pure.tue.nl · ·~.r.:eling der technische !latuurkund~ vakgroep transportfysica ~e response of a...
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Eindhoven University of Technology
MASTER
The response of a turbulent boundary layer to a step change in surface roughness
Schols, J.L.J.
Award date:1979
Link to publication
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~; Drs. A.M. Kopp1'v..s
Pro.f. Dr. K. k'Y'I'shnc.t ~V'Cl5a.d
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B.IO
·~.r.:eling der Technische !latuurkund~
Vakgroep Transportfysica
~e response of a turbulent boundary layer to a • Titel: step change in surface roughness
Jacq L.JJ. Schols ~.,Auteur:
'• D:<ttum: May 1979
f. ~ocent/contactpersoon: prof.dr. D.A. de Vries
)e Begeleiders:
~. Afstudeerverslag no.:
~. Intern Rapport no.:
)., Korte ~~menvatting:
prof.dr. K.Krishna Prasad drs. A.M. Koppius
R-386-A
The calculation of the response of a turbulent boundary layer to a step change in surface roughness in determining transport processes is of vital importance in meteorology, and it will also lead to the development of a more comprehensible theory of turbulent shear flows. During this investigation a predietien methad developed by Bradshaw,Ferriss and Atwell(1967) is used to carry out the calculations. The turbulent shear stress appears to be the most difficult quantity to calculate,because it is much more sensitive to changes in boundary-conditiona than the longitudinal component of mean velocity. The obtained results are compared with data of wind-tunnel experiments.
l>e afdeling ::ler 'l'echnische Natuurkunde v!ln de 'l'echnir;che Eog·eschool
F:inrlhoven <l..:lnvRardt geen verantwoordelijkheid voor ·le inhoud VA.n c'iit
Vt~rr.:;l'lg/rappo!'t.De 'l'echnische ~[otT,eschool Eindhoven o.anvo.ardt rlerh!'llve
geen :-'anspr"'lkelijkhei<l. voor event·1ele .schade ont.st.~ .. ·tn door het opvolgen
van in het versVJ.g/rapport vermelrle s.dviezen.
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s•SET•THELIBRARY 'BEGIN' S'INCLUOE•"TURB/PICTURE"
$ 1000000+100 'fiLE'0UT,ORAWINU<KIND=PLOTTER11>~DRAWINTCKIND=PLOTTER11)~ DRAWINU1<KINO=PLOTTER11>•DRAWINU2CKIND=PLOTTER11)~ ORAWINT1<KIND=PLOTTER11>~ ORAWINOC~INO=PLOTTER11>~DRAWINC<KIND=PLOTTER11);
'fiLE'UBR<KIND=PACK~PACKNAME="USER1."~FILETYPE=7• TITLE="TURB/UBR.">;
1 FILE 1 TBR<KIND=?ACK~PACKNAME="USER1."~FILETYPE:7, TITLE="TURB/TBR.">;
•FILE 1 LW (KI~D=PACK~PACKNAME="USER1·"~fiLETYPE=7~ TITLE="TURB/LW .");
1 fiLE•GW CKINO=PACK~PACKNAME="USER1."~fiLETYPE=7~ TITLE="TURB/GW .");
1 fiLE 1 GAFW <KINO=PACK~PACKNAME="USER1."~FILETYPE=7• TITLE="TURB/GAFW.">;
'fiLE'URW<KINO=PACK•PACKNAME="USERl."•fllETYPE=O•UNITS=WOROS, MAXRECSIZE=240,BLOCKSIZE=240,TITLE="TURB/UR·">;
'FILE'TRWCKIND=PACK,PACKNAME="USERl."•fiLETYPE=O~UNITS=WOROS• MAXRECSIZE=240~BLOCKSIZE=240~TITLE="TUR8/TR.");
'fiLE 1 URR<KIND=PACK~PACKNAME="USER1.",fiLETYPE=7~ TITLE="TURB/UR.">;
1 fiLE 1 TRR<KINO=PACK~PACKNAME="USER1."~fiLETYPE=7~ TITLE="TURB/TR.">;
1 INTEGER'K•I•Q,JMAX,I1MAX•J•Z~QMAX,RAS,COUNf,JHAX•BE~SUBTRACT; 1 BOOLEAN 1 PR~CGN01•CON02~CON03.CONDI~WR~SMOOTH~AL~PAL~STOREi
1 BOOLEAN 1 PLOT~TEXf,PRINT~PLOTL~PLOTH.TPL; 'B00LEAN'ADAP,K1~SK~BR~Rc~ROUGH.SPL~As.sYNTH~sc~LOGLAWi
1 1NTEGER'TEL~II~IMAXO.zJ,NR·N~KC,KU,KB~BK~STP,Jl,J2,LR;
00002000 00003000 00004000 01000000 01000100 0100u110 01000120 01000130 01000200 0 lOCO 300 01000400 01000500 01000600 01000700 01000800 01000900 01001000 01001100 01001110 01001120 01001130 01001140 01001150 01001160 01001170 01001180 01001200 01001300 0100140;) 01001500 01001600
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U1 I
'REAL'OELTAO~YSTEP•A~MX,XST.Uf,HMl•HH2•UDUOX•KK•AA,OELl•DEL2•MT, ACCU• MI ·EO, t4~ ... XHA x~
Cf..,sL..,USTER ... crT ... REOO ... Mr ... ToO ... TON•XO ... UO ... MN•RETHETAO ... MfA,MfR•XTR•OH~CH, f,,rN.THETA.OELST,X.XSTEP,H,Oif•DELTA,CHO•CHl~SHAPE,RH,XRTR,RY; 'REAL'ALfA•VCHO•VCHl.ALfAP·UfO ... EKSP•BLS•YP,UT,T.TAUO.CfO;
'REAL'OCU; •REAL 11 ARRAY'
MINMAXU..,MINMAXT,MINMAXD•MINMAXCC1:4l• ~INMAXU1,MINMAXU2 ... MINMAXT1C1:4],
XP,CfP,CfLQG,CfLUTI•CfHINZE,CfROTTA.DELTAH,OELTAP.OQDP,THETAP.Uff,HP• 0 ELS T P.., R PC 0 : 90 1 ,
Y,LNY,RCU·RCT(0:40l ... C0Ef•COC0:1], r1.r2 ... r3 ... ua.ra.rco:21J;
'STRING'C0MMENTUC60J,COMMENTTC60l•TEXTXASUC30J,TEXTXASTC30J, CO MM EN 0 ( 60 J, C 0 MME N CC 60 J • TE X T X A SC • T EX T X AS DC 30 J, T EXT Y AS D ( 3 0 l •
TEXTYASCC 30J ... TEXTYASUC30l ... TEXTYASH 30], C0MMENTU1C60J,COMMENTU2C60l ... COMMENTT1C60l• TEXTX ASU1C30J .TEXTX ASU2( 301 .TEXTXAST1C301 • TEXTYASU1C30J..,TEXTYASU2C30J,TEXTYAST1C301i
$ 2000000+100 ' P R 0 CE 0 URE ' 0 A Y T I ME C OU T > ; 'fILE • 0 UT; 'BEGIN•
'INTEGER'HRS•MIN•SEC; 'REAL'R; SEC:=TIMEC1>160i MIN:=SEC'DIV'60i SEC:=SEC·CMIN*GO>; t-4RS:=HIN'OIV'60; MIN:=MIN-<HRS*60); W R I TE ( 0 U T , < 1 e ( " *" > I " * " .., X 1 6 • "*"I "*. 0 AT E_ : " ~ A 2 • C 4 • " ___ * " t• *" • X 16 ~
"*"/"*.TIME :"•I2~":"..,I2,":",I2 ... " *"/"*"•X16•"*"/ 1B<"•">II/>;R:=TIMEC15>•R•HRS ... MIN;SEC>;
'ENO•PROCEDURE OAYTIME; %7.%%%%%%X7.%%%%%%%4%%%%%%%%%%%%%%%%%%%%%7.%%%%%%%%%%%%%%%%%%%
%%%%%%%%7.%%%%%%%%%7.%%%%%%%%%7.%%%%%%%%7.%%%%%%%%%%%%%%%%%%%%%
0100i700 01001710 01001800 01001900 01002000 01002010 01002100 01002300 01002350 01002450 01002451 01002500 01002600 01002700 01002750 01002800 01002810 01002820 01002830 02000000 02000100 02000200 02000300 02000400 02000500 02000600 02000700 02000800 02000900 02001000 02001100 02001200 02001300 02001400 02001500 02001600
I CP ' tv o--1
1 PROCEOURE 1 MAXVALUE< A,.N,.K,.HX>; 'VALUE'Ni 'INTEGER •N.Ki 'REAL' MXi 1 REAL 1 'ARRAY 'A( •H 1 8EGIN 1
'INTEGER 1 Ii M X : = A [ 0 1i K : =0 ; 1 FOR•I:=1 1 STEP'l'UNTIL'N • o o • • Ir • Ac I 1' G TR • M x
'TH EN I I BEG I :\1 I
MX:=ACiliK==I 'END'
'EN0 1 PROCEDURE MAXVALUE; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%1.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
'PROCEDURE 1 TH ICKNE SS CC U,. UD ,.Q ,.K H 1 VALUE 1 UD;
'INTEGER'IO 1 REAL 1 Uo,.o;
1 RE A L 1 1 A R RA Y • CU [ * 1 ; 'BEGIN'
1 RE AL 1 I ; I:= 1;
1 WrliLE 1 CUCil 1 LSS•UO I 00 • I :=I~ 1;
K:=r;o:=cUctli •ENO•PROCEDURE THICKNESS; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 'REAL 11 PROCEOURE'SIMPSONCF,.A,.B,.Hl; 1 V A LU E' A,. 8,. H; • r N rE GE R • A,. B; 'REAL •H; 1 REAL 11 ARRAY 1 FC•H 1 BEGIN'
02001700 02001800 02001900 02002000 02002100 02002200 02002300 02002400 02002500 02002600 02002700 02002800 0200290:> 02003000 02003100 02003200 02003300 02003400 02003500 02003600 02003700 02003800 02003900 02004000 02004100 02004200 02004300 02004400 02004500 02004600 02004700 02004800 02004900 02005000 02005100 02005200
, CP . rV ~
I
•INTEGER' I; •REAL•S: •IF•B·A•NEQ'2•CCB•A>'OIV 1 2> ' TH EtJ ' '8 EG I N '
S:=3•<FCB1•FCB-1J)/2; •FOR•I:=A 1 STEP 1 2 1 UNTIL'B-2 'DG'S:=S+FCI1+4•FCI+ll+f(I+21
•ENO• ' EL SE' ' BEGIN '
S: =O; 1 FOR•I:=A•STEP•2•UNTIL 1 B•1 'D0'S:=S+FC!l+4*F(I+ll+FCI+21
•END•; SIMPSON:=S•H/3
'END' PROCEDURE SIMPSQN; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 1 PROCEOURE 1 LINTERPOL<f,fF,N,OT>; 'VALUE'N,OT: 'I~TEGER' N; •REAL•DT; 1 RE AL 1 ' ARRAy t F, F f( * 1; 'BEGIN'
'lr-.&TEGER'l,Ji J: = o; ' FO R' I: = 1' ST EP' 1' U NT I L' N t DO • • BEGIN'
'WHILE'J'LEQ'I*DT 1 00' 'BEGIN'
•END' i
FFCJJ:= FCI•11+(J/OT·<I·l>>•CfCil•FCI•11>; J:=J+1;
1 E NO ';
ff(JJ:=FCN-11+< J/OT•<N·l>>•<FCNJ•f[N•11>; 'END'PROCEDURE LINTERPOL; XX%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%7.%%%%%%%%%~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
02005300 02005400 02005500 02005600 02005700 02005800 02005900 02006000 02006100 0200&200 02006300 02006400 02006500 02005600 02006700 02006800 02006900 02007000 02007100 02007200 02007300 02007400 02007500 0200760() 02007700 02007800 02007900 02008000 02008100 02008200 02008300 02008400 02008500 02008600 02008701) 02008800 02008900
t O'J • N GO
I
•PROCEOURE•HERLINTPOLCNFl~Nf2,Nf3,YI~f1YI,f2YI,F3YI,uf,OEL•MM,ySJEP, TEKEN,N,z>;
1 VALUE 1 Uf,OEL,M~~N~YSTEPi 'INTEGER•N,.z;
1 REAL 1 UF,OEL,MM,YSTEPi 'BOOLEAN' TEKEN; 'REAL 1 'ARRAY'Nft,Nf2,Nf3~YI,F1YI,f2YI,F3YIC•li
'BEGIN' • INTEGER' I ,p ,Q, IN; 'lf'TEKEN 1 TH EN ' ' BEGIN '
P:=UQ:=OiiN:=2i 'E f~O'
•ELSE"BEGIN' P : =0 ; Q: = 1 ; I N : = 1 ;
•END'; 1 FOR 1 I:=IN 1 STEP'l'UNTIL 1 N
1 00"BEGIN' F2YICIJ:=Nf2[I-Pl+CYICIJ-YSTEP•<I-P>>IYSTEP
•<NF2CI+Ql-NF2CI-PJ)i fl'f Hil:=NF1C I-PJ +( YHIJ•YSTEP•CI-p))/YSTEP
* C NFlC I +Q]·NFH I-PJ >; F 3 Y I (ll : = NF 3 (I- P 1 + < Y I(! l ·Y ST EP*< I •P > > /Y 5 T EP
•<NF3(I+Ql-NF3CI•Pl>i 'EN 0';
'ENO'PROCEOURE HERLINTPOL; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% X%X%%%XXX%%%Z%%X%%%%%%%%%%XXX%%%%%XX%%%%%%%%%%%%%%%%%%XXX%% 1 PROCEDURE•MECCU,N,J,YSTEP,UF,UOUOX,XST,fO,fN,THETA,DEL2,QELST,H~DIF~
T D 0 , T 0 N, M f·, CHO, CH 1, SG ,z H
'VAL~E'N,J,YSTEP,Uf,UDUDX,XST,TO,fN,DEL2,TOO,TDN,HFi 1 INTEGER•N,J,z;
1 REAL'YSTEP .. Uf,UOUDX,XST,TO,TN,DEL2,THETA,DELST,H,Oif,CHO,CHl,SG,TOO, TON, Hf;
1 REAL' 1 ARRAY'CU(•li
02009000 02009100 020C9200 02009300 02009400 02009500 02009600 02009700 02009800 û2009900 02010000 02010100 02010200 02010 300 02010400 02010500 02010600 02010700 02010800 02010901) 02011000 02011100 02011200 020113CO 02011400 02011500 0201160j 02011700 02011800 02011900 02012000 02012100 02012200 02012300 02012400 02012500
' CP . ~
I
1 13EGIN• 'INTEGER'!; ' RE AL ' A ,. B}
A : = S I MP S 0 N ( CU ,. Z -1 ,. N ,. Y ST EP >I U f"; 'f"OR' r:=O'STEP' 1' UNTIL' N 'D 0 'CU C IJ : = C UC I J * * 2;
B:=SIMPSONCCu,.z-1,.N,.YSTEP>ICUf"••2>; 1 FOR•I:=O•STEP 1 1'UNTIL'N ' D 0 ' CU ( I 1 : = S QR TC C U ( I l >; 'lF 1 J•GEQ 1 1 1 THEN••BEGIN'
CHO:=CH H C 1-1 1: = < 0 • 5 *X S T I C U F * * 2 > * C C T N • T 0 - T 00 • T 0 N > * M f" * * 2 -U 0 U 0 X* CDELST+OEL2-A•2•CHO>>+CHO>I<1+UOUOX•XSTICUF**2>>;
OIF:=CCHl·CA-B>>ICA•B); • E NO' ;r HET A: =A- 8; 0 ELS T: = OEL2 • A; H: =DEL ST I TH ET A;
SG:=UF/MF/SQRTCTN>•C1-1/H); 'IF 1 J=O I TH EN ' ' BE G I NI
OIF:=O;CH1:=THETA; 'ENOt:
'END • PRO CEOURE ME; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1 PROCEOURE'VTAN<CU,.cT,.NF2,.CV,.TANl,.TAN2,.RV,.A,.MM,.UF,.UOUOX,.YSTEP,.IMAX,. ~F,. Z > ;
'VALUE'A,.MM,.IMAX,.Uf,.UOUOX,.YSTEP,.Hf"; 1 INTEGER 1 IMAX,.z;
1 REAL•A,.MM,.UF,.UOUOX,.YSTEP,.MF; 'REAL''ARRAY'CU,.CT,.CV,.NF2,.TANl,.TAN2,.RV(*]; 'BEGIN'
• INTEGER' I; •REALtf; •FOR• I:=0 1 STEP 1 11 UNTIL 1 Z-1
1 00'CVCIJ:=TANl(Il:=TAN2CIJ:=RVCIJ::Q; CV ( Z l : = RV ( Z l : =0; T:=SQRT<CA•NF2(Z1•MM/UF*MM•MF••2>••2+2•A•CTCZJ•MF••2>;
02012600. 02012700 02012800 02012900 02013000 02013100 02013200 02013300 02013400 02013500 02013600 02013700 02013800 02013900 02014000 02014100 02014200 0201430\l 02014400 02014500 02014&00 02014700 02014800 02014900 02015000 0201510() 02015200 02015300 02015400 02015500 02015600 02015700 C2015800 02015900 02015901 02015902 02016000
, CP • u.J 0 t
TAN1CZJ:=CCVCZl+A*Nf2CZl*MM/Uf*HH*Ht**2+Tl/CUCZJ; TAN2CZJ:=CC~Zl+A•Nf2CZl•MH/Uf•HH•Hf••2·T)/CU(ZJ;
• FORti: =z + 1 •S T EP' 1 'U NT IL' I HAX 'DD"BEGIN'
CV C I ]: =CC U C I l * C VC I •ll -c CT C I J ·CT C I •1 J > * H F• *2 • UDUDX*YSTEP>ICUCI•1];
T:=SQRT< CA*Nf2Cil•MM/UF•HH•Hf••2>••2+2*A*CTCIJ•HF••2J; TAN1CIJ:=CCVCI1+A•Nf2Cil*MM/UF•HH*HF••2+Tl/CUCI]; TA N 2 (l l := <CV C I l +A *N F2 (I l*HH /Ut* MH *H f• * 2 •T ) I CU C I l; RVCil:=CVCil/CUCIJ;
'END' 'END• PROCEDURE VTAN; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%X%%XXXX%%%%%%%X%%XX%X X%%%%%%%%%%ZXX%%%%%%%%%%%%%%%%%X%%%%XX%%%%%%%%%%%%%%%%%%%%% 'PROCEDURE'INTPROFCCU,cT,UI,TI,YI,N,TEKEN,TANI,YSTEP,XSf,z,REP,QUT>; 'VALUE•N,YSTEP,XST;
'INTEGER'N•z; 'RE AL 'Y ST EP • X ST;
•FILE•OUT; •BOOLEAN•TEKEN,REP;
' RE AL t • AR RA Y ' CU , CT, U I , T I , Y I , T A N I [ * l ; '8E.GIN'
'INTEGER•I,IN,K; 'REAL'SLOPE;
•IFtfEKEN •THEN'lN:=2 •ELSEtiN:=l;
•FOR•I: =IN+Z•1•STEP'1'UNTIL'N·1 •DO"BEGIN'
YICIJ:=YSTEP•I·TANICil•XST; UICtl:=CUCIJ+ 1!<2•YSTEP>•CCUCI+1l•CUCI-11>
•<YICIJ·YSTEP•I>+ 0.51CYSTEP•*2>•CCU(I•1J+CU{I+11•2•CUCI1) •<YICIJ·YSTEP•I>••2;
TH I l:=CT (I l+ 11< 2•YSTEP>•CCTCI+1 J•CTCI-1 1>
02016100 02016200 02016300 0201640J 020165oa 02016600 02016700 02016800 02016900 02017001) 02017100 02017200 02017300 02017400 02017500 ()2017600 02017700 02017800 02017850 02017900 0201800~ 02018100 02018200 02018201 02018300 0201840P 02018500 02018600 02018700 02018800 02018900 02019000 02019100 02019200 02019300
I 0' •
(J.) -f
•< YICI J•YSTEP•I>+ 0.5/CYSTEP••2>•<CTCI-1l+CTCI+tl·2•CTCIJ> •< YICI J•YSTEP•I >••2;
'Ir 1 TICIJ•LEQ 1 01 THEN''BEGIN' WRITECOUT~<t~~J=~~r3~/~~IMAX=~~t3~"I="~I3~"TI="~r12.7>~J~IMAX~I~Titil>;
WRITECOUT~</r"XST="~rl2.4>~XST>;WRITECOUT~</~"TEKEN=">}r W R I TE ( 0 UT, I, T EKEN> ; ' EN 0 1 ;
'ENDt; 1 IF••NOT 1 TEKEN 1 THEN' UICZJ:=CUCZJ+<CUCZ+ll·CUCZJ)/LN<CZ+l>IZ>•LN<YICZJ/YSTEP/Z);
'EN0 1 PROCEDURE. I~TPROrr %%%%%7.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 1 PROCEOURE 1 SIGPHil<r1YI,r2YI,r3Y!,UirTirSirPl•A•XSTrUDUDX~MMrTEKlN,N~
UrrMrrOELlrZ>; 'VALUE'A~UDUOX~MM~N,XST,Mr~DELl~Ur;
1 INTEGER •N.z; ' RE AL ' A , U OU D X ~ M M , X S T, M r , 0 EL 1 ~ U r ; 1 REAL''ARRAY 1 rlYirr2YI~r3YI~UI,TI~SI,PI(*]; 1 BOOLEAN' TEKEN; 'BEGIN'
1 INTEGER' I, I ~; 1 Rt:AL•SIGN; 1 Ir'TEKEN t T HEN I ' BEG I N t s I GN : = 1; I N : = 2 I EN 0. 1 ELSE 1 'AEGIN 1 SIGN:=-t;IN:=t•EN0 1 r
•FOR•t:=tN+Z·1•STEP'l'UNTIL 1 N-1 'DO" BEGIN'
SICil:=f2YICIJ•MM••2/Ur•MF••2+SIGN•SQRT<CF2YICil•MM••2/Uf• MF••2>••2+2•TICIJ/A•MF••2>;
PH I l: =TI C I l *U I C I J -C. 5• SIr I l *TI CI l + XS T* TICIJ/UICil•CUOUDX+A•CSQRTCTICIJ>•Mr/OELl/flYi(Il+ F3YICIJ•MM••2•Hf**2/DEL1/UF>•SICIJ>r
•ENO•; 'END• PROCEDURE SIGPHil; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%1%%%%%%%%%%%%%%%%7.%%%%%%% %%%%%%%%%%%~%i.%%%%%%%%%%%~ï.%%%%%%%%%%%%%%%%%%%%%%%%%%X%%%%%
02019400 02019500 02019600 02019610 02019620 02019630 02019640 02019700 02019705 02li19710 02019800 02019900 02020000 02020100 0202020~ 02020300 020 20 400 02020500 02020600 02020700 02020800 02020900 02021000 02021100 02021200 02021300 02021400 02021500 02021600 02021700 02U21800 02021900 02022000 02022100 02022200 02022300 02022400
J cP • Q) tv I
'PROCEOURE'NEWPROFCSt~s2~Pt~P2~Tt~rz~cr~cu~KK~AA~YSTEP,IMAX,REP,wR~ RC,MM2,UF~F2Y2~Nt2~F3Y2~Nr3~PR~J,II~Y1,Y2,
REOQ,M~l,MF,OEL1,AOAP~RH~OCU,QCT,TANl~TAN2,
F1Y2,NF1,U1~U2,DEL2~Xsf,UDUOX,A,z,our,ALFA,RY,AS,TR~BK,EO); 'VALUE•KK,AA,I~AX,YSTEP,XST~OEL2,UOUDX~A,MM2,UF,J,
REDO,OEL1,MF,MM1; t I NT EG ER ' I MA X, J , I I , Z , 8 K; 'REAL'KK,AA~YSTEP,XST,DEL2,UOUOX~A,MM2~UF,RH,REDO~Mr~OEL1,MM1,ALFA,EQ,
RY .. TR; 1 BOOLEA~'REP,PR~WR,AOAP~RC,AS;
'REAL''ARRAY 1 Sl,S2,P1,P2,f1,f2~cr,cu,NF1,F1Y2,Ul,U2,F2Y2,NF2,F3Yi,NF3,
Y1,Y2,QCU,OCT,TAN1~TAN2(*]r
•FILE• OUT; 'BEGIN'
'I NT EGER' I, BOU ND; 'REAL'T~TAUS,UST,US,UR,TM1,TM2,UM,LM,TM,GM,GAFH,USTR,TAUR,ALFAR~HPLUS;
•REAL 1 HM~YP,UT,FAC; •REAL' 'ARRAY 'Y Y ,RCT[ t: 40 J, CO ,CORCO: 1];
1 REAL''PROCEDURE'VELCYP,UT>; 1 VALUE•yp; 'REAL'YP,UT; • BEGIN'
VEL:=UT+EXPC·AA>•<EXPCKK•UT>•l•KK•UT· ( K K *UT)* *2 /2-( KK•UT>••3/6• <KK•UT>••4/24• <KK•UT>••5/120-{KK•UT>••6/720>·YP;
'END' PROCEDURE VEL; t RE AL ' • P R 0 C E D U RE ' NU L < TA US ); t RE AL tf AUS; 'BEGIN' •FILE 1 0UT;
02022500 02022600 02022700 02022800 02022900 02023000 0202310:> 02023200 02023300 02023400 02023500 02023600 02023700 02023800 02023900 02024000 02024001 02024100 02024101 02024102 02024103 02024104 02024105 02024106 02024107 02024108 02024109 02024110 02024111 0202420() 02024300 02024400 02024401
J 0' .. o.> IJ.)
I
CHBKJ:=T~USi • fOR' I: =1 • STEP 11' UN TIl' 3 '00' ' BEGIN'
YYCIJ:=YSTEP•<BK·1+!)i RCTC IJ :=CTC BK•1 +I H
1 END'; LEAST SQUARES POLYNOMIAL<YY,RCT,3,1,CO>i Alf A: =COC 11;
C TC 0 J : = TA US- Alf A* Y S TE Pi • If 1 AS 1 THEN' CTCOJ :=TAUS;
UST:=SQRT<CTCOJ>i US:=UST/KK•<LN<BK•UST•YSTEP•REDO>+AA-
2•LN< < SQR T< TAU St CT[ 01) +1 >t2> + 2• ( S Q RH TAUSIC T ( 0 l > ·1) H
'lftREP 'T HEN' 'BEGIN 1
TAN2CBKJ:=-SQRT<2•A•TAUSJ/USi Y2(BKl: =YSTEP•BK•XST•TAN2[ BK];
f 1 Y 2( BK]:= Nr H BK 1 + < Y2 ( Bt\l -BK* YS T EP> /Y ST EP*( Nf 1 (BK+ 1 J· Nf 1 [BK l J; T2CBKJ:=OCTCBKJ+.5/YSTEP•COCTCBK+1J•OCTCBK-1l>•<Y2(8Kl•BK•YSTEP>+
.5t<YSTEP••2>•<0CTCBK·1J+OCTCBK+1J·2•0CTCBKJ)• CY2[BKl•BK•YSTEP>••2;
U2CBKJ:=OCUCBKJ+COCUCBK+ll•OCU[BKJ)/LN<<BK•l>IBK>*LN<Y2CBKJ/BK/YSTEP>; LM:=<f1Y2(BKl•OELl+Nfl(8Kl*DEL2)/2i UM:=<U2CBKl+US)/2i TM:=<T2(8Kl+TAUS>/2i
•EN0 1
'ELSE''BEGIN 1 UM:=U2CBKJiTM:=T2CBKJiLM:=flY2CBKl*OEL1;•EN0'i S2CBKJ:=-SQRT<2•TM/A)i P2[8KJ:=TM •U2CBKJ•0.5•S2[8Kl•T2(8K]+
XST•TM/UM•<UOUOX+A*CSQRT<TM>ILM>* S2CBKJ);
NUL:=TAUS·2•<TM•US·P2CBKJ )/S2(8Kli 'END' PROCEDURE NUU
02024416. 02024420 02024421 02024422 02024423 02024424 02024425 02024426 02024428 02024429 02025200 02025300 02025400 02025500 02025600 02025700 02025701 02025702 02025703 02025704 02025705 02025706 0 20 25 70 7 02025751 02025800 02025900 02025905 02025910 02026000 02026100 02026200 02026300 02026600 02026624
I CP . u>
..!:" \
•REAL ••PROCEOURE'NULR<TAUR>; 'REAL'TAUR;
•BEGIN••FILE•OuT; ~STR:=SQRTCTAUR); .
UR :=USTR/KK•<LN< CYSTEP+EO>!RH>+3.1•KK); 'IF"'REP 'THEN• •BEGIN'
TAN2CZJ:=-SQRTC2•A•TAUR>IUR; Y2CZl :=Z•YSTEP·XST•TAN2CZJ; flY2CZJ:=NF1CZl+CY2(ZJ·Z•YSTEP>IYSTEP•<NF1CZ+ll•NF1CZJ>; T2CZJ:=OCTCZ1+.5/YSTEP•<OCTCZ+lJ•OCTCZ•ll)•CY2CZl-Z•YSTEP>+
.SICYSTEP••2>•<0CTCZ-ll+OCTCZ+1J-2•0CTCZJ>• CY2CZJ·Z•YSTEP>••2;
U2CZJ:=OCUCZl+COCUCZ+lJ-OCUCZJ>/LNCCZ+l>IZ>•LN<Y2(ZJ/Z/YSTEP>; LM:~F1Y2CZJ•DEL1+NF1CZJ•DEL2>12;
- -··-~-----
UM:=CU2CZl+UR)/2; TM :=CT2CZl+TAUR>/2;
'E NO • 1 ELSE 1 'BEGIN'U~:=U2CZJ;TM:=T2CZJ;LM:=F1Y2CZl•OEL1;•ENO•; S2CZJ:=•SQRT<2•TM/A >;
P2CZJ:=TM •U2CZJ•O.S•S2CZl•T2CZ1+ XST•TM/UM•CUOUOX+A•<SQRT<TM>ILM>•
S2CZJ>; NULR:=TAUR-2•<TM•UR•P2CZll/S2CZJ;
' EN 0 1 P R D CE 0 U R E NUL R; . 1 IF"N0T'RC 'THEN''BEGIN'
•FOR•I:=BK+l 1 STEP'1 1 UNTIL'IMAX•l •oo••BEGIN'
'IF' 'NOT' REP ' TH E N' ' BE G I N'
TM1:=T1CIJ;TM2::T2CIJ;•EN0' • ELS E 1 ' BEGIN' TM1 ::(TH I l+CTC IJ l/2; TM2: =<T2C I l+CTC 11 )/2;
'EN 0';
02026630 02026631 02026632 02026633 02026638 0202664() 02026641 02026642 02026643 02026644 02026645 02026646 C2026647 02026648 02026649 02026650 02026651 02026652 02026653 02026654 02026655 02026656 02026657 02026658 02026659 0202670() 02026701 02026710 02026720 02026730 02025740 02026750 02026760 02026710 02026780. 02026790
\ CP . \)l Ul I
T:=S1CIJ•TM2 -S2CIJ•TM1 ; CUC I J:=<S'lC Il *P2( Il •S2[ Il•P1[ Il >ITr CTCIJ:=CTM1 •P2CIJ-TM2 •P1CIJ>/T•2;
'END'; •IF•REP tTHEN• 'BEGIN'
1 IF'AS 1 T~EN'FAC:=a·2'ELSE•FAC:.:.7; •IF•ZERO IN AB<NUL<TAUS),TAUS,FAC•TR,G•TR,a•&,a•&>
1 THEN' 'BEGIN' CHBKl:=TAUS;
'F OR ' I : = 1' STEP ' 1' U NT I L ' 3 1 00 1 •9EGIN' _
YYC I1 :=CBK•1+I>•YSTEP; RCTCI J:=CTCBK•1+I H
1 E NO t; LEAST SQUARES PCLYNDMIAL<YY,RCT,3,1,CO>; ALFA:=C0(11;
'FDR' I:=O' STEP 1 1 1 UNTIL 1 BK-1 •o0• 1 BEGIN 1 CTCI1:=TAUS-ALFA*YSTEP;'IF 1 AS'THEN'CTCil:=TAUS;•ENO•; UST:=SQRT<CTCOJ>; C U [ BK J : =U S T I K K * < L N< B K *U ST * Y S T EP *RED 0 ) + A A •
2•LN< CSQRT<CHBKl/CTCOJ >+1>12>+ 2•CSQRT<CTCBKJ/CTC01>·1>>;
1 IF 1 BK>1 1 THEN"BEGIN 1
1 F0R' I:=BK' STEP 1 -l'UNTIL 1 1 'D 0 ''BEG IN'
YP:=SQRHCH OJ >*YSTEP•REDO•I; •IF'ZERO IN AB<VEL<YP,UT>,uT,C,UF/SQRT<CTCOJ>,a·G,a-6>
• TH EN ' • BE GI N ' ' I F ' I= BK 'TH EN' M M :=UT* S QR T <CT CO 1 >; •IF•I<BK 1 THEN 1 CU(IJ:=UT•SQRT<CTCOJ>+CUCBKJ·MM;•ENO•
'EL SE ' 'BE GI N' WR I T [(OUT, <I, "NO-sOL UT ION- FO R-uT", X 4," I=", I 3, X4,"J:",I3>,I,J>;WRITECOUT,</"UT=",X8,"VEL=",/>); T:=UF/SQRT<CTCOJ);
•FOR•UT:=0,.1,.2,.3,.4,.5,.6,.7,.8,.9,1 1 DO•WRITE<OUT,</,F8.4,X8,F8.4>,UT•T,VEL<YP,UT•T>>;
ALARM<'< 'NO·SOLUTION-FOR·UT• >' H
1 ENQ•; 1 ENO'
'END' ; 'END' ;
02026800 02026810 02026820 02026830 02027000 02027100 02031600 02031700 02031800 02031810 02031820 02031830 02031840 02031850 02031860 0203187() 02031920 02031930 02031931 02031932 02031933 02031934 02032006 02032007 02032008 02032009 02032010 02032011 02032012 02032013 02032014 02032015 02032016 02032017 02032018 02032019 02032020 02032021 02032022 02032500
' Cf' • uJ c;-. I
1 ELSE 1 'BEGIN• WRITECOUT~<I~"N0-SOLUTION-FOR-TAUS"~X4~"J="~I3>~J>;
h RI TE C 0 UT • <I~ " AS= .. > ); WR I TE ( 0 UT~ I~ AS > ; hRITECOUT•<I~"REP=">);WRITECOUT~I~REP>;
WRITECOUT,<I~"TAUS="•X6~"NUL="~I>);
'FOR tT AUS: =él- 3•. 7~ 1• 2~ J~ 4, ~. 6, 7
'00 1 WRITECOUT,<I~F8.4,X6~F8.4>~TAUS•TR~NULCTAUS*TR>>;
AL AR M < ' C ' NO • S 0 LU T I 0 N - F 0 R - TA U S ' > ' >; 'E NO 1 ;
CUCOJ:=O; 'E NO' ;
•tF•RC 'THEN''BEGIN' z:=u
'END';
1 FOR•I:=Z+1 1 STEP'l'UNTIL•IMAX•1 •00 1 'BEGIN'
' I F ''NOT ' REP ' T H EN 1
' 8 EG IN '
I
TM1:=T1CIJ;TM2:=T2CIJ;•ENO• 'ELSE''BEGIN' TM 1 : =< T H I J +CT C I l >I 2; TM2:=CT2C I l+CTCil>IV
tEN 0 t ; T:=SUil•TM2 -S2CIJ•TM1 ; CUC I J:=<S lC IJ •P2C IJ -S2C IJ•PH IJ >lH CTCIJ:=<TMl •P2CIJ•TM2 •P1CIJ>IT•2;
'END';
02032600 02032700 02032710 02032750 02032800 02032900
02033100 020332GO 02033300 02034COO 02035000 02035010 02035050 02035051 02035052 02036000 02036001 02036002 02036003 C2036004 02036005 02036006 02036007 02036008 02036009 02036010 02036011 02036012
OJ • (,).)
'1-1 I
'IF'REP 'lHEN••BEGIN'
1 IF 1 ZERO IN AB<NULR<TAUR>,TAUR,.25•TR,10•TR,a-G,a-G> •THEN"REGIN 1
•FOR•I:=O•STEP• l'UNTIL'Z ' 0 0 'CT ( I l : =TA UR; USTR:=SQRT<CTCOJ>; 1 F 0 R 1 I : = 0 ' STEP' 1 ' U NT I L' Z- 1 ' 0 0 1 C U C I 1 : =0 ;
CUCZ1:=USTR/KK•<LN<<YSTE?+EO>/RH>+3.1•KK); •END'
'ELSE''BEGIN' HRITECOUT,</,"NO-SOLUTION-FOR·TAUR",X4r"J=",I3>,J>;
WRITE<OUT,</r"REP=">);WRITE<OUTr/rREP); WRITE<OUT,</r"TAUR="rXGr"NULR="r/>);
'F 0 R 'T A U R: =. 2 , 1, z, 3, 4, 5, 6, 1, 8, 9, 10, 11 1 00 1 WRITE<OUT,</,f8.4rX6rf8.4>,TAUR•TR,NULR<TR*TAUR>>;
ALARM< 1 ( 1 NO-SOLUTION-FOR·TAUR• >• >; 'E NO' ;
'END•; 1 ENO•;
'END'PROCEOURE NEWPROF; %%%%%%%%%%%7.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 9 PROCEDURE•SIGPHI2<flYirF2YlrF3YirNF1rNF2rNf3,UirTI,CU,CTrSI,PirA,XST,
UDUDXrMM2rUFrOEL2rTEKEN•N,MH1,DEL1,MfrZ>; 1 VALUE 1 ArXST,UDUOXrMM2rUFrOEL2•NrMMlrDELlrMf;
'lNTEGER•N,z; 'REAL'ArXST.UOUOXrMM2rUFrDEL2rMMlrDEL1,MF; 'B00LEAN 1 TEKEN; 1 REAL''ARRAY 1 F1YI,F2YirF3YirNFl,NF2rNF3,ui,TlrCU,CTrSirPIC*l; 'BEGIN'
'INTEGER• I, I~; •REAL'SlGN,GM,fM,UM,LMrGAFM;
02036050 02036051 02036052 02036053 02036C54 02036055 02036056 02036057 02036058 02036063 02036090 02036091 02036100 02036101 02036102 02036103 02036104 02036105 02036110 02036120 02036130 02036500 02036600 02036700 02036800 02036900 02037000 02037100 02037200 02037300 02037400 02037500 02037600 0 20 37 700
CP . U)
00
'
•.If" 'TEKEN ' TH EN 1 ' BEG I N 'S I GN : = U I N : = 2' EN 0' 1 ELSE''BEGIN'SIGN:=·1;IN==1'ENO';
'f" OR' I: =IN +Z -1 'STEP' 1' UN TIL' N -1 ' 00 • • BEGINt
GM:=<f"2YICIJ•MM1/Uf+Nf"2Cil*MM21Uf)/2;
TM::CTICI J+CTCI 1>12; UM:=<UICIJ+CUCIJ>/2; LM:=<fl YI CI J•OELl+Nfl(I l•OEL2J/2; GAfM:=Cf"3YICil*MM1/DEL1/Uf+Nf3CIJ•MM2/0EL2/Uf)/2; SICil:=GM*MM2*Mf*•2+SIGN*SQRT<<GM•MM2•Mf••2>••2+2•TM/A*
Mf••2); PH I J:=TM•UH IJ·O.S•SH Il•TIC IJ
'E NO';
+XST•TM/UM•CUOUDX +A•<SQRT<TM>•Mf/LM+GAfM•MM2•Mf••2>•SICIJ>;
•EN0 1 PROCEDURE SIGPHI2; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%i.%%%%%%%%%%%%%%%%%i.%%%%%%%%%%%%%%%%%%
1 PROCEOURE•DEV<CU,cT,LCU,LCT,QU,QT,N,z); 'VALUE' N;
'INTEGER•N,z; 1 REAL 11 ARRAY•cu,cr,ou,oT,LCU,LCTC•J; 'BEGIN'
'INTEGER • I; 'f"OR•I:=O•STEP'l•UNTIL'Z-1 1 00'
OTCOl:=<CTCOl•LCTtOJJ/LCTCOJ; . 1 f0R'I:=Z 1 STEP 1 11 UNTIL'N
1 00"BEGIN' OU (I 1: = < CU( IJ-L CUC I 1 )/LC UC IJ; 0 TC I l : = < C H I l • L C TC I J ) I LC TC I J ;
'ENO' 'ENO'PROCEOURE OEV; %%%%%%%%%%%%%%%%%%%%%%%%%%1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%i.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%i.%%%%%%%i.
02037800 02037900 02038000 02038100 02038200 02038300
0 20 38400 02038500 02038600 02038700 0203880i) 02038900 02039000 02039100 02039200 02039300 02039400 02039500 02039600 02039700 02039800 02039900 02040000 02040100· 02040200 02040310 02040320 02040400 02040500 02040600 020 40 700 02040800 02040900 02041000 02041100
I CP . I.>)
\..S)
I
'PROCEOURE•REAOO~TA<fiLE~N~x~Y>; 'VALUE'Ni 'INTEGER' Ni 'ARRAY' X,YC•H 1 fiLE•fiLE; 'BEGIN'
•INTEGER'Ki REAO Cf!LE~•,•FOR'K:=O•STEP 1 1 1 UNTIL•N•DO•XCKJ>; READ CfiLE'*''fOR'K==~'STEP 1 1 1 UNTIL•N•DO•YCKl)i
'END'PROCEDURE READDATA; XX%%%%%%%%%~%%~%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
' RE AL ' ' P R 0 C E D U RE ' V E L < Y P ~ U Tl ; 'VALUE'YPi 1 REAL 1 YP~ur;
'BEGIN • VEL:=UT+EXP<-AA >•<EXP<KK•UT>-1-KK•UT•
( K K *UT> * •2 I 2-CKK•UT>*•316-<KK•UT>••4/24-< K K •U Tl* •51120-<KK•UT>••61720>·Y~;
' EN 0' P R 0 CE D U R E V EL ; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
•PROCEDURE•WRITEOATA<fiLE'N'X,Y>; 'VALUE•N; ' 1 NT EG ER • N; 'ARRAY'l(,Y(•]; •FILE• FILE; 'BEGIN'
'lNTEGER•K; WRITE<flLE'*''fOH•K:=O•STEP•l•UNTIL•N•OOtX[K]); WRITE<fiLE,•~•roR•K:=O'STEP'l'UNTIL'N'00'Y(Kl>i LOCK<fiLE,CRUNCH>i
•END •PROCEDURE \<!RI TE DATA; %%%%%%i.%%%%%i.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%i.%%%%%%%%i.i.i.i.
02041200 02041300 0201.1400 02041500 02041600 02041700 02041800 02041900 02042000 02042100 02042200 02042201 020422()2 02042203 02042204 02042205 02042206 02042207 02042208 02042209 02042210 02042211 02042300 02042400 02042410 02042420 02042430 02042440 02042450 02042460 02042470 02042480 02042490 02042500 02042510
I CP • ..1':: 0 l
$ 3000000+100 'PROCEOURE 1 PROf<CU~cr~cv~Rv~IMAX~TAN1~TAN2.F1,f2~f3~YSTEP~
XST~J~II,AOAP~UO•RH~ MF ~RE DO , T DO ~ T ON, ·oELl~DEL2~Rc.PR ~uf,MH1,MM2~A~UOUOX~KK,AA~WR•Z~OUT•
ALfA~RY.AS~PRINT.ACCU•MI•TR,BK~Eo>; 1 VALUE•DEL1,Uf,HM1~A·UDUOX,KK,AA~XST,YSTEP~J•Hf,REOO;
'INTEGER•IMAX~J,II•Z•BKi •REAL'XST.YSTEP,OEL1•DEL2•RH.UD ,ur.MH1,MM2,A,UOUOX•KK~AA~Hr~TDN,TDO~
ACCU~MI·TR•EO~ R E 0 0 , AL f A , R Y ;
• RE AL'' ARRAY' CU~ CT, CV • RV ~TA N1 ~ T AN2 ~ f 1~ f z, f 3 C * H 'BOOLEAN•PR~WR,AOAP~Rc~As~PRINTi
•rtLE•our; 'BEGIN'
' I N T E GE R • I , K , I H AX A; 'REAL'f;
'REAL'O~MX.MVi 1 REAL''ARRAY'U1~uz,T1,T2•Y1~Yz, Nf1,Nf2~Nf3~f1Y1•~1Y2,f2Y1~f~Y2, f3Y1,F3Y2~s1~s2~P1~P2[0:2.1•IMAX+1l~
L C lJ ~ L CT • 0 CU , OC T , 0 U • D T , A 0 U ~ A 0 H 0 : < 2 • 1 * I M A X + 1 > • 0 I V • 5 l ; 1 f 0 R' I : = :> ' ST EP ' 1' U NT I L ' I MA X 1 0 I V ' 5 1 00"BEGIN'
0 CU [ IJ : =C U [ I l ; 0 CT ( I 1 :=CT [ I 1 'ENo•;
lNTPROF<Cu.cr~ul.Tl~Y1.IMAX,•TRUE•,TAN1~YSTEP,XST,z~•fALSE•~OUT>;
I NT PROf (CU~ CT, U2, T2 ~ Y 2, I M AX ~' f ALS E' ~ T AN 2, YS TE P, XS T ~ Z • 'f AL SE'~ OUT); 'f0R•I:=IMAX•4 1 STEP'l'UNTIL'IMAX•1
'00"BEGIN 1
t I F • T 2 ( I J < 0 ' 0 R 1 (f 1 CI l = 0 ' A N D' T 2 [I J = 0 ) 'THEN• •BEGIN•T2CIJ:=T2CI-1J;WRITE<OUT,</•"IMAX="~I3,"I="~I3>•IMAX~I>i
WRITE<OUT~</,wVALUE-OF-SHEAR·STRESS·CORRECTED">); 'END•; • I f • T 1 [ I 1 < 0' 0 R ' CT 1[ I l = 0 • A N 0 • T2 C I l = 0 ) 1 THEN' '8EGIN'T1CIJ:=T1CI-1J;WRITE<OUT~</•"IMAX="~I3•"I="•I3>,IMAX~I>;
WRITE<OUT,</~"VALUE-Of-SHEAR-STRESS·CORRECTED"•/>);•ENO•;
'E NO t;
03000000 03000100 03000200 0 3000 300 03000400 03000500 03000600 03000700 03000800 03000810 03000900 03001000 03001100 03001200 03001300 03001400 03001500 03001600 030017(10 03001800 03001900 03001901 03001902 03001903 03001904 03002000 03002100 03002110 03002120 03002130 03002140 03002150 030C2153 03002154 03002155 03002160
1 o::> .
..J::" -I
LINTERPOLCF1,NF1,2l,(IHAX>t20>r LINTERPOL<F2,NF2,21,<IMAX>t20>; LINTERPOL<F3,NF3,21•<IHAX)/20>;
HERLINTPOLCNf1,NF2,NF3,Y1,F1Yl,F2Y1,F3Y1,UF,OELl•HMl,YSTEP•'fRUE'• IMAX,z>;
HERLINTPOL<Nf1,NF2,Nf3,Y2,f1Y2,F2Y2,F3Y2,UF,OEL1,MM1,YSTEP,•FALSE•, IMA X, Z);
SIGPHI1Cf1Yl•F2Y1,F3Yl,U1,T1,Sl•Pl•A•XST•UDUOX,MMl•'TRUE•, IMAX,Uf,Hf,OELl,Z>;
SIGP~I1CF1Y2,F2Y2,F3Y2•U2,T2,S2,P2,A,XST,UDUOX,MM1,•FALSE•,
IMAX,UF,MF•DELl,Z>; NEWPROF<Sl,S2,Pl,P2,fl•T2,CT,CU,KK,AA,YSTEP,IMAX ,•FALSE•,wR,
RC,MM1,Uf,f2Y2,NF2,f3Y2,NF3,PR•J•II•Yl•Y2• REQO,MMl,Mf,OELl•ADAP,RH•OCU,QCT,TANl,TAN2,
F1Y2,Nf1,Ul,u2,0ELl•XST,UOUOX,A,z,ouT,ALFA,RY,AS,TR,BK•EO>; oEvccu.cr.ocu.ocr.ou,or.IMAX'DIV'5·Z>;
1 FOR• t: =O•STEP '1 1 UNTIL 1 IMAX'OIV'5 '00 ' ' BEGIN •
ADUC I 1 :=ABS< DUC I l >; AI)TC I l :=ABS ( OTC I l );
'END t; MAXVALUE<AOU,IMAX 1 DIV•5•K•MX);T:=HX;Hv:~OU[K];
M A X V AL U E C A D T , I MA X • 0 I V ' 5 , I , H X H MX:=MAXCT,MX l;
•IF•HX'EQL•T 1 THE~' 'BEGIN'
I: =K; •IF 1 PRINT'THEN'WRITE<OUT•</•"VELOCITY:",/>);
'ENO''ELSE''BEGIN'MV:=OTCIJ; •IF•PRINT•THEN'WRITE<OUT,</,"SHEAR•STRESS:",/>);tEND•;
'If 1 PRINT'THEN'WRITE<OUT,</,"I="•l3•X4•"MAX·REL·OEV="•F8.4•///>,l,HV);
0 3003000. 03003100 0 3003200 03003300 03003400 03003500 03003600 03003700 03003800 03003900 03004000 03004500 03004600 03004700 03004800 03004801 03004802 03004803 03004804 03004805 03004806 03004807 03004808 03004809
03004812 03004813 03004814 03004815 03004816 03004617 03004818
I 'Ç>) -t::" ~ I
ACCU:=< 1+MV>•ACCU;M I :=MI +H THICKNESS<CU~uo~o~K>;
•rr•o-cucK-ll'LSs•o.ooz•o 1 THEN•K:=I(-U
OEL2:=K•YSTEP; TON ::CT CK H
IMAXA:=K; M~2:=SQRT<CTCIMAXA'OIV'4J>;
o:=o; 'THRU' I1'00' 1 BEGIN 1
03004820 03004900 03005000 03005100 03C05200 03005300 03005400 03005500 03005510 03005600
0:=0+1; 03005611 LINTERPOL<F2~NF2~21~IMAXA/20>; 030Q5700
VTAN<cu~cr~NF2~cv~TAN1~TAN2~RV~A~MM2~ur~uOUOX,YSTEP,IMAX 1 01V 1 5,Mf,z); 03005800 INTPROF<OCU·OCT,U1,T1~Y1,IMAX'01V'5~•TRUE•,TAN1,YSTEP,XST~z~•TRUE•,OUT>i03005900 INTPROF<OCU·OCT,U2,T2,Y2.IMAX'DIV'5,•FALSE'~TAN2,YSTEP~xsr~z~•TRuE•~ 03006000
OUT); 03006010 LINTERPOL<f2,Nf2,21•<IMAX>t20>; 03006100
LINTERPOL< F1~NF 1,21 ~< IM6.X )/20 H 03006200 L INTERPOL< F3~NF3,21~< IMAX >t20 >; 03006300
HERLINT?OL<NF1~NF2,NF3~Yl~F1Yl~f2Yl,F3Yl~ur~OELl~MM1~YSTEP,•rRUE'~ 03006400 IMAX 1 D!V'5~z>; 03006500
HERLINTPOL<Nfl,NF2~Nf3,Y2~FlY2~f2Y2~f3Y2,Uf,OELl~MMl,YSTEP~'fALSE•, 03006600 IMAX'OIV'5,Z>; 03006700
LINTERPOL<fl,Nf1,21,IMAXA/20>; 03006800 LINTERPOL(f2,Nf2,21,IMAXA/20>; 03006900 LINTERPOUf3~Nf3, 2l•IHAXA/20H 03007000 SIGPHI2<F1Y1.F2Yl~F3Yl,Nfl~NF2~NF3~Ul,Tl,CU,CT,Sl~P1~A~XST ,uOUOX, 03007100
MM2~ur,OEL2, 1 TRUE'~IMAX 1 0IV•5~MM1~0El1,MF,z); 03007200 SIGPHI2<F1Y2,F2Y2~f3Y2~NFl~NF2~NF3,U2~T2,CU,cT,s2,P2~A~XST ,UOUOX, 03007300
MM2,UF~OEL2,'FALSE'~IMAX 1 DIV 1 5,MM1~0EL1~MF,z>; 03007400 t f 0 R • I : = 0 ' S T EP ' 1' U N T I L ' I M A X ' 0 I V 1 5 0 3 0 0 7 5 0 0 'OO"BEGIN' 03007600
LCUC Il: =CU( I H LCTC 11 :=CT( Il 03007700 •ENOt; 030C7800
I \j) .
..1::' <.Y I
NEHPROF<Sl.S2,Pl,P2,Tl,T2,CT,CU,KK•AA,YSTEP•IMAX'DIV'5•'TRUE'•WR• RC,MM2,UF,F2Y2•Nf2,F3Y2.~F3,PR,J,Il•Yl,Y2•
RED0,MM1,Mf,DEL1,ADAP,RH,QCU,QCT,TAN1,TAN2• F1Y2.NF1,Ul,u2,DEL2.XST,UDUOX,A,z,our,ALFA,RY,AS•TR•BK,(0)i
DEV<CU,CT.LCU,LCT•DU,OT,IMAX'OIV'5•Z>; 'FO R. I: =0. sTEp '1. UN TIL. I MAXI DI V I 5 • DO I • BEGIN'
Af)U[ IJ :=ABS (OU( IJ H A 0 T ( I l :=A BS < D T C I l > ;
'END'; HAXVALUE<AOU,IMAX 1 0IV 1 5•K•MX>iT:=MX;MV:=OU(Kli M AX V AL U E < A 0 T , I MA X ' 0 I V ' 5, I , M X > ;
MX:=MAX<T,MX); 'lr 1 MIC •EQL'T 'THEN' 'BEGIN'
I: =K; 1 IF•PRINT 1 THEN 1 HRITE<OUT,</•"VELOCITY:",/>)i
'END''ELSE''BEGIN'MV:=OTCili 1 IF•PRINT•THEN 1 WRITE<OUT,</•"SHEAR-STRESS:",f>>i•END•;
1 IF 1 PRINT'THEN'HRITECOUT•<I•"I="•I3,)(4,"MAX•REL-DEV="•F8.4,///>,1•MV>; 1 IF•PRINT 1 THEN'WRITE<OUT,</•"NR-OF•INNER-IT.="•I3,/>•D>i
ACCU:=<l•M~)*ACCUiMI:=MI+Ii 1 lr 1 PRINT 1 THEN 1 WRITE<OUT.</•"CUM.-REL··DEV.="•F12.4•/,"MEAN
INDEX="•F8.4,/>,ACCU•l,MI/J/(l+O>>; 'END•:
IMAX:=IMAXAi •E~O•PROCEOURE PROF; %%%%%%%%%%%%%%%%Z%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%4%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%~%%%%%%%%%%%%%%%%%4%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%7.%%%%%%%%%7.%7.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
03007900 03006000 03008100 03008200 03006300 0300831() 03006320 03008330 03008340 03008350 03008400 03008410 03008420 03008502 03u08503 03008504 03008505 03008506 03008507 03008508 03008510
C3008511 03008512 03008513 03008600 03008700 03008800 03008901) 0300900() 03009100 03009200
t o:> •
...t:-..e.:-
s 4000000+100 PLOT:=•f"ALSE•;
TEXT:=•f"ALSE'; PRINT :=•f"ALSE•; PAL:='TRUEt; STORE:=•f"ALSE•;
OAYTI HE <OUT H LOGLAH := 'TRUE'; PLOTL:=•TRUE'; PLOTH:='TRU[•;
A~:= 'f AL SE'; SYNTH:='f"ALSEt;
z:=UBK:=U NR:=20; SC:='f"ALSE';
RC:=•f"ALSE•; ROU GH: = • TRU E• ;
SM 0 0 TH:=' FA LS E '; WR:=•f"ALSEt;
PR:='f"ALSEt; AOAP: ='fALSE •;
K 1 : = ' fA L SE ' ; SK:='f"ALSEt;
BR:='TRtJE•; AL:= 'TRUEt; II ::U
IMAXO:=SQ; / OELTA0:=4.8~·2;Ur0:=5.49;Mf::1;TAUO::O.OS1;cr0:=34a•4;
'If"•ROUGH•THEN''BEGIN' RH:=.0254/8;EQ:=.ó4*RH;•ENO•; EKSP:=7;
BL S: =. 15; BL:=BLS;
A==o.ts; QHAX:=20;
JMAX: =200;
04000000 04000001 04000002 04000003 04000004 04000005 0400C100 04000110 04000120 040CC130 04000200 04000300 04000400 04000500 04000600 04000700 0400080:l 04000900 040\)1100 0400120() 04001300 04001600 04001700 04001800 04001900 04002000 04002100 04002200 04002210 04002300 04002400 04002500 04002600 04002700 04002750
f CP . ..1:'" U1 I
'BEGIN' 'REAL''ARRAY'STATPR[Q:QMAXJ.rR, UU.TT.TTANl.TTAN2.VV.RV.RRV,CT.CU.CV.TANl,TAN2•ABSTAN2•Nf2•
ccu.ccrco:2.l*IMAX0+2l; REAODATACURR.2l•F•UB>i READDATA<TRR.21•F•TB)i
REAODATA(LW,2l•f•Fl >i READDAT A< GW·2l•F .F2>; READDATA<GAFW.2l•f•F3>i
'IF'SYNTH 'THEN' 'BEGIN' .
WRITE<OUT,</•"SY~THETIC-PROFILES:",/• "U/UF=CY/DELTA)**Cl/EKSP>"•/• "T/TW=l-<YIDELTA>•CU/UF>••2"•/• "EK SP=", F ó. 2, I> , EK SP) i
1 FOR' I:=O• STEP 1 1 1 UNTIL•21 'D 0' ' BEGIN '
•ENO•; •roR•uouox:=O '00" BEGIN•
Q::J::();
UBCIJ:=0.995•C0.05•I>••<11EKSP>; TBCI1:=1·0.05*I*UBCIJ••2i
'ENO 'i
ACCU:=liMI:=Oi IMAX:= IMAXOi
LINTERPOLCUR.CU.21,IMAX/20>; LINTERPOL<TA•CT•2l•IMAX/20>;
'FOR' I:=O•STEP'l'UNTIL'IMAX 1 D0"8EGIN•
CUCil:=CUCil•UFQ; CT ( I l : =CT [I 1 *TA lJ 0;
1 ENo•;
04002800 04002900 04002901 04002902 04003000 04003100 04003200 04003300 04003400 04003500 04003600 04003700 04003800 04003900 04004000 04004100 04004200
04004300 04004400 04004500 04004600 04004700 04004800 04004900 04004901 04005000 04005100 04005200 04005210 04005220 (14005230 04005240 04005250
I ry .
..c..-c--l
1 If•RC•THEN••BEGIN' RE A 0 0 A T A ( U R R , I M A X , f R , CU H REAOOATA<TRR,JMAX,fR,CT>;
'END•; uo: =O. 995•ur o;
Ut: =U fv; 0 EL 1: =DEL TA 0; YSTEP:=OELl/IMAX;
'IF•ROUGH 'THEN'WRITECOUT,</,"ROUGHNESS-CHANGE",I>);
'lf 1 BR 'THEN' 'BEGIN'
WRITE<OUT,<I,"BRAOSHAW",I>>; 'E NO';
'lf'Kl 1 THEN"BEGIN•
WRITECOUT,</"KESSELS",/>); X 0: = 40 '*OE L T AO; KK:=.4;AA:=2.096;REOO:=l/l.S7a-5;
'ENOt; TN:=TAUO;CTCOl:=TAUO;
'IF 'B R 'THEN''BEGIN'
RE 0 0 : = 1/ 1 • 5 7- •5; KK:=0.41;AA:=2.132iX0:=61*0ELTAO;
•ENOt; 1 IF 1 AL 1 THEN 11 BEGIN'
X0:=2.44;KK:=.41;AA::2.009;REOO:=li1.4--S; WRITE<OUT,</,"ANTONIA-ANO-LUXTON",I>li
1 IF 1 RC 1 THEN'X0:=3.62; ' END ';
1 IF 11 NOT'RC 1 THEN''BEGIN 1
K:=ENTIERCBL*IMAX); •FOR• I:=K•STEP•·l'UNTIL'l '00' 'BEGIN'' IF' SQRTCCTCO l>•YSTEP*I*RE00' GEQ 1 40 1 THEN 1
C.U C I l :=CU C I+ 11 ·S Q RT < C TC 0 l >I KK *L N < ( I+ 1 >I I l; 'E NO •;
'ENOt;
04005260 04005261 04005262 04005263 04005300 04005400 04005500 04005601 04005602 04006400 04006500 04006700 04006800 0400691)0 04007000 04007100 C4007200 04007300 04007400 04008400 0400920:> 04009300 04009400 04009500 04009550 04009560 04009561 0 40095.62 04009563 04009570 04009580 04009601 04009602 04009603 04009604 04009614 04009615
\ .'()) . ..c-...1
I
'Ir •SORTC CTC 0)) •Y STEP•REDO•Mf'LSS' 40 'T~EN' •BEGI~" Ir' 'NOT'RC'THEN'
W R I TE < 0 UT , < I , " M E SH - P 0 I N T< S > -A T - X 0 - 8 EL 0 W - T U R SU L E NT - C 0 R E" , I , "UST•DY/NU=",r8.4,f>,SQRTCCTCOJ>•MF•REDO•YSTEP>;
K:=Oi YP:=SQRT< CTCOJ >•YSTEP•REDO•Hr;
'WHILE'K•YP'LSS 1 40 1 D0'K:=K+l;sK:=K;
YP:=K•YP;•IF' 'NOT•RC'THEN'
WRITE<OUT,</,"NUMBER•OF-FIRST•MESH•POINT•IN·TURBULENT-CORE:", I3,1,"UST•Y/NU<IN-THIS•MESH-POINT>=",F8.4,/>,K,YP);
'END•; ' I F 1
' N 0 T ' R C ' T H EN ' ' B E G I N ' 'IF•BK>l 1 THEN"BE{i!N'
• F 0 R' I :=BK' ST EP '·1' UN TIL' 1 '0 0 ''BEGIN'
YP: =SQ R HC H 0 l >•YS TEP•REOO •I; •IF•ZERO IN AB<VEL<YP,UTl,UT,O,UFISQRT<CTCOJ>,~-6,~·6)
1 TH EN' 'BE GI N' ' I F' I= BK 'TH EN' M M :=UT *S Q R T ( CT ( 0 l > ; •IF 1 I<BK 1 THEN'CUCI1:=UT•SQRT<CTC0l)+CUCBKJ·MM;•EN0 1
1 ELSE''BEGIN'WRITE<OUT,</,"NO·SOLUTION·FOR·UT",x4,"I=",I3, X4,"J=",I3>,I,J>;WRITE<OUT,</"UT=",X6,"VEL=",/>); T : = UF IS QR T< Cf( 0 1 H
•roR•uT:=o,.t,.2,.3,.4,.5,.6,.7,.s,.9,t 1 0 0 • WR I TE< OUT,< I, F 8. 4, X 8, F 8. 4>, UT* T, VEL< YP, UT* T) H
ALARM<'< 1 NO·SÖLUTION·FOR·UT 1 ) 1 );
'END'; ' EN 0' ;
'ENOt; 'ENDt;
04009620 04009621 04009622 04009623 04009624 04009625 04009626 04009621 04009628
04009629 04009630 04009631 04009639 04009640 04009641 040C9ó42 04009&43 04009644 C4009645 04009646 (.\4009647 04009648 04009649 04009650 04009651 04009652 04009653 04009654 04009655 04009&56 04009657
f c:P • ~ C7.)
I
'lf''NOT'RC'THEN'BE:=l'ELSE'BE:=Z; ME<CUiiMAXrJrYSTEPrUfrUDUOXrXSTrTOrTNrTHETArDELlrOELSTrHrDIFrTOO.TONr
f<!f • CH 0, CH 1 r SH AP Er BE >; DELSTP(QJ:=10•DELSTIDELTAO;QQDPCOJ:=O.S•DEL110ELST;HPCOJ:=H;
THET APCOJ: =THETA;UFPCOJ: =UF; 'IF 'K 1 'THEN" BEGIN'
1 FOR 1 J:=0 1 STEP 1 11 UNTIL'IMAX t DO • CH I l : = < 1.• C CU C I l I UF 0 > * * 2* I* Y STEP I OE l TA() >*TA UO;
'ENOt; •IF•CTCIMAXl'LSS'O 'THEN 1 'BEGIN'
HRITECOUT,</r"NEGATIVE•VALUES•OF•STRESS-AT•EOGE•CORRECTED"r/>); I:~IMAX; 'WHILE 1 CTCIJiLSS 1 0 •oo•I:=I-U K: =H •FOR•I:=K+1'STEP'1 1 UNTIL 1 IMAX
• DO 1 CT ( I 1: =C H KJ* C I MA X+ 1• I )/ C I MA X·K); CT [K +11 : = (CT [ K l +CT C K + 2 l) /2;
•E NO'; STATPRC01:=2.S4; STATPRC1J:=2.69; ST AT P R [ 21 : =2 • 9 s; STATPRC31:=3.33; STATPRC 41 :=3 .sa; ST AT P R C 51 : =4 • 2 2;
STATPRC 6 ]::4. sa; XTR: =2. 44;
XRTR:=STATPRC 1 H X MA X : = 3 • 6 2 ;
WRITECOUTr</r"VISCOSITY="rE10.4r/r"MF="rF8.4r/r"KK="•F6.4r/, "AA="rF8.4r/r"X0="rF6.4r/rftREYNOLOS•NO.="•E10.4r/>, 1/ REOOrMFrKKrAArXOrREOO•XO•UFOH
x:=xo; K:=ENTIERCBL•IMAX);
1 FOR•I:=l'STEP'1'UNTIL'K 1 00"BEGIN 1
F 1 { I l : = F 1 [ I l * K K/ 0 • 4; 1 END'i
04009&59 04009&60 04009&61 04009662 040096&3 04009670 04009671 04009672 04009673 04009674 04009700 04009800 04009900 04010000 04010100 04010200 04010300 04010400 04010500 04010600 04010700 04010800 04010900 04011000 04011100 04011200 04011300 04011400 04011600 04011700 04011750 04011800 04011900 04012000 v4012too 04012200 04012300 04012400 04012500 04012600
l (5J . .J::· \.Sj
I
WRITECOUTr</r"IMAX:",I3,X2r"VEL.-AT•EOGE:",F6.4r/>•IHAX.UOl: TO:>:=CTCIHAXJ;
Mt'il:=SQRHCTCIMAX'OI V'4l); MINHAXUl(l]::Q;HINMAXU1[2J:=.S;MINMAXU1[3)::0;MINMAXUlC4]::ZO;
MINMAXU2(1J:=O:MINMAXU2[2J:=.3;MINMAXU2C3l:=O;MINHAXU2[4l:=1.3; MI~HAXTlClJ::O;MINMAXT1[2J:=.l;HINMAXT1[3]::0;MINHAXTlC4J:=10;
COMMENTUl:=• <'VELO CITY-DEFECT• P; COMMENTU2:=•< 1 VELOCITY '> •; C0MMENTT1:=• ( 'SHEAR-STRESS• l •;
T EX TX AS U l: = • ( ' ( Y +EO >*US TI UF I 0 ELS T' l'; TE X T X AS U 2 : = ' < ' SQ R T < Y > ' > ' ; TEXTXASTl:=•<•Y•)•; T EX T Y AS U 1: = ' ( ' <U F •U >I US T ' ) ' ; T EX T Y A S U 2 : = ' < ' l../ U F' > ' ; T EX T Y AST 1: = 1 ( ' 2~ 3 •T A U /U F I UF' J t;
COMMENTU:=•<•VELOCITY•>•;CQMMENTT:=•<•REYNOLDS SHEAR•STRESS•>•; CUMMENC:=•<•FRICTION-COEFFICIENT')'; CO MM EN 0: = • ( 'BO U t\0 A RY- L AY ER- T 1-t IC K NE SS' l ';
T E >c. T X AS U: = ' < ' Y I D EL T .~' > ' ; T E X T X AS T : = ' < ' Y I 0 EL T A ' > 1 ;
TEXTYASU:=•< 1 U/UF'>';TEXTYAST:=•<•TAU/TAUW•>•; T EX T X AS 0 : = 1 < ' X I DEL T A 0 • > ' ; TE X T X ASt : = ' < 1 RE- T 1-t ET A ' > ' ;
TEXTYASD:=•C 'LENGTH/DELTAO'> •; TE.:XTYASC:=•< 'CF/CFO' )t;
MINMAXUC1J:=O;MINMAXUC2]::1;MINMAXUC3J::O;MINMAXU[4J:=l; MIN M AX T [ 1 J : = 0 ; MI NM A X H 2 l : = 1; M ItJ MA X T [ 3 1 : = 0;
MINMA>CT[4 ]::z; HINMAXC[lJ:=REDO•UFPCOJ•THETAPCOJ;MINMAXOClJ:=xO/DELTAO;
'lf'i>LOT 'THEN' 'BEGIN' WRITE<OUT•<//,"PLOT-OF-PROFILES"r//>);
TEKHARK SC OR AWINU ,I, 1, IHAX ,y STEP•I/DELt, CU[ I l/ UF,
MINHAXU•O•l•ll,.ts>; TEKCURVE<DRAWINU,I•3•IMAX,YSTEP•I/DELl•CUCIJ/UFrMINMAXU•C•lr1);
TEKMARKS<ORAWINT,I,O•IMAXrYSTEP*I/DEL1,CTCil/CTCOJ•MINMAXT,O~l• 11 •• 15);
04012700 04012800 04012900 04012901 04012902 04012903 04012904 04012905 04012906 04012907 04012908 C4012909 04012910 04012911 04012912 04013000 04013010 04013020 04013100 04013200 04013210 04013220 04013230 (\4013300 04013400 0401350:> 04013610 040137.00 04013800 04013900 04014000 04014100 04014200 04014301) 04014400 04014500
t 0' • lT1 0 l
TE KC U R V E C D RA W IN T , I , 0 d H A X , Y S T"E P * I I DE L 1 ' CT { I l I CT ( 0 l , M I N HA X T , Q,l,lH
TEKAXISZCORAWINU,HINMAXU,l,lO,lO,COMMENTU,TEXTXASU,fE~TYASU); TEKAX ISZCORAWINT,MI NMAXT,l,lO ,lO,COMMENTT,TEXTXAST,TEXTYASTH 'lf'AL 1 THEN''BEGIN 11 IF''N0T'RC'THEN 1 EO:=O'ELSE 1 E0:=.64•RH;
TEKHARKSCDRAWINUl'I'1'IMAX,(I•YSTEP+EO>!UFIOELST•SQRTCCT(0J), CUF•CUCIJ>ISQRT<CTCOJ>,MINMAXU1,Q,1,11,.15>;
TEKCURVE<ORAWINUl,I,3,IMAX,(l*YSTEP+EO>tUFIDELST•SQRT<CT(0J>, <UF-CUCill/SQRTCCTC0J),MlNMAXU1,Q,l,l>;
TEKAXISZ<ORAWINU1,MINMAXU1,1,5,20,COMMENTU1,TEXTXASU1,TEXTYASU1>; TEKAXIS2CORAWINU2,MINHAXU2,1,15,13,COHMENTU2,TEXTXASU2,fEXTYASU2);
'ENOt; 'EN 0 t;
CF:=CFO; LINTERPOLCF2,NF2,21,IHAX120>;
VTANCCU,Cf,NF2,CV,TANl,TAN2,RV,A,HM1,Uf,UOUOX,YSTEP,IMAX,Mf,Z); ~RITE<OUT•</,"UDUOX:",E13.6,111>,UOUDX>;
1 IftfEXT 'THEN" BEGIN' WRITE<OUT,<I,"PRINT·OF·PROfiLES",/,"U=",X8,"V/U=",X6,"TAU=",x2,
"INDEX=",/>); ' F 0 R' I:= 0 ' ST EP' 1' U N TIL' I MA X 'D 0' WRITECOUT,</,3CF8.4),13>,CU{IJ,RV[IJ,CT[IJ,!);
'ENOt; 1 f0R 1 I:=l 1 STEP'1'UNTIL'3
1 00''BEGIN 1 Y[Il:=YSTEP•CZ•1+I>;RCTCIJ::CTCZ•l+Ili•ENO•; LEAST SQUARES POLYNOMIALCY,RCf,3,1,CO>; ALFA:=COCll;
WRITECOUT,</,"X0=",f8.3 ,1,"0ELTA0=",f8.5,1,"0ISPL.THO=",f8.5,1~ "THETA0=",f8.5,1,"H0=",f8.5,1,"REL_ERR._MI0= 8 ,f8.5,1,
"G0:",f8e4,/>,X,OEL1,0ELST,THETA,H, Olf,SHA?E>;•If' 1 NOT 1 RC 1 THEN 1 WRITE<OUT,</,"ALPHA=",f9.4,1>,ALfA);
04014600 04014700 04014800 04014900 04014901 04014902 04014903 04014904 04014909 04014910 04014915 0401491& 04014916 04015000 04015100 04015200 04015300 04v15400 04015500 04015600 04015700 04015800 0 4015900 040160CO 04016100 04016110
04016120 04016130 04016140 04016200 04016300 04016400 04016500
, cP . tn
~==ENTIER<9L•I~AXJi WRITE<OUT,</•"UPPER-INOEX•OF-LOG•REGIQN:",t3,/>,K);
'If''NOT•RC'THEN'LR:=BK'ELSE'LR:=z; 1 IF•K·LR+1 1 GTR•1
1 T HEN' ' BEGIN ' •FOR• I:=l 1 STt:P'1 1 UNTIL'K·LR+l
1 00 1 ' BEGIN 1
'IF 1 'N0T'RC'THEN'E0:=0iY[Il:=YSTEP*<LR·1+I>+EO;Eo:=.ó4•RH; RCU(Il:=CUCLR-1+Ili
L N Y ( I l : = LN < Y [ I l ) ; 1 ENO•;
LEAST SQUARES·POLYNOMIALCLNY,RCU,K•LR+l~l~COEF>;
USTER:=cOEFCll•KK/MF; WRITE<OUT,</,"CF0=",F8.4,Xl,"CFLOG0="•F8.4,/,"REL.OEV_CFLOGO. ESTIMATEO·WITH·LOG·LAW="~F8.4,/>,CF,(USTER/Uf>**2*2*Mf**2' CCUSTER/UF)**2•2•MF••2•CFl/CF>;
•E NO' 'ELSE'WRITE<OUT,</,"LOG-REGION·TQO•SMALL•TQ-ESTIMATE·UST",/>);
C FT : = 0 • 2 4 6 * 1 0 * * ( ·0 • ó 7 8 * H l * < U F * T HET A * R E 0 0 ) * * < - 0 • 2 6 8 ) ; WRITECOUT,</,"CF=",F8.4,Xl,"CFT="'F8.4,X2,"REL.DEV.CFT.CALC·WITH.
L.T.FORM=",f8.4,/>,CF,CFT,<CFT·CF>ICF>; MFR:=l/C5.75•LOG<UF•DELST•RE00>+3.7);
WRITE<OUT,</,"CF0=",f8.4,Xl,"CFR=",F8.4,X2,"REL-DEV· CFR•CALC-WITH·ROTTA-FORM=",f8.4,/>,CF,2•MFR**2,<2•MFR•*2-CF)/CF);
OH:= <CUF /UFO• X/XO> **< < 1·-h 1> /( 3•H-1 > > >tUF•UFO•DEL T AO; wRITE<OUT•</,wDELTA0=",F8.4,X1,"0ELTA·HINZE=",F8.4'/'
"REL·DEV-DH-FROM·OELTA=",F8.4,f>,OELl,QH,(0H·DEL1>tDEL1>i CH:=CUF/UFO•X/X0>**(-2*(H•l)/(3•H-ll)•CFO; kRITE<OUT·</,"CF=",F8.4,Xl,"CF-HINZE="•F8.4,/,
"REL ·D EV- CH- F ROM-CF=", F 8. 4, I>, CF, Cl·h < CH- CF )/CF); TEL= =0; Z J: =0; 'I F'S M 0 OT H' TH EN' RAS : =0' ELS E 'RAS : = NR +1; C OU NT: =0;
STP: =O; Jl: = J2: =- 2i SUBTRA CT ::Q;
0401&700 0401&800 0401&850 04016900 04017000 04017100 04017200 04017300 04017700 040180CO 04018100 04018200 04018300 04018400 04018500 04018600 04018700 04016800 04019300 04019400 04019500 04019700 04019800 04019900 04020000 04020100 040202CO 04021)300 04020400 04020500 04021800 04021810
I o:> ~
V1 N \
1 HHILE'X'LEQ'XHKX'AN0 1 TIHEC2J'LEQ 1 6400 '00 11 BEGIN • J:=J+l;
' I F 'A DA P 1 THEN"BEGIN 1
• IF• J> 100• ANO' TEL=O ' TH EN • ' BEG I N t
'F0R'I:=0 1 STEP 1 1'UNTIL'IMAX • 0 0 ' 1 8 EG IN'
CCUCIJ:=CUCilrCCTCIJ:=CTCIJ; IE NO I;
TEL:=1iX:=XOiQ:=O;OEL1:=0EL2:=DELTAO;J::O;UF::UFO; LINTERPOLCCCU,cU,IMAX,IMAXO/IMAX>i LINTERPOL<CCT,cT,IMAX,IMAXO/IMAX>;
IMAX:=IMAXO;z: =liBK: =UYSTEP:=DEL1/IMAX; M M1: = SQ RT < C TC I MA X 'D I V t 4 l >;
LINTERPOL<f2,Nf2,21,IMAX/20); VTAN<CU,CT.NF2,CV,TAN1,TAN2,RV•A•MM1,UF,UDUOX,YSTEP,IMAX,MF,z>;
WRITE<OUT,</,"PROFILES.AOAPTEO-TO-MODEL"•/,"U="•X8,"V/U="•Xó,"TAU="•X2, " INDEX =",I>);
'FOR' I:=0 1 STEP'1'UNTIL' IMAX 1 D0 1
WRITE<OUT.</,fe.4,F8.4,f8.4,I3>,CUCIJ,RVCil,CTCil•I>i 1 IF 11 NOT 1 RC 1 THEN'BE:=1 1 ELSE 1 BE:=Z;
ME<CU,IMAX,J,YSTEP,uf,UDUOX,XST,TO,TN,THETA,OELl•DELST,H,OIF,TOU,TON, MF•CHO,CH1,SHAPE,BE);
OELSTPCOJ:=lO•OELST/DELTAOiOQOpCOJ::O.S•DELl/DELST; WRITE<OUT,</,"XO=",F8.3 ,f,"DELTAO-AD="•FS.S,J,"DISPL.THO•AD="•Fö.S,/,
"THETAO•AD="•F8.S,/,"H0·AO="•F8.S,/,"REL.ERR._MI0-AD="•Fb.S•/• "G0-AO="•f8.4•/>•X,QELl,OELST•THETA,H,
DIF,SHAP[);
04021900 04022000 04022100 04022200 04022300 04022400 04022500 04022600 0402270() 04022800 04022900 04023000 04023100 04023200 04023300 04023400 04023500 04023600 04023700 04023800 04023900 04024000 04024010
04024iOO 04024200 04024201 04024300 04024400 04024500 04024600
I cP . 0"1 (J)
I
•IF 1 SQRTCCTC0l)•YSTEP•REOO•~F'LSS•40 04024&01 •THEN''8EGIN'!IF 11 NOT 1 RC 1 THEN 1 04024602
WRITE<OUT,</,"HESH·POINT<S>·AT-XO·BELOW-TURBULENT•CORE",/, 04024603 "UST•OY/NU=",F8.4,/>,SQRTCCTCOJ>•~F•REOO•YSTEP>; 04024604
tu=O; 04024605 yp: =SQRT< CH 01) •YSTEP•REOO•MF; 04024606
I WHILE 1 K•YP 1 LSS 1 40 04024607 1 00 1 1'\:=K+l;BK:=K; 04024óC8
Y?:=K•YP; 'IF' •NOT' RC 1 THEN' 04024609 WRITECOUT,</,"NUMBER•OF-FIRST·MESH-POINT-IN-TURBULENT·CORE:", 04024610
I3,/~"UST•Y/NU<IN-THIS·MESH-POINT>=",F8.4,/>,K,yp); 04024611 'ENO'; 04024612
CF:=2•<SQRT<CTCOJ>IUF>**2*Mt**2; 04024700 K:=ENTIER<BL•IHAX>; 04024900
WRITE<OUT,</,"UPPER-INCEX·QF•LOG•REGION:",I3,/>,K); 04025000 •tr••NOT 1 RC 1 THEN'LR:=BK 1 ELSE 1 LR:=z; 04025050 1 IF•K·LR+l'GTR'1 04025100
'THEN• 'BEGIN' 04025200 1 FOR 1 I:=l'STEP 1 l'UNTIL'K•LR+1 04025300
1 00' 'BEGIN' 04025400 1 IF••NOT 1 RC 0 THEN 1 EO:=O;Y(Il:=YSTEP•<LR·l+I>+EO;EQ:=.64•RH; 04025500
RCUCIJ:=CUCLR•l+IJ; 04025900 L N Y C I l : =L N 0' C Il >; C 4 0 2 6 2 0 0
1 ENDt; 04026300 LEAST SQUARES POLYNOMIAL<LNY,RCU,K·L~+l,l,COEF>r 04026400
USTER:=COEFCll•KK/MF; 04026500 wRITECOUT,</,"CF-AD=",f8.4,Xl,"CFLOG·AD=",F8.4,/,"REL.OEV.CFLOG. 04û2660l ESTIMATEO•WITH-LOG·LAW=",F8.4,/>,CF,(USTERtUF>••2•2•MF**2, 04026700 <<USTER/UF>••2•2•MF••2·CF)/CF); 04026800
•END' 04026900 'ELSE 1 WRITE<OUT,</,"LOG•REGION-TOO-SMALL-TO·CALCULATE•UST",/>); 04027000
LEAST SQUARES POLYNOMIAL<Y,cT,3,1,COEF>r · 04027100 ALFA: =COEFC 1J; 'IF" NOT' RC 'THEN' , 04027200
WRITECOUT,</,"ALFA=•,ra.4,X6,"T0ALFA-AO",F8.4,/>,ALFA,CTC1J•ALfA*YSTEP);04027300 CFT:=0.246•10••<•0.ó78•H>•<UF•THETA•RED0>••<·0.268); 04027400
WRITECOUT•</,•CF•A0="-F8.4•Xl,"CFT=",F8.4,X2,"REL.DEV_CFT_CALC·WITH_ 0402750J L.T.rORM=",ra.4,t>.cr,crr,ccrr-cr>tcr>; 04027600
I o:> ~
l.'tt J::"
'
MFR:=l/(5.75•LOGCUf-•DELST•REOO>+J.7>; WRITE<OUT,</~"CFO•AD"~ra.4~xt,"CFR="~ra.4,X2,"REL•OEV·
CfR·CALC•WIT~·ROTTA-f0RM="•F8.4•/>,Cf,2•MFR**2,<2•HFR•*2-Cf)/Cf)i DH:=<<Uf/UFO•X/XO>**<<~+l)/C3•H-l>>>tUf•UFO*DELTAO; WRITE<OUT,</,"OELTAO·AO.=",f8.4~Xl~"OELTA·HINZE="•f8.4~/, "REL-DEV·OH-FROM-DELTA·AD.="~F8.4,/>,DEL1,0H,(OH-DELl>IDELl)i
CH:=CUF/UFO•X/X0>••<-2*(H•1)/C3•H·l>>•CFO; WRITE<OUT,</~"Cf•AD·=",f8.4,X1~"Cf•HINZE="•f8.4,/, "REL·DEV·CH•FROM·Cf-AD.=",F8.4,/>,Cf,CH,(CH·CF>!CF>;
IE f'JD I; 'END t;
IMAX:=IMAX+2; CU[ IMAX l :=CU[ I MAX •1 l: =UF;
CT [ IHAX-1 l ::Q; CT[ IHAXJ ::O;
LINTERPOLCF2,Nf2~21~IMAX/20>; VTAN<cu~cr~Nr2.cV,TANl~TAN2,RV.A,MMl•Uf,UOUOX,YSTEP•IMAX,Hf•Z>i
HAXVALUE<TANl,IHAX,K.MX);MT:=MX;
•FOR•I:=O•STEP'l'UNTIL'lHAX•D0 1 ABSTAN2Cil:=ABS<TAN2CI1); HAXVALUE<ABSTAN2•IMAX,K,MX);
MX: =HAX<MT~HX); XSTEP :=YSTEP/MX;
X:=X+XSTEP; Uf:=SQRTCUF0••2+2•UOUOX•<X•XO>>; uo:=.995•ur;
'!f 1 ADAP 1 THEN 11 BEGIN'
1 lf 1 TEL=1 1 THEN''BEGIN'TEl:=2rWR:=•TRUE•;•ENO•; 'ENOt;
XST:=XSTEP;TO:=CTCOl;
04027800 04027900 04028000 04028100 04028200 04028300 04028400 04028500 04028600 04028700 04028800 0402900J 04029100 04029200 04029 300 04029400 0402950() 04029600
04029601 04029602 04029603 04029604 04029700 040297i0 04029720 04033300 04033400 04033500 04033600 04033650
I o:' . CJ1 Ul l
• I F • X • L E Q ' S T A T PR ( ST P J ' A N 0 ' S TA T P R ( S T P l -X ' L E Q • X S T EP 'THEN''BEGIN'
Jl:=J+l;J2:=J+2rSTP:=STP+1r ~RI TE< OUT,.< I,." X•P RE V I OU S< =X ·STAT" ,.f,.
"XSTEP="•Fl2.S,./>,.XSTEP>r •ENrJ•
'ELSE''BEGIN' •IF 1 X-STATPRCSTPl<XSTEP 1 AN0 1 X•STATPRCSTPl>O
' TH E N' 1 BE G I N ' J1::J;J2:=J+1;STP:=STP+l;
WRITE<OUf,.</,."X·PREVIOUS>X-STAT""/" "XSTEP="•F12.8,./>,.XSTEP>;
' EN 0' ; • ENO •;
'IF•ROUGH
• I F ' J= J 1' T HEN ' ' 8 E G I N' XST:=STATPR!STP-11-X+XSTEP; X: =STAT PR ( ST P •1]; ur:=SQRT<UF0**2+2*UOUOX*<X-X0)); U D: = • 9 9 5* U f;
'ENDe;
'THEN''BEGIN' 1 IF'X'GTR 1 XTR
•THEN 1 RC:=•TRUE•; 1 IF'X'GTR 1 XRTR 1 AN0 1 SMOOTH
'THEN"BEGIN' RC:='FALSE•; S C : = 'T R UE ' ;
•ENf)t; 'ENDt;
' I F ' R C ' T HE N • Z J : =Z J + 1 ; 'IF 'ROUGH' AN0 1 SC' AND' COUNT' EQL 1 0
'THEN' •BEGIN' WRITE<OUT,.</~"TRANSITION•ROUGH•TO•SMOOTH""/"
"NUMBER-Or·RUNS•ON-ROUGH-SURFACE:",. I 3,. I>,. Z J >;
04033700 04033710 04033720 04033730 04033740 04033790 04033800 04033810 04033820 04033830 04033840 04033850 04033930 04033910 04033920 04033930 04033940 04033950 04033960 04033970 04034000 04034010 04034020 04034030 04034040 04034050 04034060 04034070 04034080 04034090 04034100 04034110 04034120 04034130 04034140 04034150
I es:> • VJ ~
I
C 0 U NT : = C 0 U NT+ 1; BL:=BLS;
Z: = 1i 8 K: = 1; 'E NO 'i
'IF•X •GTR'XRTR 'AND' RAS'LEQ' NR 'THEN' 'BEGIN'
~s:=•TRUE•;
RAS:=RAS+l; 'E NO'
'ELS E' AS:=' F ALS E'; 'IF'ZJ=l 1 THEN• PR:=•TRUE' 'ELSE 1 PR:=•FALSE•;
'IF'PR
'THEN• 'BEGIN' BL:=BLS;
kRITECOUT.<I~"R0UGH•5URFACE"~/~"ROUGH·WALL·LAW:"~I~ "UIUST=1/K•CLNCCY+EO>IH>+B"~/~"ROUGHNESS•HEIGHT="~F12.6,/,
"ERROR-IN-ORIGIN="~F12.8,/~ "J="~t3.1,"Q=",I3,/>•RH~Eo~J,Q);
'ENOt; TPL:=.J=JU
'IFtfPL•Tf-fEN' PRINT:=•TRUEt;
'IF tT PL 'ff-fEN'WRITECOUT,</,"PRINT·START"~/>);
1 IF'TPL'THEN'WRITECOUT~</~"J="~I3~/>~J); 1 IF•TPL•T~EN•WRITECOUT,<I,"UF=",F8.4~/,"UOUDX=",E13.6~/>~
UF • UDUD ·o; • I F • T PL' T HEN' WR I TE C OUT, <I," XS T=" ~ F 8. 4, I>, XS T); .. __ .
04034160 04034170 04034180 04034190 0403420i) 0403421() 04034220 04034230 04034240 04034250 04034260 04034270 04034280 04034290
04034300 04034320 04034330 04034340 04034345 04034350 04034360
.04047152 04047153 04047154 04047155 04047156 04047157 04047156 04047159 04047160
I cP . 1.)1
-..J I
PROFCCU,CT,CV,RV,IHAX,·TANl,fAN2,Fl,F2,F3,YSTEP, XST,J,JI,AOAP,UC,RH'
HF,REQO, TOO, TON, OELl,OEL2,RC,PR,UF,HMl,MM2,A,UOUDX,KK,AA, HR,z,ouT,ALfA,RY,
AS , P R I NT , A C CU , MI , C H 0 l , 8 K, E 0 > ; TN:=cTCOJ;'IF' 'NOT 1 RC'THEN 1 BE:=l'ELSE 1 BE:=z; ME<CU.IMAX,J,YSTEP,UF,UDUDX,XST,TO,TN•THETA•DEL2,0ELST~H,OIF,
TDO,TON,MF, CHO,CHl,SHAPE,BE>;
' I F tf EX T ' A N D ' T PL 'THEN' 'BEGIN' LINTERPOLCF2,NF2,21,IMAX/20>;
VTANCCU,Cf,NF2.CV,TAN1,TAN2•RV•A•HM2,UF,UOUOX,YSTEP,IMAX,MF,z>; ~RITECOUT.</~"UQ=",X7,"VQ/UQ:",X2,"TAUQ:",X2,"INOEX=",/>); 1 F0R' I:=O•STEP '1'UNTIL' IHAX
'00 1 WRITECOUT,</,Ftl.4,F8.4,F8.4,I3>,CUC!l•RV[!l,CTCIJ~t>; IE NO t;
SPL: =J=JU 'lf'PLOT•A~~>'SPL
' TH EN 'I BEGIN' TEKMARKSCORAWINU,I~l•IMAX,YSTEP*IIOEL2,CUCll/UF~
MIN~AXU,O~t,Q,.15>;
TtKCURVE<ORAWINU,J,3,IMAX,YSTEP•I/OEL2,CUCIJ/UF,MINMAXU,O,l•l>; TEKMARKS<ORAwiNT,I,O,IMAX.YSTEP•I/OEL2,CTCIJ/CT[Ol•
MINMAXf,Q,l ,Q ... lS>; 'IF"'AL
'TH EN ' I BEGIN' • IF' 1 N 0 T 1 R C' TH EN 'E 0: = 0' ELS E' EO : = • 6 4 *RH; TEKMARKS<ORAWINU1,I•1•IMAX,CI•YSTEP+EO>/UF/DELST•SQRTCCTC0J),
CUF·CU(IJ>ISQRTCCT(OJ>,MINMAXU1,0•l•Q,.ls>; T EK CJ RV E C 0 R A W I NU 1 , I , 3 , I MA X, C I * Y ST EP+ E 0 > I U F I 0 ELS T * S Q R T (CT ( 0 l > , < UF·C U( I l l/SQRT<CH 0 l >•MI Nr~Al(U1 ,c" ,1,1 ); TEKMARKSCORAWINU2,J,1,IMAX,SQRT<I•YSTEP>, (Q•SUBTRACT>Il0+CU(!J/UF,MIN~AXU2,0,l,Q,.1S>; TEKCURVE<r>RAwii\U2,I ,3,rMAX.SQRTCYSTEP•I ), < Q- SU B T R A C T > I 1 0 + C U( I.] I U F , H I N M A X U 2 , 0 , 1 , 1 H
'E NO'; Q:=Q+l;
1 E NO';
04047200 04047300. 04047400 04047500 04047501 04047510 04047511 04047512 04047513 04047600 04047601 04047602 04047603 04047605 04047&06 04047607 04047608 04047609 04047610 04047611 04047613 04047614 04047615 04047615 04047617 0'•047620 04047621· 04047622 04047623 04047628 04047629 04047630 04047631 04047632 0401+7633 04047634 04047640 04(147698
I CP ._
t]1
co J
PR I NT I • ' rAL ~ é: '; 'If'Q'4'ANO'~AL'TM(~''9EGI~'PAt:••fALS(•;SUBTRACT:aQ;
'lf'AL'ANO'PLOT'THE~''BEGIN' SKIPPAPERCORA~INU2l:HRITE<OUT~<t~"PLOT<VEL.VS.Y••.5lSKIPPEO"~/>); TEKAXIS2<0RAftiNU2,HINMAXU2,1~15,13,COMHENTU2,TEXTXASU2,TEXTYA~U2)r
•END•; 'E NO';
CF:=2•CSQRT<CTC0J)IUF>••2•MF••2;
tiF•SQRTCCTCOJ>•YSTEP•REOO•MF'LSS•40 •THEN••BEGIN••IF•TPL'ANO''NOT'RC•THEN•
~RITECOUT,</,"~ESH·POINT<S>-BELOW·TURBULENT·CORE"•I• wusT•OYINU=",F8.4,/>,SQRTCCT[0J>•MF•RE00•YSTEP>;
K:=o; YP:=SQRTCCTCOJ>•YSTEP•REOO•MF;
1 WHILE'K•YP'LSS 1 40 'D0'K:=K+1rBK:=K;
YP:=K•YP;•IF•TPL'AN0 11 NOT•RC•THEN• WRITECOUT,<I,"NUMBER-OF-FIRST-HESH-POINT-IN•TURBULENT•CORE:",
I 3, I, "US T *YIN UC IN-TH I S- HE SH -p 0 INT>=", F8. 4, I>, K, YP H 'EN!)';
K: =ENT IER C B L * IMA X>; 'I F 'T PL 'T HEN' WRITECOUT,<I,"U?PER-INDEX-OF·LOG•REGION:",J3,1>•K>;
•IF••NOT'RC'THEN 1 LR:=BK'ELSE'LR:=z;•tF•K-LR+1•GTR 1 1 'THEN' 'BEGIN'
1 F 0 R ' I : = 1 ' S T EP ' 1 ' U N T I L ' K- L R + 1 '00"BEGIN'
'IF••NOT 1 RC 1 THEN'EO:=O;YCil:=YSTEP•CLR·1+I>+EO;E0::.64•RH; RCUCil==GUCLR-1+IJ;
L N Y C I l : = LN < Y[ 11 H 'END t;
LEAST SQUARES POLYNOMIALCLNY,RCU,K•LR+1,1•COEF>; ·-- ..... --~------ .. -
Clo0lt7699 040t..7750 04047751 Ot..047752 04047753 04047754 04047755 C4047901
04047902 04047903 04047904 04047905 04047906 0 40 4 7 90 7 04047908 04047909 04047910 04047911 04047912 04047913 04047915 04047916 04047917 04047918 04047919 04047920 04047921 04047922 04047923 _04047924 04047925
\ ~ .. 0'1
û) I
u s rE R : = c a E n 1 J • !'( 11'( 1 Hf ;- • Ir • r P L • r ~ ( ·• I kRITE<OUT,</~~cro=·~re.4~xt."CfLOGO=~,rs.4•/•"REL.OEV.CFLOGQ• ESTIMATEO-WITH-L0G-LAW=··r8.4.t>.Cf.<UST(R/UF)••2•2•HF••2• <<USTER/UF>••2•2•MF••2-CF>!CF>;
1 EN o 1 1 ELs E • • sE GIN • • Ir • T P L • TH EN • W R IT E C 0 U T , < I , " L CG- RE G I 0 N - T 0 0 - S MAL L - T 0 - CAL C U L AT E- US T " , I > > ; • E N 0 ' ; t I Ft w R • 0 R • • N 0 T • .AD A P 'l HEN' 'BEG I N ' ' I F' T PL ' TH EN' ~RITE<OUT,.<//,"XSTAT="•F3.4, /,"OELTA="•Fa.s,./,."DISPL•TH.="•F8.5,./,.
"TiiETA="•F8.5•/ •"H="•f8.5•/,."REL. ERR. ME=",F8.5,. - -I ,"GQ=",.F8.4,. X6•"J=",.I3,.X6,"IMAX="•I3,X6,."T0="•F8.4,.X6,/,.
"TN=",.F8.4,.X6,"T00="•F8.4,X6,."TON="•F8.4,.X6,."THETA2="•F8.4,./>,. X,OEL2,0ELST,THETA,.H•DIF•SHAPE• J, I M AX , TI') • T N ,. TO 0, T 0 N,. C H 1 >;
'If 11 NOT'RC'ANO'TPL 1 THEN 1 WRITE<OUT,.</,."ALPHA="•F9.4,.1>,ALFA>; CFT:=0.246•10••<·0.678•H>•<UF•THETA•REOO>••<·G.268>;•IF•TPL•THEN• WRITE<OUT,<I,"CF="•F8.4,.Xl,."CFT="•F8.4,X2,"REL_DEV.CFT.CALC·
WITH_L.T.FORM="•F8.4,f>,CF,.CFT,.<CFT•CF)/CF>; M FR : = 1/ < 5. 7 5 * LOG< U F * 0 EL S T * RE 0 0 ) • 3 • 7 > ; • I F ' T P L ' TH E N •
wRITECOUT,.</,"CFA="•F8.4,Xl,."CFR=",F8.4,X2,."REL-OEV· CFR·CALC·WITH·ROTTA·FORM="•F6.4,f>,Cf,.2•MFR••2,.(2•HFR••2·CF)/CF>;
OH:=<<UF/UFO•XIXO>••<<H•1>1<3•H-l>>>IUF•UFO•DELTAO;•IF 1 TPL'THEN• ~RITE<OUT.</,"0ELTAQ="•F8.4,X1,"DELTA·HINZE="•F8.4•/• "REL·DEV•DH-FROM·DELTA="•F8.4,/>,.DEL2•0H,(OH-OEL2>1DEL2);
CH: = <U F I UFO• X /XO >• * < -2 * < H-1 >I< 3• H ·1 > ) * CFO; 'I F' T P l' TH EN' WRITE<OUT,.</,"CF="•F8.4,Xl,"CF-HINZE="•F8.4•1•
"REL"DEV-CH·FROM·CF="•F8.4,/>,Cf,CH,<CH·CF>ICF); M X :=CT ( I MA X ' 0 I V ' 41 ; ' I F ' T PL ' T HEN •
WRITE<OUT,</,"TAUOQ:",.F8.4,X2,"TMAX="•f8.4,X4~"INOEX="•F6.4•/>,.
CT COl •MXdMAX'0IV'4H •END';
ToO:=ToN;
0404792& 04047927 04C47926 04047929 04047930 04047931 04047932 04047933 04047934 04047935 04047936 04047937 04047936 04047939 04047940 04047941 04047942 04047943 04047944 04047945 04047946 04047947 04047946 04047949 0404795() 04047951 04047952 04047953 04047954 04047955 04047956 0tt047957 04048000
)
o:> . o-0
j
•IF•J•MOD 1 10 1 EQL 1 0 1 THEN''BEGIN'
N:=J'DIV'lO;XP[NJ!=X/DELTAO;HP[NJ::H; CFPCNJ:=2•CTCOJ/UF••2/CFO;THETAPCNJ::THETA;UFPCNJ::UF;
K::O;RP[NJ:=REDO•THETA•Ur; K:=ENTIER<BL•IHAX>J
'IF••NOT•RC•THEN 1 LR:=BK 1 ELSE'LR::z;•IF•K·LR+l•GTR•l•AND•LOGLAW 'THE~''BEGIN'
•FOR•I:=1 1 STEP 1 1'UNTIL'K·LR+l t00''BEGIN' 'lr 11 NOT•RC 1 THEN'EO:=O;YCil:=YSTEP•CLR•l+I>+EO;EQ:=.ó4*RH;
RCUCil:=CUCLR•l+IJ; LNYCil==LNCY(IJ>;
•END'J LEAST SQUARES POLYNOMIAL<LNY~RcU~K-LR+l~t~COEF>;
USTER:=COEFC1l*KK/MF; CFLOGCNJ:=2•<USTER/UF>••2/CFO;
'ENO' 1 ELSE 1 LOGLAW:=•FALSE•;
CFLUTICNJ:=<0.246•10••<-0.676•H>*<UF•THETA•RED0>••<·0.268))/CFO; MFR:=l/C5.75•LOGCUF•DELST•RED0>+3.7>;CFROTTACNJ:=2*MFR••2/CFO;
CFHINZECNJ:=<UF/UFO•X/X0>••<-2•<H•l)/(3•H-1>>;0QOPCNJ:=.5•DEL2/DtlST; OELTAHCNJ:=<<UF/UFO•X/XO>••<<H+l>1<3•H·1)))/UF•UFO;
OELTA?CNJ:=DEL2/DELTAO;OELSTPCNJ::10•DELST/DELTAO; WRITE<OUT~</~"J=",I3,/~"N~",I3,/>,J~N)J
WRITECOUT.<wPRCCESSTIHE:",I3,/>,TIHE<2>160); WRITE<OUT,<"IO•TIHE:",·I3,/>,TIHE(3)/60);
'END•; CFPCOJ:=CFLUTICOJ:=CFHINZECOJ:=DELTAHCOJ:=OELTAPCOJ:=t; CFROTTACOJ:=CFLOGCOJ:=1;XPCOJ ::·XOtDELTAOJ RPCOJ:=REOO•THETAPCOJ•UFP[QJ;
04048001 04048002 04048003 04048004 04048005 04048006
04046007 04048008 04048009 04048010 04048014 04048015 04048016 04048019 04048020 04048021 04048022 04048023 04048024 04048()25 04048026 04048027 04048028 04048029 04048030 04048031 04048032 04048033 04048034 04048035 04048036
1 ö) • a--J
'(f' 'I~UX'GEO•Z• (M4'(C
• T H E N ' ' 9 EG I ~p WRITECOUT.</•"J:•,z3,/r"IHAX="•I3r/>rJriHAX);
IHAX:=IMAX 1 DIV'2; YST(P:=2•YSTEPr
1 FOR' t:=l •STEP•l• UNTIL• IMAX ' DO ' ' BEG I N'
CUCil:=CUC2*Il;CTCIJ:=CTC2*Il; 'E:\1 D • ;
WRITE<OUTr</r"X="rf8.4r/r"IMAX="•I3r/>rX•IMAX); LINTERPOL<f2rNF2r21riMAX/20>;
VTAN<CUrCT.Nf2rCVrTAN1rTAN2rRVrArMM2rUfrUOUOXrYSTEPriMAXrMfrZ>; WRITE<OUTr</r"U="rX9r"V/U="•X5r"TAU="•X3r"I="•/>);
' F 0 R' I : = 0 1 ST EP ' 1' U NT I L ' I MA X 1 0 0' W R I TE< OUT • <Ir 3 CF 8. 4 l • I 3> • CU ( I l • RV ( I l • CT [ I l • I >;
•IF•SQRTCCTCOJ>•YSTEP•REOO•Mf'LSS 1 40 1 THEN 11 BEGIN 11 IF' TPL 1 AND 1 'NOT'RC'THEN'
kRITE<OUT.</r"MESH·POINT<S>·BELOW-TURBULENT•CORE"•I• "UST".DY/NU=" rf8.4r/>•SQRT<CH0l >•MF•REDO•YSTEP>;
K:=o; YP:=SQRT<CTCOl>•YSTEP•REDO•MF;
'WHILE'K•YP'LSS 1 40 •OO•K:=K+l;BK:=K;
YP: =K•YP; 1 IF' TPL'ANO' 1 NOTt RC•THEN• WRITE<OUTr<lr"NUMBER-OF-FIRST-MESH-POINT•IN•TURBULENT·CORE:"r
I 3r/r"UST•Y/NUC IN-THI S·MESH·POINT >="rf8.4r/>rKrYP H 'ENDt;
'E NO' ; OEL1:=0EL2rMM1:=MM2;
•Ir•PR 1 THEN 1 WRITE<OUTr</r"NUMBER•OF-FIRST-MESH•POINT-BEYONO•ROUGHNESS="•
12r/> • Z); 'IF'TPL 'THEN'kRITECOUTr</r"ENO-OF-PRINT"r/>);
•ENO•;
0404~100 04048200 04048300 04048400 04048500 04048600 04048700 04048800 04045900 04049000 04049100 04049200 04049300 04049400 04049500 04049510 04049511 04049512 04u49513 04049514 04049515 04049516 04049517· 04049516 04049519 04049520 04049521 0 40 4 9'600 04049700 04049800 04049900 04050000 04050010 04050020 04050100
I ~ • a~
I
HRITECOUT•<•PROCESSTIME-AFT(R-ENO-QF-LOOP:-,13•/>•TlHECZ)/bO)i WRITECOUT,<"IC•TIHE-AFTER-ENO-QF-LOQP:-,I3•/>•TIMEC3)/ó0)r
hRITE<OUT,</,"X="•f8.4,/,"IMAX=",I3,/>,X,IMAX>; WRITECOUT,</,"J="•I3,X2•"Q="•I3,x2,"N="•I3,/>,J,Q,N>i
MINMAXC[3J::Q;MINMAXCC4J:=8iMINMAXOC2J:=X/OELTAO; M I N M A X 0 C 3 l : = 1 ; M I N~1 A X D C 4 J : = 6; M I N M A XC ( 21 : = RE 0 0 *U f P ( N l * TH E T A P C N ];
~s:=O;KU:=NiK:=OiKC:=Nr 1 IF•REDO•UFPCNJ•THETAPCNJ<~3 '0R'REDO•UFPCOJ•T~ETAPCOJ>~4 1 THEN•PLOTL:='fALSE'i
1 IF'REDO•UFP(Nl•XPCNJ•OELTAO<O.Sa6 1 0R'RE00•UFPCOJ•XPCOJ•OELTA0>~7
'THEN•PLOTH:=•FALSE•; 'IF•REDO•UFPCOJ•THETAPCOJ 'GEQ 1 ~3 'THEN"BEGIN'
I:=OiK:=Oi 1 HHILE'RED~•UFPCil*THETAPCil'LEQ 1 a4 1 AN0'I'LEQ 1 N
•oo•r:=I+l; KC:= I• U
'END' 'ELSE ''BEGIN'
r:=o; 1 WHILE 1 REDO•UFPCil•THETAPCI1<a3
•oo•t:=I+U K:=Ii
1 WHILE•REOO•UFPCil•THETAPC IJ 'LEQ•a4'ANO•I•LEQ• N •oo•t==I+l; Kc:=r-t;
1 ENDt;
04050110 04050115
04050120 040 50 200 04050210 04050220 04050221 04050222 04050223 04050224 04050225 04050226 040 50 227 04050226 04050229 04050230 04050231 04050232 04050233 04050234 04050235 04050236 04050237• 04050238 04050239 04050240 04050241 04050242 04050243
I CP ., (J""-.. \,).)
I
•If'REOO•UFP(0l•X~[0]•0ELTA0'GEQ•O.S4G
•THEN ''BEGIN' r:=o;Ks:=o;
' WH I L E' RE!) 0 *U r PC I l * XP CI l * 0 EL T AO ' L E Q' ~ 7' A N 0 1 I ' L E Q' N •OO•I:=I+1; KU: = I• U
'END' 'ELSE''BEGIN'
I: =0; 'WHILE'REOO•UfPCIJ•XPCil•OELTA0<0.5~6
'00' I:=I+U KB:=I;
'WHILE•REnO•UfPCil•XPCIJ•OELTA0 1 LEQ•~7'ANO•I•LEQtN •oo• I== I+ U KU:=I·1;
'E NO'; W R IT E C OU T ,. < " P L 0 TH= "> ) ; W R I T E < 0 UT ,. I ,. P L 0 T H > ; WRITECOUT,.</,."PLOTL=">);WRITE COUT,.t,.PLOTL>; 'If'PLOTH'THEN'WRITECOUT,.</,."KU-KB=",.I3,./>,.KU•KB); 1 If•PLOTL•THEN'wRITECOUT,.</,."KC-K=",I3,/>,.KC•K);
'lf'PLOT 'THEN"BEGIN' TEK~ARKSCDRAWINO,.I,.O,.N,.XPCIJ,DELTAP[IJ,MINMAXO,O,.l,ll,.l5);
TtKCURVECORAWINO,.I,.Q,.N,.XPCll•DELTAPCIJ,.MINMAXD,.C•l,1); •Ir•PLOTH•AN0'CKU-K8)>1
'THEN •' BEGIN'WRITEC OUT•<I•"HI NZE-PLOT",f> >; TEKHARKS<ORAWINQ,.I,.KB,.KU,.XPCIJ,.OELTAHCIJ.MINMAXQ,Q,.1,2 •• 15>; TEKCURVE<DRAWINO•I•KB,.KU.XPCil.DELTAHCil·MINMAXO,.Q,.l,.l);
TEKMARKS<ORAwiNC• J,Ka.KU,RPCIJ,CfHINZECIJ,MINMAXC,O.l,.z,.15); 'E NO t;
TE KM AR KS (DRAW INC • I • 0,. N,. R PC IJ • C fROT TA ( I l ,. H I NM AX C,. 0,. 1,. 3 • .15 >; 'lf'PLOTL'ANC'CKC·K>>1'THEN''BEGIN'WRITE<OUT,.</,"L.T.-PLOT",./>); TEKMARKS<ORAWINC,I•K,.KC,.RPCIJ,.CFLUTICIJ,MINMAXC•O•l,l4,..15); 1 ENO';
TE KM ARK S ( DRAW IN C, I ,. 0, N,. R PC I l ,. C fl 0 G( I ],. MI NMA XC, 0,. 1,. 12 , • 1 5 ) ; TEKMARKSCDRAWINC"I'O•N,RPCIJ,.CfPCIJ,.MINMAXC,.O,.l,.ll,..lS)r
04050244 04050 245 04050246 04050247 04050248 04050249 04050250 04050251 04050252 04050253 04050254 04050255 0 40 St' 256 04050257 04050258 04050259 04050260 04050261 04050262 04050263 C4050300 04050400 04050401 04050402 04050403 04050404 04050405 04050406 04050407 04050408 04050409 04050410 0405G411 04050412 04050413
' cP . o
-I::-
I
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TEKMARKS<DRAWINO~t~O~N•XPCil~THETAPCil/T~ETAP(Ol•"I~HAXO~Q,lr4~.~5); TEKMARKSCORAWI~O~IrOrNrXP[IJr3•HP(llrHIN~AXOrOrl•0••15>; TE KC UR V E ( 0 RA~ I~ 0 r I r 0 r N r X PC I l ,3 *HP ( I l r M IN HA X 0 r J , 1 rl > ;
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