Typical combustion chamber surrounding systems
1. Introduction
In 2013, the Comisión Federal de Electricidad (CFE Some acronyms are written after their name or phrase spelling in Spanish. A full definition of the used acronyms in this chapter is listed in Section 8.
Between others, like modernisation, an important factor of economical and performance results of a power plant, including those based on gas turbines, is the training of their operators. It is not easy to quantify the impact of training but there exists some feedback from plant’s directors about improvement in operation skills. A classical study [2] demonstrated the importance of training power plants operators.
The Simulation and Advanced Training Systems Department (GSACS) is part of the Electrical Research Institute (IIE) and it is formed by a specialised group in training simulators that designs and implements tools and methodologies to support the simulators development, exploiting and maintenance.
Modelling the process of power plants for training is not an easy task and involves multidisciplinary work. In this chapter a general review of training simulator modelling is addressed with special emphasis on the combustion process.
The main attribute of a combustion model for training is to reproduce the behaviour of the phenomenon in order to report the variables in the control station of a power plant operator. The measurement of NOx present in the exhaust gases is a very important variable. The major part of the sulphur, NOx, and dust emissions from stationary installations result from fuel combustion to produce heat and power [3]. How to simulate these variables in a real time training simulator in a relatively easy approach is the goal of this chapter.
2. Mathematical modelling previous works
Depending on the application, a phenomenon may be represented by a mathematical model formulated by different techniques. Some examples of models applications are: design, analysis, optimisation, education, training, general tendencies,
Some authors detail the general formulation of the combustion process considering the different conditions where the phenomenon is achieved. The model must be solved together with continuity, momentum and transport equations but any possible numerical method is not mentioned [4].
CFD methods model the phenomenon based on Navier–Stokes equations considering a finite volume partitioned normally into millions of cells considering the detailed geometry of the simulated space. Interaction with the solid boundaries is taken in account. A 3-D visualisation is normally achieved but accuracy depends on the detailed models used and, in the case of combustion, serious errors would arise. In fact, for example, it has been claimed that the design and development of combustors, until recent past, was more an art than science [5]. Although the author applies a CFD by using prePDF combustion model (it took nearly 2000 h of CPU time in a 4 node sun server with main memory of 128 GB) he states that validation must be attempted in future studies.
Studies consider different phenomenology like supersonic combustion [6], chilling of the combustor liner by film cooling [7], micro-turbine engine with annular combustion chamber design [8], comparison of several turbulence models [9], swirling air flow [10,11], and many others. In spite of the promise of having good results, this approach is far enough to be used in real time applications.
Models with less spatial details are intended for design. A “simplified” methodology has been developed where different fuels and inlet conditions were studied for steady state conditions [12]. Direct fuel injection and diffusion flames, together with numerical methods like Newton-Raphson, LU Factorization and Lagrange Polynomials, are used for the calculations. Diesel, ethanol and methanol fuels were chosen for the numerical study. Finally, a computer code sequentially calculates the main geometry of the combustor. Design modes are not suitable for real time simulators.
A model was presented to study the influence of different air cooling systems validated against real plant data [13]. Gas composition was not included and an ideal gas model was considered. The input data were the air cooling system configuration and the ambient conditions. The combustion was simulated just increasing the gas temperature as a function of the mass flowrate and the fuel high heating value.
A model for desktop for excel was elaborated for a standard air Brayton cycle [14]. A total of five components and the combustion reaction stoichiometric with possibilities of excess of oxygen were considered. The output temperatures of the turbine were simulated as a second degree equation in function of the enthalpy instead using well known thermodynamic properties. The inputs variables are efficiencies, some pressure drops, temperatures,
In other approach, the ideal gas assumption was adopted even when other aspects were modelled in detail like the flow through the equipment, the heat transfer phenomena and basing the process on a temperature-entropy diagram [15]. In this case the gas composition and the combustion process were ignored (considering only an increase of the temperature of gas) and the model, designed for optimisation, runs around the full load point.
A model based on Simulink was used to analyse the dynamical behaviour of an industrial electrical power system [16]. An ideal gas approach was used. The model was validated against real data but not details of the combustor model are mentioned.
The most important feature of a combustion model for training is the capacity of reproducing the behaviour of, at least, the variables reported in the control station of a power plant operator in such a way he cannot distinguish between the real plant and the simulator. Nowadays, the measurement of NOx present in the exhaust gases is a very important factor to consider in an operator training program. However, the authors did not find a single paper where this theme is developed for real time training simulation.
Combustion models used specifically for training simulators are those created by companies that develop real time simulators, so the information is proprietary and the formulation is not available [17], in [18] an excellent explanation of the uses of training simulators is explained but presents not a single equation of the process model.
For a real time simulator application, the variables affecting the operation of a plant, including the combustion process, may be taken in account. The model is not developed to design a combustion chamber or burners, but to reproduce the plant operation data with the capacity to predict the plant behaviour during the transients occurred during all the normal and emergency operational scenarios. The real time execution characteristics required by a training simulator is accomplished by the present model.
3. Power plant simulation for training
High-performance computing help engineers and scientists apply modelling and simulation. One of the most useful applications is the use of software to make environments for training in different technological areas. In a power plant, for example, it is important to train personnel in risk and unusual actions; a tool which has been widely tested is training simulators.
The IIE has developed several power plant simulators for Thermal-Electric Units, Nuclear, Geo-Thermal, Dual (Coal and liquid fuel), Gas Turbine, Combined Cycle, VU-60 Boiler and simulators with new web technologies.
The simulators must accomplish the ANSI norm [19] and are tested in the whole operation range; including malfunctions and transients according the operation procedures designed by the clients who are the final users of the simulator.
A simulator is designed to recreate a particular control room where operators may practise the plant procedures. An instructor coordinates and guides the simulator sessions (practical lessons).
3.1. Typical software configuration
The simulation environment is called MAS a trade mark software of the IIE; designed as a general tool to support simulators. MAS is both: a development tool and a man-machine interface for instructors; basically consists of three independent and coordinated tasks:
The
The instructor console has icons for fast access; also has the possibility to modify the simulation velocity of the simulator to be increased up to ten times or to be decreased up to 10 times respect to real time. Another function is to simulate step by step, it means to run the whole simulation cycle on the minimum unit time in which simulator models are executed; it is equivalent to 0.1 s.
Most of first level instructor console menus are shown in Figure 2.
3.1.1. Control menu
The main functions of this menu are
3.1.2. Initial conditions menu
An initial condition (IC) contains the necessary information to start-up a simulation session in any predefined plant condition (from cold condition up to nominal operation point). In the simulator are four IC options, namely P
3.1.3. Instruction functions menu
There are three set of functions in this menu:
3.1.4. Information functions menu
These functions are:
3.1.5. Miscellaneous functions menu
This menu is formed by
3.2. Hardware configuration
The standard hardware configuration consists in a PC network and several monitors for the Instructor and operation consoles; normally the instructor console is installed in a different room than the operation console separated by a glass wall; in the first area the simulation sessions are initiated and guided by the instruction consoles and in the second area the hardware looks as a replica of the real plant control stations and it is here where the operator is trained. Figure 3 shows a typical hardware configuration of a simulator.
An example of an IPD where the operator may monitor the whole process and act on the plant is presented in Figure 4. In this case is the main screen of a gas turbine power plant with the summary of the plant conditions.
4. Modelling of combustion surrounding systems
The models of any simulated plant were divided in two groups: process and control models.
4.1.1. Process models
Traditional methods of modelling and simulation considered approaches often using empirical relations and approximated procedures in model development. The models of a modern training simulator are a set of algebraic and differential equations obtained from the application of basic principles (energy, momentum, mass balances and constitutive equations). The models are designed to work under a full range of operational conditions, from 0% to 100% of load including all possible transients that may exist during operational manoeuvres, including malfunctions and changes of external parameters, always replicating the real plant comportment. The simulator was developed applying a methodology developed by the IIE [20].
Process models may be divided in electrical, mechanical, and fluid phenomena. All are important but in this chapter only a brief summary on thermal fluid modelling is revised.
Changes in the state of a fluid are not instantaneous. When a system is perturbed to change the steady state conditions of a system (a fluid in this case) takes a minimal time. Time of getting a new steady state is a function of the perturbation magnitude and the inertia of the system (which normally depends on the mass of the system).
In the IIE, the fluid mechanics phenomena are modelled with algebraic equations. A generic model that automatically solves the mass and moment balances and constitutive equations for pressure drops in valves, pipelines and other fittings like elbows, pumps, compressors, fans, turbines,
A flows and pressures network is constituted of nodes and streams. A node is a point where two or more streams converge in or divert from. A stream transports a fluid and has fittings that arise or drop pressure through them. If not mass accumulation is assumed and a simplified expression relating mass flowrate and pressure drop is used, an equation system may be stated with a continuity equation for each node and a flow-pressure drop expression for each stream:
The equations are solved simultaneously and the flowrate of each stream and the pressure of each node are then known. Initial values for these variables have to be established as initial value for iterations.
There exist other nodes not being part of the flows and pressures networks. Normally, they are considered to accumulate mass (like a steam header or a pressurised air tank), so, a proper mass balance should be stated, one equation for each stream component
Commonly, elements simulated with differential equations, like Equation (3), are denominated capacitive nodes. The variables associated with derivatives are “state variables” and their values define the condition of a system. These variables have an initial condition to start any simulation session.
For these nodes normally the pressure is also a state variable. The more simple case is when the node is assumed to behave like an ideal gas:
In this case,
Also enthalpy is a variable associated with a derivative:
More complex cases exist by considering other phenomena like phases’ equilibrium, separation process, chemical reactions, evaporation and condensation situations,
Numerical methods to solve algebraic and differential equations are employed. For algebraic equation the most used method is Newton-Raphson either, with analytical or numerical derivatives calculations. For differential equations, the Euler method is enough for training simulator models. As an example of this method, let’s considered the integration of the pressure of any node:
Normally, the integration step
Capacitive nodes intrinsically have an inertia affecting the derivative calculation.
Algebraic equations, by definition, are assumed to reach instantaneously its final value (an instant, numerically, is a time period with a value of
that may be reported in an operation consoles. Note that if
4.1. Control models
The control models acquire and process the actions realised by the operator in the control room by actions on the operation consoles. These models generate,
For the development of the plant control models, generally two approaches are followed:
To develop in a graphic environment a copy of the control diagrams provided by the client or control developer. Once the diagrams have been drawn, this environment is embedding into the simulator to be sequenced and executed in real time. These diagrams are drawn in the format defined by the Scientific Apparatus Makers Association (SAMA).
To translate the control algorithms as well as the IPD of the operation consoles, obtained from the control station of the real plant. The control is an exact copy of the functioning control system (both, logical and analogical), including PID constants.
4.2. Combustion chamber surrounding systems
By using the proper equations as that presented in section 4.1, the systems that feed or extract flow or energy from a combustion chamber may be simulated.
A couple of examples of systems around the combustion chamber are shown in Table 1. There are included both, process and control models.
5. Combustion modelling
5.1. General approach
For the so called thermal NOx,
NOx increases strongly with fuel-to-air ratio or with firing temperature.
NOx increases exponentially with combustor inlet air temperature.
NOx increases with the square root of the combustor inlet pressure.
NOx increases with increasing residence time in the flame zone.
NOx decreases exponentially with increasing water or steam injection or increasing specific humidity.
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Air System: | IGV Control Compressor Air Heater |
Air System: | Induced Fan Draft Forced Fan Draft Air/Vapour Pre-Heater Ljunström Heater BMS Control |
Fuel Systems: | Gas Combustion Control |
Fuel Systems: | Gas Liquid Fuels Atomising Steam BMS Control |
Water Injection System | Soot Blowers System | ||
Gas Turbine | Convective Heat Zone |
The formation of NOx due to oxidation of organically bound nitrogen in the fuel (fuel-bound nitrogen), called “organic NOx” is important only for crude or residual oils and it is not included in this model.
A generic model for the combustion process was developed by the IIE. The stated objective was to calculate flame temperature and composition of the burned gases including the simulated heat transfer phenomena. It is possible simulate a mixture up to twenty components, all displayed in Table 2.
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1 | N2 | Nitrogen | 11 | C6H14 | n-Hexane |
2 | O2 | Oxygen | 12 | C7H16 | n-Heptane |
3 | H2S | Hydrogen Sulphide | 13 | C8H18 | n-Octane |
4 | CO2 | Carbon Dioxide | 14 | C9H20 | n-Nonane |
5 | CH4 | Methane | 15 | C10H22 | n-Decane |
6 | C2H6 | Ethane | 16 | H2O | Water |
7 | C3H8 | Propane | 17 | CO | Carbon Monoxide |
8 | C4H10 | n-Butane | 18 | NO | Nitrogen Monoxide |
9 | iC4H10 | i-Butane | 19 | NO2 | Nitrogen Dioxide |
10 | C5H12 | n-Pentane | 20 | SO2 | Sulphur Dioxide |
Thermodynamic properties were calculated using cubic state and corresponding states equations for non-polar substances. The application range is for low pressure up to 80 bars.
Cubic equations properties are in next general form [23]:
where
where
For the solution of any of the equations for a gas mixture, the Newton-Raphson method is used.
For the water, thermodynamic properties data [24] were adjusted as a function of pressure and enthalpy or temperature. Functions were adjusted by least squares method. The application range is between 0.1 and 4520
5.2. Definition of efficiencies
To calculate the products of the reaction as a function of the inlet reactants moles, the stoichiometric coefficients are needed. However, in the approach proposed by the authors, a couple of efficiencies are defined to be used in these calculations.
Total combustion efficiency
Partial combustion efficiency
A special case is the production of
In this approach, by now, the value of efficiencies is proposed by the programmer in order to fit the results of the reference plant.
5.3. Simple example
In order to explain the model used for the combustion in a clear way, a simple reaction will be contemplated.
Let’s assume the ideal case where
Coefficients of Equations (11) represent moles, no mass. Up to now, the stoichiometric is not included.
In general, the
Considering the stoichiometric coefficients and the efficiencies of each reaction, by knowing the reactants feed streams, it is possible to calculate the moles reactions (considering also the possible reactant that appears also as a product, for example the
Let’s assume next arbitrary definition of efficiencies just for this example (efficiency values for production of
Considering stoichiometric of reactions:
Tables 3, 4, and 5 present three different cases for this example. The difference is the inlet moles of air feed to the combustion chamber. The inlet mole flowrates is a function of the oxygen excess (
In Tables 3, 4, and 5 the way to verify that calculated mole flowrates of products are correct is that sum of moles of elements must be equal in reactants and products.
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2.5885 |
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0.5000 |
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9.6142 |
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5.1769 |
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9.5700 |
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5.1769 |
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1.0000 |
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19.2285 |
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0.0000 |
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19.2285 |
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9.5700 |
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1.0000 |
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0.0885 |
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1.0000 |
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2.0000 |
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4.0000 |
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0.0000 |
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4.0000 |
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1.0000 | |||||||
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0.0000 | |||||||
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0.0000 | |||||||
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2.0000 | |||||||
Total | 13.2027 | 29.4054 | Total | 10.7268 | 29.4054 | ||||
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1.3460 |
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0.0572 |
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4.9994 |
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2.6920 |
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4.9925 |
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2.6920 |
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1.0000 |
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9.9988 |
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0.0000 |
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9.9988 |
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0.0138 |
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1.0000 |
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0.0138 |
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1.0000 |
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1.2750 |
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4.0000 |
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0.0000 |
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4.0000 |
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0.3000 | |||||||
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0.2500 | |||||||
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0.4500 | |||||||
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1.5000 | |||||||
Total | 7.3454 | 17.6908 | Total | 7.5635 | 17.6908 | ||||
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0.4659 |
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0.4659 |
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1.7306 |
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0.9318 |
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1.7306 |
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0.9318 |
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1.0000 |
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3.4611 |
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0.0000 |
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3.4611 |
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0.0000 |
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1.0000 |
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0.0000 |
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1.0000 |
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0.0000 |
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4.0000 |
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0.0000 |
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4.0000 |
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0.0000 | |||||||
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1.0000 | |||||||
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0.0000 | |||||||
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0.0000 | |||||||
Total | 3.1965 | 4.0000 | Total | 3.1965 | 4.0000 | ||||
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5.4. Full combustion reactions
The whole model considers up to twenty reactants. Full components possible reaction may be stated as:
The reactions that have an associated efficiency are shown in Table 6:
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Considering basically the same general assumptions that those presented in the simple example explained above, including the linear interpolation between the efficiency definitions as a function of
In order to avoid imbalances in the reactions, next restriction must be addressed at any moment:
Upper limit
If efficiencies values are known, moles flow of products may be calculated as a function of moles flow of reactants. In next equations, input data (
A proper sequence must be addressed in the calculations. Components present in more than one reaction must be calculated at the end of sequence. Total flow of products in more than one reaction is the results of the sum of the products of all reactions.
The efficiencies could be substituted for any function, according the available plant data. A very important factor not used in this work is the actual flame temperature.
Although no kinetics is taken into account, this approach considering these original two efficiencies, allows simulate the behaviour of a combustion chamber for training purposes (whatever, a combustor of a gas turbine or the furnace zone of a boiler).
So, the combustion chamber simulation should be able to predict the amount of heat generated by the reactions, the products temperature leaving and the products flowrates and compositions.
The transferred heat toward the combustion chamber surroundings depends on the desired design. For example, for a combustor, the designer wants the heat not to be transferred in order to have more potential work to be done in the gas turbine (of course a compromise with the NOx production must be considered). For a furnace, the heat transfer depends on the boiler type (radiant, convective, once-through,
In any case the heat transference phenomenon it is not treated in detail in this chapter but a couple of general expressions are used. A representative surrounding walls temperature
5.5. Calculation sequence
With the mass flowrate of each reactant, their mass composition and the molecular weight of the components, mass flowrates are converted into mole flowrates and mass compositions into mole compositions.
With the inlet temperature of each reactant (water, air and gas fuel), using the thermodynamic properties, the enthalpy of each inlet stream is calculated. And the total reactants enthalpy may be known:
According the present reactants they may be predicted the possible combustion products.
Reactants enthalpy (
Flame temperature
Theoretical O2 flowrate
Oxygen excess
Efficiencies are calculated with Equations (15) and restrictions shown in Equation (16). These variables are a function of
Oxygen excess is calculated as:
If
Actual products flowrates and composition are calculated with Equations (17).
Formation heat and enthalpies at 298 K and
Sensible heat of reactants
Radiant and convective heat flowing to surrounding metal walls are calculated using known heat transfer coefficients that depends on the geometry and exposed area (these coefficients correlations and calculations are beyond the subject of this chapter):
The process is complete if the sum of the heat flowrates is balanced
If
The conceptual combustor chamber model is presented in Figure 5. The reaction node represents the reactions procedure explained above to get reaction products and flame temperature. The capacitive node is solved with Equations (4) and (5). Combustion chamber temperature and density are calculated with the proper cubic equations properties.
Although there are not mentioned in the above calculations, there are taken into account possible malfunctions or events as trip of burners, sudden turning off of flame, low efficiency of combustion (simulated as a factor less than one on the combustion heat), change in fuel composition,
6. Application examples
More than a validation of the model, in this section one application example is presented. The basis for this example is a model installed in a simulator of a gas turbine power plant developed for CFE by the GSACS [26]. The reference plant produces nominally 150 MW. For this particular application of the combustion model, a linear function was used to represent each efficiency as shown in Equations (15), based only on the oxygen excess. Several real plant data were available and some of them were included in the graphics presented in this section.
The natural gas fuel and air composition of the presented test are shown in Table 7.
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78.51 | 20.88 | - | - | - | - | - | - | - | - | 0.01 |
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1.69 | - | 0.05 | 88.81 | 8.89 | 0.45 | 0.04 | 0.02 | 0.02 | 0.03 | - |
Selected results are presented here simulating an automatic start-up of the gas turbine power plant (Figures 6 to 9).
Figure 6 presents, as a reference, the simulated gas turbine speed and the generated power. Five seconds after the simulation is initiated, the start button is press and the automatic start-up procedure begins.
Figure 7 has the simulated mole flowrates of gas fuel and air feed to the combustor.
In Figure 8, real exhaust gases temperature and the result of simulation are compared. Simulation results of oxygen excess and CO2 concentration are also included in Figure 8.
In Figure 9, simulated exhaust concentration of oxygen and nitrogen oxides are compared against real plant data.
No
All results are enough to satisfy the ANSI norm for fossil power plants simulators [19]. However, it clear, according Figure 9, that efficiencies should have an extra factor besides the oxygen excess to behave no that smooth as the curve presented by simulation results. This factor is an open issue to be studied.
No plant data are presently available for emission concentration during other transient, including malfunctions, but the qualitative simulation results are acceptable for training purposes.
7. Conclusion
7.1. Remarks
From the literature review, it may be concluded that few work on simple handled combustion models for training purposes has been reported. This work intends to cover the particular needs of the GSACS. A generic model of such a combustion process designed to work in any operators’ training simulator has been presented.
Validation of the model has been intrinsically demonstrated with the inclusion of the model in a gas turbine and a combined cycle power plants simulators for operators’ training. In the proper date, CENAC endorsed and accepted as correct the results of the tests in accordance with the testing acceptance procedures and the ANSI norm.
Some others off-line examples have been presented with the objective to explain the model principles and potential.
7.2. Future work
The combustion model is established and it is a relatively easy task to add new components to the possible set of reactions. Presence of other combustion sub-products such as free radicals or carbon should be studied and eventually considered.
There were mentioned different factors affecting the efficiency of reactions but not yet studied or included as part of the calculations like burner’s tilt, ball fire position, gases recirculation, turbulent flow, bad mixing of reactants, level of pressure, kinetics,
An automatized procedure should be devised to avoid the main withdrawal of this model, the manual adjustment of efficiencies. This process should include factors as oxygen excess, the
8. Nomenclature
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f- formation or flame |
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ANSI- American National Standards Institute | IGV- Inlet Guide Vane |
BMS- Burner Management System | IIE- Electrical Research Institute |
CENAC- National Centre of Training Ixtapantongo | IPD - Interactive Process Diagrams |
CFD- Computational Fluid Dynamics | MAS- Simulation Environment |
CFE- Mexican National Utility Company | Oe- Oxygen Excess |
EGTEI- Expert Group on Techo-Economic Issues | PDF- Probability Density Function |
FLUPRE- Generic Model to Solve Flows and Pressures Networks | PID - Proportional-Integral-Derivative Controller |
GSACS- Simulation and Advanced Training Systems Department | SAMA- Scientific Apparatus Makers Association |
IC- Initial Condition |
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Notes
- Some acronyms are written after their name or phrase spelling in Spanish. A full definition of the used acronyms in this chapter is listed in Section 8.