The Beauty of Vortexes: How They Shape 3D Wings

Contrails, or line-shaped clouds in the sky, are frequently seen following a jet plane's engines. A chaotic wake is left behind the vehicle by a vortex that emerges from the tips of each wing, like two little horizontal tornadoes. Particularly for smaller aircraft that are flying along the same flight route, the wake presents a destabilizing flight danger.

When the wind blows across a structural member, a phenomenon known as "vortex shedding" occurs in which vortices are alternately shed from one side to the other and alternate low-pressure zones are created on the downwind side of the structure, creating a fluctuating force acting at right angles to the wind direction. As a fluid, such as air or water, flows through a bluff (as opposed to streamlined) body, vortex shedding occurs as an oscillating flow at specific velocities, dependent on the size and shape of the body. In this flow, the body's rear produces vortices that periodically separate from its sides to form a Kármán vortex street. The fluid flow past the object creates alternating low-pressure vortices on the downstream side of the object. The object will tend to move toward the low-pressure zone.

The frequency at which vortex shedding takes place for an infinite cylinder is related to the Strouhal number by the following equation: 

where St is the dimensionless Strouhal Number, f is the vortex shedding frequency,  D is the diameter of the cylinder, and V is the flow velocity.

 

The separation point is where an object travelling through the air ceases "sticking" to the air. The air molecules push back on an object as it moves through the air and impede its motion; this resistance is known as pressure drag. The boundary layer is created when the air "sticks" to an object as it moves around it. This "connected flow" is proceeding with great fluidity. The separation point is the location on the body where the boundary layer rises above the surface. The pressure drag often rises when the airflow separates from the surface.

Vortex patterns in bluff bodies

A body that has divided flow over a sizable portion of its surface due to its shape is referred to as a bluff body. Any body that, when retained in fluid flow, the fluid does not completely touch the object's border. The fact that the viscous and inviscid zones interact strongly is a key characteristic of a bluff body flow.

The pressure recovery is not complete when the flow separates from the surface and the wake forms. The pressure recovery is lesser and the pressure drag is higher as the wake size increases. The trick to streamlining a body is to shape its contour in such a way that separation, and by extension, wake, are minimized, or at the very least are limited to a small area of the body's back, making the wake as tiny as possible. They are referred to as streamlined bodies. If not, a body is referred to as bluff and is connected with a strong pressure drag.

Since pressure losses in the wake dominate the drag at high Reynolds numbers, cylinders and spheres are regarded as bluff bodies. Hence, when frictional drag predominates, the body is referred to as a streamlined body; whereas, when pressure drag predominates, the body is referred to as a bluff body.

The investigation of such intricate flow systems around bluff bodies has been aided by recent developments in numerical and experimental methodologies. Due to its resemblance to the majority of constructed structures and the concentration of recent study, a cylindrical bluff body is given priority as a geometry of concern. As a result of the strong pressure gradient and weak wall shear stress that formed around it, the proportionality between the radius and thickness is concluded to declare that it has the characteristics of a circular cylinder. A closed type of conic section makes it simpler to interpolate results with real assurance. As a result, the circular cross section cylinder is suitable for studying the flow structure behind bluff bodies of various shapes. The shape is also in consensus with the common feature of disturbed flow around all bluff bodies, i.e. development of similar flow structures in the separated region.

 

Reynolds number has a significant impact on the flow structures across the bluff bodies. In order to forecast the onset of turbulent flow, the dimensionless quantity estimates the relative contribution and interaction of inertial forces to liquid viscous forces for a specific flow situation. With an increase in Reynolds number, the difficulty of the transition increases, especially for a cylinder with a circular cross section.