Page 117 - Aerodynamics for Engineering Students

100 Aerodynamics for Engineering Students

3.5 b

Fig. 2.33

Example 2.4 Calculating the boundary-layer thickness in the stagnation zone at the leading
edge.
We will estimate the boundary-layer thickness in the stagnation zone of (i) a circular cylinder
of 120mm diameter in a wind-tunnel at a flow speed of 20mls; and (ii) the leading-edge of a
Boeing 747 wing with a leading-edge radius of 15Omm at a flight speed of 250mls.
For a circular cylinder the potential-flow solution for the tangential velocity at the surface is
given by 2U,sin4 (see Eqn (3.44)). Therefore in Case (i) in the stagnation zone,
x = R sin 4 N R4, so the velocity tangential to the cylinder is

X

Therefore, as shown in Fig. 2.34, if we draw an analogy with the analysis in Section 2.10.3
above, a = 2U,/R = 2 x 2010.06 = 666.7 sec-I. Thus from Eqn (2.126), given that for air the
kinematic viscosity, Y N 15 x 10-6m2/s,

6 N 2.48 = 2.4/- 666.7 = 360 pm

For the aircraft wing in Case (ii) we regard the leading edge as analogous locally to a circular
cylinder and follow the same procedure as for Case (i). Thus R = 150mm = 0.15 m and
U, = 250m/s, so in the stagnation zone, a = 2U,/R = 2 x 25010.15 = 3330s~-l and

These results underline just how thin the boundary layer is! A point that will be taken up in
Chapter 7.