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 –

P ROPULSION AND C OMBUSTION L ABORATORY C ONSERVATION OF N EW P HENOMENA C OMBUSTION E NGINEERING C ONSERVATION E QUATIONS OF M ULTICOMPONENT G ASES MASS MOMENTUM ENERGY OF A GASEOUS MIXTURE OF DIFFERENT CHEMICAL SPECIES (MASS) DIFFUSION TRANSPORT OF ENERGY BY DIFFUSION CREATION OR DESTRUCTION OF CHEMICAL SPECIES BY REACTION

G AS C ONSISTS OF M ANY R ANDOMLY M OVING M OLECULES = VELOCITY OF PARTICLE OF S TH KIND = MASS AVERAGE VELOCITY OF MIXTURE, VELOCITY OF THE C.G OF A FLUID ELEMENT = PECULIAR VELOCITY OF PARTICLE OF S TH KIND, VELOCITY OF THE PARTICLES W.R.T D EAL WITH D ISTRIBUTION FUNCTION FOR PARTICLES = P ARTICLE D ISTRIBUTION F UNCTION D EFINITION OF V ARIOUS V ELOCITIES P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING HOMEWORK : (pg. 390) #3, #18, #24, and #27 Attached a slide for your information

PROBABLE NUMBER OF PARTICLES OF KIND S PER UNIT VOLUME, WHICH AT TIME t HAVE A VELOCITY IN UNIT RANGE ABOUT NUMBER DENSITY, PARTICLES OF S TH KIND PER UNIT VOLUME AVERAGE VELOCITY OF PARTICLES OF S TH KIND MASS AVERAGE VELOCITY P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

W ANT TO K NOW A VERAGE M OTION OF A P ARTICULAR S PECIES W.R.T. = A VERAGE P ECULIAR V ELOCITY (DIFFUSION VELOCITY) T HE D IFFUSION V ELOCITY OF C HEMICAL S PECIES s IS THE R ATE OF F LOW OF M OLECULES OF s W.R.T THE M ASS A VERAGE V ELOCITIY OF THE G AS. P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING N ET R ATE OF M ASS T RANSFER BY D IFFUSION IS Z ERO, I.E.

L ET NO. OF P ARTICLES OF THE S TH K IND F OUND BY C HEMICAL R EACTION PER UNIT V OLUME, PER UNIT T IME L ET = M ASS OF O NE P ARTICLE OF S PECIES, s P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING C ONSERVATION OF M ASS M ULTIPLY BY M ASS OF S TH S PECIES F ORMED PER UNIT V OLUME PER UNIT T IME DUE TO C HEMICAL R EACTION

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING M ASS IS C ONSERVED IN C HEMICAL R EACTION O VERALL M ASS C ONSERVATION

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING D IFFUSION V ELOCITY D EPENDS ON. Maxwell-Boltzmann D ISTRIBUTION F UNCTION (G AS IN E QUILIBRIUM ) A S A P ERTURBATION S OLUTION ABOUT Boltzmann D ISTRIBUTION Chapmann & Enskog OBTAINED = M ULTI C OMPONENT T HERMAL D IFFUSION C OEFFICIENT = D IFFUSION V ELOCITY IN M ULTI C OMPONENT M IXTURE

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING = E XTERNAL F ORCE A CTING ON M OLECULE l M OLE F RACTION OF S PECIES P M ASS F RACTION OF S PECIES P CONCENTRATION OF SPECIES P

D IFFUSION F LUX A RISES FROM (i)Gradient of concentration (ii)Pressure gradient (iii)Flux due to external forces such as electromagnetic forces or gravity (iv)Temperature gradient : Thermal diffusion I N M ANY P ROBLEMS, T HERMAL & P RESSURE D IFFUSIONS ARE N EGLECTED. E XTERNAL F ORCE D IFFUSION = P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

F OR G RAVITY ONLY P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING C ONSIDER I NTERDIFFUSION BETWEEN S PECIES 1 AND 2 B INARY D IFFUSION = ACCELERATION OF GRAVITY

I F, P RESSURE D IFFUSION OF S PECIES 1 O CCURS IN THE D IRECTION OF I NCREASING P RESSURE IN S PECIES 2 I F, T HERE IS N O P RESSURE D IFFUSION. P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

I N THE A BSENCE OF, WHILE N EGLECTING P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

L ET ( T HERMAL D IFFUSION R ATIO ) = P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING M ASS F RACTION M OLE F RACTION, M ASS F RACTION F ick ’s L AW (E XACT FOR B INARY D IFFUSION)

A PPROXIMATION: F REQUENTLY U SED ( A S A D ESPERATE M EASURE) P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING C ONSERVATION OF M OMENTUM V ERY F EW C HANGES DUE TO C HEMICAL R EACTIONS = T HERMODYNAMIC OR H YDROSTATIC P RESSURE = K RONECKER D ELTA = V ISCOUS S TRESS T ENSOR STRESS TENSOR = BULK VISCOSITY ACCOUNTING FOR INTERNAL RELAXATION

F OR M ONATOMIC G AS,  = 0 ( Stokes H YPOTHESIS) = R ADIATION S TRESS T ENSOR = i th C OMPONENT OF B ODY F ORCE P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING C ONSERVATION OF E NERGY = I NTERNAL E NERGY PER UNIT M ASS = H EAT F LUX V ECTOR = R ATE OF H EAT G ENERATION PER UNIT M ASS E.G. : R ADIATION = V ISCOUS S TRESS DIADIC IF IS FOR ALL SPECIES, R EMEMBER F ORMATION E NERGY I NCLUDED !

P LANE S URFACE D IRECTION = ENERGY TRANFERRED PER UNIT AREA PER UNIT TIME DUE TO TRANSPORT EFFECTED AT A SURFACE T HE H EAT F LUX V ECTOR P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING Boltzmann CONSTANT

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING T HE A DIABATIC R EACTION S ECOND O RDER R EACTION TO R EPRESENT THE A CTUAL K INETICS WHERE : A CTIVATION E NERGY : S TERIC F ACTOR : specific reaction rate constant

M IXTURE OF I DEAL G ASES P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING A FTER R EARRANGEMENT

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING S INGLE S TEP K INETIC IS OFTEN G ENERALIZED TO THE F ORM W HERE A,a,b,n,m,E ARE D ETERMINED BY C OMPARISON WITH E XPERIMENTS OR D ETAILED K INETICS C ALCULATION.

HEAT RELEASED BY COMBUSTION OF A UNIT MASS OF FUEL FOR THE REACTION GIVEN INITIAL ENERGY F OR THE S AME S PECIFIC H EAT P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING S IMPLY C HEMICALLY R EACTING S YSTEM (SCRS) F OR A S YSTEM OF UNIT M ASS MASS OF FUEL MASS OF OXIDANT STOICHIOMETRIC FUEL MASS F OR AN ADIABATIC R EACTION

C ONDITIONS W HEN C OMBUSTION IS C OMPLETE T HIS D EPENDS ON AND P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING L ET

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING U SING

P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING D IMENSIONLESS T EMPERATURE DURING REACTION B ECOMES : P ROGRESS V ARIABLE

ASAS P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING P REVIOUSLY, W E O BTAINED

E XPONENTIAL T ERM I NCREASES D RASTICALLY P ROPULSION AND C OMBUSTION L ABORATORY C OMBUSTION E NGINEERING A S, OR, SO THAT 1.0 H OWEVER,

Homework #1 4 th reference : M. Kanury (pg.390) #3, #18, #24, and #27 1. Calculate the pressure of 28g of hydrogen contained in 1 liter vessel at 25 ℃ 2.Hydrogen Peroxide is used sometimes as an oxidizer in special power plants such as torpedoes and rockets. Determine the standard enthalpy of combustion per gram mass of the fuel for the following combustion reaction : H 2 O 2 (l) CH 4 (g) → 1.5H 2 O(g) CO 2 (g) Also Compare this enthalpy of combustion with that calculated for methane burning in pure oxygen. Assume  h 0 f 298 = kJ/mole of H 2 O 2 (l). 3.A mixture at 298 o K and 1 atm. Pressure consists of 1 mole of H 2 and 0.5 mole of O 2. They are slowly heated to 2,500 o K keeping pressure constant. What is the final equilibrium composition? 4.A heated tube reactor is operated at 2,500 o K. The flowing mixture initially contains 2 moles of H 2 O and 1 mole each of O 2 and N 2. If the total pressure is approximately 2 atm. And the outlet equilibrium mixture contains only H 2 O, O 2, H 2, N 2 and OH, calculate the outlet composition.