Proceedings of ASME Turbo Expo 2013: Turbine Technical Conference and Exposition GT2013 June 3-7, 2013, San Antonio, Texas, USA
GT2013-95824
MODELING OFF-DESIGN AND PART-LOAD PERFORMANCE OF SUPERCRITICAL CARBON DIOXIDE POWER CYCLES John J. Dyreby, Sanford A. Klein, Gregory F. Nellis, and Douglas T. Reindl University of Wisconsin-Madison, Solar Energy Laboratory Madison, WI, USA Email:
[email protected] ABSTRACT Continuing efforts to increase the efficiency of utility-scale electricity generation has resulted in considerable interest in Brayton cycles operating with supercritical carbon dioxide (S-CO2). One of the advantages of S-CO2 Brayton cycles, compared to the more traditional steam Rankine cycle, is that equal or greater thermal efficiencies can be realized using significantly smaller turbomachinery. Another advantage is that heat rejection is not limited by the saturation temperature of the working fluid, facilitating dry cooling of the cycle (i.e., the use of ambient air as the sole heat rejection medium). While dry cooling is especially advantageous for power generation in arid climates, the reduction in water consumption at any location is of growing interest due to likely tighter environmental regulations being enacted in the future. Daily and seasonal weather variations coupled with electric load variations means the plant will operate away from its design point the majority of the year. Models capable of predicting the off-design and part-load performance of S-CO2 power cycles are necessary for evaluating cycle configurations and turbomachinery designs. This paper presents a flexible modeling methodology capable of predicting the steady state performance of various S-CO2 cycle configurations for both design and off-design ambient conditions, including part-load plant operation. The models assume supercritical CO2 as the working fluid for both a simple recuperated Brayton cycle and a more complex recompression Brayton cycle.
For example, relatively small turbomachinery can be used due to the high density of carbon dioxide (464 kg/m3 at its critical point) in the region above the vapor dome. Also, heat can be rejected from the S-CO2 cycle at a comparatively higher temperature than traditional Rankine cycles; thereby, offering the potential for dry cooling. Dry cooling is a means of heat rejection, in whole or part, to the ambient air directly without water and is expected to become increasingly important in the future as water conservation efforts expand. The models developed in this work are used to predict the design point, off-design point, and part-load performance of two cycle configurations: the simple recuperated Brayton cycle, shown in Figure 1(a), and the recompression Brayton cycle, shown in Figure 1(b). The recompression Brayton cycle, which adds an additional compressor and heat exchanger, has been suggested as a viable alternative to the simple recuperated cycle due to its increased efficiency at the design point [1]. Tmc,in Pmc,in
Shaft Speed Main Comp
Turbine
Generator
Buffer Volume
Tt,in
(a)
Primary Heat Exchanger
Recuperator
Precooler
Tmc,in Pmc,in
Shaft Speed Main Comp
Turbine
Generator
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Tt,in
Recomp Comp
(b)
Precooler
Low Temperature Recuperator
Primary Heat Exchanger
!rc
INTRODUCTION This paper describes the development of models capable of predicting both the design and off-design (including part-load) performance of supercritical carbon dioxide (S-CO2) Brayton power cycles for utility-scale electricity generation. There are a number of potential advantages to using an S-CO2 Brayton cycle compared to a traditional steam Rankine cycle; these have generated significant interest across a range of industries [1-4].
Motor
High Temperature Recuperator
Figure 1. Diagram of a simple Brayton cycle (a) and a recompression Brayton cycle (b).
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MODELING METHODOLOGY The three major types of components in the Brayton cycle and its variations are the compressor(s), turbine(s), and heat exchangers. The modeling approach used in this study utilizes semi-empirical models for each component. These component models are then integrated into a system-level model where mass and energy balances are applied. The semi-empirical models use performance parameters that are based on the underlying physics of each component and therefore allow offdesign point operation to be accurately estimated. Semiempirical models are computationally much faster than completely physics-based models, which is important when using the models to investigate the annual performance of various cycle configurations. Fluid properties required by the component models are provided by REFPROP [5, 6]. The compressor model uses dimensionless flow and ideal head coefficients to describe compressor performance. The ideal head coefficient and the compressor efficiency are both functions of the flow coefficient and these functional relationships can vary between different compressor designs. The semi-empirical compressor model is flexible with respect to how the ideal head and efficiency curves are specified, allowing experimental data or numerical predictions (or a combination thereof) to define the functional relation used by the model. To facilitate development of the turbomachinery model that is currently employed by the cycle model, data obtained from a compressor being developed for use in a supercritical carbon dioxide cycle at the Sandia National Laboratory (SNL) [7] is used. This data allows the necessary relationships between the ideal head coefficient, efficiency, and flow coefficient to be estimated. An additional empirical correction for shaft speed has been proposed and allows the compressor performance map to be collapsed into a single dimensionless head-flow curve. The modified flow coefficient *
Figure 2. Result of applying Eqs. (1-3) to the SNL compressor performance map data. 0.55
0.50
*
Modified Ideal Head Coefficient
*
Eqs. (1-3) for shaft speeds greater than 35,000 rpm to the performance map data provided by the manufacturer of the compressors [8]. The relationship between modified flow and ideal head coefficients predicted by the curve shown in Fig. 2 is compared to experimental data (provided by SNL) for various compressor inlet conditions in Figure 3.
( φ ), ideal head coefficient ( ψ ), and efficiency ( η ) are, respectively, defined as: *
φ =
2
⎜
U c ⎝ N
⎛ N design ⎞
η = η ⎜
⎟ ⎝ N ⎠
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( 20φ ) *
(2)
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( 20φ ) *
Inlet Conditions 32°C, 7.54 MPa 35°C, 9.10 MPa 28°C, 7.22 MPa 28°C, 6.77 MPa 0.025
ted
*
Δhi ⎛ N design ⎞
(1)
dic
ψ =
! N $ # & ρ U c Dc2 " N design % m
0.40
Pre
*
1/5
0.45
0.030
0.035
0.040
0.045
0.050
Modified Flow Coefficient
Figure 3.
(3)
Measured and predicted modified ideal head coefficient for four compressor inlet conditions.
The measured relationship between flow and ideal head coefficients agrees well with the relationship predicted by the non-dimensional performance curve for various inlet conditions. While the measured ideal head coefficient does not decrease as rapidly as predicted at larger flow coefficients, analysis to-date has shown that, under various off-design and
where ṁ is the mass flow rate through the compressor, ρ is the density of the fluid at the compressor inlet, Uc is the tip speed of the rotor, Dc is the diameter of the rotor, N is the shaft speed, Ndesign is the design shaft speed (75,000 rpm for the SNL compressor), and Δhi is the isentropic enthalpy rise of the fluid through the compressor. Figure 2 shows the result of applying
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CYCLE COMPARISON In order to directly compare the off-design and part-load performance of the configurations considered, both cycles are constrained to generate 10 MW (net power output, excluding generator losses) at the design point with a low side (compressor inlet) temperature of 45°C, a high side (turbine inlet) temperature of 700°C, a high side pressure of 25 MPa, and a total recuperator UA value of 1,500 kW/K. This value was chosen to balance cycle performance and heat exchanger size. The design-point compressor, recompressor, and turbine efficiencies are 0.89, 0.89, and 0.93, respectively. The parameters for the two cycle configurations are summarized in Table 1, as well as the resulting design-point thermal efficiencies. Note that the thermal efficiency of the cycle does not take into account generator losses or any required auxiliary pumping or fan power for heat addition or heat rejection from the cycle. The recompression fraction, ϕrc, represents the portion of the total flow that bypasses the precooler and main compressor and is compressed by the recompressing compressor (RC). The size of the power plant and the designpoint of both the low and high side temperatures were chosen to be representative of power cycles being considered by the National Renewable Energy Laboratory (NREL) for use in concentrating solar power applications, but the results presented in this paper are intended primarily to demonstrate the capabilities of the developed modeling methodology.
part-load conditions, the compressors consistently operate with modified flow coefficients ranging from 0.021 to 0.035. Consequently, the discrepancy between the measured data and the non-dimensional performance curves at larger flow coefficients is not expected to affect the results presented in this paper. The initial turbine model is appropriate for radial turbines, which are optimal for applications up to 50 MWe [9]. A firstorder approximation to the mass flow rate through a turbine with a low rate of reaction (i.e., most of the pressure drop is through the nozzles) is proposed:
m = C s Anozzle ρ
(4)
where Anozzle is an effective nozzle area that is based on the geometry of the turbine, ρ is the density of the fluid at the turbine outlet, and Cs is the spouting velocity, which is the velocity that would be achieved if the fluid were expanded isentropically to the outlet pressure through an ideal nozzle. Chen and Baines have proposed a general relationship between the aerodynamic efficiency, ηaero, (the efficiency of an ideal turbine with no internal losses) and velocity ratio, ν, (the ratio of rotor tip speed to spouting velocity) for a radial turbine [10]. For a well-designed turbine the relationship simplifies to:
ηaero = 2ν 1− ν 2
(5)
Table 1. Parameters and inputs used for the simple and recompression cycle designs; italics signify the value is a fixed parameter and an asterisk indicates the input is used as a control variable.
The aerodynamic efficiency in Eq. (5) assumes an ideal turbine and therefore limits to 100% at a velocity ratio of 1/ 2. The efficiency predicted by Eq. (5) does not take into account internal losses (e.g., recirculation, viscous effects, etc.). To account for these losses in the semi-empirical model, the efficiency of the turbine is calculated by linearly scaling the aerodynamic efficiency predicted by Eq. (5) by the turbine efficiency at the design point. Heat exchangers are modeled assuming a counter-flow configuration using discrete sections, or sub-heat exchangers, connected in series; this approach allows the effect of the rapidly changing carbon dioxide properties near the critical point to be accurately captured. The model uses the inlet conditions of the two streams and the heat exchanger conductance (also referred to as the UA value) in order to determine the corresponding outlet temperatures; a description of the technique can be found in Nellis and Klein [11]. The UA value is strongly dependent on heat exchanger geometry but remains relatively constant over a range of operating conditions (i.e., the temperatures and pressures at the heat exchanger inlets) and is therefore useful for predicting the off-design performance of a fixed heat exchanger. The dependence of mass flow rates on heat transfer coefficients (and hence UA value) is accounted for in the model by appropriately scaling the heat exchanger UA value from its design-point value using the Dittus-Boelter correlation, as presented in Patnode [12].
Net Power LT Recuperator UA HT Recuperator UA Comp. Inlet Pressure* Comp. Outlet Pressure Comp. Inlet Temp. Turbine Inlet Temp. Main Comp. Diameter RC Comp. Diameter Turbine Diameter Effective Nozzle Area Main Shaft Speed* RC. Shaft Speed Recomp. Fraction* Thermal Efficiency Mass Flow Rate
Simple 10 MW 1,500 kW/K 8.14 MPa 25 MPa 45°C 700°C 0.181 m 0.253 m 2,392 mm2 33,224 rpm 47.6 % 77.4 kg/s
Recompression 10 MW 677 kW/K 823 kW/K 9.17 MPa 25 MPa 45°C 700°C 0.152 m 0.104 m 0.236 m 2,528 mm2 33,929 rpm 71,773 rpm 0.221 49.4 % 85.8 kg/s
The turbomachinery characteristics, low-side pressure, and distribution of UA value between the two recuperators (for the recompression cycle) were determined by optimizing efficiency
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at the specified design-point conditions. A number of alternate cases were run in order to investigate the off-design performance of the two cycle configurations. Figures 4 and 5 show the effect of changing compressor inlet temperature (CIT) on the thermal efficiency and net power output, respectively, of the two cycles while main shaft speed, compressor inlet pressure, and recompression fraction (which are also referred to in this paper as the “control variables”) are all held constant at their design-point values.
temperatures less than 52°C, but the simple cycle is predicted to have higher power output (without adjusting its shaft speed or low side pressure) as the low side temperature increases above the design point. In order to directly compare the off-design performance of the two cycles, Figure 6 shows the results of maximizing efficiency (by adjusting the control variables) while maintaining a net power output of 10 MW. 0.52
0.52 0.50
Thermal Efficiency
Thermal Efficiency
0.50 Design Point
0.48 0.46 0.44
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Design Point
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Simple Cycle
0.44
Recompression Cycle
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0.42 0.40 0.40 0.38 Recompression Cycle
0.38
35 35
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Figure 4. Off-design efficiency of the simple (solid line) and recompression (dashed line) Brayton cycles due to changes in compressor inlet temperature without adjusting the control variables.
Net Power Output (MW)
14 12 Design Point
10 8 6 Simple Cycle
4 Recompression Cycle
2 45
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As shown in Fig. 6, optimizing the off-design thermal efficiency at a fixed net power output of 10 MW results in the recompression cycle maintaining an efficiency advantage over the simple cycle for CIT values less than 58°C (for the fixed power plants designed to operate with a CIT of 45°C). As the compressor inlet temperature increases, the recuperator in the simple cycle becomes more balanced, reducing the benefit of the recompressing compressor. The values of the control variables that result in the optimal efficiencies shown in Fig. 6 are plotted in Figure 7. Note in Fig. 7 that the main shaft speed, recompression fraction, and pressure ratio do not vary significantly from their design-point values at the CIT of 45°C. However, increasing the CIT to 60°C requires the low side pressure (at the compressor inlet) to increase by nearly 2 MPa in order to produce 10 MW at the optimal efficiency. This trend shows the importance of actively controlling the low side pressure when operating either cycle configuration under offdesign conditions. The low side pressure can be varied by a process known as “inventory control” where a buffer volume connected to the system allows an increase or decrease in working fluid mass to the system in order to increase or decrease the low side pressure Figures 8 and 9 show the effect of changing turbine inlet temperature (TIT) on the thermal efficiency and net power output, respectively, of the two cycles, assuming the control variables are held constant at their design-point values.
16
40
45
Figure 6. Optimal off-design efficiency of the simple (solid line) and recompression (dashed line) Brayton cycles at 10 MW net output as a function of compressor inlet temperature.
Compressor Inlet Temperature (°C)
35
40
Compressor Inlet Temperature (°C)
65
65
Compressor Inlet Temperature (°C)
Figure 5. Off-design net power output of the simple (solid line) and recompression (dashed line) Brayton cycles due to changes in compressor inlet temperature without adjusting the control variables.
As expected, increasing the CIT without adjusting the control variables results in a decrease in both efficiency and net power output. The recompression cycle maintains an efficiency advantage over the simple cycle for compressor inlet
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0.55
0.55
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The part-load performance (e.g., during a load-following scenario) of the two cycle configurations is shown in Figure 11 using the control variables to maximize efficiency with the low and high side temperatures held constant at their respective design-point values of 45°C and 700°C. The values of the control variables that result in the optimal efficiencies shown in Fig. 11 are plotted in Figure 12. As was the case for optimal off-design CIT operation, optimal part-load operation requires significant changes to the compressor inlet pressure, further emphasizing the importance of active inventory control when operating S-CO2 Brayton cycles under off-design or part-load conditions. It is interesting to note that the efficiency of the recompression cycle decreases with net power output, while the simple cycle operates slightly more efficiently at power outputs below its design point.
Recompression Cycle
550
650
Figure 10. Optimal off-design efficiency of the simple (solid line) and recompression (dashed line) Brayton cycles at 10 MW net output as a function of turbine inlet temperature.
11
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Turbine Inlet Temperature (°C)
Figure 8. Off-design efficiency of the simple (solid line) and recompression (dashed line) Brayton cycles due to changes in turbine inlet temperature without adjusting the control variables.
Net Power Output (MW)
Simple Cycle
800
Turbine Inlet Temperature (°C)
0.50
Figure 9. Off-design net power output of the simple (solid line) and recompression (dashed line) Brayton cycles due to changes in turbine inlet temperature without adjusting the control variables.
Thermal Efficiency
0.49
For both cycle configurations, decreasing the turbine inlet temperature results in a decrease in thermal efficiency and net power output. The efficiency decrease is expected based on the Carnot efficiency, and the net power output decreases due to a decrease in the mass flow rate of the cycle. For the range of high side temperatures shown in Figs. 8 and 9, the recompression cycle is consistently more efficient than the simple cycle; the change in net power output of the two cycles as the turbine inlet temperature varies is nearly identical. As was the case for Figs. 4 and 5, the control variables for the cycles were held constant at their design-point values. Adjusting the control variables in order to maximize the efficiency of the cycle while maintaining a net power output of 10 MW results in the cycle efficiencies shown in Figure 10.
Design Point
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Figure 11. Optimal part-load efficiency of the simple (solid line) and recompression (dashed line) Brayton cycles.
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CONCLUSIONS A modeling methodology based on integrating semiempirical component models into a system-level model was developed. The resulting system-level model is capable of predicting the design-point and off-design operation of S-CO2 Brayton cycles. The methodology is flexible in regards to cycle configuration as well as with respect to how the performance curves of the individual components are specified. The methodology was used to compare the predicted off-design and part-load performance of a simple recuperated Brayton cycle and a recompression Brayton cycle. The modeling efforts presented in this paper are ongoing, with initial results indicating that high thermal efficiency can be realized with a S-CO2 Brayton cycle over a range of off-design and part-load conditions. While the current results highlight the importance of actively controlling the low-side pressure in order to optimize thermal efficiency, ongoing work is focused on modeling the off-design performance of the cycle on an annual basis. Specifically of interest is the effect of the designpoint low side temperature selection on the annual performance of the cycle.
AXL-0-40301-1. The collaboration with Steven Wright and Thomas Conboy at the Sandia National Laboratory is also greatly appreciated. REFERENCES [1] V. Dostal, P. Hejzlar And M. J. Driscoll, “The Supercritical Carbon Dioxide Power Cycle: Comparison to Other Advanced Power Cycles,” Nuclear Technology, 154, p. 283-301 (2006). [2] A. Moisseytsev And J. J. Sienicki, “Investigation of alternative layouts for the supercritical carbon dioxide Brayton cycle for a sodium-cooled fast reactor,” Nuclear Engineering and Design, 239, p. 1362-1371 (2009). [3] R. Chacartegui et al., “Alternative cycles based on carbon dioxide for central receiver solar power plants,” Applied Thermal Engineering, 31, p. 872-879 (2011). [4] C. S. Turchi, “Supercritical CO2 for Application in Concentrating Solar Power Systems,” Proc. of the S-CO2 Power Cycle Symposium, Troy, NY, USA (2009). [5] E. W. Lemmon, M. L. Huber and M. O. McLinden, “NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP,” Version 9.0, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg (2010). [6] R. Span And W. Wagner, “A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa,” J. Phys. Chem. Ref. Data, 25, 6, p. 1509-1596 (1996). [7] T. Conboy et al., “Performance Characteristics of an Operating Supercritical CO2 Brayton Cycle,” J. of Eng. for Gas Turbines and Power, 134, 111703, (2012). [8] Barber-Nichols Inc., Arvada, CO, USA, (www.barbernichols.com). [9] J. P. Gibbs, P. Hejzlar and M. J. Driscoll, “Applicability of Supercritical CO2 Power Conversion Systems to GEN IV Reactors,” SNL / MIT Topical Report, MIT-GFR-037 (2006). [10] H. Chen And N. C. Baines, “The Aerodynamic Loading of Radial and Mixed-Flow Turbines,” International Journal of Mechanical Science, 36, 1, p. 63-79 (1994). [11] G. Nellis And S. Klein, Heat Transfer, 1st Edition, Cambridge University Press, New York (2009). [12] A. M. Patnode, Simulation and Performance Evaluation of Parabolic Trough Solar Power Plants, M.S. Thesis, University of Wisconsin-Madison, (2006).
NOMENCLATURE CIT Compressor Inlet Temperature NREL National Renewable Energy Laboratory RC Recompressing Compressor S-CO2 Supercritical Carbon Dioxide SNL Sandia National Laboratory TIT Turbine Inlet Temperature UA Heat Exchanger Conductance Anozzle Effective nozzle area Spouting velocity Cs Compressor rotor diameter Dc N Shaft speed Ndesign Design-point shaft speed Compressor rotor tip speed Uc ṁ Mass flow rate Isentropic enthalpy change Δhi η Isentropic efficiency ν Ratio of turbine rotor tip speed to spouting velocity ρ Fluid density ϕ Flow coefficient Recompression fraction ϕrc ψ Ideal head coefficient ACKNOWLEDGMENTS The authors would like to thank the Concentrating Solar Power Program at the National Renewable Energy Laboratory for their sponsorship of this work under subcontract number
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Recompression Fraction
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40000
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Recompression Fraction Main Shaft Speed (rpm)
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Figure 7.
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Net Power (MW)
Control variable values that result in 10 MW net power output at the optimal efficiency for the simple (solid lines) and recompression (dashed lines) Brayton cycles; turbine inlet temperature is held constant at the designpoint value of 700°C.
Figure 12. Control variable values that result in the optimal part-load efficiency for the simple (solid line) and recompression (dashed line) Brayton cycles; compressor and turbine inlet temperatures are held constant at their designpoint values of 45°C and 700°C, respectively.
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