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SUBROUTINE SUBA
C
C UNSTEADY FLOW ANAYSIS OF A SUPERSONIC CASCADE
C
C LIFT AND MOMENT COEFICIENT
C
DIMENSION PRES1(21),PRES2(21),PRES3(21),PRES4(21),QRES4(21),
1 SBKDE1(201),SBKDE2(201),SUMSV1(201),SUMSV2(201),
2 SVKL1(201),SVKL2(201),XLSV1(21),XLSV2(21),
3 XLSV3(21),XLSV4(21)
COMPLEX SBKDE1,SBKDE2,F4,F4S,AM4,F5S,F6S,AM4TST,SUM3,SUM4,
1 AM5TT,AM6,SUMSV1,SUMSV2,SVKL1,SVKL2,F5,F5T,AM5,
2 AM5T,AI,A,B,BSYCON,ALP,F1,AM1,ALN,BLKAPM,BKDEL3,
3 F1S,C1,C2P,C2N,C2,AMTEST,FT2,BLAM1,FT3,AM2,SUM1,
4 SUM2,F2,BLAM2,FT2T,C1T,FT3T,F2P,AM2P,SUM1T,SUM2T,
5 C1P,C1N,BKDEL1,BKDEL2,BLKAP1,ARG,ARG2,FT3TST,BC,
6 BC2,BC3,BC4,BC5,CA1,CA2,CA3,CA4,CLIFT,CMOMT,
7 PRES1,PRES2,PRES3,PRES4,QRES4,FQA,FQB,T1,T2,T3,T4,
8 GUSAMP,FQ7,CEXP3,CEXP4,CEXP5,CONST,C1A,C2A
CHARACTER UFM*23
COMMON /XMSSG / UFM
COMMON /SYSTEM/ SYSBUF,IBBOUT
COMMON /BLK1 / SCRK,SPS,SNS,DSTR,AI,PI,DEL,SIGMA,BETA,RES
COMMON /BLK2 / BSYCON
COMMON /BLK3 / SBKDE1,SBKDE2,F4,F4S,AM4,F5S,F6S,AM4TST,SUM3,SUM4,
1 AM5TT,AM6,SUMSV1,SUMSV2,SVKL1,SVKL2,F5,F5T,AM5,
2 AM5T,A,B,ALP,F1,AM1,ALN,BLKAPM,BKDEL3,F1S,C1,C2P,
3 C2N,C2,AMTEST,FT2,BLAM1,FT3,AM2,SUM1,SUM2,F2,
4 BLAM2,FT2T,C1T,FT3T,F2P,AM2P,SUM1T,SUM2T,C1P,C1N,
5 BKDEL1,BKDEL2,BLKAP1,ARG,ARG2,FT3TST,BC,BC2,BC3,
6 BC4,BC5,CA1,CA2,CA3,CA4,CLIFT,CMOMT,PRES1,PRES2,
7 PRES3,PRES4,QRES4,FQA,FQB,FQ7
COMMON /BLK4 / I,R,Y,A1,B1,C4,C5,GL,I6,I7,JL,NL,RI,RT,R5,SN,SP,
1 XL,Y1,AMU,GAM,IDX,INX,NL2,RL1,RL2,RQ1,RQ2,XL1,
2 ALP1,ALP2,GAMN,GAMP,INER,IOUT,REDF,STAG,STEP,
3 AMACH,BETNN,BETNP,BKAP1,XLSV1,XLSV2,XLSV3,XLSV4,
4 ALPAMP,AMOAXS,GUSAMP,DISAMP,PITAXS,PITCOR
C
S1 = SPS - SNS
S2 = SPS*DEL - SIGMA
S3 = SPS/(DSTR**2)
S4 = SNS/DSTR
S0 = 2.0 - SPS + SNS
T1 = CEXP(-AI*SIGMA)
T2 = CEXP(AI*SIGMA)
A1 = 2.0*PI/S1
B1 = S2/S1
GAM = S2
C1P = GAM/DSTR - SCRK
C1N = GAM/DSTR + SCRK
ALP = GAM*S3 + S4*CSQRT(C1P)*CSQRT(C1N)
BC = -B1/ALP*BSYCON/SIN(PI*B1/A1)
T3 = ALP - DEL
F1 = (ALP-AMU)/T3*AI*SNS/(BETA*(GAM-ALP*SPS))
ARG2 = DEL
CALL AKAPM (ARG2,BKDEL1)
ARG = DEL - GL
CALL AKAPM (ARG,BKDEL2)
CALL DLKAPM (ARG2,BLKAP1)
INX = 0
CALL DRKAPM (ALP,INX,BLKAPM)
F1 = F1*BKDEL1/BLKAPM*(-T3/(T3+GL)*A*AI*BKDEL2/BKDEL1 +
1 B*BLKAP1+B/T3)
F1S = F1
NL = 10
RL1 = NL - 1
CEXP3 = CEXP(-AI*T3/RL1*S1)
PRES1(1) = F1S
NNL1 = NL - 1
DO 453 JL = 1,NNL1
PRES1(JL+1) = PRES1(JL)*CEXP3
453 CONTINUE
F1 = F1*AI/T3*(CEXP(-AI*T3*S1)-1.0)
AM1 = F1/(AI*T3)-F1S/(AI*T3)*S1*CEXP(-AI*T3*S1)
AMTEST = 0.0
FQB = BKDEL1/(BETA*BC)*CEXP(AI*S2/2.0)*
1 (-A*AI*BKDEL2/BKDEL1+B*BLKAP1)
DO 20 I = 1,200
R = I
GAMP = 2.0*PI*R + S2
GAMN =-2.0*PI*R + S2
C1P = (GAMP/DSTR) - SCRK
C2P = (GAMP/DSTR) + SCRK
ALP = GAMP*S3 + S4*CSQRT(C1P)*CSQRT(C2P)
T3 = ALP - DEL
IDX = I
CALL DRKAPM (ALP,IDX,BLKAPM)
C1 = (ALP-AMU)/T3*AI*SNS/(BETA*(GAMP-ALP*SPS))*BKDEL1/
1 (BLKAPM)*(-T3/(T3+GL)*A*AI*BKDEL2/BKDEL1+B*BLKAP1+B/T3)
C1N = (GAMN/DSTR) - SCRK
C2N = (GAMN/DSTR) + SCRK
ALN = GAMN*S3 + S4*CSQRT(C1N)*CSQRT(C2N)
T4 = ALN - DEL
IDX =-I
CALL DRKAPM (ALN,IDX,BLKAPM)
C2 = (ALN-AMU)/T4*AI*SNS/(BETA*(GAMN-ALN*SPS))*BKDEL1/
1 (BLKAPM)*(-T4/(T4+GL)*A*AI*BKDEL2/BKDEL1+B*BLKAP1+B/T4)
F1 = F1+C1*AI/T3*(CEXP(-AI*T3*S1)-1.0)+C2*AI/
1 T4*(CEXP(-AI*T4*S1)-1.0)
AM1 = AM1+C1/(AI*T3)*(-S1*CEXP(-AI*T3*S1)+AI/
1 T3*(CEXP(-AI*T3*S1)-1.0))+C2/(AI*T4)*
2 (-S1*CEXP(-AI*T4*S1)+AI/T4*(CEXP(-AI*T4*S1)-1.0))
C2A = C2
C1A = C1
AA = S1/RL1
CEXP3 = CEXP(-AI*T3*AA)
CEXP4 = CEXP(-AI*T4*AA)
TEMP = 2.0*PI*R
CEXP5 = CEXP(AI*(SIGMA-SNS*DEL)/S1*AA)
CONST = 4.0*FQB/TEMP
PRES1(1) = PRES1(1) + C1 + C2
DO 454 JL = 1,NNL1
CONST = CONST*CEXP5
C1A = C1A*CEXP3
C2A = C2A*CEXP4
PRES1(JL+1) = PRES1(JL+1) + C1A + C2A
PRES1(JL+1) = PRES1(JL+1) + CONST*SIN(TEMP*JL/RL1)
454 CONTINUE
IF (CABS((AM1-AMTEST)/AM1) .LT. 0.0005) GO TO 45
AMTEST = AM1
20 CONTINUE
GO TO 9992
9992 WRITE (IBBOUT,3005) UFM
3005 FORMAT (A23,' FROM AMG MODULE. AM1 LOOP IN SUBROUTINE SUBA DID ',
1 'NOT CONVERGE.')
CALL MESAGE (-61,0,0)
45 CONTINUE
AA = S1/RL1
CEXP3 = CEXP(AI*(SIGMA-SNS*DEL)/RL1)
CONST = FQB
TEMP = 2.0*AA/(SPS-SNS)
PRES1(1) = PRES1(1) - FQB
DO 4541 JL = 1,NNL1
CONST = CONST*CEXP3
PRES1(JL+1) = PRES1(JL+1) - CONST*(1.0-JL*TEMP)
4541 CONTINUE
Y = 0.0
Y1 = SNS
ARG = DEL - GL
CALL ALAMDA (ARG,Y,BLAM1)
CALL ALAMDA (ARG,Y1,BLAM2)
CALL AKAPPA (ARG,BKAP1)
FT2 = A*AI*(DEL-GL-AMU)*BLAM1/BKAP1
FT2T = A*AI*(DEL-GL-AMU)*BLAM2/BKAP1
ARG = DEL
CALL ALAMDA (ARG,Y,BLAM1)
CALL ALAMDA (ARG,Y1,BLAM2)
CALL AKAPPA (ARG,BKAP1)
GAM = SQRT(DEL**2-SCRK**2)
S5 = SIN(SNS*GAM)
S6 = COS(SNS*GAM)
C1 =-1.0/(BETA*GAM*S5)
C1T = C1*(AI*SPS*T2*S6-SNS*DEL/GAM*T2*S5)-BLAM2/BKAP1*DEL/GAM*(S5
1 +GAM*SNS*S6)/(GAM*S5)
C1 = C1*(ARG/GAM*SNS*S5+AI*SPS*T2)-BLAM1/BKAP1*DEL/(GAM*S5)*(S5/
1 GAM+SNS*S6)
FT3 =-B*(BLAM1/BKAP1+(DEL-AMU)*C1)
FT3T =-B*(BLAM2/BKAP1+(DEL-AMU)*C1T)
IF (GL .EQ. 0.0) GO TO 50
F2 = FT2*(CEXP(2.0*AI*GL)-CEXP(AI*GL*S1))/(AI*GL)+
1 FT3*S0+B*AI*(DEL-AMU)*BLAM1/BKAP1*(4.0-S1**2)/2.0
AM2 = FT2*(2.0*CEXP(2.0*AI*GL)/(AI*GL)-S1/(AI*GL)*CEXP(GL*AI*S1)+
1 (CEXP(2.0*AI*GL)-CEXP(AI*S1*GL))/GL**2)+FT3*(4.0-S1**2)/2.0
2 +B*AI*(DEL-AMU)*BLAM1/BKAP1*(8.0-S1**3)/3.0
F2P = FT2T*T1*CEXP(AI*GL*SNS)/(AI*GL)*(CEXP(2.0*AI*GL)-
1 CEXP(AI*GL*S1))+FT3T*T1*S0+B*AI*(DEL-AMU)*T1*BLAM2/
2 BKAP1*(S0**2/2.0+SPS*S0)
AM2P = FT2T*T1*(CEXP(AI*GL*SPS)/(AI*GL)*S0*CEXP(AI*GL*S0)+
1 CEXP(AI*GL*SPS)/(GL**2)*(CEXP(AI*GL*S0)-1.0))+
2 FT3T*T1*S0**2/2.0+B*AI*(DEL-AMU)*T1*BLAM2/BKAP1*(S0**3/3.0+
3 SPS*S0**2/2.0)
GO TO 55
50 CONTINUE
F2 = FT2*S0+FT3*S0+B*AI*(DEL-AMU)*BLAM1/BKAP1*(4.-S1**2)/2.
AM2 = FT2*(4.0-S1**2)/2.0+FT3*(4.0-S1**2)/2.0+B*AI*(DEL-AMU)*
1 BLAM1/BKAP1*(8.0-S1**3)/3.0
F2P = FT2T*T1*S0+FT3T*T1*S0+B*AI*(DEL-AMU)*T1*BLAM2/BKAP1*(S0**2
1 /2.0+SPS*S0)
AM2P = FT2T*T1*S0**2/2.0+FT3T*T1*S0**2/2.0+B*AI*(DEL-AMU)*T1*BLAM2
1 /BKAP1*(S0**3/3.0+SPS*S0**2/2.0)
55 CONTINUE
NL2 = 20
RL2 = NL2 - 1
AA = SPS - SNS
CONST = B*AI*(DEL-AMU)*BLAM1/BKAP1
TEMP = S0/RL2
C1A = AI*GL
CEXP3 = CEXP(C1A*AA)
CEXP4 = CEXP(C1A*TEMP)
DO 455 JL = 1,NL2
XL = AA + TEMP*(JL-1)
PRES2(JL) = FT2*CEXP3 + FT3+CONST*XL
CEXP3 = CEXP3*CEXP4
455 CONTINUE
CALL SUBBB
RETURN
END
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