Page 169 - Aerodynamics for Engineering Students

152 Aerodynamics for Engineering Students
Therefore to obtain the components of this velocity vector perpendicular and tangential
to panel i take the scalar product of the velocity vector with ii; and Z; respectively to obtain
.
-+
Nu = VPQ . ii; = vXQn; tj + vraii; . iij (3.99a)
A
*
.
tj
*
A
T.. - ?PQ . Z; = ~,~t; + vYQti . nj (3.99b)
II-
A computational routine in FORTRAN 77
In order to see how the calculation of the influence coefficients works in practice, a
computational routine written in standard FORTRAN 77 is given below, with a descrip-
tion of each step.
SUBROUTINEINFLU(XC, YC, AN, AT, NHAT, THAT, N, NM)
Onexit XCandYCare columnmatrices oflengthNcontainingtheco-ordinatesof
thecollocation points; ANandATaretheN*Ninfluencecoefficientmatrices; and
NHATandTHATaretheN*2matricescontain~ngtheco-ord~natesoftheun~tnormal
and tangent vectors, the first andsecondcolumns contain thexandy co-ordinates
respectively.NisthenumberofpanelsandNMisthemaximumnumberofpane1s.
PARAMETER(NMAX=200,PI=3.141592654)
REAL NHAT,NTIJ,NNIJ
DIMENSION XC (NM), YC (NM ), AN (NM, NM ), AT (NM, NM)
DIMENSION XP (NMAX),YP (NMAX),NHAT (NM, 2),
& THAT (NM, 2) , S (NMAX)
OPEN(7,FILE='POINTS.DAT',STATUS='OLD')
DO 10 I=l,N Readinginco-ordinatesofpanel
10 READ(7,*) XP(I), YP(1) end-points.
CLOSE (7
)
DO 20 J=l,N
IF (J.EQ.1) THEN
XPL=XP(N)
YPL=YP(N)
ELSE
XPL=XP (J - 1)
YPL=YP (J - 1)
ENDIF
XC (J) = 0.5* (XP (J) +XPL) Calculating co-ordinates of
YC(J) =0.5*(YP(J)+YPL) collocationpoints.
S(J)=SQRT((XP(J)-XPL)**2+(YP(J)-YPL)**2) Calculatingpanel length.
= (XP(J)-XPL) /S(J) Calculatingxco-ordinateof unit tangent vector.
THAT(J,l)
= (YP(J)-YPL)/S(J) Calculatingyco-ordinateof unit tangentvector.
THAT(J,2)
NHAT (J, 1) = -THAT (J, 2 ) Calculatingxco-ordinateof unitnormal vector.
NHAT(J,2) THAT(J,l) Calculatingyco-ordinateofunitnormalvector.
=
20 CONTINUE
Calculationofthe influence coefficients.
DO 30 I=l,N
DO 40 J=l,N
IF (I. EQ. J) THEN
AN(1,J) =PI Case of i= j.
AT(1,J) =O.O
ELSE
DX=XC(I)-XC(J) Calculatingxandycomponentsofline
DY=YC(I)-YC(J) joining collocationpoint iand j