Andrew Schroder doctoral dissertation: a study of power cycles using supercritical carbon dioxide as the working fluid . Monday, March 14 th , 2016 University of Cincinnati 0
outline Introduction Supercritical CO 2 Heat Exchanger and Cycle Analysis A Closed Loop Recuperated Lenoir Cycle using Supercritical CO 2 Combined Cycle Engine Cascades Conjugate Heat Transfer With Supercritical CO 2 Novelty of the Current Work Conclusions Recommended Future Work 1
introduction .
introduction ∙ Supercritical Carbon Dioxide (S-CO 2 ) Power cycles can possess some favorable qualities of both the Rankine and Brayton cycles. ∙ S-CO 2 Power cycles are typically proposed as an alternative or compliment to traditional Rankine and Brayton cycle engines. ∙ Because of their complexity, a S-CO 2 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 co 2 (s-co 2 ) 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 - c p vs temperature 15.0 15.0 8.4 MPa 8.4 MPa 8.4 MPa 7.4 MPa 7.4 MPa 7.4 MPa 10.0 10.0 9.4 MPa 9.4 MPa 9.4 MPa Cp (kJ/kg-K) Cp (kJ/kg-K) 6.4 MPa 6.4 MPa 6.4 MPa 10.4 MPa 10.4 MPa 10.4 MPa 11.4 MPa 11.4 MPa 11.4 MPa 5.00 5.00 12.4 MPa 12.4 MPa 12.4 MPa 5.4 MPa 5.4 MPa 5.4 MPa 20.4 MPa 20.4 MPa 20.4 MPa 2.4 MPa 2.4 MPa 2.4 MPa 1.4 MPa 1.4 MPa 1.4 MPa 0.000 0.000 300. 300. 400. 400. Temperature (K) Temperature (K) 5
supercritical co 2 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/m 3 to ∼ 788 kg/m 3 . ∙ High exergy efficiencies. 6
supercritical co 2 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 co 2 heat exchanger and cycle analysis .
proposed system layout Starter High Temperature Heater Recuperator tank 9 AC Electricity 10 ∙ Three compressors and several flow splits are used 9 Power Generator 5 6 4 5 to help mitigate heat transfer issues due to specific 8 heat mismatches. Recompression Mass Fraction ∙ Four shafts are utilized to better match optimal 8 6 ReHeater 4 4 3 operating speeds of each turbomachinery R eC 11 7 14 component. 10 Starter Medium Temperature Recuperator 7 6 tank ∙ Due to the small size of the turbomachinery, as 14 PreC well as the use of multiple shafts, each assembly 7 Low Temperature Recuperator Main Mass Fraction Total Mass Fraction 13 7 (except for the power turbine and generator) can 12 11 be placed inside a pressure vessel to avoid the 6 Cooler Main 2 3 need for high speed, high pressure seals. 1 7 2 15 ∙ Tanks and a blow down startup procedure are used 14 13 Total Mass Fraction to eliminate the need to attach a motor to the Low Temperature Recuperator Main Mass Fraction higher speed shafts. Cooler 15 1 12 Cooler 9
proposed system layout Starter High Temperature Heater Recuperator tank 9 AC Electricity 10 9 Line widths scaled by mass fraction. Power Generator 5 6 4 5 8 1,000 Constant 8 Pressure 6 Lines Recompression Mass Fraction 10.06MPa 900 10.00MPa 8 6 20.47MPa ReHeater 4 4 3 20.39MPa R eC 20.39MPa 11 5 7 800 20.19MPa 14 8.24MPa 10 Starter 7 8.18MPa Medium Temperature Recuperator Temperature [K] 7 2.75MPa 9 700 6 tank 2.52MPa 14 PreC 7 Low Temperature Recuperator Main Mass Fraction 600 Total Mass Fraction 13 7 4 12 11 500 3 6 10 Cooler Main 2 3 1 7 400 2 2 11 14 15 14 12 13 15 Total Mass Fraction 300 1 Low Temperature Recuperator Main Mass Fraction 13 Cooler 1,000 1,500 2,000 2,500 3,000 3,500 4,000 15 1 Entropy [J/(kg)] 12 Cooler 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 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 ∆ T min =5.0 K, Pressure Drop=0 Pa/K, Inlet Pressure Ratio=2.3, φ =0.57, ε =0.98 3000 20 2.0 c p,Cooled ∆ T C Heated /C Cooled c p,Heated 1 C Cooled 2500 C Heated 15 1.5 Heat Capacity Ratio, C Heated /C Cooled c p , [J/(kg*K)] and C, [J/(kg Cooled *K)] 2000 ∆ T = T Cooled − T Heated , [K] 1500 10 1.0 1000 5 0.5 500 0 0 0.0 300 320 340 360 380 400 420 440 300 320 340 360 380 400 420 440 Temperature, Cooled Side, [K] Temperature, Cooled Side, [K] 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- 0.001 0.991 ponent Mass Fraction 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 Cycle Efficiency: 49.57% Cycle Efficiency: 49.57% Line widths scaled by mass fraction. Line widths scaled by mass fraction. 5,000 1,023 1,400 1,000 Constant Constant 8 700 Pressure 6 Pressure Lines Lines 4,580 943 c p , Specific Heat at Constant Pressure [J/(kg*K)] 8 11.29MPa 11.29MPa 6 900 1,200 11.27MPa 11.27MPa 600 34.92MPa 4,160 34.92MPa 862 34.87MPa 34.87MPa 34.87MPa 34.87MPa 800 7 34.64MPa 3,740 34.64MPa 782 1,000 500 5 20.88MPa 20.88MPa 5 7 20.85MPa 20.85MPa Temperature [K] Temperature [C] Temperature [K] Enthalpy [kJ/kg] 700 6.88MPa 9 3,320 6.88MPa 701 9 6.66MPa 400 6.66MPa 800 Critical Temperature: 304.13K 2,900 621 Critical Temperature: 304.13K 600 Critical Pressure: 7.377MPa Critical Pressure: 7.377MPa 300 4 2,480 541 600 4 10 500 200 2,060 460 2 3 11 10 400 2 3 400 14 1,640 13 380 100 11 1 300 14 1,220 200 299 0 1 13 800 219 1,000 1,500 2,000 2,500 3,000 1,000 1,500 2,000 2,500 3,000 Entropy [J/(kg*K)] Entropy [J/(kg*K)] 15
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