Page 27 - Computational Fluid Dynamics for Engineers

12 1. Introduction

MACH=0.15
15
-
/vTo.2/^^
12 ^0.25
|AC P
9 -
6
3
-
0 1 ! I I I
0 4 8 12 16 20 Fig. 1.11. Variation of |Z\C P | with chord
Reynolds number R c at maximum lift con-
Re ditions.

location of flaps and slats is one of the aims of CFD development efforts in
high-lift research.
The Pressure Difference Rule of Valarezo and Chin [6] is based on the ex-
amination of wind tunnel data which indicates that, at a given Reynolds/Mach
number combination, there exists a certain pressure difference AC V between
the suction peak of an airfoil (Cp) min and its trailing edge (C p)te a t the max-
imum lift condition. For the case of a multielement airfoil, the same rule ap-
plies to whichever element (leading-edge or main) is critical at maximum lift.
Thus, at a given freestream Mach number, there is a "pressure difference"
l(C P) (Cp)te| variation with Reynolds number (Fig. 1.11) that
\AC n
indicates when maximum lift is attained. This correlation applies whether or
not the airfoil has an auxiliary leading-edge device. Even though the Pressure
Difference Rule is based on two-dimensional data, Valarezo and Chin assume
the correlation in Fig. 1.11 to be valid also for three-dimensional flows. They
determine the maximum lift coefficient of multielement transport wings by the
following procedure:
1. Use a panel method to obtain flow solutions at various angles of attack for
the desired geometry. While any reliable panel method can be used for this
purpose, they use the Hess panel method discussed in detail in [4, 5, 7]. They
recommend sufficient surface paneling to ensure adequate definition of the
geometry at the leading and trailing edges.
2. For a given freestream Reynolds number and Mach number, construct a
pressure difference \AC P\ distribution vs. span based on the wing chord
distribution.
3. Determine graphically at what spanwise wing station and wing lift coef-
ficient the solutions obtained from the panel method (Step 1) match the
curve constructed in Step 2.

Valarezo and Chin validated this method with RAE experimental data [8]
obtained for a high-lift system. The wing had an aspect ratio of 8.35 and wing