doctoral dissertation: a study of power cycles using supercritical - - PowerPoint PPT Presentation

doctoral dissertation: a study of power cycles using supercritical carbon dioxide as the working fluid

.

Andrew Schroder Monday, March 14th, 2016

University of Cincinnati

• utline

Introduction Supercritical CO2 Heat Exchanger and Cycle Analysis A Closed Loop Recuperated Lenoir Cycle using Supercritical CO2 Combined Cycle Engine Cascades Conjugate Heat Transfer With Supercritical CO2 Novelty of the Current Work Conclusions Recommended Future Work

1

introduction .

introduction

∙ Supercritical Carbon Dioxide (S-CO2) Power cycles can possess some favorable qualities of both the Rankine and Brayton cycles. ∙ S-CO2 Power cycles are typically proposed as an alternative or compliment to traditional Rankine and Brayton cycle engines. ∙ Because of their complexity, a S-CO2 engine has not yet been installed into production use. ∙ Ongoing research and development aims to make such engines a reality. The present work seeks to help those efforts.

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 of carbon dioxide (7.4 MPa). ∙ Possible applications:

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

∙ Possible Configurations:

∙ Combined cycle using waste heat from a traditional open loop gas turbine ∙ Primary cycle with nuclear and solar energy heat sources

4

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

5

supercritical co2 power cycle - strengths

∙ Low Pressure Ratio ∙ Large amounts of recuperation possible. ∙ Low back work ratio: Decreased sensitivity of compressor/turbine efficiency on cycle efficiency. ∙ High Power Density

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

∙ High exergy efficiencies.

6

supercritical co2 power cycle - weaknesses

∙ Nonlinear specific heat mismatch causes difficulties exchanging heat between high and low pressure sides at lower temperatures. ∙ Heating power in recuperators can be 350% of the net output power and 180% of the input heating power. ∙ Closed loop design presents additional system complexities. ∙ High pressures present increased structural loading and seal leakage issues. ∙ 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.

7

supercritical co2 heat exchanger and cycle analysis .

proposed system layout

tank

Heater Cooler

High Temperature Recuperator

Low Temperature Recuperator Total Mass Fraction

Medium Temperature Recuperator

Low Temperature Recuperator Main Mass Fraction

Cooler

ReHeater

Cooler

Generator tank Starter Starter

Recompression Mass Fraction

Main Mass Fraction

Total Mass Fraction

Main R eC PreC 6 6 6 6 5 5 4 4 3 3 2 2 1 1 7 7 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 14 15 15 4 7 Power AC Electricity

∙ 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

• perating 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. 9

proposed system layout

tank

Heater Cooler

High Temperature Recuperator

Low Temperature Recuperator Total Mass Fraction

Medium Temperature Recuperator

Low Temperature Recuperator Main Mass Fraction

Cooler

ReHeater

Cooler

Generator tank Starter Starter

Recompression Mass Fraction

Main Mass Fraction

Total Mass Fraction

Main R eC PreC 6 6 6 6 5 5 4 4 3 3 2 2 1 1 7 7 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 14 15 15 4 7 Power AC Electricity 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]

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

Line widths scaled by mass fraction.

10

variable property heat engine cycle analysis code

∙ A thermodynamic cycle analysis code was created from scratch using Python. ∙ Variable fluid properties are implemented as a function of both temperature and pressure using REFPROP. ∙ 0-D counterflow heat exchanger model was developed to account for variable fluid properties, yet maintaining high solution speed. ∙ Design space for the inputs is explored in parallel and can run on as many processors as are available.

11

0-d heat exchanger modeling

∙ Minimum temperature difference is defined instead of an effectiveness or surface area and convection coefficients. ∙ Pressure drop is not computed based on an assumed geometry, but is approximated to be linearly dependent upon temperature drop in the heat exchanger. ∙ Initial guess for the location of the minimum temperature difference and the corresponding unknown boundaries is made by comparing heat capacities of each fluid stream. ∙ A root finding technique is used with the initially guessed heat exchanger minimum temperature difference and unknown boundaries in order to find the actual minimum temperature difference and unknown boundaries.

12

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] 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=8.0MPa, Mass Fraction=1.00 Heated Side Inlet: Temperature=305.0K, Pressure=18.5MPa, Mass Fraction=0.6000 ∆Tmin=5.0 K, Pressure Drop=0 Pa/K, Inlet Pressure Ratio=2.3, φ=0.57, ε=0.98

13

cycle optimization constraints

Parameter Minimum Maximum PreCompressor Pressure Ratio 1.0 4.0 Main Compressor Pressure Ratio 1.1 4.1 Recompression Fraction 0.000 0.991 Low Temperature Recuperator Main Fraction High Pressure Com- ponent Mass Fraction 0.001 0.991 Main Compressor Outlet Pressure 2 MPa 35 MPa Maximum Temperature 923 K [650◦C] 923 K [650◦C] Minimum Temperature 320 K [47◦C] 320 K [47◦C] Main Compressor Isentropic Efficiency 0.850 0.850 PreCompressor Isentropic Efficiency 0.875 0.875 ReCompressor Isentropic Efficiency 0.875 0.875 Power Turbine Isentropic Efficiency 0.930 0.930 Main/Re/Pre Compressor Turbine Isentropic Efficiency 0.890 0.890 Heat Exchanger Minimum Temperature Difference 5 K 5 K Heat Exchanger Pressure Drop 500 Pa/K 500 Pa/K

14

cycle t-s and h-s diagrams

100 200 300 400 500 600 700 Temperature [C] 1,000 1,500 2,000 2,500 3,000 Entropy [J/(kg*K)] 300 400 500 600 700 800 900 1,000 Temperature [K]

13 1 2 4 6 7 8 9 5 3 10 11 14 Critical Temperature: 304.13K Critical Pressure: 7.377MPa Constant Pressure Lines 11.29MPa 11.27MPa 34.92MPa 34.87MPa 34.87MPa 34.64MPa 20.88MPa 20.85MPa 6.88MPa 6.66MPa

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: 49.57% Line widths scaled by mass fraction. 1,000 1,500 2,000 2,500 3,000 Entropy [J/(kg*K)] 200 400 600 800 1,000 1,200 1,400 Enthalpy [kJ/kg]

13 1 2 4 6 7 8 9 5 3 10 11 14 Critical Temperature: 304.13K Critical Pressure: 7.377MPa Constant Pressure Lines 11.29MPa 11.27MPa 34.92MPa 34.87MPa 34.87MPa 34.64MPa 20.88MPa 20.85MPa 6.88MPa 6.66MPa

219 299 380 460 541 621 701 782 862 943 1,023 Temperature [K] Cycle Efficiency: 49.57% Line widths scaled by mass fraction.

15

cycle p-v and t-p diagrams

5 10 15 20 25 30 35 40 Specific Volume [L/kg] 5 10 15 20 25 30 35 40 Pressure [MPa]

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

Supercritical Fluid Liquid Gas

Vapor Liquid+Vapor

219 299 380 460 541 621 701 782 862 943 1,023 Temperature [K] Cycle Efficiency: 49.57% Line widths scaled by mass fraction. 100 200 300 400 500 600 700 Temperature [C] 5 10 15 20 25 30 35 40 Pressure [MPa] 300 400 500 600 700 800 900 1,000 Temperature [K]

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

Supercritical Fluid Liquid Gas

Vapor

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: 49.57% Line widths scaled by mass fraction.

16

cycle efficiency & recompression fraction vs max & min temperature

400 500 600 700 800 900 1000 Maximum Temperature [K] 10 15 20 25 30 35 40 45 50 55 Cycle Efficiency [%]

306.0 K 310.4 K 314.8 K 319.2 K 323.6 K 328.0 K

500 600 700 800 900 Maximum Temperature [K] 307.5 310.0 312.5 315.0 317.5 320.0 322.5 325.0 327.5 Minimum Temperature [K] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Recompression Fraction

17

cycle efficiency & recompression fraction vs pressure ratios

1.5 2.0 2.5 3.0 3.5 4.0 PreCompressor Pressure Ratio 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 Main Compressor Pressure Ratio 30.0 32.1 34.2 36.3 38.4 40.5 42.6 44.7 46.8 48.9 51.0

Cycle Efficiency [%]

1.5 2.0 2.5 3.0 3.5 4.0 PreCompressor Pressure Ratio 1.2 1.6 2.0 2.4 2.8 3.2 3.6 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

18

cycle efficiency vs heat exchanger minimum temperature difference

10 20 30 40 50 Heat Exchanger Minimum Temperature Difference [K] 42.0 43.5 45.0 46.5 48.0 49.5 51.0 52.5 54.0 Cycle Efficiency [%]

0.0 Pa/K 62.5 Pa/K 125.0 Pa/K 250.0 Pa/K 375.0 Pa/K 500.0 Pa/K

19

cycle efficiency vs recompression fraction & maximum pressure

0.0 0.2 0.4 0.6 0.8 1.0 Recompression Fraction 46.8 47.1 47.4 47.7 48.0 48.3 48.6 48.9 49.2 49.5 49.8 Cycle Efficiency [%] 1 2 3 4 5 Main Compressor Outlet Pressure [Pa] 1e7 5 10 15 20 25 30 35 40 45 50 Cycle Efficiency [%]

20

impact of the main compressor efficiency and power take off point

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Main Compressor Isentropic Efficiency 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5 51.0 Cycle Efficiency [%]

Dedicated Turbine Powered Power Turbine/Electrically Powered

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Main Compressor Isentropic Efficiency 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 Main Compressor Pressure Ratio

Dedicated Turbine Powered Power Turbine/Electrically Powered

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Main Compressor Isentropic Efficiency 0.32 0.40 0.48 0.56 0.64 0.72 0.80 0.88 0.96 1.04 Recompression Fraction

Dedicated Turbine Powered Power Turbine/Electrically Powered

21

cycle efficiency vs number of reheat stages

2 4 6 8 10 12 Number of ReHeat Stages 46.2 46.8 47.4 48.0 48.6 49.2 49.8 50.4 51.0 Cycle Efficiency [%]

22

a closed loop recuperated lenoir cycle using supercriti- cal co2 .

investigation of an alternative closed loop recuperated carbon dioxide cycle with constant volume heat addition

∙ A recuperated Lenoir cycle using supercritical carbon dioxide was studied. ∙ No other recuperated Lenoir cycle studies or Lenoir cycle studies with carbon dioxide have been identified. ∙ Efforts were inspired by the efficiency gains predicted for cycles that aim to approximate the Humphrey cycle, variation in fluid properties of carbon dioxide near the critical point, and the large amounts of recuperation used in the cycle presented previously. ∙ Cycle currently modeled using many moving chambers with pistons that are heated at constant volume and then expand allowing work to be done on the piston. ∙ Current analysis is an ideal cycle. ∙ The same minimum and maximum temperatures were used as in the previous studies (320 K [47◦C] and 923 K [650◦C]).

24

recuperated lenoir cycle - 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 1 2 4 5 3 6 1.100 1.200 1.225 1.250 1 . 3 1.300 1.400 1 . 4 1.500 1.200 1.225 1 . 2 5 1.300 1.400 1.500 Constant Pressure Lines 6.65MPa 30.00MPa 6.61MPa 6.61MPa

1.0 1.3 1.6 1.9 2.2 2.5 2.8 3.1 3.4 3.7 4.0 γ, cp /cv Cycle Efficiency: 44.73% Line widths scaled by mass fraction.

25

recuperated lenoir cycle - conclusions

∙ The ratio of specific heats was too high, particularly at low temperatures, limiting the amount of recuperation possible. ∙ Low pressure was varied to find the optimal cycle efficiency. ∙ A significant amount of work was required to compress the fluid at constant pressure. ∙ Larger heat addition and heat rejection temperature ranges resulted in lower cycle efficiency. ∙ A more complex layout could be possible, improving the cycle efficiency, but the increased complexity coupled with the complex constant volume heat exchanger are believed to be less feasible and beneficial than increasing the amount of reheat and intercooling in the previously studied cycle.

26

combined cycle engine cascades .

topping cycle with fuel cell

Generator Cool Intake Air

CH4

AC Electricity

O2 Pressurized Methane (CH4) Fuel N2 O2 N2 CO2

Electrolyte Anode Cathode

Heat Generation Heat Generation Heat Generation

DC Electricity

H2O H2O CO2

Combustor

Solid Oxide Fuel Cell

28

intermediate and bottoming engines

Waste Heat Waste Heat AC Electricity

tank

Cooler

High Temperature Recuperator

Low Temperature Recuperator Total Mass Fraction

Medium Temperature Recuperator

Low Temperature Recuperator Main Mass Fraction

Cooler Cooler

Generator tank Starter Starter

Recompression Mass Fraction Main Mass Fraction Total Mass Fraction

Main R eC PreC 6 6 6 6 5 5 4 4 3 3 2 2 1 1 7 7 7 8 9 9 10 10 11 11 12 12 13 13 14 14 14 15 15 4 7 Power

Heat Exchanger

29

general combined cycle engine

Engine 1: Low/Medium Pressure T

• pping Cycle (Airbreathing Gas T

urbine with Fuel Cell) Engine 2: High Pressure Intermediate Cycle (S-CO2 Engine) Engine 3: High Pressure Intermediate Cycle (S-CO2 Engine) Engine 4: High Pressure Bottoming Cycle (S-CO2 Engine)

Hot Exhaust Warm Exhaust Gases

Waste Heat Waste Heat AC Electricity

Waste Heat Waste Heat AC Electricity

Waste Heat Waste Heat AC Electricity

Generator Cool Intake Air

CH4 AC Electricity O2 Pressurized Methane (CH4) Fuel N2 O2 N2 CO2

DC Electricity H2O H2O CO2

Solid Oxide Fuel Cell

30

combined cycle engine

200 400 600 800 1000 1200 1400 1600 Temperature [C] 1,000 1,500 2,000 2,500 3,000 Entropy [J/(kg*K)] 400 600 800 1,000 1,200 1,400 1,600 1,800 Temperature [K] Combined Cycle Efficiency: 64.95% Line widths scaled by mass fraction. Air cycle entropy reference is arbitrary and does not follow the same conventions as CO2. Combined Cycle Efficiency: 64.95% Line widths scaled by mass fraction. Air cycle entropy reference is arbitrary and does not follow the same conventions as CO2.

Engine Work Fraction Marginal Combined Cycle Efficiency Engine Efficiency Engine Exergy Efficiency Type Number % % % % Gas Turbine 1 70.05 45.49 45.49 54.28 S − CO2 Engine 2 18.60 12.08 49.59 75.02 S − CO2 Engine 3 9.45 6.14 33.53 63.79 S − CO2 Engine 4 1.90 1.23 14.14 46.10 Combined 100.00 64.95 64.95 77.5

31

efficiency vs s − co2 engine peak pressure & topping cycle turbine inlet temp

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Main Compressor Outlet Pressure [Pa] 1e7 63.0 63.2 63.4 63.6 63.8 64.0 64.2 64.4 64.6 64.8 65.0 Cycle Efficiency [%] 1200 1300 1400 1500 1600 1700 1800 1900 Gas Turbine Rotor Inlet Temperature [K] 48 50 52 54 56 58 60 62 64 66 Cycle Efficiency [%]

306.0 K 310.4 K 314.8 K 319.2 K 323.6 K 328.0 K

32

efficiency vs number of engines & topping cycle comp isentropic efficiency

1 2 3 4 5 6 Maximum Allowable Number of Engines 46 48 50 52 54 56 58 60 62 64 66 Cycle Efficiency [%] 0.80 0.82 0.84 0.86 0.88 0.90 Gas Turbine Compressor Isentropic Efficiency 64.00 64.25 64.50 64.75 65.00 65.25 65.50 65.75 66.00 66.25 66.50 Cycle Efficiency [%]

33

combined cycle engine with fuel cell

200 400 600 800 1000 1200 1400 1600 Temperature [C] 1,000 1,500 2,000 2,500 3,000 Entropy [J/(kg*K)] 400 600 800 1,000 1,200 1,400 1,600 1,800 Temperature [K] Combined Cycle Efficiency: 65.84% (HHV), 73.09% (LHV) Line widths scaled by mass fraction. Air cycle entropy reference is arbitrary and does not follow the same conventions as CO2. Combined Cycle Efficiency: 65.84% (HHV), 73.09% (LHV) Line widths scaled by mass fraction. Air cycle entropy reference is arbitrary and does not follow the same conventions as CO2.

Engine Work Fraction Marginal Combined Cycle Efficiency Engine Efficiency Engine Exergy Efficiency Type Number % HHV, % LHV, % % % Fuel Cell 1 71.14 91.15 46.84 60.01 52.00 66.63 52.00 (LHV) 66.63 (LHV)

• Gas Turbine

20.01 13.17 14.63 30.47 (LHV) S − CO2 Engine 2 6.44 4.24 4.71 41.00 69.99 S − CO2 Engine 3 2.41 1.59 1.76 23.02 55.52 Combined 100.00 65.84 73.09%

• 34

conjugate heat transfer with supercritical co2 .

conjugate heat transfer with supercritical co2

∙ Little experimental and theoretical research has been conducted related to supercritical carbon dioxide power cycle applications. ∙ Other efforts have focused on heat transfer with supercritical carbon dioxide and constant heat flux or constant temperature boundary conditions. ∙ Accurate understanding of real heat exchangers is critical in assessing real engine cycle performance, potentially more significant than the turbomachinery.

36

heat exchanger geometry and boundary conditions

0.5mm 1.5mm

Solid

Low Pressure Fluid High Pressure Fluid length

High T emperature T

• tal T

emperature Uniform Mass Flux Inlet Low T emperature T

• tal T

emperature Uniform Mass Flux Inlet Low Pressure Static Pressure Outlet High Pressure Static Pressure Outlet Symmetry Plane Symmetry Plane Adiabatic Wall Adiabatic Wall

37

2-d heat transfer cases

Case ReDh , High Pressure Inlet Viscous Model Low Pressure Inlet Total Temperature Low Pressure Outlet Static Pressure High Pressure Inlet Total Temperature High Pressure Outlet Static Pressure High Pressure Mass Fraction Length Notes I 10 Laminar 450 K 5 MPa 305 K 25 MPa 0.565 1 m Low Re, Low ∆Tmin II 50 Laminar 450 K 5 MPa 305 K 25 MPa 0.565 1 m Low Re, Medium ∆Tmin III 3,000 Turbulent 450 K 5 MPa 305 K 25 MPa 0.565 1 m High Re, High ∆Tmin IV 4,000 Turbulent 450 K 5 MPa 305 K 25 MPa 0.565 1 m High Re, High ∆Tmin V 3,000 Turbulent 450 K 5 MPa 305 K 25 MPa 0.565 10 m High Re, Low ∆Tmin VI 3,000 Turbulent 700 K 1 MPa 600 K 5 MPa 1.000 10 m Nearly Constant and Nearly Similar Specific Heats

38

geometry and fluid property grids

Geometry Grids

Grid Top Half Channel Points Top Channel First Point Spacing From Wall Bottom Half Channel Points Bottom Channel First Point Spacing From Wall Solid Wall Points Length Points Total Points 00 41 1.00E-5 m (laminar), 2.50E-6 m (turbulent) 41 1.00E-5 m (laminar), 5.000E-6 m (turbulent) 17 2,609 258,291 11 21 2.00E-5 m (laminar), 5.00E-6 m (turbulent) 21 2.00E-5 m (laminar), 1.000E-5 m (turbulent) 9 1,305 66,555 22 11 4.00E-5 m (laminar), 1.000E-5 m (turbulent) 11 4.00E-5 m (laminar), 2.000E-5 m (turbulent) 5 653 17,631

Fluid Property Grids

Grid Level Minimum Temperature Maximum Temperature Temperature Points Minimum Pressure Maximum Pressure Pressure Points Total Points 00 304.22 K 500 K 3001 4.4 MPa 26.0 MPa 217 651,217 11 304.22 K 500 K 1501 4.4 MPa 26.0 MPa 109 163,609 22 304.22 K 500 K 751 4.4 MPa 26.0 MPa 55 41,305 39

case i: high pressure inlet redh=10, laminar, 1m long

Reynolds Numbers and Average Dynamic Viscosities vs Length Position

0.0 0.2 0.4 0.6 0.8 1.0 Position [m] 10 20 30 40 50 60 70 80 90 100 ReDh

High Pressure Channel ReDh High Pressure Channel Viscocity Low Pressure Channel ReDh Low Pressure Channel Viscocity

16 24 32 40 48 56 64 72 80 88 96 Dynamic Viscocity [µPa ∗s] Local Reynolds Number and Dynamic Viscocity

Average Densities vs Length Position

0.0 0.2 0.4 0.6 0.8 1.0 Position [m] 100 200 300 400 500 600 700 800 900 1000 Density [kg/m3 ]

High Pressure Channel Low Pressure Channel

Fluid Density

40

case i: high pressure inlet redh=10, laminar, 1m long

Total Temperature Contours

41

case i: high pressure inlet redh=10, laminar, 1m long

Temperatures vs Length Position

0.0 0.2 0.4 0.6 0.8 1.0 Position [m] 304 312 320 328 336 344 352 360 368 376 384 392 400 408 416 424 432 440 448 456 Temperature [K]

Low Pressure Channel Centerline Total Temperature Low Pressure Channel Enthalpy Weighted Average Total Temperature Low Pressure Channel Wall Total Temperature High Pressure Channel Centerline Total Temperature High Pressure Channel Enthalpy Weighted Average Total Temperature High Pressure Channel Wall Total Temperature

Temperatures

Average ∆T and Specific Heats vs Temperature on the Low Pressure Side

1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6 Low Pressure Temperature - High Pressure Temperature [K]

∆T - 2-D CFD ∆T - 0-D

300 320 340 360 380 400 420 440 460 Temperature, Low Pressure/Cooled/Top Channel [K] 1050 1200 1350 1500 1650 1800 1950 2100 2250 2400 Specific Heat [J/(kg ∗K)]

Low Pressure Channel High Pressure Channel

Temperature Difference, Low Pressure Channel to High Pressure Channel

42

case i: high pressure inlet redh=10, laminar, 1m long

Heat Fluxes vs Length Position

0.0 0.2 0.4 0.6 0.8 1.0 Position [m] 15 30 45 60 75 90 105 120 135 150 W/m2

High Pressure Channel Low Pressure Channel

Wall Heat Flux Magnitude

Heat Transfer Coefficients and Average Thermal Conductivities vs Length Position

20 40 60 80 100 120 140 160 180 200 W/(m2 ∗K)

h - High Pressure Channel h - Low Pressure Channel Nu - High Pressure Channel Nu - Low Pressure Channel

6 7 8 9 10 11 12 13 14 15 Nu 0.0 0.2 0.4 0.6 0.8 1.0 Position [m] 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 Thermal Conductivity [W/(m ∗K)]

High Pressure Channel Low Pressure Channel

Heat Transfer Coefficient and Thermal Conductivity

43

case v: high pressure inlet redh=3,000, turbulent, 10m long

Reynolds Numbers and Average Dynamic Viscosities vs Length Position

2 4 6 8 10 Position [m] 3000 6000 9000 12000 15000 18000 21000 24000 27000 30000 ReDh

High Pressure Channel ReDh High Pressure Channel Viscocity Low Pressure Channel ReDh Low Pressure Channel Viscocity

16 24 32 40 48 56 64 72 80 88 96 Dynamic Viscocity [µPa ∗s] Local Reynolds Number and Dynamic Viscocity

Average Densities vs Length Position

2 4 6 8 10 Position [m] 100 200 300 400 500 600 700 800 900 1000 Density [kg/m3 ]

High Pressure Channel Low Pressure Channel

Fluid Density

44

case v: high pressure inlet redh=3,000, turbulent, 10m long

Temperatures vs Length Position

2 4 6 8 10 Position [m] 304 312 320 328 336 344 352 360 368 376 384 392 400 408 416 424 432 440 448 456 Temperature [K]

Low Pressure Channel Centerline Total Temperature Low Pressure Channel Enthalpy Weighted Average Total Temperature Low Pressure Channel Wall Total Temperature High Pressure Channel Centerline Total Temperature High Pressure Channel Enthalpy Weighted Average Total Temperature High Pressure Channel Wall Total Temperature

Temperatures

Average ∆T and Specific Heats vs Temperature on the Low Pressure Side

8.0 8.8 9.6 10.4 11.2 12.0 12.8 13.6 14.4 Low Pressure Temperature - High Pressure Temperature [K]

∆T - 2-D CFD ∆T - 0-D

300 320 340 360 380 400 420 440 460 Temperature, Low Pressure/Cooled/Top Channel [K] 1050 1200 1350 1500 1650 1800 1950 2100 2250 2400 Specific Heat [J/(kg ∗K)]

Low Pressure Channel High Pressure Channel

Temperature Difference, Low Pressure Channel to High Pressure Channel

45

case v: high pressure inlet redh=3,000, turbulent, 10m long

Heat Fluxes vs Length Position

2 4 6 8 10 Position [m] 400 800 1200 1600 2000 2400 2800 3200 W/m2

High Pressure Channel Low Pressure Channel

Wall Heat Flux Magnitude

Heat Transfer Coefficients and Average Thermal Conductivities vs Length Position

100 200 300 400 500 600 700 800 900 1000 W/(m2 ∗K)

h - High Pressure Channel h - Low Pressure Channel Nu - High Pressure Channel Nu - Low Pressure Channel

15 30 45 60 75 90 105 120 135 150 Nu 2 4 6 8 10 Position [m] 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 Thermal Conductivity [W/(m ∗K)]

High Pressure Channel Low Pressure Channel

Heat Transfer Coefficient and Thermal Conductivity

46

case vi: high pressure inlet redh=3,000, turbulent, 10m long, nearly constant cp

Fluid Property Grid II

Grid Level Minimum Temperature Maximum Temperature Temperature Points Minimum Pressure Maximum Pressure Pressure Points Total Points 00 590 K 710 K 3001 1 MPa 5 MPa 217 651,217 47

case vi: high pressure inlet redh=3,000, turbulent, 10m long, nearly constant cp

Reynolds Numbers and Average Dynamic Viscosities vs Length Position

2 4 6 8 10 Position [m] 2640 2680 2720 2760 2800 2840 2880 2920 2960 3000 3040 ReDh

High Pressure Channel ReDh High Pressure Channel Viscocity Low Pressure Channel ReDh Low Pressure Channel Viscocity

28.0 28.4 28.8 29.2 29.6 30.0 30.4 30.8 31.2 31.6 32.0 Dynamic Viscocity [µPa ∗s] Local Reynolds Number and Dynamic Viscocity

Average Densities vs Length Position

2 4 6 8 10 Position [m] 5 10 15 20 25 30 35 40 45 Density [kg/m3 ]

High Pressure Channel Low Pressure Channel

Fluid Density

48

case vi: high pressure inlet redh=3,000, turbulent, 10m long, nearly constant cp

Temperatures vs Length Position

2 4 6 8 10 Position [m] 600 606 612 618 624 630 636 642 648 654 660 666 672 678 684 690 696 702 Temperature [K]

Low Pressure Channel Centerline Total Temperature Low Pressure Channel Enthalpy Weighted Average Total Temperature Low Pressure Channel Wall Total Temperature High Pressure Channel Centerline Total Temperature High Pressure Channel Enthalpy Weighted Average Total Temperature High Pressure Channel Wall Total Temperature

Temperatures

Average ∆T and Specific Heats vs Temperature on the Low Pressure Side

2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 Low Pressure Temperature - High Pressure Temperature [K]

∆T - 2-D CFD ∆T - 0-D

600 620 640 660 680 700 720 Temperature, Low Pressure/Cooled/Top Channel [K] 1080 1088 1096 1104 1112 1120 1128 1136 1144 1152 Specific Heat [J/(kg ∗K)]

Low Pressure Channel High Pressure Channel

Temperature Difference, Low Pressure Channel to High Pressure Channel

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case vi: high pressure inlet redh=3,000, turbulent, 10m long, nearly constant cp

Heat Fluxes vs Length Position

2 4 6 8 10 Position [m] 60 120 180 240 300 360 420 480 540 600 W/m2

High Pressure Channel Low Pressure Channel

Wall Heat Flux Magnitude

Heat Transfer Coefficients and Average Thermal Conductivities vs Length Position

20 40 60 80 100 120 140 160 180 200 W/(m2 ∗K)

h - High Pressure Channel h - Low Pressure Channel Nu - High Pressure Channel Nu - Low Pressure Channel

10 15 20 25 30 35 40 45 50 Nu 2 4 6 8 10 Position [m] 0.041 0.042 0.043 0.044 0.045 0.046 0.047 0.048 0.049 0.050 Thermal Conductivity [W/(m ∗K)]

High Pressure Channel Low Pressure Channel

Heat Transfer Coefficient and Thermal Conductivity

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novelty of the current work .

novelty of the current work

∙ A new shaft layout and startup procedure are presented. ∙ With the multi-shaft configuration, turbomachinery can be placed inside pressure vessels to avoid high pressure ratio seals. ∙ A new variable property cycle analysis code was developed. ∙ The design space of the proposed cycle layout has been optimized and explored in detail in a very general manner. ∙ A cycle efficiency of 49.57% has been predicted with a turbine inlet temperature of 923 K [650◦C] and a heat rejection temperature of 320 K [47◦C]. ∙ The significance of implementing multiple reheat stages in the turbine on cycle efficiency were explored. ∙ A closed loop recuperated Lenoir cycle using supercritical carbon dioxide was investigated.

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novelty of the current work

∙ Combined cycle configurations using supercritical carbon dioxide power cycles in conjunction with a fuel cell and gas turbine has been explored and optimized. ∙ A combined cycle efficiency of 64.95% was predicted for the combined cycle without a fuel cell with a turbine inlet temperature of 1,890 K [1,617◦C] and a rejected heat temperature of 306 K [33◦C]. ∙ A combined cycle efficiency of 73.09% was predicted for the combined cycle with a fuel cell with a rejected heat temperature of 306 K [33◦C]. ∙ Two dimensional conjugate heat transfer was studied with a simple channel geometry using supercritical carbon dioxide and variable fluid property formulations. ∙ Averaged two dimensional results were in close agreement with the zero dimensional heat exchanger solver, validating its applicability in the cycle analysis code.

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conclusions .

conclusions

∙ Supercritical CO2 Power Cycles have the potential for high efficiencies at low turbine inlet temperatures. ∙ Highly nonlinear fluid properties present significant challenges in cycle and component design. ∙ Appropriate modeling of heat exchangers is critical in assessing correct cycle performance. ∙ In order to use a 0-D heat exchanger model, a sufficiently long heat exchanger is assumed. ∙ Further investigations of the recuperated Lenoir cycle are not recommended. ∙ Supercritical carbon dioxide power cycles can be very beneficial in combined cycle configurations, provided multiple supercritical carbon dioxide power cycles are used and each cycle is optimized individually.

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recommended future work .

recommended future work

∙ Allow for variable turbomachinery efficiencies which are dependent on the inlet conditions and pressure ratio. ∙ Improve pressure drop relationships for heat exchangers in the 0-D heat exchanger solver. ∙ Support condensation and boiling in heat exchangers. ∙ Further investigate the use of CoolProp as a replacement for REFPROP. ∙ Incorporate a cost model into the cycle optimization process. ∙ Conduct numerical simulations of more realistic heat exchanger geometries. ∙ Conduct preliminary design and numerical simulations of turbomachinery components.

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Questions?

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