structural modeling of a gas turbine system

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RESEARCH ARTICLE

Naresh YADAV, Irshad Ahmad KHAN, Sandeep GROVER

Structural modeling of a typical gas turbine system

Higher Education Press and Springer-Verlag Berlin Heidelberg 2011

Abstract This paper presents an approach for thestructural modeling and analysis of a typical gas turbinesystem. This approach has been applied to the systems andsubsystems, which are integral parts of a typical gas

turbine system. Since a gas turbine system performance ismeasured in terms of uid ow energy transformationsacross its various assemblies and subassemblies, the

performance of such subsystems affects the overallperformance of the gas turbine system. An attempt hasbeen made to correlate the associativity of such subsystemscontributing to overall gas turbine system functionalevaluation using graph theoretic approach. The character-istic equations at the system level as well as subsystemlevel have been developed on the basis of associativity ofvarious factors affecting their performance. A permanentfunction has been proposed for the functional model of agas turbine system, which further leads to selection,

identication and optimal evaluation of gas turbinesystems.

Keywords system modeling, gas turbine system evalua-tion, graph theoretic approach

1 Introduction

The use of gas turbines for power generation has increasedin recent years and is likely to continue to increase in thefuture. At present, the demand of gas turbine systems in

electrical power generation [1,2] accounts for more than50% of the world market of the thermal power plants. Gasturbine systems working on combined cycles [3] have

widely replaced the demand of steam power plants due totheir comparatively low capital cost, shorter constructionlead time and environmental statutory regulations. In a gasturbine system, the powering unit, consisting of a

compressor, a combustor and a turbine, is considered tobe the heart of the system. The performance of thepowering unit directly affects the entire performance of thepower generation system. Various support systems, like airatomizing system, lubrication system, water coolingsystem, and re protection system, etc., along with thecontrol system, help in governing of the best matching

performance of the powering unit in a typical powergeneration environment.

Many research studies have been carried out onanalyzing design and performance strategies related tothe subsystems of the thermal power plants. The quality ofthe thermal power plants [4] has been evaluated using

graph theoretic approach by identifying interactionsamong the critical but conicting parameters. Similarstudies have been conducted for the real time reliabilityindex evaluation [5] and real time commercial availabilityindex evaluation [6] for the steam power plants. Thesystem modeling [7] and the maintenance strategy [8] ofthe coal based power plants have also been performed inthe past using the subsystem studies. A remarkable

progress has been observed worldwide over the adapt-ability of gas turbine systems in power generation sector. Atypical gas turbine based power generation unit operatingin India has been shown in Fig. 1.

For the gas turbine systems, some of the researchershave worked for the improvement of the gas turbinesystem efciency [9] by considering optimization ofvarious parameters in the existing systems or the usageof advanced technologies related to power augmentation[10], NOxcontrol or the safety standards. Thermodynamic

performance aspects of such systems have been paidattention to signicantly. Thermodynamic analysis [11,12]in terms of energy and exergy analysis have been made to

predict the energy utilization in such systems. Performanceoptimization of such gas turbine systems [13] has beencalculated in terms of minimizing fuel consumptionsubject to constrained specic thrust and turbine blade

Received May 5, 2011; accepted June 30, 2011

Naresh YADAV (), Irshad Ahmad KHAN

Mechanical Engineering Department, Jamia Millia Islamia, New Delhi110025, IndiaE-mail: [email protected]

Sandeep GROVERMechanical Engineering Department, YMCA University of Science andTechnology, Faridabad 121006, India

Front. Energy 2012, 6(1): 5779DOI 10.1007/s11708-011-0164-8


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temperature conditions. Various advanced gas turbinecycles [14] have also been critically analyzed andcompared to take full advantage of thermodynamiccharacteristics of the systems. However, any study on thegas turbine system as a whole for its modeling and analysis

based on its subcomponent performance in terms ofinterdependencies of the attributes or performance vari-ables of these subsystems is still unknown.

The performance of the gas turbine systems is primarilyrepresented in terms of its structural conguration,functional relationships of its subcomponents and theresponse characteristics of its control system. Thestructural conguration can be represented in terms ofmechanical linkages, type of contacts, nature and materials

of assemblies. However, once a preliminary gas turbinesystem is designed to get the performance outcomes for theoperating cycles, attention is to be paid to the functionalrelationships of its various sub-components and theresponse of the control systems. The performance ofvarious subsystems is again based on its design features.The design of various support systems also contributessignicantly to achieving the desired performance out-comes i.e., thermal efciencies, reliability, operationalexibility, etc. of such gas turbine systems.

In the present paper, effort has been made to develop amathematical model for the typical gas turbine system interms of functional relationships of its various subsystemsfor the uid ow paths, i.e., air, fuel and the exhaust.Wherever necessary, the structural linkages and theresponse of the control systems have been considered foranalyzing the connectivity and the associativity of varioussubsystems. The manufactures of such systems likeGeneral Electric [15], Bharat Heavy Electricals Limitedin India1) and the control system developers likePetrotech2) have provided vast literature related to

performance and evolutions, manufacturing & assemblies

and the control features of such gas turbine systemsrespectively. The graph theory [16] has been used forunderstanding and analyzing the whole gas turbine systemup to its subcomponent or subsystem levels. Thistechnique has already been successfully applied todeveloping the mathematical model of other engineeringsystems like structures [17] and thermodynamic cycles[18], etc. in the past. This procedure permits the analysisand synthesis of such complex gas turbine systems withmuch ease as compared to other alternative techniquesavailable in literature.

2 System structure modeling of gas turbine

unit

For the system structure modeling of a gas turbine unit, thesystem is modeled on the basis of structural and functionalrelationships among various subsystems of the gas turbineassembly analyzed along the ow directions including air,liquid fuel ow, gas fuel ow and the combustion gasesincluding cooling and lubrication media. In order todevelop a mathematical model of the structural associa-tivity and functional relationships amongst turbine sub-systems, the gas turbine system is modeled into thefollowing fourteen subsystems:

1)Air inlet system;2)Powering unit system;3)Gas fuel system;4)Liquid fuel system;5)Starting and drive system;6)NOx abatement system;7)Water wash system;8)Enclosure and ventilation system;9)Fire protection system;10)Exhaust system;

Fig. 1 View of a gas turbine power station

1) BHEL-gas turbine support systems. ESCI Lecture Notes-Power and Energy Division, July 2009

2) Product bulletin 94091, 94023. http://www.petrotechinc.com/

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11)Lubrication system;12)Water cooling system;13)Atomizing air system;14)Control system.The above subsystems contribute directly or indirectly

the specic outcomes of the gas turbine system and are also

interdependent with varying degree on functional relation-ships.

2.1 S1: Air inlet subsystem

The air inlet subsystem, as illustrated in Fig. 2, comprisesthe following:

1) The ambient air enters the lter compartment and theninto the compressor inlet plenum through the duct, thesilencer, the lined elbow, and the transition piece.

2) The compressor discharge air with reverse ow ispumped into the lter compartment to clean the lter

segment intermittently.3) To enhance the power augmentation of the gas turbinesystem through inlet air cooling system, the chiller coilcools the incoming ltered air to reduce the air temperatureat the inlet to the compressor.

4) Since the gas turbine systems are to be designed forall weather conditions, anti-icing features are alsoincorporated. Anti-icing module containing inlet heatingmanifold in the lter compartment operated through acontrol valve is tted in the line of compressor discharge

fraction admitted to lter compartment of the inlet system.The split thrash screen in the system protects againstingestion of ice as well as thrash. Further, a pressure switchindicates an alarming situation to initiate for a controlledshut down when the inlet system pressure drop reaches a

predetermined level.

2.2 S2: Powering unit subsystem

The powering unit, the most important subsystem of thegas turbine system, consists of an integrated module ofcompressors, combustors and the turbine unit, whichcontributes to the energy transformation responsible fordesired outcomes of the gas turbine system. In the presentcase, a 17-stage axial ow compressor coupled with 3-stage axial ow gas turbine through annulus can combustassembly with provisions of power augmentation and NOxabatement systems. The powering unit subsystem, as

demonstrated in Fig. 3, comprises the following:1) The air from the inlet plenum enters the compressorthrough variable inlet guide vanes (IGVs) into the rststage wheel-dovetail-blade assembly mounted on forwardstub shaft.

2) After the compression of this air in 1st to 4th stagecascade (wheels tied with each other through tie bolts), afraction of the air is extracted through expansion port at 5thstage which is used for cooling of all bearing assemblies,seals, wheel assemblies in compressor including wheels

Fig. 2 Schematics of inlet subsystem

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and spacers in the gas turbine and reconnected to turbineexhaust main line through turbine exhaust frame to theexhaust diffuser of the gas turbine.

3) The compressed air at 5th stage is further directedthrough blade cascades between 5th and 10th stage of the

compressor. The stator blades are mounted in the aft casingand the rotor wheels are tie bolted. A fraction of the air isagain extracted from the expansion port at 11th stage forthe pulsation control during the start up and shut down ofthe gas turbine. No bleed is permitted from this expansion

Fig. 3 Schematics of power unit subsystem

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port during other time of the operation.4) The compressed air at the exit of 11th stage is further

admitted to 11th stage to 17th stage cascade assembly fromwhere a fraction is again extracted prior to 17th stagethrough expansion port, which is used to cool turbine 1stand 2nd stage buckets and rotor wheel spaces. This air is

again admitted to exhaust air through the exhaust diffuserof the gas turbine.

5) The compressor discharge air as extracted from thecombustion wrapper is fed into the ow sleeve in thecombustion chamber. A fraction of the same is also usedfor liquid fuel atomizing the air, the anti-icing mechanismin the inlet air system, reverse ow dust removal from thelters in the inlet air system, cooling 1st stage shrouds and2nd stage nozzle cooling of the gas turbine. Except for airfraction required for dust removal and anti-icing mechan-ism, the entire cooling air is again fed into the turbineexhaust through exhaust diffuser to the exhaust plenum of

the gas turbines.6) Steam from the steam injection subsystem is alsoadmitted to the compressed air discharge line for poweraugmentation and lowering of NOx emission. A fraction(i.e., almost 10%) of the compressed air enters the slottedcombustion liner cap zone, 20%30% in the cooling zoneof the combustion liner and the rest enter the dilution zoneto provide sufcient air condition for complete combus-tion.

7) In the combustion liner interaction takes place withatomized spray consisting of gaseous fuel and atomizedliquid fuel through duel fuel nozzle assembly and the

products of combustion with high heating value advances

through different zones of the combustion liner to theturbine inlet nozzle blades. The hot gases advance throughturbine cascades producing work output in terms ofrotational motion of the drive shaft, which can be furtherconverted to desirable form of work or power likeelectricity.

8) Other air fractions also join this main exhaust gas lineat the exit section of the turbine.

2.3 S3: Gas fuel subsystem

The gas fuel subsystem, as displayed in Fig. 4, comprises

the following:1) The gas fuel enters the speed ratio valve and advances

to gas fuel control valve through gas stop valve. Each valvehas its own specic function for gas fuel ow.

2) The gas fuel enters the gas fuel measuring devicewhere the pressure and temperatures of the gas fuel oware measured through the input/output unit of the control

panel subsystem and signals of the same are transferred tothe actuators from the control panel unit for necessarycorrective measures of the ow.

3) The measured gas fuel enters the gas fuel intakemanifold of the dual fuel nozzle assembly tted in thecombustion chamber outer casing assembly.

Fig. 4 Schematics of gas fuel subsystem

Fig. 5 Schematics of liquid fuel subsystem



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2.4 S4: Liquid fuel subsystem

The liquid fuel subsystem, as exhibited in Fig. 5, comprisesthe following:

1) The liquid fuel is fed to fuel the conditioning unitfrom the fuel pump in order to remove contamination in the

liquid fuel.2) The conditioned fuel is fed into the fuel pump through

a fuel stop valve. A bypass line is also provided across thefuel pump.

3) This fuel is further fed into the ow measuring device,which interacts with the input-output unit of the control

panel for corrective actions with respect to the referencevalues of pressure, temperature, pressure drop, temperaturedrop, etc.

4) The outlet fuel from the ow measuring device issupplied to selector valve assembly through a ow divider,so that each can combustor is supplied with equal fuel ow

for the uniform combustion in all the nozzles of thesecombustors.

5) The fuel received from the selector valve assembly isfed into the intake manifold of the dual fuel nozzleassembly tted in the combustion chamber.

A schematic of the liquid fuel subsystem is shown inFig. 5.

2.5 S5: Starting and drive subsystem

The starting and drive subsystem, as presented in Fig. 6,comprises the following:

1) The power source drives the torque converter with thehelp of the induction motor. The torque converter providesthe starting torque to the gas turbine drive unit through anaccessory box coupled with the over speed trip assemblyand jaw clutch.

2) The accessory gear box enhouses drive units fordriving gas turbine power drive unit shafts 1 and 2. Theshaft 2 in turn supports drive system integration for shafts

3A, 3B and 4 (both end driving) through gear meshing.These shafts integrate the drive unit assembly for driving

Fig. 6 Schematics of starting and drive subsystem

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fuel pump, atomizing air compressor, high pressurehydraulic pump and lubricating oil pump, respectively.

3) The AC power source also provide power for drivingall redundant devices like the vent fans, motors, mis-cellaneous pumps in the gas turbine circuit.

2.6 S6: NOx abatement subsystem

Although gas turbines are low emitters of exhaustpollutants, the stringent restrictions imposed by statutoryregulations have made it necessary to reduce the level ofcertain pollutants, especially NOx. The steam injectionsystem is considered for the NOx abatement techniqueadopted in the present system. The NOx subsystem, asdepicted in Fig. 7, comprises the following:

1) The steam generated in the heat recovery steamgenerator (HRSG) section mounted in the exhaustsubsystem is fed into the solenoid controlled pneumatically

controlled steam stop valve through a metered ori

ce andthe strainer.2) The stop valve opens to permit the steam injection

ow and closes to shut off the ow when the system is notoperating or is tripped.

3) The down stream side drain valves serve to heat thesteam prior to admission in the compressor discharge lineand the ow control valve regulates the ow of steam,

which receives the signal from the input-output unit of thecontrol subsystem.

4) This conditioned steam is fed into the compressordischarge line or directly into the primary combustion zoneof the combustion chamber.

2.7 S7: Water wash subsystem

The water wash subsystem comprises the following:1) The water washing subsystem involves the processes

like ringing the compressor with hot water, mixing thedetergent with water in the proper ratio and injecting it tothe compressor after initial rinsing, soaking and subse-quently rinsing the compressor.

2) During the water washing, the gas turbine is kept incranking mode.

3) The water is drained from the gas turbine systemthrough drain ports and the exhaust plenum.

A schematic of the water wash subsystem is shown inFig. 8.

2.8 S8: Enclosure and ventilation subsystem

The enclosure and ventilation subsystem, as shown inFig. 9, comprises the following:

1) Three separate enclosures namely accessory compart-

Fig. 7 Schematics of NOx abatement (steam injection) subsystem Fig. 8 Schematics of water wash subsystem



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ment, gas turbine unit compartment and the load gearcompartment have provisions of ambient air inlet as well as

ltered air inlet and its venting.2) The vent fans mounted on each compartment sucks

the air from the air inlet windows of the compartment andvents them through the air out vent sections.

3) These vent fans exhibit the redundancy in thesubsystem and are run by using separate power sourcesand ensure the minimum number of air changes andventilation in the subsystem control volume.

4) Fuel leakage vapours from the liquid fuel subsystemand gas fuel subsystem are also fed to the exhaust by thesevent fans.

2.9 S9: Fire protection subsystem

The re protection subsystem, as displayed in Fig. 10,comprises the following:

1) The temperature rise detectors send the signals to theunit control panel, which further actuates the control valvesto release the CO2 in the accessory compartment, gasturbine compartment and load gear compartment.

2) The CO2gas ow is controlled and supplied from theCO2 bottle bank by separating pipelines for ooding aswell as extended discharge to each of the three compart-ments.

3) Minimum CO2 ow is also maintained in the com-partments forre extinguishing purpose during operation.

2.10 S10: Exhaust subsystem

The exhaust subsystem, as described in Fig. 11, comprisesthe following:

1) The exhaust gases as received from the turbineexhaust diffuse to the exhaust plenum of the gas turbine

unit.2) The further ow of these exhaust gases are

controlled by using guillotine damper or the diverterdamper as either these gases are ew away to thestack directly through the control or diverter damper orare fed into the HRSG unit through the guillotinedamper.

3) In the HRSG unit, the heat energy of the exhaustgases is utilized for producing steam from the waterreceived from the steam power cycle through indirectheating process.

4) The steam is fed to the steam turbine unit, where

the heat energy of these exhaust gases is utilized forproducing power to run the generator. A part of thissteam is also fed into the compressor inlet for poweraugmentation and limiting NOx in the gas turbine unit.

5) These exhaust gases, after releasing their energy intothe water, are allowed to y off through the duct unit toopen atmosphere.

2.11 S11: Lubrication subsystem

The lubrication subsystem, as presented in Fig. 12,comprises the following:

1) The main lube oil pump driven by the accessory shaft

4 and an auxiliary lube oil pump driven by an AC motorand an emergency lube oil pump driven by DC motorregulate the ow of lube oil through lube oil lters from thelube oil reservoir to all the bearing, seals, gear meshes inthe gas turbine circuit.

2) The pressure and temperature measuring devicecontrols the ow of lube oil through the control panelresponse.

3) After completing the circuit, the lube oil is drainedback to the lube oil reservoir sufciently large for the lubeoil to retain its lube properties during the ow.

2.12 S12: Water cooling subsystem

The water cooling subsystem, as illustrated in Fig. 13,comprises the following:

1) The water from the water source is conditionedthrough a ltering and deionising unit.

2) This conditioned water is circulated through thecoolers, especially lube coolers and the atomizing aircooler controlled using three way bypass valves.

3) The cooling water is further cooled by eitheran open system cooling tower or an industrial-typewater-to-air type heat exchanger operating in a closedloop.

Fig. 9 Schematics of enclosure and ventilation subsystem

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2.13 S13: Atomizing air subsystem

The atomizing air subsystem, as demonstrated in Fig. 14,comprises the following:

1) The high pressure air received from the compressordischarge is fed into a pre-cooler, i.e., heat exchanger,where it is cooled.

2) The cooled air is further boosted to higher pressure in

Fig. 10 Schematics ofre protection subsystem

Fig. 11 Schematics of exhaust subsystem



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the main atomizing air compressor.The booster air compressor coupled in the suction of the

main atomizing compressor supplies adequate pressure

during start up when main atomizing compressor speed isinsufcient to boost up the air pressure.

3) Sufcient number of drain points is provided alongwith isolation valves to allow condensed water to drain out.

4) The atomized air is supplied to fuel nozzles to breakup the fuel into small droplets to facilitate efcientcombustion.

2.14 S14: Control subsystem

The control subsystem, as given in Fig. 15, comprises thefollowing:

1) The signals received from the ow measuring devices

through the input/output control panel are fed into thecommon data processor.

2) The common data processor interacts with the

interface data processor to get the manual input and printoutput if required.

3) The signal/information from the common dataprocessor is transmitted to all the control processors(high level of redundancy) for voting. The control

processor also sends signals to back up display in case ofemergency stops or operating conditions.

4) The control processor shares the information with theprotective processors (high level of redundancy) throughsensor inputs for the voted value of signals.

5) The control processor is hardwired connected with thetrip card for protective action actuation.

Based on the structural and functional relationships of

Fig. 12 Schematics of lubrication subsystem

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above mentioned subsystems contributing to the functionaloutput of the system, a typical gas turbine system can berepresented in the form of a system model with well

dened constrained relationships. The 14 subsystems ofthe gas turbine system interact directly or indirectly witheach other affecting the performance of the subsystems as

Fig. 14 Schematics of atomizing air subsystem

Fig. 13 Schematics of water cooling subsystem



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well as the gas turbine system. For example, in case of thegas turbine system working on multi-fuel option, withoutthe atomizing air system, the liquid fuel injected into dualnozzle fuel assembly at the combustor inlet will not

provide peakring temperature during its combustion andthus affecting the net power output of the gas turbinesystem.

Similarly, at the sub-subsystem level, the net poweroutput can be enhanced by making adequate arrangementfor inlet air cooling and anti-icing methods in the airinlet system along with steam and/or water injectiontechniques in the compressor exit or combustion chambercontributing to lower NOx emission levels and increased

power outputs.

3 Graph theoretic model of a gas turbinesystem

The graph theory is a branch of mathematics that has beensuccessfully used to represent several different types ofsystem as stated earlier. In the present paper, it is used torepresent the gas turbine system consisting of 14subsystems as identied from Figs. 2 to 15. A digraph

has been used to represent the whole gas turbine system interms of interactions among fourteen subsystems.

It is to be noted that some of the interconnections ofsensors, actuators related to some of the sub-subsystemshave been omitted while preparing the diagraph assumingthat some separate panel arrangements along with power

sources may exist in those systems. However, insertion ofthese additional links or directed edges may complicate thegeneralized diagraph, as shown in Fig. 16. The subsystemshave been represented as vertices (Ti,i = 1, 2, , 14) andinterconnections (Tij, i, j = 1, 2, , 14) among thesesubsystems as directed edges in the digraph.

4 Matrix representation of the gas turbinesystem

The above digraph representation of the gas turbine systemdesign provides only logical information about thesubsystems or the attributes of the gas turbine system.Further, it is difcult to process the logical informationavailable directly from the digraph representation. Sincethe matrix representations of information available about

any system can be processed easily, the extractedinformation from the digraph is represented into equivalentmatrix format, which is exible enough to incorporate thestructural and functional information of the subsystems aswell as sub-systems of the gas turbine system.

4.1 System structure of the gas turbine system

Consider a generalized case of a typical gas turbine systemwith Nsubsystems as stated above. An adjacency matrix(0, 1) of order NN is developed for the gas turbinesystem. The off-diagonal elements of this adjacency

Fig. 16 Gas turbine system digraph

Fig. 15 Schematics of control subsystem

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matrix represent the connectivity between subsystem iand subsystem j such that Tij = 1, if subsystem i isconnected to subsystem j, and 0 otherwise. ThusTii= 0, if any subsystem icannot to be connected to itself.Only in case of self loops, the subsystems will be

connected to themselves and thus, Tii = 1 for suchcases. On the basis of interconnections specied in thedigraph of gas turbine system shown in Fig. 3, theadjacency matrix A for the subsystems is written byEq. (1).

This adjacency matrix does not provide any informationabout the level of the interdependency of the subsystems.Further, no information is furnished by this matrix aboutthe effect of subsystems as all diagonal terms of the matrixare zero. Since the characteristic features of the subsystemsdo not come into picture, a characteristic system structurematrixis dened for the gas turbine systems.

4.2 Characteristic system structure matrix for the gas

turbine system

Various subsystems or the characteristic features of any

system can be realized by using the characteristic systemstructure matrix B = [T IA]. This kind of matrix haswidely been used in mathematics for characterizing thesystem elements. In the present matrix, T and I are thesystem characteristic and the identity matrix, respectively.The system characteristics may be either subsystems or theattributes affecting the performance outcome of thesystem. For the present case of typical gas turbine system,the characteristic system structure matrix B is given byEq. (2).

In the above matrix, the values of all the diagonalelements are the same. But in a real system, the attributesor the subsystems may have different levels of inher-itances, i.e., the value of diagonal elements in matrix B.Moreover, the interdependencies have been assigned only

for presence. No representation about the level ofinterdependency among various subsystems or the attri-

butes exists in this matrix. In order to consider this fact, anew matrix variable characteristic system structurematrix is considered for the gas turbine system.



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4.3 Variable characteristic system structure matrix for the

gas turbine system

A variable characteristic system structure matrix S isdened by considering all the system attributes in terms oftheir inheritance levels as well as their interdependency

levels. Consider a matrix Cij (i, j= 1, 2,

, 14)representing the interconnections between the subsystems

Cij instead of 1, where subsystem i is connected tosubsystem j, and 0 otherwise. Similarly, anothermatrix D with its variable diagonal elements Di (i = 1, 2,, 14) representing the characteristic structural features ofthe gas turbine system is dened. Then the variablecharacteristic system structure matrix for the gas turbine

system is given by Eq. (3).

S DC:

The matrix can provide useful information through itsdeterminant. But, the determinant contains some positiveterms as well as some negative ones. During thecalculations, some of the useful system informationmay get lost. Hence, it does not provide completeinformation about the gas turbine system. In order toavoid this loss of information, another matrix variable

permanent system structure matrix for the gas turbinesystem is considered.

4.4 Variable permanent system structure matrix for the gas

turbine system

For realistic characterization of the gas turbine system, theeffect of all the subsystems should contribute to itsmaximum in the system desired output. For the statedreasons, the new matrix Variable permanent systemstructure matrix Pis written by Eq. (4).

P D C:

This matrix contains the information about the inheri-tance levels as well as the interdependencies of the attri-

butes. Hence, this matrix can serve the purpose of realisticcharacterization of attributes of the gas turbine system.

4.5 Variable permanent function for the gas turbine system

Since the digraph and the matrix representations are notunique, as these changes with labeling of the nodes or

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vertices. In order to develop a unique representation of thesame, the permanent function of the variable permanentsystem structure matrix for the gas turbine is proposed. The

permanent function is a standard matrix function in thecombinatorial mathematics. The permanent function iscalculated in the same manner as the determinant. But, the

negative terms are converted to positive ones. Thiscomputation results in a multinomial, where every termhas its signicance and no information due to any negativeterm is lost. This permanent function for the present gasturbine system consisting of fourteen subsystems isrepresented by Eq. (5).

perP 14

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16/23

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T12$T23$T34$T45$T56$T67$T78$ $T13,14$T14,1

): (5)

This permanent function of the matrix is a mathematicalexpression in symbolic form. Each term in Eq. (5)represents a physical subset of the system. The multi-nomial, i.e., the permanent function when written in N+1group as represented above, presents an exhaustive way ofstructural analysis of a gas turbine system at differentlevels (subsystem level up the component level) and links

to improve the performance characteristics of the system.The physical signicance of various groupings isexplained as follows:

1) The rst term (grouping) represents a set of fourteenindependent subsystem characteristics as T1, T2, T3, ,T14.

2) As there are no self loops within the system itself,therefore second grouping is absent.

3) Each term of the third grouping represents a set of twoelements attribute loops i:e:, Tij$Tji and is the resultantdependence of attributei and jand the evaluation measureofN2 connected terms.

4) Each term of the fourth grouping represents a set ofthree element attribute loops Tij$Tjk$Tkj or its pair Tik$Tkj$Tji and the evaluation measure ofN-3 unconnectedelements or attributes within the system.

5) The fth grouping contains two subgroups. The termsof the rst subgrouping consists of four element attributeloops i:e:, Tij$Tjk$Tkl$Tli and the 10-subsystem evalua-tion index componentT5$T6$ $T14. The terms of thesecond grouping are the product of two element attributes

loopsTij$TjiTkl$Tlk

and the index evaluation compo-

nenti:e:, T5$T6$ $T14.6) The terms of the sixth grouping are arranged in two

subgroupings. The terms of the rst subgrouping are ofve element attribute loop i:e:, Tij$Tjk$Tkl$Tlm$Tmi orits pair Tim$Tml$Tlk$Tkj$Tji. The second subgroupingconsists of a product of two attributes loops i:e:, Tij$Tjiand a three attribute loop i:e:, Tkl$Tlm$Tmk or its pairi:e:, Tkm$Tml$Tlk and the index evaluation componenti:e:, T6$T7$ $T14.

7) The terms of the seventh groupings are arranged infour subgroupings. The rst subgrouping of the seventhgrouping is a set of 3-two element attribute loopsi:e:, Tij$Tji,Tkl$Tlk,Tmn$Tnm and a subsystem evaluation indexcomponent T7$T8$ $T14. The terms of the second

subgrouping of the seventh grouping are of two elementattribute loop i:e:, Tij$Tji and four element attributeloop i:e:, Tkl$Tlm$Tmn$Tnk with subsystem evaluationindex component T7$T8$ $T14. The terms of thethird subgrouping of the seventh grouping are of twothree-element attribute loopsi:e:, Tij$Tjk$Tki and Tlm$Tmn$Tnl with subsystem evaluation index component

T7$T8

$

$T14. The terms of fourth subgrouping of the

seventh grouping are of six elemental attribute loop i:e:, Tij$Tjk$Tkl$Tlm$Tmn$Tniand subsystem evaluation indexT7$T8$ $T14.

8) The terms of the eighth grouping are arranged infour subgroupings. The rst subgrouping of the eighthgrouping is a set of three element attribute loop i:e:,Tmn$Tnp$Tpmand two element structural diads as Tij$Tji

and Tkl$Tlk. The second subgrouping is a set of a twoelement diad Tij$Tji and a ve element attribute loopi:e:, Tkl$Tlm$Tmn$Tnp$Tpk. The third subgrouping con-sists of a three element attribute loopi:e:, Tij$Tjk$Tki) anda four element attribute loop i:e:,

Tlm$Tmn$Tnp$Tplrespectively. Similarly, the fourth subgrouping of theeighth grouping is a seven elemental attribute loop i:e:,Tij$Tjk$Tkl$Tlm$Tmn$Tnp$Tpi each having a subsystemevaluation indexT8$T9$ $T14.

Similarly, other terms of the expression are dened up tothe fteenth grouping. Each term of the grouping as well asthe subgroupings have their own independent identitieswhich are useful for the designers and the developmentanalysts for one-to-one qualitative analysis of the gasturbine systems.

5 Evaluation of gas turbine system

The diagonal elements of matrix given by Eq. (4)correspond to the fourteen subsystems that constitute thegas turbine system. The values of these diagonal elementsare calculated as

T1 perVPSSM1, T2 perVPSSM2,



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T13 perVPSSM13, T14 perVPSSM14:

Here VPSSMnrepresents the variable permanent systemstructure matrix of nth subsystem. The procedure forcalculating theT1,T2, ,T14is the same as adopted for per(P) using Eq. (5) for the whole gas turbine system. For this

purpose, the system structure graphs of the 14 subsystemsare drawn as follows.

The schematics of these 14 subsystems (Figs. 2 to 15)are drawn by taking into account their different sub-

systems/components as S11 , S12 , , etc. as specied in

Section 2. Some of the component assemblies of the gasturbine system, which may assume to be integrated for the

purpose of functional relationships with other subsystems,may be grouped to form a unit link of the subsystem.Identify the interaction between different subsystems/components of these subsystems on the basis of theirfunctional relationships.

While drawing the system structure digraph some of theequipment/sub-subsystems showing grouped behavior inthe assembly have been represented by a subsystem linkonly. Some of the links or edges shown for the structuralassembly relationships only, have been omitted duringdigraph representation due to their lower order signicancetowards functional outcomes of the subsystem or theintegrated system. Thus, the digraph representation may be

slightly varying with respect to the system structure graphsof these subsystems. However, it has been ensured that theobjective of the evaluation of gas turbine system remainunaffected. Based on the above assumptions, the digraphof all the 14 subsystems has been represented in Figs. 17(a)17(n).

The methodology as adopted for the system digraph maybe utilized for each of the subsystems up to its sub-subsystem levels sequentially for analysis of the whole gasturbine system. The salient features of the 14 subsystemsof the gas turbine systems are described in the followingsubsections.

5.1 Air inlet system

In this subsystem, the provisions for the air inlet cooling,anti-icing, etc. have limited importance as these are eitherconsidered for weather constraint or slight power augmen-tation, i.e., up to 10%14% only. However, the lterefciency is the most prominent constraint which affectsthe inlet air quality to its maximum. Therefore, T1may betaken as approximately equal to lter efciency if

performance of other sandwiched techniques in the airinlet system has been xed.

5.2 Powering unit

As the powering unit expresses the desired systemperformance, i.e., net power output, thrust or specicfuel consumption, the cascade unit performance ofcompressor, combustors and the gas turbines becomes

the most signicant criteria. For preliminary gas turbinesystem design, the net thermal efciency of the gas turbinesystem may be considered as reference. ThereforeT20.40, if 45% is the net thermal efciency as in generalcase, it varies from 21% to 45% for a simple cycle gasturbine plant. However, while evaluating at subsystemlevels, the individual performance parameters of thecompressors, combustors and the turbines may beconsidered as criteria and the relative effect of otherattributes affecting the individual subsystem performancemay be taken into account so thatT2can be enhanced.

5.3 Gas fuel system

As the gas fuel system is very sensitive to inlet gas pressureand temperature; hence, a range of operating pressures andtemperatures are to be prescribed depending upon theframe size of the gas turbine. Wobbie index is one of themost appropriate function for analyzing the gas fuel systemin terms of variety of gas fuels to be used, skid type with adual manifold and dual set of fuel nozzles or the a dual fuelsystem. Therefore, T3 may be selected from the Wobbieindex permissible limits for the given gas turbine systemnormalized over a scale of 0 to1.

5.4 Liquid fuel system

As the fuel system is to be designed for operating athigher pressures, the efciency of the fuel pump driven

by the accessory gear box helps in distribution of fuelevenly to all corners of the combustion chamber. Betterresults can be obtained by maintaining higher fuel

pressures. The spray nozzle performance is also improveddue to fuel pump pressure. Hence,T4may be appropriatelyscaled up for operating limits of the pressure ratios of fuel

pump.

5.5 Starting and drive system

The starting system mainly affects the cranking of the gasturbine before ring to breakaway from standstill, accel-erate to ring speed and subsequently to self-sustainablespeed and speed rotating for its cooling purpose after shutdown. Since the electrical work efciency is very high,approximately equal to 0.98, the overall transmissionefciency of the gear trains of the accessory gear box andother driving units are approximately 95%97%. Hence,T4may be taken as average of two terms or slightly higher(i.e.,T50.965).



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Fig. 17 Digraph of the 14 subsystems

(a) Inlet subsystem; (b) gas fuel subsystem; (c) liquid fuel subsystem; (d) powering unit subsystem; (e) starting and drive subsystem;

(f) NOxabatement subsystem; (g) water wash subsystem; (h) enclosure and ventilation subsystem; (i) re system protection subsystem;

(j) exhaust subsystem; (k) water cooling subsystem; (l) control subsystem; (m) lubrication subsystem; (n) atomizing air subsystem

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5.6 NOx abatement system

As low NOxemission levels in the gas turbine systems areone of the most essential parameters due to statutoryregulation, any method (i.e., steam injection or waterinjection technique) adopted for this purpose is highly

appreciated for the gas turbine performance evaluation.Therefore, the inheritance for the NOx abatement systemT6is generally rated as per the customer desires and the usagecommunity constraints. However, in general, this factorshould be kept more than 0.7 over a scale from 0 to 1.

5.7 Water wash system

Since the water wash system enhances the power output ofthe gas turbine unit by reducing the fouling in thecompressor, etc., its presence makes it useful for gasturbine system life without its degradation. Its importance

T7 may be represented in terms of ratio of fouling basedpower output to the maximum power output due to foulingreduction per water washing operation either ofine oronline.

5.8 Enclosure and ventilation system

Apart from cooling the space in the enclosure, ventilationalso helps in evacuating fuel vapours formed due to fuelleakages and the containment area for CO2gas, and helpsto extinguish re. Even though the ventilation system isdesigned for minimum number of air changes, there is highdegree of redundancy in this system. 100% redundant fans

are provided in the gas turbine unit. Therefore, the value ofT8approaches 1.0 as condition of minimum number of airchanges is always ensured.

5.9 Fire protection system

In the case of this subsystem, high degree of redundancyexists as separate lines ooding and extended discharge ofCO2 gas exist for each of the gas turbine systemcompartment. But, in case of re in the gas turbinecompartment, there is no option except for extendeddischarge of CO2gas to extinguish re and system safety.

Therefore, the value ofT9also approaches 1.0.

5.10 Exhaust system

In the case of exhaust system, the heat energy of theexhaust gases is to be utilized for steam generation throughheat recovery steam generator and subsequently the poweroutput from the steam turbine. Therefore, T10 may beconsidered to be equal to work efciency (ratio of workoutput by the steam turbine unit to the total heat energy ofthe exhaust) of the steam turbine unit installed in theexhaust line. However, at the sub-subsystem level, thecriteria may be different.

5.11 Lubricating oil system

Since the proper lubrication system is considered to be the

lifeblood of the gas turbine system, the performancedegradation is measured with respect to the adequacy ofthe lubrication measures adopted. In the present case, the

factorT11 for the lubricating system may be considered as aratio of degradation of gas turbine unit under actualconditions to the idealistic service life of the turbomachin-ery used in the gas turbine system.

5.12 Water cooling system

Since the effectiveness of the heat exchanger arrangementin HRSG unit primarily affects the gas turbine systemdirectly. The inheritance level T12 may be considered toapproximate the value of effectiveness of the heatexchanger unit. The effectiveness of the HRSG coils

mounted in the exhaust pipe primarily affects the netpower output from the exhaust system.T12 may be takenequal to, or slightly less than the maximum effectivenessvalue, i.e., T120.6, if 0.6 is the effectiveness of HRSGcoils. At the sub-subsystem level, the heat transferrelationship under convection Q h$A$T for liquidto liquid interaction or for radiationQ $T4for pipingto air interaction or both may be used for dening theinheritance levels.

5.13 Atomizing air system

As the liquid fuel droplets are to be converted into ne

droplets of mist like mixture facilitated by high pressure airthrough the pre-cooler for removing the moisture before

being fed to the combustion chamber, the effectiveness ofthe pre-cooler and the continuous drain system plays a keyrole in designing the atomizing air system as the type offuel and the type of turbomachinery fused for desired

pressure ratio are almost const for a given system.Therefore, T13 may account for the effectiveness of the

pre-cooler and continuous drain performance.

5.14 Control system

The control system does not increase or decrease theperformance of the gas turbine unit. However, it supportsthe gas turbine subsystems to perform better throughdynamic decision making for the operating variables.Since the sensitivity of the control unit for the signals isresponsible for the better performance of the subsystems,the inheritance valueT14may be considered to be equal tosensitivity of the control unit.

The values of the interactions Tij (i, j = 1, 2, , 14)between different subsystemsS1,S2, ,S14can be writtenas a multinomial or a matrix, the values depending uponthe type of interaction/interdependency. The subsystemcan again be treated as a system and the similar procedure



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as adopted for the subsystem may be adopted again. Theadequate normalization of the data in terms of permanentscalculated for the diagonal elements of the respectivematrices is to be carried out, so that no diagonal element

becomes so stiffened that the effect of groupings or thesubgroupings becomes redundant or ineffective at any

stage of permanent calculation. Work is in progress forconducting the performance analysis of the gas turbinesystem from different perspectives using the structuralmodel presented in this paper.

6 Methodology

A methodology for the gas turbine system structuralmodeling described in Sections 25 based on graph theoryand matrix methods is summarized as below:

1) Identify the gas turbine system and analyze its

con

guration in terms of type of turbomachinery used,special arrangements, nature of fuels to be used, materialsof construction, ow passage for air and fuels includingexhaust, special provisions like inlet air cooling methods,heat recovery arrangements, etc.

2) Develop the structural topology of the constituentparts or subsystems interacting with air/fuel or exhaustows contributing to desired performance of the gasturbine system at the macroscopic level as well asmicroscopic level.

3) Obtain the functional relationship among the aboveidentied subsystems using structural topology of the gasturbine system and develop a system functional digraph

using the interactions among the subsystems. Thesubsystems are to be represented as nodes and theinteractions are to be represented as edges.

4) Develop the generalized system structure variablepermanent matrix of the above digraph using concepts ofgraph theory and represent the permanent function for thesame in the form of a multinomial.

5) Evaluate the functions/values of the diagonalelements and the off-diagonal elements of the systemmatrix on the basis of the subsystem inheritance levelsand the interdependency levels of these subsystemscontributing to performance outcome of the gas turbine

system.The values of the interactions among the subsystems of

the gas turbine system can be obtained by analyzing thetype of interaction, functional constraints of the subsystemetc. The inheritance levels of these subsystems can becalculated by using the contribution as well as possiblecompromise limits of the subsystem usage. The step is to

be repeated at the sub-subsystem level up to the componentlevel to precisely analyze the inheritance and interdepen-dency levels of the attributes, sub-systems of the gasturbine system.

6) Calculate the permanent function value for a givengas turbine system using precise information about the

inheritance levels as well as interdependency levels ofthe attributes/sub-systems, which can also be used formaking decisions towards further improvements at thesubsystem level or the sub-subsystem levels in the gasturbine system.

This methodology has been adopted in the present paper

for developing the complete multinomial permanentfunction for a typical gas turbine system. Efforts arefurther in progress for calculating the performance analysisof a gas turbine system from different perspectives.

7 Conclusions

The graph theoretical model of the gas turbine systempresented in this paper represents its structural informationincluding its subsystems, sub-subsystems up to thecomponent level. Using this methodology, a real life gas

turbine system consisting of 17-stage axial

ow compres-sor- annulus can combustor 3-stage axial ow turbine hasbeen modeled in the form of block diagrams at thesubsystem levels and the graph theoretic representation fora typical as turbine system. The permanent function of thegas turbine system represents the characteristic features ofall the combinations of its subsystems. These combinationsform a powerful tool for the structural modeling of the gasturbine systems. To the best knowledge of the authors, thismethod has been adopted for the rst time in this paper forsuch gas turbine system. This methodology is exible toaccommodate any design or performance variations forsuch typical systems.

This method may be further used for the optimumselection, criteria based decision making about gas turbinesystems, benchmarking and the sensitivity analysisthrough the permanent function evaluation for the devel-oped digraph and matrix representations of the gas turbinesystems.

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