# Effect of Surface Roughness on Aerodynamic Loads of Bluff Body in Vicinity of Smoothed Moving Wall
## 1 Introduction
In addition, marine pipelines and risers are often under the action of flows at high Reynolds numbers, covering from the subcritical to the transcritical regime [31]. Therefore, Reynolds number values of \(\mathrm{O}(10^{4})\) and \(\mathrm{O}(10^{5})\) are typical in engineering applications. Rough cylinder surfaces influencing the Strouhal number were experimentally investigated by [PERSON] and [PERSON] [32] for Reynolds numbers varying between \(6\times 10^{3}\) and \(5\times 10^{6}\). A rapid increase in the Strouhal number was observed in critical flow conditions. For increasing the values of roughness, this increase in the Strouhal number became smaller and smaller. According to [PERSON] and [PERSON] [1], for cylinders with a relative roughness greater than \(3\times 10^{-3}\), the critical, supercritical, and upper transition flow regimes merge in a narrow region and change directly to the transcritical regime. This occurs at low Reynolds numbers. [PERSON] and [PERSON] [32] also presented experimental results for the behavior of the drag coefficient as a function of the Reynolds number (\(\mathrm{C}_{\mathrm{D}}\times\mathrm{Re}\)) and identified that for a relative roughness \(\varepsilon/\mathrm{D}\geq 3\times 10^{-3}\), the \(\mathrm{C}_{\mathrm{D}}\) tended to converge to a value around 1.2 for the lower interval of the subcritical regime--this study had a limiting roughness of \(\varepsilon/\mathrm{D}=30\times 10^{-3}\). Another flow configuration of engineering interest is the condition where a cylindrical body is close to a wall [33; 34; 35]. Under this condition, vortex shedding is expected to depend on the Reynolds number, the gap-to-diameter ratio \(\mathrm{G}/\mathrm{D}\), and the wall boundary layer characteristics [36]. The action of the flow under a pipe placed on the seabed can cause the drag of the soil (erosion) and establish suspended spans at a small height of the bottom, usually in the orders of 0.1 to 1D [1], for example. Among the changes that the ground effect can cause in the flow around a stationary smooth cylinder, for Reynolds numbers of \(\mathrm{O}(10^{3})\), one can mention the following [1]: the suppression of vortex shedding for distances less than \(\mathrm{G/D}=0.3\); the stagnation point moves to a lower angular position as the cylinder approaches the horizontal wall; the angular position of the cylinder separation point goes upstream on the free-flow side and downstream on the interference side of the wall; and the pressure is higher on the side of the cylinder under the free flow than on the interference side of the wall. [PERSON] et al. [13] reported the total cessation of vortex shedding in flows with Reynolds numbers of \(\mathrm{O}(10^{5})\) for \(\mathrm{G/D}<0.35\). The use of a moving wall serves to eliminate the less influential effects of the boundary layer formed on the wall [12; 37]. [PERSON] et al. [14] stated that the physically correct experimental method for modeling the ground effect is to employ a belt moving at free-flow velocity. However, the author considers that \"It is difficult to maintain the correct moving ground condition. The rollers could vibrate and the belt may experience lateral movement. The negative pressure field generated by a model may lift the belt at high speed\". These aspects added to the difficulties of flow regimes at high Reynolds numbers [38], and the costs involved encourage computational investigations. The suppression of vortex shedding under the action of the Venturi effect in turbulent flows around a smooth cylinder very close to a moving wall was numerically reported by [PERSON] el al. [39] using a Discrete Vortex Method--DVM. Numerical studies on the influence of cylinder roughness height on the induction of vortex shedding suppression when it is allocated at various distances from a moving wall have been reported by [PERSON] et al. [37] and [PERSON] et al. [11]--the roughness model used was that of [PERSON] et al. [27]; the previous approach of our research group did not geometrically construct the rough cylinder surface.