Real Fluid Flow

There are two different types of real fluid flow: laminar and turbulent. In laminar flow, the fluid moves in layers called laminas. Laminar flow need not be in a straight line. For laminar flow, the flow follows the curved surface of the airfoil smoothly, in layers. The closer the fluid layers are to the airfoil surface, the slower they move. Moreover, the fluid layers slide over one another without fluid being exchanged between the layers.

In turbulent flow, secondary random motions are superimposed on the principal flow and there is an exchange of fluid from one adjacent sector to another. More importantly, there is an exchange of momentum such that slow moving fluid particles speed up and fast moving particles give up their momentum to the slower moving particles and slow down themselves.

Another example of a common occurrence of laminar and turbulent flow is the water faucet. Opened slightly, at low speeds the water flows out in a clear column—an instance of laminar flow. But open the faucet fully and the water speeds out in a cloudy turbulent column. In a mountain brook, the water may slide over smooth rocks in laminas. In the Colorado River after the snow has melted, the flow churns downstream in confused, turbulent rapids. It will be seen that the flow over airfoil surfaces may assume both a laminar and turbulent characteristic depending upon a number of factors.

In some cases, turbulent flow will appear "naturally" in a laminar flow as in smoke rising in the air. In other cases, by causing a disturbance, a laminar flow can be changed to a turbulent flow. The question arises as to how one can tell whether a flow is to be laminar or turbulent. In 1883, Osborne Reynolds introduced a dimensionless parameter that gave a quantitative indication of the laminar to turbulent transition.

In an experiment, Reynolds demonstrated that, under certain circumstances, the flow in a tube changes from laminar to turbulent over a given region of the tube. He used a large water tank that had a long tube outlet with a stopcock at the end of the tube to control the flow speed. The tube went smoothly into the tank. A thin filament of colored fluid was injected into the flow at the mouth.

When the speed of the water flowing through the tube was low, the filament of colored fluid maintained its identity for the entire length of the tube. However, when the flow speed was high, the filament broke up into the turbulent flow that existed through the cross section.

Reynolds defined a dimensionless parameter, which has since been known as the Reynolds number, to give a quantitative description of the flow. In equation form, the Reynolds number R is

where

For this setup, Reynolds found, by using water, that below R = 2,100, the flow in the pipe was laminar as evidenced by the distinct colored filament. This value was true regardless of the varying combinations of values of p, V, d, or µ. A transition between laminar and turbulent flow occurred for Reynolds numbers between 2,100 and 40,000 depending upon how smooth the tube junction was and how carefully the flow entered the tube. Above R = 40,000, the flow was always turbulent, as evidenced by the colored fluid filament breaking up quickly. The fact that the transition Reynolds number (between 2,100 and 40,000) was variable indicates the effect that induced turbulence has on the flow.

The numerical values given for the transition are for this particular experiment since the characteristic length chosen, d, is the diameter of the pipe. For an airfoil, d would be the distance between the leading and trailing edge called the chord length. Additionally, water was used in the Reynolds experiment whereas air flows about an airfoil. Thus, the transition number between laminar and turbulent flow would be far different for the case of an airfoil. Typically, airfoils operate at Reynolds numbers of several million. The general trend, however, is evident. For a particular body, low Reynolds number flows are laminar and high Reynolds number flows are mostly turbulent.

The Reynolds number may be viewed another way:

The viscous forces arise because of the internal friction of the fluid. The inertia forces represent the fluid's natural resistance to acceleration. In a low Reynolds number flow, the inertia forces are negligible compared with the viscous forces, whereas in a high Reynolds number flow, the viscous forces are small relative to the inertia forces. An example of a low Reynolds number flow (called Stoke's flow) is a small steel ball dropped into a container of heavy silicon oil. The ball falls slowly through the liquid; viscous forces are large. Dust particles settling through the air are another case of a low Reynolds number flow. These flows are laminar. In a high Reynolds number flow, such as typically experienced in the flight of aircraft, both laminar and turbulent flows are present.

Surface roughness also affects a body immersed in a flow field. Surface roughness causes the flow near the body to go from laminar to turbulent. As the surface roughness increases, the first occurrence of turbulent flow will move against the direction of the flow along the airfoil. The Reynolds number and surface roughness are not independent of each other and both contribute to the determination of the laminar to turbulent transition. A very low Reynolds number flow will be laminar even on a rough surface and a very high Reynolds number flow will be turbulent even though the surface of a body is highly polished.

Another important factor in the transition from laminar to turbulent flow is the pressure gradient in the flow field. If the static pressure increases with downstream distance, disturbances in a laminar flow will be amplified and turbulent flow will result. If the static pressure decreases as distance in the direction of the airflow increases, disturbances in a laminar flow will damp out (or decrease) and the flow will tend to remain laminar. Over an airfoil, the static pressure decreases up to the point of maximum thickness. A laminar flow will be encouraged in this region. Beyond the point of maximum thickness (or shoulder of the airfoil), the static pressure increases. The laminar flow now is hindered and may go turbulent before reaching the trailing edge.