PRODUCTS OF COMBUSTION OF GASEOUS FUELS AND CALCULATED FLAME TEMPERATURE

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PRODUCTS OF COMBUSTION OF GASEOUS FUELS AND CALCULATED FLAME TEMPERATURE Gheorghe CAUNEI FLORESCU Lt Eng Constantn NISTOR PhD Student Assocate Professor Amado George STEFAN GENERAL DIRECTORATE NATIONAL SYSTEM HAIL - MINISTRY OF AGRICULTURE AND RURAL DEVELOPMENT MILITARY TECHNICAL ACADEMY Abstract The work contans elements of combuston stochometry It defnes the rato of the mass of the fuel m c and ar mass m a called fuel-ar dose d Commercal lqud fuels for engnes of petroleum orgn as natural gas s generally complex mxtures of hydrocarbons and other organc substances For the calculaton of combuston ar and combuston products s consder a pure substance consdered as representatve of a partcular class of commercal fuels Can be represented by octane gasolne (C 8 H 8 ) desel wth cetane (C 6 H 34 ) or dodecanese (C H 6 ) natural gas by methane (CH 4 ) Correspondng quanttes of products are ν CO ν CO ν HO ν H mol/mol fuel T fa adabatc flame temperature s determned by solvng the equaton vp [ hp( Tp) hp( Ts) vr [ hr( Tr) hr( Ts) Qps 0 Keywords: Stochometrc combuston Thermodynamcs INTRODUCTION Ar needed for combuston as the composton of the combuston products are determned by the equaton expressng global fuel oxdaton reactons respectng the prncple of conservaton of mass for each of the elements of reactants If the fuel composton s a hydrocarbon C m H n generated global full oxdaton reacton has the form CmHn ao bco c HO () where: stochometrc ratos ( a b c) are expressed n moles Conservaton of mass of carbon s expressed by the condton b = m and hydrogen n the condton c = n/ Conservaton of mass requres oxygen provded a = m + n / 4 Equaton () takes the form CmH n + ( m n/4) O = mco + ( n/) HO () Dry atmospherc ar contans 095% (volume) oxygen 7809% ntrogen 093% argon the other components beng consdered neglectable proportons The usual calculatons that follow defne the thermodynamc propertes of the reactants and products are neglected and the presence of argon consderng that ar conssts of % (vol) and oxygen and 79% ntrogen expressed n moles For each mole of oxygen s consdered ( 0095) / 0095 = 3773 mole of ntrogen The normal calculaton s consdered that the ntrogen does not partcpate n the combuston reacton Therefore the equaton for the complete combuston n the ambent ar hydrocarbon C m H n has the form CmH n ( m n/ 4) (O 3773N ) mco ( n/ ) HO 3 773( m n/ 4) N (3) If fuel contans oxygen n ts molecular structure t s released and partcpates n combuston reactons and should therefore be consdered n the overall balance of oxygen Per mole of fuel C m H n O r formula corresponds to the followng theoretcal amount of oxygen requred for complete combuston (a stochometrc amount) n r Os m [mol/mol comb] (4) 4 and that the amount of ar theoretcally requred (stochometrc) n r As m [mol/mol comb] (5) 0 4 For example for the combuston of ethanol (C H 5 OH) corresponds d m c / mao s = 3 mol / mol combnaton And respectvely As = 3/0 = = 4 86 mol / mol combnaton The amount of TERMOTEHNICA /03 76

PRODUCTS OF COMBUSTION OF GASEOUS FUELS AND CALCULATED FLAME TEMPERATURE ar avalable for combuston s expressed n terms of stochometrc rato As wth the dosage coeffcent = A /As (6) It s common also to defne the relatonshp between the fuel mass m f and ar mass m a n combnaton called the dosage of fuel n ar d d = m f / m a (7) If the masses on fuel and ar s n a stochometrc rato resultng dosage stochometrc d s = (m f / m a ) s (8) Dependng on the fuel and ar masses raport R (dosage) s also defned equvalence rato fuel / ar (m f / m a ) d R (m f / m a ) s d s (9) It s noted that the rato of the dosage can be expressed as the followng / R (0) COMBUSTION PRODUCT COMPOSITION The flue gases generally consst of a large number of substances as a result of complex mechansms of the combuston reacton Defnng the thermodynamc propertes of the combuston products can be made wth an accuracy generally satsfactory f we take nto account the reactons products overall oxdaton fuel components Further smplfcaton acceptable to moderate combuston temperatures (up to 700 000 K) s obtaned by neglectng the chemcal equlbra In ths case the waste gases consst generally of CO CO H O O H and N n a rato dependent on the fuel composton and the dosage In the λ > (mxng wth excess ar or poor dose) t s generally accepted that the oxdaton reacton s fully develop resultng n CO H O O (excess amount) and N Fuel per mole of the formula known C m H n O r resultng n the equaton (3) and the relatonshp (4 6) the quanttes of products CO m HOn / O mn/ 4 r / and ν 3773 c/ h/ 4 o/ 3 [mol/mol fuel] N 3 FLAME TEMPERATURE CALCULATION A smple steady-state thermal energy balance can be constructed around a constant-pressure combuston system The fgure present the energy balance of the combuston system Fg Combuston system dagram The hgher heatng value takes nto account the latent heat of vaporzaton of water n the combuston products and s useful n calculatng heatng values for fuels where condensaton of the reacton products s practcal (eg n a gas-fred boler used for space heat) If the gross calorfc value s used then H R should contan a latent heat term equal to the mass of water produced per klogram of fuel multpled by the latent heat of evaporaton of water at 5 o C (h fg ) If the net calorfc value s used then the flue gas enthalpy wll consst of sensble heat terms only We are concerned wth predctng the temperature reached wthn the flame hence the net calorfc value/sensble heat terms system s the more approprate 4 ADIABATIC FLAME TEMPERATURE Flame temperatures for some common fuels s presented n the table Fuel Adabatc flame temperature ( o C) Natural gas 070 Kerosne 093 Lght fuel ol 04 Medum fuel ol 0 Heavy fuel ol 0 Btumnous Coal 7 Anthracte 80 The energy balance about the system can be wrtten as: Hr CV HpQc Qu () TERMOTEHNICA /03 77

Gheorghe CAUNEI FLORESCU Constantn NISTOR Amado George STEFAN where CV s the calorfc value; Hr the sensble heat n the ar and fuel s very small and often neglected The case loss from the outsde of the plant Qc s also generally small compared to the other energy fluxes and s smlarly often consdered neglgble It s assumed that combuston takes place under adabatc condtons e no heat transfer s permtted across the boundary of the system The mplcaton of ths s that Qc = 0 and Qu = 0 Hence equaton () smplfes down to HrCV Hp () The specfc heats of the fuel oxygen and ntrogen can be evaluated at the mean temperature (T + 5)/ and the enthalpy of the reactants s thus easly evaluated The rght-hand sde of equaton () however s not so easly evaluated as t s defned by n f pp Hp ( t 5) m c where t f s the flame temperature Ths relatonshp cannot be solved explctly for t f as there wll be a consderable dfference between t f and the reference temperature 5 o C hence the value of t f s requred to evaluate the specfc heats of the combuston products 5 MOLAR ISOBARIC HEAT It adopts the form sobarc molar heat: 3 Cp( T) aat a3t a4 T For the reactants the sobarc molar heat and the specfc heats dependng on temeprature are: for CH 4 : CpCH4( T ) 6 76 0 07T 5 9 3 940 T 7680 T kj/(kmol K) cpch4( T ) CpCH4( T ) kj/(kg K) 6 for O : 4 CpO( T ) 33 79 6 9680 T 7 0 3 8 397 0 T 690 T kj/(kmol K) cpo( T ) CpO( T ) kj/(kg K) 3 for CO : 6 CpCO( T ) 30 857 0 03T 9 89 0 T 0 3 9 070 T kj/(kmol K) cpco( T ) CpCO( T ) 44 kj/(kg K) for H O: CpHO( T ) 8 4 0 06 T 6 0 3 3 0060 T 8990 T kj/(kmol K) cpho( T ) CpHO( T ) 8 kj/(kg K) for N : 3 CpN( T ) 6 59 7 979 0 T 6 0 3 00 0 T 740 T kj/(kmol K) cpn( T ) CpN( T ) kj/(kg K) 8 6 CALCULATION ALGORITHM A straght forward method for the calculaton of adabatc flame temperature s to execute the followng steps: () evaluate the left-hand sde of equaton Hr CV Hp; () guess a value for t f and use ths to fnd the specfc heats of the combuston products at the average between the flame and the reference temperature e [(t f + 5)/] o C; (3) solve equaton Hr CV Hp for t f ; (4) compare the new value of t f wth the orgnal estmate and f there s a substantal dfference use the new value to re-evaluate the specfc heats loopng back to step () untl satsfactory convergence s acheved 7 CASE STUDY Fnd the adabatc flame temperature for a stochometrc methane/ar flame f the ntal temperature of the fuel and ar s 5 0 5 and 0 o C Take the net calorfc value of methane as CV = 504 0 6 [J/kg] The frst step s to evaluate for /6 kmol methane ( kg) the mass of each of the reactants and products 78 TERMOTEHNICA /03

PRODUCTS OF COMBUSTION OF GASEOUS FUELS AND CALCULATED FLAME TEMPERATURE For kg CH 4 follows: the reactants (R) and products of combuston (P) mro = 4 kg mrn=367 kg mpco=75 kg mpho=5 kg mpn=367 kg The ntal temperature of the fuel and ar 4 T( ) = 736 + 5 5 T() 5 786 0 836 3 5 886 4 0 936 Standard temperature o ts 5 C Ts = 736 ts Ts = 986 K The average temperature of the reactants between the ntal temperature and standard temperature TmR ( ) T( ) Ts Flame temperature ratng Tef ( ) 4000 K Average temperature of the combuston products between standard temperature and flame temperature measured TmP ( ) Tef ( ) Ts Solvng equaton () and determnng the temperature calculated by teraton frst communon HR() ( T() Ts) ( mch4) cpch4( T mr()) mrocpo( TmR ( )) mrn cpn( TmR ( )) HP() ( T() c Ts) ( mpco) cpco( T mp()) mpho cpho( T mp( )) mpncpn( T mp( )) After the frst teraton we obtan the followng numercal values T() HR() [kj/kg] Tc() Tc()- Tef() 786-3989 75-5 836-994 79-3 886-998 83-73 4 936-000 87-33 Second teraton It adopts: T ef( ) T c( ) T mp( ) Tef() Ts and repeat the algorthm Results the data n table T() Tc() Tc() Tc()-Tef() 786 75 9 78 836 79 95 675 3 886 83 99 6 4 936 87 30 589 Thrd teraton It adopts: T3 ef( ) T c( ) T3 mp( ) T3ef() Ts and repeat the algorthm Results the data n table Tc() Tc() T3c() T3c()-T3ef() 75 9 90-450 79 95 93-375 3 83 99 97-300 4 87 30 300-5 The fourth teraton It adopts: T4 ef( ) T3 c( ) T4 mp( ) T4ef() Ts and repeat the algorthm Results the data n table Tc() T3c() T4c() T4c()-T4ef() 9 90 899 0346 95 93 934 0336 3 99 97 976 035 4 30 300 3004 035 CH 4 flame temperature calculated: TfCH4( ) T 4 c( ) tfch4( ) TfCH4( ) 736 Intal temperature CH 4 Flame temperature CH 4 / ar calculated T() t() TfCH4() tfch4() [ o C] [ o C] 786 5 899 067 836 0 934 00 3 886 5 976 037 4 936 0 3004 07 8 CONCLUSIONS In the study of combuston there are two types of adabatc flame temperature dependng on how the process s completed constant volume and constant pressure descrbng the temperature the combuston products theoretcally reach f no energy s lost to the outsde envronment TERMOTEHNICA /03 79

Gheorghe CAUNEI FLORESCU Constantn NISTOR Amado George STEFAN The constant volume adabatc flame temperature s the temperature that results from a complete combuston process that occurs wthout any work heat transfer or changes n knetc or potental energy The constant pressure adabatc flame temperature s the temperature that results from a complete combuston process that occurs wthout any heat transfer or changes n knetc or potental energy Its temperature s lower than the constant volume process because some of the energy s utlzed to change the volume of the system (e generate work) Fg Temperature varatons ratng flames accordng to the ntal temperature CH 4 / ar at teraton algorthm Fg 3 Varaton of flame temperature calculated accordng to the ntal temperature CH 4 / ar Hgher (HHV) and Lower (LHV) Heatng values of some common fuels [3] Fuel HHV [MJ/kg] HHV [kj/mol] LHV [MJ/kg] Hydrogen 480 86 996 Methane 5550 889 5000 Ethane 590 560 4780 Propane 5035 0 4635 Butane 4950 877 4575 Pentane -- -- 4535 Gasolne 4730 -- -- BIBLIOGRAPHY [] Apostolescu N Chrac R Combuston process n nternal combuston engne Techncal Publshng House Bucharest 998 [] Caune Florescu Gh Stefan A G and others Elements of the theory n flud jets and applcatons n burnng gaseous fuels Scentfc Unverse Publshng Bucharest 00 [3] Lews B Combuston Flames and explosons of gases Academc Press New York 95 [4] Marnescu M Baran N Radcenco V Techncal Thermodynamcs Matrx Rom Bucharest 998 [5] Stefan St Paraschv T Codreanu I Poradc P Flud Mechancs Specal chapters Vol I II III Ed AT Mltary Bucharest 994 [6] Stefan A G Marn G Cmpean M Nstor C Knetcs and dffuse burnng gaseous fuels Theory modelng Scentfc Unverse Publshng Bucharest 0 [7] Zeldovc ZB Barenblatt GL Lbrovch VB The mathematcal theory of combuston and exploson Nauka Moskow 980 80 TERMOTEHNICA /03

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