TEXT(Realisable KE_2D Elliptic Round Free Jet: T309 TITLE DISPLAY The problem considered is the submerged free turbulent round jet in stagnant surroundings. The jet issues from a pipe of diameter D at a Reynolds number of 38,500. The calculation is carried out with the elliptic solver for a domain which is 30D long by 7.5D wide. Calculations are performed with the standard k-e & k-w models, and the following k-e variants: Chen-Kim, RNG and Realisable k-e models. The experimental data indicate a velocity half- width spreading rate of 0.086 in the self-similar region of the jet. The present calculations predict the following spreading rates: data k-e chen-kim RNG Realisable k-w dyh/dz .086 .11 .11 .168 .10 ? All results are in poor agreement with the experimental data, especially the RNG model. The realisable k-e model performs best by almost having the discrepancy found with the standard k-e model. The half-width spreading rate is calculated approximately using In-Form commands and then written to the text output file named inforout. As noted by Menter [1992] the current form of Wilcox k-w model dates from 1988, and it predicts much higher eddy viscosities than the k-e model, which leads to a much larger jet spreading rate. Therefore, this form of the model isn't suited for the prediction of free jets, but it is coded here in preparation for a future extension to the Wilcox 1998 model which performs much better for free jets. - F.R.Menter, "Improved 2-equation k-w turbulence models for aerodynamic flows", NASA TN 103975, (1992). ENDDIS GROUP 1. Run title and other preliminaries REAL(WINJ,WIN_FS,KE_FS,EP_FS,KEINJ,EPINJ,DIAM,PRADO,PRADI,CD) REAL(OM_FS,OMINJ,LAMVIS,ENUT_FS,TINJ,TIN_FS,REYNO) REYNO=3.85E4 DIAM=0.058;PRADI=0.5*DIAM;PRADO=15.*PRADI CD=0.1643 ** jet-inflow conditions WINJ=20.;TINJ=0.05 KEINJ=(TINJ*WINJ)**2; EPINJ=CD*KEINJ**1.5/(0.1*PRADI) ** laminar kinematic viscosity LAMVIS=WINJ*DIAM/REYNO ** free-stream conditions WIN_FS=WINJ/100.;TIN_FS=0.05 ENUT_FS=5.*LAMVIS KE_FS=(TIN_FS*WIN_FS)**2;EP_FS=0.09*KE_FS**2/ENUT_FS GROUP 3. X-direction grid specification CARTES=F;XULAST=0.1 GROUP 4. Y-direction grid specification INTEGER(NYF,NYO,NYG) NYF=10;NYO=50;NYG=NYF+NYO NREGY=2;NY=46 IREGY=1;GRDPWR(Y,NYF,PRADI,1.0) IREGY=2;GRDPWR(Y,NYO,-(PRADO-PRADI),1.04) GROUP 5. Z-direction grid specification NZ=120;GRDPWR(Z,NZ,-(30.*DIAM),1.01) GROUP 7. Variables stored, solved & named SOLVE(P1,V1,W1);STORE(ENUT) SOLUTN(P1,P,P,Y,P,P,P);SOLUTN(V1,P,P,P,P,P,N) SOLUTN(W1,P,P,P,P,P,N) INTEGER(JKO);JKO=0 CHAR(CTURB) MESG( Enter the required turbulence model: MESG( KEM - Standard k-e model MESG( CKM - Chen Kim k-e model MESG( RNG - RNG k-e model MESG( KOM - Wilcox k-omega model MESG( RKE - Realisable k-e model (default) MESG( READVDU(CTURB,CHAR,RKE) CASE :CTURB: OF WHEN KEM,3 + TEXT(standard KE_2D Elliptic Round Free Jet + MESG(Standard k-e model + TURMOD(KEMODL) WHEN CKM,3 + TEXT(Chen-Kim KE_2D Elliptic Round Free Jet + MESG(Chen Kim k-e model + TURMOD(KECHEN) WHEN RNG,3 + TEXT(RNG KE_2D Elliptic Round Free Jet + MESG(RNG k-e model + TURMOD(KERNG) WHEN KOM,3 + TEXT(KO_2D Elliptic Round Free Jet + MESG(k-omega model + TURMOD(KOMODL) + STORE(EP);OMINJ=EPINJ/(0.09*KEINJ) + OM_FS=EP_FS/(0.09*KE_FS) + JKO=1 WHEN RKE,3 + TEXT(Realisable KE_2D Elliptic Round Free Jet + MESG(RK k-e model + TURMOD(KEREAL) + STORE(CMU,C1E) + OUTPUT(CMU,P,P,P,P,Y,Y);OUTPUT(C1E,P,P,P,P,Y,Y) ENDCASE GROUP 8. Terms (in differential equations) & devices GROUP 9. Properties of the medium (or media) ENUL=LAMVIS GROUP 11. Initialization of variable or porosity fields FIINIT(W1)=WIN_FS PATCH(INIT,INIVAL,1,NX,1,NYF,1,NZ,1,LSTEP) INIT(INIT,W1,0.0,WINJ); FIINIT(KE)=KEINJ;FIINIT(EP)=EPINJ GROUP 13. Boundary conditions and special sources ** Jet Inlet Conditions INLET(IN1,LOW,1,NX,1,NYF,1,1,1,LSTEP) VALUE(IN1,P1,RHO1*WINJ); VALUE(IN1,W1,WINJ) VALUE(IN1,KE,KEINJ);VALUE(IN1,EP,EPINJ) IF(JKO.GT.0) THEN +VALUE(IN1,OMEG,OMINJ);FIINIT(OMEG)=OMINJ ENDIF ** Free Boundary Conditions INLET(IN2,LOW,1,NX,#2,#2,1,1,1,LSTEP) VALUE(IN2,P1,RHO1*WIN_FS);VALUE(IN2,W1,WIN_FS) VALUE(IN2,KE,KE_FS);VALUE(IN2,EP,EP_FS) IF(JKO.GT.0) THEN +VALUE(IN2,OMEG,OM_FS) ENDIF PATCH(FREEB,NORTH,1,NX,NYG,NYG,1,NZ,1,LSTEP) COVAL(FREEB,W1,ONLYMS,WIN_FS) COVAL(FREEB,KE,ONLYMS,KE_FS);COVAL(FREEB,EP,ONLYMS,EP_FS) COVAL(FREEB,P1,1.E3,0.0) IF(JKO.GT.0) THEN +VALUE(FREEB,OMEG,OM_FS) ENDIF OUTLET(OUT,HIGH,1,NX,1,NYG,NZ,NZ,1,LSTEP) COVAL(OUT,P1,1.E3,0.0) VALUE(OUT,V1,0.0); VALUE(OUT,W1,0.0) VALUE(OUT,KE,0.0);VALUE(OUT,EP,0.0) IF(JKO.GT.0) THEN +VALUE(OUT,OMEG,0.0) ENDIF GROUP 15. Termination of sweeps LSWEEP=1000 GROUP 16. Termination of iterations GROUP 17. Under-relaxation devices KELIN=3 REAL(RLXFAC); RLXFAC=8.*ZWLAST/WINJ/NZ RELAX(V1,FALSDT,RLXFAC); RELAX(W1,FALSDT,RLXFAC) RELAX(KE,LINRLX,0.4); RELAX(EP,LINRLX,0.4) CASE :CTURB: OF WHEN RKE,3 + RELAX(KE,FALSDT,RLXFAC); RELAX(EP,FALSDT,RLXFAC) + RELAX(ENUT,LINRLX,0.2) + VARMAX(ENUT)=0.1 WHEN KOM,3 +RLXFAC=ZWLAST/WINJ/NZ +RELAX(V1,FALSDT,4.*RLXFAC);RELAX(W1,FALSDT,4.*RLXFAC) +RELAX(EP,LINRLX,1.0);RELAX(ENUT,LINRLX,0.25) +RELAX(KE,FALSDT,4.*RLXFAC);RELAX(OMEG,FALSDT,4.*RLXFAC) ** ENUT is limited to 0.06 m^2/s to prevent an unrealistic final solution +VARMAX(ENUT)=0.06 +LSWEEP=1800 +OUTPUT(EP,P,P,P,P,Y,Y) ENDCASE GROUP 18. Limits on variables or increments to them GROUP 20. Preliminary print-out ECHO=T GROUP 21. Print-out of variables NYPRIN=1 GROUP 22. Spot-value print-out TSTSWP=-1 IYMON=NYF+2;IZMON=NZ-1;NPLT=10;ITABL=3;NZPRIN=1 GROUP 23. Field print-out and plot control GROUP 24. Dumps for restarts ** compute half-width spreading rate for inforout file (stored of wh is 0.5*W1[&1&] ) (stored of YGP is YG) PATCH(HWIDTH,CELL,1,NX,2,NY-1,1,NZ-1,1,LSTEP) (stored of YH is 0.0) (stored of YH at HWIDTH is YGP with IF(W1.GT.WH.AND.W1[,+1,].LT.WH)) INTEGER(IZ1);IZ1=3*NZ/4 PATCH(HWIDTH1,CELL,1,NX,2,NY-1,IZ1,IZ1,1,LSTEP) PATCH(HWIDTH2,CELL,1,NX,2,NY-1,NZ-1,NZ-1,1,LSTEP) (make1 dyhdz) (MAKE1 YH1) (store1 of YH1 at HWIDTH1 is MAX(YH,1.1E-10)) (PRINT YH1 IS YH1) (MAKE1 YH2) (store1 of YH2 at HWIDTH2 is MAX(YH,1.1E-10)) (PRINT YH2 IS YH2) (stored of ZGM is ZG) (store1 of dyhdz is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