unknown temperature is then known as a function of the enthalpy and another state property 3 2 4 Calculation options for the off design calculation Also for the off design calculation the two mass equations and the energy equation is used The energy equation can be used again to calculate either an unknown mass flow EEQCOD I or an unknown enthalpy EEQCOD 2 In addition the thermal transfer equation is also availabie to calculate an extra unknown temperature Below the possible calculation options are described which result from this Calculation of an unknown mass flow EEQCOD 1 The energy equation is in this case added to the set of systemequations and is used to calculate an unknown mass flow In addition it is possible with the heat transfer equation to calculate an unknown temperature The following options are thus possible messin rears U K u K K U K K u K K u u K K K u K u K K known specified for an appa
79. oss is kept in the program as an enthalpy drop over this outlet pipe of the turbine A user specified value for DELH in this pipe is ignored by this and overwritten DELH cannot therefore be specified for outlet pipes of turbines The enthalpies at the inlet and outlet of the pipe are in spite of the internal value of DELH equal to each other as the printed value of the enthalpy is that of the total enthalpy that is including the value of the velocity term 2 Inv Interpretation of the output The expansion line end point in the turbine cannot be clearly specified In general the pressure in the condenseris specified where the velocity of the steamis negligible At the exhaust of the last row of blades the steam velocity is not negligible the exhaust of the last row of blades in the program means the outlet of the turbine The pressure at this point is dependent on the steam velocity and of the efficiency of the diffusor between the last row of blades and the condenser The space between the last row of blades of the turbine including the diffusor is represented in the scheme by the pipe between the turbine and condenser The values printed in the output for pressure temperature enthalpy and vaporquality for the turbine exhaust must be regarded as notional values as intended by Spencer et alia The value of the pressure at the exhaust of the last row of blades will be a little lower than the printed value as the pressure increases in a
80. po Manual Technical Notes Step 7 Diffe rence in mass flo ws After the main iteration has been carried outa minimum of twice for each pipe the relative and absolute difference is determined in the mass flows for the previous main iteration For each pipe a check is made as to whether it meets the break off criterion Eon lt E or n 1 lt 0 001 Pn A For each pipe the printout shows how many pipes do not meet the criterion and in which pipe the maximum relative and in which the maximum absolute difference occurs Step 8 Break off criterion compositions mass flo ws The break off criterion forthe main iteration is All the pipes must meet both the criterion for the compositions and the criterion for the mass flows If both conditions are met the required accuracy is reached and the last mass flows calculated are regarded as the solution of the system If one or both of these conditions is not met then there is a return to step 3 Step 9 Calculating compositions In the solution of the mass flows the relevant compositions are calculated These compositions are then regarded as the solution of the system The result is printed out in the table Composition of fluids Step 10 Calculating p T h With the solution for the mass flows and compositions once again all the unknown pressures temperatures and enthalpies are calculated All the pipe data are printed out in the table Data for all pipes with for
81. provided the following data are known for the turbine which means specified or calculated by other apparatuses the outlet pressure this will in general be calculated in off design situations from data for the condenser anumber of results from the design case these must be specified as Off design input data for the relevant apparatuses These design datacan also be found at the end of the output file under option View Text Output Cycle Tem po Manual Technical Notes th a T 5 EE E E 5 Figure 3 1 Diagram of apparatus type 3 the turbine The turbines and turbine sections distinguished by the program can be classified in two categories distinguished from each other by the turbine code TUCODE general turbines TUCODE 0 specific steam turbines TUCODE 10000 and higher The general turbine type can where necessary also be used as a steam turbine but is intended more as an expansion section of a gas turbine installation and as turbine type for various media The user will have to specify the internal efficiency of the turbine himself or this must be calculated from the conditions at the inlet and outlet of the turbine For a number of types of steam turbine data are available from which the internal efficiency is calculated by the program If one wants to use these data then one must select the relevant turbine type in accordance with Table 2 2 of part Reference Guide of the manual This is
82. ratus orto be determined from another apparatus u unknown to be calculated with the equations of the condenser model 3 18 Apparatus models Calculation of an unknown temperature EEQCOD 2 The energy equation is in this case not added to the set of system equations butis used to calculate an unknown enthalpy In addition it is possible with the heat transfer equation to calculate an extra unknown temperature The following option is then possible Temperatures known specified for an apparatus or to be determined from another apparatus model u unknown to be calculated with the equations of the condenser model 3 19 Cycle Tem po Manual Technical Notes 3 3 Combustor type 13 3 3 1 Applications The combustor model in Cycle Tempo is suitable for various applications To getan idea in setting it up the requirements arising out of three specific applications have been taken into account model for the combustor ofa gas turbine model for the furnace of a steam generator model for an additional firmg burner or afterburner These applications result in different requirements with regard to the input data and the variables to be calculated Before going into the possible combinations of input data first the general assumptions ofthe model are explained 3 3 2 Assumptions Heat transfer in the combustor In the model no allowance is made for the heat exchanging area in the combustor However in o
83. rder for example to model a hearth including heat exchanging area in Cycle Tempo one or more heat exchangers can be included after the combustor In addition it is possible to specify a heat loss Qhoss Fuels In the combustor model a number of fuels can be used With the help of the input window for pipe data the following fuels can be specified Solid or liquid fuels with unknown chemical composition mass fractions of the present elements and the lower heating value specified molar fractions of the present elements and the lower heating value specified standard composition 3 20 Apparatus models Gaseous fuels molar fractions specified standard Slochteren natural gas Flue gas composition In the combustor a chemical reaction takes place between the fuel and oxidant The heat released here is determined by the course of the reaction 1 e the composition of the reaction product flue gas In order to determine the heat produced it is therefore essential to calculate this composition Under ideal conditions residence time mixture the composition of the flue gas will be the same as the equilibrium composition corresponding to the composition of the reactants and the reaction conditions Pyeacts react Under actual conditions the reactions will however not run to equilibrium The degree to which the initial composition differs from the equilibrium composition is determined by factors which depend on t
84. re and inlet temperature and the relative humidity RELHUM specified by the user 3 8 2 Calculation of the gas composition in the gas outlet pipe The molar fraction water vapour in the gas outlet pipe can be calculated in three ways It can be specified with MLFH20 The molar fraction water vapour Xoutgas H20 18 considered to be equal to MLFH20 Then the molar fractions of the othercomponents are calculated see below Or the amount of water to be evaporated can be specified with DELMW If PIPE is also specified DELM W is relative compared to another mass flow The amount of water to be evaporated is DELMW x pipe In order to calculate the molar fraction water vapour in the gas outlet pipe the number of moles water to be evaporated are calculated after which 0 QD mol in gas H O m mol watertobeevaporated 3 48 out gas H O Dd mol in gas total mol watertobeevaporated The mole flows are calculated by dividing the mass flows by the mole mass If MLFH20 nor DELMW are specified the molar fraction water vapouris calculated out of the pressure and the temperature in the gas outlet pipe In order to calculate the composition of the outgoing gas first the partial pressure of the water vapouris determined at the temperature of the outgoing gas 3 49 Cycle Tem po Manual Technical Notes Pout gas H 0 RELHUM x Paou 3 49 Then the molar fraction water vapour can be calculated P outgast O Nout H O
85. re of the fuel cell or 2 the oxidant utilisation In the first case EEQCOD 1 the energy balance is added to the system matrix Dm a inxNa int Dim C inXhc in Dm a outXN a out Dm C outXhg out Poc Qoss 3 28a If the oxidant utilisation the second case has been specified the oxidant fuel ratio Xop kg kg is calculated in the model and used in the system matrix XoF x Dm a in Dm a out 3 28b If the oxidant utilisation has been specified or the mass flow oxidant is calculated elsewhere the energy balance is used to calculate the outlet temperature EEQCOD 2 in which case identical temperatures are assumed for anode and cathode outlets 3 33 Cycle Tem po Manual Technical Notes 3 4 3 Modelling ofthe process in the fuel cell 1 anode inlet area 2 active anode area chemical current distribution equilibrium cell voltage Treact Preact outlet conc anode outlet conc cathode 3 cathode Figure 3 5 Framework ofthe model Figure 3 5 shows how the process is modelled in the fuel cell Block 1 If the reaction temperature is specified the fuel is supposed to react to chemical equilibrium at Preacts Treact This calculation block can be used for instance to model a pre reforming reaction in the cell stack This process is assumed to occur at a constant temperature it is assumed that the necessary heat is taken from the reactions in the fuel cell Block 2 In this block that
86. s break off criteria mass flows a calculate compositions 10 calculate p T h output 12 exergy analysis Basicconceptof Cycle Tempo 2 3 Creating the system matrix Mass flows are calculated from mass balances of an apparatus energy balance of an apparatus Mass flow h specific enthalpy b mass or energy loss Apparatus Figure 2 5 Energy and mass balance of an apparatus Mass balances are of the type ya Drie 0 7 gt Prout 1 z b k jel i l k number of equations Energy balances are of the type gt Prin J x h J gt Pn our x AJ b 1 j l i l 1 number of equations The mass balances can also be prepared from atomic balance of an apparatus prescribed mass flows prescribed mass flow ratios The equations drawn up mass and energy balances are written in matrix form 6 Cycle Tempo Manual Technical Notes Am b The solution to this systemgives the mass flow for each pipe in the system The calculation must however meet three conditions The matrix must be square which means that the number of equations must be equal to the number of pipes in the system The matrix must be independent If there are coefficients in the matrix which are dependent on the mass flows an iterative calculation is necessary This iteration process must be converging 2 3 1 Closed processes To obtain an independent systemof equations for a closed cycle for eac
87. s not specified then the efficiency which is not specified is setequal to 1 Hence Nm is specified and ne not then Narive i Nm i And vice versaif Ne is specified and Nm not then Ndrivel1 Nel Processing the results Il If none of both efficiencies are specified then the total efficiency is calculated by interpolation from Figure 5 1 Efficiencies of electromotors al Q 2 2 E uy 1000 Power kW gt Figure 5 1 The efficiency of electromotors including the mechanical efficiency ofthe motor and pump compressor as a function ofthe power at the shaft of the pump compressor b Auxiliary power consumption The user may specify additional power consumption of not modelled consumers at General Data Auxiliary Power Consumption For these just the name chosen and the electric or mechanical power consumption are used The total own energy consumption is now Total own consumption a b Cycle Tem po Manual Technical Notes 5 1 5 Efficiencies l Gross thermal efficiency 2 Net thermal efficiency Total produced electric mechanical power Total energy input Total produced electr mech Power total own consumption Total energy input Only if a Heat Sink or a sink source with subtype 1 specified has been defined 3 Heat efficiency 4 Total net efficiency 5 8 Total heat production Total energy input net thermal efficiency heat efficienc
88. tem matrix An additional possibility for the calculation of an enthalpy value is present if it appears during the calculation that above mentioned procedure does not contain sufficient data The programme will then try to calculate the inlet enthalpy out of the outlet enthalpy or the outlet enthalpy out of the inlet enthalpy by means of the Mollier diagram through an isentropic efficiency ETHAI that has been specified in the input This is illustrated in Figure 3 7 Figure 3 7 Calculation ofenthalpies No additional possibility exists for the SULZER compressors at the moment In case ofa design calculation the isentropic efficiency can be calculated out of the inlet volume flow and in case of an off design calculation from the inlet volume flow and the pressure ratio For type A it is also possible to calculate the isentropic efficiency with off design calculations from the inlet volume flow and the number of revolutions This calculation preceeds the enthalpy calculation via the Mollier diagram 3 9 3 Calculation isentropic efficiency with design conditions SULZER compressors For the calculation of the isentropic efficiency with design conditions a direct relation is determined between the inlet volume flows and the isentropic efficiency This relation is shown in Figure 3 8 3 53 6 Cycle Tempo Manual Technical Notes gt e Lal al a da clas i pl 20 40 BO 50 300 420 440 7160 160 00 220
89. tgoing process flow is used for chemical or thermo mechanical purposes Therefore it is not possible to define a generally workable functional efficiency Note In cases in which functional efficiency cannot be specified one can always get an impression ofthe quality of the conversion using the universal efficiency In drawing conclusions one must bear in mind that the universal efficiency always has a value larger than or identical to the functional efficiency 5 28 List ofs ymbols ex specific exergy Ex exergy flow ac power AEx exergy changein a flow n efficiency Dn mass flow subscripts Ex exergy f functional p primary S secondary u universal superscripts ch chemical tm thermo mechanical Processing the results kJ kg kW kW kW kg s 5 29 6 Cycle Tempo Manual Technical Notes 5 30 Literature Literature SPENCER R C COT70N K C and CANNON C N A method for predicting the performance of steam turbine generators Journal of Engineering for Power Vol 85 Oct 1963 revised July 1974 MIEDEMA J A LIEFHEBBER F and OP DEN BROUW H Programmers Manual of the Computer program CYCLE III Report EV 1158 1980 Delft University of Technology Laboratory for Thermal Power Engineering GORDON S and McBRIDE B J Computer Program for Calculation of complex Chemical Equilibrium Compositions Lewis Research Center NASA SP 273 1971 DOWNING RT C and KNIGHT B W
90. th figures are valid for the medium air and a constant inlet temperature 3 54 Apparatus models Polytropic efficiency n n NP MA IE EI AAA I A A SI SR 90 100 110 120 7 p volume V Figure 3 9 Off design characteristic SULZER type A In Cycle Tempo the following method is applied for both types Input design data for off design calculations VOLDES inlet volume flow with design conditions PRATID pressure ratio with design conditions From the calculation results Dy offdes inlet volume flow with off design conditions Toda pressure ratio with off design conditions the pressure ratio can also be specified as PRATI POUT PIN 3 55 Cycle Tem po Manual Technical Notes Polytropic efficiency Suction volume V Figure 3 10 Off design characteristic SULZER type AV From these data the percentage inlet volume flow and the percentage pressure ratio 7 of off design compared to design can be derived PP PD de 100 3 54 DESVOL T off des 1 Pr x100 3 55 PRATID 1 From the characteristics the polytropic efficiency percentage np will then result The polytropic efficiency with design conditions np is calculated out of the isentropic efficiency n parameter ETHAID at off design input data with the formula 3 56 Apparatus models k l Ke A a pE PRATID 1 k 14 3 56 P k 1 1 x PRATID 1 The polytr
91. the cell temperature and pressure Block 3 The mass transport of cathode to anode O for the SOFC Oy and CO for the MCFC is also calculated from the cell flow I The total mass flow O from cathode to anode is given by I m 0 c gt a M wnol 0 A AF 3 32 In addition CO is also transported from the cathode to the anode in the MCFC For this mole flow it holds that I 3 33 coda okt gt p 3 35 Cycle Tem po Manual Technical Notes From the mole balances for the components at the cathode the composition at the cathode outlet can now be calculated Energy balance Using the energy balance over the apparatus blocks 1 to 3 the temperature at the outlet is calculated the temperatures at the anode and cathode outlets are assumed to be identical 3 4 4 Relations for calculating the cell voltage Figure 3 6 shows two designs of fuel cells diagrammatically the tubular monocell Figure 3 6a that is applied in several SOFC designs and the flat plate cell Figure 3 6b the usual MCFC design a tubular type b flat plate type Figure 3 6 Types of design of fuel cells To calculate im V and P useis made of a one dimensional model of the active surface That is the temperatures pressures and compositions are supposed to be constant in a cross section perpendicular to the direction of the fuel cell flow In the model ofthe cell area the distribution of the flow density is calculated in
92. the combustion reaction For each component and pipe the user may specify what fraction of the added oxidant and fuel remain outside the reaction The variables in this stream are indicated with the index ncec Non Chemical Equilibrium Composition In the same way a part of the oxidant and fuel streamis passed directly to the ash pipe Here heating up to the ash temperature takes place Where this is not specified or calculated elsewhere this is equal to the flue gas temperature The main stream reacts to equilibrium and is therefore marked with the index cec Chemical Equilibrium Composition After the reaction this stream is cooled down to the flue gas temperature When no data are given by the user with regard to the reaction conditions Preact and Tyeact the program calculates the equilibrium underthe outlet conditions Pout and Tout The user can also specify the reaction conditions himself ora difference between the calculated outlet conditions and the equilibrium conditions Apreact and ATyeact In this latter case the calculation is carried out with Preact Pout AD reset 3 25 Cycle Tem po Manual Technical Notes Tiaa Ton AT eai 3 3 4 Calculations and relations In this paragraph the different calculations and relations which are used in the combustor model are explained These are successively calculation of oxidant fraction OF from the flue gas temperature calculation of oxidant fraction OF
93. the electrodes are negligible in the x direction This means thatthe cell voltage is supposed to be constant over the fuel cell Thus equation 3 36 becomes as follows V E AV 3 37 The voltage loss can be regarded as the driving force for the reactions in the fuel cell and thus for the current density On the basis of 1 it is now assumed that the current density is proportional to the voltage loss By analogy with Ohm s law the proportionality constant is indicated with the equivalent cell resistance Req ohm m It then follows for the current density in the cross section x that Ix AVx Reg 3 38 Finally the velocity with which H is converted in a cross section x can be calculated from the current density dn i t 3 39 dx 2F The changes in the concentrations of the components can be calculated using this equation the mole balances for the components and the reaction balances for shift and possibly reforming reactions On the basis of the given equation the voltage and current density can be calculated in a cross section Use is made of numerical routines to calculate the course of these quantities over the cell List of symbols A cell area m E reversible voltage V Eo reversible voltage at standard pressure 1 bar V F Faraday s constant C mole 1 current density A m2 I current A n number of moles mole On mass flow kg s 3 38 NDCAC Indices
94. the x direction along the cell area e in the direction ofthe flow ofthe fuel The following local variables indicated with index x are calculated 3 36 Apparatus models reversible voltage E current density ix concentrations y H2 CO H20 CO and CH3 This section states the relations in an implicit form from which these variables are solved If the processes in a cross section x of the fuel cell occur without losses the cell voltage is identical to the reversible voltage or Nernst voltage E For the SOFC the reversible voltage if the gases are supposed to behave ideally is identical to Y E Poe 4 RT In YO Ya a x P 3 34a 2F Y H 0 a And for the MCFC Y RT c a Y E Er mp a Se y rsh 3 34b H O a 7 CO a E y is the standard reversible voltage for hydrogen that only depends on the temperature and is calculated from the change in the Gibbs energy AG AG 2F E 3 35 The second term in the equation 3 34 is a corrective term for the real partial pressures In reality the processes in the cell occur irreversibly so that the cell voltage V the real voltage difference between the electrodes is smaller than the reversible voltage The difference between reversible and real voltage is indicated with the voltage loss AV V E AV 3 36 3 37 Cycle Tem po Manual Technical Notes In the model it is assumed that the voltage losses on the level of
95. ting value henceforth indicated as LHV and HHV respectively of all pipes of the medium type GASMIX are calculated For this calculation the definitions established in DIN 5499 Brennwert und Heizwert Begriffe January 1972 were assumed The heating value is defined as the energy that must be discharged when heating 1 Cycle Tem po Manual Technical Notes kilogramme of fuel when the fuel oxidant and flue gas are all supplied or discharged at a pressure of atm and a temperature of 25 C In gaseous fuels it is assumed for the HHV that the water generated by the heating reactions 1 e not the water thatis already present in the gas or in the air fully condenses Atthe LHV this water is fully present as vapour in the flue gas Apart from the water generated at the heating the water present in the fuel is also taken along in the event of solid and liquid fuels Oxygen is used as oxidant No heating value can be calculated for pipes of the medium type FUEL as the component composition is not known The LHV must therefore always be stated through the parameter LHV The HHV is calculated by determining the humidity of the flue gas and calculating its condensation heat The HHV is then equal to the LHV plus the condensation heat In the event of deviating pressure and temperature the heating values can be calculated at the conditions specified by the user at General Data Environment Definition 5 1 2 Energy input For the ener
96. tion during which energy of formation of the components will be released or absorbed If this results in a reaction the calculated temperature will be clearly influenced by it Behaviour during the first iteration of Cycle Tempo In the first iteration of Cycle Tempo pressures temperatures enthalpies and mass flows will not yet be known during the calculation of the gas composition whilst a pressure and mass flows are needed If the inlet pressure an estimation of 1t or PREACT is specified a new composition will be calculated if not the composition at the outlet will be considered to be equal to that at the inlet When an unknown temperature is calculated DELE is put on zero in the first iteration unless ESTMAS is specified If various inlet pipes are connected the composition of the total original gas mixture has to be calculated This requires the mass flows in the inlet pipes or the ratios between them For the first iteration RMASS can be specified If RMASS is not specified the mass flows in the inlet pipes are considered to have the same size 3 48 Apparatus models 3 8 Saturator type 28 3 8 1 Functioning ofthe model ofthe saturator The model of the saturatoris based on a counterflow saturator It is used to moisturize a gas with water vapour The composition of the gas to be moisturized is free to be chosen and can be defined by the user himself The composition of the outgoing gas is calculated with the inlet pressu
97. trix For this the following notation is used DP mass flow kg s OF Okxidant Fuel ratio kg kg AF Ash Fuel ratio kg kg 3 23 6 Cycle Tempo Manual Technical Notes Indices fu fuel ox oxidant fg flue gas as ash Option 1 2 mass flows specified or calculated elsewhere total mass balance Is placed in system matrix for another apparatus Idem 2 mass ratio ash tuel AF Note equation 4 is only added where ash pipe is connected the energy equation is used to determine the flue gas temperature Option 2 1 mass flow and flue gas temperature specified or calculated elsewhere total mass balance is placed in system matrix for another apparatus mass ratio oxidant fuel OF calculated from energy equation mass ratio ash tuel AF Note Equation 4 is only added where ash pipe is connected 3 24 Apparatus models total mass balance is placed in system matrix for another apparatus mass ratio oxidant fuel OF calculated from air factor mass ratio ash fuel AF Note equation 4 is only added where ash pipe is connected the energy equation is used to determine the flue gas temperature Options regarding the compositions of flue gas and ash In the combustor model the incoming streams oxidant and fuel are split into three separate streams Part of the oxidant and the fuel is only heated up to the flue gas temperature but does not take part in
98. value for the isentropic efficiency ETHAID is not specified default values in accordance with Table 3 1 are taken Since the data date from 1963 and the 1974 update contained no changes to the isentropic efficiencies the efficiencies calculated are perhaps still on the low side by selecting a higher basic value for ETHAID than in accordance with the table one can alter the isentropic efficiency to the state of the technology applied If one wants to arrive at a particular value of the isentropic efficiency then one will have to make an estimate of ETHAID by trial and error This situation may occur for example when one knows the isentropic efficiency at full load and wants the value for part load to be determined by the program As shown in 3 1 ETHAI is proportionate to ETHAID only the outlet loss can cause an alteration here for turbine types 5 8 and 9 In that case one can in different calculations by having the value of ETHAI calculated for two values of ETHAID estimate ETHAID by interpolation or extrapolation to arrive at the required value of ETHA LI Data of Stork For turbines with turbine code t 6 and 7 back pressure turbines a direct method for the calculation of the isentropic efficiency is proposed by VMF Stork nowadays NEM Hengelo the Netherlands and incorporated in the program For this method corrections are made for part load conditions with respect to the actual value of the isentropic efficiency under design co
99. w underdesign conditions the ratio between the outlet pressure in the design situation and the inlet pressure figure 10 the mass flow ratio at the inlet for part load calculations figure 11 the number of inlet valves figure 12 6 Cycle Tempo Manual Technical Notes Table 3 2 Conditions for which no efficiency corrections are necessary Turbine y a t2 DIAIN POUTDS FMIN POUTRT Steam code PIN FMIND PIN inlet m t ms conditions see Figure 3 2 see Figure 3 2 In this table 1s Did volume flow at inlet under design conditions m s FMIND mass flow at inlet under design conditions kg s FMIN mass flow at inlet off design kg s t2 number parallel flows in the turbine section in condensing sections of the intermediate pressure turbine ts number inlet valves for the governing stage of the turbine section in high pressure turbines Turbine code t 4 non reheat turbine with two row governing stage the volume flow under design conditions the ratio between the pressure at the outlet of the governing stagein the design situation and the inlet pressure figure 2 the inlet conditions with a view to the moisture content of the steam at the end of expansion figure 14 the mass flow ratio at the inlet and the ratio between the inlet pressure and the pressure at the outlet of the governing stage in the design situation for part load calculations figure 4 the mass
100. wing possibilities are available for preparing the system matrix worked out for Figure 2 6 but this is to be extended to larger systems 1 Specify the power for an apparatus in the chain and calculate the mass flows 1 mass balance and 1 energy balance 2 Specify the incoming mass flow of the system and calculate the outgoing mass flow of the system 2 mass balances 3 Specify the outgoing mass flow of the system and calculate the incoming mass flow of the system 2 mass balances 2 11 Cycle Tem po Manual Technical Notes Also for open processes one must select energy equations to be specified with a right hand side such that these are independent of the mass balances In this example possibility 1 alone gives an independent systemif h ho 2 12 Apparatus models Chapter 3 Apparatus models 3 1 Turbine type 3 3 1 1 Introduction The apparatus type 3 the turbine is used to model an expansion process irrespective of the medium expanding in the turbine Each turbine can in addition to an inlet and an outlet have a maximum of 8 extractions as indicated in Figure 3 1 The outlet pressure and the extraction pressures ofa turbine cannot be specified with the parameter POUT but must be calculated from data which are specified for apparatuses or pipes downstream For off design calculations the extraction pressures are calculated on the basis of Traupel s formulae 8 a refinement of Stodola s cone law
101. y Processing the results 5 2 Calculation of exergy efficiencies 5 2 1 Introduction Besides systemcalculations Cycle Tempo can perform exergy calculations the results of which form the basis for an exergy analysis of the systemunder consideration For such an exergy analysis it is important to have available exergy values of process flows and exergy losses in apparatuses as well as exergy efficiencies of apparatuses The evidence has shown that for exergy efficiencies a variety of definitions is conceivable which in turn may result in strongly differing efficiency values fora given process or system Using uniform definitions for these efficiencies will strongly improve the usefulness of exergy efficiencies There are no internationally recognized definitions available for exergy efficiencies however various authors among others 9 10 and 11 have made propositions to this end These propositions show mutual differences but have been insufficiently worked out for application in practice The efficiencies used in Cycle Tempo should be regarded as a proposition to define exergy efficiencies that can be used in practice 5 2 2 Possibilities for using exergy efficiencies In the thermodynamic analysis of processes and systems we try to obtain a good picture of the place the size and the cause of losses Losses may occur as a result of undesired drainage of energy to the environment for example in the form of heat losses buta
102. y at the exhaust from the last row of blades which is important in relation to possible erosion of the lastrow of blades by moisture droplets The recovery of pressure in the diffusor after the turbine is included in the calculation of the exhaust loss according to Spencer et alia Any pressure increase is not however expressed in the method of General Electric and hence also not in the output of the program the pressure at the outlet of the turbine and at the inlet of the condenser are equal to each other as in Figure 3 3 If one wants to deviate from this then it is possible to simulate the recovery of pressure from the steam velocity in the diffusor by specifying the pressure at the exhaust from the last row of blades as inlet pressure of the pipe at the outlet of the turbine in the form of PINL as an extra condition for the relevant pipe This value must then be lower than 3 12 Apparatus models the pressure in the condenser If necessary anegative value for DELP or DELPR can be specified for the outlet pipe If one wants to calculate the turbine efficiencies purely with the method of General Electric then this procedure is not recommended The thermodynamic data at the extractions are calculated on the basis of the expansion line as this results from the conditions at the turbine inlet up to the expansion line end point ELEP hence before setting off the exhaust losses For extractions with a pressure close to the outlet pressure th
103. y of the secondary flow will decrease Figure 5 3 visualizes the exergy change in the process flows heat exchanger Figure 5 3 change in exergy quantities at heat transfer Cycle Tem po Manual Technical Notes The universal exergy efficiency for this heat exchanger follows from comparison 1 Ex Ex 8 s out p out Tex u heatexchan en gt amp EX in EX in If we look only at the exergy quantities involved in the process we see the exergy quantities Ex in and Ex out flowing through the process without any change These flows can be regarded as ballast flows that are not part of the process and thus need not be considered in the process assessment If possible the specification of a functional efficiency should relate only to changes in exergy quantities It is assumed that the purpose of the heat exchanger is to heat the primary flow The exergy change AEx of the primary flow can be regarded as Exproduct from comparison 4 The secondary flow provides the supply of exergy The exergy change AEx of the secondary flow can thus be regarded as Exsource For the functional exergy efficiency of the heat transfer process we can then write AEX EX us EX yin 9 AEX Ex Ex S In S out Mex f heatexchangen In this comparison the exergy flows seen as ballast are not taken into consideration Actually in comparison 8 the exergy loss is related to the total exergy supplied Ex in Ex in W

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