Supercritical Carbon Dioxide Cycle Control Analysis

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Supercritical Carbon Dioxide Cycle Control Analysis ( supercritical-carbon-dioxide-cycle-control-analysis )

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dynamic time step control. Eventually, the time step becomes too small such that the Dynamic Code calculations are halted on a time step lower limit criterion (<10-10 s). Figure 2 analyzes in details the conditions during the onset of the oscillations. Even though it is difficult, due to the interdependency of the equations, to pinpoint the parameter which starts to oscillate first, it is clear that oscillations first start for the parameters calculated for the main compressor (Compressor No. 1) which is the cycle component operating closest to the critical point. Note that when the oscillations start, significant surge and choke margins are calculated for the compressor (in fact, Figure 1 demonstrates that the compressor can stably operate at lower margins during the transient). Also, Figure 2 shows that the control (valve) action is smooth during the oscillations meaning that the oscillations are not caused by the control system. One of the most probable reasons for the oscillation is mathematical interpolation between the compressor performance lines obtained from the precalculated performance maps. To check this hypothesis, an option has been added to the Plant Dynamics Code to use the performance subroutines directly in the dynamics calculations. Under this option, the compressor characteristics, such as flow rate and outlet temperature, are calculated by the same performance subroutines which were used to generate the performance maps. Since those subroutines incorporate several layers of iterations on flow rate and CO2 conditions, using those subroutines significantly slows down the dynamic calculations (compared to the maps option). It was found, however, that using the performance subroutines instead of the precalculated maps did not improve the results; the oscillations were still calculated. Based on the analysis, it is suggested that the oscillations are based on limits of the applicability of the compressor performance calculation approach to the S-CO2 cycle conditions. The current approach is based on calculating the CO2 conditions only at few key locations inside the compressor, such as the impeller inlet, impeller outlet, diffuser inlet, and diffuser outlet. Then, the empirical loss coefficients are applied to each component (impeller or diffuser) based on the average between inlet and outlet conditions. It is noted from Figure 2 that the CO2 enters the main compressor impeller at subcritical pressure and leaves the compressor at supercritical pressure while the inlet temperature is still close to but above the critical value. Therefore, a transition through a pseudocritical point must occur somewhere inside the compressor. Even though the property change at pseudocritical conditions is not as sharp as at the critical point, this change could still be significant. Therefore, there might be a condition where, depending on flow parameters, the location of the pseudocritical conditions might shift from impeller to diffuser and back. If this happens, it is expected that the parameters calculated on some average values, such as loss coefficients for example, might change significantly for both affected impeller and diffuser resulting in significant variation of the outlet conditions and, therefore, the flow rate through the compressor. It is difficult however to verify those conditions with the current performance models under the dynamic calculations. Based on the results of the analysis, it is recommended that a more detailed performance (and design) model to be implemented in the dynamics code. This model should better account for the properties variation inside each compressor component (rather than relying on inlet and outlet conditions only) with correspondingly more detailed loss calculations for each component. Also, the applicability of the currently used empirical loss coefficients to S-CO2 conditions should be investigated. Until such an 9

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