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varying degrees. Because ofviscosity, a realfiuid always sticks to the body surface.
In other words, the fluid velocity at any point on the body surface is always zero.
However, the ideal fluid theory predicts a finite, nonzero velocir}r on the body
surface. In fact, in the ideal fluid theory, the body surface is a part ofjthe stagnation
streamline. At the front and rear stagnation points (Si and S2 in Fig. 1.2), the
fiuid velocity is zero. Downstream of the front stagnation point Si, the velocity
increases and may even exceed the freestream value and then drop back to zero at
the rear stagnation point S2. A typical variat.ion of the velocity on the surface of
an airfoil and a circular cylinder in crossfiow are shown in Figv1.3. For a circular
cylinder, the peak velocit)r occurs at the maximum thickness point and is equal to
2 Vw, where Va, iS the freestream velocity.
In real fiuid flow, the velocity on the surface of the body is equal to zero and rises
rapidly to thelocal value Vt within a small distance 8 as shownin Fig. 1.4a. The thin
layer in which the increase from zero to local value Vi occurs is called the bound-
ary layer. The concept of boundary layer was introduced by L. Prandtl in 1904.1
REVIEW OF BASIC AERODYNAMIC PRINCIPLES 3
Positivc
Pret
~
a) Streamlined body (airfoil)
V
Voo
b) Bluff body (circular cylinder)
Fig. 1.2 Ideal fluid flow over bodies.
Z
90
e
180
Fig. 1.3 lrelocity distribution over bodies in ideal fluid flow.
Negaji'e Pressure's
4 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
y
y
0 V
a) Dypical boundary-layer profile
V(y)
Equal Areas
b) Concept of displacement tluckness
Fig.1.4 Schematic velocity distribuhonin boundarylayer.
REVIEW OF BASIC AERODYNAMIC PRINCIPLES 5
a) Given body
b) Gi-ven body with boundarylayer
c) Equwalent body
Fig.1.5 Concept equrvalent body.
He postulated that the thickness 8 of the boundary layer is small in relation to
the characteristic dimension L of the body (8]L << 1) so that the effects of fluid
viscosity are assumed to be essentially confined within this thin boundary layer.
Outside the boundary layer, the fiuid fiow practically oeha'ves as though it is in-
viscid. With this hypothesis, one can consider the effect of fiuid viscosit)r or the
boundary-layer effect as equivalent to shifting the inviscid (potential) flow by a
small amount equal to boundary-layer displacement thickness 8*, whic~ is def:nyed
as
1 .00
8*-- V1 j [Vi- V(y)ldy (i.io)
The concept of 8* is illustrated in Fig. 1.4b.
The actual body shape now consists of the given shape plus a displacement
thick:ness 8* as shown schematically in Fig. 1.5. The concept of boundary layer
leads to a simple and practical method of finding the pressure distribution over a
given body surface as follows: 1) using the ideal fluid theory, obtain the inviscid
velocity and pressure distribution and 2) with this velocity distribution, obtain the
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