Scale Effects

The Reynolds number Re for flow about any body is defined as

Re =

or

V is a reference velocity, usually the free-stream velocity and / is a character­istic length of the body. For an airfoil / is usually taken to be the chord, p, the fluid mass density, p, the dynamic viscosity, and v, the kinematic viscosity. By writing R as

p-

P(V/1)

it can be seen that, in a sense, R is the ratio of dynamic forces to viscous forces. Hence geometrically similar flows will have the same ratio or “scale” of these forces if R is the same for both flows.

Scale effects on airfoil characteristics are limited mainly to those dimensionless coefficients dependent on viscous action. Thus the slope of the lift curve, dC,/dot and Cmac are not affected appreciably by changes in R below the stalling angle of attack; C/max, on the other hand, is the result of the boundary layer separation off the upper surface. Because the boundary layer growth depends significantly on Re, C, max varies noticeably with Re. In general, C/max decreases with decreasing Re. A decrease in Re by a factor of 4, for example, can produce a decrease in CJmax of 20 or 30%, depending on the airfoil section.

The drag coefficient also varies with Re, primarily because of the effect of changes in the boundary layer on the skin-friction drag. Normally the form drag does not vary too much with Re, and we can correct drag measurements for changes in R by calculating the changes in the skin – friction drag according to Fig. 2-20.