Flow pass a circular cylinder

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TITLE

Flow pass a circular cylinder

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OBJECTIVE

The objective of the experiment is to study the pressure profile and flow characteristics for flow around a circular cylinder.

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INTRODUCTION

In most situations it is inevitable that the boundary layer becomes detached from a solid body. This boundary layer separation results in a large increase in the drag on the body. We can understand this by returning to the flow of a non-viscous fluid around a cylinder. The pressure distribution is the same on the downstream side of the cylinder as on the upstream side; thus, there were no unbalanced forces on the cylinder and therefore no drag. If the flow of a viscous fluid about a body is such that the boundary layer remains attached, then we have almost the same result--we'll just have a small drag due to the skin friction. However, if the boundary layer separates from the cylinder, then the pressure on the downstream side of the cylinder is essentially constant, and equal to the low pressure on the top and bottom points of the cylinder. This pressure is much lower than the large pressure which occurs at the stagnation point on the upstream side of the cylinder, leading to a pressure imbalance and a large pressure drag on the cylinder. For instance, for a cyl inder in a flow with a Reynolds number in the range, 10 3 < Re < 10 5 the boundary layer separates and the coefficient of drag is C D ~ 1.2, much larger that the coefficient of drag due to skin friction, which we would estimate to be about 10 -2.

Figure 1: Flow patterns for flow over the cylinder

A Reynolds number-independent drag coefficient leads to a drag force D ~ ρU 2 A/2. More importantly, the power P required to m aintain a constant speed in the presence of this drag is P = DU = ρU3 A/2, so that it increases with the cube of the speed. Most of the resistance at this speed is due to aerodynamic drag (there are other sources, such as mechanical friction, rolling friction, and so on, but I don't think they dominate at this speed). Boundary layers tend to separate from a solid body when there is an increasing fluid pressure in the direction of the flow this is known as an adverse pressure gradient in the  jargon of fluid mechanics. Increasing the fluid pressure is akin to increasing the potential energy of the fluid, leading to a reduced kinetic energy and a deceleration of the fluid. When this happens the boundary layer thickens, leading to a reduced gradient of the velocity profie ( / decreases), with a concomitant decrease in the wall shear stress. For a large enough pressure gradients the shear stress can be reduced to zero, and separation often occurs.

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THEORETICAL BACKGROUND

The structure and development of viscous flow over a cylinder is described in Figure 2 below. The development of the boundary layer and changes in velocity profile from the stagnation point at A until flow separation at point E are described in Figure 3. these changes are closely linked to the change of pressure gradient from A to F. negative pressure gradient tends to maintain laminar boundary layer, while positive pressure gradient will accelerate it to turbulent and (subsequently) reverse flow resulting in flow separation.

Figure 2: Boundary layer separation location

Figure 3: Typical boundary layer

Figure

velocity

distributions for inviscid flow and

profiles

at

various

location on the cylinder.

4:

Surface

pressure

boundary layer flow.

Figure 4 compares the pressure distribution (it is customary to plot the coefficient of pressure ) around the cylinder between low Re number and high Re flows and of that predicted by inviscid flow theory.