# Design Point Performance and Optimization of Humid Air Turbine Power Plants
## 3 Results and Discussion
### Heat Exchanger Size and Cost Analysis
When the effectiveness of the heat exchangers increases from 0.75 to 0.85 (\(C_{5}^{40}\)\(\rightarrow\)\(B_{5}^{40}\)), the total weight increases by 14% and the total cost by 28%. For a further effectiveness increase to 0.95 (\(B_{5}^{40}\)\(\rightarrow\)\(A_{5}^{40}\)), the weight rises by 46% and the cost by 80% with respect to the baseline cycle. On the other hand, the thermal efficiency shows a quasi-linear correlation with the cycle design parameters. From \(C_{5}^{40}\) to \(B_{5}^{40}\), the efficiency rises by 2.8 pp, and from \(B_{5}^{40}\) to \(A_{5}^{40}\), an increase of 2.7 pp is observed (Figure 3). Considering each heat exchanger separately, between cycles \(A_{5}^{40}\) and \(C_{5}^{40}\), the intercooler is the component that undergoes the largest variation in weight, manifesting a reduction of 77%. The economizer shows a reduction of 65% with regards to its reference cost, followed by the aftercooler with a reduction of 60%, and, finally, the recuperator with a reduction of 40%. On the other hand, the intercooler is the component that suffers the largest reduction in cost--82% of its reference cost, followed by the economizer, the aftercooler, and the recuperator--70%, 67%, and 35%, respectively. This demonstrates that the variations in the total weight of the heat exchangers and the variations in cost are linearly related, as the changes in cost are directly correlated with the variations in weight of each component. Moreover, when comparing cycles \(D_{5}^{40}\), \(E_{5}^{40}\), \(F_{5}^{40}\), and \(G_{5}^{40}\) with \(A_{5}^{40}\), it can be seen that the reduction of the technology level of a heat exchanger has a knock-on effect on the remaining heat exchangers of the system (see Figure 9). The aftercooler is the heat exchanger that experiences the largest reduction in weight and cost--88% and 87%, respectively. In addition, both the weight and cost of the aftercooler are cut by 39% when the effectiveness of the intercooler is reduced from 0.95 to 0.75 (\(A_{5}^{40}\)\(\rightarrow\)\(F_{5}^{40}\)). However, both the weight and cost of the aftercooler are cut by 39% and 17%, respectively, when the effectiveness of the economizer is reduced from 0.95 to 0.75 (\(A_{5}^{40}\)\(\rightarrow\)\(D_{5}^{40}\)). The weight and cost of the economizer is reduced by 43% and 14%, respectively, when the recuperator effectiveness is changed from 0.9 to 0.8 (\(A_{5}^{40}\)\(\rightarrow\)\(G_{5}^{40}\)). Hence, the design of the power plant must account for the impact of the technology level of one of the components on the design, cost, and weight of the remaining heat exchangers. The overall system estimated acquisition cost and weight is shown in Figure 10 normalized against the baseline cycle \(A_{5}^{40}\) metrics. In terms of total weight, the change produced by the economizer and the recuperator--20% and 22% of the reference weight, respectively--is an order of magnitude higher than the changes produced by the intercooler, or the aftercooler--9%, and 1%, respectively. On the other hand, the changes produced by the intercooler, the recuperator, and the aftercooler--34%, 20%, and 8% of the reference cost, respectively--are one order of magnitude higher than the ones the economizer can create which is around 2%. In addition, from the contours illustrated in Figures 3 and 10b, it can be demonstrated that the most efficient way to reduce the total cost of the heat exchangers is to reduce the effectiveness of the aftercooler. The ratio of the percentage variation in cost to the variation in thermal efficiency \(\Delta c(\%)/\Delta\eta(\%)\) is 17--i.e., the cost drops by 17% per percentage point drop of thermal efficiency, whereas, when reducing the effectiveness of the intercooler, recuperator and economizer, these ratios become 16, 9 and 1, respectively. Figure 10: **(a)** heat exchanger total normalized weight and (**b**) total normalized acquisition cost index across the range of heat exchanger effectiveness for \(\mathit{OPR}\) = 40 & \(\Delta\Gamma_{\mathit{ps}}\) = 5 K.