# Performance Analysis of the Supercritical Carbon Dioxide Re-compression Brayton Cycle
## 3 Results and Discussion
### Heat Transfer Area Coefficient (UIA) and Turbonachinery Size (SP) Values  
_UA_ and _SP_ values are the parameters for the estimation of the cost of the system. _UA_ value indicates the area required for heat exchangers, and thus indicates their cost. As the _UA_ value increases, the total heat transfer area in the heat exchangers also increases, thereby increasing the investment and maintenance costs of the heat exchangers, and thus the system [21]. _SP_ values indicate the size of the turbomachinery in the system; thus, a lower value is desirable.  
Figure 10 illustrates the relationship of _UA_ with the different heat exchangers in the _sCO\({}_{2}\)_ re-compression Brayton cycle with different \(T_{7}\) values. It should be noted that the _UA_ value for the primary heat exchanger was the highest and increased at an increasing rate, whereas the _UA_ value for the HTR showed a linear increase with respect to \(T_{7}\). The net result is that for a high \(T_{7}\) value, a large heat exchange area is required when considering all of the heat exchangers in the system. The gas cooler showed the lowest _UA_ value and was not sensitive to \(T_{7}\).  
Figure 8: Total exergy destruction at different compressor outlet pressures (P\({}_{2}\)).  
Figure 7: Exergy destruction in different components of the cycle at \(T_{7}\) = 700 \({}^{\circ}\)C.  
Figure 9: Total exergy destruction at different compressor inlet temperatures (\(T_{1}\)).  
Figure 11 shows the effect of \(T_{1}\) on the heat exchanger sizes, as indicated by the _UA_ value for each heat exchanger. It should be noted that the _UA_ values of the primary heat exchanger, gas cooler and LTR all decrease with increasing \(T_{1}\), whereas that of HTR shows only a slight increase. As shown in Figure 12, the net result was a decrease in the _UA_Total_ value with increasing \(T_{1}\), which implies that the total area required for heat exchange decreases, and smaller heat exchanger sizes will be required for higher compressor inlet temperatures (which are much higher than the critical temperature value).  
Figure 13 shows the relationship between _UA_Total_ and \(x\) in the \(sCO_{2}\) re-compression Brayton cycle. The plot shows a maximum _UA_Total_ value at \(x\) = 0.74, which is the same point at which \(\eta_{th}\) was maximum. This implies that the size, and thus, the cost of the heat exchangers in the system, will need to be high to achieve the maximum efficiency.  
Figure 11: Heat transfer area coefficient (_UA_) vs. compressor inlet temperature (\(T_{1}\)).  
Figure 12: Total heat transfer area coefficient (_UA_Total_) vs. compressor inlet temperature (\(T_{1}\)).  
Figure 10: Heat transfer area coefficient (_UA_) vs. turbine inlet temperature (\(T_{7}\)).  
Figures 14 and 15 show the \(SP\) values for the turbine, main compressor and re-compressor in the \(sCO_{2}\) cycle. The \(SP\) of the turbine increases at higher \(T_{7}\) values, implying that a large turbine should be used for high \(T_{7}\) values. Moreover, the \(SP\) values of the main compressor and re-compressor are much less sensitive to \(T_{7}\), meaning that the same compressor size can be used when \(T_{7}\) is either low or high. The main compressor has a higher \(SP\) value than the re-compressor. Figure 15 shows the variation in \(SP\) of the different turbomachinery components with \(T_{1}\). The \(SP\) of the turbine does not depend on \(T_{1}\), as can be seen by the straight line. However, the \(SP\) values of the main compressor and re-compressor increase with an increase in \(T_{1}\). Moreover, the increase in the \(SP\) value for the main compressor is more pronounced than that of the re-compressor. Hence, relatively large compressor sizes will be required at a high \(T_{1}\).  
Figure 14: Size parameter (\(SP\)) vs. turbine inlet temperature (\(T_{7}\)).  
Figure 13: Total heat transfer area coefficient (\(U\!A_{Total}\)) vs. split mass fraction (\(x\)) at \(T_{7}\) = 700 \({}^{\circ}\)C.  
Figure 15: Size parameter (\(SP\)) vs. compressor inlet temperature (\(T_{1}\)).