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Combustion Theory and Applications in CFD

Combustion Theory and Applications in CFD
Combustion Theory and Applications in CFD CEFRC Combustion Summer School 2014 Prof. Dr.Ing. Heinz Pitsch Copyright ©2014 by Heinz Pitsch. This material is not to be sold, reproduced or distributed without prior written permission of the owner, Heinz Pitsch. What is Combustion • What is the difference between combustion and fuel oxidation in a fuel cell • In contrast to isothermal chemically reacting flows  Heat release induces temperature increase  Thereby combustion is self accelerating • Important  Each chemical or physical process has associated time scale • Interaction of flow (transport) and chemistry  Laminar and turbulent combustion  New dimensionless groups (similar to Reynolds number) • Damköhler number, Karlovitz number, … 2 Combustion Applications: Examples • Premixed combustion Example: SIengine  Sparkignition engine  Premixed • Nonpremixed combustion Example: Aircraft engine  Diesel engine  Aircraft engine 3 Impact of Combustion Demand for energy: • Transport and electricity • Atmospheric pollution • Global warming 4 DOE’s International Energy Outlook 2011 15 World Energy Consumption 10 Btu • Increase in world wide energy consumption from 2008 until 2035: 53 • Fossil fuels: great share (80) of the world wide used energy • Mineral oil remains dominating source of energy • Traffic and transport: Share of about 15 World Energy Consumption by Fuel 10 Btu 25 5 DOE’s International Energy Outlook 2011 • Increase of renewable energy by a factor of 2 • Combustion of fossil fuels remains dominating source of energy • Nearly 80 of energy consumption covered by fossil fuels 6 Greenhouse Gas Emissions • 85 of Greenhouse gas emissions CO 2 EPA Inventory of US Greenhouse Gas Emissions, 2006 7 Sources of CO 2 Combustion of fossil fuels: World EnergyRelated CO Emissions billion tons 2 • 95 of CO emissions 2 • 80 of all greenhouse gas emissions • Expected increase of CO 2 emissions: 43 from 2008 until 2035 Quelle: International Energy Outlook, 2011 8 Reduction of Greenhouse Gas Emissions Various approaches: • Hydrogen economy • CO sequestration (Carbon Capture and Storage, CCS) 2 • Biofuels • … • Increase in efficiency Combustion Theory 9 New Technologies • Challenge of concurrent optimizing of efficiency, emissions and stability • Examples of new technologies • Aircraft turbines NASA Lean Direct Injection • Lean direct injection (LDI) Aircraft Engine Combustor • Automotive sector • Homogeneous charge compression ignition (HCCI, CAI) • Electricity generation • Oxycoal combustion • Integrated gasification combined cycle (IGCC) • Flameless oxidation (FLOX) / MILD combustion • Progress in technology increasingly supported by numerical simulations • New technologies often lead to changes in operating range  New challenges in the field of combustion theory and modeling Aim of this Course • Develop understanding of combustion processes from physical and chemical perspectives • Fundamentals:  Thermodynamics  (Kinetics  see parallel course)  Fluid mechanics  Heat and mass transfer • Applications:  Reciprocating engines  Gas turbines  Furnaces 11 Course Overview Part I: Fundamentals and Laminar Flames Part II: Turbulent Combustion 12 Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass balances of combustion systems • Thermodynamics, flame temperature, and equilibrium • Governing equations • Laminar premixed flames: Kinematics and Burning Velocity • Laminar premixed flames: Flame structure • Laminar diffusion flames 13 Course Overview Part II: Turbulent Combustion • Turbulence • Turbulent Premixed Combustion • Turbulent NonPremixed Combustion • Modeling Turbulent Combustion • Applications 14 Fundamentals and Mass Balances of Combustion Systems Combustion Summer School 2014 Prof. Dr.Ing. Heinz Pitsch Thermodynamics The final state (after very long time) of a homogeneous system is governed by the classical laws of thermodynamics Prerequisites: • Definitions of concentrations and thermodynamic variables • Mass and energy balances for multicomponent systems 16 Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass • Definitions, Equation of State, Mass balances of combustion systems Balance • Thermodynamics, flame • Elementary and Global Reactions temperature, and equilibrium • Coupling Functions • Governing equations • Stoichiometry • Laminar premixed flames: • Mixture Fraction Kinematics and Burning Velocity • Laminar premixed flames: Flame structure • Laminar diffusion flames 17 Definitions, Equation of State, Mass Balance • In chemical reactions mass and chemical elements are conserved • Combustion always in (gas) mixtures The mole fraction • Multicomponent system with k different chemical species 23 • Mole: 6.0236 ·10 molecules are defined as one mole  Avogadro number N A • Number of moles of species i: n i • Total number of moles: • Mole fraction of species i: 18 The mass fraction • Mass m of all molecules of species i is related to its number of moles by i where W is the molecular weight of species i i • Total mass of all molecules in the mixture: • Mass fraction of species i: • Mean molecular weight W: • Mass fraction and mole fraction: 19 The mass fraction of elements • Mass fractions of elements are very useful in combustion • Mass of the species changes due to chemical reactions, but mass of the elements is conserved • Number of atoms of element j in a molecule of species i: a ij • Mass of all atoms j in the system: where k is the total number of elements in the system, W is e j molecular weight of element j 20 The mass fraction of elements • The mass fraction of element j is then • From the definitions above it follows 21 The partial molar density (concentration) • Number of moles per volume V or partial molar density, the concentration: • Total molar density of the system is then 22 The Partial Density • The density and the partial density are defined • The partial molar density is related to the partial density and the mass fraction by (relation often important for evaluation of reaction rates) 23 The thermal equation of state • In most combustion systems, thermally ideal gas law is valid • Even for high pressure combustion this is a sufficiently accurate approximation, because the temperatures are typically also very high • In a mixture of ideal gases the molecules of species i exert on the surrounding walls of the vessel the partial pressure • Universal gas constant equal to 24 Dalton's law x x • For an ideal gas the total pressure is equal to the sum of x x x the partial pressures x • Thermal equation of state for a mixture of ideal gases x x + o o • From this follows o o = • And for the volume x x o x x x o x o x o x 25 Example: Methane/Air Mixture • Known: CH airmixture; 5 mass percent CH , 95 mass percent air 4 4 Air: 21 (volume fraction) O , 79 N (approximately) 2 2 • Unknown: Mole fractions and element mass fractions • Solution:  Molar masses:  Mass fractions in the air:  In the mixture:  Mean molar mass: 26 Example: Methane/Air Mixture • Mole fractions of Components: • Molar mass of elements: • with: • Mass fractions of elements: • Simplification: Whole numbers for values of the molar masses 27 Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass • Definitions, Equation of State, Mass balances of combustion systems Balance • Thermodynamics, flame • Elementary and Global Reactions temperature, and equilibrium • Coupling Functions • Governing equations • Stoichiometry • Laminar premixed flames: • Mixture Fraction Kinematics and Burning Velocity • Laminar premixed flames: Flame structure • Laminar diffusion flames 28 Elementary and Global Reactions • Distinction between elementary reactions and global reactions important • Elementary reactions  Describes actual microprocess of chemical reaction  Only take place, if collisions between reactants take place  Reaction velocities can be determined experimentally oder theoretically • Global reactions  Conversion of educts to products  Ratios of amounts of substance  Does not represent a chemical microprocess  Temporal process of the reaction cannot be given 29 Elementary Reactions • Observe the conservation of elements • Chemical changes due to collisions of components • Transition from educts to products symbolized by arrow • Example: Bimolecular elementary reaction • Elementary reactions also proceed backwards: • Often symbolized by a double arrow: 30 Global reactions • Conservation of elements • Global ratios of amounts of substance • Do not take place on atomic scale • Global balance of a variety of elementary reactions • Equality sign for global reactions • Example for global reaction: meaning that 2 mol H react with 1 mol O , yielding 2 mol H O 2 2 2 31 Global reactions • Multiples of the equation are also valid:  This does not hold for elementary reactions • Multiplication of the equation of the global reaction by the molar masses → Mass balance during combustion • Example: Combustion of H using the foregoing equation 2 32 Global reactions • Stoichiometric coefficient of reactants i: • Stoichiometric coefficient of products i: • Stoichiometric coefficient of a component (only for global reactions): • Note:  Stoichiometric coefficients n of the educts are negative i  Whereas n‘ are defined to be positive i 33 Global reactions Formulation of global reactions: • Combustion of hydrocarbon fuel or an alcohol • Atoms in the fuel: Carbon, hydrogen and oxygen  Number of atoms in the fuel • Stochiometric coefficients of the global reaction are derived from n ‘ B  Balances of atoms • C: • H: • O: • Example: 34 Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass • Definitions, Equation of State, Mass balances of combustion systems Balance • Thermodynamics, flame • Elementary and Global Reactions temperature, and equilibrium • Coupling Functions • Governing equations • Stoichiometry • Laminar premixed flames: • Mixture Fraction Kinematics and Burning Velocity • Laminar premixed flames: Flame structure • Laminar diffusion flames 35 Coupling functions Global reaction, e.g.: n F + n O = n P 1 2 3 • Conversion of: • n moles of component 1 1 • n moles of component i i • Reaction has taken place n /n or n /n times  n /n = n /n 1 1 i i 1 1 i i • Differential notation: • Integrating, e.g. for fuel and oxygen from the unburnt state → Coupling function: 36 Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass • Definitions, Equation of State, Mass balances of combustion systems Balance • Thermodynamics, flame • Elementary and Global Reactions temperature, and equilibrium • Coupling Functions • Governing equations • Stoichiometry • Laminar premixed flames: • Mixture Fraction Kinematics and Burning Velocity • Laminar premixed flames: Flame structure • Laminar diffusion flames 37 Stoichiometry • Stoichiometric: Fueltooxygen ratio such that both are entirely consumed when combustion to CO and H O is completed 2 2 • For example, Global reaction describing combustion of a single component hydrocarbon fuel C H (subscript F for fuel) m n Stoichiometric coefficients are where may be chosen arbitrarily to unity 38 Stoichiometric Mass Ratio • Mole number ratio for stoichiometric condition or in terms of mass fractions where n is called the stoichiometric mass ratio • Typical value: Methane: n = 4 • Mass ratio n  Fuel and oxidizer are both consumed when combustion is completed 39 Stoichiometric Mass Ratio • This is consistent with coupling function, since leads to • Complete consumption of fuel and oxygen leads to 40 Extra: Minimum oxygen requirement • Minimum oxygen requirement (molar): o min,m  Fuel/air mole number ratio before combustion at stoichiometric conditions  Ratio of the stoichiometric coefficients • Minumum oxygen requirement (mass): o min 41 Extra: Minimum air requirement • Minimum air requirement:  Mass of air per mass of fuel in complete combustion • Relation between minimum oxygen and minimum air requirement: with: • Mass fraction Y = 0,232 O2,air • Mole fraction X = 0,21 O2,air 42 The equivalence ratio • The equivalence ratio is the ratio of fuel to oxidizer ratio in the unburnt to that of a stoichiometric mixture • For combustion with oxygen • Can be written also in terms of • Fuel to air ratio • Mole fractions • Stoichiometric mass ratio n obtained from global reaction 43 Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass • Definitions, equation of state, mass balances of combustion systems balance • Thermodynamics, flame • Elementary and Global Reactions temperature, and equilibrium • Coupling Functions • Governing equations • Stoichiometry • Laminar premixed flames: • Mixture Fraction Kinematics and Burning Velocity • Laminar premixed flames: Flame structure • Laminar diffusion flames 44 The mixture fraction • Equivalence ratio important parameter in combustion • Mixture fraction quantifies local fuelair ratio in nonpremixed combustion • Consider two separate feed streams of  Fuel  Oxidizer (air, pure oxygen) • Streams mix and burn • Fuel stream  Often consists of one component only  In general does not contain oxidizer • Oxidizer stream  Generally does not contain fuel 45 The mixture fraction In the following: • Fuel stream: Subscript 1 • Oxidizer stream: Subscript 2 Definition mixture fraction • Mass fraction of the fuel stream in the mixture: where m and m are the local mass originating from the individual streams 1 2 • Mixture fraction always between zero and one • Fuel stream: Z = 1 • Oxidizer stream: Z = 0 46 The mixture fraction Note: Index B means fuel • Mass fraction of fuel in the fuel stream: Y B,1 • Mass fraction of oxygen in the oxidizer stream: Y O ,2 2  Before combustion: Dividing by the total mass flow, yields  Mixture fraction linear with fuel mass  Coupling function: 47 The mixture fraction • Mixture fraction: • For stoichiometric composition:  The first two terms in the numerator have to cancel out  Stoichiometric mixture fraction: 48 Mixture fraction definition by Bilger • Consider elements C, H, O in combustion of a C H fuel with oxygen or air m n n C H + n O = Products F m n O2 2 • Changes in elements or in terms of element mass fraction • Coupling function:  Changes in b should vanish 49 Mixture fraction definition by Bilger • Normalizing this such that Z = 1 in the fuel stream and Z = 0 in the oxidizer stream, one obtains Bilger's definition or • Because elements are conserved during combustion, element mass fractions calculated from do not change 50 Relation of mixture fraction with equivalence ratio • Fuelair equivalence ratio • Introducing and into leads with to a unique relation between the equivalence ratio and the mixture fraction 51 The equivalence ratio • This relation is also valid for multicomponent fuels (see exercise below) • It illustrates that the mixture fraction is simply another expression for the local equivalence ratio Exercise: The element mass fractions of a mixture of hydrocarbons and its mean molecular weight W are assumed to be known Determine its stoichiometric mixture fraction in air Hint: 52 Diffusion Flame Structure at Complete Conversion Profiles of Y and Y in the unburnt gas F O 2 53 Diffusion Flame Structure at Complete Conversion • Stoichiometric composition • If Z Z , fuel is deficient st • Mixture is fuel lean • Combustion terminates when all fuel is consumed: (burnt gas, subscript b) • Remaining oxygen mass fraction in the burnt gas is calculated from as 54 Diffusion Flame Structure at Complete Conversion • If Z Z oxygen is deficient st • Mixture is fuel rich • Combustion then terminates when all the oxygen is consumed: leading to 55 Diffusion Flame Structure at Complete Conversion • For hydrocarbon fuel C H , the element mass fractions in the unburnt mixture are m n • For the burnt gas they are for the hydrocarbon fuel considered above • Elements are conserved, hence Z = Z j,u j,b 56 Diffusion Flame Structure at Complete Conversion • This leads with and for and for to piecewise linear relations of the product mass fractions in terms of Z: where 57 Diffusion Flame Structure at Complete Conversion Profiles in the burning mixture BurkeSchumann Solution: Infinitely fast, irreversible chemistry 58 Summary Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass • Definitions, Equation of State, Mass balances of combustion systems Balance • Thermodynamics, flame • Elementary and Global Reactions temperature, and equilibrium • Coupling Functions • Governing equations • Stoichiometry • Laminar premixed flames: • Mixture Fraction Kinematics and Burning Velocity • Laminar premixed flames: Flame structure • Laminar diffusion flames 59
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