fluid_mechanics

520 Chapter 9 ■ Flow over Immersed Bodies
U
B
Bound vortex
A
Trailing
vortex
(a)
A
Low pressure
High pressure
Bound vortex
Trailing vortex
B
F I G U R E 9.37 Flow past a finite length wing: (a) the horseshoe
vortex system produced by the bound vortex and the trailing vortices; (b) the
leakage of air around the wing tips produces the trailing vortices.
(b)
F l u i d s i n t h e N e w s
Why winglets? Winglets, those upward turning ends of airplane
wings, boost the performance by reducing drag. This is accomplished
by reducing the strength of the wingtip vortices formed by
the difference between the high pressure on the lower surface of
the wing and the low pressure on the upper surface of the wing.
These vortices represent an energy loss and an increase in drag. In
essence, the winglet provides an effective increase in the aspect
ratio of the wing without extending the wingspan. Winglets come
in a variety of styles—the Airbus A320 has a very small upper and
lower winglet; the Boeing 747-400 has a conventional, vertical
upper winglet; and the Boeing Business Jet (a derivative of the
Boeing 737) has an eight-foot winglet with a curving transition
from wing to winglet. Since the airflow around the winglet is
quite complicated, the winglets must be carefully designed and
tested for each aircraft. In the past, winglets were more likely to
be retrofitted to existing wings, but new airplanes are being designed
with winglets from the start. Unlike tailfins on cars,
winglets really do work. (See Problem 9.111.)
A spinning sphere
or cylinder can
generate lift.
As is indicated above, the generation of lift is directly related to the production of a swirl or
vortex flow around the object. A nonsymmetric airfoil, by design, generates its own prescribed
amount of swirl and lift. A symmetric object like a circular cylinder or sphere, which normally
provides no lift, can generate swirl and lift if it rotates.
As is discussed in Section 6.6.3, the inviscid flow past a circular cylinder has the symmetrical
flow pattern indicated in Fig. 9.38a. By symmetry the lift and drag are zero. However, if the
cylinder is rotated about its axis in a stationary real 1m 02 fluid, the rotation will drag some of
the fluid around, producing circulation about the cylinder as in Fig. 9.38b. When this circulation
is combined with an ideal, uniform upstream flow, the flow pattern indicated in Fig. 9.38c is obtained.
The flow is no longer symmetrical about the horizontal plane through the center of the
cylinder; the average pressure is greater on the lower half of the cylinder than on the upper half,
and a lift is generated. This effect is called the Magnus effect, after Heinrich Magnus 11802–18702,
a German chemist and physicist who first investigated this phenomenon. A similar lift is generated
on a rotating sphere. It accounts for the various types of pitches in baseball 1i.e., curve ball, floater,
sinker, etc.2, the ability of a soccer player to hook the ball, and the hook or slice of a golf ball.
Typical lift and drag coefficients for a smooth, spinning sphere are shown in Fig. 9.39. Although
the drag coefficient is fairly independent of the rate of rotation, the lift coefficient is strongly