GROUP 1. Run title and other preliminaries
TEXT(2D TURBULENT FLOW THROUGH AN ORIFICE)
TITLE
DISPLAY
The case considered is 2d turbulent axisymmetric incompressible
flow through an orifice plate of 11mm thickness located in a
pipe. The pipe diameter D is 92mm and the hole in the orifice
plate has a diameter H of 64 mm. The flow Reynolds number is
75,000 based on D and the inlet bulk velocity Uin. The orifice
plate has practical value as a flowmeter.
The present case has been studied experimentally and numerically
by Erdal et al (PHOENICS Turbulence Modelling Seminar, CHAM,
(1995) ). The boundary conditions correspond to an inlet flow of
fully-developed turbulent flow located 10D upstream of the plate,
and an outlet condition of fixed pressure 17.5D downstream of the
plate, and no-slip conditions at the walls. Turbulence is
represented via the standard k-e model plus wall functions, and
the calculation of convection terms is defaulted to the linear-
upwind scheme (LUS) for momentum and the VANLH scheme for k and e.
ENDDIS
The calculation employs 85 axial grid cells, of which 16 are
located within the orifice plate, 31 upstream and 38 downsteam
of the plate. The solution is known to be sensitive to the grid
spacing in the vicinity of the upstream edge of the orifice plate,
and grid independence is not accomplished with the current mesh.
In particular, the recirculation zone within the orifice requires
greater resolution in order to model accurately the radial extent
of the vena contracta, and hence the pressure drop across the
orifice plate. The measured pressure drop across the whole domain
is 430 Pa, whereas the hybrid scheme predicts 322 Pa and the
linear-upwind scheme yields 372 Pa.
AUTOPLOT USE
FILE
PHI 5
d 1 p1 y 1;div x .092 1;shift x -10 1;plot 1;level y 430.
level y -330;scale x -10 20;scale y -350 450
msg Axial pressure distribution
msg Press to continue
pause
ENDUSE
PHOTON USE
p
10 1
0.20443E+04 0.15633E+04 CR
gr ou x 1
use patgeo;vec x 1 y 1 30 z 10 65 sh
mag gr 9
0.21789E+04 0.18043E+04 CR
msg Velocity vectors
msg Press to continue
pause
cl;con p1 x 1 y 1 30 z 10 65 shade;int 10
use patgeo
msg Pressure contours
msg Press to continue
cl;mag gr 1
mag gr 70
0.21853E+04 0.18433E+04 CR
gr x 1;use patgeo;con p1 x 1 y 1 30 z 15 65 shade;
int 10;use patgeo
ENDUSE
TEXT(2D TURBULENT FLOW THROUGH AN ORIFICE)
REAL(UR1,UR2,PR,RE,PI,UD,VIN,TSTEP,KEIN,EPIN,PD,PT,FRIC,DELT,US)
REAL(VMAX,AN,GY,GYP,GYM,GWI,GLM,GYDR,GYDR2,GYDR3,GYDR4,GKI,GEPI)
REAL(US2);INTEGER(F,UL,NZ11,NZ12,NZ13);CHAR(SCHM)
INTEGER(NZ1,NZ2,NZ3,NZ4,NZ5,NZ6,NZ7,NZ8,NZ9,NZ10,NY1,NY2,NY3)
RHO1=1.2;ENUL=15.0E-06
** UR1=orifice hole radius PR=pipe radius
UR1=0.032;PI=3.141592654;UD=PI/180.0;PR=0.046;PD=2*PR
PT=11.E-3;RE=7.5E4;VIN=RE*ENUL/PD
FRIC=1.0/(1.82*LOG10(RE)-1.64)**2
US=VIN*(FRIC/8.0)**0.5;US2=US*US;DELT=1.5*30.0*ENUL/US2
GROUP 3. X-direction grid specification
CARTES=F;NX=1;GRDPWR(X,NX,PI/8,1)
GROUP 4. Y-direction grid specification
NY1=19;NY2=10;NY3=1;NREGY=3
IREGY=1;GRDPWR(Y,NY1,UR1,-1.2)
IREGY=2;GRDPWR(Y,NY2,PR-UR1-DELT,1.2)
IREGY=3;GRDPWR(Y,NY3,DELT,1)
GROUP 5. Z-direction grid specification
** region z1 6D NZ1= 5 cells
** region z2 3D NZ2= 5 cells
** region z3 D-T NZ3= 5 cells
** region z4 T NZ4=12 cells
** region z5 T NZ5=17 cells (orifice plate)
** region z6 T NZ6=10 cells
** region z7 2.5D-T NZ7=16 cells
** region z8 15D NZ8=15 cells
NZ1=5;NZ2=5;NZ3=5;NZ4=12;NZ5=17;NZ6=10;NZ7=16;NZ8=15
NREGZ=8
Upstream region
IREGZ=1;GRDPWR(Z,NZ1,6*PD,-1.3)
IREGZ=2;GRDPWR(Z,NZ2,3*PD,-1.5)
IREGZ=3;GRDPWR(Z,NZ3,1*PD-PT,-1.4)
ORIFICE - 1 plate thickness upsteam, orifice, then 1 more
plate thickness downstream
IREGZ=4;GRDPWR(Z,NZ4, PT,-1.3)
IREGZ=5;GRDPWR(Z,-NZ5,PT, 1.4)
IREGZ=6;GRDPWR(Z,NZ6, PT, 1.2)
Downstream region
IREGZ=7;GRDPWR(Z,NZ7, 2.5*PD-pt, 1.35)
IREGZ=8;GRDPWR(Z,NZ8, 15*PD, 1.35)
F=NZ1+NZ2+NZ3+1;UL=F+NZ4
GROUP 7. Variables stored, solved & named
SOLVE(P1,V1,W1);SOLUTN(P1,Y,Y,Y,N,N,N)
TURMOD(KEMODL);STORE(ENUT,LEN1,YPLS);WALPRN=T
GROUP 8. Terms (in differential equations) & devices
MESG( Enter required convection scheme
MESG( Default: LUS for momentum; VANLH for k and eps
MESG( The alternative is:
MESG( HYB - Hybrid differencing for all variables
READVDU(SCHM,CHAR,HOC)
CASE :SCHM: OF
WHEN HYB,3
+ MESG(Hybrid-differencing scheme
+ TSTEP=30*PD/VIN/NZ
WHEN HOC,3
+ MESG(LUS for momentum; VANLH for k and e
+ TSTEP=3*PD/VIN/NZ
+ SCHEME(LUS,V1,W1);SCHEME(VANLH,KE,EP)
+ ENDIT(P1) = GRND1
ENDCASE
GROUP 11. Initialization of variable or porosity fields
FIINIT(V1)=0.0;FIINIT(W1)=VIN
KEIN=2.*US2;EPIN=0.1643*(KEIN**1.5)/(0.09*PR)
FIINIT(KE)=KEIN;FIINIT(EP)=EPIN
*** Blockage for plate
WALLCO=GRND3
CONPOR(ORIF,0,VOLUME,1,NX,-#2,NY,-#5,-#5)
GROUP 13. Boundary conditions and special sources
*** Inlet boundary; fully-developed turbulent flow
AN=1./SQRT(FRIC)
VMAX=VIN*(AN+1.)*(2.*AN+1.)/(2*AN*AN);AN=1./AN;GYM=0.
DO JJ=1,NY
+ GYP=YFRAC(JJ)*YVLAST;GY=.5*(GYP+GYM);GYDR=GY/PR
+ GYDR2=GYDR*GYDR;GYDR4=GYDR2*GYDR2
+ GWI=VMAX*(1.-GYDR)**AN;GLM=0.14-0.08*GYDR2-0.06*GYDR4;GLM=GLM*PR
+ GYDR3=GYDR2*GYDR;GKI=1.+2.*GYDR/3.+10.*GYDR3/3.;GKI=GKI*US2
+ GEPI=0.1643*GKI**1.5/GLM
+ PATCH(IN:JJ:,LOW,1,NX,JJ,JJ,1,1,1,1)
+ COVAL(IN:JJ:,P1,FIXFLU,RHO1*GWI)
+ COVAL(IN:JJ:,V1,ONLYMS,0.0);COVAL(IN:JJ:,W1,ONLYMS,GWI)
+ COVAL(IN:JJ:,KE,ONLYMS,GKI);COVAL(IN:JJ:,EP,ONLYMS,GEPI)
+ GYM=GYP
ENDDO
PATCH(OUTLET, HIGH,1,NX,1,NY,NZ,NZ,1,1)
COVAL(OUTLET,P1,1E3,0.0)
*** Wall friction for pipe wall
PATCH(T1,NWALL,1,NX,NY,NY,1,NZ,1,1)
COVAL(T1,W1,GENLAW,0.0)
COVAL(T1,KE,GENLAW,GENLAW);COVAL(T1,EP,GENLAW,GENLAW)
GROUP 15. Termination of sweeps
LSWEEP=300
GROUP 16. Termination of iterations
GROUP 17. Under-relaxation devices
RELAX(U1,FALSDT,TSTEP)
RELAX(V1,FALSDT,TSTEP);RELAX(W1,FALSDT,TSTEP)
RELAX(KE,LINRLX,0.5);RELAX(EP,LINRLX,0.5);KELIN=3
GROUP 23. Field print-out and plot control
IYMON=NY1-2;IZMON=UL+NZ5/2;TSTSWP=-1
NYPRIN=2;NZPRIN=1;ITABL=3;IZPRF=UL-5;IZPRL=UL+NZ5+5
** provision of longer names for output
spedat(LONGNAME,USOL,C,CUPWIND)
spedat(LONGNAME,CSOL,C,CCDS)
spedat(LONGNAME,QSOL,C,CQUICK)
spedat(LONGNAME,LSOL,C,CLINEAR_UPWIND)
spedat(LONGNAME,3SOL,C,CCUBIC_UPWIND)
spedat(LONGNAME,FSOL,C,CFROMM'S_SCHEME)
spedat(LONGNAME,SSOL,C,CSMART)
spedat(LONGNAME,KSOL,C,CKOREN)
spedat(LONGNAME,MSOL,C,CMINMOD)
spedat(LONGNAME,VSOL,C,CVAN_ALDBDA)
spedat(LONGNAME,BSOL,C,CSUPERBEE)
spedat(LONGNAME,HSOL,C,CHQUICK)
spedat(LONGNAME,NSOL,C,CVAN_LEER_1_(NOLL:)
spedat(LONGNAME,ZSOL,C,CVAN_LEER_2_ZHU:)
spedat(LONGNAME,OSOL,C,COSPRE)
spedat(LONGNAME,ISOL,C,CUMIST)