CDOK0 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C C *** CNM3DK *** Last revision: 08-Jul-96 C C C C Programme calculates the 2D thin plate coefficients for C C generating normal force and moment coefficients in the C C calling programme (Kuessner's and Theordorsen's analytical C C solution for pitching and plunging motion - published 1936). C C C C Kinematics: C C C C n C C 1. v = 1. ( reference a * u0 ) C C kin C C C C The respective values for the time derivative C C are obtained by multipling with i*OMS C C C C n a * u0 C C v = i*OMS ( reference ------ ) C C kin L/2 C C C C n C C 2. v = 2i*OMS(xsi-1/4) (reference a*u0 ) C C kin C C C C a is a dimensionless amplitude (e.g. an angle). C C If a is a spacial coordinate, it has to made C C dimensionless by dividing by L/2 (see below). C C C C OMEGA * L/2 C C Input: : Reduced frequency OMS := ---------- C C U0 C C - Circular frequency OMEGA C C - Onset velocity U0 C C - Chord length L C C C C Relative pitch axis XDR referred to L C C moment axis, respectively C C C C Output: Lift coefficient CN# # : eta or C C Moment coefficient CM# xsi C C C C Values referred to 2*pi C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC CEDOK SUBROUTINE CNM3DK (OMS,XDR,CNeta,CMeta,CNxsi,CMxsi) IMPLICIT COMPLEX*16(C),REAL*8(D-H,O-Z) DIMENSION ch2(0:1) SAVE OMS0,CTH DATA OMS0,CTH / 0d0,(1d0,0d0) / EXTERNAL DBSJ0,DBSJ1,DBSY0,DBSY1 C ... Theodorsen funktion if (OMS .ne. OMS0) then C ... Theodorsen funktion CTHEO C DBSJn : Besselfunction 1. kind, nth order ) IMSL C DBSYn : Besselfunction 2. kind, nth order ) Library C CH2(n) : Hankelfunctions 2. kind, nth order ) C CH2(0) = CMPLX(DBSJ0(OMS),-DBSY0(OMS)) CH2(1) = CMPLX(DBSJ1(OMS),-DBSY1(OMS)) CTH = CH2(1)/(CH2(1)+(0,1)*CH2(0)) C xxx CTH = CTHEOD(OMS) OMS0 = OMS end if C *** Values for quarter chord OMSS = OMS*OMS CIOMS = cmplx(0D0,OMS) C ... 1. "Plunge" (eta) CNeta = CTH+5D-1*CIOMS CMeta = -0.125D0*CIOMS C ... 2. "Pitch" (xsi) CNxsi = CIOMS*(CTH+0.25D0*CIOMS) CMxsi = -CIOMS*dcmplx(1D0,0.75D0*OMS)/8D0 IF (XDR .EQ. 0.25D0) GOTO 100 C *** Values for chord unequal quarter chord CMetaL4 = CMeta CNxsiL4 = CNxsi CMxsiL4 = CMxsi xsiP = XDR-0.25D0 C2IOMS = cmplx(0D0,OMS+OMS) CMeta = CMetaL4+xsiP*CNeta C Factor 2 preceding eta parts is missing due to external 2i*oms CNxsi = CNxsiL4-C2IOMS*xsiP*CNeta CMxsi = CMxsiL4+xsiP*CNxsiL4-C2IOMS*(xsiP*CMetaL4+ * xsiP*xsiP*CNeta) 100 RETURN END