AUTOPLOT USE file phi 5 da 1 p1 x 1 119 da 1 gasu x 1 119 da 1 r1 x 1 119 screen pl 1 ; colour3 1 1 msg pressure profile msg pressto continue pause screen pl 2 ; colour8 2 2 msg gas velocity msg press to continue pause screen pl 3 ;scale y 0 1;coloure 3 3 msg gas volume fraction msg press e to END enduse GROUP 1. Run title TEXT(CF=1.E7 RHO2=10. POUT=-.5 W870 TITLE DISPLAY NUMERICAL BENCHMARK PROBLEM 1.1: CONVERGENT-DIVERGENT NOZZLE Two fluids flow through a convergent-divergent nozzle. The lighter one is a compressible gas; the second one, which is in much smaller volumetric concentration, is incompressible. The density ratio is such that the pressure gradients which accelerate the gas have less effect upon the motion of the heavier fluid; but the latter is nevertheless also accelerated by the drag exerted upon it by the gas. The task is to predict the distributions of pressure, volume fraction and velocity along the duct, under various conditions. ENDDIS GROUP 3. X-direction grid specification XULAST=1.0;NX=120 REAL(XN);XN=120.0;XFRAC(1)=-XN;XFRAC(2)=1.0/XN GROUP 7. Variables stored, solved & named This is a two-phase problem. ONEPHS=F SOLVE(P1,U1,U2,R1,R2) NAME(U1)=GASU;NAME(U2)=SOLU STORE(EPOR,DEN1) GROUP 8. Terms (in differential equations) & devices The 4th-argument N's cut out the diffusion (viscous) terms TERMS(GASU,Y,Y,N,Y,Y,Y);TERMS(SOLU,Y,Y,N,Y,N,Y) TERMS(R1,Y,Y,N,Y,Y,Y);TERMS(R2,Y,Y,N,Y,N,Y) GROUP 9. Properties of the medium (or media) ENUL=0.0 The first phase is compressible. Its density obeys the law rho=(pressure)**1.0/gamma RHO1=COMPRESS;DRH1DP=COMPRESS The reference pressure is 1.0, in the units chosen, and so is the density of the first phase. This makes the sound velocity sqrt(gamma). Gamma is taken as 1.0/0.714 PRESS0=1.0;RHO1A=1.0;RHO1B=0.714;RHO1C=0.0 Second phase density RHO2=10.0 GROUP 10. Inter-phase-transfer processes and properties Interphase friction The (linear) interphase-friction factor is CFIPS*r1*r2*rho1. Here a large value is taken for CFIPS. CFIPS=1.E7 GROUP 11. Initialization of variable or porosity fields FIINIT(GASU)=0.5;FIINIT(SOLU)=0.5;FIINIT(P1)=3.0;FIINIT(R1)=0.9 FIINIT(R2)=0.1;FIINIT(DEN1)=3.0 The initial (and of course continuing) values of the porosities are specified here. Nozzle FIINIT(EPOR)=1.0 iniadd=T PATCH(CONVERGE,LINVLX,NX/4,NX,1,1,1,1,1,1) COVAL(CONVERGE,EPOR,-2.0,0.0) PATCH(DIVERGE,LINVLX,NX/2,NX,1,1,1,1,1,1) COVAL(DIVERGE,EPOR,3.0,0.0) GROUP 13. Boundary conditions and special sources Inlet INLET(INLET,WEST,1,1,1,1,1,1,1,1) The next statement introduces a flow rate of 1.5 kg/s of first-phase material VALUE(INLET,P1,1.5) It has a velocity (i.e. momentum per unit mass) of 0.5 m/s VALUE(INLET,GASU,0.5) The next statement introduces a flow of 0.5 kg/s of second-phase material VALUE(INLET,P2,0.5) Its velocity is also 0.5 m/s VALUE(INLET,SOLU,0.5) Outlet Fixed outlet pressure PATCH(OUTLET,CELL,120,120,1,1,1,1,1,1) COVAL(OUTLET,P1,1.E3,-0.5);COVAL(OUTLET,P2,1.E3*RHO2/RHO1A,-0.5) COVAL(OUTLET,GASU,ONLYMS,0.0);COVAL(OUTLET,SOLU,ONLYMS,0.0) GROUP 15. Termination of sweeps LSWEEP=200 GROUP 16. Termination of iterations RESREF(P1)=1.E-4;RESREF(GASU)=1.E-4;RESREF(SOLU)=1.E-4; RESREF(R1)=1.E-5;RESREF(R2)=1.E-4 GROUP 17. Under-relaxation devices RELAX(GASU,FALSDT,1.0);RELAX(SOLU,FALSDT,1.0) RELAX(R1,LINRLX,0.50);RELAX(R2,LINRLX,0.50) GROUP 21. Print-out of variables OUTPUT(R1,N,N,N,N,N,N) GROUP 22. Spot-value print-out TSTSWP=-1;IXMON=NX/2 GROUP 23. Field print-out and plot control IPLTF=3;IPLTL=LSWEEP;NPLT=1;NXPRIN=NX/20;ORSIZ=0.4 PATCH(LONGPLOT,PROFIL,1,NX,1,1,1,1,1,1) PLOT(LONGPLOT,P1,0.0,0.0);PLOT(LONGPLOT,R2,0.0,0.0) PLOT(LONGPLOT,GASU,-1.0,-1.0);PLOT(LONGPLOT,SOLU,-1.0,-1.0) GROUP 24. Dumps for restarts