D PFB Content of Lecture

1

Content of Lecture

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1. Phenomenology of Combustion

2. Thermodynamic Fundamentals

3. Chemical Reaction Kinetics

4. Ignition and Ignition Limits

5. Laminar Flame Theory

6. Turbulent Combustion

7. Pollutants of Combustion

8. Combustion of Liquid and Solid Fuels

9. Numerical Simulation

10. Measurement Techniques of Combustion Processes

11. Applied Aspects of Turbulent Combustion

12. Technical Burner Systems

13. Internal Combustion Engines

2

Content

2. Thermodynamic Fundamentals• Concentrations

• Balances

2.1 Mass Balance

• Reaction equation

• Air/Fuel Ratio

2.2 Thermodynamical Quantities

• Heat release

• Lower and Higher Heating Value

• Flue gas composition

• Adiabatic flame temperature

• Efficiency

• Efficient Combustion

3

Thermodynamic Fundamentals

Mass m, im [kg] (Component i)

Mass fraction m

mY i

i [-] (also ii w, )

Number of moles ni [mol] 1 mol = 6.023 • 1023

Atoms, Molecules

Mole fraction n

nX i

i [-] (also ii x, )

Molecular weight i

ii

n

mM [kg/mol] (e.g. MH = 1 g / mol, MO2 = 32 g / mol)

Mean molecular weight i

ii MXM [kg/mol]

M

MXY i

ii (2.1)

Mass density (density) V

m [kg/m³]

Molar density V

nc i

i [mol/m³] also "Concentration", "[H2O]"

2.0.1. Concentrations

Definitions

4


𝑀𝑖(g/mol) 𝑋𝑖 (%) 𝑌𝑖 (%)

Nitrogen 28.0 78.1

Oxygen 32.0 21.0

Argon 40.2 0.9

Air ഥ𝑀=

Example : Find the mass fraction of the constituent gases of air, and the mean

molar mass of the mixture.

5


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Ideal gas law: (Real gas law for high pressure, low temperature)

TRnVp m (2.2) p [Pa=N/m²]

1 bar = 105 Pa = 1000 hPa

Partial pressure V

TRnp m

ii Rm = 8.314 J/(mol K)

TR

pc

m

ii (2.3)

p

TRcX m

ii (2.4)

For gases

Mole fraction Xi ~ Volume fraction

Common for:

Vol-% = Mol-% Xi [%] • Atmosp. Gas flames, Chemistry, Lab

Mass-% Yi [%] • Liquid and solid fuels,

Gas turbine, Process with change of pressure

Combustion calculations: often related to amount of fuel:

Mass ratio B

ii

Y

Y Molar ratio

B

ii

X

Xy

ii

i

McY

Concentrations

Definitions

6


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• Definition of system boundary

• Balance of temporal change of quantity F due to

• Inflow / Outflow (Flow rates F )

• Production / Consumption (Sink- / Source term S )

S(Source/Sink)

Inflow

F1

Outflow

F2

Balance of:

• Total mass

• Mass of Species or Atoms

• Energy

• Momentum

2.0.2. Balances

Procedure

7

Mass Balance

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Material conversion in combustion is described by reaction equations

--> Regrouping of chemical atoms --> Atoms are conserved (Mass conservation)

Example for reaction equation:

H2 + 1/2 O2 --> H2O stoichiometric combustion

2 H2 + 1/2 O2 --> H2O + H2 rich (fuel rich) = more fuel than needed

H2 + 1 O2 --> H2O + 1/2 O2 lean (fuel lean) = more air than needed

Air: 21 % O2

79 % N2 (including inert gases) (2.5)

Example:

H2 + 1/2 (O2 + 3,76 N2) --> H2O + 1/2 • 3,76 N2

nL = 1/2 4,76 mol Air = 2,38 mol

nB = 1 mol

2

2

2

76,4

76,3

OL

O

N

nn

n

n

2.1.1. Reaction equations

8

Mass Balance

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(2.7) Combustion stoich. for : Luftmenge'-Mindest'

(2.6) : Luftmenge' Molare'

min,

min

B

L

B

L

n

nL

n

nL

Note: The term 'Mindest'-Luftmenge (minimum air) comes from the fact, that technical

burner generally operate with excess air nL >nL,min

(2.8) : ratio' air/fuel Relative'minmin, L

L

n

n

L

L

(also called 'air ratio', common in germany: 'Luftzahl' or 'Luftverhältnis', measure for

excess air)

International:

(2.9) Ratio' eEquivalenc'

1F

(also 'Stoichiometric ratio', 'Stoichiometry')

Minimum Air

Molar Air Ratio

2.1.2. Air / Fuel Ratio

9

Mass Balance

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Stoich. Combustion: F = 1 = 1

Rich Combustion: F > 1 < 1

Lean Combustion: F < 1 > 1

Also 'specific' = mass related quantities common (liquid or solid fuels).

(Sometimes dimension of air is given in norm cubic meters (standard cubic meters at 0°C)

and dimension of fuel is given in kg. In praxis watch for the given dimensions!).

(2.10) 1

1 : anteil'Brennstoff'

(min)(min),

(st)B,Lnn

nX

LB

B

(2.11) 1

1 , , ,:

(min)(min),

(st)B,

minmin,

min,

minlmm

mY

l

l

m

m

m

ml

m

ml

LB

B

L

L

B

L

B

L

Fuel mole fraction

Air / Fuel Ratio

10

Mass Balance

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General form of global reaction equation for hydrocarbon combustion (for 1)

for the amount of air L = nL / nB follows:

(2.12b) 1

; 4

(2.12a)N 3,76O)1( OH2

CO N 3,76O HC 222222yx

F

yxa

aay

xa

(2.13) 76,4

76,4min

aL

aL

General Reaction Equation

11

Mass Balance

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Brennstoff Mindestluftmenge Stöch. Brennstoffanteil

a Lmin [m3N/m

3N] lmin [m

3N/kg] lmin [kg/kg] XB,st [Vol%] YB,st [Massen%]

H2 0,5 2,38 26,44 34,06 29,59 2,85

CH4 2 9,52 13,29 17,12 9,51 5,52

C2H4 3 14,28 11,40 14,69 6,54 6,38

C3H8 5 23,80 12,09 15,57 4,03 6,03

C7H16 11 52,36 11,70 15,07 1,87 6,22

C8H18 12,5 59,50 11,67 15,03 1,65 6,24

Benzin 11,5

Diesel 11,2

Steinkohle ca. 8

Stoichiometric fuel fractionFuel Stoichiometric Air ("Minimum Air")

Table: Stoichiometric Air and Fuel Fraction

12

Thermodynamic Quantities

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What can be determined with heat and mass balances ?

2.2.1 Heat release

2.2.2 Heating values (LHV, HHV)

2.2.3 Equilibrium composition of flue gas

2.2.4 Adiabatic flame temperature

2.2.5 Efficiencies

2.2.6 Efficient combustion design

What else is necessary ?

Reaction rates

Reaction paths

Molecular and turbulent transport

Models to couple chemistry and turbulent flow

Energetic and exergetic balances

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Energy balance:

1. Law of Thermodynamics (Ekin, Epot is neglected in the following):

Change of internal energy = In-/Outflow of heat + In-/outflow of work

U2 - U1 = Q12 + W12 or H2 - H1 = Q12 + Wt,12 (2.14)

Depending on the system boundaries:

Internal energy U or Enthalpy H

("closed system") ("open system")

In combustion calculations enthalpy is used frequently, since combustion often takes place in

thermodynamically "open" systems for given pressure. (H = U + p V)

2.2.1. Heat Release

14


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for each component i molar enthalpy is described by:

(2.15)

The first term is the 'Standard formation enthalpy', to be measured at the formation of this

component in a formation reaction at 'standard conditions' (q = 25°C, 1 bar). Can be obtained

from tables.

The second term describes the temperature dependency. Often average values of specific

heat are used from tables.

(2.16)

T

C

ipi

f

i dTTchpTh25

, )()(,),( qq

12

2

1

2

1

)( ttcdTTct

tp

t

t

p

Heat Release

15


Pure elements in their most stable states – ∆ഥ𝐻𝑓,2980 = 0

N2 (gas)

O2 (gas)

H2 (gas)

C (graphite)

Other compounds can be formed from

reactions from those

Internal Energy and enthalpy of formation

Combustion, Warnatz, Maas and

Dibble, 4th edition

2H2(g) O2(g) -> 2 H2O (liq)

O2 (g) -> ½ O (g)

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Table: Standard Formation

Enthalpies At 25°C, 1bar

Molecule hfq

[ kJ / mol ]

O2 0N2 0H2 0H2O (g) - 241,8H2O (liq.) - 285,8CO -110,5CO2 - 393,5CH4 - 74,8C2H2 (g) 226,7C2H4 (g) 52,3C2H6 (g) - 84,7C3H8 (g) - 103,9C4H10 (g) - 124,7C6H6 (liq) 49,0C7H16 (liq) - 224,4C8H18 (liq) - 250,0

Heat Release

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Reactor with stationary combustion

Reaction chamber

12Q

Reactants RProducts P

State 1 State 2

From energy balance Eq. (2.14) follows for the heat release per unit time

(2.17)

(Note, heat flow is defined with negative sign, since leaving the system "reaction chamber".)

For mixtures of ideal gases enthalpy is the sum of the single component enthalpies:

(2.18)

With eq. (2.15), (2.16) and (2.17) the heat release can be calculated.

1212 HHQ

R P

PPRR pThnHpThnH ),(),,( 21

Heat Release

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Together the sequence of summation can be changed to:

(2.19)

The first term of r.h.s. describes the chemical change of enthalpy at standard conditions (25°C),

the second term describes the temperature dependency of initial and final components.

Example 1: Calculate the heat release, if reactants and products have 25°C (tR = tP = 25°C) ?

Now only the first term of eq. (2.19) must be calculated. It follows with tabulated standard

formation enthalpies (next page)

Example: H2 + 1/2 O2 --> H2O (gaseous)

The standard formation enthalpies of stable species H2 and O2 are zero, thus follows per mole

of fuel : Q12 = -241,8 kJ/mol.

For a fuel flow of 1 mol/s follows the heat release rate is 241,8 kW.

P R 25

,

25

,

P R

,,1212 )()(-RP T

C

RpR

T

C

PpPRf

RPf

P dTTcndTTcnhnhnHHQ qq

Heat Release

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Example 2: Calculate the heat release, if the temperature of the products is tP =

2200°C (tR = 25°C) ?

Here some of the released chemical energy will remain as sensible energy in the

hot products, thus the heat release is lower.

Calculation of the second term of eq. (2.19) (for example with cp from table in

"Baehr, Thermodynamik", Appendix) gives Q12 = (-242 + 97) kJ/mol fuel = -145

kJ/mol fuel.

For a fuel flow of 1 mol/s the heat release rate is 145 kJ/s = 145 kW.

Heat Release

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Note: for technical furnaces as much heat as possible should be utilized,

therefore the temperature of the exhaust should be as low as possible just above

the dew point (condensation of H2O).

Hence, in typical technical combustion systems the temperature dependent

second term in eq. (2.19) is relatively low. Often it can be neglected compared to

the first term.

The first term is a pure property of the fuel, being independent of the form of the

oxidant, either stoichiometric air, excess air ( > 1) or pure O2 ) (Reason: the

standard formation enthalpy of N2 is zero).

This simplifies the calculation of heat release significantly, and thus only fuel data

is enough

Introduction of HEATING VALUE of a fuel:

2.2.2. Heating Value

P R 25

,

25

,

P R

,,1212 )()(-RP T

C

RpR

T

C

PpPRf

RPf

P dTTcndTTcnhnhnHHQ qq

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Heating value (molar)

(2.20)

Heating value (mass)

/12 Bu nQH

The heating value is the released heat of combustion per unit mol or

mass of fuel, if reactants and products are at standard temperatures

(25°C).

(Note: No different symbol for molar and mass based heating value is used.

Differentiate by the given dimension.)

/12 Bu mQH

The heat release per mol fuel is then:

(2.21) )()( R P 25

,

25

,12

12

PR T

C

Pp

B

P

T

C

Rp

B

Ru

B

B dTTcn

ndTTc

n

nH

n

Qq

Heating Value

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H2O in the products can be gas or liquid (after condensation). Then

additional heat is released from condensation enthalpy. Therefore we

differentiate:

'Higher Heating Value' Ho if H2O liquid

'Lower Heating Value' Hu if H2O gaseous

Other names are:

'Higher Heating Value' HHV, 'higher calorific value', 'gross calorific value',

german 'Brennwert', or 'oberer Heizwert' Ho

'Lower Heating Value' LHV, 'lower calorific value', 'net calorific value',

german 'Heizwert', or 'unterer Heizwert' Hu ,

Ho > Hu

Heating Value

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Table: Heizwert and Brennwerte (Examples)

Fuel mol.HeizwertHu

[kJ/mol]

mol.BrennwertHo

[kJ/mol]

spez.HeizwertHu

[MJ/kg]

spez.BrennwertHo

[MJ/kg]

H2 241,8 285,8 119,9 141,8

CH4 802,3 890,3 50,0 55,5

C3H8 2044 2220 46,4 50,3

C8H18, fl. 5074 5471 44,4 47,9

Coal ca. 30 ca. 31

Heizöl EL 42,9 45,8

Waste ca. 15

Memorize: Typical Fuels (CxHy) release around 45 MJ/kg

Heating Value

24


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Calorific value method

Brennwert-Kessel (boiler)

• Brennwert > Heizwert

• Traditional: Exhaust temperature > dew point (typ. 70°C), to avoid condensation

in chimney (from corrosion, especially from sulfuric acid). -> Heizwert.

• Today: 'Brennwert-Kessel' with exhaust temperature < dew point -> Brennwert.

(only for fuels without sulfur -> natural gas)

• Historically (in Germany) the 'Efficiency of the boiler' ('Kesselwirkungsgrad')

hk is based on the Heizwert Hu (hk typ. 0,86 - 0,95).

• --> Thus for Brennwert-Kessel hk can be > 1 !!!

Brennwert-Technology

with 108 % efficiency !

Is that possible ???

Heating Value

25


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• For most combustion reactions the

thermodynamic equilibrium is far on

the product side.

• At high temperatures a significant

amount of intermediate products can

exist in the thermodynamic

equilibrium (CO, OH, ... ).

• Calculation of the equilibrium

concentration is possible from the

minimum of Gibbs free enthalpy.

(Result of the 2. law of

thermodynamics. Details see

textbooks).

1,0E-07

1,0E-06

1,0E-05

1,0E-04

1,0E-03

1,0E-02

1,0E-01

1,0E+00

1200 1800 2400

T [K]

Mo

len

bru

ch

Xi

NO

CO

CO2

Methan/Air, =1, 1 bar

2.2.3. Equilibrium-Composition of Flue Gas

26



• Chemical equilibrium

Elementary reaction : A + B + … -> C + D + …

From thermodynamics considerations (2nd law) – minimum in Gibbs free

enthalpy 𝐾𝑝 = ς𝑖𝑝𝑖

𝑝0

ν𝑖𝐾𝑝 = exp −

∆𝑅 ത𝐺0

𝑅𝑇

• Method : Calculation of equilibrium composition – Example C2H4 – O2

mixture

• Choice of chemical system : S Species

• e.g. CO2,CO,H2O,H2,O2,O,H,OH (S=8)

• Components of system : K Components (K=3)

• e.g. C, H, and O

• Need R = S-K independent reactions (R=5)

27



• Calculations : Example C2H4 – O2 with CO2,CO,H2O,H2,O2,O,H,OH

1. Total pressure (1 equation)

2. Fixed ratio of mass ( 2 equation)

3. Equilibrium conditions (5 equations)

28


• Dissociation increases with temperature. It is generally considered

negligible below 1600°C.

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• Adiabatic flame temperature: Reaction without heat leaving or entering the

reactor ('adiabatic'), i.e. qB12 = 0 in eq. (2.21).

• For calculation, solve eq. (2.21) for Tad = TP .

• The flame temperature is an important quantity for processes in flames

(--> Reaction kinetics, pollutant formation, material stress).

• In real flames the maximum flame temperature is below the adiabatic flame

temperature, since heat is lost by radiation or due to soot formation.

• Note: Tad depends on the thermodynamic equilibrium composition of the

products. Since this depends by itself on the temperature Tad both has to be

calculated iteratively for detailed calculations.

Adiabatic flame temperature := theoretically achievable maximum

combustion temperature

2.2.4. Adiabatic Flame Temperature

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• Influence of dissociation.

Adiabatic flame temperature := theoretically achievable maximum

combustion temperature

2.2.4. Adiabatic Flame Temperature

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Adiabatic flame temperature depends on air/fuel ratio

Tad (for =1, to=25°C, 1 bar):

H2-Air 2380 K

H2-O2 3083 K

CH4-Air 2226 K

C2H2-Air 2539 K

C2H2-O2 3069 K

C3H8-Air 2267 K

C8H18-Air 2275 K

• Tad increases for preheated air, or for O2 instead of air.

• Tad decreases, if cooled exhaust gas is mixed with reactants

(Exhaust gas recirculation EGR).

Tad

Air/Fuel Ratio

1 2

Adiabatic Flame temperature

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Defined, if use of heat is the primary aim:

(2.22)

being traditionally based on Lower Heating Value (in Germany). Also for

Brennwert-Technology, then hF can be larger than 100%).

Exhaust Loss (Abgasverlust)

The exhaust loss (Abgasverlust) q A (in %) is the part of the combustion energy

leaving the furnace with the heated exhaust. It can be related to the firing

efficiency (feuerungstechnischer Wirkungsgrad) assuming no further heat loss:

(2.23)

In Germany the maximum exhaust loss is reglemented e.g. for heating boilers.

Firing Efficiency (Feuerungstechnischer Wirkungsgrad)

ValueHeating Lower

heat Available12 u

B

FH

qh

A

F q %100h

2.2.5. Efficiencies

33


)()( R P 25

,

25

,12

12

PR T

C

Pp

B

P

T

C

Rp

B

Ru

B

B dTTcn

ndTTc

n

nH

n

Qq

Effect of Excess Air and Oxygen enrichment on exhaust loss

At fixed Tp (70°C), and without preheating, the efficiency decreases with

The energy used to heat inert gas molecules (N2) to 70°C is lost.

Limit in excess air (~1.2), requires precise metering

Oxygen enrichment can reduce loss but O2 cost must be considered.

B

P

n

n

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Excursion: Measurement of the Exhaust Loss

Following the german 'Kleinfeuerungs-Anlagen-Verordnung' (Small burner system

reglementation) (1. BImSchV), the exhaust loss (Abgasverlust) of a heating system has to be

checked every year from the chimney sweeper (Schornsteinfeger).

Limit for oil and gas boiler (4 - 25 kW) (from 2004): q A < 11%.

Estimated from *

(2.24)

Factors based on the type of fuel:

A2 = 0,68 (Heizöl), 0,65 (natural gas); B = 0,007 (Heizöl), 0,009 (natural gas)

Required measurements are

Temperature of incoming air TL

Temperature of exhaust gas TA

Exhaust concentration of O2 (in %, measured in dry flue gas)

Can be determined alternatively from CO2 measurement instead of O2 measurement.

* see Recknagel, Sprenger, Hönmann, Taschenbuch für Heizung+Klimatechnik, Oldenburg Verlag

B

O

ATTq LA

A

)21()(

2

2

Efficiencies

35


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• Maximum efficiency of a heat engine (Wärme-

Kraft Maschine) is described by the Carnot cycle:

(2.25)

• This was one of the most important guiding rules

in the past for burner development !

• Today NOx formation is of importance: Then

reduction of combustion temperature is needed !

Note on thermal efficiency

if technical work is desired output.

in

outin

in

CT

TT

Q

P h

Thermal efficiency increases, if the

combustion temperature TComb increases.

Combustion

WKM

Tout

T1

Tin = TComb.

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Efficiencies

36

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What can be determined with energetic and exergetic balances ?

2.2.1 Heat release

2.2.2 Heating values (LHV, HHV)

2.2.3 Equilibrium composition of flue gas

2.2.4 Adiabatic flame temperature

2.2.5 Efficiencies

2.2.6 Efficient combustion design

What else is necessary ?

Reaction rates

Reaction paths

Molecular and turbulent transport

Models to couple chemistry and turbulent flow

Documents

D PFB Content of Lecture