TEXT(CHEN KIM K-E MODEL_PARAB PLANE JET :T104 TITLE DISPLAY The problem considered is the submerged free heated turbulent plane jet in essentially 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 slot width at z = 0, thereafter being caused to increase linearly with downstream distance so as to accommodate the lateral spread of the jet. The number of forward steps NZ is set equal to 560, so that the marching integration is terminated at an axial distance of about 60 slot width's 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 0.65. The experimental data indicate velocity and temperature half- width spreading rates of dyw/dz=0.11 and dyt/dz=0.14 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 0.11 0.104 0.095 0.122 0.116 - dytdz 0.14 0.128 0.123 0.157 0.161 - The standard k-e and k-w models produce particularly good agreement with the measured spreading rates, although the k-w solution is known to be fairly sensitive to the free-stream value of w. The Chen-Kim model and RNG models fare less well but are in reasonable agrrement with the measured values. A converged solution could not be obtained with the realisable k-e model. This needs further investigation. 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) REAL(WJET,REYNO,HSLOT,TJET,TFREE,TKEIN,EPSIN,EPSFRE,ENULAM) REAL(TKEFRE,WFREE) REYNO=5.E5;HSLOT=0.1;WJET=10.;TJET=1.0;TFREE=0.0 ENULAM=WJET*2.*HSLOT/REYNO WFREE=1.E-4*WJET TKEFRE=(0.01*WFREE)**2;EPSFRE=0.09*TKEFRE**2/ENULAM TKEIN=(0.01*WJET)**2;EPSIN=TKEIN**1.5/(0.035*HSLOT*.1643) GROUP 4. Y-direction grid specification NY=80;YVLAST=HSLOT;YFRAC(1)=-80.;YFRAC(2)=1.0/80. *** Linear grid expansion with slope DYGDZ REAL(DYGDZ);DYGDZ=0.24;AZYV=1.0;ZWADD=HSLOT/DYGDZ GROUP 5. Z-direction grid specification PARAB=T;NZ=560;AZDZ=PROPY ** set DZW1=DZ/YVLAST value for AZDZ option DZW1=0.02 GROUP 7. Variables stored, solved & named NAME(H1)=TEMP;STORE(ENUT,LEN1);SOLVE(P1,V1,W1,TEMP) 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 PLANE JET :T104 + MESG(Standard k-e model + TURMOD(KEMODL);TLSC=EP WHEN KO,2 + TEXT(K-OMEGA MODEL_PARAB PLANE JET :T104 + MESG(k-omega model + TURMOD(KOMODL);TLSC=OMEG + STORE(EP);EPSIN=EPSIN/(0.09*TKEIN);EPSFRE=EPSFRE/(0.09*TKEFRE) WHEN RNG,3 TEXT(RNG K-E MODEL_PARAB PLANE JET :T104 + MESG(RNG k-e model + TURMOD(KERNG);TLSC=EP WHEN RKE,3 TEXT(Realisable K-E_PARAB PLANE JET :T104 + 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 STORE(YHLF,YHLT) 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)=0.65 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.E4,0.0) COVAL(HIGHY,W1,ONLYMS,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 velocity and temperature at slot PATCH(SLOT,LOW,1,1,1,NY/2,1,1,1,1);COVAL(SLOT,P1,FIXFLU,RHO1*WJET) COVAL(SLOT,W1,ONLYMS,WJET);COVAL(SLOT,TEMP,ONLYMS,TJET) COVAL(SLOT,KE,ONLYMS,TKEIN);COVAL(SLOT,:TLSC:,ONLYMS,EPSIN) 3. Inlet Boundary-- uniform velocity and temperature PATCH(OUTSIDE,LOW,1,1,NY/2+1,NY,1,1,1,1) COVAL(OUTSIDE,P1,FIXFLU,RHO1*WFREE) COVAL(OUTSIDE,W1,ONLYMS,WFREE) COVAL(OUTSIDE,TEMP,ONLYMS,TFREE);COVAL(OUTSIDE,KE,ONLYMS,TKEFRE) COVAL(OUTSIDE,:TLSC:,ONLYMS,EPSFRE) GROUP 14. Downstream pressure for PARAB=T IPARAB=1 GROUP 16. Termination of iterations LITHYD=50; RESREF(P1)=1.E-6; RESREF(V1)=1.E-6; RESREF(W1)=1.E-6 RESREF(TEMP)=1.E-6; RESREF(KE)=1.E-6; RESREF(:TLSC:)=1.E-6 GROUP 17. Under-relaxation devices RELAX(V1,FALSDT,10.0); RELAX(W1,FALSDT,10.0); RELAX(TEMP,FALSDT,10.0) RELAX(KE,FALSDT,10.0); RELAX(:TLSC:,FALSDT,10.0) GROUP 19. Data communicated by SATELLITE to GROUND DWDY=T GROUP 21. Print-out of variables OUTPUT(P1,Y,Y,Y,Y,Y,Y);OUTPUT(V1,Y,Y,Y,Y,Y,Y) OUTPUT(W1,Y,Y,Y,Y,Y,Y);OUTPUT(TEMP,Y,Y,Y,Y,Y,Y) 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 )=3.413E-02;EX(V1 )=1.386E-01 +EX(W1 )=1.290E+00;EX(KE )=4.839E-01 +EX(EP )=6.581E-01;EX(TEMP)=1.452E-01 +EX(YHT )=6.961E-03;EX(YH )=5.364E-03 +EX(YGP )=7.304E-01;EX(TH )=1.750E-01 +EX(WH )=1.949E+00;EX(YHLT)=5.569E-01 +EX(YHLF)=4.291E-01;EX(LEN1)= 1.269E-01 +EX(ENUT)= 3.850E-02 WHEN KE,2 +EX(P1 )=3.166E-02;EX(V1 )=1.329E-01 +EX(W1 )=1.378E+00;EX(KE )=4.989E-01 +EX(EP )=5.658E-01;EX(TEMP)=1.508E-01 +EX(YHT )=8.331E-03;EX(YH )=6.505E-03 +EX(YGP )=7.304E-01;EX(TH )=1.603E-01 +EX(WH )=1.777E+00;EX(YHLT)=6.665E-01 +EX(YHLF)=5.204E-01;EX(LEN1)=1.065E-01 +EX(ENUT)=4.207E-02 WHEN KO,2 +EX(P1 )=3.933E-02;EX(V1 )=1.323E-01 +EX(W1 )=1.548E+00;EX(KE )=6.106E-01 +EX(EP )=5.702E-01;EX(TEMP)=1.723E-01 +EX(YHT )=9.016E-03;EX(YH )=6.277E-03 +EX(YGP )=7.304E-01;EX(TH )=1.556E-01 +EX(WH )=1.803E+00;EX(YHLT)=7.213E-01 +EX(YHLF)=5.021E-01;EX(OMEG)=8.140E+00 +EX(LEN1)=2.819E-01;EX(ENUT)=9.902E-02 WHEN RNG,3 +EX(P1 )=4.475E-02;EX(V1 )=1.417E-01 +EX(W1 )=1.400E+00;EX(KE )=6.371E-01 +EX(EP )=6.475E-01;EX(TEMP)=1.522E-01 +EX(YHT )=8.787E-03;EX(YH )=6.961E-03 +EX(YGP )=7.304E-01;EX(TH )=1.560E-01 +EX(WH )=1.723E+00;EX(YHLT)=7.030E-01 +EX(YHLF)=5.569E-01;EX(LEN1)=1.165E-01 +EX(ENUT)=5.415E-02 WHEN RKE,3 +EX(P1 )=2.498E-04;EX(V1 )=1.538E-02 +EX(W1 )=4.574E-01;EX(KE )=1.000E-10 +EX(EP )=1.273E-04;EX(TEMP)=4.574E-02 +EX(YHT )=7.989E-04;EX(YH )=7.989E-04 +EX(YGP )=7.304E-01;EX(TH )=4.867E-01 +EX(WH )=4.867E+00;EX(YHLT)=6.720E-02 +EX(YHLF)=6.720E-02;EX(C1E )=4.300E-01 +EX(DWDY)=6.946E+00;EX(DVDY)=1.000E-10 +EX(EPKE)=1.273E+06;EX(CMU )=2.475E-01 +EX(LEN1)=1.440E-06;EX(ENUT)=2.169E-11 ENDCASE