DISPLAY MONO-PROPELLANT ROCKET COMBUSTION 2-dimensional (x-y), Cartesian, steady, two-phase, elliptic simulation The problem considered is that of the injection of monopropellant droplets through small holes in one end of a rocket motor. These droplets burn (i.e undergo a phase change involving the disappearance of high-density liquid and its replacement by low- density gas), at a rate dependent upon the droplet diameter. As a consequence, a pressure gradient is set up which accelerates the gas and, to a lesser extent, the liquid. Friction between the droplets and the gas causes the former at first to deccelerate and later to accelerate. The model is highly idealised, and does not represent any particular motor or propellant. You will have an opportunity to vary the interphase-friction coefficient and the injection velocity of the liquid. enddis PHOTON USE p phi gr ou z 1 set vec comp au1 cv1 - msg Gas-velocity vectors vec z 1 sh msg Pressto continue pause vec off;red set vec comp bu2 dv2 - msg Droplet-velocity vectors vec z 1 sh msg Press to continue pause vec off;red msg volume fraction of liquid con liq z 1 sh;int 50 msg Press to continue pause msg Note that the grid is very coarse gr z 1 msg Press e to END enduse GROUP 1. Run title TEXT(Rock2; 2D MONOPROPELLANT ROCKET :W971 TITLE MESG(PC486/50 time last reported as 1.5 min DISPLAY The problem considered is that of the injection of monopropellant droplets through small holes in one end of a rocket motor. These droplets burn (i.e undergo a phase change involving the dis- appearance of high-density liquid and its replacement by low- density gas), at a rate dependent upon the droplet diameter. As a consequence, a pressure gradient is set up which accelerates the gas and, to a lesser extent, the liquid. Friction between the droplets and the gas causes the former at first to deccelerate and later a accelerate. The main task is to compute the distance from the injector at which the propellant is fully consumed, as functions: of the injection velocity, of the propellant and combustion-product properties, and of a measure of the relative speed of momentum and heat transfer. The GX-subroutine GXDROP is used for this case. ENDDIS Locally-defined parameters: FLOW mass flow rate at the inlet VELIN inlet velocity XLEN the length of the rocket motor CHATIM relaxation factor REAL(FLOW,VELIN,XLEN,CHATIM) FLOW=1.E3;VELIN=50.0;XLEN=1.0 CHATIM=XLEN/VELIN mesg(Two-dimensional monopropellant rocket GROUP 3. X-direction grid specification GRDPWR(X,100,XLEN,1.0) grdpwr(x,10,xlen,1.0) GROUP 4. Y-direction grid specification grdpwr(y,10,0.5*xlen,1.0) GROUP 7. Variables stored, solved & named ** Solve for one pressure, two velocities, the volume fractions of the two phases and the "shadow" volume fraction of the second (denser) phase. ONEPHS=F;SOLVE(P1,U1,U2,R1,R2,RS) NAME(U1)=AU1;NAME(U2)=BU2;NAME(R1)=GAS;NAME(R2)=LIQ;NAME(RS)=SHAD SOLUTN(GAS,Y,N,N,N,N,N);SOLVE(V1,V2);NAME(V1)=CV1;NAME(V2)=DV2 STORE(MDOT,CFIP) GROUP 8. Terms (in differential equations) & devices ** Cut off built-in sources and diffusion terms TERMS(GAS,Y,Y,N,Y,Y,Y);TERMS(LIQ,Y,Y,N,Y,N,Y) TERMS(SHAD,Y,Y,N,Y,N,Y);TERMS(AU1,Y,Y,N,Y,Y,Y) TERMS(BU2,Y,Y,N,Y,N,Y) GROUP 9. Properties of the medium (or media) RHO1=1.E1;RHO2=1.E4;PRESS0=1.E7 GROUP 10. Inter-phase-transfer processes and properties CFIPS=GRND1;CFIPC=1.0E5;CMDOT=1.0;rlolim=1.e-9 mesg(friction coefficient = :cfipc: mesg(enter a new value, or press readvdu(cfipc,real,1.e5) GROUP 11. Initialization of variable or porosity fields FIINIT(GAS)=0.999;FIINIT(LIQ)=0.001;FIINIT(SHAD)=0.001 FIINIT(AU1)=VELIN;FIINIT(BU2)=VELIN;FIINIT(MDOT)=0.01*FLOW GROUP 13. Boundary conditions and special sources ** Inlet at west end INLET(INLET,WEST,1,1,1,ny/2,1,1,1,1) VALUE(INLET,P2,2.0*FLOW);VALUE(INLET,BU2,VELIN) mesg(liquid-injection velocity = :velin: mesg(enter a new value, or press READVDU(VELIN,REAL,VELIN) VALUE(INLET,BU2,VELIN) ** Outlet at east end PATCH(OUTLET,CELL,NX,NX,1,ny/2,1,1,1,1) COVAL(OUTLET,P1,FIXP,0.0);COVAL(OUTLET,P2,FIXP*RHO2/RHO1,0.0) COVAL(OUTLET,AU1,ONLYMS,0.0);COVAL(OUTLET,BU2,ONLYMS,0.0) GROUP 15. Termination of sweeps LSWEEP=200 GROUP 16. Termination of iterations SELREF=T; RESFAC=1.E-2 GROUP 17. Under-relaxation devices RELAX(SHAD,LINRLX,0.6);RELAX(LIQ,LINRLX,0.6);RELAX(LIQ,LINRLX,0.2) RELAX(AU1,FALSDT,CHATIM);RELAX(BU2,FALSDT,CHATIM) RELAX(CV1,FALSDT,0.1*CHATIM);RELAX(DV2,FALSDT,0.1*CHATIM) GROUP 18. Limits on variables or increments to them VARMIN(10)=1.E-9;VARMAX(10)=1.E-3 GROUP 19. Data communicated by SATELLITE to GROUND ** PRTSIZ=T activates GXDROP PRTSIZ=T GROUP 21. Print-out of variables OUTPUT(GAS,N,N,N,N,N,N);OUTPUT(MDOT,Y,Y,Y,Y,Y,Y) GROUP 22. Spot-value print-out TSTSWP=5;IXMON=NX/2;NXPRIN=NX/20;UWATCH=T GROUP 23. Field print-out and plot control NPLT=1;ORSIZ=0.4;ITABL=1 PATCH(XPROFILE,PROFIL,1,NX,1,1,1,1,1,1) PLOT(XPROFILE,SHAD,0.0,0.0);PLOT(XPROFILE,LIQ,0.0,0.0) PLOT(XPROFILE,AU1,-1.0,-1.0);PLOT(XPROFILE,BU2,-1.0,-1.0) PATCH(XPROFIL2,PROFIL,1,NX,1,1,1,1,1,1) PLOT(XPROFIL2,CFIP,0.0,0.0);PLOT(XPROFIL2,MDOT,0.0,0.0) GROUP 24. Dumps for restarts TSTSWP=-1