Page 208 - Computational Fluid Dynamics for Engineers

196 6. Inviscid Flow Equations for Incompressible Flows

6.5.2 Subroutine COEF

This subroutine calculates the elements aij of the coefficient matrix A from Eqs.
(6.5.1) and (6.5.4) and the elements of b from Eq. (6.5.5). We note that iV + 1
corresponds to KUTTA, N to NODTOT and

cos(6i -0j)= cos 6i cos 6j + sin 0* sin Oj = CTIMTJ
sin(0i -Oj) = sin 6i cos Oj - cos 0i sin 6j = STIMTJ

6.5.3 Subroutine GAUSS

The solution of Eq. (4.5.23) is obtained with the Gauss elimination method
described in Section 4.5.

6.5.4 Subroutine VPDIS

Once x is determined by subroutine GAUSS so that source strengths qi (i =
.
1,2, ..,iV) and vorticity r on the airfoil surface are known, the tangential
velocity component (V*) at each control point can be calculated. Denoting qi
t
with Q(I) and r with GAMMA, the tangential velocities (V )i are obtained
with the help of Eq. (6.4.8b). This subroutine also determines the distributions
of the dimensionless pressure coefficient C p (= CP) defined by

P
= -f^ (6.5.8a)
C p

which in terms of velocities can be written as

2
yt\
C p = 1 - ( — ) (6.5.8b)
^OO
The output of this subroutine includes the distribution of source strength qi
(= Q), C p (= CP), VV^oo (= UE) and vorticity strength r (GAMMA).

6.5.5 Subroutine CLCM

The dimensionless pressure in the appropriate directions is integrated to com-
pute the aerodynamic force and the coefficients for lift (CL) and pitching mo-
ment (CM) about the leading edge of the airfoil.