DISPLAY Simulation of heat transfer to and from the solid material surrounding a tunnel, when a moving heat source (eg a train) passes along it. Air also flows along the tunnel. ENDDIS GXNEPA is employed for this case. The locally-defined variables are as follows: H1IN = inlet enthalpy of air J/kg H1INIT = initial enthalpy of solid J/kg FLO1 = mass-flow rate of air kg/s TIME = transit time of train s INTVLS = number of time intervals SPECHT = specific heat of solid J/kg.deg SPEAIR = specific heat of air J/kg.deg COND = thermal conductivity of solid J/m.deg DENSTY = density of the solid kg/m**3 DENAIR = density of air kg/m**3 VELAIR = air velocity m/s REAL(H1IN,H1INIT,FLO1,TIME,DENSTY,COND,SPECHT,HEATSO) REAL(DENAIR,SPEAIR,VELAIR) INTEGER(INTVLS) SPECHT=880.0; HEATSO =1.0E6; TIME =200.0; INTVLS=20 DENSTY=1460.0; COND =1.3; DENAIR=1.0; SPEAIR=1.E3 VELAIR=5.0; H1IN =0.0; H1INIT=0.0 FLO1 =VELAIR*DENAIR*SPEAIR/SPECHT GROUP 1. Run title TEXT(Transient Tunnel Heat Transfer TITLE GROUP 2. Transience; time-step specification STEADY=F; TLAST=1.0; LSTEP=INTVLS TFRAC(1)=-LSTEP/2; TFRAC(2)=2.0*TIME/LSTEP TFRAC(3)=LSTEP/2; TFRAC(4)=TFRAC(2)*10.0 GROUP 3. X-direction grid specification CARTES=F;GRDPWR(X,1,2.0*3.14159,1.0) GROUP 4. Y-direction grid specification NY=10;YVLAST=1.0 **The tunnel has a radius of 5 m; and the surrounding solid is subdivided into cylindrical layers 0.015m thick. YFRAC(1)=-1.0;YFRAC(2)=5.0;YFRAC(3)=9.0;YFRAC(4)=0.015 GROUP 5. Z-direction grid specification **The tunnel is 1 km long GRDPWR(Z,10,1.E3,1.0) GROUP 7. Variables stored, solved & named SOLVE(H1);STORE(NPOR,VPOR) GROUP 8. Terms (in differential equations) & devices **The built-in source and convection terms are cut out, convection being handled by the NEL1 source below. TERMS(H1,N,N,Y,Y,Y,Y) GROUP 9. Properties of the medium (or media) RHO1=DENSTY;PRNDTL(H1)=ENUL*DENSTY*SPECHT/COND GROUP 11. Initialization of variable or porosity fields INIADD=F FIINIT(H1)=H1INIT;FIINIT(NPOR)=1.0;FIINIT(VPOR)=1.0 PATCH(TUNNEL,INIVAL,1,1,1,1,1,NZ,1,1) **The north porosity is set so as to express the fact that heat travels into the first solid layer from its inner surface, not from the the point within the air cell which PHOENICS assumes. INIT(TUNNEL,NPOR,0.0,(YFRAC(2)+YFRAC(4))/YFRAC(4)) **The volume porosity is set to the ratio below, so that the transient terms are correctly computed. INIT(TUNNEL,VPOR,0.0,SPEAIR*DENAIR/(SPECHT*DENSTY)) GROUP 13. Boundary conditions and special sources **Low boundary; fluid inlet ; PATCH(INLEH1,LOW,1,1,1,1,1,1,1,LSTEP) COVAL(INLEH1,H1,FLO1,H1IN) **Flow of fluid along IY=1 PATCH(NEL1,LOW,1,1,1,1,2,NZ,1,LSTEP) COVAL(NEL1,H1,FLO1,LOCNE) **Heat source which moves from one cell to the next in each time step, ie at speed ZWLAST/TIME, which equals 18 km/h in this case. DO II=1,10 + PATCH(HEATR:II:,CELL,1,1,1,1,II,II,II,II) + COVAL(HEATR:II:,H1,FIXFLU,HEATSO) ENDDO GROUP 15. Termination of sweeps RESREF(H1)=1.E-6*HEATSO LSWEEP=2 SPEDAT(SET,GXMONI,TRANSIENT,L,F) GROUP 21. Print-out of variables OUTPUT(H1,Y,Y,Y,Y,Y,Y) OUTPUT(NPOR,N,N,N,N,N,N) OUTPUT(VPOR,N,N,N,N,N,N) GROUP 22. Spot-value print-out IZMON=NZ/2;TSTSWP=1;ITABL=2 GROUP 23. Field print-out and plot control NZPRIN=NZ/5;IZPRL=NZ-1;IPLTL=LSWEEP;NPLT=1 NTPRIN=1 PATCH(LONGPLOT,PROFIL,1,1,2,2,1,NZ,1,LSTEP) PLOT(LONGPLOT,H1,0.0,0.0) PATCH(MAP,CONTUR,1,1,2,NY,1,NZ,1,LSTEP) PLOT(MAP,H1,0.0,10.0) PATCH(TIMEPLOT,PROFIL,1,1,2,2,NZ/2,NZ/2,1,LSTEP) PLOT(TIMEPLOT,H1,0.0,0.0)