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Assumng 100kmoles of dry mixture

PRODUCTS OF COMBUSTION COMPOSITION IN PERCENTS
10% CO2
1% CO
4% H2
2% CH4
0.46% C8H18
1% SO2
2% NO2
79.54% N2
COMBUSTION EQUATION TAKES FORM GIVEN BELOW : Assuming 100Kmoles of Produts Mixture :
2.085C8H18 + 1S + 25.691[O2 + 3.76N2] ----> 2CH4 + 0.46C8H18 + 4H2 + 10CO2 + 1CO + 8.88O2 + 1SO2 +2NO2 + 6.625H2O + 96.6N2
OXYGEN BALANCE ON BOTH SIDES OF EQUATION :
25.691 = 25.693
HYDROGEN BALANCE ON BOTH SIDES OF EQUATION :
18.765 = 18.765
CARBON BALANCE ON BOTH SIDES OF EQUATION :
16.68 = 16.68
COMBUSTION EQUATION TAKES FORM GIVEN BELOW : Assuming 1Kmoles of Produts Mixture :
1C8H18 + 0.48S + 12.32182[O2 + 3.76N2] ----> 0.9592CH4 + 0.2206C8H18 + 1.92H2 + 4.7962CO2 + 0.4796CO + 4.259O2 + 0.4796SO2 +0.9592NO2 + 3.1775H2O + 46.3309N2
OXYGEN BALANCE ON BOTH SIDES OF EQUATION :
12.32182 = 12.32255
%age EXCESS AIR IN THE EQUATION :
Excess Air :
Stichometric/Chemically Correct Equation is :
1C8H18 + 8.06355[O2 + 3.76N2] ----> 0.9592CH4 + 0.2206C8H18 + 1.92H2 + 4.7962CO2 + 0.4796CO + 0.4796SO2 + 0.9592NO2 + 3.1775H2O + 30.32N2
OXYGEN BALANCE ON BOTH SIDES OF EQUATION :
8.06355 = 8.06355 Excess Air : 53%
Air/Fuel Ratio :
Air/Fuel Ratio : 14.89
Dew Point Temperature Of Products :
Total Number of Moles : 63.5818
Dew Point Pressure : 5.0637kPa
dew point temperature is saturation temperature at pressure P_H2O = 5.0637kPa
is
'A psychrometric chart is a graphical representation of the psychrometric processes of air. Psychrometric processes include physical and thermodynamic properties such as dry bulb temperature, wet bulb temperature, humidity, enthalpy, and air density.'
T_dewpoint = T_Saturation@11.1260kPa =
ADIABATIC FLAME POINT Temperature Of Products [ METHOD I ]:
1 KJ/Kgm = 1 J/gm
As 100 Kmoles of Mixture was Assumed ,So Divide Total Moles by 1000/100 =10
Molecular Wt Of Fuel :114.230gm/mol
dQ_CV = -3009938.856 - [ -249950 ] = -2759988.856KJ/Kmol      OR     -2416.168J/gm of Fuel
T_Adiabatic_Flame_Point:1608.721 K
ADIABATIC FLAME POINT Temperature Of Products [ METHOD II ]:
Enthalpy Products :77760.0477031 Btu/Ibmol
Enthalpy Reactants : -89681.973 Btu/Ibmol
Enthalpy : [ -121689.54458714 ] Btu/Ibmol = [ -283051.09760513 ] J/mol OR [ KJ/Kmol ] = [ -2477.905 ] KJ/Kgm Of Fuel At T_Adiabatic_Flame_Point:1616.05 K
1700 = [ 1600 ] = [ 1616.05 ]
T_Adiabatic_Flame_Point:1616.05 K
Cp,Cv,R, Mol_wt OF PRODUCTS OF COMBUSTION :
111.68600192594
SubstanceVolume per m3 MixtureMol WtProportional WtWt Per Kgm Of MixCp[J/Kgm-K]Cv[J/Kgm-K]Cp_mix[J/Kgm-K]Cv_mix[J/Kgm-K]
(a)(b)c=(a.b)d=[c / sum of c](e)(f)g=(d.e)k=(d.f)
CH40.0216.043 0.320.012253.701735.4022.5417.35
C8H180.0046114.230 0.530.021711.301638.5034.2332.77
H20.042.016 0.08060.002714310.0010183.0038.6427.49
CO20.144.011 4.40.15846.00657.00126.998.55
CO0.0128.011 0.280.011040.00744.0010.47.44
O20.0432.000 1.280.041181.00653.0047.2426.12
SO20.0164.060 0.640.02888.30503.0017.7710.06
NO20.0246.008 0.920.031284.00696.0038.5220.88
N20.7528128.016 21.090.711039.00743.00737.69527.53
Sum (a)=0.99741Sum (c)=29.54sum (d)=0.99sum Cp = 1073.93sum Cv =768.19


Adiabatic T(K) :1608.721454089K
Cp_mixture :1073.93J/Kgm-K
Cv_mixture :768.19J/Kgm-K
R_mixture :305.74J/Kgm-K
Gama_mix :1.4
Mol_Wt_mixture :27.19Kgm/Kmol
V_CO2 :0.10743471320262m3
V_Cylinder :0.0003994015311m3

MEAN EFFECTIVE PRESSURE OF ENGINE [ MEP ]

Mean Effective pressure Calculations URL[ British Units ]=http://www.harleyc.com/prelude/articles/allaboutmeaneffectivepressure
Mean Effective pressure Calculations URL[ SI Units ]=https://x-engineer.org/automotive-engineering/internal-combustion-engines/ice-components-systems/mean-effective-pressure-mep/
ENGINE HP = 170hp OR 1 hp = 746 Watts , Power(Watts) = T . w = Engine Torque = 241.869 N-m Or Joules
ENGINE TORQUE = 178.393 ft-Ibf
CID=Displacement in cc [Engine Power in cc] / 16.387 = 97.333 cubic inches.
Mean Effective Pressure can be calculated using the following formula:
MEP = Power/Vol_Cylinder =1905150.1177382 N/m2
P_em = 19.052Bar


REACTION MASS CALCULATION OF ENGINE

https://sciencing.com/calculate-mass-reaction-mixture-8620099.html Mass Air Flow Rate =0.175539717Ibm/sec
Mass m Of Mixture at T_Adiabatic_Flame_Point: 1.961Kgm
Mass m Of Mixture at T_Adiabatic_Flame_Point: 5.7E-5Kgm
Enthalpy of Combustion of OCTANE from website url :http://www.ausetute.com.au/heatcomb.html is dH = -5460 KJ/mol
Conversion of molar enthapy from site url :http://www.conversiontables.info/index.php?page=online_conversion&item=Enthalpy%20[Molar]
Enthalpy Change Calculator site url : http://www.calistry.org/calculate/enthalpyChageCalculator
Enthalpy Calculations :https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Thermodynamics/State_Functions/Enthalpy/Heat_of_Reaction
https://socratic.org/questions/methanol-ch3oh-reacts-with-oxygen-from-air-in-combustion-reaction-to-form-water-
http://fluid.wme.pwr.wroc.pl/~spalanie/dydaktyka/combustion_MiBM/fund/Stoichiometry.pdf
http://yeahchemistry.com/questions/stoichiometryfind-mass-co2-formed-combustion-reaction-given-mass-hydrocarbon
https://www.scientificamerican.com/article/experts-weight-ratio-co2-fuel/
https://www.convertunits.com/from/moles+Octane/to/grams


ENGINE CALCULATIONS URL :http://chemistry.oregonstate.edu/courses/ch221-3/ch222/2011/Gases%20II.pdf


dH : dU + (n_R - n_P) x R x T ,n=no of moles [gm/mol] or [ Kgm / KMol ]
dH : ( ( n_Total- ax ) x[ Cv x Mol_Wt_Mix ] x (T2 - T1)) + ( ( n_P - n_R ) * R_Universal x T )
dU :1722890961.94 J
dH :1723731800.97 J
dH :1723731.8 KJ
dH :27543659.67 KJ/Kmol,As 100 Kmoles of Mixture was Assumed ,So Divide Total Moles by 1000/100 =10
dH :-2754.37 KJ/mol Or -1184.166 BTU/Ibmol at 2908.09 R


dQ_CV = ( H_Products - H_Reactants ) KJ/Kmol
dQ_CV :-2759988.856KJ/Kmol
dH_CV :-2759.99KJ/mol Or -1186.582 BTU/Ibmol at T_Adiabatic_Flame:2894.902 R


dQ_H_BTU = dH = H_Products - H_Reactants
dQ_H_BTU :-44840.99BTU / Ibm
dQ_H_BTU :-104292.97KJ/Kgm of Fuel
dQ_H_KJ :-2835725.85KJ/Kmol
dQ_H_KJ :-2835.73KJ/mol of Fuel Or -1219.144 BTU/Ibmol at T_Adiabatic_Flame:2908.09 R


TURBINE CALCULATIONS
GUIDE BLADE INLET PROPERTIES [ ACT AS NOZZLES ]:
P_Inlet :276.312Psi
T_Inlet :2895.699R

TURBINE INLET PROPERTIES [CRITICAL POINT OR CHOCKING OF NOZZLE ]:

Pc :145.51Psi
Tc :2403.09R


TURBINE EXIT PROPERTIES [SHOCKLESS EXIT TO ATMOSPHERE ]:
P_Exit :18Psi
T_Exit :1308.73R

ADIABATIC ENTHALPY DROP IN GUIDE BLADE [Hd = H1-Hc ] : 1 BTU = 778 ft-Ibf [ E.H LEWITT PAGE 374 , 773]

Hd : 96268.9ft/Ibf Per Pound of air
Hd : 123.74 BTU

ADIABATIC ENTHALPY DROP IN GUIDE BLADE WITH FRICTIONAL REHEATING[Hd_f = Frictional_Reheat_CoEff_GuideBlades * Hd ] : 1 BTU = 778 ft-Ibf [ E.H LEWITT PAGE 374 , 773]
Hd_f : 105 BTU

FRICTIONAL REHEAT TEMPERATURE IN GUIDE BLADE Tc[ Tc_Actual = Tc + ( ( 1 - Frictional_Reheat_CoEff_GuideBlades ) * Hd ) / Cp_mix ] : 1 BTU = 778 ft-Ibf [ E.H LEWITT PAGE 374 , 773]
Tc_Actual : 2475.44 R

[ Ui^2/2 x 2g = Hd ] : Ui = 224 sqrt(k x Hd) :[ E.H LEWITT PAGE 365 ]
Ui : 2297.27ft/sec

[ VOLUME OF FLOW ,Vc = ( R_mix x m_Rate x Tc / 144 x Pc ): [ E.H LEWITT PAGE 365 ]
Volume Of Flow [ Discharge ] , Vc [ Turbine Inlet ]: 6.8675ft3/sec

[ WEIGHT OF FLOW ,Wc = ( 144 x Pc x Vc = R_mix x Wc x Tc ): [ E.H LEWITT PAGE 365 ]
Weight Of Flow [ Weight Rate OF Flow ] , Wc [ Turbine Inlet ]: 1.0538Ibf/sec

ADIABATIC ENTHALPY DROP IN TURBINE BLADES [Hd1 = Hc-H2 ] : 1 BTU = 778 ft-Ibf [ E.H LEWITT PAGE 374 , 773]

Hd1 : 220302.52ft/Ibf Per Pound of air
Hd1 : 283.17 BTU

TOTAL ADIABATIC ENTHALPY DROP IN TURBINE [Hd_Total = H1-H2 = [ H1 - Hc ] + [ Hc - H2 ]] : 1 BTU = 778 ft-Ibf [ E.H LEWITT PAGE 374 , 773]
Hd_Total : 406.91BTU

NET ENTHALPY DROP IN TURBINE BLADES [ Hd1_Net = Eff x [ H1-H2 ] [ E.H LEWITT PAGE 793 ]
Hd_Net : 325.53 BTU

NET ENTHALPY DROP IN ROTOR [ Hd_X = Hd_Net - Hd_f ] [ E.H LEWITT PAGE 775 ]
Hd_X : 220.53 BTU

FRICTIONAL REHEATING IN ROTOR BLADES [ Hd_f_Reheating = Hd1 - Hd_X ] [ E.H LEWITT PAGE 775 ]
Hd_f_Reheating : 62.64 BTU

ADIABATIC TEMPERTAURE AT POINT 3 :
T3:2054.32

ACTUAL FRICTIONAL REHEAT EXIT TEMPERATURE AT TURBINE OUTLET T_Exit_Actual[ T_Exit_Actual = T_Exit + ( Hd_f_Reheating / Cp_mix ] [ E.H LEWITT PAGE 374 , 773]
T_Exit_Actual : 1552.88 R

Your browser does not support the HTML5 canvas tag. [ VOLUME OF FLOW AT EXIT TO TURBINE ,Ve = ( R_mix x m_Rate x T_Exit_Actual / 144 x P_Exit ): [ E.H LEWITT PAGE 365 ]
Volume Of Flow At Exit To Turbine [ Discharge ] , Ve [ Turbine Outlet ]: 35.8744ft3/sec

TURBINE BLADE SPEED AT INLET [ Ubi = Pi x Inlet_Dia x N / 60 ] [ E.H LEWITT PAGE 793 ]
Ubi : 1337.47 ft/sec

TURBINE BLADE SPEED AT OUTLET [ Ubo = Pi x Outlet_Dia x N / 60 ] [ E.H LEWITT PAGE 793 ]
Ubo : 1133.28 ft/sec

[ Area Of Flow Inlet = ( k.Pi . Di . ti ) / 144] : [ E.H LEWITT PAGE 793 ]
Area Of Flow Afi [ Turbine Inlet ]: 0.0677ft2

[ Area Of Flow Outlet = ( k.Pi . Do . to ) / 144] : [ E.H LEWITT PAGE 793 ]
Area Of Flow Afo [ Turbine Outlet ]: 0.0574ft2

[ Axial Area Of Flow At Inlet and Outlet = ( k.(Pi/4).((Do^2 - Di^2) / 144) ): [ E.H LEWITT PAGE 793 ]
Area Of Flow , Afx ,[ Axial Flow Area Of Turbine ]: 0.0092ft2

VELOCITY OF FLOW AT TURBINE BLADE INLET [ Ufi = Vc / Area Of Flow at Inlet ] [ E.H LEWITT PAGE 793 ]
Ufi : 101.44 ft/sec

VELOCITY OF FLOW AT TURBINE BLADE OUTLET [ Ufo = Ve / Area Of Flow at Outlet ] [ E.H LEWITT PAGE 793 ]
Ufo : 624.99 ft/sec

CALCULATION OF Uwi = sqrt ( Ui^2 - Ufi^2 ):[ E.H LEWITT PAGE 793 ]
Uwi : 2295.03 ft/sec

CALCULATION OF GUIDE BLADE ANGLE INLET ,Alhpa = atan( $Ufi/$Uwi ) x ( 180 / Pi ):[ E.H LEWITT PAGE 793 ]
Alhpa : 2.53 Degrees

CALCULATION OF Ux = Uwi - Ubi :[ E.H LEWITT PAGE 793 ]
Ux : 957.56 ft/sec

CALCULATION OF Uri = sqrt ( Ux^2 + Ufi^2 ):[ E.H LEWITT PAGE 793 ]
Uri : 962.92 ft/sec

CALCULATION OF ROTOR BLADE ANGLE AT INLET ,Theta = atan( $Ufi/$Ux ) x ( 180 / Pi ):[ E.H LEWITT PAGE 793 ]
Theta : 6.04 Degrees

CALCULATION OF Uwo:[ E.H LEWITT PAGE 793 ]
(Hc - H3) + [ Ui^2/2g ] - [ Uo^2/2g ] = [ Uwi x Ui ]/ g - [ Uwo x Uo ]/ g
Cp_Mix.(Tc_Actual - T_Exit_Actual) + [ Ui^2/2g ] - [ Uwo^2 + Ufo^2/2g ] = [ Uwi x Ui ]/ g - [ Uwo x Uo ]/ g

1Uwo^2/2g + 1133.28Uwo/g =-164701.17
1Uwo^2 + 1133.28Uwo -10606755.35=0
Quadratic Formula : -b + sqrt ( b^2 - 4 . a . c ) / 2 . a
Uwo : 2610.14ft/sec
CALCULATION OF Uro = sqrt( ( Uwo + Ubo )^2 + Ufo^2 ) :[ E.H LEWITT PAGE 793 ]
Uro : 3795.23 ft/sec

CALCULATION OF Uo = sqrt ( Uwo^2 + Ufo^2 ) :[ E.H LEWITT PAGE 793 ]
Uo : 2683.92 ft/sec

CALCULATION OF Uxx = abs( Uwo ) + abs( Ubo ) :[ E.H LEWITT PAGE 793 ]
Uxx : 3743.42 ft/sec

CALCULATION OF ROTOR BLADE ANGLE AT EXIT ,Phi = atan( $Ufo/$Uxx ) x ( 180 / Pi ):[ E.H LEWITT PAGE 793 ]
Phi : 9.47 Degrees

CALCULATION OF ROTOR BLADE ANGLE AT EXIT ,Si = atan( $Ufo/$Uwo ) x ( 180 / Pi ):[ E.H LEWITT PAGE 793 ]
Si : 13.45 Degrees

NET HORSE POWER DEVELOPED BY THE TURBINE : HP_Net = M_Rate x Hd_X x 778 / 550 : [ E.H LEWITT PAGE 795 ]
HP_Net : 485.23

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