GROUP 1. Run title TEXT(De Laval Nozzle X Direction TITLE DISPLAY Transonic flow in a convergent-divergent nozzle is considered. The throat is situated at one-third of the length of the duct. The geometry of the nozzle is: convergent section, inlet area = 1.34; throat area= 1.0 divergent section, outlet area = 1.65. The inlet Mach number is 0.5, and the design exit Mach number is 0.6 for which Pexit/Po =0.784. Consequently, a standing shock wave is created in the divergent section. The alteration of the cross-sectional area as a function of x is provided by means of the east-face porosity factor. ENDDIS Locally-defined parameters: GAMMA Specific heats ratio GASCON Perfect gas constant P0 Stagnation pressure T0 Stagnation temperature RHO0 Stagnation density MACHIN Inlet MACH number RHOIN Inlet density CIN Inlet sound speed VELIN Inlet gas velocity PIN Inlet pressure PEXIT Exit pressure INTEGER(IXTHR);REAL(GAMMA,GASCON,PEXIT,GAM1,POWER) REAL(TINDT0,RHO0,T0,P0,RHOIN,MACHIN,PIN,VELIN,CIN) REAL(CMASS,VMASS) ** Gas constants GAMMA=1.4;GASCON=287.0 GAM1=GAMMA-1.0;POWER=GAMMA/(GAMMA-1.0) ** Total pressure, temperature, density, inlet Mach Number P0=1.0; T0=1.0;RHO0=P0/(GASCON*T0); MACHIN=0.5 ** Inlet sound speed & velocity CIN=(GAMMA*P0/RHO0)**.5; VELIN=MACHIN*CIN ** Inlet static pressure & density TINDT0=1./(1.+GAM1/2.*MACHIN**2) RHO1B=1./GAMMA; RHO1A=RHO0/(P0**RHO1B) PIN=P0*TINDT0**POWER; RHOIN=RHO1A*PIN**RHO1B ** Exit pressure PEXIT=P0*0.784 GROUP 3. X-direction grid specification GRDPWR(X,60,1.0,1.0) GROUP 7. Variables stored, solved & named SOLVE(P1,U1);STORE(RHO1,EPOR) GROUP 8. Terms (in differential equations) & devices ** Remove viscous terms TERMS(U1,P,P,N,P,P,P) GROUP 9. Properties of the medium (or media) ** Select isentropic gas law RHO1=COMPRESS;DRH1DP=COMPRESS GROUP 11. Initialization of variable or porosity fields INIADD=F FIINIT(U1)=2.0*VELIN;FIINIT(RHO1)=0.5*RHOIN FIINIT(P1)=0.5*(P0+PEXIT) ** Convergent section: inlet area = 1.34; throat area= 1.0 PATCH(CONV,LINVLX,1,NX/3,1,1,1,1,1,1) INIT(CONV,EPOR,-1.0,1.34) ** Divergent section: outlet area = 1.65 PATCH(DIV,LINVLX,NX/3+1,NX,1,1,1,1,1,1) INIT(DIV,EPOR,1.0,1.0) GROUP 13. Boundary conditions and special sources ** The prescription of the stagnation pressure at the nozzle inlet is obtained from the following relationship between the stagnation pressure and the inlet values of Mach number and density: p0=rhoin*[1+0.5*(gamma-1)*Min**2]**[gamma/(gamma-1)]. When the inlet mass-flow per unit area is made the subject of this equation, the familiar co & val form results: rhoin*uin=co*(val-pP), where, co=2*gamma/[uin*(gamma-1)], val=p0*rhoin/rho0. For this case, the inlet velocity which appears in co ie. uin is assumed known. Strictly speaking this quantity is a function of the calculation, and should hence be re-calculated in GROUND as the calculation proceeds. CMASS=2.*POWER/VELIN;VMASS=RHOIN*P0/RHO0 PATCH(INLET,WEST,1,1,1,1,1,1,1,1) COVAL(INLET,P1,CMASS,VMASS) COVAL(INLET,U1,ONLYMS,VELIN) ** The static pressure is prescribed at the outlet PATCH(OUTLET,EAST,NX,NX,1,1,1,1,1,1) COVAL(OUTLET,P1,10.,PEXIT) COVAL(OUTLET,U1,ONLYMS,0.0) GROUP 15. Termination of sweeps LSWEEP=100 GROUP 17. Under-relaxation devices RELAX(U1,FALSDT,0.05*XULAST/VELIN) GROUP 22. Spot-value print-out IXMON=NX-5;TSTSWP=LSWEEP/10;ITABL=1 GROUP 23. Field print-out and plot control IXPRF=NX/2;NXPRIN=NX/10;ORSIZ=.4 PATCH(PLOT,PROFIL,1,NX,1,1,1,1,1,1);PLOT(PLOT,P1,0,0) PLOT(PLOT,U1,0,0)