GAS TURBINE PERFORMANCE WHAT MAKES THE MAP?

Transcription

1 GAS TURBINE PERFORMANCE WHAT MAKES THE MAP? by Rainer Kurz Manager of Systems Analysis and Field Testing and Klaus Brun Senior Sales Engineer Solar Turbines Incororated San Diego, California Rainer Kurz is Manager of Systems Analysis and Field Testing for Solar Turbines Inc., in San Diego, California. His organization is resonsible for redicting gas comressor and gas turbine erformance, for conducting alication studies, and for field erformance tests on gas comressor and generator ackages. Dr. Kurz attended the University of the Federal Armed Forces in Hamburg, Germany, where he received the degree of a Dil.-Ing., and, in 1991, the degree of a Dr.-Ing. He has authored numerous ublications in the field of turbomachinery and fluid dynamics. Klaus Brun is a Senior Sales Engineer for Solar Turbines Inc., in San Diego, California. Previously he was emloyed as a Research Engineer at the ROMAC Laboratories of the University of Virginia and a Senior Project Engineer at Blue Ridge Numerics Inc. Dr. Brun received his Ph.D. from the University of Virginia and has ublished more than 15 journal and conference aers on turbomachinery and related toics. ABSTRACT The ower and efficiency characteristics of a gas turbine are the result of a comlex interaction of different turbomachines and a combustion system. This tutorial addresses the basic characteristics of each of the comonents, and defines the rules under which they interact, as well as tyical control limits and control concets. Imortant nondimensional characteristics such as Mach number and Reynolds number are introduced. The concet of comonent matching is exlained. INTRODUCTION Gas turbines for industrial alications consist either of an air comressor driven by a gas generator turbine with a searate ower turbine (two-shaft engine) or of an air comressor and a turbine on one shaft, where the turbine rovides both ower for the air comressor and the load (single-shaft engine, Figure 1). The ower and efficiency characteristics of a gas turbine are therefore the result of a comlex interaction of different turbomachines and a combustion system. This tutorial addresses the basic characteristics of each of the comonents, and defines the rules under which they interact, as well as tyical control limits and control concets. Imortant nondimensional characteristics such as Mach number and Reynolds number are introduced. The concet of comonent matching is exlained. 247 Figure 1. Single-Shaft (Cold End Drive) and Two-Shaft (Hot End Drive) Gas Turbines. Based on this foundation, the effects of changes in ambient temerature, barometric ressure, inlet and exhaust losses, relative humidity, accessory loads, different fuel gases, or changes in ower turbine seed are exlained.

2 248 PROCEEDINGS OF THE 29TH TURBOMACHINERY SYMPOSIUM The following toics are discussed: The gas turbine as a system Comonent matching Off-design behavior of gas turbines Low fuel gas ressure Accessory loads Single-shaft versus two-shaft engines Variable inlet and stator vanes Control temerature Transient behavior Thermodynamical arameters of exhaust gases The toics resented should enhance the understanding of the rinciles that are reflected in erformance mas for gas turbines, or, in other words, exlain the oeration rinciles of a gas turbine in industrial alications. WHAT DO TYPICAL PERFORMANCE MAPS SHOW? Because the gas turbine erformance varies significantly from one design to the other, the rocedure to determine the erformance of the engine for a secified oerating oint is to use the manufacturer s erformance mas. Tyical engine erformance mas are shown in Figure 2 for single-shaft engines and in Figures 3, 4, and 5 for two-shaft engines. In general, these mas can be used to determine the engine full load outut at a given ambient temerature, and a given ower turbine seed. They also show the fuel flow at any load, as well as exhaust flow and temerature. Additional mas (Figure 5) allow correction for inlet and exhaust losses as well as for the site elevation. For diagnostic uroses, the mas also allow determination of the exected comressor discharge ressure, control temerature (tyically ower turbine inlet temerature or exhaust temerature), and gas generator seed at any oerating oint. Discreancies between the exected and the actual values may be indicative of engine roblems. In order to fully understand the information dislayed on engine erformance mas, one wants to determine what the reason is for an engine to behave the way it does. API 616 (1998) rescribes another form of reresenting engine erformance than described above. The ma for single-shaft engines in API 616 (1998) is not articularly useful for single-shaft engines driving generators, because it shows the erformance as a function of gas generator seed. For these generator set alications, however, the gas generator seed is always constant. The API 616 mas used to reresent two-shaft engines do not allow descrition of the engine erformance at varying ambient temeratures. Also, the control temerature for two-shaft engines is usually not the exhaust temerature (as ostulated bin one of the API 616 curves), but the ower turbine inlet temerature. The most useful curve in API 616 (1998) is essentially a subset of the ower turbine curve in Figure 4. It should be noted that, articularly in the field, the measurement of ower outut, heat rate, exhaust flow, and exhaust temerature is usually rather difficult (Brun and Kurz, 1998). Understanding the oerating rinciles of the engine is therefore a useful tool of interreting data. GENERAL REMARKS ON GAS TURBINE THERMODYNAMICS The conversion of heat released by burning fuel into mechanical energy in a gas turbine is achieved by first comressing air in an air comressor, then injecting and burning fuel at aroximately constant ressure, and then exanding the hot gas in turbine (Brayton cycle). The turbine rovides the necessary ower to oerate the comressor. Whatever ower is left is used as the mechanical outut Figure 2. Tyical Performance Mas for a Single-Shaft Gas Turbine, Driving a Generator. of the engine. This thermodynamic cycle can be dislayed in an enthaly-entroy (h-s) diagram (Figure 6). The air is comressed in the engine comressor from state 1 to state 2. The heat added in the combustor brings the cycle from 2 to 3. The hot gas is then exanded. In a single-shaft turbine, the exansion is from 3 to 7, while in a two-shaft engine, the gas is exanded from 3 to 5 in the gas generator turbine and afterward from 5 to 7 in the ower turbine. The difference between Lines 1-2 and 3-7 describes the work outut of the turbine, i.e., most of the work generated by the exansion 3-7 is used to rovide the work 1-2 to drive the comressor. In a two-shaft engine, the distances from 1 to 2 and from 3 to 5 must be aroximately equal, because the comressor work has to be rovided by the gas generator turbine work outut. Line 4-5 describes the work outut of the ower turbine. For a erfect gas, enthaly and temerature are related by: h = c T (1) The entire rocess can be described (assuming that the mass flow is the same in the entire machine, i.e., neglecting the fuel mass flow and bleed flows, and further assuming that the resective heat caacities c, c,e, and c,a being suitable averages): c,a (T 1 T 2 ) c,e (T 3 T 7 ) = P. W (2) c (T 3 T 2 )W = E f W f (3)

3 GAS TURBINE PERFORMANCE WHAT MAKES THE MAP? 249 Figure 4. Tyical Performance Mas for a Two-Shaft Gas Turbine (Second Part). Figure 3. Tyical Performance Mas for a Two-Shaft Gas Turbine (First Part). In Equation (2), the first term is the work inut by the comressor, the second term describes the work extracted by the turbine section. Equation (3) yields the temerature increase from burning the fuel in the combustor. For two-shaft engines, two additional relationshis can be derived, taking into account that the gas generator turbine has to balance the ower requirements of the comressor, and that the useful ower outut is generated by the ower turbine: c,a (T 2 T 1 ) = c,e (T 3 T 5 ) (4) c,e (T 5 T 7 ) = P. (5) W GENERAL REMARKS ON TURBOMACHINERY AERODYNAMICS Any gas turbine consists of several turbomachines. First, there is an air comressor, and after the combustion has taken lace, there is a turbine section. Deending on the design of the gas turbine, the turbine section may consist either of a gas generator turbine, which oerates on the same shaft as the air comressor, and a ower turbine, which is on a searate shaft (two-shaft design), or only of a gas generator turbine (single-shaft, Figure 1). Comressor The task of the comressor is to bring the inlet air from ambient ressure to an elevated ressure. To do this, ower is necessary, i.e., the comressor imarts mechanical ower on the air. The fundamental law describing the conversion of mechanical energy into ressure in a turbomachine is Euler s law: A comressor stage imarts energy on the fluid (air) by increasing the fluid s angular momentum (torque). The increase of the tangential velocity comonent of the air is simly (Figure 7): The mathematical exression for torque is: c u =c u2 c u1 (6) τ=w r c u (7) and thus the change of angular momentum of the fluid is: τ=w (r c u )=W (r 2 c u2 r 1 c u1 ) (8)

4 250 PROCEEDINGS OF THE 29TH TURBOMACHINERY SYMPOSIUM Figure 5. Tyical Correction Curves for Elevation and Inlet and Exhaust Losses. Figure 6. Enthaly-Entroy Diagram for the Brayton Cycle. Power (work/time) is defined as torque multilied by the angular seed, i.e.,: P=ω τ=ω W (r c u )=ω W (r 2 c u2 r 1 c u1 ) (9) This equation is called Euler s angular momentum equation. From Euler s equation one can also determine the head (enthaly difference) er stage as follows: P H=h 2 h 1 = =ω (r 2 c u2 r 1 c u1 ) (10) W And since it is known that h = c T one can estimate the temerature increase across the comressor stage: ω T 2 = (r 2 c u2 r 1 c u1 ) T 1 (11) c Since this is a comressor we are really more interested in the ressure increase than the temerature increase er stage. The isentroic relationshis give us a function between ressure and temerature ratios. However, when emloying the isentroic relationshis in this context one has to remember that they aly for ideal (no losses) thermodynamic rocesses. In this case the rocess is not ideal and thus a comressor efficiency has to be introduced: Ideal (Isentroic) Head h η c = = 2s h 1 T = 2s T 1. (12) Actual Head h 2 h 1 T 2 T 1 Figure 7. Energy Conversion in a Comressor Stage.

5 GAS TURBINE PERFORMANCE WHAT MAKES THE MAP? 251 When combining the above efficiency with the exression for temerature and the isentroic relationshi for temerature and ressure (T 2 /T 1 = (P 2 /P 1 ) γ/γ 1 ) we obtain after some algebra: P 2 P 1 γ = 1 ηω (r 2 c u2 r 1 c u1 ) γ 1. (13) c T 1 This exression gives us the ressure ratio er stage as a function of the tangential air velocity. Using the exression for head one can also rewrite this as follows (to relate head to ressure ratio): P 2 P 1 γ = 1 η H γ 1. (14) c T 1 The above set of equations is an extremely owerful engineering tool. From basic knowledge of the tangential flow velocities inside the comressor rotating blade assage one can determine the head, required ower, temerature ratio, and ressure ratio across a comressor stage. Turbine The same relationshis that aly to the comressor can also be alied to the turbine. P=ω τ=ω W (r c u )=ω W (r 2 c u2 r 1 c u1 ) (15) All that has to be considered is that while the comressor imarts energy to the fluid, thus c u2 > c u1, the turbine extracts energy from the fluid, and thus c u2 < c u1. The visible exression of this fact is the change in the sign for the ower. The ressure ratio and temerature ratio over the turbine are thus: ω T 2 = (r 2 c u2 r 1 c u1 ) T 1 (16) c The ower turbine Mach number deends on its seed, the ower turbine inlet temerature, and the exhaust gas comosition. Because for a given geometry the reference diameter will always be the same, one can define the machine Mach number also in terms of a seed, for examle the gas generator seed, and get the so-called corrected gas generator seed: NGP corr = NGP. (20) γ R T (γ R T) ref Even though NGP corr (corrected gas generator seed) is not dimensionless, it is a convenient way of writing the machine Mach number of the comonent. In the following text, the simlified exression N/ T, which is based on the above exlanations, will also be used. Any aerodynamic comonent erformance will change if the characteristic Mach numbers are changed. The dramatic change of the flow velocities in a turbine nozzle is shown in Figure 8. For turbine nozzles, one of the effects connected with the Mach number is that it limits the maximum flow that can ass through the nozzle. Beyond a certain ressure ratio, the amount of actual flow that can ass through the nozzle can no longer be increased by increasing the ressure ratio. With increasing ressure ratio, the velocity or Mach number levels in the nozzle become higher and higher, until the seed of sound (= Mach 1) is reached in the throat (for a ressure ratio of 1.7 in the examle). A further increase of the ressure ratio yields higher velocities downstream of the throat, but the throughflow (which is roortional to the velocity at the inlet into the nozzle) can no longer be increased (Kurz, 1991). and γ ηω = (r 2 c u2 r 1 c u1 ) 1 γ 1. (17) P 2 P 1 c T 1 Mach Number The Mach number is one of the most imortant arameters influencing the erformance of turbomachinery comonents. An increasing Mach number can comletely change the aerodynamic behavior of a comonent (shown later in Figure 12). Mach numbers are used to comare a velocity with the seed of sound: w M =. (18) γ R T The Mach number increases with increasing velocity w, and decreasing temerature T. It also deends on the gas comosition, which determines the ratio of secific heats γ and the gas constant R. Frequently, the machine Mach number M n is used. M n does not refer to a gas velocity, but to the circumferential seed u of a comonent, for examle a blade ti at the diameter D: u 2πD N M n = =. (19) γ R T γ R T This oints to the fact that the Mach number of the comonent in question will increase once the seed N is increased. The consequences for the oeration of the gas turbine are that: The engine comressor Mach number deends on its seed, the ambient temerature, and the relative humidity. The gas generator turbine Mach number deends on its seed, the firing temerature, and the exhaust gas comosition (thus, the load, the fuel, and the relative humidity). Figure 8. Velocity Distribution in a Turbine Nozzle at Different Pressure Ratios. Another effect of changes in the Mach number is the strong deendency of losses and enthaly rise or decrease for a given blade row on the characteristic Mach number. Figure 9 shows how the losses increase for an axial comressor stage, while the range is reduced with a rising Mach number (Cohen, et al., 1996). The ractical conclusion is that the erformance of any aerodynamic comonent will change if the characteristic Mach number changes. Because each gas turbine consists of several aerodynamic comonents, the Mach number of each of these comonents would have to be ket constant in order to achieve a similar oerating condition for the overall machine. While the characteristic

6 252 PROCEEDINGS OF THE 29TH TURBOMACHINERY SYMPOSIUM (Kurz, 1991). A change in the ambient temerature from 0 F to 100 F changes the Reynolds number of the first comressor stage by about 40 ercent. The tyical oerating Reynolds numbers of comressor blades and turbine blades are above the levels where the effect of changing the Reynolds number is significant. Figure 9. Losses and Range of an Axial Comressor Stage at Different Mach Numbers. temerature for the engine comressor is the ambient temerature, the characteristic temerature for the gas generator (GP) turbine and the ower turbine is the firing temerature T 3 and the ower turbine inlet temerature T 5, resectively. The Mach number is indeed the most imortant nondimensional characteristic for the gas turbine behavior. If two oerating oints (o1 and o2) yield the same machine Mach numbers for the gas comressor and the gas generator turbine, and both oerating oints are at the resective otimum ower turbine seed, then the thermal efficiencies for both oerating oints will be the same as long as second order effects, such as Reynolds number variations, effects of gas and clearances, etc., are not considered. The requirement to maintain the machine Mach number for comressor and gas generator turbine can be exressed by NGP corr = constant (which leads to identical Mach numbers for the comressor): THE GAS TURBINE AS A SYSTEM When the comressor, the gas generator turbine, and the ower turbine (if alicable) are combined in a gas turbine, the oeration of each comonent exeriences certain oerating constraints. The comonents are designed to work together at their highest efficiencies at a single oerating oint, but the oeration of the comonents at any other than the design oint must also be considered. The constraints and requirements are different for single-shaft and two-shaft engines, hence they are treated searately. In the following section, we will look into the interaction between the engine comonents, because it is this interaction that generates the tyical behavior of gas turbines. Single-Shaft Engines Consider the single-shaft gas turbine erformance first. The oeration of the comonents requires the following comatibility conditions: Comressor seed = Gas generator turbine seed Mass flow through turbine = Mass flow through comressor Bleed flows Fuel mass flow Comressor ower < Turbine ower Tyical comressor and turbine mas are shown in Figures 10 and 11, resectively. NGP NGP corr =constant= o1 NGP = o2. (21) γ R T 1,o1 γ R T 1,o2 and, in order to maintain at the same time the same Mach number for the gas generator turbine, which rotates at the same seed as the comressor: T 3,o1 T = 3,o2 (22) T 1,o1 T 1,o2 The engine heat rate will remain roughly constant, while the engine ower will be changed roortionally to the change in inlet density. The emhasis lies on the word roughly, because this aroach does not take effects like Reynolds number changes, changes in clearances with temerature, changes in gas characteristics (γ, c ), or the effect of accessory loads into account. This aroach also finds its limitations in mechanical and temerature limits of an actual engine that restrict actual seeds and firing temeratures (Kurz, et al., 1999). Figure 10. Tyical Comressor Performance Ma with Oerating Lines for a Single-Shaft Engine. Reynolds Number While the Mach number essentially accounts for the comressibility effects of the working gas, the Reynolds number describes the relative imortance of friction effects. The Reynolds number is defined by: Re = w L. (23) ν The kinematic viscosity υ deends on the gas, the temerature, and the ressure. In industrial gas turbines, where neither the working temeratures nor the working ressures change as dramatically as in the oeration of aircraft engines, the effects of changes in the Reynolds number are tyically not very ronounced Figure 11. Tyical Turbine Performance Ma.

7 GAS TURBINE PERFORMANCE WHAT MAKES THE MAP? 253 The relationshis between the work inut and the ressure ratio of turbine and comressor (assume 7 = 1 and W c = W t = W to make the examle simler) are given by: T c 1 γ 1 = [( 2 ) γ 1] (24) T 1 η c 1 T t γ 1 =η t [1 ( 7 ) γ ] (25) T 3 3 These relationshis are a consequence of the relationshis between temerature rise and ressure ratio in isentroic systems. The introduction of the comonent efficiencies then bridges the ga between the isentroic and the real rocess. The gas generator turbine and the comressor oerate on the same shaft, thus: = N T 1 (26) T 1 T 3 A ossible algorithm for determining an arbitrary oerating oint is described in APPENDIX B. Two-Shaft Engines N T 3 A similar examle for the erformance of a two-shaft gas turbine is now described. The oeration of the comonents requires the following comatibility conditions: Comressor seed = Gas generator turbine seed Mass flow through turbine = Mass flow through comressor Bleed flows Fuel mass flow Comressor ower = Gas generator turbine ower ( mechanical losses) The subsequent free ower turbine adds the requirement that the ressure after the GP turbine has to be high enough to force the flow through the ower turbine. Tyical turbine and comressor mas are shown in Figures 11 and 12, resectively. Note that the comressor oerating oints are very different between a single-shaft and a two-shaft engine. However, an additional condition is found, because the absorbed comressor ower must be rovided by the gas generator turbine: T c,c c 1 T =c,t t T 3 (29) T 1 η m T 3 T 1 Also, the gas generator turbine and the comressor oerate on the same shaft, thus: N N T = 1 (30) T 3 T 1 T 3 In APPENDIX C a ossible algorithm for determining an arbitrary oerating oint is described. Two-shaft engines oerate with the gas generator turbine and the ower turbine in series. The ower turbine ressure ratio 5 / a is thus related to the comressor ressure ratio 2 / a by the identity: 5 = (31) a a 2 3 This has some interesting imlications: If the ower turbine oerates at a nonchoked condition, the gas generator will be restrained to oerate at a fixed ressure ratio for each ower turbine ressure ratio. The ressure ratio is controlled by the swallowing caacity of the ower turbine. Moreover, if the ower turbine is choked, it will cause the gas generator turbine to oerate at one fixed nondimensional oint (Figure 13). In reality, the roblem may be even less comlex. The gas generator turbine first-stage nozzle often also oerates at or near choked flow conditions. In this case, the actual flow through this nozzle is constant. This means that the mass flow through the turbine can be calculated from: (γ 1) W= 3 γ ( γ 1 ). (32) A * 2(γ 1) RT 3 2 Figure 13. Tyical Performance Mas for a Gas Generator Turbine and a Power Turbine in Series. Figure 12. Tyical Comressor Performance Ma with Oerating Lines for a Two-Shaft Engine. One can again write for the relationshis between the work inut and the ressure ratio of comonents. To make the examle easier to follow, again assume 7 = 1 and W c = W t = W. Unlike for the single-shaft engine, the ressure ratio for the turbine, 3 / 5, is not known beforehand. T c 1 γ 1 = [( 2 ) γ 1] (27) T 1 η c 1 T t γ 1 =η t [1 ( 5 ) γ ] (28) T 3 3 The mass flow is only deendent on the combustor exit ressure 3 (which can be substituted by the comressor exit ressure 2 ), the firing temerature T 3, the gas comosition (which determines γ), and the geometry of the nozzle, which determines A* (in reality, it is determined by the critical nozzle area, the clearance area, and the effective bleed valve area). The above relationshi has the following consequences: Increasing the firing temerature, without changing the geometry, will lead to a lower mass flow. Increasing the GP seed, thus increasing 2, will allow for a larger mass flow. With variable inlet guide vanes (IGVs) the airflow can be altered, thus also setting a new T 3 and a different comressor

8 254 PROCEEDINGS OF THE 29TH TURBOMACHINERY SYMPOSIUM ressure ratio 2 / 1. The relationshi between 2 / 1 and T 3 remains, however, unchanged: The turbine flow caacities alone determine the gas generator match, not the IGV setting. Closing the IGVs will raise the seed of a temerature toed gas generator, but since the temerature remains constant, the airflow tends to remain unchanged (because the flow through the gas generator turbine nozzle Q 3 remains constant). At high ambient temeratures, when the gas generator would normally slow down, IGVs can be used to kee the seed at a higher level, thus avoiding efficiency enalties in the gas generator turbine. The setting of the flow function above obviously has a great influence on the ossible oerating oints of the gas generator. Analyzing the equations above shows that for a high resistance of the ower turbine (i.e., low mass flow W for a given 5 / 1 ) the gas generator reaches its limiting firing temerature at lower ambient temeratures than with a low resistance of the ower turbine. By altering the exit flow angle of the first stage ower turbine nozzle the required ressure ratio for a certain flow can be modified (i.e., the swallowing caability). This effect is used to match the ower turbine with the gas generator for different ambient temeratures. This concet will be discussed more in the next section. COMPONENT MATCHING Each gas turbine consists of three artially indeendent aerodynamic comonents (comressor, gas generator turbine, and ower turbine). These comonents need to be matched, such that the overall erformance of the gas turbine is otimized for a defined oerating ambient temerature. Two-shaft engines have a ower turbine that is not mechanically couled with the gas generator. The seed of the gas generator is therefore not controlled by the seed of the driven equiment (as it is in single-shaft generator set alications). The gas generator seed only deends on the load alied to the engine. If the ower turbine outut has to be increased, the fuel control valve allows more fuel to enter the combustor. This will lead to an increase both in gas generator seed and in firing temerature, thus making more ower available at the ower turbine. Due to mechanical constraints, both the gas generator seed and the firing temerature have uer limits that cannot be exceeded without damaging the engine or reducing its life. Deending on: The ambient temerature, The accessory load, and The engine geometry (in articular the first ower turbine nozzle), the engine will reach one of the two limits first. At ambient temeratures below the match temerature, the engine will be oerating at its maximum gas generator seed, but below its maximum firing temerature (seed toing). At ambient temeratures above the match temerature, the engine will oerate at its maximum firing temerature, but not at its maximum gas generator seed (temerature toing). The match temerature is thus the ambient temerature at which the engine reaches both limits at the same time (Figure 14). As discussed reviously, the first ower turbine nozzle determines the amount of ressure ratio needed by the ower turbine to allow a certain gas flow. In turn, this determines the available ressure ratio for the gas generator turbine. If the ressure ratio available for the gas generator does not allow balancing of the ower requirement of the engine comressor (see enthaly-entroy diagram), the gas generator will have to slow down, thus reducing the gas flow through the ower turbine. This will reduce the ressure ratio necessary over the ower turbine, thus leaving more head for the gas generator to satisfy the comressor ower requirements. Some effects can cause the gas generator to exhibit an altered match temerature: Gas fuel with a low heating value or water injection increase the mass flow through the turbine relative to the comressor mass flow. The temerature toing will thus be shifted to higher ambient temeratures. Dual fuel engines that are matched on gas will to early on liquid fuel. This is caused by the change in the thermodynamic roerties of the combustion roduct due to the different carbon to hydrogen ratio of the fuels. The matching equations indicate that a reduction in comressor efficiency (due to fouling, inlet distortions) or turbine efficiency (increased ti clearance, excessive internal leaks, corrosion) will also cause early temerature toing. Accessory loads also have the effect of leading to remature temerature toing. When IGVs oen too far, increased airflow W is the result. Again, the matching equations indicate that early toing is the result. The match of any engine can be altered by altering the flow characteristic of the first ower turbine nozzle. Oening this nozzle, which means that the flow out of this nozzle is more in the axial direction than before, will lower the flow resistance of the ower turbine. Therefore, the match oint will move to higher ambient temeratures (Figure 14). Matching of a Gas Generator and Free Power Turbine Simlified mass and energy conservation retain the essential hysical relationshis and allow derivation of the two fundamental matching conditions, using the comressor ressure ratio R c = 2 / 1. Mass conservation, Q 3 3 W = const =. (33) RT 3 in a choked nozzle, where yields T 3 γ R (γ 1)/(γ 1) 2 1 /2 γ 1 W = (34) A * 3 T 3 Q 3 R c (35) θ W c θ Energy conservation yields γ 1 T Q γ 3 T std (1 K 3 R ) c 1. (36) θ Q 5 η c η g Figure 14. Matching of the Power Turbine. Note that the matching is not affected by elevation or inlet ressure loss. However, flow caacities of the gas generator turbine nozzle Q 3 and the ower turbine nozzle Q 5, as well as comonent efficiencies directly affect the matching. K is considered a constant.

9 GAS TURBINE PERFORMANCE WHAT MAKES THE MAP? 255 The turbine geometry determines both actual flows Q 3 and Q 5, as well as the gas generator turbine efficiency. The comressor geometry and seed set the airflow. With variable IGVs the airflow can be altered, thus also setting a new T 3 and a different comressor ressure ratio R c. The relationshi between R c and T 3 remains, however, unchanged: The turbine flow caacities alone set the gas generator match, not the IGV setting. Closing the IGVs will raise the seed of a temerature toed gas generator, but since the temerature remains constant, the airflow tends to remain unchanged (because Q 3 remains constant). If, however, η gt increases due to the change in seed, T 3 /θ has to dro, leading to an increase in W c : The gas generator ums more airflow with the IGV closed and the higher seed than with the IGV oen and the lower seed. The IGVs thus allow trimming of the engine such that the rated T 3 is always reached at full corrected NGP. Matching of Single-Shaft Engines A single-shaft engine has no unique matching temerature. Used as a generator drive, it will oerate at a single seed, and can be temerature toed at any ambient temerature as long as the load is large enough. SINGLE-SHAFT VERSUS TWO-SHAFT ENGINES The choice of whether to use a single-shaft or two-shaft ower lant is largely determined by the characteristics of the driven load. If the load seed is constant, as in the case of an electric generator, a single-shaft unit is often secified. An engine secifically designed for electric ower generation would make use of a singleshaft configuration. An alternative, however, is the use of a two-shaft engine. If the load needs to be oerated at varying seeds, the two-shaft configuration is the most advantageous. The running lines for single-shaft and two-shaft units are shown in the comressor mas (Figures 10 and 12). In the case of the single-shaft engine driving a generator, reduction in outut ower results in only minute changes in comressor mass flow as well as some reduction in comressor ressure ratio. There is little change in comressor temerature rise because the efficiency is also reduced. This means that the comressor ower remains essentially fixed. With a two-shaft engine, however, reducing net ower outut involves a reduction in comressor seed and hence in air flow, ressure ratio, and temerature rise. The comressor ower needed is therefore areciably lower than for the single-shaft engine. It should also be evident from a comarison of the mas that the comressor oerates over a smaller range of efficiency in a two-shaft engine. Comaring the outut characteristics of single- and two-shaft engines, indicates that at low ambient temeratures, the ower and heat rate of the single-shaft machine tend to become better than for the two-shaft machine. This is due to the fact that the two-shaft engine oerates at seed toing, i.e., with a declining firing temerature, while a single-shaft engine is able to oerate at the maximum firing temerature over the full range of ambient temeratures. It should be noted that a two-shaft engine with variable geometry can overcome this disadvantage. Both tyes are enalized in the same way by the increase in comressor Mach number (both run at seed toing, but with falling temerature the Mach number rises). At high ambient temeratures, the erformance is almost identical (because both engines reach their maximum firing temerature). The two tyes also have different characteristics regarding the suly of waste heat to a cogeneration or combined cycle lant, rimarily due to the differences in exhaust flow as load is reduced; the essentially constant air flow and comressor ower in a singleshaft unit results in a larger decrease of exhaust temerature for a given reduction in ower, which might necessitate the burning of sulementary fuel in the waste heat boiler under oerating conditions where it would be unnecessary with a two-shaft. In both cases, the exhaust temerature may be increased by the use of variable inlet guide vanes. Cogeneration systems have been successfully built using both single-shaft and two-shaft units. The differences in efficiency between single-shaft and two-shaft machines at art load deend largely on the articular design of the comonents, and not on the number of shafts. The torque characteristics, however, are very different and the variation of torque with outut seed at a given ower may well determine the engine s suitability for certain alications. The comressor of a single-shaft engine is constrained to turn at some multile of the load seed, fixed by the transmission gear ratio, so that a reduction in load seed imlies a reduction in comressor seed. This results in a reduction in mass flow hence of outut of torque as shown in Figure 15. This tye of turbine is not very suitable for mechanical drive uroses. The normal flat torque curve of an internal combustion engine is shown dotted for comarison. Figure 15. Torque Characteristics of a Single-Shaft and a Two- Shaft Engine, Comared with an Internal Combustion Engine. The two-shaft unit, having a free ower turbine, however, has a more favorable torque characteristic. For a constant fuel flow, and constant gas generator seed, the free ower turbine can rovide relatively constant ower for a wide seed. This is due to the fact that the comressor can suly an essentially constant flow at a given comressor seed, irresective of the free turbine seed. Thus at fixed gas generator oerating conditions, reduction in outut seed results in an increase in torque as shown in the seedtorque ma. It is quite ossible to obtain a stall torque of twice the torque delivered at full seed. The torque characteristic is also clearly suerior to that of a recirocating engine (Figure 13). The actual range of seed over which the torque conversion is efficient deends on the efficiency characteristic of the ower turbine. The tyical turbine efficiency characteristic shown in Figure 3 suggests that the efficiency enalty will not be greater than about 5 or 6 ercent over a seed range from half to full seed. Thus quite a large increase in torque can be obtained efficiently when the outut seed is reduced to 50 ercent of its maximum value. OFF-DESIGN BEHAVIOR OF GAS TURBINES OR WHAT CREATES THE PERFORMANCE MAPS This section will exlain the behavior of single and two-shaft turbines at the following off-design conditions: Varying ambient temerature Varying ambient ressure Varying humidity

10 256 PROCEEDINGS OF THE 29TH TURBOMACHINERY SYMPOSIUM Varying load Varying ower turbine (PT) seed Also touched on will be the effect of accessory loads (like lube oil ums or other ums driven through a ower takeoff directly from the gas generator), and the effect of insufficient fuel gas ressure. The means of controlling the behavior of the engine, such as fuel control valves, bleed valves, and variable geometry, will also be included. The term firing temerature will be used in a generic way, since for these considerations it is inconsequential whether this term is defined as T 3, TIT, or TRIT. Usually, T 3 and TIT are defined as the combustor exit or gas generator inlet temeratures, while TRIT designates the inlet temerature into the first gas generator turbine rotor. Due to the introduction of cooling flows in the first stage nozzle, TRIT is slightly lower than TIT. However, TRIT is more meaningful in judging the heat exosure of the first stage rotor, which exeriences higher mechanical stresses than the first stage nozzle. Several concets need to be introduced to hel in the understanding of the behavior. These are: The h-s diagram of the gas turbine cycle The concet of equal mach numbers (corrected NGP) The influence of variable geometry The concet of matching Tyical control concets The h-s diagram has been introduced reviously (Figure 6). From the h-s diagram can be derived some general ideas of the gas turbine oeration. Since the mass flow through the entire engine is almost constant (neglecting the additional fuel mass flow), the enthaly difference created in the comressor has to be balanced by the enthaly extracted by the GP turbine. Whatever isentroic enthaly (i.e., ressure ratio) is left, can be used in the ower turbine. In this discussion, the ossibility of variable geometry, esecially variable inlet guide vanes (VIGV), will be initially disregarded. At this oint, note that VIGVs are able to vary the comressor ma while the seed remains constant. Counter swirl will increase flow and head (normally at the exense of efficiency), swirl will reduce head and flow. Variable geometry introduces an additional control variable that can affect changes in the engine oeration indeendent of gas generator seed and firing temerature, which are both controlled by the fuel flow. For examle it can be used to kee NGP at otimum level even at high ambient temeratures, when NGP would normally dro. Imortant considerations about off-design behavior of a gas turbine include two imortant dimensionless figures, the Mach and the Reynolds number. Changes in either one of them can lead to significant changes in the erformance characteristics of turbomachinery comonents. Another oint worth mentioning is that the erformance of any gas turbine deends to some extent on the size of running clearances. These clearances can deend more or less on the revalent oerating temerature. No general relationshis are available to describe the oening and closing of clearances with oerating temerature. It also should be noted that some engines are limited in ower outut (esecially at low ambient temeratures) not for aerothermodynamic reasons, but for mechanical reasons: The engine shaft may be designed for a certain maximum torque, which would be exceeded at low ambient temeratures if the engine were to be run at maximum firing temerature or maximum gas generator seed. Varying Ambient Temeratures If the ambient temerature changes, the engine is subject to the following effects: 1. The density changes. At constant seed, where the volume flow remains aroximately constant, the mass flow (and with it the ower outut) will increase with decreasing temerature and will decrease with increasing temerature. 2. The ressure ratio of the comressor at constant seed gets smaller with increasing temerature. This is due to: κ h s = c T 1 (( 2 ) κ 1 1) (37) 1 and h s N 2 (38) In other words, to maintain a given ressure ratio (in a two-shaft engine), more seed, more head, and thus more ower is needed to drive the comressor (Figure 16). This ower has to be rovided by the gas generator turbine, and is thus lost for the ower turbine, as can be seen in the enthaly-entroy diagram. Tyically, a reduction in gas generator seed occurs at high ambient temeratures. This is due to the fact that the equilibrium condition between the ower requirement of the comressor (which increases at high ambient temeratures if the ressure ratio must be maintained) and the ower roduction by the gas generator turbine (which is not directly influenced by the ambient temerature as long as comressor discharge ressure and firing temerature remain) will be satisfied at a lower seed. The lower seed often leads to a reduction of turbine efficiency: The inlet volumetric flow into the gas generator turbine is determined by the first stage turbine nozzle, and the Q 3 /NGP ratio (i.e., the oerating oint of the gas generator turbine) therefore moves away from the otimum. Variable comressor guide vanes allow keeing u the gas generator seed constant at higher ambient temeratures, thus avoiding efficiency enalties. A single-shaft, constant seed gas turbine will see a constant head (because the head stays roughly constant for a constant comressor seed), and thus a reduced ressure ratio. Again, because the comressor requires a larger ortion of the turbine ower, the ower outut is reduced. Figure 16. Enthaly-Entroy Diagram for a Gas Turbine, Showing the Effect of Increasing Ambient Temerature. 3. The comressor discharge temerature at constant seed increases with increasing temerature. Thus, the amount of heat that can be added to the gas at a given maximum firing temerature is reduced. 4. NGP corr (alas the Mach number) at constant seed is reduced at higher ambient temerature. As exlained reviously, the inlet mach number of the engine comressor will increase for a given seed, if the ambient temerature is reduced. The gas generator Mach number will increase for a reduced firing temerature at a constant gas generator seed. 5. The relevant Reynolds number changes.

11 GAS TURBINE PERFORMANCE WHAT MAKES THE MAP? 257 The net effect of higher ambient temeratures is an increase in heat rate and a reduction in ower. At full load, single-shaft engines will run at temerature toing at all ambient temeratures, while two-shaft engines will run either at temerature toing (at ambient temeratures higher than the match temerature) or at seed toing (at ambient temeratures lower than the match temerature). At seed toing, the engine will not reach its full firing temerature, while at temerature toing, the engine will not reach its maximum seed. The enthaly-entroy diagram (Figure 16) describes the Brayton cycle for a two-shaft gas turbine. Lines 1-2 and 3-4 must be aroximately equal, because the comressor work has to be rovided by the gas generator turbine work outut. Line 4-5 describes the work outut of the ower turbine. At higher ambient temeratures, the starting oint 1 moves to a higher temerature at 1'. Because the head roduced by the comressor is roortional to the seed squared, it will not change if the seed remains the same. However, the ressure ratio roduced, and thus the discharge ressure, will be lower than before. Looking at the combustion rocess 2-3 and 2'-3', and considering that the firing temerature T 3 is limited, less heat inut is ossible (because T 3 -T 2 is smaller than T 3 ' -T 2' ). The exansion rocess 3 '-4'-5' has, due to the lower 2 = 3, less ressure ratio available. Furthermore, a larger art of the available exansion work is being used u in the gas generator turbine, leaving less work available for the ower turbine. The effects of increased ambient temerature are therefore a lower ower turbine outut and less fuel flow (however, also a lower efficiency). The increased ambient temerature lowers the density of the inlet air, thus reducing the mass flow through the turbine, and therefore reduces the ower outut (which is roortional to the mass flow) even further. Engine erformance mas tyically show a reduction of engine mass flow with increasing ambient temerature. On the engine erformance ma for a two-shaft engine, one can see that the decline in full load ower is much steeer at temeratures above the match oint. This distinguishes a two-shaft engine (without adjustable geometry) from a single-shaft engine. The effect of the gas generator seed reduction is more significant than the reduction in firing temerature at low ambient temeratures. Change in Ambient Pressure If the ambient ressure changes, only the density of the gas changes, while the volumetric flow and all comonent efficiencies remain the same. This means that the heat rate is unaffected and the ower is reduced roortional to the density reduction. However, if the engine drives accessory equiment through the gas generator, this is no longer true because the ratio between gas generator work and required accessory ower (which is indeendent of changes in the ambient conditions) is affected (Figure 5). Inlet and Exhaust Losses Any gas turbine needs an inlet and exhaust system to oerate. The inlet system consists of one or several filtration systems, a silencer, ducting, and ossibly de-icing, fogging, evaorative cooling, and other systems. The exhaust system may include a silencer, ducting, and waste heat recovery systems. All these systems will cause ressure dros, i.e., the engine will actually see an inlet ressure that is lower than ambient ressure, and will exhaust against a ressure that is higher than the ambient ressure. These ressure losses reduce the engine erformance (Figure 5). Effects of Humidity The effects of humidity become clearer if we look at the water content of the inlet air. Relative humidity is the ratio between the amount of water in the air comared to the maximum amount of water the air can carry under the revailing conditions of ressure and temerature. At low temeratures, even a high relative humidity does not mean there is a large amount of water in the air, whereas at high temeratures, the mole or weight ercentage of water can be rather high. The engine erformance at low ambient temeratures will thus hardly show any effects of changing relative humidity, while the engine erformance at high ambient temeratures will be effected somewhat by changes in relative humidity (Figure 17). What are the effects of increasing the amount of water vaor in the air? Because water vaor is lighter than air, the mass flow of the engine will be reduced at constant seed. For the same reason, the ressure ratio for a given head and seed will go down. The secific heat of the exhaust gas will increase with increased amounts of water vaor (refer to thermodynamic arameters for exhaust gases). Therefore the turbine can create more ower under otherwise the same conditions. The measurement of the control temerature, i.e., the ratio between TRIT and T 5 (refer to thermodynamic arameters for exhaust gases) may be affected. Figure 17. Effect of Relative Humidity on Gas Turbine Performance (Examle). For a two-shaft engine, the following is exected: When the engine oerates on NGP toing (the engine seed cannot be increased) higher humidity rather reduces ower (items 1 and 2), and when the engine oerates on T 5 toing higher humidity rather increases ower (items 3 and 4). However, engines with active guide vane control (AGVC), i.e., engines where the variable guide vanes of the comressor can be modulated according to a control schedule, are on NGP toing and T 5 toing on warm and hot days. The intent of the AGVC is to modulate the IGVs to maintain maximum NGP while also maintaining maximum T 5. But, when the humidity increases, T 5 dros (item 4), and the engine becomes toed on NGP at cooler T 5, thus the ower is reduced rather than increased. Another issue to consider is that the engine is usually controlled at a constant T 5, not a constant TRIT. For examle, at a constant T 5, the TRIT of a given engine design may dro more than that for another engine design. For the relationshi between T 5 and TRIT refer to the section on control temerature. The result is a net loss of ower for the former, while leaving the latter design with a net gain in ower. For a single-shaft, constant seed gas turbine, at full load and constant TRIT, two effects counteract each other: Increasing relative humidity decreases air mass flow at the constant NGP (which would decrease ower, item 1), but the increasing humidity increases the secific heat (item 3) to offset the loss of air flow. Whether the engine gains or loses ower with relative humidity deends on the articular engine design. While the above sounds rather cumbersome, it must be noted that the overall effect of changes in relative humidity is rather small (Figure 17).

12 258 PROCEEDINGS OF THE 29TH TURBOMACHINERY SYMPOSIUM Part Load To oerate the engine at art load, the fuel flow is adjusted, until some control arameter (for examle the flow through the driven gas comressor, or a certain kw value for a generator) is satisfied. For a single-shaft engine, which has to oerate at constant gas generator seed (to kee the generator frequency constant), this means that the firing temerature will be reduced with load. The airflow will remain almost constant, and the comressor discharge ressure will reduce only slightly. If variable guide vanes are used (for examle, to kee the fuel to air ratio within a small window for emissions control), the airflow will be reduced, while the firing temerature dros less than without variable guide vanes. For a two-shaft engine, both gas generator seed and firing temerature dro at art load. The dro in gas generator seed means that the comressor now oerates at a lower Mach number, and thus behaves the same way as for a full load oint at a higher ambient temerature. The airflow and usually the comressor discharge ressure are reduced. For both single- and two-shaft engines, art load oeration tyically causes an increase in heat rate. How fast the heat rate increases with art load deends largely on the engine comonent characteristics, but hardly on the configuration, i.e., whether it is a single-shaft or two-shaft engine. Changing Power Turbine Seed For any given set of hot gas inlet conditions, the ower turbine will have one otimum seed, which is the seed where the ower turbine works at its highest efficiency, thus roducing the highest outut ower. The otimum working oint of a turbine is characterized by a given ratio of ti seed u (which deends on the rotor seed NPT) and axial velocity c ax. The axial comonent of the velocity c ax is roortional to the volume flow at the ower turbine inlet. The volume flow deends on the ambient temerature and the load. This exlains why the otimum ower turbine seed is a function of ambient temerature and load. Off-otimum seed of the ower turbine reduces the efficiency and the ability to extract head from the flow. Even if NGP (and the fuel flow) does not change, the amount of ower that is roduced by the PT is reduced. Also, because of the unchanged fuel flow, the engine heat rate increases and the exhaust temerature increases accordingly. Theoretically, any engine would reach its maximum exhaust temerature at high ambient, full load, and locked PT. To understand the effects of changing the ower turbine seed, one has to consider the velocity olygons. Figure 18 shows velocity olygons for a reaction turbine: Leaving the flow area and the flow constant (because the flow condition from the gas generator is not changed), the axial ortion of the velocity remains unchanged. Also, the exit flow angles of both rotor (in the absolute frame) and stator (in the rotating frame) will not change, because they are set by the geometry of the blades. The ti seed will change from u to u* due to the change in seed. Figure 18. Velocity Polygon for a Turbine Stage at Design and Off- Design Seed. For the design oint: c u2 0 c u1 u (39) h u 2 The change in seed from N to N* yields and, with P = W h, we get c u2 u * u c u1 u (40) h u * (c u1 * c u2 * ) u * (2u u ) P * P h = * N =2 * N [ * ] 2. (41) h N N This correlation yields the seed-ower relationshi for the turbine stage, and is lotted in Figure 19, which is remarkably similar to a real ower turbine characteristic as in Figure 3. The dro in ower for off-otimum seeds is in reality somewhat larger, because we neglected the reduction of the turbine efficiency due to higher incidence angles and higher swirl in the exit flow. The ressure ratio over the turbine therefore remains almost constant for a wide flow range. Figure 19. Theoretical Turbine Characteristic Derived from the Velocity Polygon. Another interesting result of the above is the torque behavior of the ower turbine: τ * τ P = * N N = 2 *. (42) P N * N The torque is thus a linear function of the seed, with the maximum torque at the lowest seed (Figure 15). This exlains one of the great attractions of a free ower turbine: To rovide the necessary torque to start the driven equiment is usually not difficult (comared to electric motor drives or recirocating engines) because the highest torque is already available at low seeds of the ower turbine. Different Fuel Gas Gas turbines can oerate on a wide variety of gas and liquid fuels. A way of characterizing gas fuels is through the Wobbe index, which describes the amount of energy contained within a given volume of fuel: LHV WI =. (43) SG Fuel gas with a large amount of inert comonents (such as CO 2 or N 2 ) have a low Wobbe index, while substances with a large amount of heavier hydrocarbons have a high Wobbe index. Pieline quality natural gas has a Wobbe index of about The Wobbe index by itself does not describe the flame characteristics of the fuel. For examle: hydrogen has a low Wobbe index, but a very hot flame, while gas with a high CO 2 content also has a low Wobbe index, but a relatively cool flame. Nonetheless, the

13 GAS TURBINE PERFORMANCE WHAT MAKES THE MAP? 259 Wobbe index clearly describes the amount of fuel volume necessary to rovide the rescribed fuel energy flow. The amount of fuel gas that is added and burned in the combustor influences the amount of exhaust gas, which, now at high ressure and high temerature, is exanded through the turbine section. The ower generated in the turbine section is obviously roortional to the mass flow through the turbine section. Similarly, the ower needed to drive the air comressor is roortional to the mass flow through the comressor. If the Wobbe index of the fuel gas is low, the fuel mass flow must be increased to oerate the gas turbine at full load. Even though the fuel mass flow is a very small art of the overall mass flow (about 1 to 3 ercent), the mass flow through the turbine section is increased, while the comressor air mass flow remains roughly the same. Thus, the added mass flow causes the overall turbine outut to increase roortionally to the added mass flow. The air comressor is forced to oerate at a slightly higher discharge ressure due to the added mass flow that has to be ushed through the turbine section. The net effect is an increase in outut ower. The above is valid irresective of whether the engine is a twoshaft or single-shaft engine. Influence of Emission Control Technologies All emission control technologies that use lean-remix combustion require a recise management of the fuel to air ratio in the rimary zone of the combustor (i.e., where the initial combustion takes lace) as well as a recise distribution of combustor liner cooling and dilution flows. Deviations in these areas can lead to increased NO x roduction, higher CO or UHC levels, or flame-out. Lean-remix combustion achieves reduction in NO x emissions by lowering the flame temerature. The flame temerature is determined by the fuel to air ratio in the combustion zone. A stoichiometric fuel to air ratio (such as in conventional combustors) leads to high flame temeratures, while a lean fuel to air ratio can lower the flame temerature significantly. However, a lean fuel to air mixture also means that the combustor is oerating closer to the lean flame-out limit. Any art load oeration, and even more so during load transients, will cause reduction of fuel to air ratio, because the reduction in air flow is smaller than the reduction in fuel flow. Several different aroaches to control the fuel to air ratio are ossible to avoid flame-out at art load or transient situations, for examle: Bleeding air overboard, Using variable inlet guide vanes, and Managing the air distribution between rimary zone and dilution zone through a valve system, to name a few. Obviously, all these aroaches can have an effect on the art load erformance characteristics of the gas turbine. Low Fuel Gas Pressure The fuel gas ressure at skid edge has to be high enough to overcome all ressure losses in the fuel system and the combustor ressure, which is roughly equal to the gas generator comressor discharge ressure (PCD). Note that PCD usually decreases with increasing ambient temerature (refer to discussion of h-s diagram). Insufficient fuel suly ressure at low ambient may well be sufficient for full load oeration at higher ambient temeratures. If the fuel suly ressure is not sufficient, singleand two-shaft engines show distinctly different behavior, namely: A two-shaft engine will run slower, such that the PCD ressure can be overcome by the fuel ressure (Figure 20). If the driven equiment is a gas comressor (and the rocess gas can be used as fuel gas), bootstraing is often ossible: The fuel gas is sulied from the gas comressor discharge side. If the initial fuel ressure is sufficient to start the engine and to oerate the gas comressor, the gas comressor will increase the fuel gas ressure. Thus the engine can roduce more ower, which in turn will allow the gas comressor to increase the fuel ressure even more, until the fuel gas ressure necessary for full load is available. Figure 20. Effect of Low Fuel Gas Pressure on Different Engine Designs. A single-shaft engine, which has to run at constant seed, will exerience a severe reduction in ossible firing temerature and significant loss in ower outut, unless it uses VIGVs. With VIGVs, PCD can also be influenced by the osition of the VIGVs, thus leading to less ower loss (Figure 20). Without VIGVs, the only way to reduce PCD ressure is by moving the oerating oint of the comressor on its ma. This can be done by reducing the back ressure from the turbine, which requires a reduction in volume flow. Since the seed is fixed, only a reduction in firing temerature which reduces the volume flow through the gas generator if everything else remains unchanged can achieve this. A reduced volume flow will reduce the ressure dro required for the gas generator turbine. Accessory Loads While the accessory load can be treated fairly easily in a singleshaft engine its ower requirement is subtracted from the gross engine outut this is somewhat more comlicated in a two-shaft machine. In a two-shaft gas turbine, the accessory load is tyically taken from the gas generator. In order to satisfy the equilibrium conditions the gas generator will have to run hotter than without the load. This could lead to more ower outut at conditions that are not temerature limited. When the firing temerature is limited (i.e., for ambient temeratures above the match oint), the ower outut will fall off more raidly than without the load. That means that an accessory load of 50 h may lead to ower losses at the ower turbine of 100 or more h at higher ambient temeratures. The heat rate will increase due to accessory loads at all ambient temeratures. The net effect of accessory loads can also be described as a move of the match oint to lower ambient temeratures. Variable Inlet and Stator Vanes Many modern gas turbines use variable inlet guide vanes and variable stator vanes in the engine comressor. Adjustable vanes allow altering of the stage characteristics of comressor stages (refer to exlanation on Euler equations) because they change the head making caability of the stage by increasing or reducing the reswirl contribution (Figure 21). This means that for a rescribed ressure ratio they also alter the flow through the comressor. It is therefore ossible to change the flow through the comressor without altering its seed. There are three imortant alications: During startu of the engine it is ossible to kee the comressor from oerating in surge. The airflow can be controlled to maintain a constant fuel to air ratio in the combustor for dry low NO x alications on single-shaft machines.

14 260 PROCEEDINGS OF THE 29TH TURBOMACHINERY SYMPOSIUM Two-shaft engines can be ket from droing in gas generator seed at ambient temeratures higher than the match temerature, i.e., the gas generator turbine will continue to oerate at its highest efficiency. Figure 21. Head-Flow Characteristic for a Comressor with Variable Inlet Guide Vanes. Control Temerature One of the two oerating limits of a gas turbine is the turbine rotor inlet temerature (TRIT or T 3 ). Unfortunately, it is not ossible to measure this temerature directly a temerature robe would only last for a few hours at temeratures that high. Therefore, the inlet temerature into the ower turbine (T 5 ) is measured instead. The thermodynamic relationshi between T 3 and T 5 is described in the section THE GAS TURBINE AS A SYSTEM. The ratio between T 3 and T 5 is determined during the factory test, where T 5 is measured and T 3 is determined from a thermodynamic energy balance. This energy balance requires the accurate determination of outut ower and air flow, and can therefore be erformed best during the factory test. On single-shaft engines, the exhaust temerature T 7 can be used for uroses of monitoring TRIT. This is not ractical for two-shaft engines, because T 7 also deends on the ower turbine seed. Rather than controlling T 3 the control system limits engine oerations to the T 5 that corresonds to the rated T 3. However, the ratio between T 3 and T 5 is not always constant, but varies with the ambient temerature and with the relative humidity: The ratio T 3 /T 5 is reduced at higher ambient temeratures. Maintaining a constant T 5 means that the engine will not reach its maximum allowed T 3 or TRIT on hot days, thus enalizing its ower outut. The reason that the ratio T 3 /T 5 deends on the ambient conditions is quite interesting: The water content of air deends on the ambient temerature and the relative humidity. At constant relative humidity, the content of water in the air increases with increasing ambient temerature. As outlined in the discussion on combustion roducts, the amount of water in the combustion gas has a significant imact on roerties like γ and c in the combustion gas. With the ressure ratio over the gas generator turbine essentially constant, T 3 /T 5 is a function of γ, and therefore a function of the ambient temerature and the relative humidity. Engines with T 3 control use an algorithm in the control system that corrects the T 3 /T 5 ratio according to the ambient temerature. This has no imact on the life of the engine, because both T 3 and T 5 controls obey the same uer limit for TRIT. There are also no hardware differences. The caability to reach its full TRIT on hot days imroves the erformance of the T 3 controlled version of the two-shaft engines significantly. Engines can also be controlled by their exhaust temerature (T 7 ). For single-shaft engines, measuring T 7 or T 5 are equivalent choices. For two-shaft engines, measuring T 7 instead of T 5 adds the comlication that the T 7 control temerature additionally deends on the ower turbine seed, while the relationshi between T 3 and T 5 does not deend on the ower turbine seed. TRANSIENT CONDITIONS Change of Load In a single-shaft, constant seed engine, the only controlled oerating arameter is the firing temerature. A governor will kee the seed constant and will increase the fuel flow with increasing load, thus increasing the firing temerature, until the control limit is reached. For a given mass flow, any increase in firing temerature will increase the volume flow through the turbine section. Therefore, the ressure dro over the turbine increases. This means that the ressure sulied from the comressor has to be increased. Since the comressor also oerates at constant seed, the result is a reduction of mass flow until equilibrium is reached. A tyical erformance ma for a single-shaft engine shows this increase in comressor discharge ressure at increased load. If the engine is equied with VIGVs to kee the fuel to air ratio in the combustor constant, a reduction in load will require a closing of the VIGVs to reduce the airflow. Closing the VIGVs also reduces the ressure ratio of the comressor at constant seed. For a two-shaft engine the situation is somewhat different: An increase in load at the ower turbine will cause the fuel flow to increase. Because the gas generator is not mechanically couled with the ower turbine, it will accelerate, thus increasing airflow, and comressor discharge ressure. At the same time the increasing fuel flow will also increase the firing temerature. The relative increase is governed by the fact that the ower turbine requires a certain ressure ratio to allow a given amount of airflow ass. This forces an equilibrium where the following requirements have to be met: The comressor ower equals GP turbine ower. This determines the available ressure ustream of PT. The available ressure ratio at the ower turbine is sufficient to allow the airflow to be forced through the ower turbine. Deending on the ambient temerature and the engine match temerature, the fuel flow into the engine will either be limited by reaching the maximum firing temerature or the maximum gas generator seed. The ambient temerature where both control limits are reached at the same time is called engine match temerature. Transient Behavior All the above considerations were made with the assumtion that the engine oerates at steady-state conditions. The engine oeration during load transients should be briefly discussed, i.e., when load is added or removed. Figure 22 shows the engine limits (for a two-shaft engine) from start to the full load design oint: The engine initially is accelerated by a starter. At a certain GP seed, fuel is injected and light-off occurs. The fuel flow is increased until the first limit, maximum firing temerature, is encountered. The engine continues to accelerate, while the fuel flow is further increased. Soon, the surge limit of the engine comressor limits the fuel flow. While the starter continues to accelerate the engine, a oint is reached where the steady-state oerating line can be reached without violating surge or temerature limits: at this oint, the engine can oerate self sustaining, i.e., the starter can disengage. The maximum acceleration (i.e., the maximum load addition) can now be achieved by increasing to the maximum ossible fuel flow. However, the maximum ossible fuel flow is limited by either the surge limit of the engine comressor or the maximum firing temerature. If the load suddenly dros, the maximum rate deceleration is limited by the flame-out limits of the engine.

15 GAS TURBINE PERFORMANCE WHAT MAKES THE MAP? 261 APPENDIX A THERMODYNAMICAL PARAMETERS FOR EXHAUST GASES The secific heat and ratios of secific heats, which determine the erformance of the turbine section, deend on the fuel to air ratio, the fuel comosition, and the relative humidity of the air. For mixtures of gases the following equations can be alied to determine c, R, and γ: 1 c,ex = Σ c,i m i (A-1) 100 Figure 22. Start and Acceleration Ma for a Gas Turbine. CONCLUSION The revious sections have given some insight into the working rinciles of a gas turbine, and what the effect of these working rinciles on the oerating characteristics of gas turbines is. Based on this foundation, it was exlained what the effects of changes in ambient temerature, barometric ressure, inlet and exhaust losses, relative humidity, accessory loads, different fuel gases, or changes in ower turbine seed are. The toics resented aim at enhancing the understanding of the oeration rinciles of a gas turbine in industrial alications. NOMENCLATURE A = Throughflow area c = Velocity vector in stationary frame c = Secific heat H = Head h = Enthaly L = Length M = Mach number M n = Machine Mach number N = Rotational seed in rm = Stagnation ressure P = Power Q = Volumetric flow rate q = Heat flow q R = Lower heating value R = Secific gas constant s = Entroy T = Temerature U = Blade velocity W = Mass flow rates w = Velocity vector in rotating frame ν = Kinematic viscosity = Difference η = Efficiency τ = Torque γ = Secific heat ratio ω = Rotational seed in rad/sec = 2πN/60 Subscrits 1 = At engine inlet 2 = At engine comressor exit 3 = At turbine inlet 5 = At ower turbine inlet 7 = At engine exit t = Turbine c = Comressor u = Tangential direction s = Isentroic R ex = 1 Σ R i m i (A-2) 100 c γ ex =,ex. (A-3) c,ex R ex m i is the mole fraction of the individual comonent. The main constituents of the exhaust gas are nitrogen, oxygen, carbon dioxide, and water. The secific heat (c ) and gas constants (R) of all these constituents are known, so it is easy to calculate the overall c and γ, once the mole fractions of the constituents are known. Table A-1 gives γ, c, and R of the above substances at 10 bar, 800 C. Table A-1. Secific Heat (c ), Ratio of Secific Heats (γ) and Gas Constants (R) for Some Comonents of Exhaust Gas. c (kj/kgk) R(kJ/kgK γ = 1/(1-R/c ) Air CO H 2O Assuming an exansion over a constant ressure ratio, and constant efficiency, then: h η T= = t h s = c,ex c,ex γ 1 η t T 3 (1 ( 4 ) γ ) 3 (A-4) Thus, the temerature differential over the turbine deends on the fuel gas comosition, and the water content of the inlet air. The ractical consequence of the above is the fact that most engines measure T 5 rather than T 3 for control uroses. The ratio T 5 /T 3 is often assumed constant. However, in reality it is deendent on the fuel to air ratio, the fuel gas and the water content of the air (i.e., the relative humidity and the ambient temerature). Another effect that must be considered is the fact that the relationshi between the ressure ratio and the Mach number deend on γ. That means that the maximum volumetric flow through the first stage GP nozzle and the first stage PT nozzle also deends on the exhaust gas comosition, which means that different fuel comositions (if the differences are very large) can influence the engine match. APPENDIX B ALGORITHM FOR SINGLE-SHAFT ENGINES The equations: γ 1 T c 1 = [( 2 ) γ 1] (B-1) T 1 η c 1

16 262 PROCEEDINGS OF THE 29TH TURBOMACHINERY SYMPOSIUM T t γ 1 =η t [1 ( 7 ) γ ] (B-2) T 3 3 N = N T 1 (B-3) T 3 T 1 T 3 are all couled by the firing temerature ratio T 3 /T 1 (Cohen, et al., 1996). This ratio has to be determined by trial and error for oeration at any arbitrary oint of the comressor characteristic using the following method: 1. On the comressor ma, chose any oint on the N/ T 1 line. The characteristics then yield 2 / 1,W T 1 / 1, T c /T Guess a value of 3 / 5. The turbine characteristic then gives W T 3 / 3, and T 3 /T 1 can be obtained from the second equation, and furthermore allows the calculation of N/ T With the turbine efficiency from the ma, T t /T 3 can be calculated and, using the ower balance equation, another ratio T 3 /T 1 results. 4. Because this ratio T 3 /T 1 normally is not the same as the initial one, a new ratio 3 / 5 has to be guessed, until the same ratio T 3 /T 1 is obtained. At this oint, a comatible oerating oint is found, if the resulting T 3 is within the allowed oerating limits of the engine. 5. The ower outut finally becomes the difference between turbine ower and comressor absorbed ower: P t =(c,t T t c,c T c 1 γ 1 ) W=(c,t T 3 η t [1 ( 3 ) γ ] η m a (B-4) 1 γ 1 c,c T 1 [( 2 ) γ 1]) W η c η m a Using the above method, one can determine the erformance of a single-shaft gas turbine at any oerating oint. Note that the above method works for engines with or without variable geometry. The difference would be introduced by the comonent mas. APPENDIX C ALGORITHM FOR TWO-SHAFT ENGINES The equations (assume 7 = 1 and W c = W t = W) T c T 1 T t T 3 γ = [( ) γ 1] (C-1) η c 1 γ 1 5 =η t [1 ( ) γ ] (C-2) 3 T c,c c 1 T =c,t t T 3. (C-3) T 1 η m T 3 T 1 N N T = 1 (C-4) T 3 T 1 T 3 are all couled by the firing temerature ratio T 3 /T 1 (Cohen, et al., 1996). This ratio can be determined by trial and error for oeration at any arbitrary oint of the comressor characteristic, using the following method: 1. In the comressor ma, chose any oint on the N/ (T 1 ) line. The characteristics then yield 2 / 1,W (T 1 )/ 1, and T c /T 1 from above. 2. Guess a value for 3 / 5. The turbine characteristic gives W (T 3 )/ 3, and T 3 /T 1 can be obtained from the second equation. Furthermore, this characteristic allows calculation of N/ (T 3 ), using the same seed N as reviously for the comressor. 3. With the turbine efficiency from the ma, T t /T 3 can be calculated and, using the ower balance equation, another ratio T 3 /T 1 results. Because this ratio T 3 /T 1 normally is not the same as the initial one, a new ratio 3 / 5 has to be guessed, until the same ratio T 3 /T 1 is obtained. At this oint, a comatible oerating oint is found, if the resulting T 3 is within the allowed oerating limits of the engine. 4. For the ower turbine, the following relations aly: W T 5 W T 1 1 T 5 = (C-5) T 1 T t T 5 γ 1 =η t [1 ( a ) γ ] (C-6) 5 This condition adds another constraint, because the available ressure ratio 5 / 1 has to be sufficient to move the mass flow W through the ower turbine section. If the available ressure ratio is too low, another oerating oint at a lower mass flow (i.e., lower gas generator seed) has to be selected. 5. Combining the relationshis for the gas generator and the ower turbine yields: W T 5 W T T 5 = 3 3 (C-7) T 3 T 5 γ 1 = 1 η t [1 ( 5 ) γ ] (C-8) T = (C-9) a a Finally, the engine outut is the ower that the ower turbine generates at the available gas generator exit temerature and the ressure ratio over the ower turbine: γ 1 7 P t =c T t W=c T 5 η t [1 ( ) γ ]W (C-10) 5 Note that the ower turbine efficiency deends strongly on the actual ower turbine seed deviation from its otimum seed. REFERENCES API Standard 616, 1998, Gas Turbines for Refinery Service, Fourth Edition, American Petroleum Institute, Washington, D.C. Brun, K. and Kurz, R., 1998, Measurement Uncertainties Encountered During Gas Turbine Driven Comressor Field Testing, ASME Paer 98-GT-1. Cohen, H., Rogers, G. F. C., and Saravanamuttoo, H. I. H., 1996, Gas Turbine Theory, Longman, Harlow. Kurz, R., 1991, Transonic Flow through Turbine Cascades with 3 Different Pitch-to-Chord Ratios, Proc. 10. ISABE, Nottingham, United Kingdom. Kurz, R., Brun, K., and Legrand, D. D., 1999, Field Performance Testing of Gas Turbine Driven Comressor Sets, Proceedings of the Twenty-Eighth Turbomachinery Symosium, Turbomachinery Laboratory, Texas A&M University, College Station, Texas,