Paper Airfoil Aerodynamics3 - Reynolds
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In 1883 Osborne
Reynolds, a British engineer and physicist, demonstrated that
the transition from laminar to turbulent flow in a pipe depends upon the
value of a mathematical quantity equal to the average velocity of flow
times the diameter of the tube times the mass density of the fluid divided
by its absolute viscosity. This mathematical quantity, a pure number
without dimensions, became known as the Reynolds number and was
subsequently applied to other types of flow that are completely enclosed
or that involve a moving object completely immersed in a
fluid. The two forces of
drag, Viscous and Inertial produce a drag effect as an airfoil flows
through a fluid. It can also
be said that the Reynolds number is the ratio of the viscous forces to
those of the drag forces. The
Reynolds number is directly related to the average speed of the fluid, and
the length over which the fluid travels along the surface. It is inversely proportional to
the viscosity of the fluid.
Because of this, the force due to drag can also be said to vary as the Reynolds number changes. At low Reynolds numbers, the drag force is roughly linearly related to the speed, the viscosity, and the size. At higher numbers, the drag force varies at the square of the speed, the square of the size, and linearly with the density of the fluid. Figure 3.1 discusses the ranges over which drag reacts. Figure 3.2 gives a comparison of the Reynolds numbers for various arbitrary airfoils gives a relative idea of the drag forces associated with them. It is fairly clear that the Reynolds number for the wing of a Cessna is higher by a factor of 100 in comparison to that of a paper airfoil. Both drag functions play a role in the drag produced by an object, although in high Reynolds numbers (Greater than 1000) it is possible to neglect most viscous forces, while in low Reynolds numbers (Less than 10) it is possible to neglect most linear resistance forces. For the case of both airfoils it is clear that we can neglect most viscous forces to get a reasonable approximation of the drag, however it is impossible to completely neglect all forces due to viscosity, as we'll see in the next section.
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Figure 3.1 ? Approximate drag functions for high and low Reynolds numbers.
Figure 3.2 ? Reynolds numbers of two different wings. | ||||||||||||||||||||||||||||
