05 Combustion

Combustion

in

SI Engines, CI Engines, and Gas Turbines

Combustion Introduction

Combustion is the process of chemical reactions with

oxygen

Combustion is defined as a rapid exothermic reaction

that liberates substantial energy as heat and flames as

combustion reactions with the ability to propagate

through a suitable medium

Characterization of combustion involves measurements

of quantitative combustion characteristics, including

temperature, pressure, heat release, or the amount of

gaseous and particulate emission

Combustion studies involve some concepts and

definitions


Some definitions

A chemical reaction is the exchange and/or rearrangement

of atoms between colliding molecules

In the course of chemical reaction, the atoms are conserved

but the molecules are not reactant molecules are

rearranged to become product molecules with simultaneous

release of heat

Atoms and molecules are conveniently counted in terms of

amount of substance or mole numbers (unit mol)

The mass is the fundamental property of matter (unit kg)

and molar mass is the mass of 1 mol of the substance

(unit gm/mol)

Mass density (density) has the unit kg/m3 and molar

density (concentration) has the unit mol/m3


Combustion research in the past was directed to fluid

mechanics that included global heat release by chemical

reaction

The heat release was often described simply with the help

of thermodynamics, which assumed infinitely fast chemical

reaction

This approach was useful to some extent for designing

stationary combustion processes; it was not sufficient for

treating transient processes like ignition or quenching or in

treating pollution formation

Combustion studies, now-a-days, treat the coupling of

chemical reaction and fluid flow


In combustion processes, fuel and oxidizer (typically air)

are mixed and burned

There are several combustion categories based upon

whether the fuel and oxidizer is mixed first and burned

later (premixed) or whether combustion and mixing

occurs simultaneously (nonpremixed)

Each of these categories is further subdivided based on

whether the fluid flow is laminar (low Reynolds number) or

turbulent (high Reynolds number)

A flame is a combustion reaction which can propagate

subsonically through space

The existence of flame motion implies that the reaction is

confined to a zone which is small in thickness the

combustion chamber

NeonTypewriter

Combustion Systems

Flames

Laminar premixed flame

With premixed combustion the fuel-oxidizer mixture must

always be close to stoichiometric for reliable ignition and

combustion

The flame moves relative to the reactants, so separating

the reactants and products (velocity of about 0.5 m/s)

A laminar flat flame and a Bunsen flame

Flames

The burning of freely burning premixed laminar flat flames

into the unburnt mixture can be characterized by laminar

burning velocity or flame velocity or flame speed

The burning velocity depends only on the mixture

composition ( or ), the pressure and the initial temperature

is the fuel-air equivalence ratio a ratio of actual fuel-air

ratio to stoichiometric fuel-air ratio

is the inverse of , and is termed as the relative air-fuel

ratio

If the laminar burning velocity is less than the velocity of

the unburnt gases, the flame blows off

Flames

Non-premixed or diffusion laminar flames

The flame occurs at the interface between fuel and

oxidizer

The products of combustion diffuse into the oxidizer, and the

oxidizer diffuses through the products

Similar processes occur on the fuel side of the flame, and the

burning rate is controlled by diffusion

The term diffusion applies strictly to the molecular diffusion of

chemical species

Laminar counterflow

and coflow diffusion

flames

Flames

Non-premixed flames include more complex chemistry

than premixed ones, because the equivalence ratio covers

the whole range from 0 (air) to (pure fuel)

Rich combustion occurs on the fuel side and lean combustion

on the air side

The flame front, which is usually characterized by intense

luminescence, is fixed to regions near the location of

stoichiometric composition = 1, since this is where the

temperature is the highest

Unlike premixed flames, non-premixed flames do not

propagate, and therefore, cannot be characterized by a

laminar flame speed

Flames

Turbulent premixed flames

In this case, premixed flame fronts burn and propagate

into a turbulent fluid flow

If the turbulence intensity is not too high, curved laminar

premixed flame fronts are formed

The advantage of premixed combustion is that much

greater control of the combustion is possible

By lean premixing ( < 0.7), high temperatures are avoided

and hence combustion with low production of NO is

accomplished; also, a very small amount of soot is formed as

soot is largely a product of rich combustion

It is not widely used because of the potential for accidental

collection of large volumes of premixed reactants, which

could burn in an uncontrolled explosion

Flames

For premixed combustion the effect of turbulence is to

break up, or wrinkle the flame front

There can be pockets of burnt gas in the unburnt gas and

vice versa thus increasing the flame front area and speeds

up combustion

Laminar and turbulent flame fronts for premixed combustion

Flames

Turbulent non-premixed flames

In this case, turbulent convection mixes the fuel and air

together on a macroscopic basis

Molecular mixing at the small scales, i.e., molecular

diffusion, then completes the mixing process so that

chemical reactions can take place

Turbulence enhances the burning velocity

Fuel is injected as a fine spray into the air which is hot

enough to vaporize and ignite the fuel

The ordered air motion is also important because it

sweeps away the vaporized fuel and combustion products

from the fuel droplets

Flames

The flames can be further classified as steady or

unsteady

The distinguishing feature here is whether the flame

structure and motion change with time

Flames in engines are unsteady, and are turbulent

Yet another classification of flames comes from the initial

phase of reactants gas, liquid, or solid

The conventional spark-ignition flame is thus a premixed

unsteady turbulent flame, and the fuel-air mixture through

which the flame propagates is in the gaseous state

The diesel engine combustion process is predominantly an

unsteady turbulent diffusion flame, and the fuel is initially in

the liquid phase

Combustion Stoichiometry

Ideal gas model

The gas species that make up the working fluids in internal

combustion engines (e.g., oxygen, nitrogen, fuel vapor,

carbon dioxide, water vapor, etc.) can usually be treated

as ideal gases

The ideal gas law is:

where p is the pressure, V the volume, m the mass of gas,

R the gas constant for the gas, T the temperature, the

universal gas constant (8314.3 J/kmol K), M the molecular

weight, and n the number of moles

~~R

pV mRT m T nRTM

~

R


In combustion, oxygen is the reactive component of air.

It is usually sufficiently accurate to regard air as

consisting of 21 percent oxygen and 79 percent inert

gases taken as nitrogen (often called atmospheric or

apparent nitrogen)

For each mole of oxygen in air there are 3.773 moles of

atmospheric nitrogen

The molecular weight of air is 28.962, usually

approximated by 29

Because atmospheric nitrogen contains traces of other

species, its molecular weight is calculated to be 28.16

Thus, the value for the density of dry air at 1 atmosphere

(1.0133 x 105 Pa) and 25C is 1.184 kg/m3


The fuels most commonly used in internal combustion

engines (gasoline or petrol, and diesel fuels) are blends

of many different hydrocarbon compounds

These fuels are predominantly carbon and hydrogen

(typically about 86 percent carbon and 14 percent

hydrogen by weight) though diesel fuels can contain up

to about 1 percent sulfur

Other fuels of interest are alcohols (which contain

oxygen), gaseous fuels (natural gas and liquid petroleum

gas), and single hydrocarbon compounds (e.g., ethane,

propane, isooctane) which are often used in engine

research


By balancing the combustion reaction equation for a

particular fuel one can determine how much fuel and air

should be injected in order to completely burn both

A stoichiometric mixture contains the exact amount of

fuel and oxidizer such that after combustion is

completed, all the fuel and oxidizer are consumed to

form products

This ideal mixture approximately yields the maximum

flame temperature, as all the energy released from

combustion is used to heat the products

Combustion stoichiometry for a general hydrocarbon

fuel, CaHbOg, with air can be expressed as:


The coefficients associated with each species in the

above equation are unknown. By balancing the atomic

abundance on both the reactant and product sides, one

can find the coefficient for each species

These coefficients are called the reaction stoichiometric

coefficients

The amount of air required for combusting a

stoichiometric mixture is called stoichiometric or

theoretical air

The above formula is for a single-component fuel and

cannot be applied to a fuel consisting of multiple

components

2 2 2 2 2C H O (O 3.76N ) CO H O 3.76 N4 2 2 4 2

a b g

b g b b g a a a


There are two typical approaches for systems with

multiple fuels

The first method develops the stoichiometry of combustion

using the general principle of atomic balance, making sure

that the total number of each type of atom (C, H, N, O) is

the same in the products and the reactants

The other method of balancing a fuel mixture is to first

develop stoichiometry relations for each component

individually then, multiply the individual stoichiometry

equations by the mole fractions of the fuel components

and add them

In practice, fuels are often combusted with an amount of

air different from the stoichiometric ratio


If less air than the stoichiometric amount is used, the

mixture is described as fuel rich

If excess air is used, the mixture is described as fuel lean

The stoichiometric air/fuel ratio (AFR)s or fuel/air ratio

(FAR)s depends on fuel composition

The (FAR)s is given by

where mf and ma are the respective masses of the fuel

and the air and where Mf and Ma (~28.84 kg/kmol) are

the average masses per mole of fuel and air,

respectively

a

f

sa

f

1

ss M76.424

M

m

m

F

A

A

F

g

ba


Most hydrocarbon fuels have a stoichiometric fuel-air

ratio, (FAR)s, in the range of 0.050.07, i.e., the

stoichiometric AFR of gasoline is about 14.7

For most hydrocarbon fuels, 1420 kg of air is needed for

complete combustion of 1 kg of fuel

Normalizing the actual FAR by the stoichiometric FAR

gives the equivalence ratio,

mixture rich :1

mixture tricstoichiome :1

mixture lean :1

)FAR(

)FAR(

s

actual1


The amount of air in excess of the stoichiometric amount

is called excess air (EA) the percent excess air %EA is

defined as

Given one of the three variables (f, , and %EA), the

other two can be deduced as summarized in the following

table with their graphic relations

a as a

as as

m m m%EA 100 100 1

m m


In general, the products of combustion include many

different species in addition to the major species (CO2,

H2O, N2, O2), and the balance of the stoichiometric

equation requires the use of thermodynamic equilibrium

relations

However, assuming that the products contain major

species only (complete combustion) and excess air, the

global equation for lean combustion 1 is

2 2

2 2 2 2

1C H O (O 3.76N )

4 2

3.76 1 CO H O N 1 O

2 4 2 4 2

a b g

b g a

b b g b g a a a


The amount of excess air can be deduced from measurements of

exhaust gases

The ratio of mole fractions between CO2 and O2 is

2 2

2 2 2 2

100In terms of %EA, may be replaced by and the result is

%EA + 100

%EAC H O 1 (O 3.76N )

100 4 2

%EA %EA CO H O 3.76 1 N O

2 100 4 2 4 2 100

a b g

b g a

b b g b g a a a

2

22

2

CO

COO

O

x %EA

x%EAx 100

4 2 100 4 2 x

a a

b g b g a a


For rich combustion (>1), the products may contain CO,

unburned fuels, and other species formed by the

degradation of the fuel

Often additional information on the products is needed for

complete balance of the chemical reaction

If the products are assumed to contain only unburned

fuel and major combustion products, the corresponding

global equation can be written as

2 2

2 2 2

1C H O (O 3.76N )

4 2

3.76 1 CO H O N 1 C H O

2 4 2

a b g

a b g

b g a

a b b g a

Combustion Thermodynamics

In a combustion process, fuel and oxidizer react to

produce products of different composition

The actual path by which this transformation takes place

is understood only for simple fuels such as hydrogen and

methane

For fuels with more complicated structure, the details are

not well defined

The first law of thermodynamics relates changes in

internal energy (or enthalpy) to heat and work transfer

interactions

Care must be exercised in relating the reference states at

which zero internal energy or enthalpy for each species or

groups of species are assigned


Consider a system of mass m which changes its

composition from reactants to products by chemical

reaction as indicated below

Applying the first law to the system between its initial and

final states gives

QR-P WR-P = UP UR


First consider a constant-volume process where the

initial and final temperatures are the same, T', then the

equation becomes

QR-P = U'P U'R = (DU)V, T'

The internal energy of the system has changed by an

amount (DU)V, T' which can be measured or calculated

Combustion processes are exothermic, therefore, the

systems internal energy decreases, i.e., QR-P and (DU)V, T'are negative

If the above eqn is expressed per mole of fuel, then

(DU)V, T' is known as the increase in internal energy at

constant volume, and is known as the heat of reaction at

constant volume at temperature T'


For a constant-pressure process where the initial and

final temperatures are the same, T', the eqn can be

rewritten as

QR-P p(V'P V'R) = U'P U'R

or QR-P = (U'P + pV'P) (U'R + pV'R)

= H'P H'R = (DH)p, T'

since for a constant pressure process

If the eqn is written per mole of fuel, (DH)p, T' is called the

increase in enthalpy at constant pressure and (DH)p, T' is

called the heat of reaction at constant pressure at T'

P

R P P RRW pdV p(V V )


Note that the slope of

these lines increases with

increasing temperature;

also, the magnitude of

(DU)V, T' [or (DH)p, T']

decreases with increasing

temperature because cv,

(or cp) for the products is

greater than for the

reactants


The difference between (DH)p, T' and (DU)V, T' is

(DH)p, T' (DU)V, T' = p(VP VR)

Only if the volumes of the products and reactants in the

constant pressure process are the same are (DH)p, T'and (DU)V, T' equal

If all the reactant and product species are ideal gases,

then the ideal gas law gives

(DH)p, T' (DU)V, T' = Ru(n'P n'R)T'

any inert gases do not contribute to (n'P n'R)


With a hydrocarbon fuel, one of the

products, H2O, can be in the

gaseous or liquid phase

The internal energy (or enthalpy) of

the products in the constant volume

(or constant pressure) processes will

depend on the relative proportions of

the water in the gaseous and liquid

phases

The internal energy differences

between the curves is mH2Ou'fg H2O ,

where the first term is the mass of

water in the products and the second

term is the internal energy of

vaporization of water at the

temperature and pressure of the

products


Similar curves and relationships

apply for enthalpy

For some fuels, the reactants

may contain the fuel as either

liquid or vapor

The U-T (or H-T) line for the

reactants with the fuel as liquid

or as vapor will be different

The vertical distance between

the two reactant curves is mfufgf (or mf hfgf) where the

subscript f denotes fuel

Heating Values of Fuels

In combustion processes, reactants are consumed to

form products and energy is released which comes from

a rearrangement of chemical bonds in the reactants to

form the products

The enthalpy of formation of a chemical compound is

the enthalpy increase associated with the reaction of

forming one mole of the given compound from its

elements, with each substance in its thermodynamic

standard state at the given temperature

Elements at their reference state are arbitrarily assigned

zero enthalpy at the datum temperature

Enthalpies of formation are tabulated as a function of

temperature for all commonly occurring species


For inorganic compounds, the JANAF Thermochemical

Tables are the primary reference source

The molar base enthalpy of formation has units of MJ/kmol,

and the mass base enthalpy of formation has units of

MJ/kg

Elements in their most stable forms, such as C(graphite), H2,

O2, and N2, have enthalpies of formation of zero

For a given combustion reaction, the enthalpy of the

products at the standard state relative to the enthalpy

datum is given byo~

o

P iproducts f,i

H n h D


and the enthalpy of the reactants is given by

The enthalpy increase, , is then obtained from the

difference

Heating values of a fuel (units of kJ/kg or MJ/kg) are

traditionally used to quantify the maximum amount of heat

that can be generated by complete combustion with air at

standard conditions (STP) (25C and 101.3 kPa)

For fuels where the precise fuel composition is not known, the

enthalpy of the reactants cannot be determined from the

enthalpies of formation of the reactant species the heating

value of the fuel is then measured directly

o~o

R ireac tants f,i

H n h D

op,T( H)D

o o

P R(H H )


The heating value QHV or calorific value of a fuel is the

magnitude of the heat of reaction at constant pressure or

at constant volume at a standard temperature [usually

25C (77F)] for the complete combustion of unit mass of

fuel

For fuels containing hydrogen, H2O in the products is in

the liquid or gaseous phase affects the value of the heat

of reaction

The term higher heating value QHHV (or gross heating

value) is used when the H2O formed is all condensed to the

liquid phase; the term lower heating value QLHV (or net

heating value) is used when the H2O formed is all in the

vapor phase

p o

V o

HV p,T

HV V,T

Q ( H)

and Q ( H)

D

D


The two heating values at constant pressure are related

by

The term in the bracket is the ratio of mass of H2O

produced to mass of fuel burned

2

p p 2

H O

HHV LHV fg H O

f

mQ Q h

m

Adiabatic Flame Temperature

One of the most important features of a combustion

process is the highest temperature of the combustion

products that can be achieved

The temperature of the products will be greatest when

there are no heat losses to the surrounding environment

and all of the energy released from combustion is used to

heat the products

The final temperature of the products in an adiabatic

combustion process is called the adiabatic flame

temperature

For an adiabatic constant-volume process

UP UR = 0

when UP and UR are evaluated relative to the same

datum


Frequently, however, the tables or graphs of internal

energy or enthalpy for species and reactant or product

mixtures which are available give internal energies or

enthalpies relative to the species or mixture value at

some reference temperature To, i.e., U(T) U(To) or

H(T) H(To) are tabulated

Since

UP(To) UR(To) = (DU)V, To

it follows that

[UP(T) UP(To)] [UR(T) UR(To)] = - (DU)V, To

relates the product and reactant states

Given the initial state of the reactants (TR, V) one can

determine the final state of the products (TP, V)


Similar relationships may be developed for an adiabatic

constant-pressure combustion process

[HP(T) HP(To)] [HR(T) HR(To)] = - (DH)p, To

Given the initial state of the

reactants (TR, p) one can determine

the final state of the products (TP, p)

Combustion Efficiency

The combustion efficiency is defined as the fraction of

fuel energy supplied released during the combustion

processes

The exhaust gas of an internal combustion engine

contains incomplete combustion products as well as

complete combustion products

Under lean operating conditions the amounts of

incomplete combustion products are small

Under fuel-rich operating conditions these amounts

become more substantial since there is insufficient oxygen

to complete combustion


The engine can be analyzed as an open system which

exchanges heat and work with its surrounding

environment (the atmosphere)

Reactants (fuel and air) flow into the system; products

(exhaust gases) flow out

The net chemical energy release due to combustion

within the engine for a mass, m, is given by

Enthalpy is the appropriate property since pR = pP = patm.

ni is the number of moles of species i in the reactants or

products per unit mass of working fluid

o o~ ~

f,i f ,iR A P A i ii, reac tants i, products

[H (T ) H (T )] m n h n h

D D


The amount of fuel energy supplied to the control volume

around the engine which can be released by combustion

is mf QHV

Hence the combustion efficiency is given by

R A P Ac

f HV

H (T ) H (T )

m Q

Maximum Work and Efficiency

By applying the second law of thermodynamics to a

control volume surrounding the engine, one can derive

an expression for the maximum useful work that the

engine can deliver

For a mass m of fluid passes through the control volume

surrounding the engine, the first law gives

DQ DWU = DH

where DWU is the useful work transfer (i.e., non-p dV

work) to the environment and DH = HP HR

Since the heat transfer DQ occurs only with the

atmosphere at ambient temperature TA, from the second

law:


These equations combine to give

DWU - (DH TADS) = - DB

where B is the steady-flow availability function, H TAS

Usually pR = pA and TR = TA

The maximum work will be obtained when pP = pA and TP= TA

Under these conditions,

ST

Q

A

DD

AA

AAAP,ATAP,AT

P,TmaxU

P,TRPU

)G(W or

)G(])TSH()TSH[(W

DD

DD


G is the Gibbs free energy, H TS

A fundamental measure of the effectiveness of any

practical internal combustion engine is the ratio of the

actual work delivered compared with this maximum work

This ratio called the availability conversion efficiency, a,

is given as

The property availability is the maximum useful work

transfer that can be obtained from a system-atmosphere

(or control-volume-atmosphere) combination at a given

state

AA P,Tmax U

a)G(

W

W

W

D

D

D

D


We saw earlier that the fuel conversion efficiency is

defined as:

The fuel conversion efficiency is the most commonly

used definition of engine efficiency because it uses an

easily measured quantity, the heating value (usually

lower heating value), to define the usable fuel energy

supplied to the engine

For hydrocarbon fuels, the fuel conversion efficiency and

the availability conversion efficiency are closely

comparable in value

LHVf

cf

Qm

W


In practice, not all the fuel energy supplied to the engine

is released by the combustion process since combustion

is incomplete: the combustion efficiency is less than

unity

It is sometimes useful to separate out the effects of

incomplete combustion by defining an efficiency which

relates the actual work per cycle to the amount of fuel

chemical energy released in the combustion process

This is the thermal conversion efficiency t:

The fuel conversion, thermal conversion, and

combustion efficiencies are related by: f = ct

HVfc

c

T

c

APAR

ct

Qm

W

)H(

W

)T(H)T(H

W

A

D

Equilibrium Composition of Products

The equilibrium composition of the products of combustion of isooctane-air

mixtures at selected temperatures and 30 atm pressure at various

equivalence ratios

Self-Ignition Temperature

If the temperature of an air-fuel mixture is raised high

enough, the mixture will self-ignite without the need of a

spark plug or other external igniter

The temperature above which this occurs is called the

self-ignition temperature (SIT)

This is the basic principle of ignition in a compression

ignition engine

Self-ignition (or pre-ignition, or auto-ignition) is not

desirable in an SI engine, where a spark plug is used to

ignite the air-fuel at the proper time in the cycle

When self-ignition does occur in an SI engine higher than

desirable, pressure pulses are generated which can cause

damage to the engine and quite often are in the audible

frequency range, termed as knock

Self-Ignition Temperature

If the temperature of a fuel is

raised above the self-ignition

temperature (SIT), the fuel

will spontaneously ignite after

a short ignition delay (ID)

time

The higher above SIT which

the fuel is heated, the shorter

will be ID

The values for SIT and ID for

a given air-fuel mixture are

ambiguous, depending on

many variables which include

temperature, pressure,

density, turbulence, swirl,

fuel-air ratio, presence of

inert gases, etc.

Flame Propagation

In normal combustion, the forward boundary of the

reacting zone is called the flame front

In stationary flames the gas moves through the flame,

rather than the flame through the gas usually seen in gas

turbines

The motion of a flame in a mixture confined in a chamber

of constant volume is complicated by the fact that

expansion of the burned gases compresses the

unburned part of the charge

The boundary of the unburned charge next to the flame

front moves relative to the chamber

The observed flame motion is the sum of two

movements:

Flame Propagation

The rate at which the flame moves into the unburned

portion of the charge is called the burning velocity

The rate at which the flame front is pushed forward by the

expansion of the burned gases is called the transport

velocity

The relation between flame position and pressure can be

determined by means of the observed fact that the

fraction of the mass burned is proportional to the fraction

of the total pressure rise; i.e.,

b 1

2 1

M p p

M p p

where, Mb = mass burned

M = total mass of the charge

p1 = initial pressure

p2 = pressure at the end of combustion

p = pressure at the instant under

consideration

Flame Propagation

If it is assumed that the unburned portion of the charge is

compressed adiabatically and is a perfect gas, then

u ub u

u

(k 1) / k

u 1

1

1 u u1

2 1

pV m M M M M

RT

pAlso T T

p

where the subscrcipt u refers to the unburned portion

Combining the above equations, we obtain

p V mp p 1

p p

1/k

1 1

p

MRT p

Flame Propagation

Burning angle or burning time: is the period between

spark and peak pressure

Lag angle or lag time: is the period between ignition

spark and the appearance of a measurable rise of

pressure above the motoring-pressure curve

Effective burning angle or time: is the difference

between the burning angle and lag angle

Average flame speed: is the distance from the spark to

the most remote part of the combustion chamber,

divided by the burning time

Parameters Affecting Flame Propagation

Effect of engine speed

The flame speed must increase nearly in proportion to

engine speed

The increase of flame speed with increasing engine speed is

due to the marked effect of turbulence

Effect of inlet and exhaust pressure

Flame speed increases with increasing inlet pressure

Effect of exhaust to inlet pressure

Dilution with inert gas reduces flame speed

In engines, increasing ratio of exhaust to inlet pressure

increases the fraction of residual gas in the charge and thus

reduces flame speed

Parameters Affecting Flame Propagation

Fuel-air ratio

The lean limit is where the flame speed is zero, i.e., the

flame will not propagate

The value of lean limit varies with fuel composition, engine

design, and operating conditions, but is generally in the

neighbourhood of 60-80% of the chemically correct

mixture

The burning velocity peaks slightly

rich of stoichiometric for all fuels

Other operating variables

The following variables have small

effects on flame speed: air-inlet

temperature, humidity, and engine

operating temperatures

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05 Combustion