Question

In flow over cylinders, why does the drag coefficient suddenly drop when the flow becomes turbulent? Isn't turbulence supposed to increase the drag coefficient instead of decreasing it?

Short answer

Question: Explain why the drag coefficient in flow over cylinders suddenly drops when the flow becomes turbulent, despite the common perception that turbulence should increase the drag coefficient. Answer: The drag coefficient in flow over cylinders decreases when the flow becomes turbulent due to the delayed separation of flow, resulting in a smaller wake region and reduced pressure drag. Although turbulence does increase the skin friction drag, the overall drag coefficient drops mainly because this increase in skin friction drag is not enough to outweigh the significant reduction in pressure drag caused by the delayed flow separation.

Step-by-step solution

Understanding Laminar and Turbulent Flow

Laminar flow is a smooth and orderly flow of fluid, where the fluid particles move in parallel layers with minimal mixing between them. Turbulent flow, on the other hand, is a chaotic and highly disordered flow, where the fluid particles move in unpredictable patterns, causing them to mix and create eddies and swirls.

Drag Coefficient

The drag coefficient, denoted by Cd, is a dimensionless quantity that describes the resistance of an object (in this case, a cylinder) to the flow of fluid around it. The drag coefficient not only depends on the shape and size of the object but also on the properties of the fluid and the flow conditions.

Separation of Flow

When fluid flows around a cylinder, the flow separates at the rear side of the cylinder, forming low-pressure wake regions behind the object. In laminar flow, this separation occurs early, leading to a large wake region and higher pressure drag. In turbulent flow, the separation of flow happens further downstream and results in a smaller wake region, reducing the pressure drag.

Boundary Layer Transition

The transition from laminar to turbulent flow in the boundary layer (layer near the surface of the cylinder) plays a significant role in reducing the drag coefficient. In turbulent boundary layers, there is enhanced momentum transfer and better attachment of the flow to the surface of the cylinder due to the mixing of the fluid. This delayed separation of flow reduces the size of the wake region and decreases the overall pressure drag.

Increase in Skin Friction Drag

It is important to note that turbulent flow does indeed increase the skin friction drag (friction between the fluid and the cylinder surface). However, this increase in skin friction drag is not enough to outweigh the significant reduction in pressure drag caused by the delayed flow separation. As a result, the overall drag coefficient decreases when the flow becomes turbulent.

Conclusion

In summary, the drag coefficient in flow over cylinders decreases when the flow becomes turbulent due to the delayed separation of flow. Although turbulence increases the skin friction drag, the overall drag coefficient is decreased primarily because of the significant reduction in pressure drag caused by the smaller wake region and delayed flow separation.