Study On The Mechanism Of Drag Reduction In The Flow Past A Hydrophobic Circular Cylinder

The slip length has a significant effect on the velocity field and the pressure field when it reaches the same characteristic dimension of the flow field.For the laminar flow between two infinitely large parallel plates with slip wall boundary condition,the drag is directly related to the viscous force only.The pressure fieldaffects the wall resistance through the velocity field.For a cylinder cross flow,however,the pressure field and the velocity field are coupled,and the pressure drag is a part of the flow resistance due to the change of the separation point caused by the curvature of the cylinder wall.It is found that the pressure resistance is much larger than the viscous resistance.Therefore,the effect of the pressure distribution on total drag is important for the study of cylinder drag reduction mechanism.In this paper,the pressure and viscous resistance under cylindrical slip boundary conditions are analyzed and numerically studied.It is found that with the increase of the Reynolds number and the slip length,the influence of slip on the pressure resistance increases.Due to small proportion of viscous drag to total drag coefficient,the effect of viscous drag on the total drag is less important.To study the causes of the above results,numerical calculations were conducted to study the local pressure resistance and viscous resistance distribution on the cylindrical wall.The results show that,for slip boundary condition,the pressure increases at the rear of the cylinder,which in turn reduces the pressure resistance significantly.The higher the pressure at the rear of the cylinder,the lower the pressure resistance.It is also found that the pressure at the rear of the cylinder is very sensitive to the slip velocity.When increasing the slip velocity,the separation point on the cylinder surface moves downstream and the flow field at the wake of the cylinder is changed.The greater the slip,the more stable the wake,thus the lower the pressure loss.The viscous drag is mainly affected at the front region of the cylinder.This is because that the slip boundary condition does not visibly change the boundary flow field of the cylinder,the effect of slip condition on the viscous resistance has a certain similarity.In order to analyze the pressure distribution on the cylindrical wall,the theoretical analysis of the vortices gradient in the radial direction(?)?/(?)r and the convection of the fluid along the wall u?/r·(?)u?/(?)?|wall are applied.For no slip boundary condition,the pressure gradient is only associated with the vorticity gradient along r direction(?)?/(?)r.However,for slip boundary condition,it is also associated with fluid convection along the surface of circular cylinder u?/r·(?)u?/(?)?|wall and the unsteady term(?)u?/(?)t|surf.Due to the adverse pressure gradient,it is found that in the range of 80°???120°,the vorticity gradient in the r direction increases with the increase of the slip length,which leads to a rapid increase in the pressure.This is related to the fact that the separation point of the boundary layer moves downstream with the increase of the slip length.This region is the most critical area which affecting the pressure distribution.The area near or at the flow cross-sectional area(perpendicular to the x-axis interface)shrinks,and at upstream of the boundary layer separation point,the flow velocity decreases and the pressure increases.At the same time,the pressure contour shows that the slip condition can make the flow field become more stable.In addition,the fluctuation of velocity is used to quantify the stability of the flow field and to verify the above conclusions.The essence of the slip effect is equivalent to the shrinkage of the cylindrical wall,that is,from the cylindrical wall surface to the elliptical column wall surface.For walls with curvature,the drag reduction is mainly determined by the change in pressure resistance.