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

Answer: When the flow becomes turbulent, the boundary layer has more energy and is better able to resist the adverse pressure gradient, delaying the separation point along the cylinder's surface. This results in a smaller wake behind the cylinder and a smaller pressure drag force, leading to a lower drag coefficient.

Step-by-step solution

1. Understanding Laminar and Turbulent Flow

Laminar flow is a type of fluid flow where the fluid moves smoothly and predictably in layers (or streams) parallel to each other. Turbulent flow, on the other hand, is fluid motion characterized by chaotic changes in pressure and flow velocity. It occurs when the inertial forces (which tend to cause disorder) dominate over the viscous forces (which tend to create order).

2. Flow over a Cylinder and Drag Coefficient

When fluid flows over a cylinder, it creates a pressure distribution around the surface of the cylinder. This pressure distribution causes a net force on the cylinder, known as the drag force. The drag coefficient quantifies the drag force experienced by the object, and it depends on the shape of the object, the fluid properties, and the flow regime (laminar or turbulent).

3. Boundary Layer Separation

In both laminar and turbulent flow regimes, a boundary layer forms around the cylinder as the fluid flows over its surface. The boundary layer is a thin layer of fluid that clings to the surface of the object and is affected by the object's surface roughness and viscosity. At some point along the surface of the cylinder, the boundary layer separates from the surface, causing a wake to form behind the cylinder. In the case of laminar flow, boundary layer separation occurs earlier compared to turbulent flow.

4. Influence of Turbulent Flow on Drag Coefficient

When the boundary layer becomes turbulent, it has more energy and is better able to resist the adverse pressure gradient, causing the separation point to move further downstream along the cylinder's surface. This results in a smaller wake being formed behind the cylinder, and therefore a smaller pressure drag force. As drag coefficient is a measure of the drag force, a smaller pressure drag force leads to a lower drag coefficient.

5. Conclusion

Although it may seem counterintuitive, the drag coefficient actually decreases when the flow becomes turbulent in flow over a cylinder. This is because a turbulent boundary layer is better equipped to resist separation, leading to a smaller wake behind the cylinder, and ultimately, a smaller drag force and lower drag coefficient.

Key concepts

Laminar and Turbulent Flow

Understanding the difference between laminar and turbulent flow is crucial when analyzing fluid dynamics. Laminar flow is defined by its smooth, orderly movement of fluid layers with minimal mixing, typically at lower velocities. It's analogous to sliding sheets of paper over one another where each sheet moves steadily and predictably.

In contrast, turbulent flow is characterized by chaotic, irregular movements where fluid particles mix intensively. Imagine a fast-moving river where water churns and whirls unpredictably—that's turbulence in action. The transformation from laminar to turbulent flow is not instant; it occurs beyond a certain speed, defined by the Reynold's number. Turbulent flow has greater kinetic energy, which enables the fluid to overcome adverse pressure gradients more effectively, impacting the drag force exerted on objects within the fluid. But despite the chaotic nature of turbulent flow, it sometimes results in reduced drag force under specific conditions, such as flow over a cylinder.

Boundary Layer Separation

The phenomenon of boundary layer separation is a pivotal concept that influences drag force in fluid dynamics. The boundary layer is a thin layer of fluid that's in direct contact with the surface of an object, like a cylinder. Due to viscosity, the fluid in this layer adheres to the object's surface to some extent and moves gradually slower compared to the free-stream velocity of the surrounding fluid.

A critical aspect of boundary layer behavior is its tendency to separate from the surface as it encounters an adverse pressure gradient. This occurs when the fluid slows down and changes direction, often caused by the object's curvature. In laminar flow, separation occurs sooner, resulting in a larger wake formation behind the object, which contributes to increased pressure drag. On the other hand, a turbulent boundary layer, with its chaotic and energetic motion, manages to cling to the surface longer before separating, thereby reducing the size of the wake and the resultant pressure drag.

Flow Over a Cylinder

When examining flow over a cylinder, we are looking at how fluid—like air or water—behaves when it encounters a cylindrical shape, which could range from a simple pipe to an aircraft fuselage. As the fluid approaches the cylinder, it divides and streams around the object, leading to varying pressure distributions. The difference in pressure between the front and rear of the cylinder generates drag force, which opposes the motion of the cylinder through the fluid.

The nature of the flow (laminar or turbulent) significantly affects this drag force. Given the abrupt drop in the drag coefficient seen when the flow transitions to the turbulent regime, it's important to note that the flow type has a direct impact on the fluid's capacity to adhere to the cylinder's surface, consequently altering the wake pattern and drag. This complex interplay makes the study of fluid flow over cylinders not just fascinating but critical for many engineering applications, from designing efficient vehicles to understanding natural phenomena.