Universidad Politecina de Madrid Escuela Tecníca Superior de Ingeriero Industriales
Nuevos desarollos del programa de simulación de ciclos termodinámicos
CicloWin
: aplicación a ciclos combinados y ciclos inversos
New development of the software of simulation of thermodynamics cycles
CICLOWIN
: applications on combined cycles and reverses cycles
Tutor : Rafael Nieto Calier
Dardenne François - 3° EM-ERG - Erasmus student Academic year 2006-2007
Contents Introduction
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I CicloWin
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1 Presentation of
CicloWin
1.1 Introduction . . . . . . . . . 1.2 Case of Use . . . . . . . . . 1.2.1 Design a cycle . . . . 1.2.2 Represent a cycle . . 1.3 Model of the domain . . . . 1.4 Not functional requirements 1.5 Choice of architecture . . .
2 Design of
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CicloWin
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2.1 Subsystem of calculation . . . . . . . . . . . . . . . . . . . . . 20 2.2 Subsystem of interface . . . . . . . . . . . . . . . . . . . . . . 23 2.3 Subsystem of representation . . . . . . . . . . . . . . . . . . . 25
3 Methods of calculi in
CicloWin
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3.1 Properties of CicloWin . . . . . . . . . . . . . . . . . . . . . . 26 3.2 The main algorithm of caluclation . . . . . . . . . . . . . . . 27
II Thermodynamics cycles
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4 The reverse cycle
4.1 Ideal cycle . . . . . . . . . . . . . . . . . 4.2 Coe cient of performance . . . . . . . . 4.3 Corresponding real cycles in ideal cycles 4.3.1 Overheating of the vapor . . . . 2
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4.3.2 Subcooling of the liquid . . . . . . . . . . . . . . . . . 31 4.3.3 COP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5 The combined cycle 5.1 5.2 5.3 5.4 5.5 5.6
Introduction . . . . . . . . . . . . . . Principles . . . . . . . . . . . . . . . Design principle . . . . . . . . . . . . E ciency of CCGT plants . . . . . . Supplementary ring . . . . . . . . . Fuel for combined cycle power plants
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III Thermodynamics models of the new components 6 The requirements of 6.1 6.2 6.3 6.4
CicloWin
Requirements of reverse cycle . Requirements of combined cycle Improvement of CicloWin . . . Updates to realize . . . . . . .
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7.1 R407C . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Description of the uids . . . . . . . . 7.1.2 Physical Properties . . . . . . . . . . . 7.1.3 Equations . . . . . . . . . . . . . . . . 7.2 R123 . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Description of the uids . . . . . . . . 7.2.2 Physical Properties . . . . . . . . . . . 7.2.3 Equations . . . . . . . . . . . . . . . . 7.3 Enthalpy and entropy departure calculations . 7.4 Air . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Description of the uids . . . . . . . . 7.4.2 Equations . . . . . . . . . . . . . . . .
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8 Properties of news systems
8.1 The evaporator . . . . . . . . . . 8.1.1 Descriptions of the system 8.1.2 Equations . . . . . . . . . 8.1.3 Schema . . . . . . . . . . 8.2 The compressor . . . . . . . . . .
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7 Properties of new uids
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8.3
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8.2.1 Descriptions of the system 8.2.2 Equations . . . . . . . . . 8.2.3 Schema . . . . . . . . . . The air compressor . . . . . . . . 8.3.1 Descriptions of the system 8.3.2 Equations . . . . . . . . . 8.3.3 Schema . . . . . . . . . . The combustion chamber . . . . 8.4.1 Descriptions of the system 8.4.2 Equations . . . . . . . . . 8.4.3 Schema . . . . . . . . . . The gas turbine . . . . . . . . . . 8.5.1 Descriptions of the system 8.5.2 Equations . . . . . . . . . 8.5.3 Schema . . . . . . . . . . The HRSC . . . . . . . . . . . . 8.6.1 Descriptions of the system 8.6.2 Equations . . . . . . . . . 8.6.3 Schema . . . . . . . . . .
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IV Source code of the new components
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9 Source code for news uids
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9.1 News classes derived from TEstado . 9.1.1 The private declaration . . . . 9.1.2 The public declaration . . . . . 9.2 The Newton's method . . . . . . . . . 9.3 Source code for the R407C . . . . . . . 9.4 Source code for the R123 . . . . . . . . 9.5 Source code for the air . . . . . . . . . 9.6 Adaptation of CicloWin for new uids
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10 Source code for news systems 78 10.1 Classes derived from TSistema . . . . . . . . . . . . . . . . . 78 10.2 10.3 10.4 10.5 10.6
Source code for the evaporator . . . . . Source code for the air compressor . . . Source code for the chamber combustion Source code for the gas turbine . . . . . Source code for the HRSG . . . . . . . . 4
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11 Source code for the improvements
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V Examples of CicloWin 4.0
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12 Example of simulation of reversed cycle
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13 Example of simulation of combined cycle
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Conclusion
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11.1 Table of valor . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 11.2 Presentation of the results . . . . . . . . . . . . . . . . . . . . 84 11.3 Choice of the uid in the graph panel . . . . . . . . . . . . . . 84
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Nomenclature Cp Cv df = 1/vf dg = 1/vg hf hf g hg H pf pg Q sf sg S t T vf vg V W
heat capacity at constant pressure in kJ/(kg) (K) heat capacity at constant volume in kJ/(kg) (K) density of saturated liquid in kg/m3 density of saturated vapor in kg/m3 enthalpy of saturated liquid in kJ/kg enthalpy of vaporization in kJ/kg enthalpy of saturated vapor in kJ/kg enthalpy of superheated vapor in kJ/kg pressure of saturated liquid (bubble point) in kPa (abs) pressure of saturated vapor (dew point) in kPa (abs) thermic power in watt entropy of saturated liquid in kJ/(kg) (K) entropy of saturated vapor in kJ/(kg) (K) entropy of superheated vapor in kJ/(kg) (K) temperature in °C temperature in K + °C + 273.15 volume of saturated liquid in m3/kg volume of saturated vapor in m3/kg volume of superheated vapor in m3/kg mechanical power in watt
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Introduction The goals of this thesis are to improve the software of thermodynamic's cycle simulation CicloWin developed inside the Education Unit of Thermodynamics and Phisicochemistry (Energy Engineering and Fluids Mechanics Dpt. of the Escuela Tecníca Superior de Ingenieros Industriales) of the University Polytechnics of Madrid (UPM). More especially, the work consist to introduce all the new elements to provide to the program the ability to simulate inversed cycles and reverse cycles.
History of CicloWin Indeed, since 1999, a few students have worked, on the supervisory control of the Professor D. Fernando Herrero Acebes, on the development of a software which be able to construct graphically and simulate easily the thermodynamics cycles. The advantage of CicloWin is his interface graphics. It is actually easy to draw a thermodynamic cycle in dropping and dragging system and next, link them. Once the cycle constructed, we can introduce the minimum of data necessary (system and state of the cycle) for resolve the cycle and obtain all the thermodynamics variables as well as the power of every system, the output, and so on. We can see directly the layout of the cycle on the thermodynamics diagrams the most used (T − s and h − s). At the same time to this principal goal, the second objective is that the program keep a structure the most opened possible to facilitate the extension of his code in the future. The complexity of the analysis of thermodynamics cycles can be extend enormously and the reader need to know, for the moment, the model used is fairly simple.
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Graphics simulation of thermodynamics cycle The reason to realize this project is due to the big matter of the thermodynamics cycle. This cycles are very complicated, only in the most simple cases, we can analyze this kind of cycle with facilities without additional help. Furthermore, the parametric analysis of cycle is a task witch require a lot of calculi. An other advantage of the numeric simulation is the existent of equation of state for the most commons uids searched out by experimental data. Indeed, read a thermodynamics graphics to nd the relation between the variable of state is very inaccuracy. With the development of equation of state for a large range of uids, we make a model of the thermodynamics properties with an acceptable curacy and the rapidity of calculi of the computers make the all very quickly. In the rst step of the establishment of a model for thermodynamics cycles, we need to give details on the precision of this model.In this project, we don't pretend to give a simulation with the level of the big commercial thermodynamics program (like ThermoFlow ) witch needs years of work of a dozen or so engineer. For the beginning, we have worked on a program more didactic witch allows analyze and compare dierent basics cycles.
Structure of the project Our part of work in this project consist to give to CicloWin the possibility to simulate inversed cycle and combined cycle. Function of this, we structure the project in four big parts. The rst step of this paper will consist to present shortly the structure of CicloWin. How is organized this program, what is his design and internal structure ? The second step consists in a presentation of the inversed cycle and combined cycle. In the this thermodynamics part, we will introduce the concepts required for the good comprehension of this type of cycle. En function of the dierent components met in the rst part and the already existent system of CicloWin, we will establish in a third part a list of new component and work uids required for the good development of this 8
improvements. The model of each component and work uids will be developed. The fourth part called Source code of the new components present a part of the source code that we added or modi ed to attend our principal objective. For a correct understanding of the source code, a few basics knowledges of C++ are required. After this, we will illustrate this modi cations across two examples of simulation of reverse and combined cycles with the help of CicloWin. For conclusion, we will present a shortly summary of the realized work, a prospect improvements of CicloWin and his possible use and future.
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Part I
CicloWin
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Chapter 1
Presentation of CicloWin 1.1 Introduction In this part, we will explain all the development of the simulator of thermodynamics cycles CicloWin. It begins with the rst stage, the presentation of the analysis of the abilities of this software. In the next chapter, we will expose the design of the program, where the internal structure of the program is established. His content contains principally problems of software engineering. Along the chapter the language UML is used largely for the graphic description of the dierent level of architecture. The diagrams of classes have special importance, which are the ones that describe the framework of classes of the program, both in the content and in their interrelations.
1.2 Case of Use A case of use is an interaction between a user and the system, the rst one hopes to obtain a functionality of the second one. The user is named a "actor". These interactions are represented, in UML, using diagrams of cases of use. For the simulator that we have developed, the following general cases of use have been established (diagram 1.1). To design a cycle: the user has a space where he draws the cycle
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Figure 1.1:
Case of Use of
CicloWin
graphically, establishing the systems that compose it and his interconnections, as well as the properties of the same ones and the values of the variables of the states. To load and to save a cycle: on having chosen an option of the menu,
the information of the cycle is saved in a le on hard disc, which can then be loaded from another option of the principal menu.
To solve the cycle: as soon as the design of the cycle was realized, an
option of the menu will allow to calculate the cycle from the introduced information.
To represent the cycle: after the calculation of the cycle the same one
will be represented in the diagrams T-s and h-s.
To analyze the eect of the change of parameters: the user will be able
to change information of the cycle to calculate it again and to will be able to compare the dierence in the results.
To obtain a summary of the cycle: the user can see in any moment the
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principal results of the cycle like they are total e ciency, potency, etc.
1.2.1 Design a cycle After this general description, some cases of use are more important and we insist more on this concretes ones. The case of use related to the design of the cycle is illustrated in the diagram 1.2.
Figure 1.2:
Case of Use of design a cycle
To design a cycle includes a series of cases of use: To introduce systems in the cycle. The user chooses a system in panel
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bar where we retrieve all the systems of CicloWin and pulsates on the space of design. A graphic representation of the system appears indicating his points of entry and of exit. To connect systems. On having dragged the exit of a system on the
entry of other, there is created a state that represents the point of connection. The state appears as a graphic object on the space of design.
To edit properties of the systems. On having pulsated on a system,
there is opened a window that shows the properties of this system and allows to modify them.
To edit properties of the states. On having pulsated on a state, a
window is opened. This window shows the values of the variables of this state and allows to modify them. The values of the variables dier in colors as be of design (introduced by the user), of calculation (result of calculation of the program) or they have just been modi ed by the user but they have not been validated yet.
To see the variables of the states. With the window's design a table
appears with the values of the variables for each of the states. It is possible to choose the units in which it is wanted that the values appear.
To move systems and states. The systems and the states are graphic
objects that can be placed where it is wanted dragging them with the mouse inside the space of design.
To move connections between systems.
These connections can be planned by freedom displacing a few intermediate points of the connection with the mouse inside the space of design.
1.2.2 Represent a cycle The case of use to represent a cycle is illustrated in the diagram 1.3. To represent a cycle includes several cases of use: To choose the type of diagram. Selecting an option in a list it is chosen
between showing the diagram T-s or the h-s. 14
Figure 1.3:
Case of Use of represent a cycle
To extend zones of the diagram. Dragging the mouse on the diagram
a rectangle is planned on the same one. After the mouse releases the chosen part is represented in the diagram only.
To undo zoom. A button allows to return to the state previous to the
last zoom, or to represent the nished diagram without extending.
To know the value of the variables in a point. To move the cursor
on the diagram shows simultaneously the value of the variables of the diagram (T and s or h and s) corresponding to the point on which the cursor is.
1.3 Model of the domain This program consists of a simulator of thermodynamic cycles. What do we understand for a thermodynamic cycle? Open systems interconnected between them by currents of uids are a cycle. Every system will have a series of entrances and exits, and there him will be applicable a series of equations. On the other hand, every uid will be in a certain thermodynamic state represented by the value of a few thermodynamic variables. Also, these variables are related between them across a series of equations of state, which will be dierent depending on the type of substance.
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The previous textual description of a thermodynamic cycle, although it helps to center the ideas, is still too vague to be able to codify exactly in a program. We will represent it in a diagram of classes UML (Uni ed Modeling Language) to specify it better ( gure 1.4.
Figure 1.4:
Diagram of classes UML of
CicloWin
We see that a cycle consists of several systems and uids. If cycle does not exist, neither systems nor uids exist. Every uid is related to two systems: it goes out of one and enters other. For the case of opened cycles, one of the systems will be the environment: it will have own that enter or go out of the environment. Every uid has a certain state, and every state corresponds only to one uid. It turns out then that uid and state can join in one only entity that groups them. A uid can be a water, air, freon or others. 16
Every state contains several variables. These variables can be the temperature, pressure, enthalpy... Every variable, also, is related to others across an equation. On the other hand, every cycle has several systems. These systems have entrances and exits, each of which is a uid. Dierent systems can be turbines, pumps, boiler and so on. With the diagram (1.4) we can simulate a thermodynamic cycle. It is not necessarily the scheme of classes that will be used in the program, but it is closer to it that a simple textual description and also it does not present ambiguities.
1.4 Not functional requirements It is named a not functional requirements a properties of the global system that is not tied to a concrete utility of the same one. For the pretender the following ones are established: The program will work under Windows 9x/NT/XP; The les where the cycles are stored will be les of crude text; The representation of the diagrams will do in real-time, from the equa-
tions of state of the uids;
He must allow to design several cycles simultaneously to be able to
compare them;
The structure of the program must be opened, so that in the future
new systems could be developed.
1.5 Choice of architecture It stays, nally, to choose the architecture on the one that thee program will be developed. It is a decision in certain arbitrary form, which depends on external factors to the program. In this case one has decided to use Borland C++ Builder 5, for the following reasons: the language that it uses is C++, that it is OOP (Object-Oriented
Programming), allows a big exibility simultaneously of being very e cient. Since the program is going to have portions of code with intensive calculation (as it is the case of the equations of state), a rapid language is necessary in the calculation; 17
it facilitates enormously the design of the graphic interface, on having
been provided with visual designers and with a big bookstore of graphic classes;
The decision to use this architecture will determine the further design of the program, since it will be directed to make use to the maximum of the resources with which it provides us. Here we conclude the analysis of requisites of the program, and can go on to the presentation of the design of CicloWin.
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Chapter 2
Design of
CicloWin
Once the analysis of requirements was concluded we already know for what functionality we expect from the program. We describe now the design of the same one. In this stage we try to develop the framework of classes that are going to compose the program. For it we will use fundamentally the diagrams of classes in UML language. In the program we can distinguish three big subsystems: 1. The subsystem of calculation understands all the classes related to the architecture of the cycle (systems, states, relations between them) and the calculation of the same one. 2. The subsystem of interface understands all the classes that shape the user's interface: windows, systems's pictures, graphic components, etc. 3. The subsystem of representation contains the classes related to the thermodynamic diagrams of the cycle. The subsystem of calculation depends on the subsystem of interface, while the systems and states have a graphic representation in the space of design of the cycle. The subsystem of interface, in turn, depends on the subsystem of calculation because he is the one that allows to construct the architecture of the cycle. Finally, the subsystem of representation depends on the two previous ones for it takes the information of the cycle to draw a diagram in the user's interface. We will describe longer the classes that compose each of the subsystems.
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Figure 2.1:
Principals subsystems of
CicloWin
2.1 Subsystem of calculation We represent in the diagram of classes ( gure 2.2) the basic structure of this package. If we compare this diagram with the correspondent to the model of domain ( gure 1.4) we will see that it has similarities, but it is not exactly equal. This is something normal, the model of domain shapes the real entities and does not correspond exactly with the implementation in software. A cycle consists in a sef of systems and states. These are two abstract classes: the rst one represents the open systems and the second one the uids that interconnect the systems. Like each of these uids can be only in a thermodynamic state, we have created a class called TEstado. This class contains both the variables of state, and the equations of state. These equations are virtual functions that will implement the derivative classes. This way, there exists a class TAgua that is already not abstract since it implements the equations of state of the water. It is the same process for the other uids. The method ExpandirDatos() is important: if the su cient variables of state exist, he calculates the remaining ones from them using the equations of state. All the systems work about the same way : they all have a series of entrances and exits, and a method Calcular() that will calculate the system 20
Figure 2.2:
Subsystems of calculation
according to these entrances and exits. This method is virtual, it will be implemented by the derivative classes from TSistema. Only the concrete systems, like TTurbina, knows how to be calculated. The most important method of TCiclo is Calcular(). This method calls all the states to expand his information and the systems so that they are calculated. It does not guarantee the nished calculation of the cycle, but if it obtains the biggest number of possible results according to the available information. Like it is possible to see in the diagram 2.2, a state contains a series of variables TTemperatura, TPresion, etc. What sound these variables? We 21
can see it in diagram 2.3
Figure 2.3:
Diagram UML of a state in
CicloWin
A thermodynamic variable, at rst view, is only a value. A long double might have been used for her. Nevertheless, a thermodynamic variable is more than a numerical value. First, it is possible that it has an unknown value (as it is when it has not been calculated yet). It has neither a few limits of validity (there are no absolute negative temperatures, nor e ciency higher than one). It has also a few units, and a dierent value according to the select units. Finally, it can be a user's variable (the user introduces her as fact in the cycle) or not (it is a result of calculation). The class TNumero is introduced to represent to a number that it can have or not an assigned value, and that has a few minimal and maximum limits. The operators'surcharge is used so that one endures as nearby as possible a double (to allow allocation and comparison). The class TVariable derives from the previous one, including the support 22
for units. Every variable can be assigned in a few certain units and be read of equal form. This class is abstract, it cannot instantiate. For it a class stems for every concrete variable (temperature, pressure,...) that implements his own units and limits of validity.
2.2 Subsystem of interface In this package there gather together the classes related to the graphic interface of the program. There are especially important the classes related to the graphic edition of the cycle. The diagram UML 2.5 represents to these classes. TMadre is the principal window of the program. It is a window MDI (multiple-document interface) on which the windows of the cycles are opened: TProblema. This class contains other three: TDiagrama, TGra ca and TResultados.
The diagram treats with special detail the design of the diagram. The class TDiagrama is the one in charge of the graphic edition of the cycle. Like it is logical, it is related to TCiclo since it is the one that he adds, it erases and links systems and states. The graphic components of the diagram derive from the class TComponente. This class is in charge of showing in the diagram an icon representative of the component and of handling all the events related to the dragging of the components on the diagram. It forces, also, that all the components de ne the method MuestraPropiedades(), called when the user wants to show the properties of this component (for a system or a state). From TComponente it derives TRedimensionable, who adds to the previous one the management of the graphic resize property of the component. Directly from this one they already derive the systems, which also contain a series of active points, TPuntoActivo. These are the points wherefrom they go out and bring in the connections between systems. Another class derives from TComponente, it'is TCurvaEditable. This class is a graphic element that represents a connection between two systems. It contains a TPuntoActivo of beginning and other of end, and a series of intermediate points (TPuntoCurva ). These intermediate points determine 23
Figure 2.4:
Diagram UML of
CicloWin
the points for which the connection happens, and can be dragged by the diagram. Thus it is achieved the edition of the tracing of the curve.
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From TCurvaEditable it derives TEstado, a state is an interconnection between two systems. TGra ca is the class responsible for the representation of the thermodynamic diagram of the cycle. Finally, TResultados will contain a summary of the cycle (rate, potency, etc).
2.3 Subsystem of representation In this package there gather together the classes related to the graphic representation of the cycle. It consists of only one class TGra co.
Figure 2.5:
Diagram UML of the subsystem of representation ofCicloWin
The class TGra ca, of interface, contains a TGra co, which is the diagram in strict sense. This thermodynamic diagram shows on a TBitmap of the interface, and allows to do zoom and to undo it. It is related to TCiclo, since it represents in the diagram the corresponding states.
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Chapter 3
Methods of calculi in CicloWin It would be too long to explain all the classes and the complete stucture of CicloWin. It's not the purpose of this project to present the whole programming code but in this chapter, we will present a resume of the method of calculi to resolve thermodynamics cycles with CicloWin. For more explanations, we recommend the lecture of [1] and [4]. A thermodynamic cycle consists of a set of systems and thermodynamic states related between in such a way that the position of every element remains established inside this cycle.
3.1 Properties of
CicloWin
The Cycle has been implanted in the simulator of the following way: There is a list of states and a list of systems (ordinated by order of
creation), each one of which it is possible to cover (to test in a loop for) pointing at every element of the list separately with Sistema(k) and Estado(k) from k=0 up to k= number of elements of the list;
There are functions that deal with reserving dynamic memory to create
or to erase so much systems and states and to add them or to eliminate them of the lists of the cycle;
Every cycle will have in general a system focused or activated, that
it will be possible to locate thanks to the function SistemaActivo(), which return a pointer on the active system present in the cycle; 26
Every cycle will have an associate environment characterized by a ex-
terior pressure and temperature, and a dialog window which allows his modi cations;
Also they are useful and suitable utilities that return the number of
systems of certain type that exist in the cycle, and a function that he returns if really they exist or not systems of certain type;
Calcular() the cycle, of returning to the information initially introduced by the user with DeshacerCalcular(), and the test Calculado(), which veri es that nothing stays for calcu-
There are the routines of
lating;
Macromagnitudes associated with the cycle can be obtained so im-
portant as they are the Potentia() in terminals of the alternator, the RendimientoEnergetico(), the RendimientoExergetico(), the De-
struccionExergetica () of the whole cycle,...
3.2 The main algorithm of caluclation The main algorithm of calculation of a thermodynamic cycle consists basically of covering a loop in which in every step there are returned all the systems associated with the cycle and, referring sequentially to each of them, the following actions are carried out: Balance of Mass; Balance of Enthalpy; Expansion of data, this is, to obtain the rest of thermodynamic vari-
ables, if we had su cient information, from the equations of state of the uids;
Detection of inconsistencies, this is, to detect situations as that the
temperature to the exit of a boiler is minor that at the entrance or that the uid gains pressure to his step along a heat exchanger;
This loop repeats itself until to ful ll the condition of which the quantity of information relative to the cycle calculated at the end of the loop is not higher that the quantity of information before the beginning of the last loop.
27
Part II
Thermodynamics cycles
28
Chapter 4
The reverse cycle In the eld of energy, there are two bigs broads witch depend of the utility eect considered : the production of the driving force; the production of cool and the re-value of heat
In the second case, the whole of the used cycles may be quali ed of reverse (in opposition of motor cycle or direct).
4.1 Ideal cycle In every thermal machine, intervene two forms of energy : a thermal energy Q, then a noble energy witch take a mechanical form W . This two forms of energy are involved successively or simultaneously during thermodynamics transformations imposed to a cycled work uid. There is a lot of dierent cycles for the reverses cycles machines. For example, on the gure 4.1, we illustrate four con gurations of cycles with two sources. The Carnot machine work with 2 isotherms and 2 isentropics. The Stirling machine work like a reverse cycle with 2 isotherms and 2 isochores (v =Cte). The Ericsson machine work like a reverse cycle with 2 isotherms and 2 isobars (P =Cte). The Brayton-Joule machine work with 2 isentropics and 2 isobars (P =Cte)
29
Figure 4.1:
Exemples of reverses cycles with one source and one heat well
4.2 Coe cient of performance The quality of a ideal reverse cycle is approached by one analog notion to the notion of e ciency of the motor machine. In this case, we talk about the coe cient of performance (COP). The COP is obtained with the ratio of the thermal eect on the energetics expending required for the previous eect : COP =
usef ul thermal energy energetics expending
(4.1)
4.3 Corresponding real cycles in ideal cycles The analysis which follows is going to be centered on the machine of Carnot in 2 sources for illustration but exposed notions are transposable in quite other machine.
30
When refrigerant uid sudden a suite of transformations including changes of stage, it is always the passage of the liquid state in the vapor state (it occurs in a heat exchanger called evaporator), and the second one is the passage of the vapor state in the liquid state (it occurs in the heat exchanger called condenser). In each of both interchanges, they are in the presence of one blend diphasique. If they neglect the losses of pressure in interchanges and by assuming that cycled uid acts as a pure body, then transformation corresponding thermodynamics am isobaric and thermally insulated. However, it takes there place to point out that technical realization of a isentropic compression or expansion stays very problematic in diphasique or humid regime. It goes therefore introduce distortions in the cycle of Carnot. Then, realization in humid regime of a expansion with recovery of energy remain very di cult. Also, as it is uently used the relaxation of JouleThomson, without heat exchange nor job mechanics with the outside (expansion isenthalpic); it is translated by a deterioration of energy.
4.3.1 Overheating of the vapor For reasons of security of functioning, the supplied vapor of the compressor must be a dry vapor. So, it is necessary to introduce one superheating of the steam guaranteeing the absence of liquid droplets in entrance of the compressor. It is translated on the gure 4.2 by the existence of transformation 7←1. A superheating of the steam in the evaporator before aspiration remain costly in surface of exchange and also aect levels of temperature of refrigerant uids.
4.3.2 Subcooling of the liquid The isenthalpic expansion valve requires to be supplied by liquid for technical reasons. This sub-cooling can be made in dierent places; if it is made in the condensator, then there is increase of eect thermal of the sensitive heat taken from liquid.
31
4.3.3 COP Cycle represented on the gure 4.2 is a cycle of Rankine-Hirn. By considering cycled uid, they express COP then in function of dierence of enthalpy. So, for a heat pump: COPRank =
Figure 4.2:
h2 − h4 h2 − h1
(4.2)
Cycle of Rankine-Hirn with overheating
The de nition of the COP's can be a little dierent that the equation 4.2 in function of the used cycle but the main principle of the reversed cycle are already presented in this chapter.
32
Chapter 5
The combined cycle 5.1 Introduction Combined cycle is a term used when a power producing engine or plant employs more than one thermodynamic cycles. Heat engines are only able to use a portion of the energy their fuel generates (usually less than 30%). The remaining heat from combustion is generally wasted. Combining two or more "cycles" such as the Brayton cycle ( gure 5.3) and Rankine cycle ( gure 5.3) results in improved overall e ciency.
5.2 Principles In a combined cycle power plant (CCPP), or combined cycle gas turbine (CCGT) plant, a gas turbine generator generates electricity and the waste heat from the gas turbine is used to make steam to generate additional electricity via a steam turbine; this last step enhances the e ciency of electricity generation. Most new gas power plants are of this type. In a thermal power plant, high-temperature heat as input to the power plant, usually from burning of fuel, is converted to electricity as one of the outputs and low-temperature heat as another output. As a rule, in order to achieve high e ciency, the temperature of the input heat should be as high as possible and the temperature of the output heat as low as possible (see Carnot ef ciency). This is achieved by combining the Rankine (steam) and Brayton (gas) thermodynamic cycles.
33
5.3 Design principle In a steam power plant water is the working medium. In this case high pressure has to be employed which leads to bulky components. High cost of special alloys that endure high temperature limit practical steam temperature to 655°C. For compact gas turbines this limitation does not apply and gas cycle ring temperature in excess of 1,200°C is practicable. In the combined cycle plant the thermodynamic working cycle is operated between the high ring temperature and the ambient temperature at which low temperature waste heat can be disposed.
Figure 5.1:
Brayton cycle (gas turbine
In a gas turbine set, composed primarily of a compressor, burner and the gas turbine proper, the input temperature to the gas turbine is relatively high (some 900°C to 1,350°C) but the output temperature of the ue gas is also relatively high (some 450°C to 650°C). The output heat of the gas turbine ue gas is utilized to generate steam by passing it through a heat recovery steam generator (HRSG) and therefore is used as input heat to the steam turbine power plant. Flue gas temperature is su cient for production of steam in the second, steam cycle (Rankine cycle), with live steam temperature in the range of 420°C to 580°C. 34
Figure 5.2:
Rankine cycle (steam turbine
The lowest temperature of the steam cycle depends on the ambient temperature and the method of waste heat disposal, either by direct cooling by lake, river or sea water, or using cooling towers. Therefore, by combining both processes, high input temperatures and low output temperatures can be achieved and the power plant e ciency can be increased. The output heat of the gas turbine ue gas is utilized to generate steam by passing it through a heat recovery steam generator (HRSG) and therefore is used as input heat to the steam turbine power plant. We can observe on the gure 5.3, the heat transfer between the two thermodynamics cycles.
5.4 E ciency of CCGT plants The thermal e ciency of a combined cycle power plant is normally in terms of the net power output of the plant as a percentage of the lower heating value (LHV) or net calori c value (NCV) of the fuel. In the case of generating only electricity, power plant e ciencies of up to 59% can be achieved. A diagram of this type of installation is presented on the gure 5.4.
35
Figure 5.3:
Simple CCGP diagram
Figure 5.4:
Simple CCGP diagram
5.5 Supplementary ring The HRSG can be designed with supplementary ring of fuel after the gas turbine in order to increase the quantity or temperature of the steam generated. Without supplementary ring, the e ciency of the combined cycle 36
power plant is higher, however supplementary ring allows the plant to respond to uctuations of electrical load. Supplementary burners are also called duct burners. Supplementary ring is possible because turbine exhaust gas ( ue gas) contains considerable fraction of unused oxygen. Due to temperature limitation at the gas turbine inlet, excess air, above the optimal stoichiometric ratio is used. Often in gas turbine designs part of the compressed air ow bypasses the burner and is used for cooling of the turbine blades.
5.6 Fuel for combined cycle power plants Typical combined cycle plants are powered by natural gas, although other sources of fuel can be used such as fuel oil or synthetic gas. Supplementary fuel may be natural gas, fuel oil or coal.
37
Part III
Thermodynamics models of the new components
38
Chapter 6
The requirements of CicloWin In this chapter, we will de ne all the news components or news uids which are necessary to give the abilities to simulate the reverse and combined cycles in CicloWin.
6.1 Requirements of reverse cycle As we have seen in the chapter 4, the four basics components of a reverse cycle are the evaporator, the pump, the condenser and the lamination valve. In the current version of CicloWin, we can already use the pump (only for liquid water), the condenser and the lamination valve. Therefore, we need to add a evaporator and adapt the pump to vapor. Furthermore, we know that this type of cycle works with refrigerant uids. CicloWin contain only the thermodynamics models of water. We have to add the EOS of new refrigerant uids (R407c, R123). We need also a new method for the presentation of the results. Indeed, we need to present the COP and the cool (or heat) power. This news functions will be included in the result's window.
6.2 Requirements of combined cycle First of all, we need to program the thermodynamics properties of the air (not yet include in CicloWin ) which is used in the gas turbine and in the 39
heat recovery steam generator (HRSC). Always in the Brayton cycle, a model of air compressor, a combustion chamber and gas turbine are necessary to complete the gas cycle. Evidently, we have to add the HRSC. All the others systems of the Rankine cycle already exist. The calculation of the e ciency and the presentation of the results will be modify for the combined cycle application.
6.3 Improvement of CicloWin In the same time of this component's additions, we will modify several functions of CicloWin like the results presentations, the exception's alerts, the component's links ( uids compatibly), the code of diagram's drawing, and so on. A resume of all this updates that we added at CicloWin are presented directly in the chapter 11.
6.4 Updates to realize The table 6.1 resume all the new systems and uids that we need to incorporate in CicloWin to be able to modelize simple reverse and combined cycles. Reverse cycle Combined Cycle Systems Evaporator Air compressor Compressor Combustion chamber Gas turbine HSRC Fluids Refrigerants Air Table 6.1:
Compulsory news components to added
40
Chapter 7
Properties of new uids The rst step in the development of the software CicloWin consist in insert new uids in the database, more especially, refrigerant uids. In fact, as we have showed in the chapter ?? on the reverse cycle, we need to use refrigerant uids with special properties (low vapor saturation). In this chapter, we will see how we have made to modelize the thermodynamics properties of the refrigerant.
7.1 R407C 7.1.1 Description of the uids The most popular refrigerant was the chlorodi uoromethane (R-22 or HCFC22). In fact this uids has been used as a refrigerant in various refrigeration, industrial cooling, air conditioning, and heating applications for over ve decades. The low ozone depletion potential of R-22 compared to CFC-11 and CFC-12 and its excellent refrigerant properties have helped facilitate the transition away from CFCs. However, R-22 will be phased out in the rst quarter of the 21st century. In preparation for this phaseout, the chemical industry has developed new refrigerants more safe for the environment. One of this new uids is the R407C (ASHRAE designation: R-407C(23/25/52)) environmentally acceptable alternatives to R-22. For this reason, we choose to modelize this uids with a view to participate to the acceleration of the phaseout of use of R22.
41
Suva® 407C is a non-ozone-depleting blend of three hydro uorocarbon (HFC) refrigerants. It exhibits performance characteristics similar to R-22.
7.1.2 Physical Properties The table 7.1 present the physical properties of the R407c refrigerant. Chemical Formula
CH2F2/CHF2CF3/CH2FCF3 (23/25/52% by weight) Molecular Weight 86.20 Boiling point at one atmosphere -43.56 Critical Temperature Tc 86.74 (359.89 K) Critical Pressure Pc 4619.10 kPa (abs) Critical Density Dc 527.30 kg/m3 Critical Volume Vc 0.00190 m3/kg Table 7.1:
Physical Properties of the
R407C
7.1.3 Equations Equation of State : PRSV An equation of state (EOS) is a model for the P-V-T behavior of a uid. Generalized equations of state assume the compressibility factor is a function of the reduced temperature and pressure, and sometimes a third parameter. These equations are valid for both the vapor and the liquid state. Many equations of state have been proposed in the literature with either an empirical, semi empirical or theoretical basis to improve the modelisation. One of this is due to Peng and Robinson (1976). The form of the PR EOS is : P =
RT a(T ) − (V − b) V (V + b) + b(V − b)
(7.1)
Stryjek and Vera (1986) proposed a modi ed temperature functionality
a(T ) for the Peng-Robinson equation of state to extend the range of applica-
bility to polar components. It's become the PRSV EOS.
42
The advantage of the PRSV equation is that not only does it have the potential to more accurately predict the phase behavior of hydrocarbon systems, particularly for systems composed of dissimilar components, but it can also be extended to handle non-ideal systems with accuracies that rival traditional activity coe cient models. The only compromise is increased computational time and the additional interaction parameter that is required for the equation. So, the PRSC EOS of the R407c is de ned by the next expression: P =
RT a − 2 (V − b) V + 2bV − b2
(7.2)
where P is in kPa, T is in K, V is in m3/mole, and R = 0.008314 kJ/(mole)(K). The constants a and b are calculated as follows: a=
3 X 3 X
xi xj aij
b=
i=1 j=1
3 X
xi bi
(7.3)
i=1
where xi =mole fraction of component i, aij is a coe cient function of the temperature and bi is a constant for each component of the refrigerant. This PRSV EOS and whole equations of this section are issue of [3] where we can nd all the constant coe cients that are not expressed in the next paragraphs.
Vapor Pressure logn Psat = A +
B + C logn T + DT 2 T
(7.4)
where Psat is in kPa, T in Kelvin and the factor A,B,C and D are dierent if we calculate the bubble point or the dew point.
Density of the Saturated Liquid df = a0 + a1 z + a2 z 2 + a3 z 3 + a4 z 4 Dc
where z = (1 − T /Tc ) 3 − t0 . 1
43
(7.5)
7.2 R123 7.2.1 Description of the uids DuPont produces HCFC-123 (DuPontSuva©123) refrigerant as a replacement for CFC-11 in chillers and is providing this new refrigerant to chiller manufacturers for use in new and existing chillers.
7.2.2 Physical Properties The table 7.2 present the physical properties of the R123 refrigerant. Chemical Formula CHCl2 CF3 Molecular Weight 152.93 Boiling point at one atmosphere 27.85°C Critical Temperature Tc 183.68 (359.89 K) Critical Pressure Pc 3668.0 kPa (abs) Critical Density Dc 550.0 kg/m3 Critical Volume Vc 0.00182 m3/kg Table 7.2:
Physical Properties of the R123
7.2.3 Equations Equation of State : MBWR The Modi ed Benedict-Webb-Rubin (MBWR) equation of state was used to calculate the tables of thermodynamic properties. It was chosen as the preferred equation of state because it provided the most accurate t of the thermodynamic data over the entire range of temperatures and pressures presented in these tables. The MBWR EOS take the following expression : 9 15 X X an an 2 P = + exp(−Vc /V ) Vn V 2n−17 n=1
(7.6)
n=10
where the an coe cients depend of the temperature and Vc is the critical vomume. T is in K, P is in kPa, V is in m3/mole and R = 8.314471 J/mole.K.
44
This MBWR EOS and whole equations of this section are issue of [2] where we can nd all the coe cient's expressions that are not expressed in this section.
Vapor Pressure The vapor pressure equation used in this model correspond to the standard type for this kind of thermodynamics properties. log10 Psat = A +
B (F − T ) + Clog10 T + DT + E log10 (F − T ) T T
(7.7)
where T and P are the temperature in Kelvin and the pressure in kPa. The others coe cients are constants (see [2]).
Density of the saturated liquid Always in the article [2], we come across the equation for the model of the density of the saturated liquid which is used for the determination of the liquid density. df = Af + Bf (1 − Tr ) 3 + Cf (1 − Tr ) 3 + Df (1 − Tr ) + Ef (1 − Tr ) 3 (7.8) 1
2
4
where df is the density in kg/m3 and Tr is equal to T /Tc (Tc is the critical temperature). All the others coe cients are constants.
7.3 Enthalpy and entropy departure calculations For the two refrigerants uids, the enthalpy and entropy calculations may are performed rigorously using the following exact thermodynamic relations: Z V h − hid 1 ∂P =Z −1+ T( )V − P dV RT RT ∞ ∂T Z V s − sid P 1 ∂P 1 = ln(Z) − ln( 0 ) + ( )V − dV RT P R ∂T V ∞
(7.9) (7.10)
where Z is the compression factor (P v/RT ) and P 0 the reference pression. hid and sid represent respectively the ideal gas enthalpy and entropy basis. 45
These two equations are applied to each EOS of the two news uids (R407c and R123) to obtain the enthalpy and entropy. The whole development of the calculi process is presented in the chapter 7.
7.4 Air 7.4.1 Description of the uids A thermodynamic property formulation for standard dry air based upon available experimental P − ρ − T , heat capacity and vapor-liquid equilibrium data are provided in the article [5]. This formulation is valid for liquid, vapor, and supercritical air at temperatures from the solidi cation point on the bubble-point curve (59.75 K) to 2000 K at pressures up to 2000 MPa but in the case of conventional thermodynamics cycles, we use only air upon a vapor phase. Therefore, we have restricted the model only to vapor air.
7.4.2 Equations Equation of State The equation of state for air used in the article [5] is explicit in the non dimensional Helmholtz energy : α(δ, τ ) =
a(ρ, T ) = α0 (δ, τ ) + αr (δ, τ ) RT
(7.11)
where α0 is the ideal-gas contribution to the Helmholtz energy given in the previous section, αr is the residual contribution to the Helmholtz energy, δ = ρ/ρj is the reduced density, τ = Tj /T is the reciprocal reduced temperature, ρj is th density at the maxcondentherm, and Tj is the temperature at the maxcondentherm. The ideal gas contribution to the Helmholtz energy of air is given by α0 = ln δ +
5 X
Ni τ i−4 + N6 τ 1.5 + N7 ln τ + N8
i=1
ln [1 − exp(−N11 τ )] + N9 ln [1 − exp(−N12 τ )] +
(7.12)
N10 ln [2/3 + exp(−N13 τ )]
46
and the residual Helmholtz energy contribution to the equation of state is given by r
α (δ, τ ) =
10 X k=1
ik jk
Nk δ τ
+
19 X
Nk δ ik τ jk exp(−δ lk )
(7.13)
k=11
The coe cients Nk , ik , jk , and lk of the equation of state are given in Table 13 of [5].
Calculation of thermodynamic properties The functions used for calculating pressure, enthalpy and entropy are given as r ∂α P = ρRT 1 + δ ∂δ τ 0 r r h ∂α ∂α ∂α =τ + +δ +1 RT ∂τ δ ∂τ δ ∂δ τ r 0 ∂α s ∂α + − α0 − αr =τ R ∂τ δ ∂τ δ
47
(7.14) (7.15) (7.16)
Chapter 8
Properties of news systems The news components of reverse and combined are the object of this project, and these are composed of certain open systems joined by means of tubes represented by thermodynamic states.
8.1 The evaporator 8.1.1 Descriptions of the system An evaporator is only a heat exchanger that use the latent heat of vaporisation of a primary uid to do a transfer of energy from a uid secondary to the primary one. The work temperature of the evaporator is xed by the pressure inside the evaporator. For his de nition, we are sure that, at the exhaust of the evaporator, the primary uid will be, without overheating, characterised by a pressure equal to the work pressure, the temperature equal to the vaporisation temperature and the quality of the vapor will be 1.
8.1.2 Equations If the work pressure is xed to pev , with this type of inlet thermodynamics properties, without overheating, it is easy to calculate the exhaust properties.
48
(8.1) (8.2) (8.3)
Tout = Tsat (pev ) Xout = 1
where the function Tsat (pev ) depends of the uids and it express by the equations of the chapter 7. We make the assumption that the evaporator have only one entrance and one exit. By consequently the mass balance is very simple : (8.4)
min = mout
8.1.3 Schema The schematic representation of the evaporator in CicloWin is illustrated on the gure 8.1
RS
Figure 8.1:
Schematic representation of the evaporator
8.2 The compressor 8.2.1 Descriptions of the system In the case of reverse cycle, the compressor will compress the refrigerant uid in gas fase. Indeed, it'es very important to assure that the uid is in a complete gas state before the entrance in the compressor to avoid to damage the compressor with uids particles. !!! volumetric compressor The compressor is characterized by its relation of compression and by its isotropic e ciency. If we introduce this two variable, we can nd the others variables. 49
8.2.2 Equations
hout
pout = pin .rp (hout iso − hin ) = hin − ηc Tout = f (pout , hout ) sout = f (pout , hout ) xout = 1 xin = 1 mout = min
(8.5) (8.6) (8.7) (8.8) (8.9) (8.10) (8.11)
where rp and ηc are respectively the relation of compression and isentropic e ciency of the compressor.
8.2.3 Schema The schematic representation of the refrigerant compressor in CicloWin is illustrated on the gure 8.2
Figure 8.2:
Schematic representation of the volumetric compressor
8.3 The air compressor 8.3.1 Descriptions of the system An air compressor is a machine that increases the pressure of a gas or vapor (typically air), or mixture of gases and vapors. The pressure of the uid is increased by reducing the uid speci c volume during passage of the uid through the compressor. For it, the air compressor must communicate work to the uid. In a Gas Turbine Power Plant, this work is communicated by the movement of a turbine across which a gas expands (gas turbine). Dynamic-type compressors 50
use rotating vanes or impellers to impart velocity and pressure to the uid. It is this type of compressor witch are used in gas turbine power plant. In the machines they take place irreversibilities or energy degradations essentially of two types: thermal type, in a heat exchange for temperature dierences; mechanical type, for friction.
The compressor suers of mechanics irreversibilities, which forces, for his suitable description, to the de nition of the so-called " isentropic e ciency", that represents the relation between the potency that the compressor consumes and the one that it would consume if energy degradation did not take place. The increase of pressure is de ned by the relation of compression p2 /p1 and an isentropic e ciency.
8.3.2 Equations
hout
pout =in .rp (hout iso − hin ) = hin − ηc Tout = f (pout , hout ) sout = f (pout , hout ) mout = min
(8.12) (8.13) (8.14) (8.15) (8.16)
With the simple model we use for describe the opened systems, the set of equations for air compressor and for volumetric compressor are the same (we only don't have the equation for X because we work always with air gas). But it's important to make a dierence between the both for a further improvement.
8.3.3 Schema The schematic representation of the air compressor in CicloWin is illustrated on the gure 8.3 51
Figure 8.3:
Schematic representation of the air compressor
8.4 The combustion chamber 8.4.1 Descriptions of the system The combustion chamber receives high pressure air from the compressor. A steady stream of fuel is injected into air via a ring of fuel injectors. The fuel usually used is kerosene, jet fuel, propane or natural gas. The mixture can be burnt at temperatures of up to 2000 degrees Kelvin. This temperature is way above the melting point for many metals which is obviously a problem. Special cooling methods are used to ensure that the structure can withstand the high temperatures. The biggest problem is keeping a ame burning continuously with very high velocity air passing over it. The solution is to use a ame holder which is a hollow, perforated piece of metal. The air enters through the perforations which allow it to burn continuously without being blown out.
8.4.2 Equations pout = pin − ∆p(8.17) f uel mout = mair in + min (8.18)
mout hout =
f uel f uel f uel f uel air air mair in (hin − h25deg ) + min (hin − h25deg ) + min P CI
ηcc
(8.19)
Tout = T (pout , hout )(8.20) sout = f (pout , hout )(8.21)
where ∆p and ηcc are respectively the pressure drop and the e ciency of f uel the combustion chamber. hair 25deg and h25deg are the enthalpy of air and fuel at 25°C because the PCI is de ned at this temperature.
52
8.4.3 Schema The schematic representation of the combustion chamber in CicloWin is illustrated on the gure 8.4
Figure 8.4:
Schematic representation of the combustion chamber
8.5 The gas turbine 8.5.1 Descriptions of the system The high temperature, high velocity gas passes through a set of turbine blades. Energy is removed from the gas. Each turbine has one or more stages of alternate rotating and stationary aerofoil section blades. The blades are attached to a shaft which is also attached to the compressor. The blades extract energy from the hot, expanding air to help drive the compressor and for use in power generation. Exhaust gases are usually vented through an exhaust pipe. Sometimes heat is extracted from the exhaust gases to preheat the air before entering the combustion chamber or for some other purpose. The gas owing through the turbine is at a temperature high enough which could melt the blades so various cooling techniques have had to be implemented. Most turbine blades are made of nickel based alloys which often have low thermal conductivity coatings over their surface. The design of the blades can help to reduce the surface temperature greatly. Many turbine blades use water or air cooling over the surface of the blades to help reduce surface temperatures.
53
8.5.2 Equations hout
iso
= h(pout , sin )
hout = hin − ηT (hin − hout
iso )
Tout = T (pout , hout ) sout = s(pout , hout ) mout = min
(8.22) (8.23) (8.24) (8.25) (8.26) (8.27)
where pout is gived in the problem and ηT is the isentropic e ciency of the gas turbine.
8.5.3 Schema The schematic representation of the gas turbine in CicloWin is illustrated on the gure 8.5
Figure 8.5:
Schematic representation of the gas turbine
8.6 The HRSC 8.6.1 Descriptions of the system A HRSG (Heat Recovery Steam Generator) is a heat exchanger producing steam with boiler water present on the shell-side of the heat exchanger. The boiler water absorbs heat from a hot uid passing through the tubes. The hot uid is often a high temperature gas resulting from combustion or other chemical reaction. Moderate temperature gases, liquids, and slurries are also used.
8.6.2 Equations Depends of the stucture of the HRSC!!! 54
8.6.3 Schema The schematic representation of the HRSC in CicloWin is illustrated on the gure 8.6
Figure 8.6:
Schematic representation of the HRSC
55
Part IV
Source code of the new components
56
Chapter 9
Source code for news uids This chapter is dedicated to the detailed description of the algorithms applied in the most complex methods. It emphasize the equations of state, especially those obtained on having made an implied variable explicit in another equation. The program departs from only a few equations of state obtained of experimental information, obtaining the others applying numerical algorithms to the previous ones. These equations are the nucleus of calculation of the program, being evaluated thousands of times during the resolution and representation of the cycles.
9.1 News classes derived from TEstado As we have seen and the chapter 2, the equation of state are included in the private part of the class called TEstado. On the gure 2.2, we can see the relation of this important class with the structure of CicloWin.
9.1.1 The private declaration Before this project, there was only one uid, water, and for this the equation of state was de ned in "
