Dan Harter
Combustion HW 4
1.
"a C3H8O0 + b O2 + c N2 -> d H2O + e CO2 + f N2 + g O2 + h CO + i NO + j H2 + k OH + l H + m O + n
N"
"Fuel Properties"
Carbon=3
Hydrogen=8
Oxygen=0
nfuelr=1
a=nfuelr
"100% Theoretical Air"
b=Hydrogen/4+Carbon
b=percentair*no2r
percentair=1
"Air is 79% N2, 21% O2"
c=3.76*b
"Carbon Balance"
Carbon*a=e+h
e=nco2p
h=ncop
"Hydrogen Balance"
Hydrogen*a=2*d+2*j+k+l
d=nh2op
j=nh2p
l=nhp
"Oxygen Balance"
Oxygen*a+2*b=d+2*e+2*g+h+i+k+m
g=no2p
k=nohp
m=nop
"Nitrogen Balance"
2*c=2*f+i+n
c=nn2r
f=nn2p
i=nnop
n=nnp
"nnp=.001"
"Temperature Settings"
Tfuel=298
Tair=298
"Tp=2264"
"Energy Equation"
0=nfuelr*hfuelr+no2r*ho2r+nn2r*hn2r-nh2op*hh2op-nco2p*hco2p-nn2p*hn2p-no2p*ho2p-ncop*hcopnnop*hnop-nh2p*hh2p-nohp*hohp-nhp*hhp-nop*hop-nnp*hnp
"Enthalpies"
hfuelr=enthalpy(C3H8,T=Tfuel)
ho2r=enthalpy(O2,T=Tair)
hn2r=enthalpy(N2,T=Tair)
hh2op=enthalpy(H2O,T=Tp)
hco2p=enthalpy(CO2,T=Tp)
hn2p=enthalpy(N2,T=Tp)
ho2p=enthalpy(O2,T=Tp)
hcop=enthalpy(CO,T=Tp)
hnop=enthalpy(NO,T=Tp)
hh2p=enthalpy(H2,T=Tp)
hohp=enthalpy(OH,T=Tp)
hhp=enthalpy(H,T=Tp)
hop=enthalpy(O,T=Tp)
hnp=enthalpy(N,T=Tp)
"Equilibrium Equations"
gco2p-gcop-go2p/2=0
2*gnop-go2p-gn2p=0
gh2op-gh2p-go2p/2=0
gh2op-gohp-gh2p/2=0
gh2p-2*ghp=0
go2p-2*gop=0
gn2p-2*gnp=0
"Gibbs Free Energy"
gco2p=hco2p-Tp*sco2p
gcop=hcop-Tp*scop
go2p=ho2p-Tp*so2p
gnop=hnop-Tp*snop
gn2p=hn2p-Tp*sn2p
gh2op=hh2op-Tp*sh2op
gh2p=hh2p-Tp*sh2p
gohp=hohp-Tp*sohp
ghp=hhp-Tp*shp
gop=hop-Tp*sop
gnp=hnp-Tp*snp
"Entropies"
sco2p=entropy(CO2,T=Tp,P=pco2p)
scop=entropy(CO,T=Tp,P=pcop)
so2p=entropy(O2,T=Tp,P=po2p)
snop=entropy(NO,T=Tp,P=pnop)
sn2p=entropy(N2,T=Tp,P=pn2p)
sh2op=entropy(H2O,T=Tp,P=ph2op)
sh2p=entropy(H2,T=Tp,P=ph2p)
sohp=entropy(OH,T=Tp,P=pohp)
shp=entropy(H,T=Tp,P=php)
sop=entropy(O,T=Tp,P=pop)
snp=entropy(N,T=Tp,P=pnp)
"Partial Pressures"
p=1
pco2p=xco2p*p
pcop=xcop*p
po2p=xo2p*p
pnop=xnop*p
pn2p=xn2p*p
ph2op=xh2op*p
ph2p=xh2p*p
pohp=xohp*p
php=xhp*p
pop=xop*p
pnp=xnp*p
"Molar Fractions"
ntotp=nh2op+nco2p+nn2p+no2p+ncop+nnop+nh2p+nohp+nhp+nop+nnp
xco2p=nco2p/ntotp
xcop=ncop/ntotp
xo2p=no2p/ntotp
xnop=nnop/ntotp
xn2p=nn2p/ntotp
xh2op=nh2op/ntotp
xh2p=nh2p/ntotp
xohp=nohp/ntotp
xhp=nhp/ntotp
xop=nop/ntotp
xnp=nnp/ntotp
2.
"a C3H8O0 + b O2 + c N2 -> d H2O + e CO2 + f N2 + g O2 + h CO + i NO + j H2 + k OH + l H + m O + n
N"
"Fuel Properties"
Carbon=3
Hydrogen=8
Oxygen=0
nfuelr=1
a=nfuelr
"100% Theoretical Air"
b=Hydrogen/4+Carbon
b=no2r
"Air is 79% N2, 21% O2"
c=3.76*b
"Carbon Balance"
Carbon*a=e+h
e=nco2p
h=ncop
"Hydrogen Balance"
Hydrogen*a=2*d+2*j+k+l
d=nh2op
j=nh2p
l=nhp
"Oxygen Balance"
Oxygen*a+2*b=d+2*e+2*g+h+i+k+m
g=no2p
k=nohp
m=nop
"Nitrogen Balance"
2*c=2*f+i+n
c=nn2r
f=nn2p
i=nnop
n=nnp
"nnp=.001"
"Temperature Settings"
Tfuel=298
Tair=298
"Tp=2264"
"Energy Equation"
0=nfuelr*hfuelr+no2r*ho2r+nn2r*hn2r-nh2op*hh2op-nco2p*hco2p-nn2p*hn2p-no2p*ho2p-ncop*hcopnnop*hnop-nh2p*hh2p-nohp*hohp-nhp*hhp-nop*hop-nnp*hnp
"Enthalpies"
hfuelr=enthalpy(C3H8,T=Tfuel)
ho2r=enthalpy(O2,T=Tair)
hn2r=enthalpy(N2,T=Tair)
hh2op=enthalpy(H2O,T=Tp)
hco2p=enthalpy(CO2,T=Tp)
hn2p=enthalpy(N2,T=Tp)
ho2p=enthalpy(O2,T=Tp)
hcop=enthalpy(CO,T=Tp)
hnop=enthalpy(NO,T=Tp)
hh2p=enthalpy(H2,T=Tp)
hohp=enthalpy(OH,T=Tp)
hhp=enthalpy(H,T=Tp)
hop=enthalpy(O,T=Tp)
hnp=enthalpy(N,T=Tp)
"Equilibrium Equations"
gco2p-gcop-go2p/2=0
{2*gnop-go2p-gn2p=0}
gh2op-gh2p-go2p/2=0
gh2op-gohp-gh2p/2=0
gh2p-2*ghp=0
go2p-2*gop=0
{gn2p-2*gnp=0}
"Gibbs Free Energy"
gco2p=hco2p-Tp*sco2p
gcop=hcop-Tp*scop
go2p=ho2p-Tp*so2p
gnop=hnop-Tp*snop
gn2p=hn2p-Tp*sn2p
gh2op=hh2op-Tp*sh2op
gh2p=hh2p-Tp*sh2p
gohp=hohp-Tp*sohp
ghp=hhp-Tp*shp
gop=hop-Tp*sop
gnp=hnp-Tp*snp
"Entropies"
sco2p=entropy(CO2,T=Tp,P=pco2p)
scop=entropy(CO,T=Tp,P=pcop)
so2p=entropy(O2,T=Tp,P=po2p)
snop=entropy(NO,T=Tp,P=pnop)
sn2p=entropy(N2,T=Tp,P=pn2p)
sh2op=entropy(H2O,T=Tp,P=ph2op)
sh2p=entropy(H2,T=Tp,P=ph2p)
sohp=entropy(OH,T=Tp,P=pohp)
shp=entropy(H,T=Tp,P=php)
sop=entropy(O,T=Tp,P=pop)
snp=entropy(N,T=Tp,P=pnp)
"Partial Pressures"
p=1.01325
pco2p=xco2p*p
pcop=xcop*p
po2p=xo2p*p
pnop=xnop*p
pn2p=xn2p*p
ph2op=xh2op*p
ph2p=xh2p*p
pohp=xohp*p
php=xhp*p
pop=xop*p
pnp=xnp*p
"Molar Fractions"
ntotp=nh2op+nco2p+nn2p+no2p+ncop+nnop+nh2p+nohp+nhp+nop+nnp
xco2p=nco2p/ntotp
xcop=ncop/ntotp
xo2p=no2p/ntotp
xnop=nnop/ntotp
xn2p=nn2p/ntotp
xh2op=nh2op/ntotp
xh2p=nh2p/ntotp
xohp=nohp/ntotp
xhp=nhp/ntotp
xop=nop/ntotp
xnp=nnp/ntotp
"Molar Concentrations"
vtotp=ntotp*R*Tp/p
R=8.314e-2
mn2p=nn2p/vtotp
mo2p=no2p/vtotp
mop=nop/vtotp
mohp=nohp/vtotp
mhp=nhp/vtotp
mnop=nnop/vtotp
mnp=nnp/vtotp
"Reaction Rates"
k1=1.8e11*exp(-38370/Tp)
k2=3.8e10*exp(-425/Tp)
k3=1.8e7*Tp*exp(-4680/Tp)
k4=3.8e6*Tp*exp(-20820/Tp)
k5=7.1e10*exp(-450/Tp)
k6=1.7e11*exp(-24560/Tp)
"N Production"
dndt=k1*mop*mn2p-k2*mnop*mnp-k3*mnp*mo2p+k4*mnop*mop-k5*mnp*mohp+k6*mnop*mhp
dndt=0
"NO Production"
dnodt=k1*mop*mn2p-k2*mnop*mnp+k3*mnp*mo2p-k4*mnop*mop+k5*mnp*mohp-k6*mnop*mhp
mnop=integral(dnodt,time)