# On the Accuracy of Turbulence Model Simulations of the Exhaust Manifold
## 3 Exhaust Manifold Analysis
### Grid Analysis and Mesh  
An essential aspect of CFD simulations includes the careful determination of grid size. The grid must have sufficiently large dimensions to accurately represent the geometry, while also considering that a higher node count can result in longer CPU processing times. To determine the best mesh size for this analysis, a grid sensitivity study was implemented using eight different cell sizes, and two parameters were chosen to represent each grid: heat transfer and the velocity at the outlet. The study compared the changes in these parameters and their magnitudes at the exhaust gas outlet for the different mesh sizes, and the results showed that a grid size of 31,038 cells gave satisfactory results. Although a grid size of 109,668 also gave satisfactory results, it significantly increased the computational time. Therefore, a grid size of 31,038 cells was chosen for the simulation as it did not affect the results significantly. Table 3 shows the average velocity and maximum velocity for each grid and provides the percentage deviations from the chosen grid size.  
In near-wall regions, the solution gradients are very high, but accurate calculations are paramount to the success of the simulation. Since the calculations deal with solid-fluid variables, the near-wall treatment is essential. In Figure 3, mesh inflation is employed around the exhaust gas to ensure a y+ value of less than 1 throughout all simulations. An inflation mode with 5 layers is also used, adding extra layers of mesh cells near the solid boundaries where significant flow gradients are present (e.g., [PERSON] et al. [35]). These layers are gradually refined toward the wall to provide better resolution of the boundary layer and to capture the flow phenomena in that region. This technique is commonly used in CFD simulations to achieve higher resolution when capturing near-wall flow behavior.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Zone** & **Velocity** & **Temperature** & **Pressure** & **Turbulence** & **Hydraulic** \\  & **Magnitude** & & & **Intensity** & **Diameter** \\ \hline Inlet 1 & 20 m/s & 790 K & — & 5\% & 0.06 m \\ \hline Inlet 2 & 20 m/s & 800 K & — & 5\% & 0.06 m \\ \hline Inlet 3 & 20 m/s & 810 K & — & 5\% & 0.06 m \\ \hline \hline \end{tabular}
\end{table}
Table 2: Boundary conditions.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Mesh \#** & **Mesh** & **Number of** & **Average** & **Maximum** & **Deviation of** & **Deviation of** \\
**Sizing (mm)** & **Nodes** & **Velocity (m/s)** & **Velocity (m/s)** & **AveVelocity** & **MaxVelocity** \\  & & & & **(m/s)** & **(m/s)** & **(m/s)** \\ \hline
1 & 2 & 109,668 & 59.9909 & 64.0716 & 0.025\% & 6.360\% \\
2 & 3 & 33,639 & 59.9631 & 59.6708 & 0.021\% & 0.946\% \\
3 & 7 & 32,518 & 59.9895 & 64.0739 & 0.023\% & 6.363\% \\
4 & 10 & 31,038 & 59.9758 & 60.2405 & 0.002\% & 0.015\% \\
5 & 20 & 30,642 & 60.0115 & 60.0423 & 0.060\% & 0.329\% \\
6 & 25 & 30,281 & 60.0244 & 60.3088 & 0.081\% & 0.113\% \\
7 & 30 & 29,944 & 59.9605 & 60.4498 & 0.026\% & 0.347\% \\
8 & 40 & 29,531 & 60.0202 & 60.0982 & 0.074\% & 0.236\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mesh convergence study.