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Mapping the Design Space of a Recuperated, Recompression, Precompression Supercritical Carbon Dioxide Power Cycle with Intercooling, Improved Regeneration, and Reheat Andrew Schroder Mark Turner University of Cincinnati Outline Overview

SLIDE 1

Mapping the Design Space of a Recuperated, Recompression, Precompression Supercritical Carbon Dioxide Power Cycle with Intercooling, Improved Regeneration, and Reheat

Andrew Schroder Mark Turner

University of Cincinnati

SLIDE 2

Outline

◮ Overview of Supercritical CO2 Power Cycles ◮ Proposed System Layout ◮ Variable Property Heat Engine Cycle Analysis Code ◮ Heat Exchangers with Nonlinear and Dissimilar Specific Heats ◮ Results of the Design Space Exploration ◮ Conclusions

SLIDE 3

About Supercritical CO2 (S-CO2) Power Cycles

◮ Closed loop configuration. ◮ Main compressor inlet temperature and pressure are at or near

the critical point.

◮ Carbon dioxide is the proposed working fluid because it is

cheap, inert, and has a critical temperature of 304K (31◦C), which is near typical ambient temperatures of ∼ 294K (21◦C).

◮ High system pressures occur due to the high critical pressure

f carbon dioxide (7.4 MPa).

◮ Possible applications:

◮ Base load terrestrial electrical power generation ◮ Marine, Aviation, and Spacecraft electrical power generation

◮ Possible Configurations:

◮ Bottoming cycle using waste heat from a traditional open loop

gas turbine (traditional Brayton cycle)

◮ Primary cycle with nuclear and solar energy heat sources ◮ Primary cycle with the combustion of fossil fuels as a heat

source

SLIDE 4

State of the Art

◮ The earliest reference to a supercritical carbon dioxide power

cycle is that of a patent by Sulzer in 1948.

◮ Vaclav Dostal revived interest in supercritical carbon dioxide

power cycles with the publication of his doctoral thesis in 2004.

◮ Sandia National Laboratories has developed two supercritical

CO2 test rigs with their contractor, Barber-Nichols and has successfully achieved startup of both a main compressor/turbine and recompressor/turbine loop. Their efforts are focused towards nuclear power applications.

◮ Echogen Power Systems has been developing an engine for

waste heat recovery applications.

◮ The United States Department of Energy began development

f engines for concentrating solar power applications in mid

2012.

SLIDE 5

Carbon Dioxide - cp vs Temperature

1.4 MPa 2.4 MPa 5.4 MPa 6.4 MPa 7.4 MPa 8.4 MPa 9.4 MPa 10.4 MPa 11.4 MPa 12.4 MPa 20.4 MPa 300. 400. 0.000 5.00 10.0 15.0

Temperature (K) Cp (kJ/kg-K)

1.4 MPa 2.4 MPa 5.4 MPa 6.4 MPa 7.4 MPa 8.4 MPa 9.4 MPa 10.4 MPa 11.4 MPa 12.4 MPa 20.4 MPa 300. 400. 0.000 5.00 10.0 15.0

Temperature (K) Cp (kJ/kg-K)

1.4 MPa 2.4 MPa 5.4 MPa 6.4 MPa 7.4 MPa 8.4 MPa 9.4 MPa 10.4 MPa 11.4 MPa 12.4 MPa 20.4 MPa

SLIDE 6

Supercritical CO2 Power Cycle - Strengths

◮ Low Pressure Ratio (optimal overall pressure ∼ 3 to 8) ◮ Large amounts of recuperation possible. ◮ Low back work ratio

◮ Decreased sensitivity of compressor/turbine efficiency on cycle

efficiency.

◮ S-CO2 - ∼35% ◮ Rankine - ∼2% ◮ Open Loop Brayton - 40-80%

◮ High Power Density

◮ High pressure and high molecular weight. ◮ Fluid densities range from ∼23 kg/m3 to ∼788 kg/m3.

◮ Narrow heat addition and heat rejection temperatures does

not require evaporative cooling, but still approximates a Carnot cycle better than an open loop Brayton cycle.

◮ High real cycle efficiency predicted

◮ >50% @ 923K (650◦C) turbine inlet temperature

SLIDE 7

Supercritical CO2 Power Cycle - Weaknesses

◮ Nonlinear specific heat mismatch causes difficulties

exchanging heat between high and low pressure sides at lower temperatures.

◮ Closed loop design presents additional system complexities. ◮ High pressures present increased structural loading and seal

leakage issues.

◮ 20MPa to 30MPa maximum pressure typically proposed

◮ Nonlinear property variations near the critical point present

turbomachinery design complications as well as challenges maintaining off design operability.

◮ High working fluid densities prohibit efficient low power, low

speed, low cost prototypes to be developed.

SLIDE 8

Proposed System Layout

◮ Three compressors and several flow splits are used to help mitigate heat transfer issues due to specific heat mismatches. ◮ Four shafts are utilized to better match optimal operating speeds of each turbomachinery component. ◮ Due to the small size of the turbomachinery, as well as the use of multiple shafts, each assembly (except for the power turbine and generator) can be placed inside a pressure vessel to avoid the need for high speed, high pressure seals. ◮ Tanks and a blow down startup procedure are used to eliminate the need to attach a motor to the higher speed shafts.

SLIDE 9

Proposed System Layout - Temperature Entropy Diagram

1,000 1,500 2,000 2,500 3,000 Entropy [J/(kg)] 300 400 500 600 700 800 900 1,000 Temperature [K]

Critical Temperature: 304.13K Critical Pressure: 7.377MPa 13 1 2 4 6 7 8 9 5 3 10 14 15 11 12 Constant Pressure Lines 10.03MPa 10.00MPa 25.21MPa 25.16MPa 25.16MPa 24.93MPa 14.65MPa 14.61MPa 5.84MPa 5.60MPa

800 1,220 1,640 2,060 2,480 2,900 3,320 3,740 4,160 4,580 5,000 cp , Specific Heat at Constant Pressure [J/(kg*K)] Cycle Efficiency: 51.94% Line widths scaled by mass fraction.

SLIDE 10

Proposed System Layout - Temperature Entropy Diagram

1,000 1,500 2,000 2,500 3,000 Entropy [J/(kg)] 300 400 500 600 700 800 900 1,000 Temperature [K]

Critical Temperature: 304.13K Critical Pressure: 7.377MPa 13 1 2 4 6 7 8 9 5 3 10 14 15 11 12

25.000 5 . 3 . 7 . 2 5 . 50.000 300.000 700.000 1000.000

Constant Pressure Lines 10.03MPa 10.00MPa 25.21MPa 25.16MPa 25.16MPa 24.93MPa 14.65MPa 14.61MPa 5.84MPa 5.60MPa

100 200 300 400 500 600 700 800 900 1,000 1,100 1,200 1,300 Density [kg/m3 ] Cycle Efficiency: 51.94% Line widths scaled by mass fraction.

SLIDE 11

Proposed System Layout - Temperature Pressure Diagram

5 10 15 20 25 30 Pressure [MPa] 300 400 500 600 700 800 900 1,000 Temperature [K] Supercritical Fluid Liquid Gas

Vapor 13 1 2 4 6 7 8 9 5 3 10 14 15 11 12

800 1,220 1,640 2,060 2,480 2,900 3,320 3,740 4,160 4,580 5,000 cp , Specific Heat at Constant Pressure [J/(kg*K)] Cycle Efficiency: 51.94% Line widths scaled by mass fraction.

SLIDE 12

Proposed System Layout - Temperature Entropy Diagram

1,000 1,500 2,000 2,500 3,000 3,500 4,000 Entropy [J/(kg)] 300 400 500 600 700 800 900 1,000 Temperature [K]

Critical Temperature: 304.13K Critical Pressure: 7.377MPa 13 1 2 4 6 7 8 9 5 3 10 14 15 11 12 Constant Pressure Lines 10.06MPa 10.00MPa 20.47MPa 20.39MPa 20.39MPa 20.19MPa 8.24MPa 8.18MPa 2.75MPa 2.52MPa

Cycle Efficiency: 47.31% Line widths scaled by mass fraction.

SLIDE 13

Variable Property Heat Engine Cycle Analysis Code

◮ Cycle analysis code created from scratch. ◮ Developed with Python, NumPy, SciPy, and matplotlib. ◮ Variable fluid properties are utilized.

◮ i.e. h = h(T, p), cp = cp(T, p), s = s(T, p) ◮ Fluid property data used from REFPROP

◮ Specialized 1-D counterflow heat exchanger model was

developed to account for variable fluid properties, yet maintaining high solution speed.

◮ Cycle iteratively solved for unknown pressures. ◮ Inputs include maximum temperature, minimum temperature,

compressor pressure ratios, turbomachinery component efficiencies, heat exchanger pressure drop, main compressor inlet pressure, and mass fraction for flow splits.

◮ Design space for the inputs is explored in parallel and can run

n as many processors as are available.

SLIDE 14

Variable Property Heat Engine Cycle Analysis Code Limitations and Assumptions

◮ Currently the code only supports gases and supercritical fluids.

Liquids and and liquid vapor mixtures are not yet supported.

◮ Heat source currently modeled is that of a constant heat flux

(i.e. solar) or a highly regenerated combustion system (heater efficiency is assumed to be 100%).

◮ Pumping power for the ambient pressure side of the heaters

and coolers are assumed to be low.

SLIDE 15

Heat Exchangers - Overview

◮ The current heat exchanger model assumes the limiting case

where the convection coefficient is very high.

◮ The temperature difference between the high pressure to the

low pressure side of the heat exchanger is assumed to be purely due to specific heat mismatches.

◮ At at least one point in the heat exchanger there will be

approximately zero temperature difference between the high and low pressure side.

◮ Pressure drop

◮ Pressure drop is not computed based on an assumed geometry,

but is approximated to be linearly dependent upon temperature drop in the heat exchanger.

◮ Temperature drop is assumed to be related to the length of

the heat exchanger.

◮ The linear relationship between temperature drop and pressure

drop is another parameter varied as part of the design space exploration.

◮ Pressure drop is assumed to be low, allowing the present

approximation to be acceptable.

SLIDE 16

Heat Exchangers - Temperature and Specific Heat Variation

300 320 340 360 380 400 420 440 Temperature, Cooled Side, [K] 500 1000 1500 2000 2500 3000 3500 4000 cp, [J/(kg*K)] and C, [J/(kgCooled*K)]

cp,Cooled cp,Heated CCooled CHeated

300 320 340 360 380 400 420 440 Temperature, Cooled Side, [K] 5 10 15 20 ∆T =TCooled−THeated, [K]

∆T CHeated/CCooled 1

0.0 0.5 1.0 1.5 2.0 Heat Capacity Ratio, CHeated/CCooled Cooled Side Inlet: Temperature=450.0K, Pressure=8.5MPa, Mass Fraction=1.00 Heated Side Inlet: Temperature=305.0K, Pressure=18.5MPa, Mass Fraction=0.60 Pressure Drop=5000 Pa/K, Inlet Pressure Ratio=2.2, φ=0.60

SLIDE 17

Heat Exchangers - Temperature and Specific Heat Variation

300 310 320 330 340 350 Temperature, Cooled Side, [K] 200 400 600 800 1000 cp, [J/(kg*K)] and C, [J/(kgCooled*K)]

cp,Cooled cp,Heated CCooled CHeated

300 310 320 330 340 350 Temperature, Cooled Side, [K] 2 2 4 6 8 10 ∆T =TCooled−THeated, [K]

∆T CHeated/CCooled 1

0.0 0.5 1.0 1.5 2.0 Heat Capacity Ratio, CHeated/CCooled Cooled Side Inlet: Temperature=350.0K, Pressure=1.0MPa, Mass Fraction=1.00 Heated Side Inlet: Temperature=305.0K, Pressure=1.0MPa, Mass Fraction=1.00 Pressure Drop=0 Pa/K, Inlet Pressure Ratio=1.0, φ=1.00

SLIDE 18

Heat Exchangers - Temperature and Specific Heat Variation

300 320 340 360 380 400 420 440 Temperature, Cooled Side, [K] 200 400 600 800 1000 cp, [J/(kg*K)] and C, [J/(kgCooled*K)]

cp,Cooled cp,Heated CCooled CHeated

300 320 340 360 380 400 420 440 Temperature, Cooled Side, [K] 10 20 30 40 50 60 ∆T =TCooled−THeated, [K]

∆T CHeated/CCooled 1

0.0 0.2 0.4 0.6 0.8 1.0 Heat Capacity Ratio, CHeated/CCooled Cooled Side Inlet: Temperature=450.0K, Pressure=1.0MPa, Mass Fraction=1.00 Heated Side Inlet: Temperature=305.0K, Pressure=1.0MPa, Mass Fraction=0.60 Pressure Drop=5000 Pa/K, Inlet Pressure Ratio=1.0, φ=0.63

SLIDE 19

Heat Exchangers - Temperature and Specific Heat Variation

310 315 320 325 330 335 340 345 350 Temperature, Cooled Side, [K] 500 1000 1500 2000 2500 3000 cp, [J/(kg*K)] and C, [J/(kgCooled*K)]

cp,Cooled cp,Heated CCooled CHeated

310 315 320 325 330 335 340 345 350 Temperature, Cooled Side, [K] 2 2 4 6 8 10 ∆T =TCooled−THeated, [K]

∆T CHeated/CCooled 1

0.0 0.5 1.0 1.5 2.0 Heat Capacity Ratio, CHeated/CCooled Cooled Side Inlet: Temperature=350.0K, Pressure=25.0MPa, Mass Fraction=1.00 Heated Side Inlet: Temperature=310.0K, Pressure=5.0MPa, Mass Fraction=1.65 Pressure Drop=0 Pa/K, Inlet Pressure Ratio=0.2, φ=1.00

SLIDE 20

Heat Exchangers - Temperature and Specific Heat Variation

300 320 340 360 380 400 420 440 Temperature, Cooled Side, [K] 500 1000 1500 2000 2500 3000 cp, [J/(kg*K)] and C, [J/(kgCooled*K)]

cp,Cooled cp,Heated CCooled CHeated

300 320 340 360 380 400 420 440 Temperature, Cooled Side, [K] 2 2 4 6 8 10 ∆T =TCooled−THeated, [K]

∆T CHeated/CCooled 1

0.0 0.5 1.0 1.5 2.0 Heat Capacity Ratio, CHeated/CCooled Cooled Side Inlet: Temperature=450.0K, Pressure=5.0MPa, Mass Fraction=1.00 Heated Side Inlet: Temperature=305.0K, Pressure=25.0MPa, Mass Fraction=0.56 Pressure Drop=0 Pa/K, Inlet Pressure Ratio=5.0, φ=0.96

SLIDE 21

Heat Exchangers - Temperature and Specific Heat Variation

300 320 340 360 380 400 420 440 Temperature, Cooled Side, [K] 500 1000 1500 2000 2500 3000 cp, [J/(kg*K)] and C, [J/(kgCooled*K)]

cp,Cooled cp,Heated CCooled CHeated

300 320 340 360 380 400 420 440 Temperature, Cooled Side, [K] 10 20 30 40 50 60 70 80 ∆T =TCooled−THeated, [K]

∆T CHeated/CCooled 1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 Heat Capacity Ratio, CHeated/CCooled Cooled Side Inlet: Temperature=450.0K, Pressure=5.0MPa, Mass Fraction=1.00 Heated Side Inlet: Temperature=305.0K, Pressure=25.0MPa, Mass Fraction=1.00 Pressure Drop=5000 Pa/K, Inlet Pressure Ratio=5.0, φ=0.55

SLIDE 22

Design Space Exploration

Dataset I - 20,155,392 permutations All Parameters - Coarse Exploration

Parameter Minimum Maximum Number of Values Value Plotted PreCompressor Pressure Ratio 1.0 4.0 6 Optimal Main Compressor Pressure Ratio 1.1 4.1 6 Optimal Recompression Fraction 0.000 0.991 4 Optimal Low Temperature Recuperator Main Fraction High Pressure Component Mass Fraction 0.001 0.991 4 Optimal Main Compressor Inlet Pressure 6 MPa 10 MPa 6 Optimal Maximum Temperature 798K 923K 3 923K Minimum Temperature 320K 333K 3 320K Main Compressor Isentropic Efficiency 0.75 1.00 4 0.85 PreCompressor Isentropic Efficiency 0.80 0.95 3 0.875 ReCompressor Isentropic Efficiency 0.80 0.95 3 0.875 Power Turbine Isentropic Efficiency 0.89 0.93 3 0.93 Main/Re/Pre Compressor Turbine Isentropic Efficiency 0.84 0.89 3 0.89 Heat Exchanger Pressure Drop 500 Pa/K 0 Pa/K 2 500 Pa/K

SLIDE 23

Design Space Exploration

Dataset II - 1,800,000 permutations Fixed Component Efficiencies and Max/Min Temp, Other Parameters Refined

Parameter Minimum Maximum Number of Values Value Plotted PreCompressor Pressure Ratio 1.0 4.0 20 Optimal Main Compressor Pressure Ratio 1.1 4.1 20 Optimal Recompression Fraction 0.000 0.991 15 Optimal Low Temperature Recuperator Main Fraction High Pressure Component Mass Fraction 0.001 0.991 15 Optimal Main Compressor Inlet Pressure 6 MPa 10 MPa 20 Optimal Maximum Temperature 923K 923K 1 923K Minimum Temperature 320K 320K 1 320K Main Compressor Isentropic Efficiency 0.85 0.85 1 0.85 PreCompressor Isentropic Efficiency 0.875 0.875 1 0.875 ReCompressor Isentropic Efficiency 0.875 0.875 1 0.875 Power Turbine Isentropic Efficiency 0.93 0.93 1 0.93 Main/Re/Pre Compressor Turbine Isentropic Efficiency 0.89 0.89 1 0.89 Heat Exchanger Pressure Drop 500 Pa/K 500 Pa/K 1 500 Pa/K

SLIDE 24

Design Space Exploration Results - Dataset II

Cycle Efficiency vs PreCompressor and Main Compressor Pressure Ratios

1.0 1.5 2.0 2.5 3.0 3.5 4.0 PreCompressor Pressure Ratio 1.5 2.0 2.5 3.0 3.5 4.0 Main Compressor Pressure Ratio

Maximum Efficiency=51.94%

0.30 0.33 0.36 0.39 0.42 0.45 0.48 0.51 0.54 0.57 0.60

Cycle Efficiency

SLIDE 25

Design Space Exploration Results - Dataset II

Optimal Recompression Fraction vs PreCompressor and Main Compressor Pressure Ratios

1.0 1.5 2.0 2.5 3.0 3.5 4.0 PreCompressor Pressure Ratio 1.5 2.0 2.5 3.0 3.5 4.0 Main Compressor Pressure Ratio 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Recompression Fraction at Maximum Efficiency

SLIDE 26

Design Space Exploration Results - Dataset II

Low Temperature Recuperator Main Fraction High Pressure Component Mass Fraction at Optimal Cycle Efficiency vs PreCompressor and Main Compressor Pressure Ratios

1.0 1.5 2.0 2.5 3.0 3.5 4.0 PreCompressor Pressure Ratio 1.5 2.0 2.5 3.0 3.5 4.0 Main Compressor Pressure Ratio 0.00 0.09 0.18 0.27 0.36 0.45 0.54 0.63 0.72 0.81 0.90

Low Temperature Recuperator Main Fraction High Pressure Component Mass Fraction at Maximum Efficiency

SLIDE 27

Design Space Exploration Results - Dataset II

Cycle Efficiency vs Recompression Fraction

0.0 0.2 0.4 0.6 0.8 1.0 Recompression Fraction 0.47 0.48 0.49 0.50 0.51 0.52 Cycle Efficiency

Maximum Efficiency=51.94%

SLIDE 28

Design Space Exploration Results - Dataset II

Cycle Efficiency vs Main Compressor Inlet Pressure

0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 Main Compressor Inlet Pressure [Pa] 1e7 0.480 0.485 0.490 0.495 0.500 0.505 0.510 0.515 0.520 Cycle Efficiency

Maximum Efficiency=51.94%

SLIDE 29

Design Space Exploration Results - Dataset I

Cycle Efficiency vs Maximum and Minimum Temperature

800 820 840 860 880 900 920 Maximum Temperature [K] 320 322 324 326 328 330 332 Minimum Temperature [K]

Maximum Efficiency=50.57%

0.30 0.33 0.36 0.39 0.42 0.45 0.48 0.51 0.54 0.57 0.60

Cycle Efficiency

SLIDE 30

Design Space Exploration Results - Dataset I

Cycle Efficiency vs Max and Min Temperature and Main and ReCompressor Efficiency

780 800 820 840 860 880 900 920 940 Maximum Temperature [K] 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51 Cycle Efficiency

Maximum Efficiency=50.57%

320 322 324 326 328 330 332 334 Minimum Temperature [K] 0.485 0.490 0.495 0.500 0.505 0.510 Cycle Efficiency

Maximum Efficiency=50.57%

0.75 0.80 0.85 0.90 0.95 1.00 1.05 Main Compressor Isentropic Efficiency 0.500 0.502 0.504 0.506 0.508 0.510 0.512 0.514 Cycle Efficiency

Maximum Efficiency=51.34%

0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 ReCompressor Isentropic Efficiency 0.498 0.500 0.502 0.504 0.506 0.508 0.510 0.512 Cycle Efficiency

Maximum Efficiency=51.18%

SLIDE 31

Web Based Graphical User Interface

SLIDE 32

Conclusions

◮ Supercritical CO2 Power Cycles have the potential for

efficiencies of 51.94% with a maximum heat source temperature of 923K (650◦C) and a minimum coolant temperature of 320K (47◦C).

◮ A new system layout has been presented which may help to

eliminate some of the design challenges with supercritical carbon dioxide engines.

◮ Highly nonlinear fluid properties present significant challenges

in cycle and component design.

◮ A cycle analysis code has been developed, along with a web

based interface for interactively exploring the design space. These tools can be continually expanded and improved to better understand supercritical carbon dioxide power cycles.

SLIDE 33