```

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 press  to 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
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
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