fundamentals of combustion _nptel

NPTEL Online - IIT Kanpur

file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture1/main.htm[10/5/2012 11:08:14 AM]

Course Name Fundamental of Combustion Department Aerospace Engineering, IIT Kanpur Instructor Dr. D.P. Mishra

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Question can never be silly,

It can be like a beautiful lily,

In the garden of knowledge,

This is still a truth, age after age. - Dr. D.P. Mishra

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Module 1: Introduction to Combustion Lecture 1: Introduction

The Lecture Contains:

Introduction to Combustion

What is Combustion?

Combustion Triangle

Applications of Combustion

Contd..

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Introduction to Combustion

Introduction

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Combustion Triangle

Essential conditions for combustion to occur

1. Presence of fuel .2. Presence of oxidizer (Not essentially oxygen).3. They must be in right proportions.4. The proportion will be dictated by flammability limit.5. Ignition energy.

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Applications of Combustion

Power PlantsChemical IndustriesDomestic BurnerAutomobiles

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Contd..

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Module 1: Introduction to Combustion Lecture 2: What is Fuel and Oxidizer?


What is Fuel and Oxidizer?

Types of Fuels and Oxidizers

Contd..

Characterization of a Gaseous Fuel

Junker's Calorimeter

Liquid Fuels and Oxidizers

Refinery End-Products of Typical Crude Oil

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What is Fuel and Oxidizer?

Electronegativity

The ability of an element to accept or donate electrons.Amount of pull that one atom exerts on the electron that it is sharing with other atom.The term electronegativity was coined by Linus Pauling, a Noble Laureate.

Element Electro-negativity



F 4 Br 2.8 B 2.0

O 3.5 C,S,I 2.5 Be,Al 1.5

N,Cl 3.0 H,P 2.1 Mg 1.2

Fluorine is having Highest Electronegativity (Most powerful oxidizer).

Oxygen has second highest electronegativity.

Carbon, Hydrogen, Aluminum and Magnesium have Low Electronegativity (Fuels).

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Types of Fuels and Oxidizers

Gaseous Fuel and Oxidizer

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Contd..

Types of Gaseous Fuel and Oxidizer

Sl. No. Fuel Oxidizer Application

1 LPG Air/O2 Domestic Burner, Furnace

2 Natural Gas (NG) Air/O2 IC Engines, Furnaces

3 Producer Gas Air/O2 EC/IC Engines

4 CH4, C3H8, H2 Air/O2 EC/IC Engines

5 Biogas Air/O2 EC/IC Engines, Burners

6 Acetylene Air/O2 Gas welding, Gas cutting

* EC=External Combustion

IC =Internal Combustion

Composition of Some Gaseous Fuels

Fuel CO2 O2 N2 CO H2 CH4 C2H6 C3H8 C4H10

LPG - - - - - - - 70 30

Natural Gas - - 5 - - 90 5 - -

Producer Gas 8 0.1 50 23.2 17.7 1 - - -

Propane - - - - - - 2.2 97.3 0.5

Biogas 33 - 1 - 1 65 - - -

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Characterization of a Gaseous Fuel

Heating Value:

Amount of heat released per unit volume when it undergoes oxidation at normal pressure andtemperature (0.1 MPa and 298 K).Lower heating value (LHV) – amount of heat released by burning 1 kg of fuel assuming thelatent heat of vaporization in the reaction products is not recovered.

Higher heating value (HHV) – heating value of the fuel when water is condensed. is the Latent heat of vaporization of water at 298.15 K

Junker's Calorimeter

(Figure 2.1)

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Determines the heating value of the gaseous fuel.Fuel and air are burnt in a burner.Cooling water in the water jacket-absorbs the heat released during combustion.Heating value- calculated from the water flow rate and rise in temperature.

Liquid Fuels and Oxidizers

Liquid fuel is one of the major energy sources in the transport sector.Crude oil is formed from organic sources, animals, vegetables – which are entrapped in rocksunder high pressure and temperature for million years.

Fuel Oxidizer Application

1 Gasoline Air S.I. Engine, Aircraft Piston Engine

2 HSD Air C.I. Engine

3 Furnace Oil Air Furnaces

4 Kerosene AirAircraft, Gas Turbine, Engines Ramjet, Domestic Burner

5 Alcohols Air I.C. Engine

6Hydrazine, UDMH, MMH, LiquidHydrogen, Triethyl Amine

Liquid O2, RFNA (Red

Fuming Nitric Acid)N2O4

Liquid propellant rocket Engines

7 Hydrogen, Kerocene Air Ramjet/Scramjet

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Refinery End-Products of Typical Crude Oil

Crude oil undergoes several process in the refinery.Generally separation of petroleum constituents occur in the distillation column.Constituents of typical crude oil is shown below.

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Module 1: Introduction to Combustion Lecture 3: Fuels


Bomb Calorimeter

Properties of Liquid Fuels

Properties of Common Liquid Fuels

Solid Fuels and Oxidizers

Contd..

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Bomb Calorimeter

Used to determine the calorific value of the liquid fuel.Liquid is burnt in the bomb in the presence of oxygen at about 2.5 MPa .The change in temperature in the water bath provides the calorific value of the fuel.

(Figure 3.2)

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SpecificGravity

: Ratio of mass density of fuel to mass density of water at the same temperature

Reference temperature for fuel and water: 288.8 KAmerican Petroleum Institute (API) Scale:

Relation between APISG and HHV:

ForGasoline

:

ForKerosene

:

Auto IgnitionTemperature

: The lowest temperature required to make the combustion self sustained withoutany external aid

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FlashPoint

: Minimum temperature at which liquid fuel will produce sufficient vapors to form aflammable mixture with air. Indicates maximum temperature at which liquid fuel can bestored without any fire hazard.

FirePoint

: Minimum temperature at which liquid fuel produces sufficient vapors to form a flammablemixture with air that continuously supports combustion establishing flame instead of justflashing.

SmokePoint

: Measure of the tendency of a liquid fuel to produce soot.

Properties of Common Liquid Fuels

Fuel Type AutomotiveGasoline

Diesel Fuel Methanol Kerosene ATF(JP8)

Specific gravity 0.72 - 0.78 0.85 0.796 0.82 0.71

Kinematics viscosity @ 293 K

(m2/s)0.8 X 10-6 2.5 X 10-6 0.75 X 10-6

3.626 X

10-6 --

Boiling point range (K) @ STP 303 - 576 483 - 508 338 423-473 442

Flash point (K) 230 325 284 311 325

Auto ignition temperature (K) 643 527 737 483 --

Stoichiometric air/fuel by weight 14.7 14.7 6.45 15 15.1

Heat of Vaporization (kJ/kg) 380 375 1185 298.5 --

Lower heating value (MJ/kg) 43.5 45 20.1 45.2 43.3

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Solid Fuels and Oxidizers Solid Fuels:

(Figure 3.2) Constituents of Solid Fuel:

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Contd..Types of Solid Fuels and Oxidizers:

S. No. Fuel Oxidizer Applications

1Biomass (Wood, Saw Dust, RiceHusk, Rice Straw, Wheat Straw,

etc)Air/O2

Domestic Burner,Engine With

Producer Gas

2 Coal, Coke, Charcoal do do

3Special Fuels

Nitrocellulose (NC), HTPB,CTPB

Nitroglycerine, AmmoniumPerchlorate , Ammonium Nitrate,

Nitrogen Tetraoxide

Solid PropellantRocket, Hybrid

Rocket

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Module 1: Introduction to Combustion Lecture 4: Characterization of Solid Fuels


Oxygen, Water and Ash Content of Certain Solid Fuels

Characterization of Solid Fuels

Various Combustion Modes

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Oxygen, Water and Ash Content of Certain Solid Fuels

Moisture in Solid Fuel:

1. Free2. Bound water

Fuel moisture content will affect rate of combustion and overall efficiency.

Ash: The inorganic materials, which remain as residue even after complete combustion.

Ash content affects the performance of the combustion system.Ash content causes fouling of the boilers.

Fuel Oxygen (Dry, Ash-free) Moisture (Ash-free) Ash (Dry)

Wood 40-45% 15-70% 0.1-1.0%

Peat 30-35% 70-90% 0.1-20%

Lignite coal 20-25% 20-30% >5%

Bituminous coal 3-5% 10-5% >5%

Anthracite coal 1-2% 2-4% >5%

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Characterization of Solid Fuels:Proximate Analysis:

Used to determine the moisture content, volatile matter, fixed carbon and ash content in thesolid fuel.To determine water content, few grams of fuel is heated around 378 K till it attains constantweight.Volatile matter is determined by heating the sample at 1173 K.

Ultimate Analysis:

Used to determine the major elemental composition of the solid fuel.Nitrogen content is determined by chemical method.Sulphur content is evaluated by burning the fuel to convert it into SO4 followed by precipitation

method. Calorific value can be determined by bomb calorimeter.

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Various Combustion Modes

Premixed Flame : Fuel and oxidizer are mixed before actual combustion.

Examples: Bunsen burner, LPG Stove

Diffusion Flame : Fuel and oxidizer are mixed in the region where chemical reactiontakes place.

Laminar and TurbulentFlames

: Based on the flow characteristics; Turbulent flow occurs in practicalcombustion devices.

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Module 1: Introduction to Combustion Lecture 5: Scope of Combustion


Scope of Combustion

Image Sources

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Scope of CombustionIndustrial Process

Thermal energy for process chemical plants, sugar industries, food processing industries areobtained through combustion.Iron, steel and other metals are produced from raw materials through combustion.Heat treatment and annealing of metals.Rotary kilns are used to produce Portlant cement.

Sugar Industry Food Processing

Process Chemical Plant Steel Plant

(Figure 5.1)

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TransportationSurface transport vehicles are operated by reciprocating IC EnginesGas turbine combustors are used widely in air and marine transportation sectors.

(Figure 5.2)

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PowerGeneration

Most of the thermal power plants are operated by burning coal.Recently gas turbine power plants are coming up.

Fluidized Bed Power Plant Coal Power Plant

Biomass Based Power Plant Gas Turbine Power Plant

(Figure 5.3)

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Waste Disposal

Combustion finds application in disposing waste materials.Incinerators are used to dispose domestic and industrial wastes.In modern hospitals, incinerators are used to dispose hospital wastes safely.

(Figure 5.4)

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FireSometimes fire causes damage to life and property.Forest Fire: Damages natural resources and lives.Structural Fire: Damages property and human lives.

Effective fire breakers should be designed and implemented to avoid fire hazard. By using properconstruction materials, Fire hazard can be minimized. Marine life is very much affected by oil spillfire.

(Figure 5.5)

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Environmental pollution

Combustion of any fuel produces certain amount of emissions such as smoke, ash, soot, andother harmful gases.Major pollution generated in combustion system are CO, CO2, NO, NO2, SO2, ash, etc.

These are due to incomplete combustion and can be minimized by increasing the residence timeof fuel-oxidizer mixture in the combustor.

Sources Particulates CarbonMonoxide

UnburntHydrocarbon

Nitrogenoxides

Sulfurdioxides

Transportation 7 79 60 15 6

StationaryCombustion

Systems/Electricity8 <1 <1 2 69

Industrial Process 23 8 32 13 25

Miscellaneous 62 13 8 70 <1

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Image Sources

Boiler : http://www.heatingoil.com/blog/39971019/

Incinerator : http://www.winderickx.pl/en/msw_municipal_waste_incinerators.php

IC Engine : http://www.engr.colostate.edu/~dga/mech324/handouts/cam_stuff/index.html

WankelEngine :

http://mazda-rx7.org/

Power Plant : http://www.teachengineering.org/view_lesson.php?url=http://www.teachengineering.org/collection/cub_/lessons/cub_earth/cub_earth_lesson08.xml

PulseDetonation

Engine :http://www.seas.ucla.edu/combustion/projects/pulsed_detonation_wave.html

RocketEngine :

http://www.lr.tudelft.nl/live/pagina.jsp?id=56438fe7-95c8-4c02-927c-82766a35721a&lang=en

Incinerator : http://www.wtert.eu/default.asp?ShowDok=13

http://www.heatingoil.com/blog/39971019/

http://www.winderickx.pl/en/msw_municipal_waste_incinerators.php

http://www.engr.colostate.edu/~dga/mech324/handouts/cam_stuff/index.html

http://mazda-rx7.org/

http://www.teachengineering.org/view_lesson.php?url=http://www.teachengineering.org/collection/cub_/lessons/cub_earth/cub_earth_lesson08.xml



http://www.seas.ucla.edu/combustion/projects/pulsed_detonation_wave.html



http://www.wtert.eu/default.asp?ShowDok=13

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Image Sources Gas Turbine Engine : http://www.azom.com/details.asp?ArticleID=90

Furnace : http://www.macarthurcoal.com.au/Operations/Products/MetallurgicalProducts/tabid/96/Default.aspx

Process ChemicalIndustry :

http://www.hasbrouckengineering.com/aroma_engineering.htm

Steel Plant : http://www.forbesmarshall.com/fm_micro/industries.aspx?id=system

Biomass PowerPlant

: http://www.treehugger.com/files/2006/10/tallahassee_flo.php

Gas Turbine PowerPlant :

http ://www.power-technology.com/projects/knapsackccgt/knapsackccgt6.html

Fluidized BedPower Plant :

http://www.britannica.com/EBchecked/topic-art/1424725/113942/Schematic-diagram-of-a-fluidized-bed-combustion-boiler

Forest Fire : http://www.cartridgesave.co.uk/news/30-amazing-pictures-of-forest-fires/

http://www.azom.com/details.asp?ArticleID=90

http://www.macarthurcoal.com.au/Operations/Products/MetallurgicalProducts/tabid/96/Default.aspx

http://www.macarthurcoal.com.au/Operations/Products/MetallurgicalProducts/tabid/96/Default.aspx

http://www.hasbrouckengineering.com/aroma_engineering.htm

http://www.forbesmarshall.com/fm_micro/industries.aspx?id=system

http://www.treehugger.com/files/2006/10/tallahassee_flo.php

http://www.power-technology.com/projects/knapsackccgt/knapsackccgt6.html





http://www.cartridgesave.co.uk/news/30-amazing-pictures-of-forest-fires/

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Image Sources

Oil Spill Fire : http://zeroequalsthree.blogspot.com/2010/09/chaos-oil-spill-chaos.html

Structural Fire : http://www.forensicmed.co.uk/pathology/fire-deaths/fire-destruction-of-bodies/

Dust Explosion : http://www.industrialairsolutions.com/industrial-vacuums/explosion-proof/explosion-proof-vacuums.htm

Gas Turbine Engine : http://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/gasturbine/gas_turbine.html

Car : http://dodge-sprinter.net/wp-content/uploads/2011/02/Dodge-Sprinter-Van-Side-View.jpg

Ambassador Car : http://4.bp.blogspot.com/_rMX3SfIKwNc/TEuA4BHyCSI/AAAAAAAAAQk/BO7ZOgEVHtQ/s1600/ambassador

Aeroplane : http://www.dailymail.co.uk/news/article-564300/Passenger-jet-makes-terrifying-10-000ft-climb-dodge-plane-pilot-showing-child.html

Ship : http://www.a1-discount-cruises.com/cruise-ships.htm

IC Engine : http://www.birkey.com/technical-illustration/engine-piston-pin-sketch/

http://zeroequalsthree.blogspot.com/2010/09/chaos-oil-spill-chaos.html

http://www.forensicmed.co.uk/pathology/fire-deaths/fire-destruction-of-bodies/

http://www.forensicmed.co.uk/pathology/fire-deaths/fire-destruction-of-bodies/

http://www.industrialairsolutions.com/industrial-vacuums/explosion-proof/explosion-proof-vacuums.htm

http://www.industrialairsolutions.com/industrial-vacuums/explosion-proof/explosion-proof-vacuums.htm

http://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/gasturbine/gas_turbine.html

http://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/gasturbine/gas_turbine.html

http://dodge-sprinter.net/wp-content/uploads/2011/02/Dodge-Sprinter-Van-Side-View.jpg%20

http://dodge-sprinter.net/wp-content/uploads/2011/02/Dodge-Sprinter-Van-Side-View.jpg%20

http://4.bp.blogspot.com/_rMX3SfIKwNc/TEuA4BHyCSI/AAAAAAAAAQk/

http://4.bp.blogspot.com/_rMX3SfIKwNc/TEuA4BHyCSI/AAAAAAAAAQk/

http://www.dailymail.co.uk/news/article-564300/Passenger-jet-makes-terrifying-10-000ft-climb-dodge-plane-pilot-showing-child.html

http://www.dailymail.co.uk/news/article-564300/Passenger-jet-makes-terrifying-10-000ft-climb-dodge-plane-pilot-showing-child.html

http://www.a1-discount-cruises.com/cruise-ships.htm

http://www.birkey.com/technical-illustration/engine-piston-pin-sketch/

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file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture6/6_a1.htm[10/5/2012 11:18:43 AM]

One who asks a question fearlessly,

For a moment he may feel miserable,

One who dares not to ask questions,

He remains as a fool year after year.

-Dr. D.P.Mishra

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Module 2: Thermodynamics of Combustion Lecture 6: Introduction


Introduction

Thermodynamic Properties

Gas Mixture

Dalton's Law of Partial Pressure

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Thermodynamics of Combustion

Introduction

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Dalton's Law of Partial Pressure

Total no of moles, ..(1)Dividing by ,

Where, are mole fraction of species A, B,..Total mass of the mixture,

Dividing by ,

Where, are mass fraction of species A, B, ..

(Figure 6.2)

= Molecular weight of mixture

Also, from ideal gas law, Substituting in (1),

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Gas Mixture

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Thermodynamic Properties

(Figure 6.1)

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Module 2: Thermodynamics of Combustion Lecture 7: Thermodynamic Laws


Enthalpy and Internal Energy

Effect of Temperature on Heat Capacity

Thermodynamic Laws

First Law

Second Law

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Enthalpy and Internal Energy

Specific internal energy of the mixture,

Mass specific internal energy of the mixture,

Specific enthalpy ofthe mixture,

Mass specific enthalpy of the mixture,

Enthalpy of a species,

Internal Energy of a species,

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Effect of Temperature on Heat Capacity

Specific heats, and are functions of temperaturefor both ideal and real gases

(Figure 7.1)

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Thermodynamic Laws

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First Law of Thermodynamics

First law applied to a closed system:

Where, – Heat added to the system (Path Function)

– Work done by the system (Path Function)

– Total energy change in the system (Point Function)

First law applied to an open system:

Where, – Specific enthalpy – Velocity of flow – Height of inlet and outlet port

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Second Law of Thermodynamics

Clausiusinequality:

For any system undergoing a cyclical process, the ratio of the sum of all heatinteractions to its temperature is equal to or less than zero.

Increase in entropyprinciple:

Second law of thermodynamics for controlvolume:

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Module 2: Thermodynamics of Combustion Lecture 8: Stoichiometry


Stoichiometry

Stoichiometry Calculation

Thermochemistry

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Stoichiometry

Stoichiometry: The elemental mass balance in a chemical reaction, describing exactly howmuch oxidizer has to be supplied for complete combustion of certain amount offuel.

Example:

Mass is conserved

(Figure 8.1)

Lean Mixture:

Quantity of oxidizer > Stoichiometric quantity

Rich Mixture:

Quantity of oxidizer < Stoichiometric quantity

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Stoichiometry Calculation

Problem: Gasoline Dry air Products (10.02% ; 5.62% ; 0.88% ; 83.48% )Determine (i) A/F Ratio; (ii) Equivalence Ratio; (iii) Stoichiometric Air Used

Solution Equation: 16.32 ( 3.76 ) 7.37 + 0.65 4.13 61.38 9

((12 8 ) 18)/(16.32(32 (3.76 28))) = 0.05089

Stoichiometric Equation:

12.5( 3.76 ) 8 9 47

((12 8 ) 18)/(12.5(32 (3.76 28))) = 0.06643

Equivalence ratio 0.766

Since <1 ; The mixture is leanStoichiometric Air Used:

Stoichiometric air = 100 / = 100/ 0.766 = 130.5%

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Thermochemistry

(Figure 8.2)

Consider the burner as shown below:

(Figure 8.3)

Assumption: (i) Negligible change in K.E. & P.E., (ii) No shaft work

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Thermochemistry

Where, HR – Total enthalpy of reactants; HP – Total enthalpy of products

niR – No of moles of ith reactant; niP – No of moles of ith product

hiR – Enthalpy of formation per unit mole of ith reactant

hiP – Enthalpy of formation per unit mole of ith product

– Standard heat of reaction

Heat of reaction depends on temperature

(Figure 8.4)

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Module 2: Thermodynamics of Combustion Lecture 9: Heat of Combustion


Heat of combustion

Hess Law

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Heat of Combustion

For the reaction :Heat of reaction is

given by :

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Heat of formation of important species at 25 °C and 0.1 MPa

Species Formula State Heat of formation (kJ/mol)

Oxygen O2 Gas 0

Hydrogen H2 Gas 0

Hydroxyl OH Gas 42.3

Water H2O Gas -242

Water H2O Liquid -286

Carbon monoxide CO Gas -110.5

Carbon dioxide CO2 Gas -394

Methane CH4 Gas -74.5

Propane C3H8 Gas -103.8

Butane (n) C4H10 Gas -124.7

Kerosene CH1.842 Liquid -51.6

Nitrogen dioxide NO2 Gas 33.9

Nitric acid NO Gas 90.4

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Hess Law

Illustration: Determine the heat of reaction for water gas shift reaction

IntermediateReactions:

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Module 2: Thermodynamics of Combustion Lecture 10: Adiabatic Flame Temperature


Adiabatic Flame Temperature

Effect of Equivalence Ratio on Adiabatic Flame Temperature

Effect of Initial Temperature on Adiabatic Flame Temperature

Effect of Pressure on Adiabatic Flame Temperature

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Effect of Equivalence Ratio on Adiabatic Flame Temperature

(Figure 10.1)

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Adiabatic Flame Temperature

Where,

S.W -K.E -P.E -

Shaft workKinetic EnergyPotential Energy

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Effect of Initial Temperature on Adiabatic Flame Temperature

(Figure 10.2)

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(Figure 10.3)

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System Tu (K) P (MPa) Tad (K)

CH4 Air 300 0.1 2200

CH4 - Air 300 2.0 2270

CH4 - Air 600 2.0 2500

CH4 - O2 300 0.1 3030

C3H8 - Air 300 0.1 2278

H2 - Air 300 0.1 2390

H2 - O2 300 0.1 3080

CO - Air 300 0.1 2400

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Module 2: Thermodynamics of Combustion Lecture 11: Chemical Equilibrium


Chemical Equilibrium

Procedure for Determining Equilibrium composition

Summary

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Module 2: Thermodynamics of Combustion Lecture 11: Chemical Equilibrium Chemical Equilibrium

Chemical reaction proceeds in the direction of increasing entropy

If the system is not adiabatic, we have to invoke Gibbs free energy, G

From 1st Law,

At constant pressure and temperature,

From 2nd Law, of Thermodynamic

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Procedure for Determining Equilibrium Composition

Equilibrium products can be estimated by adopting the following stepsStep 1: Identify probable equilibrium speciesStep 2: Identify equilibrium reactions schemeStep 3: Find out equilibrium constantStep 4: Strike balance for elemental conservationStep 5: Strike overall mass conservationStep 6: Solve all equations by iterative method (Newton- Raphson Method)

For a ideal gas mixture, Gibbs function of i th species is given by

-Gibbs function per mole of ith species.

-Partial pressure of ith species.-Temperature-Universal gas constant

Gibbs function for a ideal gas mixture

At equilibrium,

In the above equation, (Since pressure remains constant)

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Consider the reaction

Where, a, b, c and d are stoichiometric coefficientsChange in number of moles of each species is given by,

Substituting above equation in Gibbs function, We can get,

In terms of mole fraction,

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Summary

The basic thermodynamic principles are useful in estimation of properties related tocombustion.Stoichiometric calculations are useful in estimation of fuel-air requirements for a combustionprocess.Adiabatic flame temperature indicates maximum possible temperature in combustion process.Thermodynamic relations can be used to relate the change in Gibbs free energy withequilibrium constant.Equilibrium composition can be used to calculate adiabatic flame temperature using aniterative procedure.

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After asking a question about the unknown thing,

Examination of it is a must by own reasoning,

As reasoning is the backbone of everything,

That is the sole objective of all our learning.

-Dr. D.P.Mishra

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Module 3: Physics of Combustion Lecture 12: Introduction


Introduction

Laws of Transport Phenomenon

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Physics of Combustion

Introduction

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Laws of Transport Phenomenon

Newton's Law of Viscosity

Two parallel plates-separated by ‘Y'Lower plate is fixedAt t< 0; system is at restAt t=0; upper plate ismovedVelocity of plate: Vx

(Figure 12.1)

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Newton's Law of Viscosity can be expressed as,

Where, µ is dynamic viscosity (kg/ms)dVx/dy is the shear strain rate-ve sign: momentum flux in thedirection of decreasing velocity

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Fourier's Law of HeatConduction

Two parallel plates-separated by ‘Y'Lower plate is fixedAt t < 0; two plates are atthe same temperatureAt t = 0; upper plate issuddenly heated (T1 >T0 )

Lower plate – Maintainedat temperature T0

(Figure 12.2)

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Fick's Law of Species Diffusion

Two parallel plates-separated by‘Y'.Upper plate is maintained wet.Lower plate is kept dry(Dehydrating agent)Water vapour evaporates at upperplatePartial pressure of water vapour ismaintained at saturated vapourpressure of waterThus concentration gradient existsbetween the two platesMass flux-proportional toconcentration, CA inversely

proportional to distance Y

Differential form of Fick's law

(Figure 12.3)

Binary diffusitivity of species A through B

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Module 3: Physics of Combustion Lecture 13: Transport properties for gas mixture


Transport properties for gas mixture

Mass conservation equation

Momentum conservation equation

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Transport properties for gas mixture

Viscosity of gas mixture

Wassilijewa equation

Mason and Saxena modification

is the viscosity of the pure component

is the mole fraction of the ith component

Thermal Conductivity of gas mixture

Wassilijewa equation

Mason and Saxena modification

is the thermal conductivity of the pure component

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Diffusion Coefficient of any component in a gas mixture

Wilke equation

Where, is the collision diameter in

is the pressure (Bar)

is the molecular weight of the components

is the collision integral

=Boltzman's constant

=Intermolecular potential

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Mass conservation equationPrinciple of mass conservation

------ (1)

Rate of accumulation in fluid element = ------ (2)

Rate of mass in fluid element across face A = ------ (3)

Rate of mass leaving fluid element across face B = ------ (4)

The net efflux in x-direction = ------ (5)

The net efflux in y-direction = ------ (6)

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Substituting (2), (5) and (6) in (1)

Differential form of continuity equationIn vector notation,

Where, is the gradient operator

is the divergence of

For incompressible flow,

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Module 3: Physics of Combustion Lecture 14: Momentum conservation equation



Species transport equation

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Rate of momentum accumulation in x-direction =

Rate of momentum accumulation in y-direction =

Momentum in x-direction into fluid elementacross face A

=

Momentum in x-direction leaving the fluid element across face B =

=

Momentum in y-direction entering the fluidelement through face C

=

Momentum in y-direction leaving the fluidelement across face D

=

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Net forces acting on the fluid element in x-direction =

Net body forces acting in fluidelement in the x-direction

=

Momentum equation for fluid elementin x-direction

=

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Momentum equation for fluidelement in x-direction

=

where, , are components of mass velocity vector in x and y direction and are surfacestresses

Applying Stokes viscosity law, the surface stresses are given by

Momentum equation forfluid element in x-direction

=

Momentum equation forfluid element in y-direction

=

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Species transport equation

Rate of accumulation in fluid element=

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Rate of accumulation in fluid element=

Rate of mass of species A into fluid element across face A =

By Taylor's series expansion, the rate of massofspecies A leaving fluid element across face B

=

Net efflux in x direction =

Net efflux in y direction =

Mass production rate of ith species due to chemical reaction =

According to Fick's law,

Species transport equation is given by,

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Module 3: Physics of Combustion Lecture 15: Energy transport equation


Energy transport equation

Boundary layer concept

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Energy transport equation

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Heat accumulated in the fluid element =

Amount of heat entering into fluidelement through face ‘A' is given by:

Amount of heat leaving from the fluidelement through face ‘B' is given by:

Net efflux in x direction

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Amount of heat interaction in y-direction through faces ‘C' and ‘D' is

In a fluid element, heat may be absorbed or removed due to chemical reaction

The amount of heat interaction in fluid element per unit area:

By striking out an energy balance, the energy equation for a multi-component reactive systembecause.

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Boundary layer concept

Velocity of fluid increases from zero at wall to free stream velocityVelocity gradients appear near a thin region adjacent to wall

(Figure 15.1)

The thin region adjacent to wall surface is the boundary layerWall friction-causes reduction in velocity near the wall

Boundary layer thickness times the free stream velocity

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Module 3: Physics of Combustion Lecture 16: Boundary layer solutions


Boundary layer solution

Thermal Boundary layer

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Module 3: Physics of Combustion Lecture 16: Boundary layer solution


Approximate solution for steady 2D incompressible flow over a flat plate

Mass conservation

Momentum conservation

By boundary layer approximations,

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By carrying out order of magnitude analysis,

Mass conservation

Momentum conservation

From the above equation, pressure remains constant along ‘y' direction.Analytical method of Blasius gives exact solution of the above equations.

Relation between B. L. thickness and Re is

Drag coefficient for laminar flow over flat plate:

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Thermal Boundary layer

Free stream temperature Flat plate temperature

Heat transferred from fluid toplate

(Figure 16.1)

Thermal boundary layer thickness , Value of y for which

Thermal boundary layer grows with increase in distance from the leading edge

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Local heat flux due to convection,

(Newton's law of cooling)

Local heat flux at the wall,

(Fourier's law of conduction)

Combining there two equations, the convective heat transfer coefficient (h) is given by,

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Using Pohlhausen method, Nusselt number (Nu) can be expressed as

Valid for can be used for most of the gases

For laminar fully developed pipe flow, Valid for constant temperature

For laminar fully developed pipe flow, Valid for constant heat flux

Average Nusselt number for developingpipe flow,

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Module 3: Physics of Combustion Lecture 17: Transport in Turbulent Flow


Transport in Turbulent Flow

Characterization of Turbulent Flow

Turbulent Boundary layer

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Transport in Turbulent Flow

Turbulent Flow:

At high Reynolds and Grashof'snumber, the properties, velocity andtemperature exhibits random variation.Eddies move randomly back and forthacross the adjacent fluid layers.Turbulence reduces the B.L. thickness.Enhanced mass, momentum, andenergy transfer rates.

(Figure 17.1)

Where, – Time averaged value ofvelocity

– Fluctuating component ofvelocity

Turbulent diffusivity is given by,

(Figure 17.2)

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Characterization of Turbulent Flow

Length scale of Turbulence:

The distance covered by an eddy before it disappears or loses its identity.

Intensity of Turbulence:

Measure of violence of eddies.

Turbulence Intensity:

Length Scales usedin Turbulent Flow:

1. Macroscopic scale, L (Characteristic width of flow)2. Integral Scale,

3. Taylor micro scale, 4. Kolmogorov length Scale,

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Taylor microscale,

where, is the mean strain rate

Kolmogorov length scale,

Note:Kolmogorov length scale ( ) is related to integral length scale ( )( ) - Thickness of the smallest vortex present in turbulent flow

Turbulent Reynolds number based on the length scales

Note: is the characteristic velocity

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Turbulent Boundary layer

Consider 2D steady incompressible turbulent flow over a flat plate,

Momentum equation in x direction is given by,

The term is known as Reynolds stress

Energy equation for turbulent boundary layer is given by,

A simple model for Reynolds stress suggested by Bossinesq,

Similarly,

; where, is the turbulent diffusivity

; where, is the eddy diffusivity

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In analogy to kinetic theory of gases, Prandtl suggested an expression for turbulent diffusivity

Where, is the mixing length, and I is the turbulence intensity

Combining these two equations,

C, is the constant, obtained from the experimental data

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Asking a question is not the end of a thing,

One can assume it to be a humble beginning,

If explored earnestly without bothering,

One can definitely have a happy ending. -Dr. D.P. Mishra

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Module 4: Chemistry of combustion Lecture 18: Introduction


Introduction

Basic Reaction Kinetics

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Chemistry of combustion

Introduction

Chemical kinetics:The specialized branch of physical chemistry dealing with the study of chemical reactions and theirgoverning factors.

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Basic Reaction Kinetics

Reaction rate:Rate of decrease of reactant concentration or rate of increase of product concentration. Expressed in

terms of mole/m3sCompact expression for chemical reaction:

Where, and are stoichiometric coefficients of reactants and products.N is the total number of speciesM is the arbitrary specification of all chemical species

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Expressing the reaction using index notation:

Here, N=2

Here, N=3

Note: The above reactions are elementary in nature

Global reactions,3 bonds have to be broken,4 bonds have to be formed

Unlikely to occur!!

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Global reactions,

Bimolecular reactionsReaction between two molecules,

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Module 4: Chemistry of combustion Lecture 19: Law of Mass Action


Law of Mass Action

Collision Theory

Elementary Reactions

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Law of Mass Action

The rate of reaction, RR of a chemical species is proportional to the product of the concentrations ofthe participating chemical species, where each concentration is raised to the power equal to thecorresponding stoichiometric coefficient in the chemical reaction.

Where, is the specific reaction rate or rate coefficient

Note :

-depends on temperature and activation energy and not on concentration. Law of mass actionholds good only for elementary reactions

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Module 4: Chemistry of combustion Lecture 19: Law of Mass Action Collision Theory

(Figure 19.1)The colliding molecules must possess higher energy than the mean energy

Boltzman's energy distribution law:The probability of a molecule possessing the threshold energy, E is proportional to exp

Conditions for chemical reactions to occur:

Suitable molecule must collide with each otherThe molecules must collide with proper orientation (Determined by steric factor)Colliding molecules must possess energy greater than the threshold energy(E).

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From collision theory,

- Collision frequency,

- Steric factor,

- Boltaman's energy probability factor

- Activation energy

(Figure 19.2)From kinetic theory,

- Average effective collision diameter between molecules A and B,

- Boltaman's constant = 1.381 X 10-23J/K

- Reduced mass

Reaction rate

(Pre-exponential Factor)

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The form of equation in previous section is Arrhenius law

Limitations of Arrhenius law:

It cannot simulate combustion processover wide range of temperature.Rate law matches experimental data athigh temperature, but not so at lowtemperature.

Variation of RR with temperature: (Figure 19.3)An increase in temperature by 10% forsame activation energy can cause RRto be enhanced by 250 %

(Figure 19.4)

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Elementary Reactions

If the reaction occurs successfully at molecular level, the reaction is termed as elementary.

Molecularity :Number of molecules or atoms participating in each reaction leading to product.

1. Unimolecular reaction 2. Bimolecular reaction 3. Trimolecular reaction

Order of Reaction:Number of molecules or atoms whose concentration would determine the reaction rate.

Example:

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Module 4: Chemistry of combustion Lecture 20: Order reaction


First Order Reaction

Second Order Reaction

Third Order Reaction

Reverse Reaction

Chain Reaction

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First order reaction,

Consider the first order reaction,

Reaction rate,

Sepataring the variables and integrating, (Figure 20.1)

First order combustion reactions!

Note : concentration decreases exponentially with time (Refer Fig),All unimolecular reactions obey first order kinetics!All first order reactions need not to be unimolecular!!

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Second Order Reaction

Consider the second order bimolecular reaction,

Reaction rate for the above reaction,

General second order reaction

Concentration of species A and B

Reaction rate for the above reaction,

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Multiplying both sides by

Integrating,

Second order combustion reactions!

By applying we will get

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Third Order Reaction

Consider the third order, trimolecular reaction,

RR proportional to third power of concentration of participating species,

Third order combustion reactions !

Reverse Reaction Chemical reactions may proceed in both forward and reverse directions.

Net rate of consumption of A,

Substituting in the above equation, we will get

By integreting the above equation, we can get

can be estimated from the knowledge of

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Chain Reaction

In reality, combustion process involves several reactionsThe overall stoichiometric chemical reaction is unlikely to occur in nature. The elementary reactionscan be classified as;

Chain initiatingChain branchingChain carryingChain terminating

Chain branchingThe ratio of number of free radicals in the product to the reactant > 1

Chain carryingThe ratio of number of free radicals in the product to the reactant = 1

Chain terminatingThe ratio of number of free radicals in the product to the reactant < 1

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Module 4: Chemistry of combustion Lecture 21: Chain Branching Explosion


Chain Branching Explosion

Multistep Reaction Mechanism

Quasi-Steady State Approximation

Partial Equilibrium Approximation (PEA)

Global Kinetics

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Explosion:

Very rapid combustion of fuel andoxidizer, leading to violent release ofenergy.

(Figure 20.2)

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To begin with, stoichiometric mixture of H2 and

O2 is kept in a container.

Temperature is increased beyond 773 K.Result: Very rapid chemical reaction withexplosion.

(Figure 21.1)

Regimes in the explosion chart1. First limit2. Second limit3. Third limit

(Figure 21.2)

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Multistep Reaction Mechanism

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Quasi-Steady State Approximation

Radicals are formed during combustionHalf life period of radicals - Very smallRate of formation = Rate of destruction

Relate radical concentration withmeasurable concentration of other species

Consider the two step chain reaction,

; ;

Reaction rate of the three species,

Initial condition,

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Module 4: Chemistry of combustion Lecture 21: Chain Branching Explosion Applying initial condition,

Applying QSSA method to A2, (Figure 21.3)

; ;

; ;

QSSA method predicts the concentration of species especially when

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Partial Equilibrium Approximation (PEA)

PEA expresses concentration of unknown species in terms of known concentrations.

Consider NO formation mechanism,

Reaction Rate (RR) for NO species:

Note 1: O and N2 concentration are required to determine RR

Note 2: Rate of formation and destruction of O is very high

Difficult to measure the concentration of O!!!

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Step 1: Assume partial equilibrium for O2

molecule

Step 2:

Relate O2 molecule to O by

Equilibrium constant

Reaction Rate (RR) for NO species:

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Global Kinetics

Single step methane combustion:

Overall reaction rate (CH4)

Global kinetic scheme for an arbitrary hydrocarbon (CxHy):

Overall reaction rate (CxHy)

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One has to pursue questions earnestly,

Like a faithful shadow meticulously,

One should bear questions in mind,

Like a small innocent inquisitive child. -Dr. D.P. Mishra

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Module 5: Premixed Flame Lecture 22: Introduction


Introduction

One-dimensional Combustion Wave

Analysis of 1D Flame

Hugoniot Curve...

Laminar Premixed Flame

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Premixed Flame

Introduction

Premixed Flame: Fuel and oxidizer are mixed well at the molecular level before combustion

Examples of premixed flame :Bunsen burner, LPG domestic burner, SI Engine, Afterburner in jet engine

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One-dimensional Combustion Wave

(Figure 22.1)

(Figure 22.2)

(Figure 22.3)

(Figure 22.4)

s

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Analysis of 1D Flame

Continuity Equation : State Equations:

Momentum Equation :

Energy Equation :

are the density, velocity, pressure and temperature

q is the heat release per unit mass

is the mass fraction of species

heat of formation of species

Combining Continuity and Momentum Equations and expressing them in terms of Mach number,

Rearranging the energy equation, we can get

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Hugoniot Curve ..Hugoniot Curve : vs. for a

fixed value of q, inlet pressure ,and inlet density

Region I: Pressure of burnedgas Pressureof C-J detonationwave Strong detonation

Gasvelocity relativeto wave front isslowedto subsonic speed

Pressure and

density increasessignificantlyfor will be

rarely observed (Figure 22.5)

Region II: Pressure of burned gas Pressure ofC-J detonation wave Weak detonation

Gas velocity relative to wave front is slowed to subsonic speed

Burned gas velocity > speed of sound at isochoric condition weak

detonation attains infinite velocity

Region III: In this region Therfore

Hence in this region is imaginary and physically impossible

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Module 5: Premixed Flame Lecture 22: Introduction Laminar Premixed Flame

(Figure 22.6)

(Figure 22.7)

First laboratory premixed

Glame burner : Invented by

Robert Bunsen in 1855

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Luminous Zone

Flame radiation: 3300 to 4400 A°

(Figure 22.8)

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Module 5: Premixed Flame Lecture 23: Structure of 1D Premixed Flame


Structure of 1D Premixed Flame

Laminar Flame Theory

Flame Thickness

Burning Velocity Measurement Methods

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Structure of 1D Premixed Flame

Preheat zone: Negligibly small heatrelease

(Figure 23.1)

Certain chemical reactions takeplace in this zone

Reaction zone:most of the chemical energy isreleased in the form of heatDecomposition of fuel takes place,leading to intermediate radicalformationReaction zone is very thin ascompared to the preheat zone.Temperature gradient andconcentration gradient are high.

Recombination zone: CO2 and H2O are formed;

No heat release in this zone

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Laminar Flame Theory

Assumptions:1D, steady, inviscid flow.Flame is quite thin.Ignition temperature is very close to flame temperature.No heat loss including radiation; Adiabatic flame.Pressure difference across the flame is negligibly small.Binary diffusion, Fourier and Fick's law are valid.Unity Lewis number.Constant transport properties

Mass conservation: (1)

Species conservation: Energy equation:

Fuel: (2) (5)

Oxidizer: (3) Global reaction mechanism:

Product: (4) (6)

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Laminar Flame Theory (Contd.)

Heat release due to chemical reaction:

(7)

Now energy equation becomes In the reaction zone,

(8)

Boundary conditions (For preheat zone)

(10)

(11)

Recasted energy equation forpreheat zone,

Rewriting, E.g. (11).

(9) (12)

Heat transfer due to conduction is balanced byconvective heat transfer. (13)

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Laminar Flame Theory (Contd.)

Combining equations (10) and (13),

(14)

(15)

Also,Mean fuel burning rate can also beexpressed as,

(16) (19)

Combining equations (15) and (16),Expression for burning velocitybecomes,

(17)

Mean fuel burning rate per unit volume,

(18)

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Flame Thickness

Ignition temperature can be approximated as

The temperature gradient at the flame surface is

Flame thickness:

(Figure 23.2)

Where,

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Burning Velocity Measurement Methods

(Figure 23.3)Flame front visualization

Luminous photographyShadowgraph photographySchlieren Photography

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Module 5: Premixed Flame Lecture 24: Tube Method


Tube Method

Combustion Bomb Method

Soap Bubble Method

Stationary Flame Method (Bunsen Burner)

Flat Flame Burner

Effect of Equivalence Ratio on SL

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Tube Method

(Figure 24.1) Procedure: Combustible mixture is filled in the tube

On ignition at one end, the flame propagates through the tube

Features: Inner dia of tube should be greater than the quenching diameterThe flame is planar in the beginning and curved towards downstream, due tobuoyancyNatural convection distorts the planar flame front due to difference in densitiesFriction at the tube wall is also a reason for parabolic shape of the flame

The burning velocity is given by : Flame front velocity

: Unburnt gas velocity

: Cross-sectional area of tube

: Flame surface area

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Combustion Bomb Method

(Figure 24.2)

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Soap Bubble Method

(Figure 24.3)

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Stationary Flame Method (Bunsen Burner)

(Figure 24.4)

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Flat Flame Burner

(Figure 24.5)

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Effect of Equivalence Ratio on SL

(Figure 24.6)

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Module 5: Premixed Flame Lecture 25: Effect of Oxygen Concentration on SL


Effect of Oxygen Concentration on SL

Effect of Initial Pressure and Temperature on SL

Effect of Inert Additives

Flame Extinction

Flame Quenching

Simplified Analysis for Quenching Diameter

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Module 5: Premixed Flame Lecture 25: Effect of Oxygen Concentration on SL Effect of Oxygen Concentration on SL

(Figure 25.1)

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Effect of Initial Pressure and Temperature on SL

This relation is supported byexperimental datan: Overall order of global chemicalreaction

for HC flames with

for HC flames with

for HC flames with

Pressure index,

For , m is negative,indicating burning velocity increaseswith decreasing pressure

(Figure 25.2)

For , m isconstant, indicating burning velocity isconstant

For , m is positive,indicating burning velocity decreaseswith decrease in initial pressure

(Figure 25.3)

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Effect of Inert Additives

(Figure 25.4)

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Flame Extinction

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Flame Quenching

Fuel Oxidizer SL (cm/s) dq (mm)CH4 Air 40 2.5

CH4 O2 0.3

C3H8 Air 45 2.0

C3H8 O2 0.25

C2H2 Air 140 0.8

C2H2 O2 0.2

CO Air 2.8

H2 Air 210 0.5

H2 O2 0.2

Quenching diameter for various stoichiometricfuel-oxidizer ratio.

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Simplified Analysis for Quenching Diameter

Rate of heat generated per unit volume

Heat generated in flame volume

Heat loss rate due to wall conduction

(Figure 25.5)Assuming linear temperature distribution inflame, Quenching diameter

After simplification,

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Module 5: Premixed Flame Lecture 26: Flammability Limits


Flammability Limits

Effect of Pressure on Limit Mixture

Ignition

Flame Stabilization

Flame Stabilization by Burner Rim

Turbulent Premixed Flame

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Module 5: Premixed Flame Lecture 26: Flammability Limits Flammability Limits

Instrument to determine flammabilitylimit

Vertical glass tube of 1.2 m lengthand 50 mm ID

(Figure 26.1)

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Effect of Pressure on Limit Mixture

(Figure 26.2)

Fuel Oxidizer Stoichiometry (% Fuel) LFL (%) UFL (%)

Methane Air 9.5 5 15

Ethane Air 5.6 2.8 12.4

Propane Air 5.6 2.1 9.1

CO Air 29.5 12 74.2

Hydrogen Air 29.2 4 74.2

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Ignition

Energy generated in flame = Ensible enthalpy Mass

Substituting quenching diameter

Substituting flame thickness (Figure 26.3)

Fuel-Air MIE (mJ)

Dependence on pressure Methane-air 0.47

Ethane-air 0.4

Butane-air 0.34

Acetylene-air 0.03

CO-air 0.05

Hydrogen-air 0.02

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Flame Stabilization

Local gas flow velocity = Local burning velocity

(Figure 26.4)

(Figure 26.5)

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Flame Stabilization by Burner Rim

(Figure 26.6)

Stability of flame front near the rim of Bunsen burner

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Turbulent Premixed Flame

(Figure 26.7)

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Module 5: Premixed Flame Lecture 27: Flame Stabilization


Turbulent Flame Regimes

The Borghi Diagram

Turbulent Burning Velocity

Wrinkled Laminar Flame

Distributed Reaction

Flamelet in Eddies

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Reynolds number for turbulent flame: Chemical reaction time:

Chemical reaction time: Damkohler number

If Da >> 1, fast chemistry regime

If Da <<1, fast mixing regime

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The Borghi Diagram

Borghi Diagram

The plot of Da against on a log-log scaleDepicts various regimes of turbulentflames

(Figure 27.1)

Weak turbulent flameUpper region of the Borghi diagram

Wrinkled laminar flameRegion between and Chemical reaction takes place in athin zone

Flamelets in eddiesRegion between upper bold line

and

Distributed reaction regimeRegion below Reaction sheets are distributed in theturbulent flame surface This type of combustion can beestablished in a well stirred reactor.

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How to measure (ST) ? From the reactant flow rate


is the reactant flow rate

is the time average flame surface area

is the density of unburnt gas

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Wrinkled Laminar Flame

Turbulent burning velocity is given by, (Figure 27.2)

According to Damkohler, for constant laminarburning velocity According to Klimov,

Similarly for turbulent flame, According to Calvin and William,

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Distributed Reaction

(Figure 27.3)Turbulent burning velocity is given by,

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Flamelet in Eddies

(Figure 27.4)

Fuel mass burning rate,

Typically, is root mean square offluctuating fuel mass fraction, is the turbulentkinetic energy per unit.

References

1. D. P. Mishra, Fundamentals of Combustion, PHI leaming, Pvt Ltd., New Delhi, 2010.2. Stephen R. Turns, An Introduction to Combustion, McGraw Hill Publication, Singapore, 1996.3. Irvin Glassman, Combustion, Academic Press, New York, 1977.

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Module 6: Diffusion Flame Lecture 29: Theoretical Analysis


Theoretical Analysis

Theoretical Analysis (Contd.)

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Theoretical Analysis

Consider a 2D diffusion flame,

(Figure 29.1)Assumptions:

i. 2D steady laminar inviscid flow.ii. Velocity above the channel is constant everywhere iii. Fuel and oxidizer react in stoichiometric proportion at the flame surface with infinite reaction

rate (Thin flame approximation).iv. Binary diffusion between participating species.v. Mass diffusion is along x-direction only.vi. Unity Lewis number.vii. Single step irreversible reaction.viii. Radiation heat transfer is negligibly small.ix. Constant thermophysical properties.x. Mass diffusivity of both fuel and oxidizer are the same.xi. Buoyancy force is neglected.

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Conservation equations:Mass conservation:

Using assumption (ii), we can have,

Axial momentum conservation:

Species conservation equation:

Mass fraction of the product can be found from

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By thin flame approximation,

Single step irreversible reaction,

Universal concentration variables,

Rate of fuel transport from the centre to the flame surface is equal to stoichiometric rate of oxidizertransport.

Let be the mass fraction of the reactant, Instead of solving two equations (For fuel and oxidizer), we can solve a single equation as givenbelow,

This analysis is known as the Burke-Schumann's analysis

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Above equation can be converted into a diffusion equation by substituting

Inner wall exists at and outer wall at The initial and boundary conditions are as follows.

Applying boundary conditions, we obtain a closed form series solution

where, is the non-dimensional mass fraction of the reactant.

The infinite series must have a constant value at the flame surface as given below

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The series solution depends on and At the burner rim, the series constant (E) becomes a square wave

When F/A ratio is stoichiometric E becomes zero.

Roper extended the Burke-Schumann model by varying thevelocity to vary along the axial direction.

The flame height is given by,

(Figure 29.2)

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Module 6: Diffusion Flame Lecture 30: Mechanism of Soot Formation


Mechanism of Soot Formation

Liquid Fuel Combustion

Processes during droplet combustion

Liquid Fuel Combustion (Contd.)

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Process of soot formation:

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Liquid Fuel Combustion

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Processes during droplet combustion

(Figure 30.1)

Factors affecting the shape of the flame front:

Condition under which combustion takes place!

Zero gravity : Spherical flame front (No buoyancy)

Normal gravity : Elongated (Due to natural convection)

Forced convection condition : Fame aligned with flow

Energy required to vaporize the liquid fuel:

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Assumptions 1. Single droplet in quiescent

atmosphere.2. Droplet temperature is uniform.3. Density of liquid fuel much

higher than the gas phase.4. Fuel is a single component with

no solubility for gases.5. Flow velocities are assumed to

be low6. Single step irreversible

reaction! Thin flameapproximation.

7. Constant thermo-physicalproperties.

8. Unity Lewis number.9. Radiation heat transfer is

neglected.10. No other phase is formed in

the liquid fuel droplet.

(Figure 30.2)

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Module 6: Diffusion Flame Lecture 31: Overall mass conservation


Overall mass conservation


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Overall mass conservation:

-----(1)

for all r V - bulk velocity; -gas density

Momentum conservation:

Species conservation:

-----(2)

-----(3)

Single step reaction:-----(4)

T - Temperature; - energy release rate due to chemical reaction

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Fuel, oxidizer and product can be related to heat release rate as follows

-----(5)

Rearranging,

-----(6)

We can rewrite fuel species conservation equation as,

-----( 7)

Multiply eq.7 by and add by eq.3,

-----( 8)

Here a is the thermal diffusivity

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Using eq.6, eq.8 becomes,

-----(9)

Elimination of the non-linear term simplifies the analysis. This simplification is known asSchwab- Zeldovich Transformation.

Dividing eq.9 by ,

-----(10)

– Heat input required for vaporization of droplet

– Mass fraction of species at the surface of the droplet

Conserved variable for oxidizer

`

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General format of all the equations

-----(11)

Boundary conditions

;

Integrating eq.11 twice and applying the boundary conditions,

-----(12)

By applying boundary condition to Eq. 12, We can have,

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The transfer number, B is given by

Values of transfer number, B for some typical fuel:

Combustion in air B Combustion in air BISO-Octane 6.41 Kerosene 3.4

Benzene 5.97 Gas oil 2.5

n-Heptane 5.82 Light fuel oil 2.0

Avation gasoline 5.5 Heavy fuel oil 1.7

Automobile gasoline 5.3

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Module 6: Diffusion Flame Lecture 32: The Temperature Profile


The Temperature Profile

Droplet Burning Time

Droplet Combustion in Convective Environment

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Module 6: Diffusion Flame Lecture 32: The Temperature Profile The Temperature Profile

No oxygen exists in the inner flame region.No fuel exists in the outer region of flame.Using the transfer function for fuel andoxidizer,

Temperature profile for the inner region,

(Figure 32.1)Rearranging the above equation,

Temperature profile for the outer region,

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Droplet Burning Time

Importance of droplet burning time:Essential for desining combustion chamberFor complete combustion, residence time > life timeof largest droplet in spray.

Factors dictating residence time of droplet:

Air stream velocityDroplet velocityFuel injection angleCombustor geometry

Continuity equation at the surface of the droplet: (Figure 32.2)

-------(1)

Droplet mass is evaluated as follows, -------(2) Where, D is the droplet diameter at any instant

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Droplet Burning Time (Contd.)

Recall, Burning constant for typical hydrocarbons

-------(3) Fuel k 10-7 m2/s

(Calculated)k 10-7 m2/s(Measured)

Ethyl alcohol 9.3 8.1

N-Heptane 14.2 9.7

ISO-Octane 14.4 9.5

Kerosene 9.7 9.6

Benzene 11.2 9.7

Toluene 11.1 6.6

Using (1) & (2) in (3),

-------(4)

Expressing droplet diameter interms of ,

-------(5)

In this expression, varies linearly with time (See figure 32.3). Slope of the plot is the burning rateconstant, K

-------(6)

Integrating (5) with time, is law

(Figure 32.3)

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In practical devices, both free and forced convection will prevail,

Flow past the fuel droplet for Re > 20

Front portion of the droplet – Boundary layer.Rear portion – Wake region

In practical devices, forced convection is more predominant

Boundary condition at the droplet surface,

-------(1)

Where,

-------(2)

- Convective heat transfer coefficient Combining the above two expressions,

-------(3)

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Rearranging the above equation,

-------(4)

-------(5)

For high Reynolds number,

-------(6)

For unit Prandtl number, Re >> Pr,

-------(7)

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-------(8)

Then Eq. (7) becomes,

The above expression would not provide accurate predictionWake region behind the droplet is not considered here.For predicting the experimental data, the above expression is modified as,

-------(9)

Under convective condition, laminar droplet burning rate follows

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Module 6: Diffusion Flame Lecture 33: Spray Combustion Model


Spray Combustion Model

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Assumption:

Steady, 1-D flow, Laminar, inviscidMono-dispersed droplets.Pressure remains constant duringcombustion.Droplets move with same velocityas that of air.Vaporization and ignition begins atx=0.Mixing and chemical reaction timesare quite small as compared todroplet vaporization time.Constant thermophysicalproperties.Dilute spray.

(Figure 33.1)

Stoichiometric fuel-air ratio:

-------(1) =Density of liquid

= Cross sectional area

= Number of droplets = Initial diameter

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Number of droplets,

-------(2)

From mass conservation,

-------(3)

- Density of droplet laden air

-------(4)

From above two equations,

-------(5)

Energy equation across the element dx

-------(6)

- Heat release rate

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Simplifying,

-------(7)

Heat release rate per unit volume,

-------(8)

Relationship for quasi-steady state droplet vaporization,

-------(9)

Where, K – droplet combustion rate constant that can be experienced as

-------(10)

By using Eqs. (7) , and (10), we can have,

-------(11)

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Droplet diameter will vary by law

-------(12)

Boundary and initial conditions

-------(13)

By using above condition in Eq. 6.11 and integrating it, we can get

-------(14)

Adiabatic flame temperature is given as

-------(15)

By using Eng. (14), we get

-------(16)

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Zone length is given by

-------(17)

Integrating Eq. (17), we can get

-------(18)

Combustion Intensity is given by

-------(19)

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Module 6: Diffusion Flame Lecture 34: Solid Fuel Combustion


Solid Fuel Combustion

Theory For Single Coal Combustion

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Factors influencing solid fuel burning

Nature of the solid fuelType of application

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Module 6: Diffusion Flame Lecture 34: Solid Fuel Combustion Solid Fuel Combustion

(Figure 34.1) (Figure 34.2)

(Figure 34.3)

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1. Burning process is quasi steady.2. Burning takes place in quiescent, infinite ambient air medium.3. No interaction with other particles.4. Effect of natural convection is ignored.5. Burning is diffusion controlled.6. Constant thermodynamic properties7. Unity Lewis number8. Gaseous species do not enter into gaseous species9. No radiation heat transfer

10. Ideal gas law

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Mass conservation

--------(1)

Oxidizer species conservation

--------(2)

Energy conservation

--------(3)

Stoichiometric fuel-air ratio

--------(4)

Boundary Conditions:

--------(5)

--------(6)

Combining Eq. 4 and 6,

--------(7)

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Integrating Eq. 2 and applying b.c.,

--------(8)

Integrating the above equation further,

--------(9)

Applying the boundary condition,

--------(10)

increases exponentially with the increase in radius

at the solid surface

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At moderate temperature and for small particle, the oxygen mass fraction at the surface is given by

--------(11)

B is the mass transfer number

--------(12)

The carbon sphere burning rate is also governed by Law

where is the carbon burning constant.

Table: Combustion properties of slid spheres [7]

Fuel (g/cm3) MWfuel B.Pfuel (ºC) f Boxygen Bair

Aluminium 2.70 27.0 2.467 1.12 1.12 0.26

Boron 2.34 10.8 2.550 0.451 0.451 0.105

Carbon 1.50 12.0 4.827 0.75 0.750 0.174

Carbon 1.50 12.0 4.827 0.375 0.375 0.087

Magnesium 1.74 24.3 1.107 1.107 1.520 0.353

Zirconium 6.44 91.2 3.578 3.578 2.850 0.662

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You can question everything around you,

You may find tangible answers to few,

You can question everything around me,

The answers, I posses are not necessarily mine. - Dr. D.P. Mishra

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Module 7: Combustion and Environment Lecture 35: Introduction


Introduction

Air Pollution Sources

Effect of CO Exposure on Human Health[1]

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Combustion and Environment

Introduction

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Major Health Ailments Due to Environmental pollution

(Figure 35.1)

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Air Pollution Sources

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Effect of CO Exposure on Human Health [1]

Source [1] D.P. Mishra Fundamental of Combustion, PHI Learning Rt Ltd., New Delhi, 2008

(Figure 35.2)

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Module 7: Combustion and Environment Lecture 36: Atmosphere


Atmosphere

Chemical Emission From Combustion

Chemicals From Combustion (Contd..)

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Atmosphere

Figure 1: Variation of temperature with altitude

(Figure 35.3)

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Module 7: Combustion and Environment Lecture 36: Atmosphere Atmosphere

Source: http://www.theresilientearth.com/files/images/stratosphere_diagram.jpg

(Figure 36.1)

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Atmosphere (Contd..)

TroposphereRegion where we are living.Contains 90% of the mass of the atmosphere.Starts at ground level with 228 K and ends at 18 km (200 K) with 6 K drop in temperature perkm altitude.Beyond 18 km, temperature rises. This inflection point is called “Tropopause”.Tropopause divides troposphere from stratosphere.Atmospheric boundary layer - 2 km from the ground level.Combustion byproducts instantly affects this region.

Photochemical chain reaction begin with dissociation of ozone as given below

--------(1)

The atomic oxygen reacts with water vapor to form hydroxyl radical

--------(2)

The OH radical reacts with CO and initiates other chain reactions as below

--------(3)

--------(4)

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The peroxy radicals are recycled to OH by the following reaction:

----------(5)

Cycling of OH and is turned off by several reactions involving OH, and ----------(6)

NO and pair is produced via the following chain reactions.

----------(7)

----------(8)

----------(9)

--------(10)

Concentration of ozone and can also be influenced by non-photolytic reactions during nighttime.

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StratosphereRegion between tropopause (18 km) and stratopause (50 km).Contains 9.5% of atmospheric mass.The temperature increases from tropopause (220 K) to stratopause (280 K).The chemicals from troposphere that are not destroyed are dissociated in this region.CFC is converted into HF and mixture of CI compounds.The photochemistry in the stratosphere is strongly affected by ozone layer.The short wavelength cannot reach below 25 km due to the photochemistry.This is how we are protected from the harmful UV rays.Stratospheric column is the major absorber of solar UV between 220 and 320 nm.Depletion of ozone layer will change the tropospheric chemistry in two ways

i. Lowers the flux of into troposphereii. Enhances the production of OH

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Chemical Emission From Combustion

Most of the fossil fuels can be depicted by the following chemical equation

Fuels contain sulphur , oxygen, nitrogen and certain heavy metals.Air contains large amount of nitrogen.Combustion process leads to the formation of The quantities are sufficient enough to affect the quality of atmospheric air.Total amount of fossil fuel burnt was around 6.2 Gt/Yr.Another source of pollutant emission from combustion process is the biomass.Total amount of biomass fuel burnt was around 3 to 5 Gt/Yr.The combustion conditions for biomass combustion leads to higher emissions.

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Emission of

It has been observed that there is an imbalance in the atmospheric carbon-oxygen cycle.CO is released directly into the atmosphere by incomplete combustion.About 40% of CO in the atmosphere is contributed by the burning of fossil fuel.CO level in southern hemisphere in around 50 ppb and in northern hemisphere it is 120 ppb.Is the major portions CO produced form combustion?NO! from the oxidation of methane generated by anaerobic bacteria in swamps and paddies.

Why there is a climate change?

Due to the change in CO2 level.

Deforestation in recent days is the main cause for the accumulation of CO2 in the biosphere.

Changes in land used by human beings contribute around 1 Gt(C)/yr CO2 to atmosphere.

Global carbon cycle involves exchange of atmospheric CO2 with carbon reservoir in ocean

and biosphere in several time scales.It has been predicted that the freezing of current emissions would not really solve our problemimmediately.CO2 emission does not impact atmospheric chemistry directly but changes the temperature

and circulation, which indirectly changes the chemistry and climate.

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Module 7: Combustion and Environment Lecture 37: Major Sources of CO Emission


Major Sources of CO Emission

Chemicals From Combustion

Major Sources of NO Emission


Quantification of Emission

Species Emission and Its Corrected Value

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Major Sources of CO Emission

Source category Emissions (Millions tons per year) %Gasoline motor vehicles 95.8 36.69

Diesel, aircraft, trains, vessels 5.6 2.14

Off-highway vehicles 9.5 3.64

Coal 0.5 0.19

Fuel oil 0.1 0.038

Natural gas 0.1 0.038

Wood 0.1 0.038

Total stationary sources 0.8 0.30

Total fuel combustion 111.7 42.78

Industrial processes 11.4 4.36

Agricultural burning 13.8 5.28

Solid waste disposal 7.2 2.75

Miscellaneous 4.5 1.72

Total 261.1 100.0

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Chemicals From Combustion

Emission of

NO and are main components producing in troposphere.

The life of these gases are quite short even less than 1 day.

Combustion of fossil fuel is the largest source of .

The quantities are sufficient enough to affect the quality of atmospheric air.

Combustion of fossil fuel is the largest source of around 22 Mt/yr.

Stationary source contribution is around 13 Mt/yr.

Contribution of emission by biomass is quite small.

Due to combustion, there is a four fold increase in the tropospheric .

The major sources of emission and their contributions are depicted in the next section.

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Major Sources of NO Emission

Source category Emissions (Millions tons per year) %Gasoline motor vehicles 7.8 17.53

Diesel, Aircraft , trains, ships 2.0 4.49

Off-highway vehicles 1.9 4.27

Coal 3.9 8.76

Fuel oil 1.3 2.92

Natural gas 4.7 10.56

Wood 0.1 0.22

Total fuel combustion 21.7 48.76

Industrial processes 0.2 0.45

Agricultural burning 0.3 0.67

Solid waste disposal 0.4 0.90

Miscellaneous 0.2 0.45

Total 44.5 100

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Emission of Hydrocarbon

Non-methane hydrocarbons (NMHC) are short lived and highly reactive.Oxidization of these hydrocarbons leads to the formation of .Volatile organic compounds include NMHC as well as oxygenated species such as aldehydesand alcohols.These are mainly contributed by gasoline vehicles, solvent evaporation and biomass burning.These bio-organic hydrocarbons are quite reactive and are usually destroyed within theboundary layer.

Emission of Sulphur Dioxide and Sulphate AerosolsSulphur content of fossil fuels such as coal and oil is in the range of 0.5 – 2.5 by mass.Sulphur in the fossil fuel is usually emitted as and leads to the formation of sulphuricacid.

takes very less time to get converted into sulphate to wet or dry deposition on the earthsurface.Combustion of fossil fuels contributes significant amount of in troposphere, which is about80 Mt/yr.

Source SO2 (Million tons per year)

Fossil fuel 80

Metal smelting 8

Biomass burning 2

Natural sources (Ocean, oil, vegetables) 25

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Quantification of Emission

Emission levels are reported in several different ways while dealing with different devices.Gas turbine combustors: ppm by volume at 15% O2

Furnace: ppm at 3% O2

Automobiles: g/kmBoiler: g/kW

Species emission and its corrected valueGenerally combustion system is characterized in terms of level of emissions.Confusion prevails due to the change in sampling condition

Degree of dilutionDry or wet condition

If the moisture is removed from the exhaust sample then it will yield dry concentration.In some situations, it may not be possible to remove moistures, then it is known as wetconcentration.

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Consider a hydrocarbon fuel-air mixture at lean or stoichiometric condition

Wet mole fraction of species is defined as

Dry mole fraction of species is defined as

Carrying out an atom balance for O atom,

Ratio of total number of moles in wet mixture to dry mixture is

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Module 7: Combustion and Environment Lecture 38: Species Emission and Its Corrected Value



Emission Control Methods

SOx Emission and Its Control

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The oxygen coefficient is given by

OR

The measured concentration of species at given oxygen level can be corrected to a specificoxygen level as below

In order to assess the emission in a combustor or engine, it is important to define a normalizedindicator of emission level as below,

For combustion of hydrocarbon fuel, the emission index species is given by,

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Best method of reducing emission is to avoid using excess fuel.Public awareness must be initiated to avoid unwanted burning of fuels.Eco-friendly combustion devices have to be designed and developed.Cost effective methods can be devised to treat the combustion products before allowing themto the atmosphere.

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COx Emission control

Storage in oceans may not be feasible due to non-availability of technology, however, geologicalreservoirs are promising options for CO2 storage.

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Figure: Schematic diagram of a CO2 capture pilot plant for coal-based power plant

(Figure 38.1)CO2 is separated by means of absorption using mono-ethanol amine (MEA).

The plant consists of three partsi. Absorber,ii. Regenerator,iii. Exchanger.

Exhaust gas is cooled to to 40-50°C and fed to the absorption tower.In the absorber, exhaust gas is mixed with mono-ethanol amine (MEA), which captures 90%of CO2 in the exhaust gas.

Amine stripper is used in the regenerator, which separates MEA and sends back to amineabsorption tower. This plant captures 1 million CO2 per hour.

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Sulphur is relatively inert and harmless to human beings.Oxides of sulphur poses serious environmental problem.Sulphur oxides are corrosive in nature.Organic fuels such as coal, oil, wood, etc contain some sulphur.SO is a highly reactive radical and its life time is few milliseconds.Under fuel rich conditions, in addition to sulphur oxides, hydrogen sulphide, carbonyl sulphide,and elemental sulphur are formed.Understanding of the mechanism of sulphur oxides have not evolved to a maturity level.

(Figure 38.2)

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Hydrosulphurization methodEffective method of desulphurizing coal and oil fuels.This method treats fuels in the presence of hydrogen at high pressure and temperature.Finely grounded coal is mixed with anthracene oil along with hydrogen to produce slurry.The dissolved coal is passed through a pressure filtration unit in which pyretic sulphur isremoved.A flash evaporator is used to convert the dissolved coal to low sulphur coal.

(Figure 38.3)

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Module 7: Combustion and Environment Lecture 39: Emission and Its Control



Forced Oxidation Limestone Wet Scrubber

Zeldovich Mechanism

Fenimore (Prompt) Mechanism

Fuel (N2O – Intermediate) Mechanism

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Gasification methodSulphur dioxide emission due to burning of coal or fuel oil can be minimized by gasifyingthem.During gasification, coal undergoes partial oxidation resulting in CO and .

Sometimes, and other gases can also be produced during gasification of coal.In this case, sulphur content gets converted into hydrogen sulphide , which can be removedby absorption or adsorption method..In absorption method, gases are scrubbed with alkaline reagent such as sodium carbonate orethylamine.Subsequently elemental sulphur is produced.In adsorption method, ferric oxide is used to adsorb hydrogen sulphide using fluidized bedaround 400°C.

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Forced Oxidation Limestone Wet Scrubber

(Figure 39.1)

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NOx Emission and Its Control

Nitrogen in atmosphere forms 8 different oxides during combustion.The important oxides are NO, .Is NO harmful to health than ?

is more harmful as compared to NO. By what reaction NO and are formed ?

For any chemical reaction, Gibbs free energy attains a minimum value for a particulartemperature and pressure

Equilibrium constant

Standard Gibbs free energy change

Table: Equilibrium concentration of NO and NO2

300 7 X 10-31 1.4 X 106 3.4 X 10-10 2 X 10-4

500 2.7 X 10-18 130 7 X 10-4 0.04

1000 7.5 X 10-9 0.11 35 1.9

1500 1.07 X 10-5 0.011 1320 6.8

2000 0.0004 0.0035 8100 13.2

2500 0.0035 0.0018 24000 20.0

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Zeldovich Mechanism

From the above table it is clear that emission can be reduced by decreasing thetemperature.

(Figure 39.2)Thermal are formed by simple heating of oxygen and nitrogen.The radical ‘N' can react with to form NO.Thermal NO contribution is low till 1300 K and beyond which it increases rapidly.The thermal mechanism consists of the following two chain reactions.

--------(1)

--------(2)

--------(3)

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--------(6) --------(8)

--------(7) --------(9)


Fenimore (Prompt) Mechanism

Prompt mechanism refers to the which are formed very quickly by interaction of activehydrocarbon species derived from fuel with nitrogen and oxygen.They are generally not observed in flames of non-hydrocarbon flames.They cannot be formed by just heating nitrogen with oxygen.During initial phase of combustion, the radials with carbon atom react with to produce N.

--------(4)

This reaction is the main path which dictates the rate at which radical ‘N' is formed.The radical ‘N' can also be formed by the following reaction.

--------(5)

When the equivalence ratio is less than 1.2, HCN can be converted to NO as follows,

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Fuel (N2O – Intermediate) Mechanism

Thermal NOis quitesmall below

1300oCThermal NOrises sharplywithtemperatureBoth fuel NO& promptNO do notvary withtemperatureBut promptNOincreasesmarginallywithtemperature.

N2O intermediate

mechanism plays a veryimportant role for NOcontrol in lean premixedcombustion.

Three steps of N2O

intermediate mechanismare given below;

(Figure 39.3)

Several techniques are devised to control in combustion as described in next section.

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Module 7: Combustion and Environment Lecture 40: Combustion Modification Methods


NOx Control Technologies

Combustion Modification Methods

Particulate Controls

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(Figure 40.1)

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(Figure 40.2)

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Low excess air

(Figure 40.3)Proper comprise between combustion efficiency, CO and emissions have to be arrived beforedeciding the excess air.

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Staged Combustion

(Figure 40.4)Most effective method to control formation.Upstream burner operates in fuel rich mode.Additional air is added in the downstream for burning of fuel in stages.

emissions can be reduced by 10 to 40%.

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Flame CoolingThermal NO can be controlled by reducing the temperature.

These three methods reduce the peak temperatures.May lead to the formation of CO.10 to 15% reduction in NO can be achieved by these methods

(Figure 40.5)

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Particulate Controls

Cyclone and hydro-cyclone separators are also employed to remove particulates.

fundamentals of combustion _nptel

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