## 3 Results and Discussions
### Porosity (\(\beta\)) Study  
Fluid passing through holes is affected by porosity, which plays a key role in flow control. In addition to the porosity value (0.05) of the available stenter machine in the company that supports this study, four other porosity values (0.1, 0.2, 0.3, and 0.4) were  
Figure 6: The movement of the fabric over time.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Analysis** & **Fabric Temperature (K)** & **Error (\%)** \\ \hline Industrial & 122.82 & - \\ Standard k-\(\epsilon\) & 111.99 & 8.82 \\ RNG k-\(\epsilon\) & 107.56 & 12.42 \\ Realizable k-\(\epsilon\) & 117.97 & 3.95 \\ Standard k-\(\omega\) & 112.58 & 8.34 \\ SST k-\(\omega\) & 112.81 & 8.15 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Turbulence model study.  
used to examine the effects of porosity on the cooling performance of the stenter machine. Increasing porosity was carried out by increasing the number or the diameters of holes. In the present study, increasing the number of holes is preferred. Figure 7 shows the fabric temperature predicted through CFD software Ansys Fluent 14.0 in different simulations based on geometric parameters. As can be seen in Figure 7a, as the porosity increases from 0.05 to 0.4, the average fabric temperature at the end of the cooling process also increases. In other words, as porosity increases, cooling performance decreases. With increasing porosity, there are more injector holes, so more air passes through them at low velocity, and ultimately, most of the air exits the fluid domain without contacting the fabric. Figure 8 shows the temperature distribution on the fabric surface for different porosity values at the end of the cooling process (t = 1.57 s). In all the contours showing the temperature distributions on the fabric surfaces, there are mainly two different regions on the fabric surface at t = 1.57 s. One of these regions is the cooled region, which is primarily blue-green-yellow in color. This region represents the fabric that exited between the injector channels and cooled. In order to examine the cooling performance of the stenter machine, this region is considered. The other one, which can be neglected at the end of the cooling process, is the hot region which is between the injector channels at t = 1.57 s. Figure 9 depicts the velocity streamlines on the surface at the end of the upper injector channel. These streamlines provide additional insights into the effects of porosity and injector angles on airflow distribution in the fluid domain. Air jets passing through holes form vorticity. As the number of holes increases, airflow trends generate two different vortexes on both the right and the left sides. There is one order of holes in \(\beta_{1}\) porosity, whereas there are two orders in the others. With an increase in porosity, the airflow velocity at the hole decreases. High porosity values result in airflow jets passing through holes in the inner row, colliding with each other and with geometric corners, causing turbulence to dissipate.  
Figure 7: Fabric temperature values predicted by CFD for different parameters: **(a)** Porosity, **(b)** Injector angle, **(c)** Air velocity, **(d)** Fabric velocity.  
Figure 8: Contours of temperature distributions of the fabric for different porosity values at 1.57 s.  
Figure 9: Streamlines on the surface located at upper injector channel for different porosities.