Lesson 4: Fluid Flow
Section 3 - Real Fluid Flow
REAL FLUID FLOW
Now we will learn about concepts of 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. In a laminar flow, the uniform rectilinear flow, consists of air moving in straight-line layers (laminas) from left to right.
The laminas may be considered the adjacent streamtubes and then the streamlines indicate the direction of movement of these fluid layers. Laminar flow need not be in a straight line.
For an ideal fluid the flow follows the curved surface smoothly, in laminas. The closer the fluid layers are to the airfoil surface, the slower they move. In the case of streamlines, the fluid layers slide over one another without fluid being exchanged between layers.
TURBULENT FLOW
In turbulent flow, secondary random motions are superimposed on the principal flow. In this case, 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.
Consider an example in which the smoke rises from a cigarette. For some distance the smoke rises in smooth filaments which may wave around but do not lose their identity; this flow is laminar.
The filaments or streamtubes suddenly break up into a confused eddying motion some distance above the cigarette; this flow is turbulent. The transition between laminar and turbulent flow moves closer to the cigarette when the air in the room is disturbed.
Another example of a common occurrence of laminar and turbulent flow is the water faucet. If opened slightly, at low speeds the water flows out in a clear column - laminar flow. But open the faucet fully and the flow speeds out in a cloudy turbulent column.
In a mountain brook the water may slide over smooth rocks in laminas. In the Colorado River, the flow churns downstream in the confused turbulent rapids. The conclusion is 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 the smoke rising in the air. In other cases, by causing a disturbance, a laminar flow can be changed to a turbulent flow.
Here, a 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 which gave a quantitative indication of the laminar to turbulent transition.
In his experiments with a w field, Reynolds demonstrated the fact that under certain circumstances the flow in a tube changes from laminar to turbulent over a given region of the tube. Consider 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 was faired 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 NUMBER
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 given by: R = pVl/µ (10) where
p density of fluid, kg/m3 [Greek letter rho] V mean velocity of fluid, m/sec l characteristic length, m µ coefficient of viscosity (called simply "viscosity" as in the earlier discussion), kg/m-sec
For this setup, Reynolds found, by using water, that below R = 2100 the flow in the pipe was laminar as evidenced by the distinct colored filament. This value was true regardless of his varying combinations of values of p , V, l , or µ.
A transition between laminar and turbulent flow occurred for Reynolds numbers between 2100 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 2100 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 l is the diameter of the pipe. For an airfoil, l 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.
Therefore, 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 trends, however, are 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: Reynolds number ≈ Inertia forces/viscous forces (11)
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 high Reynolds number flows the viscous forces are small relative to the inertia forces.
An example of a low Reynolds number flow or what is 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, laminar and turbulent flows are present.
SURFACE ROUGHNESS EFFECTS
Now let's look at the Surface roughness effects on the flow field. The effect of surface roughness of a body immersed in a flow field is that it causes the flow near the body to go from laminar to turbulent. As the surface roughness increases, the point of first occurrence of turbulent flow will move upstream along the airfoil.
In the following figure, an airfoil surface is shown. In each succeeding case the degree of surface roughness is increased and the Reynolds number is held fixed. The flow is seen to go turbulent further upstream in each case.
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.
PRESSURE GRADIENT EFFECTS
Here, we must consider Pressure gradient effects on 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 with downstream distance, disturbances in a laminar flow will damp out and the flow will tend to remain laminar.
Remember that over an airfoil the static pressure decreased 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 increased. The laminar flow now is hindered and may go turbulent before the trailing edge.
Now, we can look at the boundary layer and skin-friction drag. We learned earlier the background needed to show how drag is produced on a body immersed in a real fluid flow.
DEMONSTRATION OF SHEAR FORCE
An important aerodynamic force during low-speed subsonic flight is the shear force caused by viscous flow over the surfaces of the vehicle. This shear force is referred to as the skin-friction force and is strongly dependent on the factors previously mentioned-Reynolds number, surface roughness, and pressure gradients.
In the next illustration, we see that in addition to the pressure forces that act everywhere normal to a body immersed in a moving fluid, viscous forces are also present. It is these viscous forces which modify the ideal fluid lift and help create the real fluid drag.
The Reynolds number has an important effect on the boundary layer. As the Reynolds number increases (caused by increasing the flow speed and/or decreasing the viscosity), the boundary layer thickens more slowly. However, even though the Reynolds number becomes large, the velocity at the surface of the body must be zero. Therefore, the boundary layer never disappears.
We can note here that a typical thickness of the boundary layer on an aircraft wing is generally less than a centimeter. Yet, the velocity must vary from zero at the surface of the wing to hundreds of m/sec at the outer edge of the boundary layer.
It is clearly evident that tremendous shearing forces (internal friction) must be acting in this region. This gives rise to the skin-friction drag.
In the example of the flat plate, a boundary layer begins to form because of viscosity. This boundary layer is very thin and outside of it the flow acts very much like that of an ideal fluid. Also, the static pressure acting on the surface of the airfoil is determined by the static pressure outside the boundary layer.
This pressure is transmitted through the boundary layer to the surface and thus acts as if the boundary layer were not present at all. But the boundary layer feels this static pressure and will respond to it.
Over the front surface of the airfoil up to the shoulder, an assisting favorable pressure gradient exists (pressure decreasing with distance downstream). The flow speeds up along the airfoil. The flow is laminar and a laminar boundary layer is present.
This laminar boundary layer grows in thickness along the airfoil. When the shoulder is reached, however, the fluid particles are moving slower than in the ideal fluid case.
This is an unfavorable condition because the previous ideal flow just came to rest at the trailing edge. It would appear now, with viscosity present, that the flow will come to rest at some distance before the trailing edge is reached.
As the flow moves from the shoulder to the rear surface, the static-pressure gradient is unfavorable (increasing pressure with downstream distance). The fluid particles must push against both this unfavorable pressure gradient and the viscous forces.
At the transition point, the character of the flow changes and the laminar boundary layer quickly becomes a turbulent boundary layer. This turbulent boundary layer continues to thicken downstream.
Pushing against an unfavorable pressure gradient and viscosity is too much for the flow, and at some point, the flow stops completely. The boundary layer has stalled short of reaching the trailing edge. It is important to keep in mind that the flow reached the trailing edge before stopping in the ideal fluid case.
THE SEPARATION POINT
This stall point is known as the separation point. All along a line starting from this point outward into the flow, the flow is stalling. Beyond this line the flow is actually moving back, upstream toward the nose before turning around.
This is a region of eddies and whirlpools and represents "dead", air which is disrupting the flow field away from the airfoil. Thus, flow outside the dead air region is forced to flow away and around it. The region of eddies as shown in the next figure is called the wake behind the airfoil.
