## 2 Materials and Methods
### Numerical Study  
#### 2.2.1 Transient Thermal and Structural Analysis  
The uncoated piston and three different coated piston models used in this study were created in the Solidworks 2022 program. While creating the geometry of the FC piston, three layers were formed: the substrate (piston material), the 0.1 mm thick undercoating layer and the 0.4 mm thick coating surface. During the assembly of the three layers, the bonded condition was defined for the surfaces between the substrate and the undercoating layer, the undercoating layer, and the piston surface. In the NC piston, the piston model was drawn as a single unit. Figure 3a shows the geometry of the FC piston and the coating thicknesses. In Figure 3b,c, the geometry of the gradually modeled pistons is given. After the drawings were completed in the SolidWorks software, the piston models were transferred to the Ansys program so that transient thermal and static analyses could be performed. Since the engine was run at 1500 rpm during the engine tests, 1 cycle was completed in 0.04 s. In the analyses, the initial time step was 4 \(\times\) 10\({}^{-4}\) s, the minimum time step was 4 \(\times\) 10\({}^{-5}\) s, and the maximum time step was 4 \(\times\) 10\({}^{-3}\) s. Transient thermal analyses were carried out for 60 s. A total of 1500 cycles was defined for the completion of 60 s in the analyses. The analyses were made with 1500 steps, 1500 valid steps, ending in 60 s with \begin{table}
\begin{tabular}{l c} \hline
**Manufacturer** & **DDJ9500E** \\ \hline Power output & 10 HP \\ Maximum torque speed & 1800 rpm \\ Engine cooling system & Air cooling \\ Intake system & Naturally aspirated \\ Engine model & DDM192 FE \\ Bore–stroke (mm) & 92–75 \\ Displacement (cm\({}^{3}\)) & 498 \\ Number of cylinder & 1 \\ Combustion system & Direct injection \\ Compression ratio & 19:1 \\ \hline \end{tabular}
\end{table} 
Table 1: Engine specifications. \begin{table}
\begin{tabular}{l c c c c c c} \hline
**Material** & **Young’s** & **Poisson’s** & **Density** & **Specific Heat** & **Thermal** & **Thermal** \\  & **Modulus (GPa)** & **Rate** & **(kg/m\({}^{3}\))** & **Capacity** & **Conductivity** & **Expansion 10\({}^{-6}\)** \\ \hline Aluminum Alloy & 71 & 0.32 & 2700 & 960 & 155 & 21 \\ \hline NiCoCrAlY & 90 & 0.27 & 7870 & 764 & 16.1 & 12 \\ \hline PYSZ & \multirow{2}{*}{205} & \multirow{2}{*}{0.25} & \multirow{2}{*}{6010} & \multirow{2}{*}{640} & \multirow{2}{*}{2.12} & \multirow{2}{*}{11.5} \\ (ZrO\({}_{2}\)–8\%Y\({}_{2}\)O\({}_{3}\)) & & & & & \\ \hline \end{tabular}
\end{table} 
Table 2: The material properties of piston substrate, bonding layer, and coating layer. time integration. The 1500 cycle pattern was for reducing the simulation run-time due to limited resources and computer infrastructure. As a result of the mesh operations performed before the analysis, the number of elements for the NC piston was 11,096, and the number of nodes was 20,111. The FC piston had 81,368 node counts and 40,876 element counts. The FC piston had the largest number of nodes and elements of the four models. The number of nodes in the PC-5 piston was 41,162, and the number of elements was 16,802. The PC-10 piston had 40,438 nodes, while there were 17,884 elements. Mesh optimization is a critical step in finite element analysis. For this study, we checked the mesh accuracy with simulation time and convergence to experimental results. The initial temperature of the piston was accepted as 300 \({}^{\circ}\)C. Boundary conditions shown in Figure 4 were applied while performing transient thermal analyses using the finite element method. Gas temperature and the heat transfer coefficient are given as functions of crank angle (CA) in Figure 4. The temperature and heat transfer coefficient values for the applied boundary conditions are given in Table 3. As a result of the thermal analyses for the four piston models, the temperature and total heat flux values on the piston, lining and coating surface were determined.