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Skin-friction forces in a real fluid flow

Pressure and viscous forces. In addition to the pressure forces that act everywhere normal to (perpendicular to) a body immersed in a moving fluid, viscous forces are also present. It is these viscous forces that modify the ideal fluid lift and help create the real fluid drag.


Boundary layer and laminar and turbulent flow

Figure (a) shows inviscid flow (the fluid is ideal) along a flat plate. Under this condition, the fluid simply slips over the surface with velocity V. No drag results if the fluid is frictionless (inviscid). Figure (b) shows viscous flow along a flat plate found under conditions of real fluid flow. A very thin film of fluid adheres to the surface. At the surface of a body, point B, the flow velocity is zero. As one moves away from the body, the velocity of the fluid gradually increases until at some point A the velocity becomes a constant value V. The layer of fluid where the velocity is changing from zero to a constant value is known as the boundary layer. Figure (c) compares laminar and turbulent flows. As is usual for turbulent flow, there is a random motion in the boundary layer.


Boundary layer on an airfoil

Real fluid flow about an airfoil. The thickness of the boundary layers and wake are greatly exaggerated. The bottom flow along lower surface is the same as on the upper surface.


Fluid flow on an airfoil

Figure (a) compares the ideal fluid case static-pressure distribution at the airfoil surface and centerline streamline with the real fluid case. Figure (b) illustrates that, in the ideal fluid case, the net static-pressure force acting on the front surface of the airfoil (up to the shoulder) parallel to the free stream exactly opposes and cancels that acting on the rear surfaces of the airfoil. In the real fluid case, shown in figure (c), the net result is a drag force due to the asymmetric pressure distribution called pressure drag. Figure (d) illustrates the lift and drag for an airfoil producing lift in both an ideal and real fluid case.

Skin-Friction Drag

An important aerodynamic force during low-speed subsonic flight is the shear force (the sideways force or internal friction) caused by viscous airflow over the surfaces of the vehicle. This shear force is referred to as the skin-friction force or skin-friction drag and depends strongly on the Reynolds number, surface roughness, and pressure gradients. In addition to the pressure forces that act everywhere perpendicular to (normal to) a body in moving air, viscous forces are also present. It is these viscous forces that modify the lift that would exist under ideal conditions (air is inviscid and incompressible) and help create the real drag.

If the airflow were ideal, that is, inviscid, the air would simply slip over the surface of a smooth plate with velocity V¥. At all points along the surface of the plate, the velocity distribution (that is, the variation in velocity as one moves perpendicularly away from the surface) would be a uniform constant value of V. No drag would result if the airflow were frictionless (inviscid).

Under real conditions, however, a very thin film of air molecules adheres to the surface. This is the very important no-slip condition. It states that at the surface of a body, the airflow velocity is zero. As one moves away from the body, the velocity of the air gradually increases until, at some point, the velocity becomes a constant value; in the case of a flat plate this value is V¥. The layer of air where the velocity is changing from zero to a constant value is called the boundary layer. Within the boundary layer, there are relative velocities between the layers and an internal friction is present. This internal friction extends to the surface of the body. The cumulative effect of all these friction forces is to produce drag on the plate. This drag is referred to as skin-friction drag.

Initially, near the leading edge of a flat, smooth plate, one has a laminar flow (the flow is layered) and the boundary layer also is steady and layered—hence, a laminar boundary layer. As one moves farther downstream, viscosity continues to act, and the laminar boundary layer thickens as more and more air is slowed down by internal friction. Eventually, a point is reached on the plate where the laminar boundary layer undergoes transition and becomes a turbulent boundary layer. As is usual for turbulent flow, there is random motion in the boundary layer as well as the downstream-directed motion. There is no slip at the surface of the plate. Another important difference from the laminar boundary layer is the fact that the velocity builds up more quickly as one moves away from the wall, although the total boundary-layer thickness is greater. The turbulent boundary layer farther away from the wall reenergizes the slower moving air nearer the wall. This condition can be seen by comparing the profile of the laminar boundary layer with the profile of the turbulent boundary layer.

The Reynolds number has an important effect on the boundary layer. As the Reynolds number increases (caused by increasing the airflow 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. Thus, the boundary layer never disappears.

It is interesting to note that a typical thickness of the boundary layer on an aircraft wing is generally less than a centimeter (2.5 inches). Yet, the velocity must vary from zero at the surface of the wing to hundreds of meters per second at the outer edge of the boundary layer. It is evident that tremendous shearing forces (internal friction) must be acting in this region. This gives rise to the skin-friction drag.

Applied to an airfoil in a real airflow, the same free-stream velocity V¥ and free-stream static pressure p¥ apply. The field of air ahead of the airfoil is only slightly modified and for all practical purposes, the velocities and static pressures are the same as for the ideal fluid case. Again a stagnation point (a point with no motion) occurs at the leading edge of the airfoil and the pressure reaches its maximum value of pt at this point (total or stagnation pressure). From this point on along the airfoil, the picture changes.

As noted earlier 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 airflow 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 air molecules 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 of the airfoil. 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 airflow moves from the shoulder to the rear surface of the airfoil, the static-pressure gradient is unfavorable (increasing pressure with downstream distance). The air molecules must push against both this unfavorable pressure gradient and the viscous forces. At the transition point, the character of the airflow 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 airflow, and at some point, the airflow stops completely. The boundary layer has stalled short of reaching the trailing edge. (Remember that the airflow reached the trailing edge before stopping in the ideal fluid case.)

This stall point is known as the separation point. All along a line starting from this point outward into the airflow, the airflow is stalling. Beyond this line, the airflow is actually moving backward, upstream toward the nose before turning around. This is a region of eddies and whirlpools and represents “dead” air that is disrupting the flow field away from the airfoil. Thus, the airflow outside the dead air region is forced to flow away and around it. The region of eddies is called the wake behind the airfoil.

Up to the separation point, the difference between the static-pressure distribution for ideal fluid flow and real airflow is not very large but once separation occurs, the pressure field in greatly modified. In the ideal fluid case, the net static-pressure force acting on the front surface of the airfoil (up to the shoulder) parallel to the free stream exactly opposed and canceled that acting on the rear surfaces of the airfoil. Under real airflow conditions, however, this symmetry and cancellation of forces is destroyed. The net static-pressure force acting on the front surface parallel to the free-stream direction now exceeds that acting on the rear surface. The net result is a drag force due to the asymmetric pressure distribution called pressure drag. This is a drag in addition to the skin-friction drag due to the shearing forces (internal friction) in the boundary layer. Additionally, the modification of the static-pressure distribution causes a decrease in the pressure lift from the ideal fluid case. The effect of viscosity is that the lift is reduced and a total drag composed of skin-friction drag and pressure drag is present. Both of these are detrimental effects.

It should be emphasized that similar processes are occurring on all the components of the aircraft to one degree or another, not only the airfoil.

Thus, the effects of a real fluid flow are the result of the viscosity of the fluid. The viscosity causes a boundary layer and, hence, a skin-friction drag. The flow field is disrupted because of viscosity to the extent that a pressure drag arises. Also, the net pressure lift is reduced.

—Adapted from Talay, Theodore A. Introduction to the Aerodynamics of Flight. SP-367, Scientific and Technical Information Office, National Aeronautics and Space Administration, Washington, D.C. 1975. Available at http://history.nasa.gov/SP-367/cover367.htm

For Further Reading:

Anderson, Jr., John D. A History of Aerodynamics. Cambridge, England: Cambridge University Press, 1997.

Hewitt, Paul G. Conceptual Physics. Sixth Edition. Glenview, Ill.: Scott, Foresman and Company, 1989.

Wegener, Peter P. What Makes Airplanes Fly? New York: Springer-Verlag, 1991.

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