TEXT(CHEN KIM K-E MODEL_PARAB ROUND JET :T105 TITLE DISPLAY The problem considered is the submerged free heated turbulent round jet in stagnant surroundings. The calculations are started at the jet discharge, and the parabolic marching integration is carried out until both the mean flow and turbulence profiles become self similar. The calculations are made with 80 grid cells across the jet and a forward step size of 2% (DZW1) of the local jet width. The y-extent of the grid is set equal to the diameter at z=0, thereafter being caused to increase linearly with downstream distance so as to accommodate the radial spread of the jet. The number of forward steps NZ is set equal to 520, so that the marching integration is terminated at an axial distance of about 50 diameters from the jet discharge. ENDDIS Calculations may be performed with the standard, Chen-Kim, RNG and Realisable k-e models, and also with the Wilcox k-w model. The turbulent Prandtl number is set equal to 0.7. The experimental data indicate velocity and temperature half- width spreading rates of dyw/dz=0.086 and dyt/dz=0.11 in the self-similar region of the jet. The present calculations predict the following spreading rates: data k-e chen-kim RNG k-w Real.k-e dyw/dz 0.086 0.116 0.117 0.169 0.248 0.088 dytdz 0.11 0.127 0.134 0.213 0.323 0.106 All models with the exception of the realisable k-e model seriously overpredict the measured spreading rates,and the Wilcox k-w model fares the worst producing excessive values. The k-W model solution is known to be fairly sensitive to the free-stream value of w. AUTOPLOT USE file iy1.csv 2 d 1 z yhlf;d 1 z yhlt;col3 1;colf 2 redr msg half-width spreading rates msg Press e to END ENDUSE PHOTON USE P PARADA 0.20443E+04 0.15633E+04 CR GR OU X 1;VEC X 1 SH; PAUSE CL;GR OU X 1;CON ENUT X 1 FI;1 PAUSE ENDUSE CHAR(CTURB,TLSC) INTEGER(JKO);JKO=0 REAL(WJET,REYNO,DIAM,TJET,TFREE,TKEIN,EPSIN,EPSFRE,ENULAM) REAL(TKEFRE,WFREE) REYNO=5.E5;DIAM=0.1;WJET=10.0;TJET=1.0;TFREE=0.0 ENULAM=WJET*DIAM/REYNO WFREE=1.E-4*WJET TKEFRE=(0.01*WFREE)**2;EPSFRE=0.09*TKEFRE**2/ENULAM TKEIN=(0.05*WJET)**2;EPSIN=TKEIN**1.5/(0.035*DIAM*.1643) GROUP 3. X-direction grid specification CARTES=F;XULAST=0.1 GROUP 4. Y-direction grid specification NY=80;YVLAST=DIAM;YFRAC(1)=-80;YFRAC(2)=1.0/80.0 *** Linear grid expansion of DYGDZ REAL(DYGDZ);DYGDZ=0.086*3.0;AZYV=1.0;ZWADD=DIAM/DYGDZ GROUP 5. Z-direction grid specification PARAB=T;NZ=520;AZDZ=PROPY ** set DZW1=DZ/YVLAST value for AZDZ option DZW1=0.02 GROUP 7. Variables stored, solved & named SOLVE(P1,V1,W1,H1);NAME(H1)=TEMP;STORE(ENUT,LEN1) SOLUTN(V1,P,P,P,P,P,N);SOLUTN(W1,P,P,P,P,P,N) MESG( Enter the required turbulence model: MESG( CHEN - Chen-Kim k-e model (default) MESG( KE - Standard k-e model MESG( KO - Wilcox k-o model MESG( RNG - RNG k-e model MESG( RKE - Realisable k-e model MESG( READVDU(CTURB,CHAR,CHEN) CASE :CTURB: OF WHEN CHEN,4 + MESG(Chen-Kim k-e model + TURMOD(KECHEN);TLSC=EP WHEN KE,2 + TEXT(K-E MODEL_PARAB ROUND JET :T105 + MESG(Standard k-e model + TURMOD(KEMODL);TLSC=EP WHEN KO,2 + TEXT(K-OMEGA MODEL_PARAB ROUND JET :T105 + MESG(k-omega model + TURMOD(KOMODL);TLSC=OMEG;JKO=1 + STORE(EP);EPSIN=EPSIN/(0.09*TKEIN);EPSFRE=EPSFRE/(0.09*TKEFRE) WHEN RNG,3 TEXT(RNG K-E MODEL_PARAB ROUND JET :T105 + MESG(RNG k-e model + TURMOD(KERNG);TLSC=EP WHEN RKE,3 TEXT(Realisable K-E_PARAB ROUND JET :T105 + MESG(Realisable k-e model + TURMOD(KEREAL);TLSC=EP + STORE(C1E);OUTPUT(CMU,Y,Y,Y,Y,Y,Y) + OUTPUT(C1E,Y,Y,Y,Y,Y,Y) ENDCASE GROUP 8. Terms (in differential equations) & devices DIFCUT=0.0;TERMS(TEMP,N,Y,Y,Y,Y,Y) GROUP 9. Properties of the medium (or media) ENUL=ENULAM;PRT(TEMP)=0.7 GROUP 13. Boundary conditions and special sources 1. Outer Boundary-- free stream PATCH(HIGHY,NORTH,1,1,NY,NY,1,NZ,1,1);COVAL(HIGHY,P1,1.0E4,0.0) COVAL(HIGHY,V1,ONLYMS,0.0);COVAL(HIGHY,TEMP,ONLYMS,TFREE) COVAL(HIGHY,W1,ONLYMS,0.0);COVAL(HIGHY,KE,ONLYMS,TKEFRE) COVAL(HIGHY,:TLSC:,ONLYMS,EPSFRE) 2. Inlet Boundary-- uniform flow PATCH(NOZZLE,LOW,1,1,1,NY/2,1,1,1,1) COVAL(NOZZLE,P1,FIXFLU,RHO1*WJET);COVAL(NOZZLE,W1,ONLYMS,WJET) COVAL(NOZZLE,TEMP,ONLYMS,TJET) COVAL(NOZZLE,KE,ONLYMS,TKEIN);COVAL(NOZZLE,:TLSC:,ONLYMS,EPSIN) GROUP 14. Downstream pressure for PARAB=T IPARAB=1 GROUP 16. Termination of iterations LITHYD=50; RESREF(P1)=1.E-8; RESREF(V1)=1.E-8; RESREF(W1)=1.E-8 RESREF(TEMP)=1.E-8; RESREF(KE)=1.E-8; RESREF(:TLSC:)=1.E-8 GROUP 17. Under-relaxation devices RELAX(V1,FALSDT,10.); RELAX(W1,FALSDT,10.); RELAX(TEMP,FALSDT,10.) RELAX(KE,FALSDT,1.0); RELAX(:TLSC:,FALSDT,1.0) IF(JKO.EQ.1) THEN + RELAX(KE,FALSDT,0.1);RELAX(:TLSC:,FALSDT,0.1) ENDIF GROUP 18. Limits on variables or increments to them VARMIN(V1)=-1.E3;VARMAX(V1)=1.E3 GROUP 19. Data communicated by SATELLITE to GROUND DWDY=T GROUP 22. Monitor print-out IZMON=NZ/2;IYMON=NY/2;ITABL=1;NPLT=1;IPLTL=LITHYD;TSTSWP=-1 ** parabolic file dumping IDISPA=1;IDISPB=1;IDISPC=NZ ** compute half-width velocity spreading rate (stored of wh is 0.5*W1[&1&] ) (stored of th is 0.5*TEMP[&1&] ) (stored of ygp is YG) PATCH(HWIDTH,CELL,1,NX,2,NY-1,1,NZ,1,LSTEP) (stored of YH is 0.0) (stored of YH at HWIDTH is YGP with IF(W1.GT.WH.AND.W1[,+1,].LT.WH)) (make1 YH1) (store1 of YH1 at HWIDTH is MAX(YH,1.1E-10)) (print YH1 is YH1) (stored of YHLF is YH1) ** compute half-width temperature spreading rate (stored of YHT is 0.0) (stored of YHT at HWIDTH is YGP with IF(TEMP.GT.TH.AND.TEMP[,+1,].LT.TH)) (make1 YHT1) (store1 of YHT1 at HWIDTH is MAX(YHT,1.1E-10)) (print YHT1 IS YHT1) (stored of YHLT is YHT1) GROUP 23. Field print-out and plot control ** generate profile .csv file named IZNZ.csv ORSIZ=0.4;PATCH(IZNZ,PROFIL,1,1,1,NY,NZ,NZ,1,1) PLOT(IZNZ,W1,0.0,0.0);PLOT(IZNZ,TEMP,0.0,0.0) PLOT(IZNZ,ENUT,0.0,0.0);NZPRIN=NZ ** generate axial .csv file named IY1.csv PATCH(IY1,PROFIL,1,1,1,1,1,NZ,1,1) PLOT(IY1,W1,0.0,0.0);PLOT(IY1,TEMP,0.0,0.0) PLOT(IY1,YHLF,0.0,0.0);PLOT(IY1,YHLT,0.0,0.0) NZPRIN=NZ NZPRIN=1;NYPRIN=1 NPLT=1;ITABL=2 DISTIL=T CASE :CTURB: OF WHEN CHEN,4 +EX(P1 )=1.166E-03;EX(V1 )=3.168E-02 +EX(W1 )=4.413E-01;EX(KE )=6.393E-02 +EX(EP )=2.908E-02;EX(TEMP)=4.437E-02 +EX(YHLT)=6.085E-01;EX(YHT )=7.606E-03 +EX(YHLF)=4.813E-01;EX(YH )=6.017E-03 +EX(YGP )=7.266E-01;EX(TH )=4.786E-02 +EX(WH )=5.770E-01;EX(LEN1)=1.347E-01 +EX(ENUT)=1.548E-02 WHEN KE,2 +EX(P1 )=1.054E-03;EX(V1 )=3.131E-02 +EX(W1 )=4.302E-01;EX(KE )=5.711E-02 +EX(EP )=2.300E-02;EX(TEMP)=4.290E-02 +EX(YHLT)=6.811E-01;EX(YHT )=8.514E-03 +EX(YHLF)=5.540E-01;EX(YH )=6.925E-03 +EX(YGP )=7.266E-01;EX(TH )=4.396E-02 +EX(WH )=5.202E-01;EX(LEN1)=1.141E-01 +EX(ENUT)=1.393E-02 WHEN KO,2 EX(P1 )=1.571E-03;EX(V1 )=2.549E-02 EX(W1 )=4.141E-01;EX(KE )=7.115E-02 EX(EP )=1.545E-02;EX(TEMP)=3.969E-02 EX(YHLT)=1.190E+00;EX(YHT )=1.487E-02 EX(YHLF)=8.446E-01;EX(YH )=1.056E-02 EX(YGP )=7.266E-01;EX(TH )=2.787E-02 EX(WH )=3.391E-01;EX(OMEG)=2.043E+00 EX(LEN1)=2.870E-01;EX(ENUT)=3.802E-02 WHEN RNG,3 +EX(P1 )=1.518E-03;EX(V1 )=2.839E-02 +EX(W1 )=4.224E-01;EX(KE )=7.378E-02 +EX(EP )=1.817E-02;EX(TEMP)=4.158E-02 +EX(YHLT)=9.173E-01;EX(YHT )=1.147E-02 +EX(YHLF)=7.538E-01;EX(YH )=9.422E-03 +EX(YGP )=7.266E-01;EX(TH )=3.335E-02 +EX(WH )=3.915E-01;EX(LEN1)=1.821E-01 +EX(ENUT)=2.622E-02 WHEN RKE,3 +EX(P1 )=9.277E-04;EX(V1 )=3.086E-02 +EX(W1 )=4.232E-01;EX(KE )=4.557E-02 +EX(EP )=2.488E-02;EX(TEMP)=4.222E-02 +EX(YHLT)=6.085E-01;EX(YHT )=7.606E-03 +EX(YHLF)=4.995E-01;EX(YH )=6.244E-03 +EX(YGP )=7.266E-01;EX(TH )=4.938E-02 +EX(WH )=5.715E-01;EX(C1E )=4.300E-01 +EX(DWDY)=7.870E-01;EX(DVDY)=1.000E-10 +EX(DUDX)=1.000E-10;EX(EPKE)=5.113E-01; +EX(CMU )=1.424E-01;EX(LEN1)=6.327E-02; +EX(ENUT)=1.058E-02 ENDCASE