PHOTON USE p phi msg CONVECTIVE COOLING OF A RADIALLY-RIBBED CYLINDER msg view z;rot 90 norm msg Velocity vectors: gr ou z 1;vec z 1 sh msg msg Pressto continue pause vec off;red msg Pressure contours: con p1 z 1 sh;int 15 msg msg Press to continue pause con off;red msg Temperature contours: con temp z 1 fi;.001 msg msg Press e to END en7duse GROUP 1. Run title and other preliminaries TEXT(Convective Cooling Of Radial Fin TITLE mesg(PC486/50 time last reported as 1.min DISPLAY Radioactive material generates heat within a horizontally- disposed cylindrical metal container, the outer surface of which is ribbed to promote convective cooling. This analysis focuses on the heat transfer and air flow in, and around, one half of one of the fins. Heat is supplied at a constant rate per unit area along the inner surface of the cylinder. Most of the heat is transferred from the metal to the air, but some is radiated away at a constant prescribed flux. A cylindrical domain of integration is used, the inner boundary of which corresponds to the inner surface of the container. The outer boundary of the domain extends well into the air. The coordinate x increases from zero at the top to 180 degrees (pi radians) at the bottom, for symmetry about the vertical plane through the cylinder is present. The large conductivity of the metal is contrived by enlarging the porosities for the cell faces in the metal. The heating of the air results in its upward motion, ie motion in the negative x sense, caused by buoyancy. ENDDIS The user-defined local variables are: NYC is the last radial cell in the metal cylinder; NYR is the last radial cell in the metal fin which protrudes from the cylinder; NZR is the number of axial cells extending from the radial symmetry plane in the fin to the edge of the fin; COND is the conductivity of the metal divided by the viscosity and the specific heat of the air; CP is the specific heat of the metal; FIXT is the ambient temperature raised to power 4; and T4 is the mean metal temperature raised to power 4. REAL(COND,CP,FIXT,T4);INTEGER(NYC,NYR,NZR) NYC=1;NYR=9;NZR=3 GROUP 3. X-direction grid specification CARTES=F GRDPWR(X,12,3.142,1.0) GROUP 4. Y-direction grid specification NY=12;RINNER=1.14 YFRAC(1)=-10.;YFRAC(2)=0.0125 YFRAC(3)=2.0; YFRAC(4)=0.05 GROUP 5. Z-direction grid specification NZ=7 ZFRAC(1)=-4.0;ZFRAC(2)=0.01/4.0 ZFRAC(3)=3.0; ZFRAC(4)=0.015/3.0 GROUP 7. Variables stored, solved & named **For economy, point-by-point solution is used for velocities and temperature (the main diffusive links are z-directed in this case, and at present there is no means of solving simultaneously in z at the linear-equation level, except for pressure corrections which are solved whole field). Harmonic averaging is selected for the temperature equations by the last argument of SOLUTN... SOLUTN(P1,Y,Y,Y,N,N,N);SOLUTN(U1,Y,Y,N,Y,P,P) SOLUTN(V1,Y,Y,N,Y,P,P);SOLUTN(W1,Y,Y,N,Y,P,P) SOLUTN(H1,Y,Y,N,Y,P,Y) NAME(H1)=TEMP GROUP 8. Terms (in differential equations) & devices **Dissipation of mechanical energy into heat is presumed to be insignificant, so the built-in source for temperature is de-activated. TERMS(TEMP,N,Y,Y,N,Y,N);DIFCUT=0.0 GROUP 9. Properties of the medium (or media) RHO1=1.163;ENUL=1.8E-5;PRNDTL(TEMP)=0.7 GROUP 11. Initialization of variable or porosity fields FIINIT(U1)=-0.5 **The following commands provide a realistic initial distribution for the temperature field... PATCH(TALL,LINVLY,1,NX,1,NY,1,NZ,1,1);COVAL(TALL,TEMP,-150.,37.) PATCH(TCYL,LINVLY,1,NX,1,NYC,1,NZ,1,1);COVAL(TCYL,TEMP,-120.,75.) PATCH(TFIN,LINVLY,1,NX,NYC+1,NYR,1,NZR,1,1) COVAL(TFIN,TEMP,-120.,75.) **The high conductivity of the metal is contrived by appropriately enlarging the cell-face porosities for cell faces which have metal on either side. The metal conductivity is 36.2 Watts per metre per degree. It is divided by the the viscosity and specific heat of the air... CP=1008.0;COND=36.2*PRNDTL(TEMP)/(RHO1*ENUL*CP) CONPOR(COND,NORTH,1,NX,1,NYR-1,1,NZR) CONPOR(COND,EAST,1,NX,1,NYC,1,NZ) CONPOR(COND,EAST,1,NX,NYC+1,NYR,1,NZR) CONPOR(COND,HIGH,1,NX,1,NYC,1,NZ) CONPOR(COND,HIGH,1,NX,NYC+1,NYR,1,NZR-1) **Cell faces which are located at the metal-air interface require porosity factors of 2 to ensure the correct transfer of heat and momentum (ie friction) across the interface. The factor of 2 is a consequence of the uniform spacing used for the cells each side of the interface, and of the fact that the large metal conductivity results in the temperature at the interface being very nearly equal to the local bulk temperature of the metal. CONPOR(2.0,NORTH,1,NX,NYC,NYC,NZR+1,NZ) CONPOR(2.0,HIGH,1,NX,NYC+1,NYR,NZR,NZR) CONPOR(2.0,NORTH,1,NX,NYR,NYR,1,NZR) **The correctness of the foregoing porosity settings can be verified by printing the fields of the porosities. GROUP 13. Boundary conditions and special sources **Fix the velocities to zero within the solid... PATCH(CYLINDER,CELL,1,NX,1,NYC,1,NZ,1,1) COVAL(CYLINDER,U1,FIXVAL,0.0);COVAL(CYLINDER,V1,FIXVAL,0.0) COVAL(CYLINDER,W1,FIXVAL,0.0) PATCH(FIN,CELL,1,NX,NYC+1,NYR,1,NZR,1,1) COVAL(FIN,U1,FIXVAL,0.0);COVAL(FIN,V1,FIXVAL,0.0) COVAL(FIN,W1,FIXVAL,0.0) **Prescribed heat flux across inner cylindrical boundary PATCH(HEATFLX,SOUTH,1,NX,1,1,1,NZ,1,1) COVAL(HEATFLX,TEMP,FIXFLU,1.811E+3/CP) **The pressures are fixed on the outer boundary of the domain for the cells where outflow is expected. PATCH(EXIT,NORTH,1,NX/2,NY,NY,1,NZ,1,1) COVAL(EXIT,P1,1.E3*FIXP,0.0);COVAL(EXIT,TEMP,ONLYMS,0.0) COVAL(EXIT,U1,ONLYMS,0.0);COVAL(EXIT,V1,ONLYMS,0.0) COVAL(EXIT,W1,ONLYMS,0.0) **The stagnation pressures are set where inflow is expected along the outer boundary of the domain. PATCH(INLET,NORTH,NX/2+1,NX,NY,NY,1,NZ,1,1) COVAL(INLET,P1,-2.0*RHO1,0.0);COVAL(INLET,TEMP,0.0,0.0) COVAL(INLET,U1,ONLYMS,SAME);COVAL(INLET,V1,ONLYMS,SAME) **The Boussinesq approximation is used to represent the buoyancy force. BUOYE=0.0;DVO1DT=9.81*10.08/3.;BUOYA=0.0;BUOYB=-1.0 PATCH(BUOYU,PHASEM,1,NX-1,1,NY,1,NZ,1,1) COVAL(BUOYU,U1,FIXFLU,BOUSS) PATCH(BUOYV,PHASEM,1,NX,1,NY-1,1,NZ,1,1) COVAL(BUOYV,V1,FIXFLU,BOUSS) **Set the presribed radiation flux... FIXT=301.0**4;T4=366.0**4-FIXT PATCH(RADBOT,NORTH,1,NX,NYC,NYC,NZR+1,NZ,1,1) COVAL(RADBOT,TEMP,FIXFLU,-9.927E-9*T4/CP) T4=360.0**4-FIXT PATCH(RADSIDE,HIGH,1,NX,NYC+1,NYR,NZR,NZR,1,1) COVAL(RADSIDE,TEMP,FIXFLU,-7.90E-9*T4/CP) T4=354.0**4-FIXT PATCH(RADTOP,NORTH,1,NX,NYR,NYR,1,NZR,1,1) COVAL(RADTOP,TEMP,FIXFLU,-3.912E-8*T4/CP) GROUP 17. Under-relaxation devices RELAX(U1,FALSDT,1.0);RELAX(V1,FALSDT,1.0) RELAX(W1,FALSDT,1.0);RELAX(P1,LINRLX,0.3) GROUP 22. Spot-value print-out LSWEEP=20;ITABL=3;IPLTL=LSWEEP;NPLT=1 IXMON=NX/2;IYMON=NY/2;IZMON=NZR+1 YZPR=T;NXPRIN=2 GROUP 23. Field print-out and plot control PATCH(TXEQ1,CONTUR,1,1,1,NY,1,NZ,1,1);COVAL(TXEQ1,TEMP,0.,15.) PATCH(TXEQ4,CONTUR,4,4,1,NY,1,NZ,1,1);COVAL(TXEQ4,TEMP,0.,15.) PATCH(TXEQ6,CONTUR,6,6,1,NY,1,NZ,1,1);COVAL(TXEQ6,TEMP,0.,15.) PATCH(TXEQ9,CONTUR,9,9,1,NY,1,NZ,1,1);COVAL(TXEQ9,TEMP,0.,15.) IPROF=3 PATCH(45DEG,PROFIL,3,3,2,NY,NZ,NZ,1,1);COVAL(45DEG,TEMP,0.,0.0) COVAL(45DEG,U1,0.0,0.) PATCH(90DEG,PROFIL,6,6,2,NY,NZ,NZ,1,1);COVAL(90DEG,TEMP,0.,0.0) COVAL(90DEG,U1,0.0,0.) PATCH(120DEG,PROFIL,8,8,2,NY,NZ,NZ,1,1);COVAL(120DEG,TEMP,0.,0.0) COVAL(120DEG,U1,0.0,0.) PATCH(165DEG,PROFIL,11,11,2,NY,NZ,NZ,1,1);COVAL(165DEG,TEMP,0.,0.0) COVAL(165DEG,U1,0.0,0.) ***actdem*** + do ii=1,5 + mesg( + enddo mesg( Initial data that can be changed: + mesga( The last radial cell in the metal fin which protrudes + mesg( from the cylinder is :NYR: + mesg( Conductivity of the metal is set to 36.2 W/m/deg + mesg( Specific heat of the metal is :cp: J/kg/deg mesga( Do you want to change settings (y/n)? (Default n) readvdu(ans,char,n) if(:ans:.eq.y) then + real(rt1);integer(it1) + do ii=1,5 + mesg( + enddo + mesg( The last radial cell in the metal fin which protrudes + mesga(from the cylinder is :NYR:. OK? If not, insert new value. + readvdu(NYR,int,:NYR:) + if(nyr.gt.ny) then + nyr=ny + endif PATCH(TFIN,LINVLY,1,NX,NYC+1,NYR,1,NZR,1,1) CONPOR(2.0,HIGH,1,NX,NYC+1,NYR,NZR,NZR) CONPOR(2.0,NORTH,1,NX,NYR,NYR,1,NZR) PATCH(FIN,CELL,1,NX,NYC+1,NYR,1,NZR,1,1) PATCH(RADSIDE,HIGH,1,NX,NYC+1,NYR,NZR,NZR,1,1) PATCH(RADTOP,NORTH,1,NX,NYR,NYR,1,NZR,1,1) + do ii=1,5 + mesg( + enddo + mesg( Conductivity of the metal is 36.2 W/m/deg. OK? + mesga( If not, insert new value. + readvdu(rt1,real,36.2) + do ii=1,5 + mesg( + enddo + mesg( Specific heat of the metal is :cp:. OK? + mesg( If not, insert new value. + readvdu(cp,real,:CP:) COND=rt1*PRNDTL(TEMP)/(RHO1*ENUL*CP) CONPOR(COND,NORTH,1,NX,1,NYR-1,1,NZR) CONPOR(COND,EAST,1,NX,1,NYC,1,NZ) CONPOR(COND,EAST,1,NX,NYC+1,NYR,1,NZR) CONPOR(COND,HIGH,1,NX,1,NYC,1,NZ) CONPOR(COND,HIGH,1,NX,NYC+1,NYR,1,NZR-1) endif output(p1,y,y,y,y,y,y) output(u1,y,y,y,y,y,y) output(v1,y,y,y,y,y,y) output(w1,y,y,y,y,y,y) selref=t; resfac=1.e-2 TSTSWP=-1