## 3 Results and Discussion
### Optimization of the LHTES Geometries for a Solar Absorption Chiller Application  
In order to showcase how the optimization algorithm aids the selection of design parameters, this study adopts the design parameters of the shell-and-tube LHTES unit developed by [PERSON] et al. at the University of Lleida (2018) for the optimization case study and assumes that this unit is used to buffer the fluctuation of a solar-absorption cooling system (as illustrated in Figure 5). Therefore, the operational parameters such as discharging power, the mass flow rate of the HTF (Syltherm 800), and the inlet temperature of HTF are fixed due to operational constraints. The solar-absorption cooling system provides 1 kW of cold energy to the end-users. The solar thermal collector supplies the heat to a single effect absorption chiller with a COP of 0.7. In order to avoid overheating and supply heat during the nighttime, an LHTES unit is deployed between the solar thermal collector and the absorption chiller. The LHTES unit is charged by excess irradiance during the daytime and uses the stored heat to drive the absorption chiller when there is a lack of solar irradiance or during the nighttime. Operation conditions of the LHTES unit are listed in the first part of Table 6 as the fixed variables. Three cases with three different PCMs selected by the material assessment process are presented. The costs of the PCMs are assumed to be USD 10 per kilogram according to the average market price. The geometric parameters are optimized for each case with minimized cost with respective PCMs, and the results are shown in the third part of Table 6 as the optimized geometric variables. The three cases receive the same amount of heat from the solar thermal collector and produce the same amount of driving heat for the downstream absorption chiller. The optimization algorithm found different global optimum LHTES geometries for different PCMs, resulting in the PCM costs ranging from around USD 850-1600 per unit, while the total cost ranges from around USD 31,000-38,000 per unit. Figure 5: The layout of the solar-absorption cooling system. Since the design parameters for operation are fixed, the containment materials' selection has the most significant impact on the total f.o.b. cost. The major cause of the high total cost listed in Table 6 is due to the using of high-cost stainless steel for both the shell and tubes. As shown in Figure 6, the costs of four shell and tube material combinations are calculated. If changing the shell/tube materials from the high corrosion resistance stainless steel/stainless steel to other material combinations, the total cost decreases significantly. If using the low corrosion resistance carbon steel/carbon steel, the total cost can be reduced by around 3/4 due to much lower material costs, ranging from around USD 8400 to 10,200 per unit. It is worth mentioning that, for each selected PCM, the optimized geometry (tube lengths and the number of tubes) varies only in a limited range for each shell and tube material combination, and the PCM costs remain the same. Therefore, using low or non-corrosive PCMs can significantly decrease the containment material cost. Selecting the correct PCMs in the prescreening to make sure that it does not corrode the containment materials not only increases the lifespan of the LHTES unit, but also saves the investment cost. Users can also try to freeze more fixed variables, for example, the tube diameter, to decrease the costs. Moreover, this methodology has been found to be considerably faster compared with CFD-based methodologies. The average computing time using this methodology to finish the design of one shell-and-tube LHTES unit, from the material assessment to the cost output, is around 5-10 s. Depending on the quality of the mesh, CFD simulation-based methodologies can cost up to several hours to finish one optimization due to the dozens and hundreds of rounds of iterations that are needed for the GA solver.