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meters, P is power in Watts, and ρ is density in kg/m3. Isentropic compression assumes ideal conditions with no losses. However, losses are incurred by leaks, heat transfer between the pump and fluid, and under or over compression leads to examination of the enthalpy difference between the compression state points. The compression cycle of SCO2 occurs between state points 1 and 2, raising the pressure from 12 to 20 MPa. Work is determined as the enthalpy difference in the isentropic and polytropic compression of the fluid as shown in Eqn. (17). This analysis yields an energy requirement of 0.2 kW to raise the pressure to the 20 MPa operating condition. W h(pi,si)h(po,si) R (17) 4.2. Expander The SCO2 in the expander undergoes near isentropic expansion in order to create mechanical energy to turn a permanent magnet alternator. The initial design was a toroidal engine with opposing pistons however, this architecture was found to be too difficult to fabricate. Therefore the expander design was revised into a more linear hexagonal variation. The latest iteration of the expander design is shown in Figure 6. This type of expander was chosen over a more conventional turbine expander due to the low volumetric flow rates within the cycle and results from calculating the specific speed and specific diameter similar to the pump selection methodology shown in Figure 5. The expander alternates intake and exhaust cycles to create axial piston movement. Each bank of three pistons is attached to a mounting plate that converts axial motion into rotational motion. A cam and a gear system is implemented to output power to a permanent magnet alternator. The design is still undergoing revision in order to optimize the expander for SCO2. Figure 6. Cutaway of opposed piston hexagonal motor. The cycle of the expander includes three optimal points: injection, expansion, and exhaust. Assumptions were made to neglect frictional losses, thermal losses through the expander itself, and steady state conditions. Figure 7 shows the ideal expansion cycle of the expander from start to finish. The cycle begins with the piston at top dead center as SCO2 is injected into the expander at 20 MPa and 200°C. This raises the pressure from 12 MPa to 20 MPa and the operating temperature of the previously expanded fluid from 90°C to 200°C within a relatively short amount of time. After the SCO2 is injected into the chamber the fluid is naturally allowed to expand, thus pushing the piston to bottom dead center. This expansion allows the pressure and temperature to drop while ideally maintaining constant enthalpy, and providing work for the system. The final leg of the cycle is a constant pressure evacuation of the piston chamber. This exhaust portion comes from the driving force done by the other side of the piston cycling through the expansion portion of the cycle. As the piston now slides back to top dead center, valves open inside the chamber allowing the SCO2 to evacuate back into the supply loop at reduced pressure and temperature of 12 MPa and 90°C. Once the expander has been built, careful testing will yield empirical data with which the theoretical results can be correlated. 7 Figure 7. P-v diagram of the expander cycle. 4.3. Internal Heat Exchanger The required heat transfer area from the heat exchanger analysis led to very large length requirements for a standard counter flow concentric pipe configuration. Plate-based heat exchangers arePDF Image | Waste Heat Energy Supercritical Carbon Dioxide Recovery Cycle Analysis and Design
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