TEXT(2D Flow In A Supersonic Diffuser
TITLE
DISPLAY
The problem considered is 2D supersonic flow in a 'supersonic
diffuser', i.e. a converging duct. The problem is solved using
the IPARAB=4 option of the parabolic solver. The flow enters
axially at MACH 2, and then passes over a 8o corner where a weak
oblique shock wave is generated of angle 37o, which is in turn
reflected from the bottom of the duct to arrive at the top corner
of the exit plane. The PHOENICS results are compared with the
results of shock theory below:
M1 M2 M3 | P1/Po1 P2/Po1 P3/Po1
Theory 2.0 1.71 1.42 | 0.128 0.197 0.293
PHOENICS 2.0 1.75 1.45 | 0.128 0.192 0.293
Here, M, P and Po denote Mach number, static pressure and total
pressure, respectively; and 1, 2 and 3 denote inlet, post
shock, and post reflected-shock, respectively.
ENDDIS
So as to allow a direct computation of dimensionless flow
variables, the flow equations are normalised such that the flow
variables can be interpreted as: P/Po; RHO/RHOo; T/To;
and U/Uref.
Here: Po, RHOo and To are the inlet total pressure, density
and temperature; Uref=Ao/SQRT(gam); and gam is the specific heat
ratio. Ao is the acoustic velocity at To (see Palacio et al, Int.
J.Heat Mass Transfer, Vol.33, No.6, p1193, [1990] ).
PHOTON USE
p
parphi
con mach x 1 fi;.01
pau;cl
vec x 1 sh
pau;cl
con p1 x 1 fi;.01
pau;cl
con rho1 x 1 fi;.01
ENDUSE
REAL(GASCON,GAMMA,PTOTAL,TTOTAL,RHOTOT,MACHI,PEXRAT,AGAM1,RGAM)
REAL(DTF,PIN,TIN,POWER,WIN,RHOIN,PEXIT,CHORD)
REAL(AIN,FLOWIN,ANG1,PI,TANA,YIN,YOUT,ZLEN)
PI=3.1415927
GASCON=1.0;GAMMA=1.4;PTOTAL=1.0;TTOTAL=1.0;RHOTOT=1.0
MACHI=2.0;YIN=1.0;ZLEN=2.3
** Corner angle
ANG1=8.0;ANG1=ANG1*PI/180.;TANA=-TAN(ANG1)
** Calculation of inlet velocity
AGAM1=GAMMA-1.;RGAM=1./GAMMA;POWER=GAMMA/AGAM1
PIN=PTOTAL/(1.+AGAM1*MACHI*MACHI/2.)**POWER
RHOIN=RHOTOT/(PTOTAL/PIN)**RGAM
WIN=MACHI*(GAMMA*PIN/RHOIN)**0.5
** Calculation of Inlet Temperature
TIN=PIN/(GASCON*RHOIN)
GROUP 1. Run title and other preliminaries
GROUP 2. Transience; time-step specification
** activate wholly-supersonic 'parabolic' solver
PARAB=T;IPARAB=4
GROUP 4. Y-direction grid specification
GRDPWR(Y,80,YIN,1.0)
AZYV=1.0;ZWADD=YIN/TANA
GROUP 5. Z-direction grid specification
GRDPWR(Z,320,ZLEN,1.0)
GROUP 7. Variables stored, solved & named
SOLVE(P1,V1,W1);STORE(RHO1,MACH)
GROUP 8. Terms (in differential equations) & devices
TERMS(V1,P,P,N,P,P,P);TERMS(W1,P,P,N,P,P,P)
V1AD=GRND1 ; DENPCO=T
GROUP 9. Properties of the medium (or media)
** Use Isentropic Density Law
RHO1=COMPRESS;RHO1A=RHOTOT/PTOTAL**RGAM;RHO1B=RGAM
RHO1C=0.;PRESS0=0.;DRH1DP=COMPRESS
GROUP 11. Initialization of variable or porosity fields
FIINIT(P1)=PIN;FIINIT(W1)=WIN;FIINIT(RHO1)=RHOIN
GROUP 13. Boundary conditions and special sources
INLET(IN,LOW,1,NX,1,NY,1,1,1,1)
VALUE(IN,P1,RHOIN*WIN);VALUE(IN,W1,WIN)
GROUP 16. Termination of iterations
AIN=YVLAST;FLOWIN=WIN*RHOIN*AIN
RESREF(P1)=1.E-12*FLOWIN
RESREF(V1)=RESREF(P1)*WIN;RESREF(W1)=RESREF(V1)
LITER(P1)=20;LITHYD=10
GROUP 17. Under-relaxation devices
RELAX(P1,LINRLX,0.7)
DTF=ZLEN/WIN
RELAX(V1,FALSDT,DTF);RELAX(W1,FALSDT,DTF)
GROUP 18. Limits on variables or increments to them
GROUP 19. EARTH Calls To GROUND Station
GROUP 22. Spot-value print-out
IYMON=NY/2;NPLT=2;TSTSWP=-1
GROUP 23. Field print-out and plot control
ITABL=2;NYPRIN=2;NZPRIN=NZ/4
IF(NZ.GT.1) THEN
+ IDISPA=2;IDISPB=1;IDISPC=NZ
ENDIF