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