C OMBUSTION P ROF. S EUNG W OOK B AEK D EPARTMENT OF A EROSPACE E NGINEERING, KAIST, IN KOREA R OOM : Building N7-2 #3304 T ELEPHONE : 3714 Cellphone: 010 – T A : Bonchan Gu R OOM : Building N7-2 # 3315 T ELEPHONE : 3754 Cellphone: 010 – P ROF. S EUNG W OOK B AEK D EPARTMENT OF A EROSPACE E NGINEERING, KAIST, IN KOREA R OOM : Building N7-2 #3304 T ELEPHONE : 3714 Cellphone: 010 – T A : Bonchan Gu R OOM : Building N7-2 # 3315 T ELEPHONE : 3754 Cellphone: 010 –

C OURSE C ODE : MAE 415 C OURSE N AME : C OMBUSTION E NGINEERING P ROFESSOR : S EUNG W OOK B AEK (Rm #3304, Ext. 3714) G RADING S YSTEM 1 Final Exam ( June 11 th, 2015 ) Homework SYLLABUS (1/4)

How to efficiently mix fuel and oxidizer Convection and diffusion How to efficiently burn fuel and oxidizer: energy saving How to reduce pollutant emission such as CO,CO 2 and NOx How to improve safety and reduce impact on environment To develop green, sustainable and alternative energy ISSUES IN COMBUSTION SCIENCE

R EFERENCES F.A.Williams, “Combustion Theory,” Addison Wesley, 2 nd Ed. D.B.Spalding, “Combustion and Mass Transfer,” Pergamon Press I.Glassman, “Combustion,” Academic Press, 2 nd Ed. M.Kanury, “Introduction to Combustion Phenomena,” Gordon and Breach Science Publishers P.A.Libby and F.A.Williams (Editors), “Turbulent Reacting Flows,” Springer Verlag L.A.Kennedy (Editor), “Turbulent Combustion,” Progress in Astronautics and Aeronautics, Vol.58 SYLLABUS (2/4)

K.K.Kuo, “Principles of Combustion,” Wiley V.R.Kuznetsoz and V.A.Sabelnikov, “Turbulence and Combustion,” Hemisphere Publishing Corporation J OURNALS Combustion and Flame Combustion Science and Technology Symposium (International) on Combustion Combustion Theory and Modeling AIAA Journal Progress in Energy and Combustion Science SYLLABUS (3/4)

Combustion, Explosion and Shock Waves Progress in Astronautics and Aeronautics Fire Safety Journal International Journal of Heat and Mass Transfer Journal of Heat Transfer Journal of Thermophysics and Heat Transfer Journal of Propulsion and Power SYLLABUS (4/4)

T hermochemistry Combustion- high temperature, moderate or high pressure, perfect gas, real gas effects for high pressure environment Thermodynamic properties of a single perfect gas Equation of state : : Universal gas constant P ROPULSION AND C OMBUSTION L ABORATORY : Molecular weight : Concentration Combustion Engineering

P ROPULSION AND C OMBUSTION L ABORATORY Combustion Engineering Internal Energy : per unit mass : Internal energy of formation : Specific heat

Enthalpy or = : Enthalpy of formation P ROPULSION AND C OMBUSTION L ABORATORY Combustion Engineering

P ROPULSION AND C OMBUSTION L ABORATORY Combustion Engineering Only change in or is important (not the absolute level) Need a convention for and 1) Prescribe a standard state, i.e.,and 2) The formation enthalpy of the chemical elements in their natural phase at and will be zero. 3), for, ::: : :

P ROPULSION AND C OMBUSTION L ABORATORY Combustion Engineering Entropy Let = Entropy at and any temperature. Gibbs Free Energy per unit mass basis

P ROPULSION AND C OMBUSTION L ABORATORY Combustion Engineering On a molar basis : Molar basis Helmholtz Free Energy

P ROPULSION AND C OMBUSTION L ABORATORY Combustion Engineering : Total number of moles per unit volume : Total number of moles of species K per unit volume : Mole fraction of species K Mixture of perfect gases ;

P ROPULSION AND C OMBUSTION L ABORATORY Combustion Engineering : Density of the mixture : Partial density of species K : Mass fraction of species K : Molecular weight of species K,

P ROPULSION AND C OMBUSTION L ABORATORY Combustion Engineering : Mean molecular weight of the mixture

E QUATION OF S TATE Partial pressure exerted by species K if it occupies the whole volume at temperature T. P ROPULSION AND C OMBUSTION L ABORATORY

Dalton’s Law but Internal Energy P ROPULSION AND C OMBUSTION L ABORATORY

where P ROPULSION AND C OMBUSTION L ABORATORY

Enthalpy when is fixed Entropy P ROPULSION AND C OMBUSTION L ABORATORY

Caution ; When there is reaction P ROPULSION AND C OMBUSTION L ABORATORY

Problem for notes Binary mixture of Specification of Composition For same P ROPULSION AND C OMBUSTION L ABORATORY

For same P and T, partial volume of species K Here, is not so that P ROPULSION AND C OMBUSTION L ABORATORY

Material Balance for Chemical Reactions Ex) Combustion of Octane with Air Air : Molecular Weight : For complete combustion (stoichiometric) Stoichiometric Coefficients : P ROPULSION AND C OMBUSTION L ABORATORY

On a mass basis, or 15.1 kg of air/ 1 kg of octane For reactants P ROPULSION AND C OMBUSTION L ABORATORY

: M EAN MOLECULAR WEIGHT OF REACTANTS M ASS OF PRODUCTS = 1831

P ROPULSION AND C OMBUSTION L ABORATORY E QUIVALENCE RATIO : F OR

P ROPULSION AND C OMBUSTION L ABORATORY : S TOICHIOMETRIC : F UEL LEAN : F UEL RICH F OR E NERGY Eq. FOR CHEMICAL REACTION C ONSTANT VOLUME SYSTEM – N O MOTION

P ROPULSION AND C OMBUSTION L ABORATORY 1 st L AW : : H EAT TRANSFER (POSITIVE WHEN ADDED TO THE SYSTEM) : I NTERNAL ENERGY : W ORK DONE BY THE SYSTEM 1: R EACTANT S TATE 2: P RODUCT S TATE

O NLY IMPORTANCE IS, NOT THE ABSOLUTE VALUES. P ROPULSION AND C OMBUSTION L ABORATORY : REFERENCE OR BASIC TEMPERATURE : INTERNAL ENERGY OF REACTION, DETERMINED IN A BOMB CALORIMETER

P ROPULSION AND C OMBUSTION L ABORATORY F OR C ONSTANT P RESSURE P ROCESS;

P ROPULSION AND C OMBUSTION L ABORATORY : E NTHALPY OF R EACTION : I NTERNAL E NERGY OF R EACTION AT F OR PERFECT GASES;

P ROPULSION AND C OMBUSTION L ABORATORY E NTHALPY OF FORMATION AND ENTHALPY OF COMBUSTION E NTHALPY OF FORMATION -THAT CHANGE OF ENTHALPY WHICH OCCURS WHEN A COMPOUND IS FORMED FROM THE ELEMENTS, WHICH ARE IN THEIR STABLE STATE, AT SAME STANDARD TEMPERATURE AND PRESSURE.

P ROPULSION AND C OMBUSTION L ABORATORY G IVES OFF cal :exothermic reaction H EAT OF F ORMATION = ALSO A COMBUSTION PROCESS ENTHALPY OF COMBUSTION HEAT OF COMBUSTION OF HEAT OF COMBUSTION

P ROPULSION AND C OMBUSTION L ABORATORY H EATING VALUES; F OR C+O 2 R EACTION,,BECAUSE THERE IS NO WORKS. IN GENERAL, H IGHER HEATING VALUES AND L OWER HEATING VALUES DEPEND ON STATE OF PRODUCTS. E NDOTHERMIC R EACTION

P ROPULSION AND C OMBUSTION L ABORATORY I MPORTANT CASE IS vs. IF IS LIQUID, LHV DIFFERS FROM HHV BY HEAT OF VAPORIZATION.

P ROPULSION AND C OMBUSTION L ABORATORY R EFERENCES FOR T HERMOCHEMICAL D ATA 1.NBS, “Tables of Selected Values of Chemical Thermal Properties”, Circular Letter JANAF Thermo-Chemical Tables (1993) 3.Penner ’ s Book 4.Van Wylen & Sonntag (SI units) 5.CHEMKIN: Software package for the analysis of gas- phase chemical and plasma kinetics (2000) E XAMPLE 10g OF H 2 (g) BURN IN AIR (  =1) AT CONSTANT PRESSURE. INITIAL TEMPERATURE IS 298K AND FINAL TEMPERATURE IS 2000K SO THAT H 2 O IS GASEOUS. CALCULATE THE HEAT LIBERATED ;

P ROPULSION AND C OMBUSTION L ABORATORY

M INUS I NDICATES T HAT H EAT WAS T RANSFERRED OUT OF THE S YSTEM. IN O THER W ORDS, THE F LAME T EMPERATURE, IF A DIABATIC, W OULD B E H IGHER THAN 2000 K. I F THE P ROBLEM WERE AT C ONSTANT V OLUME,

P ROPULSION AND C OMBUSTION L ABORATORY C ALCULATION OF E NTHALPY OF R EACTION FROM THE E NTHALPY OF F ORMATION R EACTION ;

P ROPULSION AND C OMBUSTION L ABORATORY E X) G ASEOUS CH 4 + O 2 R EACT TO Y IELD H 2 O(l)+CO 2 (g). C ALCULATE PER M OLE OF CH 4 EXOTHERMIC PER MOLE OF CH 4

P ROPULSION AND C OMBUSTION L ABORATORY C ONSIDER A C HEMICAL S YSTEM OF C ONSTANT M ASS E ITHER H OMOGENEOUS OR H ETEROGENEOUS IN M ECHANICAL AND T HERMAL E QUILIBRIUM BUT NOT IN C HEMICAL E QUILIBRIUM. T HE S YSTEM IS IN C ONTACT WITH A R ESERVOIR AT T EMPERATURE T AND U NDERGOES AN I NFINITESIMAL I RREVERSIBLE E XCHANGE OF H EAT,  Q, TO THE R ESERVOIR. P ROCESS M AY I NVOLVE C HEMICAL R EACTION AND T RANSPORT BETWEEN P HASES.

P ROPULSION AND C OMBUSTION L ABORATORY F ROM S YSTEM dS: ENTROPY CHANGE OF THE SYSTEM dS O : ENTROPY CHANGE OF THE RESERVOIR dS+dS o : ENTROPY CHANGE OF THE UNIVERSE

P ROPULSION AND C OMBUSTION L ABORATORY F ROM S YSTEM 1 ST L AW V ARIOUS C ONSTRAINTS C ASE A ; H OLD E AND V C ONSTANT ISOLATED SYSTEM C ASE B ; H OLD p AND T C ONSTANT G IBBS F REE E NERGY D ECREASES

P ROPULSION AND C OMBUSTION L ABORATORY W HEN ; H AVE C HEMICAL E QUILIBRIUM A T E QUILIBRIUM ; C ASE C ; H OLD V AND T C ONSTANT -

P ROPULSION AND C OMBUSTION L ABORATORY E QUILBRIUM OF A M IXTURE OF P ERFECT G ASES U NDERGOING C HEMICAL R EACTION C ONSIDER THE R EACTION, W E K NOW G IBBS F REE E NERGY FOR AND A NY T EMPERATURE T PER M OLE. AT A NY T AND P ;, ETC

P ROPULSION AND C OMBUSTION L ABORATORY L ET

P ROPULSION AND C OMBUSTION L ABORATORY N OTE THAT A T E QUILIBRIUM D EFINE

P ROPULSION AND C OMBUSTION L ABORATORY E FFECT OF T ON E QUILIBRIUM C OMPOSITION IS G IVEN IN Kp E FFECTS OF p ON THE T ERM. F OR THE C ASE OF, IE. C + D = A + B N O P RESSURE E FFECT E QUILIBRIUM C ONSTANT B ASED ON C ONCENTRATION ; WHERE

P ROPULSION AND C OMBUSTION L ABORATORY V ALUES OF K P A RE T ABULATED FOR S PECIFIC C HEMICAL R EACTION., ETC E X ) D ISSOCIATION O F CO 2 (1)

P ROPULSION AND C OMBUSTION L ABORATORY E X ) 100% W ATER V APOR, I NITIALLY AT 1 atm AND 2200 K D ISSOCIATES INTO H 2 (g) AND O 2 (g). A SSUMING P ERFECT G ASES THROUGHOUT, D ETERMINE THE E QUILIBRIUM C OMPOSITION E QUILIBRIUM C OMPOSITION (2) (3)

P ROPULSION AND C OMBUSTION L ABORATORY C HEMICAL R EACTION E QUILIBRIUM C OMPOSITION

P ROPULSION AND C OMBUSTION L ABORATORY E QUILIBRIUM C OMPOSITION

P ROPULSION AND C OMBUSTION L ABORATORY E XAMINE L IMITING C ONDITIONS C ASE I - L OW T EMPERATURES ; V ERY L ITTLE D ISSOCIATION L ET OR A)HIGHER PRESSURE ; LOWER  ; GREATER LESS DISSOCIATION B)HIGHER TEMPERATURE ; HIGHER K P GREATER  ; SMALLER MORE DISSOCIATION

P ROPULSION AND C OMBUSTION L ABORATORY C ASE II - H IGH T EMPERATURES ; H IGH D ISSOCIATION OR A)HIGHER PRESSURE ; HIGHER  ; HIGHER LESS DISSOCIATION B)HIGHER TEMPERATURE ; HIGHER K P ; LOWER  = MORE DISSOCIATION

P ROPULSION AND C OMBUSTION L ABORATORY E QUILIBRIUM W HEN S IMULTANEOUS R EACTIONS O CCURRING THE NUMBER OF INDEPENDENT REACTIONS, WHICH MUST BE CONSIDERED IN EQUILIBRIUM CALCULATIONS, IS EQUAL TO THE LEAST NUMBER OF EQUATIONS WHICH INCLUDE ANY REACTANT AND PRODUCT WHICH ARE PRESENT TO AN APPRECIABLE DEGREE IN THE EQUILIBRIUM MIXTURE. E X ) C ALCULATE THE C OMPOSITION OF THE E QUILIBRIUM M IXTURE O BTAINED W HEN 5 M OLES OF S TEAM, H 2 O (g) R EACT WITH 1 M OLE OF CH 4 AT E LEVATED T EMPERATURE AND S OME A RBITRARY P RESSURE

P ROPULSION AND C OMBUSTION L ABORATORY MECHANISM FOR REACTION ; 2 ACTUAL REACTIONS ARE ; C : 1= a + c + e H : 14= 4a + 2b + 2d O : 5= b + c + 2e

P ROPULSION AND C OMBUSTION L ABORATORY (1) (2)

P ROPULSION AND C OMBUSTION L ABORATORY (1) (2) ADD (3) P RODUCT R ULE FOR K P ’s

P ROPULSION AND C OMBUSTION L ABORATORY A DIABATIC F LAME T EMPERATURE POINT (2) FINAL TEMPERATURE AND H AFTER A NON-ADIABATIC REACTION POINT (2i) ISOTHERMAL REACTION POINT (c) ADIABATIC FLAME TEMPERATURE ; H 2 =H 1

P ROPULSION AND C OMBUSTION L ABORATORY C ONSTANT P RESSURE R EACTION – G ENERAL C ASE D ETERMINE T C FROM H 2 =H 1 H 2 D EPENDS ON THE b i W HICH D EPENDS ON T c W HICH D EPENDS ON THE b i.

P ROPULSION AND C OMBUSTION L ABORATORY F OR P ERFECT G ASES WHERE T O C ALCULATE T c 1.ASSUME T C FOR GIVEN PRESSURE 2.CALCULATE THE b i FROM THE K P ’s 3.SUBSTITUTE INTO H 2 =H 1 4.ITERATE UNTIL H 2 =H 1

P ROPULSION AND C OMBUSTION L ABORATORY C ALCULATE THE A DIABATIC F LAME T EMPERATURE OF A  = 0.8 M ETHANE – O 2 M IXTURE AT p = 10 atm, T AKING INTO A CCOUNT THE D ISSOCIATION OF CO 2 AND H 2 O 2 U NKNOWNS

etc. Dissociation Reactions Combustion Engineering P ROPULSION AND C OMBUSTION L ABORATORY

Procedure ; assume T c ; Calculate a,b,c,d,e Substitute into H 2 =H 1 (from Energy Equation) If T c =3000K Combustion Engineering P ROPULSION AND C OMBUSTION L ABORATORY a[ kcal/mole ]+b[ ] +c[ ]+d[ ] +e[ ] = 0.8[-17.89]+2[0] H co 2 HH20HH20 H co HH2HH2 Ho2Ho2 H CH 4 Ho2Ho2

Combustion Engineering P ROPULSION AND C OMBUSTION L ABORATORY T ables of Thermodynamic Properties

Combustion Engineering P ROPULSION AND C OMBUSTION L ABORATORY

Combustion Engineering P ROPULSION AND C OMBUSTION L ABORATORY

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Combustion Engineering P ROPULSION AND C OMBUSTION L ABORATORY

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