Барилович В.А. Основы термогазодинамики двухфазных потоков и их численное решение
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370
25 CONTINUE
26 CONTINUE
GVOUT=0.
F2V=0.
WP1=0.
VP1=0.
DO 27 I=1,NK
CALL SEVAL
(5,P(I),BAR,VPA,BVPA,CVPA,DVPA,VP,VPP,VPPP)
IF(I.NE.NK) G=DRS*HB*WP(I)/VP
IF(I.EQ.NK) G=(DRS-DELPL)*HB*WP(I)/VP
F2V=F2V+G*WP(I)*COS(ZERO)
GVOUT=GVOUT+G
WP1=WP1+(1./VP)*WP(I)
VP1=VP1+1./VP
27 CONTINUE
WP1=WP1/VP1
F1D=GK*(WKIN*(1.-X))
F1V=GK*WPIN*X
F2F=GPL*WPL*COS(ZERO)
FK=F1D+F1V+F2V+F2F
GDOUT=0.
IF(NR.EQ.0.) GOTO 29
DSIG=0.
DO 28 I=1,NR
DSIG=DSIG+FWK(I)*COS(ZERO)-RWK(I)*SIN(ZERO)
28 CONTINUE
CALL SEVAL
(5,TD,TEMP,VKAP,BVKAP,CVKAP,DVKAP,VK,VKP,VKPP)
DD=DK(I)
GD=SK/VK*HB*PI*DD**3/6.
GDOUT=GD*NR
F2D=GD*DSIG
FK=FK+F2D
29 RNK=U*FK
RNT=PROP*RNK
EFT=RNT/PTI
WRITE(4,111)
111 FORMAT(79(' ')/T2,'I',T9,'I',T23,'I',T29,'GK',T37,
& 'I',T43,'GPL',T51,'I',T57,'G',T65,'I',T71,'TG',T79,'I')
WRITE(4,112)
112 FORMAT(T2,'I______I',5('_____КГ/C____I'))
XIV
XIV
371
WRITE(4,113) VGK,DGK,GK,TG
113 FORMAT(T2,'I',T4,'IN',T9,'I',T12,F9.7,T23,'I',T26,F9.7,T37,
& 'I',T40,'0.0000000',T51,'I',T54,F9.7,T65,'I',T68,F9.5,T79,'I')
TGOUT=(GVOUT+GDOUT+GPL)*RBL*PROP/BL
WRITE(4,114)
GVOUT,GDOUT,GPL,GVOUT+GDOUT+GPL,TGOUT
114 FORMAT(T2,'I',T4,'OUT',T9,'I',T12,F9.7,T23,'I',T26,F9.7,T37,
& 'I',T40,F9.7,T51,'I',T54,F9.7,T65,'I',T68,F9.5,T79,'I')
WRITE(4,115)
115 FORMAT(T2,'I______I',5('______________I'))
WRITE(4,*) 'F1V=',F1V,'F1D=',F1D
WRITE(4,*) 'F2V=',F2V,'F2F=',F2F,'F2D=',F2D
WRITE(4,*) 'FK=',FK,'RNK=',RNK,'RNT=',RNT,' EFT=',EFT
WRITE(6,*)VOR,WPL,WP1,VISP,VP,VK
CLOSE(6)
STOP
END
SUBROUTINE DROP(FI,Y,YP)
REAL Y(4),YP(4)
COMMON /PHIS/ PI,DD,VISP,VISK,VP,VPP,VK,R2,R1,VPL
COMMON /BAR/ P0,PK,DP,CM,SK,RS,DRS,VOL,DG
COMMON /ENE/ ENTK,ENTP,EPTK,TP,CPK,EPL,EPPL,CPPL
CDR=CX(Y(1),Y(2),PK)*Y(3)/Y(2)
SQ=(2447.7-1.283*(TP-273.)-6.26E-3*(TP-273.)**2)*1E3
YP(1)=Y(2)-CDR*Y(1)
YP(2)=-Y(1)+CDR*(PK-Y(2))
YP(3)=Y(3)*Y(1)/Y(2)
YP(4)=ALKP(Y(1),Y(2),PK,TP,DD)*(Y(4)-
TP)*6.*Y(3)/DD*VK/Y(2)
& /CPK*(ENTK/SQ-1.)-1./CPK*(Y(1)*YP(1)+Y(2)*YP(2))
RETURN
END
SUBROUTINE VAP(FI,Y,YP)
REAL Y(7),YP(7)
COMMON /PHIS/ PI,DD,VISP,VISK,VP,VPP,VK,R2,R1,VPL
COMMON /BAR/ P0,PK,DP,CM,SK,RS,DRS,VOL,DG
COMMON /NET/ RT,TCKR,TTCKF,CV2,CV3,CV4
COMMON /ENE/ ENTK,ENTP,EPTK,TP,CPK,EPL,EPPL,CPPL
ENV=SET(Y(3),RT,Y(1),TCKR,Y(2),CV2,CV3,CV4)
ENV=PI*Y(7)**3*ENV/(6.-PI*Y(7)**3*ENV)
CX1=CX(Y(1),Y(2),Y(5))
CDR=CX1*Y(3)/Y(2)
XV
XVI
372
RW=Y(1)/Y(2)
SQ=(2447.7-1.283*(TP-273.)-6.26E-3*(TP-273.)**2)*1E3
RJKP=ALKP(Y(1),Y(2),Y(5),TP,Y(7))*(Y(6)-TP)/SQ
YP(1)=Y(2)-CDR*Y(1)
YP(2)=-Y(1)+CDR*(Y(5)-Y(2))
YP(3)=Y(3)*RW
DIFK=(CX1*Y(7)/VK+6.*RJKP)*(1.-Y(2)/Y(5))
YP(4)=-Y(5)/(1.+Y(5)**2*VPP/VP**2)*(DIFK+6.*
& RJKP*(1.-VK*Y(5)/(VP*Y(2))))*ENV*(RS-DRS/2.)/Y(7)
YP(5)=-VP*YP(4)/Y(5)-DIFK*ENV*(RS-DRS/2.)*VP/Y(7)
YP(6)=ALKP(Y(1),Y(2),Y(5),TP,Y(7))*(Y(6)-TP)*6.*Y(3)/Y(7)
& *VK/Y(2)/CPK*(ENTK/SQ-1.)-
1./CPK*(Y(1)*YP(1)+Y(2)*YP(2))
YP(7)=-2.*RJKP*Y(3)*VK/Y(2)
RETURN
END
SUBROUTINE FILM(FI,Y,YP)
REAL Y(3),YP(3)
COMMON /PHIS/ PI,DD,VISP,VISK,VP,VPP,VK,R2,R1,VPL
COMMON /GEO/ FIP,GCV,B1,L,FI1,XFI1,P1
COMMON /BAR/ P0,PK,DP,CM,SK,RS,DRS,VOL,DG
COMMON /ENE/ ENTK,ENTP,EPTK,TP,CPK,EPL,EPPL,CPPL
IF(Y(1).LE.0..OR.Y(1).GE.100.) RJPLP=0.
IF(Y(1).LE.0..OR.Y(1).GE.100.) GOTO 100
SQ=(2447.7-1.283*(TP-273.)-6.26E-3*(TP-273.)**2)*1E3
RJPLP=ALPLP(Y(1),Y(2))*(Y(3)-TP)/SQ
100 YP(1)=-DP/Y(1)*VPL+(CM-Y(1))*DG/Y(2)/Y(1)-
R2*Y(1)/Y(2)*WC(Y(1)
& ,Y(2))/2.
YP(2)=(DG-Y(2)*YP(1)-VPL*RJPLP*(R2-Y(2)))/Y(1)
IF(Y(1).LE.0..OR.Y(1).GE.100.) GOTO 200
YP(3)=1./(CPPL*Y(1)*Y(2))*(DG*(ENTK-EPL)+(EPL/SQ-1.)*(R2-
Y(2))*
& VPL*ALPLP(Y(1),Y(2))*(Y(3)-TP))-Y(1)/CPPL*YP(1)
200 CONTINUE
RETURN
END
SUBROUTINE EMPTY(FI,Y,YP)
REAL Y(2),YP(2)
COMMON /PHIS/ PI,DD,VISP,VISK,VP,VPP,VK,R2,R1,VPL
YP(1)=0.
YP(2)=0.
XVII
XVIII
373
RETURN
END
FUNCTION SET(RI,ROU,CKRI,CKROU,CKFI,CV2,CV3,CV4)
COMMON /BAR/ P0,PK,DP,CM,SK,RS,DRS,VOL,DG
RNV(A,B)=2.*SK*A/(B*RS*VOL)
RO=.5E-6
SET=CV2
CV2=CV3
CV3=CV4
RCX=CX(CKRI,CKFII,PK)
IF(ROU.LE.RS) SET=RNV(ABS(ROU-
RI)+RO,ABS(CKRI+CKROU)+RO)+SET
IF(ROU.GT.RS.AND.ROU.LE.RS+DRS) GOTO 1
IF(ROU.GT.RS+DRS.AND.ROU.LE.RS+2.*DRS) GOTO 2
IF(ROU.GT.RS+2.*DRS) GOTO 3
CM=0.
RETURN
1 PC=CKRI+(CKFI**2/CKRI/RI-RCX)*(RS-RI)
CM=CKFI+(-CKFI/RI+RCX*(PK-CKFI)/CKRI)*(RS-RI)
SET=RNV(RS-RI,CKRI+PC)+SET
CV2=RNV(ROU-RS,PC+CKROU)+CV2
RETURN
2 DCK=(CKFI**2/CKRI/RI-RCX)*(RS-RI)
PC1=CKRI+DCK
PC2=CKRI+DCK/(RS-RI)*(RS+DRS-RI)
CM=CKFI+(-CKFI/RI+RCX*(PK-CKFI)/CKRI)*(RS-RI+DRS)
SET=RNV(RS-RI,CKRI+PC1)+SET
CV2=RNV(DRS,PC1+PC2)+CV2
CV3=RNV(ROU-RS,PC2+CKROU)
RETURN
3 DCK=(CKFI**2/CKRI/RI-RCX)*(RS-RI)
PC1=CKRI+DCK
PC2=CKRI+DCK/(RS-RI)*(RS+DRS-RI)
PC3=CKRI+DCK/(RS-RI)*(RS+DRS*2.-RI)
CM=CKFI+(-CKFI/RI+RCX*(PK-CKFI)/CKRI)*(RS-RI+2.*DRS)
SET=RNV(RS-RI,CKRI+PC1)+SET
CV2=RNV(DRS,PC1+PC2)+CV2
CV3=RNV(DRS,PC2+PC3)+CV3
CV4=RNV(ROU-RS-2.*DRS,PC3+CKROU)
END
FUNCTION CX(RCK,FCK,PK)
COMMON /PHIS/ PI,DD,VISP,VISK,VP,VPP,VK,R2,R1,VPL
XVIII
374
DC=SQRT(RCK**2+(PK-FCK)**2)
REK=DC*DD/VISP/VP
CX=.45
IF(REK.GT.0.AND.REK.LE.1.) CX=24./REK
IF(REK.GT.1..AND.REK.LE.390.) CX=24./REK**.6667
CX=.75*CX*VK/VP*DC/DD
RETURN
END
FUNCTION WC(W,TH)
COMMON /PHIS/ PI,DD,VISP,VISK,VP,VPP,VK,R2,R1,VPL
REPL=W*TH/VISK/VK
IF(REPL.LE.400.) WC=4./REPL
IF(REPL.GT.400..AND.REPL.LE.1000.) WC=2E-7*REPL+.00992
IF(REPL.GT.1000.) WC=.057/REPL**.25
RETURN
END
FUNCTION ALKP(RCK,FCK,PKP,TP,DDD)
COMMON /PHIS/ PI,DD,VISP,VISK,VP,VPP,VK,R2,R1,VPL
REK=ABS(PKP-SQRT(RCK**2+FCK**2))*DDD/VISP/VP
PRP=1.28-4.4E-3*(TP-273.)+2.4E-5*(TP-273.)**2*1E-2
PLAM=(1.801+2.69E-3*(TP-273.)+3.02E-5*(TP-273)**2)*1E-2
ALKP=(2.+.6*REK**.5*PRP**.33)*PLAM/DDD
RETURN
END
FUNCTION ALPLP(WW,DWD)
COMMON /PHIS/ PI,DD,VISP,VISK,VP,VPP,VK,R2,R1,VPL
COMMON /GEO/ FIP,GCV,B1,L,FI1,XFI1,P1
COMMON /BAR/ P0,PK,DP,CM,SK,RS,DRS,VOL,DG
COMMON /ENE/ ENTK,ENTP,EPTK,TP,CPK,EPL,EPPL,CPPL
PRP=1.28-4.4E-3*(TP-273.)+2.4E-5*(TP-273.)**2*1E-2
IF(L.LE.FI1) XX=(R2-DWD)*L*PI/180.
IF(L.GT.FI1) XX=(R2-DWD)*(L-FI1)*PI/180.+XFI1
REX=ABS(PK-WW)*XX/VISP/VP
PLAM=(1.801+2.69E-3*(TP-273.)+3.02E-5*(TP-273)**2)*1E-2
ALPLP=PLAM/XX*.0296*REX**.8*PRP**.43
RETURN
END
SUBROUTINE
RKF45(F,NEQN,Y,T,TOUT,RELERR,ABSERR,IFLAG,WORK,
& IWORK)
EXTERNAL F
INTEGER IWORK(5)
XIX
XX
XXI
XXII
375
REAL Y(NEQN),WORK(1)
K1M=NEQN+1
K1=K1M+1
K2=K1+NEQN
K3=K2+NEQN
K4=K3+NEQN
K5=K4+NEQN
K6=K5+NEQN
K7=K6+1
C WRITE(5,*)' RKFS IN'
C PRINT *,'RELERR=',RELERR
CALL
RKFS(F,NEQN,Y,T,TOUT,RELERR,ABSERR,IFLAG,WORK(1),
&
WORK(K1M),WORK(K1),WORK(K2),WORK(K3),WORK(K4),WOR
K(K5),
&
WORK(K6),WORK(K7),IWORK(1),IWORK(2),IWORK(3),IWORK(4),
& IWORK(5))
C WRITE(5,*)' RKFS OUT'
RETURN
END
SUBROUTINE
RKFS(F,NEQN,Y,T,TOUT,RELERR,ABSERR,IFLAG,YP,H,F1,
& F2,F3,F4,F5,SAVRE,SAVAE,NFE,KOP,INIT,JFLAG,KFLAG)
LOGICAL HFAILD,OUTPUT
REAL
Y(NEQN),YP(NEQN),F1(NEQN),F2(NEQN),F3(NEQN),F4(NEQN),
& F5(NEQN)
EXTERNAL F
DATA REMIN,MAXNFE/1E-12,3000/
IF(NEQN.LT.1)GOTO 10
IF((RELERR.LT.0.).OR.(ABSERR.LT.0.))GOTO 10
MFLAG=IABS(IFLAG)
IF(MFLAG.EQ.0.OR.MFLAG.GT.8)GOTO 10
IF(MFLAG.NE.1)GOTO 20
EPS=1.
5 EPS=EPS/2.
EPSP1=EPS+1
IF(EPSP1.GT.1.)GOTO 5
U26=26*EPS
GOTO 50
XXIII
XXIV
376
10 IFGLAG=8
RETURN
20 IF(T.EQ.TOUT.AND.KFLAG.NE.3)GOTO 10
IF(MFLAG.NE.2) GOTO 25
IF(KFLAG.EQ.3.OR.INIT.EQ.0)GOTO 45
IF(KFLAG.EQ.4)GOTO 40
IF(KFLAG.EQ.5.AND.ABSERR.EQ.0.)GOTO 30
IF((KFLAG.EQ.6).AND.(RELERR.LE.SAVRE).AND.(ABSERR.LE.SA
VAE))
& GOTO 30
GOTO 50
25 IF(IFLAG.EQ.3)GOTO 45
IF(IFLAG.EQ.4)GOTO 40
IF(IFLAG.EQ.5.AND.ABSERR.GT.0.)GOTO 45
30 STOP
40 NFE=0
IF(MFLAG.EQ.2)GOTO 50
45 IFLAG=JFLAG
IF(KFLAG.EQ.3)MFLAG=IABS(IFLAG)
50 JFLAG=IFLAG
KFLAG=0
SAVRE=RELERR
SAVAE=ABSERR
RER=2.*EPS+REMIN
IF(RELERR.GE.RER)GOTO 55
RELERR=RER
IFLAG=3
KFLAG=3
RETURN
55 DT=TOUT-T
IF(MFLAG.EQ.1)GOTO 60
IF(INIT.EQ.0)GOTO 65
GOTO 80
60 INIT=0
KOP=0
A=T
CALL F(A,Y,YP)
NFE=1
IF(T.NE.TOUT)GOTO 65
IFLAG=2
RETURN
XXIV
377
65 INIT=1
H=ABS(DT)
TOLN=0.
DO 70 K=1,NEQN
TOL=RELERR*ABS(Y(K))+ABSERR
IF(TOL.LE.0.)GOTO 70
TOLN=TOL
YPK=ABS(YP(K))
C PRINT *,'YPK=',YPK
IF(YPK*H**5.GT.TOL) H=(TOL/YPK)**.2
70 CONTINUE
IF(TOLN.LE.0.)H=0.
H=AMAX1(H,U26*AMAX1(ABS(T),ABS(DT)))
JFLAG=ISIGN(2,IFLAG)
80 H=SIGN(H,DT)
IF(ABS(H).GE.2.*ABS(DT))KOP=KOP+1
IF(KOP.NE.100)GOTO 85
KOP=0
IFLAG=7
RETURN
85 IF(ABS(DT).GT.U26*ABS(T))GOTO 95
DO 90 KK=1,NEQN
90 Y(KK)=Y(KK)+DT*YP(KK)
A=TOUT
CALL F(A,Y,YP)
NFE=NFE+1
GOTO 300
95 OUTPUT=.FALSE.
SCALE=2./RELERR
AE=SCALE*ABSERR
100 HFAILD=.FALSE.
HMIN=U26*ABS(T)
DT=TOUT-T
IF(ABS(DT).GE.2.*ABS(H))GOTO 200
IF(ABS(DT).GT.ABS(H))GOTO 150
OUTPUT=.TRUE.
H=DT
GOTO 200
150 H=.5*DT
200 IF(NFE.LE.MAXNFE)GOTO 220
IFLAG=4
KFLAG=4
XXIV
378
RETURN
220 CALL FEHL(F,NEQN,Y,T,H,YP,F1,F2,F3,F4,F5,F1)
NFE=NFE+5
EEOET=0.
DO 250 K=1,NEQN
ET=ABS(Y(K))+ABS(F1(K))+AE
IF(ET.GT.0.)GOTO 240
IFLAG=5
RETURN
240 EE=ABS((-2090.*YP(K)+(21970.*F3(K)-15048.*F4(K)))+
& (22528.*F2(K)-27360.*F5(K)))
250 EEOET=AMAX1(EEOET,EE/ET)
ESTTOL=ABS(H)*EEOET*SCALE/752400.
IF(ESTTOL.LE.1.)GOTO 260
HFAILD=.TRUE.
OUTPUT=.FALSE.
S=.1
IF(ESTTOL.LT.59049.)S=.9/ESTTOL**.2
H=S*H
IF(ABS(H).GT.HMIN)GOTO 200
IFLAG=6
KFLAG=6
RETURN
260 T=T+H
DO 270 K=1,NEQN
270 Y(K)=F1(K)
A=T
C WRITE(5,*)'F IN'
CALL F(A,Y,YP)
C WRITE(5,*)'F OUT'
NFE=NFE+1
S=5.
IF(ESTTOL.GT.1.889568E-4)S=.9/ESTTOL**.2
IF(HFAILD) S=AMIN1(S,1.)
H=SIGN(AMAX1(S*ABS(H),HMIN),H)
IF(OUTPUT)GOTO 300
IF(IFLAG.GT.0)GOTO 100
IFLAG=-2
RETURN
300 T=TOUT
IFLAG=2
RETURN
XXIV
379
END
SUBROUTINE FEHL(F,NEQN,Y,T,H,YP,F1,F2,F3,F4,F5,S)
REAL
Y(NEQN),YP(NEQN),F1(NEQN),F2(NEQN),F3(NEQN),F4(NEQN),
& F5(NEQN),S(NEQN)
CH=H/4.
DO 221 K=1,NEQN
221 F5(K)=Y(K)+CH*YP(K)
CALL F(T+CH,F5,F1)
CH=3.*H/32.
DO 222 K=1,NEQN
222 F5(K)=Y(K)+CH*(YP(K)+3.*F1(K))
CALL F(T+3.*H/8.,F5,F2)
CH=H/2197.
DO 223 K=1,NEQN
223 F5(K)=Y(K)+CH*(1932.*YP(K)+(7296.*F2(K)-7200.*F1(K)))
CALL F(T+12.*H/13.,F5,F3)
CH=H/4104.
DO 224 K=1,NEQN
224 F5(K)=Y(K)+CH*((8341.*YP(K)-845.0*F3(K))+(29440.*F2(K)-
32832.
& *F1(K)))
CALL F(T+H,F5,F4)
CH=H/20520.
DO 225 K=1,NEQN
225 F1(K)=Y(K)+CH*((-6080.*YP(K)+(9295.*F3(K)-
5643.*F4(K)))+(41040.
& *F1(K)-28352.*F2(K)))
CALL F(T+H/2.,F1,F5)
CH=H/7618050.
DO 230 K=1,NEQN
230 S(K)=Y(K)+CH*((902880.*YP(K)+(3855735.*F3(K)-
1371249.*F4(K)))
& +(3953664.*F2(K)+277020.*F5(K)))
RETURN
END
SUBROUTINE SPLINE(N,X,Y,B,C,D)
DIMENSION X(9),Y(9),B(9),C(9),D(9)
NM1=N-1
IF(N.LT.2) RETURN
IF(N.LT.3) GO TO 50
D(1)=X(2)-X(1)
XXV