COMBUSTION TA : Donggi Lee PROF. SEUNG WOOK BAEK DEPARTMENT OF AEROSPACE ENGINEERING, KAIST, IN KOREA ROOM: Building N7-2 #3304 TELEPHONE : 3714 Cellphone : 010 - 5302 - 5934 swbaek@kaist.ac.kr http://procom.kaist.ac.kr TA : Donggi Lee ROOM: Building N7-2 #1304 TELEPHONE : 5754 Cellphone : 010 - 8504 - 5841 kingdonggi@kaist.ac.kr

COMBUSTION ENGINEERING CONSERVATION EQUATIONS OF MULTICOMPONENT GASES CONSERVATION OF MASS MOMENTUM ENERGY OF A GASEOUS MIXTURE OF DIFFERENT CHEMICAL SPECIES NEW PHENOMENA (MASS) DIFFUSION TRANSPORT OF ENERGY BY DIFFUSION CREATION OR DESTRUCTION OF CHEMICAL SPECIES BY REACTION PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING HOMEWORK : (pg. 390) #3, #18, #24, and #27 Attached a slide for your information DEFINITION OF VARIOUS VELOCITIES GAS CONSISTS OF MANY RANDOMLY MOVING MOLECULES = VELOCITY OF PARTICLE OF STH KIND = MASS AVERAGE VELOCITY OF MIXTURE, VELOCITY OF THE C.G OF A FLUID ELEMENT = PECULIAR VELOCITY OF PARTICLE OF STH KIND, VELOCITY OF THE PARTICLES W.R.T DEAL WITH DISTRIBUTION FUNCTION FOR PARTICLES = PARTICLE DISTRIBUTION FUNCTION PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING 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 STH KIND PER UNIT VOLUME AVERAGE VELOCITY OF PARTICLES OF STH KIND MASS AVERAGE VELOCITY PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING WANT TO KNOW AVERAGE MOTION OF A PARTICULAR SPECIES W.R.T. = AVERAGE PECULIAR VELOCITY (DIFFUSION VELOCITY) THE DIFFUSION VELOCITY OF CHEMICAL SPECIES s IS THE RATE OF FLOW OF MOLECULES OF s W.R.T THE MASS AVERAGE VELOCITIY OF THE GAS. NET RATE OF MASS TRANSFER BY DIFFUSION IS ZERO, I.E. PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING CONSERVATION OF MASS LET NO. OF PARTICLES OF THE STH KIND FOUND BY CHEMICAL REACTION PER UNIT VOLUME, PER UNIT TIME LET = MASS OF ONE PARTICLE OF SPECIES, s MULTIPLY BY MASS OF STH SPECIES FORMED PER UNIT VOLUME PER UNIT TIME DUE TO CHEMICAL REACTION PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING MASS IS CONSERVED IN CHEMICAL REACTION OVERALL MASS CONSERVATION PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING DIFFUSION VELOCITY DEPENDS ON . Maxwell-Boltzmann DISTRIBUTION FUNCTION (GAS IN EQUILIBRIUM) AS A PERTURBATION SOLUTION ABOUT Boltzmann DISTRIBUTION Chapmann & Enskog OBTAINED = MULTI COMPONENT THERMAL DIFFUSION COEFFICIENT = DIFFUSION VELOCITY IN MULTI COMPONENT MIXTURE PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

MOLE FRACTION OF SPECIES P = EXTERNAL FORCE ACTING ON MOLECULE l MOLE FRACTION OF SPECIES P MASS FRACTION OF SPECIES P CONCENTRATION OF SPECIES P PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING DIFFUSION FLUX ARISES 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 IN MANY PROBLEMS, THERMAL & PRESSURE DIFFUSIONS ARE NEGLECTED. EXTERNAL FORCE DIFFUSION = PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING FOR GRAVITY ONLY = ACCELERATION OF GRAVITY BINARY DIFFUSION CONSIDER INTERDIFFUSION BETWEEN SPECIES 1 AND 2 PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING IF , PRESSURE DIFFUSION OF SPECIES 1 OCCURS IN THE DIRECTION OF INCREASING PRESSURE IN SPECIES 2 IF , THERE IS NO PRESSURE DIFFUSION. PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

IN THE ABSENCE OF , WHILE NEGLECTING PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

LET (THERMAL DIFFUSION RATIO) = MASS FRACTION MOLE FRACTION, MASS FRACTION Fick’s LAW (EXACT FOR BINARY DIFFUSION) PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

APPROXIMATION: FREQUENTLY USED (AS A DESPERATE MEASURE) PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING CONSERVATION OF MOMENTUM VERY FEW CHANGES DUE TO CHEMICAL REACTIONS STRESS TENSOR = THERMODYNAMIC OR HYDROSTATIC PRESSURE = KRONECKER DELTA = VISCOUS STRESS TENSOR = BULK VISCOSITY ACCOUNTING FOR INTERNAL RELAXATION PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING FOR MONATOMIC GAS, = 0 (Stokes HYPOTHESIS) = RADIATION STRESS TENSOR = i th COMPONENT OF BODY FORCE PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING CONSERVATION OF ENERGY = VISCOUS STRESS DIADIC = HEAT FLUX VECTOR = RATE OF HEAT GENERATION PER UNIT MASS E.G. : RADIATION = INTERNAL ENERGY PER UNIT MASS REMEMBER FORMATION ENERGY INCLUDED ! IF IS FOR ALL SPECIES, PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING THE HEAT FLUX VECTOR = ENERGY TRANFERRED PER UNIT AREA PER UNIT TIME DUE TO TRANSPORT EFFECTED AT A SURFACE PLANE SURFACE DIRECTION Boltzmann CONSTANT PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING THE ADIABATIC REACTION SECOND ORDER REACTION TO REPRESENT THE ACTUAL KINETICS : specific reaction rate constant WHERE : ACTIVATION ENERGY : STERIC FACTOR PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING MIXTURE OF IDEAL GASES AFTER REARRANGEMENT PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING SINGLE STEP KINETIC IS OFTEN GENERALIZED TO THE FORM WHERE A,a,b,n,m,E ARE DETERMINED BY COMPARISON WITH EXPERIMENTS OR DETAILED KINETICS CALCULATION. PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING SIMPLY CHEMICALLY REACTING SYSTEM (SCRS) FOR A SYSTEM OF UNIT MASS MASS OF FUEL MASS OF OXIDANT STOICHIOMETRIC FUEL MASS HEAT RELEASED BY COMBUSTION OF A UNIT MASS OF FUEL FOR THE REACTION GIVEN INITIAL ENERGY FOR THE SAME SPECIFIC HEAT FOR AN ADIABATIC REACTION PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING LET CONDITIONS WHEN COMBUSTION IS COMPLETE THIS DEPENDS ON AND PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING USING PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING DIMENSIONLESS TEMPERATURE DURING REACTION : PROGRESS VARIABLE BECOMES PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING AS PREVIOUSLY, WE OBTAINED PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

COMBUSTION ENGINEERING AS , EXPONENTIAL TERM INCREASES DRASTICALLY HOWEVER, OR , SO THAT 1.0 PROPULSION AND COMBUSTION LABORATORY COMBUSTION ENGINEERING

Homework #1 4th 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 : H2O2(l) + 0.25CH4(g) → 1.5H2O(g) + 0.25CO2(g) Also Compare this enthalpy of combustion with that calculated for methane burning in pure oxygen. Assume h0f 298 = -187.9 kJ/mole of H2O2(l). 3. A mixture at 298oK and 1 atm. Pressure consists of 1 mole of H2 and 0.5 mole of O2. They are slowly heated to 2,500oK keeping pressure constant. What is the final equilibrium composition? 4. A heated tube reactor is operated at 2,500oK. The flowing mixture initially contains 2 moles of H2O and 1 mole each of O2 and N2. If the total pressure is approximately 2 atm. And the outlet equilibrium mixture contains only H2O, O2, H2, N2 and OH, calculate the outlet composition.