Page 170 - Aerodynamics for Engineering Students

Potential flow 153

XQ=DX*THAT(J,~)+DY*THAT(J,~) Cocvertiigtoco-ordinate system
YQ=DX*NHAT (J, 1) '3Y*NHAT (J, 2) based on panel j .
VX=O.5*(LOG((XQ+O.5*S(J))**2+YQ*YQ ) UsingEqn. (3.97)
5 -LOG( (XQ-O.S*S(J) )**2+YQ*YQ)
W=A~~((XQ+O.5*S(J))/YQ) - UsingEqn. (3.98)
*
)
& ATAX ( (XQ - 0 -5 S (J) /YQ )
Begincalculationofvarious scaiarprodactsofan5tvectorsusedinEqri. (3.99)
NTI J = C . 0
NNIJ=O.O
TTIJ= 0.0
TNI J= 0.3
DO 50 K=1,2
NTI J = NHAT (I, K) *THAT (J, K) + NTI J
hNI J = iiHA'? ( I, K) *N!IAT ( J , K) + N?Ji J
TTIJ =THAT (I, i()*THAT (J, K) + TTIJ
TKIJ = T3AT (I, K)*NHAT (J, K) + TNIJ
5c CONTINUE
Z'rdcalculationof scalararoducts.

AN(1, J) =VX*NTIJ+VY*hNIJ Using Eqn. (3.99a)
AN(I,J)=VX*TTIC+W*TNIJ Usingyqn. (3.9933)
ENDIF
LO CONTINJE
30 CONTINUE
RETURN
EN3

The routine, step by step, performs the following.
Discretizes the surface by assigning numbers from 1 to N to points on the surface
of the aerofoil as suggested in Fig. 3.37. The x and y coordinates of these points are
entered into a file named POINTS.DAT. The subroutine starts with reading these
coordinates XP(Z), YP(Z), say 4, y:, from this file for Z = 1 to N.
For each panel from J = 1 to N
The collocation points are calculated by taking an average of the coordinates at
either end of the panel in question.
The length S(J), i.e. Asj, of each panel is calculated.
The x and y components of the unit tangent vectors for each panel are calculated
as follows:

The unit normal vectors are then calculated from njx = -ti, and njy = tix. The main
task of the routine, that of calculating the influence coefficients, now begins.
For each possible combination of panels, i.e. Z and J = 1 to N.
First the special case is dealt with when i = j, i.e. the velocity induced by the sources
on the panel itself at its collocation point. From Eqn (3.93, 3.97, 3.98) it is seen that
vpQX = ln(1) = 0 when XQ = YQ = 0 (3.1 OOa)
V ~ = tan-'(oo) - tan-'(--m) = ?r when XQ = YQ = 0 (3.100b)
Q
~
When i # j the influence coefficients have to be calculated from Eqns (3.97,3.98,3.99).