Vorticity Fields on Flow with Vortex System - Bambang Yulistiyanto (Jurnal Teknik Sipil, 2009)
Abstract. The flow around a circular cylinder mounted normal to the channel bed is essentially a three-dimensional one. The flow upstream undergoes a separation of the turbulent boundary layer and rolls up to form a flow system, known as horseshoe vortex, which is swept around the cylinder. This vortex system plays an important role, if the bed material is movable. The shear stress of the vortex system is responsible to the bed erosion. The shear stress depends on the velocity gradient, may be presented as the vorticity. This study is done to gain a better understanding of the vorticity around a cylinder, especially where the system of vortices exist. Flow measurements were used to study the vorticity fields on flow with a horse-shoe vortex system around a pile. The velocity vector plots show the presence of a primary vortex upstream of the cylinder. Based on these velocity vectors, the vorticity can be analyzed by using central finite difference approximations. Results of the vorticity calculation are presented as the vorticity contours. Results of study show the greatest value of the positive-vorticity on the horse-shoe vortex system is in the plane upstream of cylinder. This value decreases in the planes downstream, attaining the lowest value in the plane downstream, where the wake vortex established. The strength of the positive vorticity increases at larger Reynolds number. Underneath the field of positive vorticity, stretching around the cylinder, it appears a field of negative vorticity. This negative vorticity near the bed is high in front of the cylinder, proportional to the bed shear stress, which is responsible to the development of local scour at the movable bed. The line of zero vorticity is plotted originated at the bed, being as the separation point. It is also concluded that the maximum positive-vorticity is not necessary coincided with the center of the vortex.