The preamble continues because an understanding Couette Flow requires a more advanced understanding of Fluid Dynamics than just the basic concepts of Viscosity and Reynolds Numbers.
The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress.
For liquids, it corresponds to the informal concept of “thickness”.
For example, honey has a much higher viscosity than water.
The viscosity of a liquid tends to decrease with increasing temperature.
The viscosity of a gas tends to increase with increasing temperature.
In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that is used to help predict similar flow patterns in different fluid flow situations.
The concept was introduced by George Gabriel Stokes in 1851, but the Reynolds number is named after Osborne Reynolds (1842–1912), who popularized its use in 1883.
The Reynolds number is defined as the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions.
Reynolds numbers frequently arise when performing scaling of fluid dynamics problems, and as such can be used to determine dynamic similitude between two different cases of fluid flow.
Osborne Reynolds [1842-1912] observed the Fluid Dynamics associated with water flowing through a glass tube by injecting a dye into the flowing water. The results were published in 1883.
When the speed of the flowing water was slow Osborne Reynolds observed Laminar Flow where the dye followed a straight line path [with some slight blurring due to diffusion].
When the speed of the flowing water was high Osborne Reynolds observed Turbulent Flow where the dye blurred and seemed to fill the entire pipe.
Turbulent Flow is characterised by eddies, vortices and other flow instabilities.
Turbulent Flow is generally associated with Reynolds Numbers above 2,300.
Laminar Flow is characterised by smooth, constant fluid motion.
Laminar Flow is generally associated with Reynolds Numbers below 2,300.
Between these two extremes there is Transitional Flow where the dye pattern changes from Laminar Flow to Turbulent Flow.
In fluid dynamics, laminar flow (or streamline flow) occurs when a fluid flows in parallel layers, with no disruption between the layers.
At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards.
There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids
Laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion;
Turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.
In practice, matching the Reynolds number is not on its own sufficient to guarantee similitude.
Fluid flow is generally chaotic and very small changes to shape and surface roughness can result in very different flows.
Nevertheless, Reynolds numbers are a very important guide and are widely used.
It should be noted, however, that the presence of eddies or recirculation alone does not necessarily indicate turbulent flow – these phenomena may be present in laminar flow as well.
Laminar Flow is a curious phenomena with some very amazing properties.
In the following demonstration of Laminar Flow three blobs of dye are mixed into corn syrup by five clockwise rotations of an inner cylinder.
The mixing process is then reversed by reversing the direction of the Laminar Flow so that after five anti-clockwise rotations the three original blobs of dye are [more or less] re-established.
The Laminar Flow of fluid around a foil provides lift for fixed-wing aircraft, ground effect vehicles and hydrofoils whilst the separation of Laminar Flow around a foil results in stalling [loss of lift].
All solid objects travelling through a fluid (or alternatively a stationary object exposed to a moving fluid) acquire a boundary layer of fluid around them where viscous forces occur in the layer of fluid close to the solid surface.
Boundary layers can be either laminar or turbulent.
Flow separation occurs when the boundary layer travels far enough against an adverse pressure gradient that the speed of the boundary layer relative to the object falls almost to zero.
The fluid flow becomes detached from the surface of the object, and instead takes the forms of eddies and vortices.
In aerodynamics, flow separation can often result in increased drag, particularly pressure drag which is caused by the pressure differential between the front and rear surfaces of the object as it travels through the fluid.
For this reason much effort and research has gone into the design of aerodynamic and hydrodynamic surfaces which delay flow separation and keep the local flow attached for as long as possible.
When the boundary layer separates, its displacement thickness increases sharply which modifies the outside potential flow and pressure field.
In the case of airfoils, the pressure field modification results in an increase in pressure drag, and if severe enough will also result in loss of lift and stall, all of which are undesirable.
For internal flows, flow separation produces an increase in the flow losses, and stall-type phenomena such as compressor surge, both undesirable phenomena.
Since air and water are governed by similar fluid equations, albeit with vastly different levels of viscosity, density, and compressibility, the hydrofoil and airfoil (both types of foil) create lift in identical ways.
The foil is shaped to move smoothly through the water causing the flow to be deflected downward which according to Newton’s Third Law of Motion exerts an upward force on the foil.
This turning of the water causes higher pressure on the bottom and reduced pressure on the top of the foil.
This pressure difference is accompanied by a velocity difference, via Bernoulli’s principle, so the resulting flowfield about the foil has a higher average velocity on one side than the other.
A ground effect vehicle (GEV) is one that attains level flight near the surface of the Earth, making use of the aerodynamic interaction between the wings and the surface known as ground effect.
Although they might look similar and/or have related technical characteristics, ground effect vehicles are not aircraft, seaplanes, hovercraft, or hydrofoils – ground effect is a separate technology altogether.
The basic design principle is that the closer the wing operates to an external surface such as the ground, said to be in ground effect, the more efficient it becomes.
A GEV is sometimes characterized as a transition between a hovercraft and an aircraft, although this is not correct as a hovercraft is statically supported upon a cushion of pressurised air from an onboard downward-directed fan.
Some GEV designs, such as the Russian Lun and Dingo, have used forced blowing under the wing by auxiliary engines to increase the high pressure area under the wing to assist the takeoff; however they differ from hovercraft in still requiring forward motion to generate sufficient lift to fly.
The Laminar Flow of fluid around a spinning sphere or cylinder also produces lift.
The Magnus effect is the commonly observed effect in which a spinning ball (or cylinder) curves away from its principal flight path.
The overall behaviour is similar to that around an airfoil with a circulation which is generated by the mechanical rotation, rather than by airfoil action.
The wake and trailing air-flow have been deflected downwards.
The boundary layer motion is more violent at the underside of the ball where the spinning movement of the ball’s surface is forward and reinforces the effect of the ball’s translational movement.
The boundary layer generates wake turbulence after a short interval.
A rotor ship, or Flettner ship, is a ship designed to use the Magnus effect for propulsion.
To take advantage of this effect, it uses rotorsails which are powered by an engine.
The Magnus effect is a force acting on a spinning body in a moving airstream, which acts perpendicularly to the direction of the airstream.
German engineer Anton Flettner was the first to build a ship which attempted to tap this force for propulsion.
A curious feature associated with the breakdown of Laminar Flow around “blunt bodies” is the shedding of vortices in a phenomena known as a Kármán Vortex Street.
Another effect of boundary layer separation is shedding vortices, known as Kármán vortex street.
When the vortices begin to shed off the bounded surface they do so at a certain frequency.
The shedding of the vortices then could cause vibrations in the structure that they are shedding off.
When the frequency of the shedding vortices reaches the resonance frequency of the structure, it could cause serious structural failures.
In fluid dynamics, a Kármán vortex street (or a von Kármán vortex sheet) is a repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid around blunt bodies.
It is named after the engineer and fluid dynamicist Theodore von Kármán, and is responsible for such phenomena as the “singing” of suspended telephone or power lines, and the vibration of a car antenna at certain speeds.
However, Laminar Flow is also fascinating when two Laminar Flows [which are moving at different speeds or in different directions] interact…. to be continued.