{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 " " 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "with(Units[Natural]):" }}{PARA 7 " " 1 "" {TEXT -1 71 "Warning, the assigned names factor and polar now h ave a global binding\n" }}{PARA 7 "" 1 "" {TEXT -1 514 "Warning, these protected names have been redefined and unprotected: *, +, -, /, <, < =, <>, =, Im, Re, ^, abs, add, arccos, arccosh, arccot, arccoth, arccs c, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, argumen t, ceil, collect, combine, conjugate, convert, cos, cosh, cot, coth, c sc, csch, csgn, diff, eval, evalc, evalr, exp, expand, floor, frac, in t, ln, log, log10, max, min, mul, normal, root, round, sec, sech, seq, shake, signum, simplify, sin, sinh, sqrt, surd, tan, tanh, trunc, typ e, verify\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Units[UseSys tem](SI):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Constants" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "pi:=evalf(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#piG$\"+aEfTJ!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "g0:=9.81*m/s^2;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#g0G,$*&$\"$\")*!\"#\"\"\"-%%UnitG6#7#*&%\"mGF*%\"s GF)F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "R:=8.314*J/K/mol ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG,$*&$\"%9$)!\"$\"\"\"-%%Uni tG6#7#*,%\"mG\"\"#%#kgGF*%\"sG!\"#%\"KG!\"\"%$molGF6F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Dlox:=1.14*g/cm^3; # LOX density" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%DloxG,$*&$\"++++S6!\"'\"\"\"-%%Uni tG6#7#*&%#kgGF*%\"mG!\"$F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Dethanol:=.789*g/cm^3; # Ethanol density" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)DethanolG,$*&$\"++++!*y!\"(\"\"\"-%%UnitG6#7#*&%#kgG F*%\"mG!\"$F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Parameters." } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Thrust: =20*lbf; # Target thrust" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'ThrustG ,$*&\"#?\"\"\"-%%UnitG6#7#%$lbfGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "ISP:=200*s; # Specific impulse" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ISPG,$*&\"$+#\"\"\"-%%UnitG6#7#%\"sGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "Tc:=3000*K; # Chamber temperature a fter combustion" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#TcG,$*&\"%+I\"\" \"-%%UnitG6#7#%\"KGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " Pc:=130.0*psi; # Chamber pressure" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#PcG,$*&$\"%+8!\"\"\"\"\"-%%UnitG6#7#%$psiGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Pe:=1*atm; # Exhaust pressure" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#PeG-%%UnitG6#7#%$atmG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Ptank:=200*psi; # Tank pressure" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&PtankG,$*&\"$+#\"\"\"-%%UnitG6#7#%$psiGF(F(" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Dpipe:=.25*inch; # feed pip e diameter" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&DpipeG,$*&$\"#D!\"#\" \"\"-%%UnitG6#7#%#inGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "o2f:=1.5; # Oxydizer to fuel ratio" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$o2fG$\"#:!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " Mg:=24.0*g/mol; # Gas molecular mass" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%#MgG,$*&$\"+++++C!#6\"\"\"-%%UnitG6#7#*&%#kgGF*%$molG!\"\"F*F*" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Gamma:=1.15; # Gamma for ga s" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&GammaG$\"$:\"!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "Viscosity:=T->6e-5*(T/(3000*K))^0.6 *kg/(m*s); # Gas viscosity (from Tom's code)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*ViscosityGf*6#%\"TG6\"6$%)operatorG%&arrowGF(-_%(Nat uralG%\"*G6$-F-6$-F-6$$\"\"'!\"&-_F.%\"^G6$-F-6$9$-_F.%\"/G6#-F-6$\"%+ I%\"KG$F6!\"\"%#kgG-F@6#-F-6$%\"mG%\"sGF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "kappa:=T->0.12*(T/(3000*K))^0.5*W/(m*K); # Gas t hermal conductivity (from Tom's code)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&kappaGf*6#%\"TG6\"6$%)operatorG%&arrowGF(-_%(NaturalG%\"*G6$-F-6 $-F-6$$\"#7!\"#-_F.%\"^G6$-F-6$9$-_F.%\"/G6#-F-6$\"%+I%\"KG$\"\"&!\"\" %\"WG-F@6#-F-6$%\"mGFFF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "Dout:=7.5*cm; # Outside Diameter of engine" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%DoutG,$*&$\"#v!\"\"\"\"\"-%%UnitG6#7#%#cmGF*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Dc:=Dout-2*1*cm; # Chamber d iameter" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DcG,$*&$\"#b!\"\"\"\"\"- %%UnitG6#7#%#cmGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "Lst ar:=2.5*m; # Characteristic combustion length" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&LstarG,$*&$\"#D!\"\"\"\"\"-%%UnitG6#7#%\"mGF*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "alpha:=30.0*degrees; # Angle into throat" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG,$*&$\"$+$!\" \"\"\"\"-%%UnitG6#7#%'arcdegGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "beta:=15.0*degrees; # Angle of nozzle" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%betaG,$*&$\"$]\"!\"\"\"\"\"-%%UnitG6#7#%'arcdeg GF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "Tinitial:=300*K; # Temperature of engine before we start" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)TinitialG,$*&\"$+$\"\"\"-%%UnitG6#7#%\"KGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "Ninjectors:=10; # number of pairs o f injector holes" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+NinjectorsG\"#5 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "Cd:=.7; # discharge coe fficient of injector holes" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#CdG$ \"\"(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Calculation of engi ne geometry." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "mdot:=Thrust/(ISP*g0); # Mass flow rate" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%mdotG,$*&$\"+OZPMX!#6\"\"\"-%%UnitG6#7#*&%#kgGF*%\"s G!\"\"F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "mdot_f:=mdot/ (1+o2f); # Fuel mass flow rate" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'m dot_fG,$*&$\"+%*)\\P\"=!#6\"\"\"-%%UnitG6#7#*&%#kgGF*%\"sG!\"\"F*F*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "mdot_o:=mdot-mdot_f; # Oxy dizer mass flow rate" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'mdot_oG,$*& $\"+U[i?F!#6\"\"\"-%%UnitG6#7#*&%#kgGF*%\"sG!\"\"F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "vdot_o:=mdot_o/Dlox;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%'vdot_oG,$*&$\"+>I^'Q#!#9\"\"\"-%%UnitG6#7#*&% \"sG!\"\"%\"mG\"\"$F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " V_pipe_o:=vdot_o/(((Dpipe/2)^2)*pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%)V_pipe_oG,$*&$\"+)))\\d`(!#5\"\"\"-%%UnitG6#7#*&%\"mGF*%\"sG!\"\" F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "vdot_f:=mdot_f/Deth anol;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'vdot_fG,$*&$\"+5ez)H#!#9\" \"\"-%%UnitG6#7#*&%\"sG!\"\"%\"mG\"\"$F*F*" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 36 "V_pipe_f:=vdot_f/(((Dpipe/2)^2)*pi);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%)V_pipe_fG,$*&$\"+([q(es!#5\"\"\"-%%UnitG6#7#* &%\"mGF*%\"sG!\"\"F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "A i_f:=(mdot_f/Ninjectors)/(Cd*sqrt(2*Dethanol*(Ptank-Pc))); # per hole " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Ai_fG,$*&$\"+!)p&*)Q*!#<\"\"\"- %%UnitG6#7#*$)%\"mG\"\"#F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Di_f:=2*sqrt(Ai_f/pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%D i_fG,$*&$\"++B^dM!#8\"\"\"-%%UnitG6#7#%\"mGF*F*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "Di_f/inches;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"+:`Ah8!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "Ai_o:=(md ot_o/Ninjectors)/(Cd*sqrt(2*Dlox*(Ptank-Pc)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Ai_oG,$*&$\"+L8kr6!#;\"\"\"-%%UnitG6#7#*$)%\"mG\"\"# F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Di_o:=2*sqrt(Ai_o /pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Di_oG,$*&$\"+%*oNiQ!#8\"\" \"-%%UnitG6#7#%\"mGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " Di_o/inches;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+]Hh?:!#6" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Rg:=R/Mg; # Gas constant for gas" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#RgG,$*&$\"+nm;kM!\"(\"\"\"- %%UnitG6#7#*(%\"mG\"\"#%\"sG!\"#%\"KG!\"\"F*F*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 75 "Cstar:=sqrt(Gamma*Rg*Tc)/(Gamma*sqrt((2/(Gamma +1))^((Gamma+1)/(Gamma-1))));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&Cs tarG,$*&$\"+j`E'f\"!\"'\"\"\"-%%UnitG6#7#*&%\"mGF*%\"sG!\"\"F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "At:=Cstar*mdot/Pc; # Throat \+ area" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#AtG,$*&$\"+hyKv!)!#9\"\"\"- %%UnitG6#7#*$)%\"mG\"\"#F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Dt:=2*sqrt(At/pi); # Throat diameter" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DtG,$*&$\"+IM*R,\"!#6\"\"\"-%%UnitG6#7#%\"mGF*F*" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "Vc:=pi*Dc^2/4*Lcm*m+pi/(24* tan(alpha))*(Dc^3-Dt^3); # Chamber volume (cylinder + truncated cone) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#VcG*&,&*&$\"+W%HeP#!#7\"\"\"%$L cmGF+F+$\"+#>)\\[P!#9F+F+-%%UnitG6#7#*$)%\"mG\"\"$F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "Lchamber:=solve(Lstar=Vc/At,Lcm)*m; # Chamber length (before it tapers down)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)LchamberG,$*&$\"+%[8'>p!#6\"\"\"-%%UnitG6#7#%\"mGF*F *" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "A:=Mach->At/Mach*((1+( Gamma-1)/2*Mach^2)/(1+(Gamma-1)/2))^((Gamma+1)/2/(Gamma-1));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"AGf*6#%%MachG6\"6$%)operatorG%&arrowGF(- _%(NaturalG%\"*G6$-F-6$%#AtG-_F.%\"/G6#9$-_F.%\"^G6$-F-6$-_F.%\"+G6$\" \"\"-F-6$-F-6$-F@6$%&GammaG-_F.%\"-G6#FC-F56#\"\"#-F:6$F8FQ-F56#-F@6$F CFF-F-6$-F-6$-F@6$FJFCFO-F56#FHF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Mach_c:=fsolve(A(x)=pi*Dc^2/4,x=.1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'Mach_cG$\"+FVjC?!#6" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 94 "unassign('T0');\nT:=Mach->T0/(1+Mach^2*(Gamma-1)/2) ; # Temperature as a function of Mach number" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"TGf*6#%%MachG6\"6$%)operatorG%&arrowGF(-_%(NaturalG %\"*G6$%#T0G-_F.%\"/G6#-_F.%\"+G6$\"\"\"-F-6$-F-6$-_F.%\"^G6$9$\"\"#-F 76$%&GammaG-_F.%\"-G6#F:-F36#FDF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "T0:=solve(T(Mach_c)=Tc,T0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#T0G,$*&$\"+KA4+I!\"'\"\"\"-%%UnitG6#7#%\"KGF*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "unassign('P0');\nP:=Mach->P 0*(T0/T(Mach))^((Gamma)/(1-Gamma)); # Pressure as a function of Mach n umber" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"PGf*6#%%MachG6\"6$%)opera torG%&arrowGF(-_%(NaturalG%\"*G6$%#P0G-_F.%\"^G6$-F-6$%#T0G-_F.%\"/G6# -%\"TG6#9$-F-6$%&GammaG-F:6#-_F.%\"+G6$\"\"\"-_F.%\"-G6#FCF(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "P0:=solve(P(Mach_c)=Pc,P0); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P0G,$*&$\"+ZkI+8!\"(\"\"\"-%%Un itG6#7#%$psiGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "v_soun d:=Mach->sqrt(Gamma*Rg*T(Mach)); # Velocity of sound as a function of \+ Mach number" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(v_soundGf*6#%%MachG6 \"6$%)operatorG%&arrowGF(-_%(NaturalG%%sqrtG6#-_F.%\"*G6$-F26$%&GammaG %#RgG-%\"TG6#9$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "v_ gas:=Mach->Mach*v_sound(Mach); # Velocity of gas as a function of Mach number" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&v_gasGf*6#%%MachG6\"6$%) operatorG%&arrowGF(-_%(NaturalG%\"*G6$9$-%(v_soundG6#F1F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "Diam:=Mach->2*sqrt(A(Mach)/p i);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%DiamGf*6#%%MachG6\"6$%)opera torG%&arrowGF(-_%(NaturalG%\"*G6$\"\"#-_F.%%sqrtG6#-F-6$-%\"AG6#9$-_F. %\"/G6#%#piGF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "rho:= Mach->P(Mach)/(Rg*T(Mach));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$rhoG f*6#%%MachG6\"6$%)operatorG%&arrowGF(-_%(NaturalG%\"*G6$-%\"PG6#9$-_F. %\"/G6#-F-6$%#RgG-%\"TGF3F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Tt:=T(1); # Throat temperature" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#TtG,$*&$\"+sMy!z#!\"'\"\"\"-%%UnitG6#7#%\"KGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Pt:=P(1); # Throat pressure" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#PtG,$*&$\"+eDuou!\")\"\"\"-%%UnitG6 #7#%$psiGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "vt:=v_gas( 1); # Gas velocity at throat" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vtG ,$*&$\"+FXTa5!\"'\"\"\"-%%UnitG6#7#*&%\"mGF*%\"sG!\"\"F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "Mach_e:=fsolve(Pe=P(x),x=20); # Exh aust mach number" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'Mach_eG$\"+([7U 4#!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Ae:=A(Mach_e); # \+ Exit area" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#AeG,$*&$\"+$[aDw\"!#8 \"\"\"-%%UnitG6#7#*$)%\"mG\"\"#F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "De:=Diam(Mach_e); # Exit diameter" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#DeG,$*&$\"+)3]!)\\\"!#6\"\"\"-%%UnitG6#7#%\"mGF*F* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "Lnozzle:=(De-Dt)/2/tan( beta); # Length of the nozzle" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(Ln ozzleG,$*&$\"+3-iK!*!#7\"\"\"-%%UnitG6#7#%\"mGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "ISP:=v_gas(Mach_e)/g0; # Specific impulse t hat can be plugged in above" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ISPG ,$*&$\"+0N\\C?!\"(\"\"\"-%%UnitG6#7#%\"sGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Ae/At;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+\"R TE=#!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "(Lnozzle+Lchamb er+(Dc-Dt)/2/tan(alpha))/(1*inches); # Total length of part" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+%4)R4Y!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Forces" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "FTop:=Pc*Dc^2 /4*evalf(Pi). # Force on the top piece from the combustion pressure" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, premature end of input\n " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Heat transfer material consta nts" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "W allConductivity:=367*W/m^2/(K/m); # Thermal conductivity of the wall" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%1WallConductivityG,$*&\"$n$\"\"\"- %%UnitG6#7#**%#kgGF(%\"sG!\"$%\"KG!\"\"%\"mGF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "WallCapacity:=3.4e6*J/K/m^3; # Wall thermal capacity" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-WallCapacityG,$*&$\"#M \"\"&\"\"\"-%%UnitG6#7#**%\"mG!\"\"%#kgGF*%\"sG!\"#%\"KGF1F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "TWallMelt:=(866+273)*K; # Wa ll melting temperature" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*TWallMelt G,$*&\"%R6\"\"\"-%%UnitG6#7#%\"KGF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Heat transfer" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Cp:=Rg*Gamma/(Gamma-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#CpG,$*&$\"+66'el#!\"'\"\"\"-%%UnitG6#7#*(%\"mG\"\"#% \"sG!\"#%\"KG!\"\"F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "R eynolds:=Mach->rho(Mach)*v_gas(Mach)*Diam(Mach)/Viscosity(T(Mach)); # \+ Reynolds number" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ReynoldsGf*6#%%M achG6\"6$%)operatorG%&arrowGF(-_%(NaturalG%\"*G6$-F-6$-F-6$-%$rhoG6#9$ -%&v_gasGF7-%%DiamGF7-_F.%\"/G6#-%*ViscosityG6#-%\"TGF7F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "Prandtl:=Mach->Viscosity(T(M ach))*Cp/kappa(T(Mach)); # Prandtl number" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(PrandtlGf*6#%%MachG6\"6$%)operatorG%&arrowGF(-_%(Nat uralG%\"*G6$-F-6$-%*ViscosityG6#-%\"TG6#9$%#CpG-_F.%\"/G6#-%&kappaGF5F (F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "hg:=Mach->0.026*k appa(T(Mach))/Diam(Mach)*Reynolds(Mach)^0.8*(Prandtl(Mach))^0.4; # Hea t transfer coefficient for gas" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#h gGf*6#%%MachG6\"6$%)operatorG%&arrowGF(-_%(NaturalG%\"*G6$-F-6$-F-6$-F -6$$\"#E!\"$-%&kappaG6#-%\"TG6#9$-_F.%\"/G6#-%%DiamGF?-_F.%\"^G6$-%)Re ynoldsGF?$\"\")!\"\"-FH6$-%(PrandtlGF?$\"\"%FOF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "q:=Mach->hg(Mach)*(T(Mach)-Tinitial); # H eat flux assuming cold wall" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qGf *6#%%MachG6\"6$%)operatorG%&arrowGF(-_%(NaturalG%\"*G6$-%#hgG6#9$-_F.% \"+G6$-%\"TGF3-_F.%\"-G6#%)TinitialGF(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 27 "q(1); # Heat flux at throat" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&$\"+,W1)>)!\"$\"\"\"-%%UnitG6#7#*&%#kgGF(%\"sGF'F(F (" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "#WallConductivity:=wco nd*W/m/K;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "#WallCapacity: =wcap*J/m^3/K;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 242 "DeltaT:= Mach->1/8*Diam(Mach)*q(Mach)/WallConductivity*(3*Diam(Mach)^4-3*Dout^4 +4*Dout^4*ln(Dout/Diam(Mach)))/(Dout^2-Diam(Mach)^2)^2;\n# Difference \+ between wall temperature where it contacts gas and average wall temper ature throught thickness." }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'DeltaT Gf*6#%%MachG6\"6$%)operatorG%&arrowGF(-_%(NaturalG%\"*G6$-F-6$-F-6$-F- 6$-F-6$-F-6$\"\"\"-_F.%\"/G6#\"\")-%%DiamG6#9$-%\"qGFC-F=6#%1WallCondu ctivityG-_F.%\"+G6$-FK6$-F-6$\"\"$-_F.%\"^G6$FA\"\"%-_F.%\"-G6#-F-6$FR -FT6$%%DoutGFW-F-6$-F-6$FWFhn-_F.%#lnG6#-F-6$Fjn-F=6#FA-F=6#-FT6$-FK6$ -FT6$Fjn\"\"#-FY6#-FT6$FAF_pF_pF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "TDot:=Mach->2*pi*Diam(Mach)*q(Mach)/(pi*(Dout^2-Diam (Mach)^2)*WallCapacity); # How fast temperature is increasing in wall " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%TDotGf*6#%%MachG6\"6$%)operator G%&arrowGF(-_%(NaturalG%\"*G6$-F-6$-F-6$-F-6$\"\"#%#piG-%%DiamG6#9$-% \"qGF;-_F.%\"/G6#-F-6$-F-6$F8-_F.%\"+G6$-_F.%\"^G6$%%DoutGF7-_F.%\"-G6 #-FL6$F9F7%-WallCapacityGF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "TDot(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&$\"+L]'\\&))!\" *\"\"\"-%%UnitG6#7#*&%\"sG!\"\"%\"KGF(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 49 "Lifetime:=(TWallMelt-DeltaT(1)-Tinitial)/TDot(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)LifetimeG,$*&$\"+\"yHW\"y!\")\"\" \"-%%UnitG6#7#%\"sGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 " plot((TWallMelt-DeltaT(x)-Tinitial)/TDot(x)/s,x=Mach_c..Mach_e);" }} {PARA 13 "" 1 "" {GLPLOT2D 606 606 606 {PLOTDATA 2 "6%-%'CURVESG6$7`o7 $$\"3:+++FVjC?!#>$\"3_ytc*[(oZ;!#:7$$\"3;1aGE[!f;#F*$\"3&zA]#*e]kr\"F- 7$$\"3<73dD`<2BF*$\"3ZRdh*HL'p)p5=F-7$$ \"3bC;9Cjr*e#F*$\"3O0wfX!HA%=F-7$$\"3\"pV7FKdA(GF*$\"3iM'4uTlS)=F-7$$ \"3%*[KG@$)zaJF*$\"3f,fBqc.1>F-7$$\"3Ib'o0#)ogH$F*$\"3VNb#>/r<\">F-7$$ \"3mhS&)>$RtV$F*$\"3%))4Ba_K[\">F-7$$\"3-o%R\">)4'yNF*$\"35lruT/p:>F-7 $$\"3ot[U=.))>PF*$\"3#zvlg'os9>F-7$$\"3r&o&*pJ@C+%F*$\"3_yC&[OH&3>F-7$ $\"3U)\\mbJi\\G%F*$\"3?M/]`q8)*=F-7$$\"3\"zu\\)4j7:aF*$\"3?$*\\xbYhN=F -7$$\"3R(*H8/.HXlF*$\"3v7iQ=#yHw\"F-7$$\"3c7[g_*R'GvF*$\"3DFVlT&*4,^)F*$\"3G>#)f%**fHk\"F-7$$\"3)GW[&\\#R`\\*F*$\"3v*=&>q# H\"*e\"F-7$$\"3!e--)*))oy/\"!#=$\"3(HpC@3U&R:F-7$$\"3\"o<4[zW!p7F`q$\" 37zsLfP)=W\"F-7$$\"3%yK;)*p?-\\\"F`q$\"3CHg;mE9g8F-7$$\"3o)Q#H-F'Gr\"F `q$\"3?C1/xgU!H\"F-7$$\"3#)\\%oZq/b$>F`q$\"3sJ^[jEkI7F-7$$\"33L2nG&)3d @F`q$\"3T*f#3')o.z6F-7$$\"32;Id_BnyBF`q$\"3=\"['GNI%Q8\"F-7$$\"3\"f\\& \\\"\\X&*y#F`q$\"35/N!y8OM1\"F-7$$\"3A:([\"G3)\\@$F`q$\"3oR*)z%4QY+\"F -7$$\"3q8q!>mm\\l$F`q$\"3'G6iHU-?b*!#;7$$\"3]tj^b9a$4%F`q$\"3!4ux=Tr&[ \"*F`t7$$\"349#Q%Q&pYa%F`q$\"3hEc:Pe%y!))F`t7$$\"3@1*H%*RB?%\\F`q$\"3N 5\"f7uH\"f&)F`t7$$\"3GS0!Rt\\$*Q&F`q$\"3zFo:D,hF$)F`t7$$\"3gS(yK$G^QeF `q$\"3'>[2/@\"\\R\")F`t7$$\"3)4/Guqk8F'F`q$\"3SJ.3+Vx%*zF`t7$$\"3'=B1r nNWm'F`q$\"3_G7wnT'4*yF`t7$$\"3Ed0xF`t7$$\" 3E$)o7e%fgR)F`q$\"3gVM`(=XBp(F`t7$$\"3q/!G5wjL%))F`q$\"3wf+y%eM'*p(F`t 7$$\"32PJkNKIp#*F`q$\"3p\"*)f\"zUHExF`t7$$\"3?7*=MREPr*F`q$\"3@8'zw\"> otxF`t7$$\"315_heX=75!#<$\"3v;%3q]]T$yF`t7$$\"3so-0Fd?c5Fjx$\"3%HE`X*) 4q\"zF`t7$$\"36(HI\"\\8$>5\"Fjx$\"3h\")eO**3)>-)F`t7$$\"3Lw'pvjN<9\"Fj x$\"3%p$GH7\"[(G\")F`t7$$\"3O@$e&f`s%=\"Fjx$\"3diQ0)*p$*f#)F`t7$$\"3z9 *>*[z8H7Fjx$\"3#H(=!ytTET)F`t7$$\"3v=B*H+(es7Fjx$\"36$Quq_c)y&)F`t7$$ \"3F0h\"p>EYJ\"Fjx$\"3yZu$z*)=bv)F`t7$$\"38=@GaNIh8Fjx$\"3+byv]1+q*)F` t7$$\"3)z\"[$fBXKS\"Fjx$\"3aiEW=jHz\"*F`t7$$\"38u\"F-7$$\"3<\")4_ysGO=Fjx$\"36z2(>()\\`&*RJA>Fjx$\"3*Q&zM;&ptJ\"F-7 $$\"3!H.j^!\\Sj>Fjx$\"3]$**zv[)Gh8F-7$$\"3yH6D&Q;s+#Fjx$\"3Ma_\"4WT.T \"F-7$$\"3RNV\">c\\\"\\?Fjx$\"3/*4BI,(\\f9F-7$$\"33+++([7U4#Fjx$\"3khC vGoy9:F--%'COLOURG6&%$RGBG$\"#5!\"\"$\"\"!FbalFaal-%+AXESLABELSG6$Q\"x 6\"Q!Fgal-%%VIEWG6$;$\"+FVjC?!#6$\"+([7U4#!\"*%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "44 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }