# Effect of Surface Roughness on Aerodynamic Loads of Bluff Body in Vicinity of Smoothed Moving Wall
## 3 Results and Discussion
If the Reynolds number is set to \(1\times 10^{5}\), drag reductions around \(16.4\%\), \(51.6\%\), and \(32.0\%\) are consolidated for the respective roughness ratios \(\varepsilon/\mathrm{D}=0.002\), \(\varepsilon/\mathrm{D}=0.003\), and \(\varepsilon/\mathrm{D}=0.007\) (Table 1) compared to the smooth surface. A similar finding was reported by [PERSON] et al. [17] for subcritical Reynolds numbers, \(5\times 10^{3}\leq\mathrm{Re}\leq 8\times 10^{4}\), and different rough surfaces, \(0.0028\leq\mathrm{k_{S}/D}\leq 0.025\) (\(\mathrm{k_{S}}\) is the representative roughness of sandpaper, netting, and dimples). For the range of \(2\times 10^{4}\leq\mathrm{Re}\leq 8\times 10^{4}\), the experimental response of reducing the average drag coefficient was on the order of \(30\%\) for \(\mathrm{k_{S}/D}=0.025\) and about \(20\%\) for \(\mathrm{k_{S}/D}=0.02\). By applying triangular roughness elements to the cylinder, we observed a reduction in the average drag coefficient by \(10.7\%\) to \(\varepsilon/\mathrm{D}=0.02\) when considering \(\mathrm{Re}=1\times 10^{5}\). In looking at Figure 9, it is clear that in setting a subcritical Reynolds number, certain roughness magnitudes can anticipate characteristics of the critical and supercritical regimes. This is in agreement with our previous observations [15] and experimental results [29; 32]. A closer inspection of Table 1 reveals that the lift coefficient assumes values around zero for rough cylinder isolated from the moving wall due to the symmetry of the flow. The Strouhal number tended to be insensitive to increasing roughness (\(\mathrm{St}=0.21\)), excluding the \(\epsilon/\mathrm{D}=0.003\) and \(\epsilon/\mathrm{D}=0.004\) roughness values. Relatively high Strouhal numbers, \(\mathrm{St}=0.22\) and \(\mathrm{St}=0.24\), respectively, are convergent with the larger separation angles, as shown in Figure 9. Figure 9 makes it explicit that the reduction in the drag coefficient, which is inversely corresponding to the increasing trend of the Strouhal number, is a consequence of the approximation of the two shear layers of opposite signs formed by the separation of the boundary layer in the cylinder, moving the separation angles downstream. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**G/D** & \(\epsilon\)**/D** & **0.000** & **0.00110** & **0.002** & **0.003** & **0.004** & **0.007** & **0.009** & **0.02** \\ \hline \multirow{4}{*}{\(\infty\)} & \(\mathrm{C_{D}}\) & 1.22 & 1.06 & 1.02 & 0.59 & 0.60 & 0.83 & 0.91 & 1.09 \\  & \(\mathrm{C_{L}}\) & 0.01 & 0.03 & 0.02 & \(-0.02\) & \(-0.05\) & 0.04 & \(-0.03\) & \(-0.03\) \\  & \(\mathrm{St}\) & 0.22 & 0.21 & 0.21 & 0.22 & 0.24 & 0.21 & 0.21 & 0.21 \\  & \(\mathrm{C_{D}}\) red. & - & 13.1 & 16.4 & 51.6 & 50.8 & 32.0 & 25.4 & 10.7 \\ \hline \multirow{4}{*}{0.5} & \(\mathrm{C_{D}}\) & 1.41 & 1.12 & 1.13 & 0.77 & 0.78 & 0.93 & 1.04 & 1.27 \\  & \(\mathrm{C_{L}}\) & 0.23 & \(-0.15\) & \(-0.04\) & \(-0.08\) & \(-0.11\) & 0.03 & \(-0.05\) & \(-0.05\) \\  & \(\mathrm{St}\) & 0.20 & 0.21 & 0.21 & 0.22 & 0.21 & 0.21 & 0.22 & 0.21 \\  & \(\mathrm{C_{D}}\) red. & - & 20.6 & 19.9 & 45.4 & 44.7 & 34.0 & 26.2 & 9.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of post-processing results for simulated cases: cylinder at large distances and near the moving wall—\(\mathrm{Re}=1\times 10^{5}\). Figure 8: Efficiency of roughness heights for controlling cylinder drag for Reynolds number range \(3\times 10^{4}\leq\mathrm{Re}\leq 2\times 10^{5}\) (\(\mathrm{Nc}=48;\ \sigma_{\mathrm{o}}=\mathrm{f}(\mathrm{Re});\ t_{\mathrm{S}}=50\)). Figure 10 is used to qualitatively explain the alterations in the wake due to the increase in the roughness. It contains the complete configuration of the wakes formed by the flow action around the cylinder (\(\mathrm{G/D}=\infty\)) for three simulated rough surfaces, \(\mathrm{\varepsilon/D}=0.00110\), \(\mathrm{\varepsilon/D}=0.004\), and \(\mathrm{\varepsilon/D}=0.009\).