Question

Why is flow separation in flow over cylinders delayed in turbulent flow?

Short answer

Answer: In turbulent flow, the chaotic movement and increased mixing of fluid particles provide additional momentum to the fluid in the boundary layer. This additional momentum helps the fluid overcome the adverse pressure gradient along the cylinder surface, delaying the point of flow separation and leading to a narrower wake region and reduced pressure drag compared to laminar flow.

Step-by-step solution

Understand Laminar and Turbulent Flows

In fluid dynamics, there are two primary types of flow: laminar and turbulent. Laminar flow is characterized by smooth, parallel layers of fluid with little to no mixing between them. In contrast, turbulent flow is characterized by chaotic and disordered movement of fluid particles, leading to increased mixing and fluctuations in flow properties such as velocity and pressure.

Flow Over Cylinders

When a fluid flows over a cylinder, the fluid follows the contours of the cylinder's surface up to a certain point, after which it will separate from the surface. This point of separation is influenced by factors such as Reynolds number, which is defined as the ratio of inertial forces to viscous forces within the fluid. When the Reynolds number is low (below approximately 2,000), the flow over cylinders is laminar, and when the Reynolds number is high (generally above 4,000), the flow becomes turbulent.

Flow Separation

The point of separation is crucial for determining the pressure distribution around the cylinder and the magnitude of forces acting on the cylinder. In laminar flow, the flow separation occurs earlier along the surface of the cylinder, which results in a larger wake region behind the cylinder and a higher pressure drag. Turbulent flows, on the other hand, have a delayed flow separation.

Turbulence and Delayed Flow Separation

The chaotic movement and increased mixing of fluid particles in turbulent flow provide additional momentum to the fluid in the boundary layer. This additional momentum can help the fluid overcome the adverse pressure gradient along the cylinder surface, delaying the point of flow separation. This results in a narrower wake region and reduced pressure drag.

Summary

Flow separation in flow over cylinders is delayed in turbulent flow due to the additional momentum provided by the chaotic mixing of fluid particles in the boundary layer. This helps the fluid to overcome the adverse pressure gradient along the cylinder surface and, as a result, leads to a narrower wake region and reduced pressure drag compared to laminar flow.

Key concepts

Laminar and Turbulent Flows

When fluids move, they exhibit behaviors categorized as either laminar or turbulent flows. Laminar flow is akin to layers of paper smoothly sliding over one another without much friction or disturbance. It occurs at lower speeds and provides a gentle, orderly motion where each layer of fluid remains uniform and undisturbed by its neighbors.

On the other hand, turbulent flow is like a bustling crowd, where every individual's movement affects the others, creating a seemingly random and chaotic environment. This type usually happens at higher speeds, where the smooth layers break down into irregular, mixing currents. The significance of these two types of flows in engineering cannot be overstated, as they determine the efficiency of transport systems, the efficacy of mixing processes, and the aerodynamics of objects moving through fluids.

Reynolds Number

The Reynolds number, a foundational concept in fluid dynamics, serves as a bridge between theoretical understanding and practical application. It's a dimensionless number that sheds light on whether a fluid's flow will be laminar or turbulent. The formula for calculating it is \( Re = \frac{\rho v L}{\mu} \) where \( \rho \) is the fluid density, \( v \) is the velocity, \( L \) is a characteristic length (like the diameter of a pipe or the width of a wing), and \( \mu \) is the fluid's dynamic viscosity.

Typically, a Reynolds number below 2,000 suggests laminar flow, while one above 4,000 predicts turbulent flow. This critical point is subject to change depending on the shapes and obstacles the fluid encounters. Understanding this number helps engineers design better equipment and predict how fluids will behave in different scenarios.

Fluid Dynamics

The study of fluid dynamics involves analyzing how liquids and gases behave when they are in motion. It falls under the broader umbrella of physics with focus on forces, energy, and momentum. Fluid dynamics is a key player in various disciplines, from meteorology predicting weather patterns, to aeronautics shaping airplanes for optimum air traversal, to civil engineering ensuring the stability of bridges and buildings against wind forces.

It employs mathematical equations and physical laws to forecast fluid behavior under varied conditions. These include the Navier-Stokes equations that serve as the roadmap guiding the motion of fluid particles through different terrains and obstacles in their path.

Pressure Drag

When it comes to the resistance an object faces while moving through a fluid, pressure drag is the predominant factor to consider. This form of drag occurs as a result of the differential pressure felt across the surfaces of an object. Imagine holding a flat plank perpendicular to a flowing stream; the force you'd need to apply to keep it steady against the stream is largely due to pressure drag.

It significantly impacts the aerodynamic and hydrodynamic efficiency of vehicles and structures. The larger the wake — the turbulent, swirling region behind the object — the greater the pressure drag. In designing shapes intended for fluid flow, minimizing pressure drag is a fundamental goal, leading to streamlined forms seen in everything from airliners to race cars.

Boundary Layer

The boundary layer is a thin sheet of fluid that wraps around an object as it moves through a fluid or as fluid moves past a stationary object. It's the interface zone where the fluid meets the object's surface, and its behavior is critical for understanding various phenomena in fluid dynamics.

Within this layer, fluid velocity changes from zero (due to the no-slip condition at the solid surface) to the free stream velocity of the fluid. The characteristics of the boundary layer — whether laminar or turbulent — affect flow separation points, drag, and heat transfer rates. A turbulent boundary layer is better at withstanding adverse pressure gradients, meaning that it can potentially delay flow separation compared to its laminar counterpart, leading to reduced drag on the object in question.