Question

QUESTION 3 (14 marks) Variation in drag cylinder is shown in Figure 2 (a) At point coefficient (CD) against Reynolds number (Re) for flow around a smooth a, point out whether drag is mainly contributed by pressure drag or friction (8 marks) drag, and explain the reason why (6 marks) (b) Explain the reason why there is a sudden drop in Co at point 400 200 100 40 20 10 60 N C, 6 Smoath cylinder 0.6 0.4 0.2 0.1 Smooth sphere 0 10 10 10 10 Re Figure 2

Answer 1

Cylinders are considered bluff bodies because at large Reynolds numbers the drag is dominated by the pressure losses in the wake.

(a) At point A the flow is laminar and drag is mainly due to the friction drag between the surface and the fluid. This friction is associated with the development of boundary layers and it scales with the Reynolds number. So, as the speed of the flow increases, Reynolds number increases and the friction drag decreases as the boundary layer helps in the smooth movement of the above layers.

(b) At point E, the flow changes from laminar to turbulent. At a Reynolds number between 10^5 and 10^6, the drag coefficient takes a sudden dip. The size of the wake decreases, indicating that the boundary layer separation on the cylinder occurs further along the surface than before. The phenomenon is related to the differences between laminar and turbulent boundary layer. The boundary layer and it's interaction with the local pressure gradient plays a major role in affecting the flow over a cylinder. In particular near the shoulder, pressure gradient changes from being negative (decreasing pressure) to positive (increasing pressure). The force due to pressure differences changes sign from being an accelerating force to being a retarding force. In response, the flow slows down. However, the fluid in the boundary layer has already given up some momentum because of viscous losses and viscous friction, and it does not have enough momentum to overcome the retarding force. Some fluid near the wall actually reverses direction, and the flow separates.