## 3 Results and Discussion
### Finite Element Analysis Results
Since the temperature difference between the piston and the combustion gasses on the piston surface is higher in the first cycle, the fluctuation in the change in total heat flux is greater than in the last cycles. In Figure 9c, the change in total heat flux in the last two cycles is given. The highest heat flux in the final cycle was 0.9472 W/mm\({}^{2}\) for the NC piston, 0.6898 W/mm\({}^{2}\) for the FC piston, 1.9565 W/mm\({}^{2}\) for the PC-5 piston, and 2.3684 W/mm\({}^{2}\) for the PC-10 piston. Heat flow occurred on the upper surface of the PC-10 and PC-5 pistons due to the temperature difference between the coating surface and the piston surface. At the same time, there was a direct heat transfer from the coating surface to the surface of the piston crown. Since the heat transfer coefficient is smaller in PYSZ material than in the lining layer and piston material, the amount of heat transfer to the lower layers is lower. One of the purposes of applying TBC to the piston surface is to reduce the amount of heat loss. Among the four piston models with the full surface coated, it was the piston that had the lowest total heat flux. [PERSON] and [PERSON] [26] in their study used YSZ as the coating material while applying TBC with 0.2, 0.4 and 0.6 mm thicknesses. In their analysis of the transient steady state, when the coating thickness was 0.4 mm, the highest total heat flux was 1.95 W/mm\({}^{2}\), 0.65 W/mm\({}^{2}\) on the coating surface, and 0.95 W/mm\({}^{2}\) on the uncoated piston. As a result of the transient thermal analyses performed in this study, the total heat flux on the coating surface was similarly lower than that of the substrate piston surface and the uncoated piston surface. The von Mises stress variations for the piston models are given in Figure 10. The von Mises stress variations on the piston surface were determined as 2207 MPa, 2764 MPa, 2740 MPa, and 2293 MPa for the NC, PC-10, PC-5, and FC pistons, respectively, after 60 s. The von Mises stress variations on the coating surface were determined as 1383 MPa, 1313 MPa, and 1818 MPa for the PC-10, PC-5 and FC pistons after 60 s, respectively. In the PC-5 and PC-10 piston models, the von Mises stresses on the coating and piston surface were determined to be close to each other. As a result of transient thermal analysis, the highest temperatures reached by the PC-5 and PC-10 piston models were found to be close to each other. As the TBC surface area on the piston surface increased, the von Mises stress value on the coating surface increased. The lowest stress value was determined in the NC piston model, and the von Mises stress values in the coated piston models were higher than in the uncoated piston model. [PERSON] and [PERSON] [27] found the highest von Mises stress value of 4564.8 MPa when they used zirconium as a coating material in their analysis. The highest stress values on the piston surface were determined in the piston pin seat. As in this study, [PERSON] and [PERSON] [28] found the highest von Mises stress values in the piston pin housing. In their study, [PERSON] and [PERSON] [29] found a von Mises stress value of 524.88 MPa on the uncoated piston and 274.53 MPa on the coated piston surface in their analysis using the finite element method. As in this study, they determined that the stress value on the coating surface was lower than that on the piston surface. While the von Mises stress calculation method is suitable for metallic substrates, it is a limitation of the study to use von Mises stress calculations for all substrates of the study like NiCoCrAlY and PYSZ. Total deformation distribution change for the four piston models is given in Figure 11. With the increase in temperature and the accompanying stress values, the total deformation of the NC piston was determined to be 0.727 mm at the end of the simulation. The total deformation values were observed as 0.696 mm, 0.718 mm, and 0.723 mm for FC, PC-5, and PC-10 models, respectively.