# Effect of Surface Roughness on Aerodynamic Loads of Bluff Body in Vicinity of Smoothed Moving Wall
## 3 Results and Discussion
The critical Reynolds number for relative roughness \(\varepsilon/\rm D=0.02\) is around \(5\times 10^{4}\), and the corresponding drag coefficient, \(\rm C_{D}\sim 0.78\). These results confirm the findings of [PERSON] and [PERSON] (2015); in two-dimensional DVM the adequate prediction of aerodynamic forces depends jointly on the relative roughness, \(\varepsilon/\text{D}\), the Reynolds number, Re, and the cutoff width, k, assumed for vorticity discretization. Applying different cutoff widths for the characteristic distribution of the vorticity field can control turbulence at large and small scales. The large scales are solved for in the advective part of the vorticity transport equation (Equation (4)), considering the influence of the undisturbed flow, the discrete vortices that make up the wake, and the singularities distributed on the discretized surfaces (body and moving wall). The small scales are modeled using the local velocity difference (Second-Order Velocity Structure Function) and are computed in the diffusive part of the vorticity transport equation (Equation (5)) using the eddy viscosity. Interestingly, a refined imposition of the wall condition is performed using the \(\text{MLDR}_{\text{VL}}\), which influences the large scales through the rough geometry and the small scales through the perturbation added at each nascent vortex. Figure 5: Changes in dispersion and intensity of discrete vortices for different characteristic vorticity distributions for rough surface \(\varepsilon/\text{D}=0.002\ (\text{Nc}=48;\ \sigma_{\text{o}}=\text{f(Re)};\ \text{ts}=50)\). Figure 6: Changes in dispersion and intensity of discrete vortices for different characteristic vorticity distributions for rough surface \(\varepsilon/\text{D}=0.02\ (\text{Nc}=48;\ \sigma_{\text{o}}=\text{f(Re)};\ \text{ts}=50)\). The velocity field resulting from the hybrid control of the shedding of vortical structures from the cylinder is shown in Figure 7 for a Reynolds number equal to \(1\times 10^{5}\) and \(\mathrm{G/D}=0.5\). As an example, the relative roughness ratios \(\varepsilon/\mathrm{D}=0.002\) and \(\varepsilon/\mathrm{D}=0.02\) are considered, whose corresponding \(\mathrm{k}\) are predicted to be \(2.0\) and \(1.7\), respectively. In the first case, the results are \(\mathrm{C_{D}}=1.13\), \(\mathrm{C_{L}}=-0.04\), and \(\mathrm{St}=0.21\), and in the second case, \(\mathrm{C_{D}}=1.27\), \(\mathrm{C_{L}}=-0.05\), and \(\mathrm{St}=0.21\). The main results of this paper are summarized in Table 1. It contains the global mean flow variables for Reynolds number fixed at \(1\times 10^{5}\), and the computational responses are discussed in the subsequent text. The upper half of the table shows the main results for the cylinder isolated from the moving wall, \(\mathrm{G/D}=\infty\), and the lower half of the table shows results for the cylinder interacting with the moving wall, \(\mathrm{G/D}=0.5\). It has been found that the mean drag coefficient of the cylinder is expressively reduced for a given roughness setting, as can be seen in Figure 8. On the one hand, roughness ratios \(\varepsilon/\mathrm{D}=0.00110\), \(\varepsilon/\mathrm{D}=0.002\), and \(\varepsilon/\mathrm{D}=0.003\) generate minimum drag coefficients for Reynolds numbers around \(2\times 10^{5}\), \(1.5\times 10^{5}\), and \(1.2\times 10^{5}\), respectively. On the other hand, roughness ratios \(\varepsilon/\mathrm{D}=0.004\), \(\varepsilon/\mathrm{D}=0.007\), \(\varepsilon/\mathrm{D}=0.009\), and \(\varepsilon/\mathrm{D}=0.02\) generate minimum drag coefficients for Reynolds numbers around \(9\times 10^{4}\), \(7\times 10^{4}\), \(6\times 10^{4}\), and \(5\times 10^{4}\), respectively. Overall, the results attest that moderate roughness values are most efficient for higher subcritical Reynolds numbers on the order of \(10^{5}\). Intermediate and high roughness values are most efficient for Reynolds numbers on the order of \(10^{4}\).