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difficulties arise during startup when the compressor or turbine is far from the design point. Still we have been able to make the dynamic simulations provide reasonable results. 4.2 Orifice Model The motor-driven compressor loop has no turbine, but uses an orifice to lower the pressure and temperature as it happens in the turbine, but without producing work. The orifice model predicts the mass flow rate given the inlet and outlet pressure and the flow area. It uses the model of compressible flow through a nozzle as described in Bird, Stewart, and Lightfoot (Bird, Stewart, and Lightfoot, 1969). This model works with choked or non-choked flow and assumes that the expansion is isenthalpic, which allows the exit temperature to be determined because the exit pressure is known. 4.3 Inventory Control Model The inventory control simulation block, simply solves for the conservation of mass. This piece of code sums the mass over all components within the loop (which is temperature and pressure dependent) to determine the total mass. The compressor inlet pressure is then adjusted via a feed-back loop to assure that the total mass in the loop equals the fill mass. For the operating conditions modeled in this problem the loop was initially filled with 16.5 kg of CO2 and the fill mass was held constant. 4.4 Results of Dynamic Simulation for the S-CO2 Compression Loop A startup transient was simulated in the RPCSIM-CO2 code as the first problem. The results are illustrated in Figure 4-2. The transient starts the compressor at a shaft speed at near zero rpm and increases it linearly to 75,000 rpm in 10 seconds. The loop structure and the initial CO2 fluid temperature were assumed to be 307 K. The cooling water started at 301 K and the flow rate increased from 0 to 43.3 gallons per minute in 10 seconds. The predicted results are shown in four plots within Figure 4-2. The top plot illustrates the power transferred to the CO2 and the cyan line shows the power transferred to the cooling water. At steady state they are the same, but initially the pump puts more power in the gas than is transferred to the cooling water which results in an increase in the ducting and gas chiller structure temperature. The second plot shows the shaft speed (rpm, cyan) and the mass flow rate in kg/s (yellow and magenta). To first order, the mass flow rate is proportional to the shaft speed. The third set of curves show the temperatures at the compressor inlet (yellow), at the compressor outlet (magenta), and at the exit of the orifice (green). The fourth curve shows the inlet (green) and outlet (magenta) compressor pressures (Pa). As expected the pressure increases as the square of the shaft speed and hence is concave up. In general the results from this prediction appear to be un-remarkable. The components behave as expected, and comparisons with steady state cycle analysis predict the same results if the same pressure ratio (~1.7) and compressor efficiency (80%) are used. However, there are a few observations that are important. First, the loop responds rapidly to changes. This means that the loop will reach its steady state temperature and pressure quickly, on the order of a few 10s of seconds. Evidence of this rapid achievement of equilibrium is seen in the power curve where the power transferred to the CO2 equilibrates with the cooling water in about 20 seconds. Of course in this simulation there are not large temperature differences thus it does not take long to get to the new temperatures. The second observation is that in this compression loop, even though the gas pressure increased by a factor of 1.7, the inlet pressure remained nearly constant. This is a result of the fact that the average density in the loop stays constant, 41PDF Image | Operation and Analysis of a Supercritical CO2 Brayton Cycle
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