# Design Point Performance and Optimization of Humid Air Turbine Power Plants
## 2 Methodology
In the economizer, condensation may also occur due to high humidity levels in the exhaust gas of the recuperator and the low temperature required at the economizer's exit. The latent heat of condensation of the water in the humid air varies the heat capacity of the gas \(C_{g}\) during condensation and generates a pinch point between the two streams within the heat exchanger (Figure 2). Therefore, this process is considered when simulating the performance of the heat exchangers. Liquid water is injected into the saturator to facilitate the humidification process. The temperature of the water at the outlet of the heat exchangers is, therefore, limited by the water saturation temperature. A safety coefficient of 0.9 is introduced into the performance calculations to avoid any steaming in the saturator as follows:  
\[T_{w,out}\leq T_{w,max}=T_{sat}(0.9\times p_{SAT}), \tag{1}\]  
where \(T_{w,out}\) is the water temperature at the outlet of the heat exchangers, \(T_{sat}\) is the saturation temperature and \(p_{SAT}\) is the pressure in the saturator. When the water temperature at the outlet of the heat exchangers exceeds the limit temperature \(T_{w,max}\), a new value of \(C^{*}\) is calculated, overwriting the imposed value. In the recuperator, the inlet properties of both streams are defined; therefore, the outlet conditions of the two streams are calculated from the prescribed recuperator effectiveness. Total pressure losses of the heat exchanger are fixed at a target value of 5% in both sides of all heat exchangers as recommended previously by [PERSON] et al. (2014) and [PERSON] et al. (2016). The conditions at the outlet of the saturator are calculated by imposing the pinch point temperature difference between the operating line of the water and the saturation line. The saturator is modelled according to the approach discussed by [PERSON] (2017) and originally developed by [PERSON] (2018). The detailed description of the thermodynamic model of the saturator and its validation against experimental data is provided in Appendix A. The impact of the key heat exchanger design parameters on the cycle thermal efficiency, plant weight and cost is assessed via a parametric study. The heat exchanger technology level is represented by their effectiveness. In terms of saturator design, the pinch temperature difference between the operating and the saturated air enthalpy lines [PERSON] (2017) is used as a design parameter, as it represents the driver for the heat and mass transfer process within the saturator. Cycle analysis has shown that the overall pressure ratio (\(OPR\)) that maximizes the thermal efficiency for the imposed TIT of 1600 K is beyond the technology today available for stationary or  
Figure 2: Heat transfer process in the Economizer. aero gas turbines (\(OPR>50\)). Therefore, two values of \(OPR\) are investigated, namely 30 and 40, as representatives of a standard and an advanced compression system technologies currently available in the market. The design envelopes of the above-mentioned variables are summarized in Table 1 and represent the range across which the parametric campaign was conducted for a total of 486 cycle designs. For each of the 486 cycles calculated, the rest of the design variables (heat capacity ratio of the water-air heat exchangers, relative pressure ratio, and saturator bypass) are optimized to maximize the thermal efficiency. This optimization is performed by means of the single objective genetic algorithm in MATLAB(R) (R2016a, MathWorks, Natick, MA, USA) (R2016b). The upper and lower bounds of these variables are reflected in Table 2. Therefore, the thermodynamic \"design vector\" comprises the effectiveness of the heat exchangers, the \(OPR\) and the humidifier pinch point as the free design variables, and the heat capacity ratios of the water-air heat exchangers, the relative pressure ratio and the saturator bypass as the optimized design variables.