# Effect of Surface Roughness on Aerodynamic Loads of Bluff Body in Vicinity of Smoothed Moving Wall
## 3 Results and Discussion
Finally, starting from point E, the vortex shedding scheme is restarted and, through this cyclic process, a Von Karman wake is formed. Based on the statistical behavior of a Gaussian distribution, [PERSON] and [PERSON] (2015) conjectured that characteristic two-dimensional vorticity distributions with smaller dispersions of the values from their means (smaller k) would result in the proper estimation of the drag coefficients for a drag crisis capture range for a given rough surface under high Reynolds numbers. This was confirmed through a satisfactory estimation of the aerodynamic force coefficients and vortex shedding frequencies for cylinders with rough and smooth surfaces. Previous work has reported the overestimation of the drag coefficients for high Reynolds numbers ([PERSON], 2019) applying LESs, i.e., in subcritical, critical, and supercritical regimes. It is well known that some of the vorticity generated from the surface of a body under the action of flow is cancelled out due to the interaction of the two opposing shear layers. Depending on the magnitude of the roughness, there is downstream movement of the separation angles and in the approach of these shear layers, as well as a corresponding decrease in \(\rm C_{D}\) and tendency to increase in St. According to [PERSON] and [PERSON] (2016), the overestimation of the mean drag force in two-dimensional simulations is related to higher Reynolds stresses in the wake. Additionally, [PERSON] et al. (2018) highlighted the difficulty of reproducing typical characteristics of the critical regime, numerically or experimentally, due to the sensitivity to perturbations of these characteristics. This, in turn, justifies the dispersions in the data found in the literature. One of the contributions of the present work is to explain how the turbulence control is conducted in the methods coupled by [PERSON] and [PERSON] (2015), namely, the DVM, \(\rm MLDRV_{\rm VL}\), and LES. Considering a Gaussian distribution, statistically, we have the concept of the \(Z-\)score, which reveals by how many standard deviations S a certain value X deviates from the mean \(\overline{\rm X}\):  
\[Z=\frac{\rm X-\overline{\rm X}}{\rm S} \tag{22}\]  
Figure 5 shows the instantaneous distribution of the intensity of the nascent vortices at time \(\rm t_{S}=50\) as a function of the \(Z-\)score, considering the cylinder with a moderately rough surface \(\varepsilon/\rm D=0.002\) and different vorticity discretization conditions. The DVM without changing the cutoff width is represented by the distribution in condition 1, \(\rm Re=1\times 10^{5}\) and \(\rm k=2.0\), which results in \(\rm C_{D}=1.00\). In the sequence, we have a distribution with modest reductions in the dispersion and magnitude of the vortex intensities, keeping \(\rm k=2.0\) for a higher Reynolds number, \(\rm Re=1.6\times 10^{5}\), in condition 2. The resulting drag coefficient is 0.88. However, if the Reynolds number, \(\rm Re=1.6\times 10^{5}\), which is the critical Reynolds number for relative roughness \(\varepsilon/\rm D=0.002\), is maintained, and the cutoff width is reduced to \(\rm k=0.7\), the corresponding \(\rm C_{D}=0.39\) is satisfactorily predicted. Under this third condition, both the magnitudes and the dispersion of vortex intensities are drastically reduced in absolute terms. Now if a high roughness is considered, \(\varepsilon/\rm D=0.02\), for example, the result summarized in Figure 6 is observed. Conditions 4, 5, and 6 are, respectively: \(\rm Re=2\times 10^{4}\) and \(\rm k=2.0\); \(\rm Re=5\times 10^{4}\) and \(\rm k=2.0\); and \(\rm Re=5\times 10^{4}\) and \(\rm k=0.6\). For these new conditions, the \(\rm C_{D}\) assumes values of 1.27, 1.14, and 0.78, respectively. It can be observed that the reduction in the dispersion of the vortex intensity value is more sensitive to the reduction in the cutoff width (\(\rm k=0.6\)) than to the simple increase in the Reynolds number from \(2\times 10^{4}\) to \(5\times 10^{4}\).