TEXT(Decay Of Turbulence. K-Epsilon Model TITLE DISPLAY Homogeneous turbulence decays behind a grid in a stream of uniform velocity. The transport equations of the k-epsilon model reduce to ordinary differential equations with analytical solutions of which that for k is: k=( k0**a - a*e0*(x-x0)/{u0*k0**(1-a)} ) ** (1/a) where k0 and e0 are k and e for x=0, and u0 is the flow velocity; a=1.0-C2E. The value of C2E that fits the experimental data is 1.9 The analytical solution is computed in the Q1 file, by way of a DO loop, and stored in the variable ANKE. The small differences between the computed KE and ANKE result from the upwind differencing: ANKE is the cell-centre value, whereas KE is the convected-out value. ENDDIS REAL(XLEN,UIN,REYNO,WIDTH,TKEIN,EPIN) XLEN=1.0;REYNO=5.E5;UIN=10.;WIDTH=0.25 GROUP 3. X-direction grid specification GRDPWR(X,200,XLEN,1.0) GROUP 7. Variables stored, solved & named STORE(U1,ENUT);TURMOD(KEMODL);NAME(ENUT)=VIST GROUP 8. Terms (in differential equations) & devices DIFCUT=0.0;ENUL=UIN*WIDTH/REYNO GROUP 11. Initialization of variable or porosity fields TKEIN=1.0;EPIN=7.5 FIINIT(U1)=UIN;FIINIT(KE)=TKEIN;FIINIT(EP)=EPIN ** Analytical solution placed in ANKE store STORE(ANKE);REAL(AA,NN,BB,ANTKE,C2E,GX);INTEGER(JJM1) C2E=1.92;NN=1./(1.0-C2E);AA=1./NN;BB=1.0-AA REAL(CON1,CON2,CON3) CON1 = TKEIN**AA ; CON2 = AA*EPIN/(UIN*TKEIN**BB) CON3 = XULAST/2.0 ; CON2=CON2 * CON3 DO JJ=1,NX + PATCH(IN:JJ:,INIVAL,JJ,JJ,1,NY,1,NZ,1,1) + GX=XFRAC(JJ) + IF(JJ.NE.1) THEN + JJM1=JJ-1; GX=(XFRAC(JJ) + XFRAC(JJM1)) + ENDIF + ANTKE=(CON1 - CON2*GX)**NN + INIT(IN:JJ:,ANKE,ZERO,ANTKE) ENDDO GROUP 13. Boundary conditions and special sources ** Inlet Boundary PATCH(INLET,WEST,1,1,1,1,1,1,1,1) COVAL(INLET,KE,RHO1*UIN,TKEIN);COVAL(INLET,EP,RHO1*UIN,EPIN) GROUP 16. Termination of iterations LSWEEP=1000;SELREF=T;RESFAC=0.0001 GROUP 21. Print-out of variables OUTPUT(U1,N,N,N,N,N,N);OUTPUT(VIST,N,N,N,N,N,N) GROUP 22. Monitor print-out IXMON=NX GROUP 23. Field print-out and plot control NXPRIN=nx/5;ORSIZ=0.4 PATCH(PROFILE,PROFIL,1,NX,1,1,1,1,1,1) PLOT(PROFILE,KE,0.0,1.5*TKEIN);PLOT(PROFILE,EP,0.0,2.0*EPIN) PLOT(PROFILE,VIST,0.0,0.0) **END OF LIBRARY CASE 230