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Methodologies for predicting the part-load performance of aero-derivative gas turbines
Energy 34 (2009) 1484–1492
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Energy journal homepage: www.elsevier.com/locate/energy
Methodologies for predicting the part-load performance of aero-derivative gas turbines F. Haglind*, B. Elmegaard Technical University of Denmark, Department of Mechanical Engineering, DK-2800 Kgs. Lyngby, Denmark
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 June 2008 Received in revised form 20 March 2009 Accepted 17 June 2009 Available online 8 August 2009
Prediction of the part-load performance of gas turbines is advantageous in various applications. Sometimes reasonable part-load performance is sufficient, while in other cases complete agreement with the performance of an existing machine is desirable. This paper is aimed at providing some guidance on methodologies for predicting part-load performance of aero-derivative gas turbines. Two different design models – one simple and one more complex – are created. Subsequently, for each of these models, the part-load performance is predicted using component maps and turbine constants, respectively. Comparisons with manufacturer data are made. With respect to the design models, the simple model, featuring a compressor, combustor and turbines, results in equally good performance prediction in terms of thermal efficiency and exhaust temperature as does a more complex model. As for part-load predictions, the results suggest that the mass flow and pressure ratio characteristics can be well predicted with both methods. The thermal efficiency and exhaust temperature, however, are not well predicted below 60–70% load when using turbine constants and assuming constant efficiencies for turbomachinery. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Aero-derivative gas turbine Performance Part-load Map Turbine constant
1. Introduction Prediction of the part-load performance of gas turbines is advantageous in various applications, such as with stationary power plants, aero engines, and mechanical drive and prime mover applications. Sometimes reasonable part-load performance is sufficient, while in other cases complete agreement with the performance of an existing machine is desirable. Which methodology for part-load performance prediction is the more appropriate to use, depends on the required accuracy and the availability of performance data. The study covered in this paper is part of research aimed at finding alternative prime movers for large ships that impact the environment less than today’s slow-speed diesel engines. One of the technologies under consideration is gas and steam turbine combined cycles. Part-load performance of naval prime movers is of great importance because of the considerable portion of the running time spent at part-load. Therefore, models are developed for accurately predicting part-load performance of gas turbines and other components included in such plants.
* Corresponding author. Tel.: þ45 45 25 41 13; fax: þ45 45 93 52 15. E-mail address: [email protected] (F. Haglind). 0360-5442/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2009.06.042
The paper is aimed at providing some guidance on methodologies for predicting part-load performance of aero-derivative gas turbines. Such gas turbine type is considered because of its common use for marine applications. For predicting part-load performance, it is widely recognised that the use of component maps is the most accurate way. However, this approach requires that suitable maps are available, which, in practice, they rarely are (other than for manufacturers). An alternative approach, which is also considered here, is the use of a turbine constant for the turbine, i.e. a constant that governs the relation among flow capacity, pressure ratio and inlet temperature for the turbine. Such approach simplifies the calculation procedure and requires no component information. In order to compare different methods for performance modelling, an existing gas turbine is selected. Performance data, covering the load range, for this machine were provided by the manufacturer. Two different design models – one simple and one more complex – are created. Subsequently, for each of these models, the part-load performance is predicted using component maps and turbine constants, respectively. Comparisons with manufacturer data are made. Other authors have used similar approaches for predicting partload performance of gas turbines. For example, Zhu and Saravanamuttoo [1] used generalized component maps and related these to an actual machine. This approach is very similar to the one
F. Haglind, B. Elmegaard / Energy 34 (2009) 1484–1492
Nomenclature
Abbreviations C compressor, CC combustion chamber, CT compressor turbine, DNA dynamic network analysis (computer simulation program), E exhaust, I inlet, MGO marine gas oil, PT power turbine. Notations COT combustor outlet temperature ( C), turbine constant, CT fraction cupper loss, FCU LHV lower heating value (MJ/kg), TIT turbine inlet temperature ( C),
presented here. Pathak et al. [2] as well as Najjar et al. [3] developed correlations for the performance based on available data for gas turbines. Deidewig and Do¨pelheuer [4] used a similar approach where they explicitly used the ideal gas law and assumed constant polytrophic efficiency. In Section 2 the numerical simulation tool used for the calculations, including the additional development of the tool required for the current study, is described. The selected gas turbine and the design models are described in Section 3. In Section 4 the different methodologies for predicting part-load performance are explained. The performance results for part-load operation are presented and discussed in Section 5. Finally, in Section 6 the conclusions are outlined. 2. DNA – the simulation tool In this section the fundamentals of the simulation program used for this work are described. Moreover, the development work of the program for the purpose of this research is explained briefly.
P R T W
h b 4 y
1485
pressure (bar), gas constant (kJ/kg K), temperature ( C), mass flow (kg/s), efficiency, auxiliary coordinate in component map, mass flow coefficient (m2), specific volume (m3/kg).
Subscripts 3 compressor turbine inlet, 4 power turbine inlet, Cis compressor, isentropic, corr corrected, D design, exh exhaust, PL part-load, std standard atmosphere (T ¼ 15 C, P ¼ 101.325 kPa), th thermal, Tis turbine, isentropic.
systems. Both steady state (involving algebraic equations) and dynamic (involving differential equations) simulations can be conducted. 2.2. Implementation of component maps in DNA For the purpose of this work, the DNA component library has been extended with steady state models describing the part-load characteristics of compressors and turbines of real gas turbine engines. These models are based on component maps provided with the GasTurb software, version 10 [8], which have been compiled by the developer of GasTurb from data published in the public domain. The maps are represented by files stating values for flow, pressure ratio, isentropic efficiency and speed for the complete operating range of the component. A schematic map file for a compressor is shown in Fig. 1. The beta lines are auxiliary coordinates which have values between 0 and 1, and in the map
Pout 2.1. Basics of DNA DNA (dynamic network analysis) is a simulation tool used for energy systems analyses [5,6]. It is the present result of an ongoing development at the Department of Mechanical Engineering, Technical University of Denmark, which began with a Master’s Thesis work in 1990 [7]. Since then the program has been developed to be generally applicable for covering unique features, and hence supplementing other simulation programs. In DNA the physical model is formulated by connecting the relevant component models through nodes and by including operating conditions for the complete system. The physical model is converted into a set of mathematical equations to be solved numerically. The mathematical equations include mass and energy conservation for all components and nodes, as well as relations for thermodynamic properties of the fluids involved. In addition, the components include a number of constitutive equations representing their physical properties, e.g. heat transfer coefficients for heat exchangers and isentropic efficiencies for compressors and turbines. The program includes a component library with models for a large number of different components existing within energy
1
Pin
β
ηis
0
N Tin
W
Tin Pin
Fig. 1. Schematic compressor map.
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they are represented by parabolic functions [9]. The introduction of beta lines is a convenient way of avoiding the ambiguity arising when the speed lines in the map are horizontal or vertical. The efficiencies can be given as contours, and these are illustrated in the figure by dotted lines. Mathematically, the map provides the relationships among flow, speed and beta lines:
f1
W
! pffiffiffiffiffiffi Tin N ; b; pffiffiffiffiffiffi ¼ 0 Pin Tin
(1)
Isentropic efficiency, speed and beta lines:
! N f2 his ; b; pffiffiffiffiffiffi ¼ 0 Tin
(2)
And pressure ratio, speed and beta lines:
f3
! Pout N ; b; pffiffiffiffiffiffi ¼ 0: Pin Tin
(3)
For turbines, only the first two relationships are needed. Suitable map files have been implemented into DNA. At design, a location within the map is selected (in terms of beta and speed), and the map data are linearly scaled (in the case of pressure ratio, it is pressure ratio - 1 that is scaled) in order to achieve the data chosen at design. Subsequently, the component data at any off-design operating point are obtained from the map file using linear interpolation. In DNA the operating point may be specified by any two of the variables in the equations, giving a high flexibility in specifying the design point and part-load operation according to a given need. 3. Design point performance In this section, the performance data for the gas turbine studied are presented, and two different design models are created. The full-load condition is chosen as design point.
Table 1 Full-load performance of the LM2500þ gas turbine Inlet mass flow [kg/s] Fuel flow [kg/s] Exhaust flow [kg/s] Compressor outlet temperature [ C] Exhaust temperature [ C] Relative inlet pressure loss [%] Relative outlet pressure loss [%] Generator efficiency [%] Compressor pressure ratio [-] Electrical power output [kW] Thermal efficiency [%]
88.4 1.934 89.5 495 533.8 1 2.9 97.5 23.54 31 207 37.70
essential parameters for full-load used to create performance models in DNA are listed in Table 1. The manufacturer data are estimated average performance data (not guaranteed) obtained using a performance model. This model is based on performance data compiled from operation data, and it is adjusted periodically as the performance data are received from the field. No component efficiencies, maximum cycle temperature or information on cooling flows were given. Neither was any variable guide vane schedule specified as related to the part power performance. Ambient conditions are 15 C and 1.01325 bar. Based on the flow figures it can be concluded that the overboard bleed, i.e. flow extracted along the compression, is 0.83 kg/s or about 1% of the inlet flow. Only the static conditions out of the compressor were given; hence, the compressor outlet temperature and pressure ratio are computed based on an assumption of the outlet Mach number. An outlet Mach number of 0.25 is assumed, which according to Walsh and Fletcher [10] is an ideal figure for the compressor outlet. When applied to marine applications, the LM2500þ gas turbine runs on a light distillate fuel with a lower heating value (LHV) of 18 400 Btu/lb, corresponding to 42.798 MJ/kg. For the modelling, a fuel composition reflecting typical figures for Marine Gas Oil (MGO) is used. 3.2. Simple model
3.1. Manufacturer data The gas turbine selected for study is the LM2500þ manufactured by General Electric. This machine, being an upgraded version of the LM2500, is commonly used for marine applications. It is an aero-derivative gas turbine originally derived from the CF6 family of aircraft engines used on wide body aircraft. The LM2500þ gas turbine is a two-shaft design, with gas generator mechanically uncoupled from the power turbine, enabling the power turbine to operate at a continuous speed of either 3600 or 3000 rpm, regardless of the speed of the gas generator. It features a 17-stage axial compressor with the first six stages provided with variable guide vanes. The compressor turbine and power turbine feature two and six stages, respectively; see Fig. 2. Performance data for design and off-design conditions for the LM2500þ gas turbine were provided by General Electric. The
In the simple model, the gas turbine is assumed to consist of a compressor, combustion chamber, compressor turbine and power turbine; see Fig. 3. No inlet or exhaust pressure losses, cooling flows, or bleed are modelled. A combustion chamber pressure loss of 3% and a mechanical efficiency of 99% are assumed. Inlet mass flow, pressure ratio and generator efficiency are defined according to the specifications (Table 1), and the compressor and turbine isentropic efficiencies and combustor outlet temperature are adjusted to meet the specifications for thermal efficiency and exhaust temperature. The results are given in Table 2. 3.3. Complex model In the complex model, the gas turbine is assumed to consist of an inlet, compressor, combustion chamber, compressor turbine, power turbine, and exhaust. Similarly as for the simple model, a combustion chamber pressure loss of 3% and a mechanical efficiency of 99% are assumed. Inlet mass flow, pressure ratio,
CC C
Fig. 2. The LM2500þ gas turbine (by courtesy of General Electric).
CT
PT
Fig. 3. Schematic figure of the simple gas turbine model.
F. Haglind, B. Elmegaard / Energy 34 (2009) 1484–1492 Table 2 Comparison of full-load performance for the LM2500þ gas turbine
hCis [%] hTis [%] COT [ C] TIT [ C] PE [kW] Texh [ C] hth [%]
GE data
Simple model
Complex model
– – – – 31 207 533.8 37.70
83.8 86.5 1236 1236 31 207 532.2 37.70
85 88 1310 1250 31 207 531.8 37.75
generator efficiency, and inlet and outlet pressure drops are defined according to the specifications. Bleed is simulated by extracting 1% of the flow after the compressor. Cooling is used to enable higher turbine entry temperatures than the maximum allowable metal temperature. This is accomplished by bleeding off a part of the compressed air which then passes through cooling passages inside the blades. Also air needs to be taken off for sealing, in order to hinder the expanding gases from penetrating the disk system. Effects of cooling are simulated by bleeding off 10% of the air flow after the compressor. Depending on where expansion work takes place, this air is mixed with the hot gases at different points along the expansion. To simulate nozzle guide vane cooling, 8% of the bleed is injected before the compressor turbine, and the remaining 2% is injected before the power turbine in order to simulate the use of rotor cooling and seals. From a modelling point of view, the cooling air flows are mixed with the exhaust gases before the turbines. When running in part-load the percentage of air taken off for cooling is retained. A schematic figure of the engine model is shown in Fig. 4. In practice, for modern gas turbines, the turbine cooling system generally is more complex than modelled here; air is usually extracted from the compressor at a number of places, matching the pressure condition where it should be injected in the turbine. Inlet mass flow, pressure ratio, generator efficiency, and inlet and exhaust pressure losses are defined according to the specifications, and the compressor and turbine isentropic efficiencies and combustor outlet temperature are adjusted to meet the specifications for thermal efficiency and exhaust temperature. Due to the losses in the turbine associated with cooling, in practice, the isentropic efficiency of the compressor turbine would be lower than that of the power turbine. Quantifying the detrimental effect of cooling on the turbine isentropic efficiency is, however, beyond the scope of the current work. Since the overall performance is of primary interest here, for simplicity, the same efficiency figure, representing an average value during the whole expansion process, is selected. The results are given in Table 2. 3.4. Comparison of model results From Table 2 it can be concluded that both the simple and complex models agree very well with manufacturer data, i.e. for a given power output the exhaust temperature and the thermal
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efficiency for both models are very close to the manufacturer data. As a consequence of cooling flows, the turbine inlet temperature (TIT) is lower than the combustor outlet temperature (COT) for the complex model, whereas these temperatures are equal for the simple model. Since various losses are excluded from the simple model, the isentropic efficiencies for the compressor and the turbines need to be lower. 4. Part-load performance In this section the models for part-load performance estimations are described. 4.1. Turbine constant The mass flow coefficient, 4, is the index of total mass flow entering the nozzle throat of an expansion, according to the relationship for a compressible, isentropic flow in a single nozzle, and it is defined as [11]:
W
f ¼ qffiffiffi P V
(4)
In a multistage turbine the expansion process can be divided into a number of segments. For each segment a nozzle analogy may be developed which treats each segment as if it were a single nozzle [11]. This analogy is known as Stodola’s Ellipse, and it states that for each nozzle the following relationship is valid [11,12]:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P fin f 1 out Pin
(5)
This proportionality is mathematically valid only for an infinite number of stages, but it has been shown to be empirically valid down to eight 50% reaction stages in a steam turbine [11]. It has been assumed that all nozzle flow areas remain constant. By applying Eq. (5) to a whole turbine and assuming ideal gas, an expression for the turbine constant (i.e. the constant that governs the relationship between the mass flow coefficient and the expression on the right-hand side of the proportionality sign of Eq. (5)) can be obtained:
pffiffiffiffiffiffi W Tin ffi CT ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P2 Pin out
(6)
This expression for the turbine constant is used in the subsequent calculations. It is recognised from Eq. (6) that for outlet pressure approaching zero, the turbine constant becomes equal to the mass flow coefficient (transformed using the perfect gas law). That the flow coefficient is equal to a constant when the back pressure becomes close to zero, is empirically known to be true for uncontrolled multistage expansion to high vacuum [11]. 4.2. Component maps
CC I
C
CT
1% 10% 8% Bleed Cooling flows
PT
E
2%
Fig. 4. Schematic figure of the complex gas turbine model.
In order to be successful with the prediction of the off-design performance using component maps, it is essential that suitable maps are used. The best option is of course to use the component maps which reflect the actual components of the machine under consideration. However, manufacturers rarely share such information. The analyses conducted by the research community, therefore, often need to be based on general map characteristics available in the public domain. Ideally a map should be selected
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35
Pressure ratio [-]
30 25 20 n=0.10
15
n=0.9
10
n=0.8
5 n=0.4 0 0
10
20
n=0.7
n=0.5 n=0.6
30
40
Corrected mass flow [kg/s]
10
9
8
n=0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0
7
6 50
60
70
80
90
0
100
1
2
3
4
5
6
8
7
Pressure ratio [-]
Corrected mass flow [kg/s] Fig. 5. The map for the compressor (scaled with respect to the design data used here) showing pressure ratio and corrected mass flow. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
Fig. 7. The map for the compressor turbine (scaled with respect to the design data used here) showing corrected mass flow and pressure ratio. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
with characteristics similar to those of the component requiring the off-design behaviour estimate. The compressor map used here, compiled from data in Stevenson and Saravanamuttoo [13], is intended to reflect the compressor of the LM2500 gas turbine. The map used for the compressor turbine reflects a high work, low aspect ratio axial turbine [14], and the power turbine is modelled using a map of an axial turbine derived from Serovy [15]. The component maps used are depicted in Figs. 5–10, where the corrected mass flow and corrected speed given in the maps are defined as follows:
When the stators are rotated away from the axial direction, the axial velocity and mass flow are decreased for a given rotational speed. At low rotational speeds, this delays stalling of the first few stages and choking in the last stage, hence improving the surge margin. Whether the compressor map used here includes any variable geometry within its characteristics is unknown.
Wcorr ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R T W Rstd Tstd
(7)
P Pstd
N Ncorr ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R T Rstd Tstd
(8)
The parameter R is the gas constant and ‘‘std’’ refers to standard atmosphere (T ¼ 15 C, P ¼ 101.325 kPa). As pointed out in Section 3.1, the compressor of the LM2500þ gas turbine is provided with a number of stages with variable geometry. In general, compressors often are provided with several rows of variable stators at the front of the compressor in order to permit large pressure ratios to be achieved in a single-shaft [10,16].
4.3. Generator efficiency According to The Ångstro¨m Laboratory, Sweden (J. Santiago, The Ångstro¨m Laboratory, Uppsala, Sweden, 2007, private communication) and theory about generator losses [17], one fraction of the generator loss (i.e. the copper losses, which are produced in the winding of the stator) is dependent on the load squared, whereas the rest of the loss is independent of the load. The efficiency of the generator is usually defined as the ratio of the electrical power output to the mechanical power input. Assuming that the copper losses constitute a fraction, FCU, of the total losses in design, the following equation for the efficiency in part-load as a function of this fraction, the efficiency at design, hD, and the load can be derived:
hPL ¼
(9)
In order to find a reasonable figure for FCU, results for the generator of the LM2500þ gas turbine are considered. This is a BRUSH DAX 2-pole turbogenerator (BDAX 71-193ER 60 Hz, 13.8 kV, 0.8PF),
100
100
90
90
80 n=0.7
70 n=0.4
60
n=0.8
Isentropic efficiency [%]
Isentropic efficiency [%]
LoadhD i h LoadhD þ ð1 hD Þ ð1 FCU Þ þ FCU Load2
n=0.9 n=1.0
n=0.6 n=0.5
50 40 30 20 10
80 70
n=0.4
60
n=0.5 n=0.6
n=0.7
n=1.0 n=0.9 n=0.8
50 40 30 20 10
0
0 0
20
40
60
80
100
Corrected mass flow [kg/s] Fig. 6. The map for the compressor (scaled with respect to the design data used here) showing isentropic efficiency and corrected mass flow. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
0
1
2
3
4
5
6
7
8
Pressure ratio [-] Fig. 8. The map for the compressor turbine (scaled with respect to the design data used here) showing isentropic efficiency and pressure ratio. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
F. Haglind, B. Elmegaard / Energy 34 (2009) 1484–1492 100
n=0.7 n=0.8 n=0.9 n=1.0
n=0.4 n=0.5 n=0.6
35
96
30
Efficiency [%]
Corrected mass flow [kg/s]
40
1489
25 20 15 10 5
92
GE Formula
88
84
0 0
1
2
3
4
5
6
80
Pressure ratio [-] Fig. 9. The map for the power turbine (scaled with respect to the design data used here) showing corrected mass flow and pressure ratio. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
which can run on either 3000 rpm, corresponding to a frequency of 50 Hz, or 3600 rpm, corresponding to a frequency of 60 Hz. Efficiency figures for this generator for the load ranging from 10% to 100% are shown in Fig. 11. For FCU equal to 0.43 very good agreement between Eq. (9) and the data is found. Eq. (9) with FCU equal to 0.43 is used in this paper for part-load modelling of the generator.
5. Results and discussion Using DNA, performance results for the models are obtained for the load ranging from 10% to 100%. For each design model, both turbine constants and maps are employed, resulting in four cases in total. The model results are compared with the manufacturer data; see Figs. 12–15. For the models using maps, the agreement with manufacturer data is very good except for the lightest loads. No results are displayed for loads below 20%, because for these conditions the operating points of the power turbine become located outside the data range included in the map. A contributing source for the deviation at low powers might be the uncertainty about operation and modelling of variable geometry for the compressor (see Sections 3.1 and 4.2). In general, the results suggest that the complex model gives slightly better agreement with manufacturer data at part-load, but the difference is indeed small.
0
20
40
60
80
100
Load [%] Fig. 11. Generator efficiency versus load for manufacturer data and results of formula.
In order to understand the part-load behaviour of the aeroderivative gas turbine, the effect of operating two turbines in series is considered, following the outline of Cohen et al. [16]. The nondimensional flow at the exit of the gas generator (index 4) is a function of the non-dimensional flow at the inlet to the compressor turbine (index 3), and the compressor turbine pressure ratio and temperature ratio; see Eq. (10). In turn, the temperature ratio is a function of the efficiency. The efficiency could be obtained from the turbine characteristics, but, in practice, the variation with rotational speed for a given pressure ratio is small, particularly over the restricted range of operation of the compressor turbine. Moreover, the effect on the non-dimensional speed becomes even smaller as it is dependent on the square root of the temperature ratio. If a mean value of efficiency at any given pressure ratio is used, the non-dimensional flow out becomes a function of the nondimensional flow in and the pressure ratio. Assuming this, a single curve representing the compressor turbine outlet flow characteristics can readily be obtained for points on the single curve of the inlet flow characteristics; see dotted curve in Fig. 16.
W
pffiffiffiffiffi pffiffiffiffiffi sffiffiffiffiffi T4 W T3 P3 T4 ¼ P4 P3 P4 T3
(10)
25
Pressure ratio [-]
20
100
Isentropic efficiency [%]
90
n=1.0
80 n=0.4
70
n=0.5 n=0.6
n=0.7
n=0.8 n=0.9
60
15
10
50 40
5
30 20 0
10
0
0 0
1
2
3
4
5
20
Pressure ratio [-] GE data
Fig. 10. The map for the power turbine (scaled with respect to the design data used here) showing isentropic efficiency and pressure ratio. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
40
60
80
Load [%]
6
Complex & maps Simple & CT
Complex & CT Simple & maps
Fig. 12. Compressor pressure ratio versus load.
100
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F. Haglind, B. Elmegaard / Energy 34 (2009) 1484–1492 100
600
90
Exhaust temperature [gr C]
Inlet mas flow [kg/s]
80 70 60 50 40 30 20
500
400
300
200
100
10 0
0 0
20
40
60
80
100
0
20
Load [%]
60
80
100
Load [%] Complex & CT
Complex & maps
GE data
40
Simple & CT
GE data
Simple & maps
Complex & maps Simple & CT
Complex & CT Simple & maps
Fig. 13. Inlet mass flow versus load.
Fig. 15. Exhaust temperature versus load.
From Fig. 16 it can be seen that the requirement for flow compatibility between the compressor turbine and the power turbine places a major restriction on the operation of the compressor turbine. The maximum pressure ratio across the compressor turbine is controlled by the choking of the power turbine (point a), and at all times the pressure ratio is controlled by the swallowing capacity of the power turbine (e.g. point b). A further consequence of the fixed relationship between the turbine pressure ratios is that it is possible to plot the compressor turbine pressure ratio versus the compressor pressure ratio. From this figure it follows that the compressor turbine pressure ratio increases with the compressor pressure ratio until the power turbine becomes choked, at which it becomes constant. At full-load, often both the compressor turbine first-stage nozzle and the power turbine nozzle operate at or near choked flow condition [18]. In the case studied here, the power turbine is operated close to choked condition, and the non-dimensional mass flow decreases first slowly and then with increasing rate with
decreasing pressure ratio. The compressor turbine is operated within a narrow range of pressure ratios, and at all times it stays choked. Considering the model with maps, the turbine flow characteristics (i.e. whether the flows are choked or not) at full-load are determined by the location of the design points within the turbine maps. That is, by choosing other design point locations within the turbine maps, giving other flow characteristics, a different partload performance would be obtained. With respect to the model with turbine constants, the turbine flow characteristics at the design point are governed by the pressure ratio and the value of the turbine constant. For illustration, the actual operating points for the turbines for the simple model with turbine constants are shown in Fig. 17. The results shown in Figs. 12 and 13 suggest that turbine constants are sufficient to predict the mass flow and pressure ratio characteristics during part-load conditions. In terms of exhaust temperature and thermal efficiency, on the contrary, the results suggest that the model with turbine constants does not predict these performances adequately at light loads (see Figs. 14 and 15). This is because the isentropic efficiencies are assumed constant. Neglecting the influence of load on the isentropic efficiency for the compressor has no significant effect, because even though the pressure ratio and non-dimensional mass flow have decreased significantly for the lowest loads, the operating point is still located in a region of the map with high efficiency.
40
Thermal efficiency [%]
35 30 25 20 15 10 5 0 0
20
40
60
80
100
Load [%] GE data
Complex & maps Simple & CT
Complex & CT Simple & maps
Fig. 14. Thermal efficiency versus load.
Fig. 16. Operation of turbines in series.
800 600 400 200 0 1
2
3
4
5
6
Non-dimensional flow
Non-dimensional flow
F. Haglind, B. Elmegaard / Energy 34 (2009) 1484–1492
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800 600 400 200 0 1
P3/P4
2
3
4
5
6
P4/Pa
Fig. 17. Actual operating points for the two turbines for the simple model with turbine constants. Marks indicate operating points between 10% and 100% load.
Since the non-dimensional flow for the compressor turbine is constant and the pressure ratio is only slightly decreased, the isentropic efficiency for the compressor turbine also is more or less unaffected by the load. What gives rise to the deviations at light loads when using turbine constants, is simply that the influence on the isentropic efficiency for the power turbine is neglected. As the load is decreased, the pressure ratio for the power turbine is decreased significantly (since the pressure ratio across the compressor turbine stays nearly constant), affecting the efficiency essentially. In the models with turbine constants and constant efficiencies for the turbomachinery, the unreasonably high efficiency for the power turbine will result in a too low exhaust temperature for light loads, which explains the deviation shown in Fig. 15. Moreover, neglecting the degradation in component efficiencies in part-load, results in an over-estimation of the thermal efficiency (see Fig. 14, a consequence which is partly counter-acted by a small over-estimation of the turbine inlet temperature).
An essential advantage with the approach of using maps is that agreement always can be found, though it may sometimes involve substantial effort. If the part-load performance achieved is not satisfactory with one set of maps, these can be replaced by others. Another parameter affecting the part-load performance which can be varied, is the location of the design point within the maps. The procedure is discussed in Kurzke [19]. If these measures would not be sufficient, the map characteristics can also be changed manually in order to attain satisfactory agreement. With the use of turbine constants no actions can be taken to change the part-load performance. The methodologies discussed here for predicting the part-load performance of aero-derivative gas turbines are of course general and can be applied to any gas turbine type. However, it is not sure that the conclusions drawn about the applicability of using turbine constants would be the same for other gas turbine types.
6. Conclusions
The authors would like to express their gratitude to Joseph Peters and Danny Hutchison at General Electric, USA, for providing information and performance data on the LM2500þ gas turbine, and Joachim Kurzke (developer of GasTurb), Germany, for providing information on the component maps provided with GasTurb 10. Furthermore, Juan de Santiago and Mats Lejon at The Ångstro¨m Laboratory, Sweden, are thanked for their guidance on generator performance. The funding from the Danish Center for Maritime Technology (DCMT) is acknowledged.
In this paper different methodologies for predicting the partload performance of an aero-derivative gas turbine have been investigated. Model results have been compared with manufacturer data for the LM2500þ gas turbine. With respect to the design models, a simple model, featuring a compressor, combustor and turbines, results in equally good performance prediction (in terms of thermal efficiency and exhaust temperature) as a more complex model including also bleed, cooling flows and pressure losses. The major drawbacks of the simple model are that unrealistically poor component efficiencies need to be used, and the lack of cooling modelling, results in unrealistic temperature levels within the cycle. Having a reasonable estimation of the maximum cycle temperature can, for example, be important if the formation of pollutant emissions should be considered. Moreover, the complex model shows slightly better agreement with manufacturer data in part-load; however, the difference is indeed small. Considering the two different methodologies for predicting the part-load performance – maps and turbine constants – the results suggest that the mass flow and pressure ratio characteristics can be well predicted with both methods. Down to about 60–70% load also the thermal efficiency and exhaust temperature can be well predicted with both methods, but below that point the use of turbine constants and assuming constant efficiencies for turbomachinery, results in an under-prediction of the exhaust temperature and overprediction of the thermal efficiency; the lower the load, the higher the deviations. For instance, at 30% load, the model with turbine constants gives a thermal efficiency 8.5% higher and an exhaust temperature 12% lower than the manufacturer data. For the same operating point, the model with maps provides agreement in thermal efficiency and an exhaust temperature 1.5% lower than manufacturer data.
Acknowledgements
References [1] Zhu P, Saravanamuttoo HIH. Simulation of an advanced twin-spool Industrial gas turbine. J Eng Gas Turbines Power 1992;114:180–5. [2] Pathak M, Suresh Kumar P, Saha UK. Prediction of off-design performance characteristics of a gas turbine cycle using matching technique. Int J Turbo Jet Engines 2005;22:103–19. [3] Najjar YSH, Lamfon NJ, Akyurt M. Modelling and simulation of gas turbine engines, part 1: design point performance at ISO conditions. Int J Power Energy Syst 1995;15(2):61–7. [4] Deidewig F, Do¨pelheuer A. Studies on NOx-emissions of SST engine concepts. In: AGARD PEP symposium on advanced aero-engine concepts and controls, Seattle, USA, AGARD-CP-572, 1995. [5] Elmegaard B, Houbak N. DNA – a general energy system simulation tool. In: Proceedings of SIMS 2005, Trondheim, Norway, 2005. [6] Elmegaard B. Simulation of boiler dynamics – development, evaluation and application of general energy system simulation tool. Ph.D. thesis, Technical University of Denmark, Department of Mechanical Engineering, Denmark, 1999. [7] Perstrup C. Analysis of power plant installation based on network theory (in Danish). M.Sc. thesis, Technical University of Denmark, Laboratory of Energetics, Denmark; 1991. [8] Kurzke J. Component map collection 2, Compressor and turbine maps for gas turbine performance computer programs. Germany; 2004, http://www. gasturb.de/. [9] Kurzke J. Preparing compressor maps for gas turbine performance modelling with SmoothC, version 8. Germany; 2002, http://www.gasturb.de/. [10] Walsh PP, Fletcher P. Gas turbine performance. Malden, USA: Blackwell Science Ltd.; 1998. [11] Cooke DH. On prediction of off-design multistage turbine pressures by Stodola’s ellipse. J Eng Gas Turbines Power 1985;107:596–606.
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[12] Csanady GT. Theory of turbomachines. New York, USA: McGraw-Hill; 1964. [13] Stevenson JD, Saravanamuttoo HIH. Simulating indirect thrust measurement methods for high bypass turbofans. ASME Paper No. 93-GT-335, 1993. [14] Stabe RG, Ehitney WJ, Moffit TP. Performance of high-work low aspect ratio turbine tested with a realistic inlet radial temperature profile. NASA TM 83665, NASA Headquarters, Suite 5K39, Washington, DC 20546-0001, USA; 1984. [15] Serovy GK. Compressor and turbine prediction system development – lessons from thirty years of history. AGARD LS 83; 1976.
[16] Cohen H, Rogers GFC, Saravanamutto HIH. Gas turbine theory. 4th ed. Essex, UK: Longman Group Limited; 1996. [17] Wildi T. Electrical machines, drives, and power systems. 6th ed. New Jersey, USA: Pearson Education, Inc.; 2006. [18] Kurz R. Gas turbine performance. Solar turbines incorporated, San Diego, California, USA; 2005, http://turbolab.tamu.edu/pubs/Turbo34/T34pg131.pdf. [19] Kurzke J. How to create a performance model of a gas turbine from a limited amount of information. In: Proceedings of ASME Turbo Expo 2005, RenoTahoe, Nevada, USA, vol. 1, 2005, pp. 145–53.
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Methodologies for predicting the part-load performance of aero-derivative gas turbines F. Haglind*, B. Elmegaard Technical University of Denmark, Department of Mechanical Engineering, DK-2800 Kgs. Lyngby, Denmark
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 June 2008 Received in revised form 20 March 2009 Accepted 17 June 2009 Available online 8 August 2009
Prediction of the part-load performance of gas turbines is advantageous in various applications. Sometimes reasonable part-load performance is sufficient, while in other cases complete agreement with the performance of an existing machine is desirable. This paper is aimed at providing some guidance on methodologies for predicting part-load performance of aero-derivative gas turbines. Two different design models – one simple and one more complex – are created. Subsequently, for each of these models, the part-load performance is predicted using component maps and turbine constants, respectively. Comparisons with manufacturer data are made. With respect to the design models, the simple model, featuring a compressor, combustor and turbines, results in equally good performance prediction in terms of thermal efficiency and exhaust temperature as does a more complex model. As for part-load predictions, the results suggest that the mass flow and pressure ratio characteristics can be well predicted with both methods. The thermal efficiency and exhaust temperature, however, are not well predicted below 60–70% load when using turbine constants and assuming constant efficiencies for turbomachinery. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Aero-derivative gas turbine Performance Part-load Map Turbine constant
1. Introduction Prediction of the part-load performance of gas turbines is advantageous in various applications, such as with stationary power plants, aero engines, and mechanical drive and prime mover applications. Sometimes reasonable part-load performance is sufficient, while in other cases complete agreement with the performance of an existing machine is desirable. Which methodology for part-load performance prediction is the more appropriate to use, depends on the required accuracy and the availability of performance data. The study covered in this paper is part of research aimed at finding alternative prime movers for large ships that impact the environment less than today’s slow-speed diesel engines. One of the technologies under consideration is gas and steam turbine combined cycles. Part-load performance of naval prime movers is of great importance because of the considerable portion of the running time spent at part-load. Therefore, models are developed for accurately predicting part-load performance of gas turbines and other components included in such plants.
* Corresponding author. Tel.: þ45 45 25 41 13; fax: þ45 45 93 52 15. E-mail address: [email protected] (F. Haglind). 0360-5442/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2009.06.042
The paper is aimed at providing some guidance on methodologies for predicting part-load performance of aero-derivative gas turbines. Such gas turbine type is considered because of its common use for marine applications. For predicting part-load performance, it is widely recognised that the use of component maps is the most accurate way. However, this approach requires that suitable maps are available, which, in practice, they rarely are (other than for manufacturers). An alternative approach, which is also considered here, is the use of a turbine constant for the turbine, i.e. a constant that governs the relation among flow capacity, pressure ratio and inlet temperature for the turbine. Such approach simplifies the calculation procedure and requires no component information. In order to compare different methods for performance modelling, an existing gas turbine is selected. Performance data, covering the load range, for this machine were provided by the manufacturer. Two different design models – one simple and one more complex – are created. Subsequently, for each of these models, the part-load performance is predicted using component maps and turbine constants, respectively. Comparisons with manufacturer data are made. Other authors have used similar approaches for predicting partload performance of gas turbines. For example, Zhu and Saravanamuttoo [1] used generalized component maps and related these to an actual machine. This approach is very similar to the one
F. Haglind, B. Elmegaard / Energy 34 (2009) 1484–1492
Nomenclature
Abbreviations C compressor, CC combustion chamber, CT compressor turbine, DNA dynamic network analysis (computer simulation program), E exhaust, I inlet, MGO marine gas oil, PT power turbine. Notations COT combustor outlet temperature ( C), turbine constant, CT fraction cupper loss, FCU LHV lower heating value (MJ/kg), TIT turbine inlet temperature ( C),
presented here. Pathak et al. [2] as well as Najjar et al. [3] developed correlations for the performance based on available data for gas turbines. Deidewig and Do¨pelheuer [4] used a similar approach where they explicitly used the ideal gas law and assumed constant polytrophic efficiency. In Section 2 the numerical simulation tool used for the calculations, including the additional development of the tool required for the current study, is described. The selected gas turbine and the design models are described in Section 3. In Section 4 the different methodologies for predicting part-load performance are explained. The performance results for part-load operation are presented and discussed in Section 5. Finally, in Section 6 the conclusions are outlined. 2. DNA – the simulation tool In this section the fundamentals of the simulation program used for this work are described. Moreover, the development work of the program for the purpose of this research is explained briefly.
P R T W
h b 4 y
1485
pressure (bar), gas constant (kJ/kg K), temperature ( C), mass flow (kg/s), efficiency, auxiliary coordinate in component map, mass flow coefficient (m2), specific volume (m3/kg).
Subscripts 3 compressor turbine inlet, 4 power turbine inlet, Cis compressor, isentropic, corr corrected, D design, exh exhaust, PL part-load, std standard atmosphere (T ¼ 15 C, P ¼ 101.325 kPa), th thermal, Tis turbine, isentropic.
systems. Both steady state (involving algebraic equations) and dynamic (involving differential equations) simulations can be conducted. 2.2. Implementation of component maps in DNA For the purpose of this work, the DNA component library has been extended with steady state models describing the part-load characteristics of compressors and turbines of real gas turbine engines. These models are based on component maps provided with the GasTurb software, version 10 [8], which have been compiled by the developer of GasTurb from data published in the public domain. The maps are represented by files stating values for flow, pressure ratio, isentropic efficiency and speed for the complete operating range of the component. A schematic map file for a compressor is shown in Fig. 1. The beta lines are auxiliary coordinates which have values between 0 and 1, and in the map
Pout 2.1. Basics of DNA DNA (dynamic network analysis) is a simulation tool used for energy systems analyses [5,6]. It is the present result of an ongoing development at the Department of Mechanical Engineering, Technical University of Denmark, which began with a Master’s Thesis work in 1990 [7]. Since then the program has been developed to be generally applicable for covering unique features, and hence supplementing other simulation programs. In DNA the physical model is formulated by connecting the relevant component models through nodes and by including operating conditions for the complete system. The physical model is converted into a set of mathematical equations to be solved numerically. The mathematical equations include mass and energy conservation for all components and nodes, as well as relations for thermodynamic properties of the fluids involved. In addition, the components include a number of constitutive equations representing their physical properties, e.g. heat transfer coefficients for heat exchangers and isentropic efficiencies for compressors and turbines. The program includes a component library with models for a large number of different components existing within energy
1
Pin
β
ηis
0
N Tin
W
Tin Pin
Fig. 1. Schematic compressor map.
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they are represented by parabolic functions [9]. The introduction of beta lines is a convenient way of avoiding the ambiguity arising when the speed lines in the map are horizontal or vertical. The efficiencies can be given as contours, and these are illustrated in the figure by dotted lines. Mathematically, the map provides the relationships among flow, speed and beta lines:
f1
W
! pffiffiffiffiffiffi Tin N ; b; pffiffiffiffiffiffi ¼ 0 Pin Tin
(1)
Isentropic efficiency, speed and beta lines:
! N f2 his ; b; pffiffiffiffiffiffi ¼ 0 Tin
(2)
And pressure ratio, speed and beta lines:
f3
! Pout N ; b; pffiffiffiffiffiffi ¼ 0: Pin Tin
(3)
For turbines, only the first two relationships are needed. Suitable map files have been implemented into DNA. At design, a location within the map is selected (in terms of beta and speed), and the map data are linearly scaled (in the case of pressure ratio, it is pressure ratio - 1 that is scaled) in order to achieve the data chosen at design. Subsequently, the component data at any off-design operating point are obtained from the map file using linear interpolation. In DNA the operating point may be specified by any two of the variables in the equations, giving a high flexibility in specifying the design point and part-load operation according to a given need. 3. Design point performance In this section, the performance data for the gas turbine studied are presented, and two different design models are created. The full-load condition is chosen as design point.
Table 1 Full-load performance of the LM2500þ gas turbine Inlet mass flow [kg/s] Fuel flow [kg/s] Exhaust flow [kg/s] Compressor outlet temperature [ C] Exhaust temperature [ C] Relative inlet pressure loss [%] Relative outlet pressure loss [%] Generator efficiency [%] Compressor pressure ratio [-] Electrical power output [kW] Thermal efficiency [%]
88.4 1.934 89.5 495 533.8 1 2.9 97.5 23.54 31 207 37.70
essential parameters for full-load used to create performance models in DNA are listed in Table 1. The manufacturer data are estimated average performance data (not guaranteed) obtained using a performance model. This model is based on performance data compiled from operation data, and it is adjusted periodically as the performance data are received from the field. No component efficiencies, maximum cycle temperature or information on cooling flows were given. Neither was any variable guide vane schedule specified as related to the part power performance. Ambient conditions are 15 C and 1.01325 bar. Based on the flow figures it can be concluded that the overboard bleed, i.e. flow extracted along the compression, is 0.83 kg/s or about 1% of the inlet flow. Only the static conditions out of the compressor were given; hence, the compressor outlet temperature and pressure ratio are computed based on an assumption of the outlet Mach number. An outlet Mach number of 0.25 is assumed, which according to Walsh and Fletcher [10] is an ideal figure for the compressor outlet. When applied to marine applications, the LM2500þ gas turbine runs on a light distillate fuel with a lower heating value (LHV) of 18 400 Btu/lb, corresponding to 42.798 MJ/kg. For the modelling, a fuel composition reflecting typical figures for Marine Gas Oil (MGO) is used. 3.2. Simple model
3.1. Manufacturer data The gas turbine selected for study is the LM2500þ manufactured by General Electric. This machine, being an upgraded version of the LM2500, is commonly used for marine applications. It is an aero-derivative gas turbine originally derived from the CF6 family of aircraft engines used on wide body aircraft. The LM2500þ gas turbine is a two-shaft design, with gas generator mechanically uncoupled from the power turbine, enabling the power turbine to operate at a continuous speed of either 3600 or 3000 rpm, regardless of the speed of the gas generator. It features a 17-stage axial compressor with the first six stages provided with variable guide vanes. The compressor turbine and power turbine feature two and six stages, respectively; see Fig. 2. Performance data for design and off-design conditions for the LM2500þ gas turbine were provided by General Electric. The
In the simple model, the gas turbine is assumed to consist of a compressor, combustion chamber, compressor turbine and power turbine; see Fig. 3. No inlet or exhaust pressure losses, cooling flows, or bleed are modelled. A combustion chamber pressure loss of 3% and a mechanical efficiency of 99% are assumed. Inlet mass flow, pressure ratio and generator efficiency are defined according to the specifications (Table 1), and the compressor and turbine isentropic efficiencies and combustor outlet temperature are adjusted to meet the specifications for thermal efficiency and exhaust temperature. The results are given in Table 2. 3.3. Complex model In the complex model, the gas turbine is assumed to consist of an inlet, compressor, combustion chamber, compressor turbine, power turbine, and exhaust. Similarly as for the simple model, a combustion chamber pressure loss of 3% and a mechanical efficiency of 99% are assumed. Inlet mass flow, pressure ratio,
CC C
Fig. 2. The LM2500þ gas turbine (by courtesy of General Electric).
CT
PT
Fig. 3. Schematic figure of the simple gas turbine model.
F. Haglind, B. Elmegaard / Energy 34 (2009) 1484–1492 Table 2 Comparison of full-load performance for the LM2500þ gas turbine
hCis [%] hTis [%] COT [ C] TIT [ C] PE [kW] Texh [ C] hth [%]
GE data
Simple model
Complex model
– – – – 31 207 533.8 37.70
83.8 86.5 1236 1236 31 207 532.2 37.70
85 88 1310 1250 31 207 531.8 37.75
generator efficiency, and inlet and outlet pressure drops are defined according to the specifications. Bleed is simulated by extracting 1% of the flow after the compressor. Cooling is used to enable higher turbine entry temperatures than the maximum allowable metal temperature. This is accomplished by bleeding off a part of the compressed air which then passes through cooling passages inside the blades. Also air needs to be taken off for sealing, in order to hinder the expanding gases from penetrating the disk system. Effects of cooling are simulated by bleeding off 10% of the air flow after the compressor. Depending on where expansion work takes place, this air is mixed with the hot gases at different points along the expansion. To simulate nozzle guide vane cooling, 8% of the bleed is injected before the compressor turbine, and the remaining 2% is injected before the power turbine in order to simulate the use of rotor cooling and seals. From a modelling point of view, the cooling air flows are mixed with the exhaust gases before the turbines. When running in part-load the percentage of air taken off for cooling is retained. A schematic figure of the engine model is shown in Fig. 4. In practice, for modern gas turbines, the turbine cooling system generally is more complex than modelled here; air is usually extracted from the compressor at a number of places, matching the pressure condition where it should be injected in the turbine. Inlet mass flow, pressure ratio, generator efficiency, and inlet and exhaust pressure losses are defined according to the specifications, and the compressor and turbine isentropic efficiencies and combustor outlet temperature are adjusted to meet the specifications for thermal efficiency and exhaust temperature. Due to the losses in the turbine associated with cooling, in practice, the isentropic efficiency of the compressor turbine would be lower than that of the power turbine. Quantifying the detrimental effect of cooling on the turbine isentropic efficiency is, however, beyond the scope of the current work. Since the overall performance is of primary interest here, for simplicity, the same efficiency figure, representing an average value during the whole expansion process, is selected. The results are given in Table 2. 3.4. Comparison of model results From Table 2 it can be concluded that both the simple and complex models agree very well with manufacturer data, i.e. for a given power output the exhaust temperature and the thermal
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efficiency for both models are very close to the manufacturer data. As a consequence of cooling flows, the turbine inlet temperature (TIT) is lower than the combustor outlet temperature (COT) for the complex model, whereas these temperatures are equal for the simple model. Since various losses are excluded from the simple model, the isentropic efficiencies for the compressor and the turbines need to be lower. 4. Part-load performance In this section the models for part-load performance estimations are described. 4.1. Turbine constant The mass flow coefficient, 4, is the index of total mass flow entering the nozzle throat of an expansion, according to the relationship for a compressible, isentropic flow in a single nozzle, and it is defined as [11]:
W
f ¼ qffiffiffi P V
(4)
In a multistage turbine the expansion process can be divided into a number of segments. For each segment a nozzle analogy may be developed which treats each segment as if it were a single nozzle [11]. This analogy is known as Stodola’s Ellipse, and it states that for each nozzle the following relationship is valid [11,12]:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P fin f 1 out Pin
(5)
This proportionality is mathematically valid only for an infinite number of stages, but it has been shown to be empirically valid down to eight 50% reaction stages in a steam turbine [11]. It has been assumed that all nozzle flow areas remain constant. By applying Eq. (5) to a whole turbine and assuming ideal gas, an expression for the turbine constant (i.e. the constant that governs the relationship between the mass flow coefficient and the expression on the right-hand side of the proportionality sign of Eq. (5)) can be obtained:
pffiffiffiffiffiffi W Tin ffi CT ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P2 Pin out
(6)
This expression for the turbine constant is used in the subsequent calculations. It is recognised from Eq. (6) that for outlet pressure approaching zero, the turbine constant becomes equal to the mass flow coefficient (transformed using the perfect gas law). That the flow coefficient is equal to a constant when the back pressure becomes close to zero, is empirically known to be true for uncontrolled multistage expansion to high vacuum [11]. 4.2. Component maps
CC I
C
CT
1% 10% 8% Bleed Cooling flows
PT
E
2%
Fig. 4. Schematic figure of the complex gas turbine model.
In order to be successful with the prediction of the off-design performance using component maps, it is essential that suitable maps are used. The best option is of course to use the component maps which reflect the actual components of the machine under consideration. However, manufacturers rarely share such information. The analyses conducted by the research community, therefore, often need to be based on general map characteristics available in the public domain. Ideally a map should be selected
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35
Pressure ratio [-]
30 25 20 n=0.10
15
n=0.9
10
n=0.8
5 n=0.4 0 0
10
20
n=0.7
n=0.5 n=0.6
30
40
Corrected mass flow [kg/s]
10
9
8
n=0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0
7
6 50
60
70
80
90
0
100
1
2
3
4
5
6
8
7
Pressure ratio [-]
Corrected mass flow [kg/s] Fig. 5. The map for the compressor (scaled with respect to the design data used here) showing pressure ratio and corrected mass flow. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
Fig. 7. The map for the compressor turbine (scaled with respect to the design data used here) showing corrected mass flow and pressure ratio. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
with characteristics similar to those of the component requiring the off-design behaviour estimate. The compressor map used here, compiled from data in Stevenson and Saravanamuttoo [13], is intended to reflect the compressor of the LM2500 gas turbine. The map used for the compressor turbine reflects a high work, low aspect ratio axial turbine [14], and the power turbine is modelled using a map of an axial turbine derived from Serovy [15]. The component maps used are depicted in Figs. 5–10, where the corrected mass flow and corrected speed given in the maps are defined as follows:
When the stators are rotated away from the axial direction, the axial velocity and mass flow are decreased for a given rotational speed. At low rotational speeds, this delays stalling of the first few stages and choking in the last stage, hence improving the surge margin. Whether the compressor map used here includes any variable geometry within its characteristics is unknown.
Wcorr ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R T W Rstd Tstd
(7)
P Pstd
N Ncorr ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R T Rstd Tstd
(8)
The parameter R is the gas constant and ‘‘std’’ refers to standard atmosphere (T ¼ 15 C, P ¼ 101.325 kPa). As pointed out in Section 3.1, the compressor of the LM2500þ gas turbine is provided with a number of stages with variable geometry. In general, compressors often are provided with several rows of variable stators at the front of the compressor in order to permit large pressure ratios to be achieved in a single-shaft [10,16].
4.3. Generator efficiency According to The Ångstro¨m Laboratory, Sweden (J. Santiago, The Ångstro¨m Laboratory, Uppsala, Sweden, 2007, private communication) and theory about generator losses [17], one fraction of the generator loss (i.e. the copper losses, which are produced in the winding of the stator) is dependent on the load squared, whereas the rest of the loss is independent of the load. The efficiency of the generator is usually defined as the ratio of the electrical power output to the mechanical power input. Assuming that the copper losses constitute a fraction, FCU, of the total losses in design, the following equation for the efficiency in part-load as a function of this fraction, the efficiency at design, hD, and the load can be derived:
hPL ¼
(9)
In order to find a reasonable figure for FCU, results for the generator of the LM2500þ gas turbine are considered. This is a BRUSH DAX 2-pole turbogenerator (BDAX 71-193ER 60 Hz, 13.8 kV, 0.8PF),
100
100
90
90
80 n=0.7
70 n=0.4
60
n=0.8
Isentropic efficiency [%]
Isentropic efficiency [%]
LoadhD i h LoadhD þ ð1 hD Þ ð1 FCU Þ þ FCU Load2
n=0.9 n=1.0
n=0.6 n=0.5
50 40 30 20 10
80 70
n=0.4
60
n=0.5 n=0.6
n=0.7
n=1.0 n=0.9 n=0.8
50 40 30 20 10
0
0 0
20
40
60
80
100
Corrected mass flow [kg/s] Fig. 6. The map for the compressor (scaled with respect to the design data used here) showing isentropic efficiency and corrected mass flow. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
0
1
2
3
4
5
6
7
8
Pressure ratio [-] Fig. 8. The map for the compressor turbine (scaled with respect to the design data used here) showing isentropic efficiency and pressure ratio. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
F. Haglind, B. Elmegaard / Energy 34 (2009) 1484–1492 100
n=0.7 n=0.8 n=0.9 n=1.0
n=0.4 n=0.5 n=0.6
35
96
30
Efficiency [%]
Corrected mass flow [kg/s]
40
1489
25 20 15 10 5
92
GE Formula
88
84
0 0
1
2
3
4
5
6
80
Pressure ratio [-] Fig. 9. The map for the power turbine (scaled with respect to the design data used here) showing corrected mass flow and pressure ratio. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
which can run on either 3000 rpm, corresponding to a frequency of 50 Hz, or 3600 rpm, corresponding to a frequency of 60 Hz. Efficiency figures for this generator for the load ranging from 10% to 100% are shown in Fig. 11. For FCU equal to 0.43 very good agreement between Eq. (9) and the data is found. Eq. (9) with FCU equal to 0.43 is used in this paper for part-load modelling of the generator.
5. Results and discussion Using DNA, performance results for the models are obtained for the load ranging from 10% to 100%. For each design model, both turbine constants and maps are employed, resulting in four cases in total. The model results are compared with the manufacturer data; see Figs. 12–15. For the models using maps, the agreement with manufacturer data is very good except for the lightest loads. No results are displayed for loads below 20%, because for these conditions the operating points of the power turbine become located outside the data range included in the map. A contributing source for the deviation at low powers might be the uncertainty about operation and modelling of variable geometry for the compressor (see Sections 3.1 and 4.2). In general, the results suggest that the complex model gives slightly better agreement with manufacturer data at part-load, but the difference is indeed small.
0
20
40
60
80
100
Load [%] Fig. 11. Generator efficiency versus load for manufacturer data and results of formula.
In order to understand the part-load behaviour of the aeroderivative gas turbine, the effect of operating two turbines in series is considered, following the outline of Cohen et al. [16]. The nondimensional flow at the exit of the gas generator (index 4) is a function of the non-dimensional flow at the inlet to the compressor turbine (index 3), and the compressor turbine pressure ratio and temperature ratio; see Eq. (10). In turn, the temperature ratio is a function of the efficiency. The efficiency could be obtained from the turbine characteristics, but, in practice, the variation with rotational speed for a given pressure ratio is small, particularly over the restricted range of operation of the compressor turbine. Moreover, the effect on the non-dimensional speed becomes even smaller as it is dependent on the square root of the temperature ratio. If a mean value of efficiency at any given pressure ratio is used, the non-dimensional flow out becomes a function of the nondimensional flow in and the pressure ratio. Assuming this, a single curve representing the compressor turbine outlet flow characteristics can readily be obtained for points on the single curve of the inlet flow characteristics; see dotted curve in Fig. 16.
W
pffiffiffiffiffi pffiffiffiffiffi sffiffiffiffiffi T4 W T3 P3 T4 ¼ P4 P3 P4 T3
(10)
25
Pressure ratio [-]
20
100
Isentropic efficiency [%]
90
n=1.0
80 n=0.4
70
n=0.5 n=0.6
n=0.7
n=0.8 n=0.9
60
15
10
50 40
5
30 20 0
10
0
0 0
1
2
3
4
5
20
Pressure ratio [-] GE data
Fig. 10. The map for the power turbine (scaled with respect to the design data used here) showing isentropic efficiency and pressure ratio. The rotational speed, n, is given as a relative corrected figure, i.e. the ratio of the corrected speed to the corrected speed at design.
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Fig. 12. Compressor pressure ratio versus load.
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Fig. 13. Inlet mass flow versus load.
Fig. 15. Exhaust temperature versus load.
From Fig. 16 it can be seen that the requirement for flow compatibility between the compressor turbine and the power turbine places a major restriction on the operation of the compressor turbine. The maximum pressure ratio across the compressor turbine is controlled by the choking of the power turbine (point a), and at all times the pressure ratio is controlled by the swallowing capacity of the power turbine (e.g. point b). A further consequence of the fixed relationship between the turbine pressure ratios is that it is possible to plot the compressor turbine pressure ratio versus the compressor pressure ratio. From this figure it follows that the compressor turbine pressure ratio increases with the compressor pressure ratio until the power turbine becomes choked, at which it becomes constant. At full-load, often both the compressor turbine first-stage nozzle and the power turbine nozzle operate at or near choked flow condition [18]. In the case studied here, the power turbine is operated close to choked condition, and the non-dimensional mass flow decreases first slowly and then with increasing rate with
decreasing pressure ratio. The compressor turbine is operated within a narrow range of pressure ratios, and at all times it stays choked. Considering the model with maps, the turbine flow characteristics (i.e. whether the flows are choked or not) at full-load are determined by the location of the design points within the turbine maps. That is, by choosing other design point locations within the turbine maps, giving other flow characteristics, a different partload performance would be obtained. With respect to the model with turbine constants, the turbine flow characteristics at the design point are governed by the pressure ratio and the value of the turbine constant. For illustration, the actual operating points for the turbines for the simple model with turbine constants are shown in Fig. 17. The results shown in Figs. 12 and 13 suggest that turbine constants are sufficient to predict the mass flow and pressure ratio characteristics during part-load conditions. In terms of exhaust temperature and thermal efficiency, on the contrary, the results suggest that the model with turbine constants does not predict these performances adequately at light loads (see Figs. 14 and 15). This is because the isentropic efficiencies are assumed constant. Neglecting the influence of load on the isentropic efficiency for the compressor has no significant effect, because even though the pressure ratio and non-dimensional mass flow have decreased significantly for the lowest loads, the operating point is still located in a region of the map with high efficiency.
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Fig. 14. Thermal efficiency versus load.
Fig. 16. Operation of turbines in series.
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Fig. 17. Actual operating points for the two turbines for the simple model with turbine constants. Marks indicate operating points between 10% and 100% load.
Since the non-dimensional flow for the compressor turbine is constant and the pressure ratio is only slightly decreased, the isentropic efficiency for the compressor turbine also is more or less unaffected by the load. What gives rise to the deviations at light loads when using turbine constants, is simply that the influence on the isentropic efficiency for the power turbine is neglected. As the load is decreased, the pressure ratio for the power turbine is decreased significantly (since the pressure ratio across the compressor turbine stays nearly constant), affecting the efficiency essentially. In the models with turbine constants and constant efficiencies for the turbomachinery, the unreasonably high efficiency for the power turbine will result in a too low exhaust temperature for light loads, which explains the deviation shown in Fig. 15. Moreover, neglecting the degradation in component efficiencies in part-load, results in an over-estimation of the thermal efficiency (see Fig. 14, a consequence which is partly counter-acted by a small over-estimation of the turbine inlet temperature).
An essential advantage with the approach of using maps is that agreement always can be found, though it may sometimes involve substantial effort. If the part-load performance achieved is not satisfactory with one set of maps, these can be replaced by others. Another parameter affecting the part-load performance which can be varied, is the location of the design point within the maps. The procedure is discussed in Kurzke [19]. If these measures would not be sufficient, the map characteristics can also be changed manually in order to attain satisfactory agreement. With the use of turbine constants no actions can be taken to change the part-load performance. The methodologies discussed here for predicting the part-load performance of aero-derivative gas turbines are of course general and can be applied to any gas turbine type. However, it is not sure that the conclusions drawn about the applicability of using turbine constants would be the same for other gas turbine types.
6. Conclusions
The authors would like to express their gratitude to Joseph Peters and Danny Hutchison at General Electric, USA, for providing information and performance data on the LM2500þ gas turbine, and Joachim Kurzke (developer of GasTurb), Germany, for providing information on the component maps provided with GasTurb 10. Furthermore, Juan de Santiago and Mats Lejon at The Ångstro¨m Laboratory, Sweden, are thanked for their guidance on generator performance. The funding from the Danish Center for Maritime Technology (DCMT) is acknowledged.
In this paper different methodologies for predicting the partload performance of an aero-derivative gas turbine have been investigated. Model results have been compared with manufacturer data for the LM2500þ gas turbine. With respect to the design models, a simple model, featuring a compressor, combustor and turbines, results in equally good performance prediction (in terms of thermal efficiency and exhaust temperature) as a more complex model including also bleed, cooling flows and pressure losses. The major drawbacks of the simple model are that unrealistically poor component efficiencies need to be used, and the lack of cooling modelling, results in unrealistic temperature levels within the cycle. Having a reasonable estimation of the maximum cycle temperature can, for example, be important if the formation of pollutant emissions should be considered. Moreover, the complex model shows slightly better agreement with manufacturer data in part-load; however, the difference is indeed small. Considering the two different methodologies for predicting the part-load performance – maps and turbine constants – the results suggest that the mass flow and pressure ratio characteristics can be well predicted with both methods. Down to about 60–70% load also the thermal efficiency and exhaust temperature can be well predicted with both methods, but below that point the use of turbine constants and assuming constant efficiencies for turbomachinery, results in an under-prediction of the exhaust temperature and overprediction of the thermal efficiency; the lower the load, the higher the deviations. For instance, at 30% load, the model with turbine constants gives a thermal efficiency 8.5% higher and an exhaust temperature 12% lower than the manufacturer data. For the same operating point, the model with maps provides agreement in thermal efficiency and an exhaust temperature 1.5% lower than manufacturer data.
Acknowledgements
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