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Page 1: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Chapter 13

Reacting Mixtures and Combustion

Photo courtesy of www.freefoto.com

Page 2: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Fundamentalsproductsfuel oxidizer reactants products

Chemical Equations:

2 2 2

11H O 1H O

2

2 2 2

11 kmol H kmol O 1 kmol H O

2

2 2 22 kg H 16 kg O 18 kg H O

Modeling Air:

• 79% Nitrogen, 21% Oxygen• Only the Oxygen reacts: Nitrogen considered inert• Mair = 28.97 kg/kmol or lb/lbmol (Tables A-1)

Air Fuel Ratio:

mass of air moles of air

mass of fuel moles of fuel air air

fuel fuel

M MAF AF

M M

1a

2b

1*b2*a

2*b2*1

OH*bO*aH*1 222

Page 3: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Fundamentals

Chemical Equations:

Common fuels modeled as simple hydrocarbons:• Natural Gas Methane (CH4)• Gasoline Octane (C8H18)• Diesel Dodecane (C12H26)

Theoretical Air: The minimum amount of air that provides the necessary oxygen for complete combustion (i.e. For one mole of octane the theoretical air is 59.5 moles)

2*d2*0.79*a N)

1*c2*b2*0.21*a O)

2*c18*1 H)

1*b8*1 C)

47.0d

59.5a

9c

8b

22222188 N*d OH*c CO*b)0.21N(0.21O*aHC*1 Stoichiometric Coefficients (Four equations and four unknowns)

Page 4: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Fundamentals

2*d2*0.79*59.5*1.5 N)

2*e1*92*82*0.21*59.5*1.5 O)

25.6e

70.5d

222222188 O*eN*d OH*9 CO*8)0.79N(0.21O*59.5*5.1HC*1

Stoichiometric Coefficients (Two equations and two unknowns)

Percent Excess Air:The percent of air supplied that is in excess of the theoretical air

Example: Combustion of Octane with 50% excess air (or 150% theoretical)

222222188 O*25.6N*70.5 OH*9 CO*8)0.79N(0.21O*25.89HC*1

Page 5: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

QuizOne kg/min of methane is burned in a combustor with 25% excess air. The temperature and pressure of the air and fuel are 25oC and 101kPa respectively. The design velocity for each intake is 15 m/s. Determine the diameter of the air intake line in meters.

Page 6: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

QuizOne kg/min of methane is burned in a combustor with 25% excess air. The temperature and pressure of the air and fuel are 25oC and 101kPa respectively. The design velocity for each intake is 15 m/s. Determine the diameter of the air intake line in meters.

CH4+a(0.21O2+0.79N2) bCO2+cH2O+dN2

C) 1*1 = b*1 b=1H) 1*4 = c*2 c=2

O) a*2*0.21 = b*2+c*1 a=9.524

Theoretical air = 9.524 kmol(air)/kmol(fuel)

Theoretical Air

Page 7: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

QuizOne kg/min of methane is burned in a combustor with 25% excess air. The temperature and pressure of the air and fuel are 25oC and 101kPa respectively. The design velocity for each intake is 15 m/s. Determine the diameter of the air intake line in meters.

Actual Mass flow rate of air

kg/min 21.5 21.5*kg/min 1.0 AF*mm

5.2104.16

97.28*9.11

M

M*AFAF

fuelair

fuel

air

Actual Air = Theoretical * (1+%excess) = 9.524*1.25

= 11.9 kmol(air)/kmol(fuel)

Page 8: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

QuizOne kg/min of methane is burned in a combustor with 25% excess air. The temperature and pressure of the air and fuel are 25oC and 101kPa respectively. The design velocity for each intake is 15 m/s. Determine the diameter of the air intake line in meters.

Diameter of air intake

m16.0m02.0*4A4

D

m02.0s60

min1*

m/s15*kg/m18.1

kg/min5.21

V)(

mA

AV)(m

kg/m18.11kPa

1kJ/m*ol28.97kg/km

298K*K-ol8.314kJ/km

101kPaM

TR

P

2

23

air

air

airair

33

airair

Page 9: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Enthalpy: Reacting SystemsTabular enthalpies inadequate due to arbitrary reference datums

Standard Reference State (Stable Elements): Tref = 298.15 K, pref = 1 atm

First Law:2 2 2 2 2 22 2

CO C O CO CO C C O OCO C OcvQ m h m h m h n h n h n h

2 0 (standard reference state)C Oh h

2

2

2 for CO at 1 atmcvCO f

CO

Qh h

n

)(formation ofenthalpy ofhh

Page 10: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Enthalpy: Reacting Systems

First Law:

, , ,f ref ref fh T p h h T p h T p h h

kJ/kmol387939

kJ/kmol9364kJ/kmol19945kJ/kmol393520

)K298()K550(kJ/kmol393520

2

2

222

CO

cv

COcv

refCOCOCOcv

n

Q

nQ

ThThnQ

0000

2222

222222

OCCOCO

ofCOcv

OO

ofOCC

ofCCOCO

ofCOcv

nnhhnQ

hhnhhnhhnQ

2222 OOCCCOCOcv hnhnhnQ

Standard Reference State

Tref = 25 oCPref = 1 atm

Page 11: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Energy Balances: Steady State

cvcvP R f fe i

e iP RF F

Q Wh h n h h n h h

n n

2 2 2 2 23.76 3.762 4 4 4

cvcvCO H O N F O N

F F

Q W b b b bah h a h h a h a h

n n

2 2 23.762 4

P CO H O Nb b

h ah h a h

2 23.764 4

R F O Nb b

h h a h a h

Page 12: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Energy Balances: Steady State

2 2 2 2 2

4 2 2 2 2 21*CH 2(O 3.76N ) CO 2H O 2*3.76N

2 2*3.76 2 2*3.76cvCO H O N F O N

F

cvP R

F

f ref

Qh h h h h h

n

Qh h

n

h h h T h T

Page 13: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Energy Balances: Steady State

22 2

22 2

4

-

-

-

2 7.52

169300 15829 4028 2 104040 13494 4258 7.52 11410 3730

289353 Btu/lbmol(fuel)

32210 Btu/lbmol(fuel)

28935

f fP ref ref refNCO H O

P NCO H O

P

fRCH

cvP R

F

h h h T h T h h T h T h T h T

h

h

h h

Qh h

n

- -3 32210 257143 Btu/lbmol(fuel)

Page 14: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Closed System Energy Balance

P R P RP R P R

Q W U U nu nu n h RT n h RT

f fP RP R

Q W n h h RT n h h RT

Page 15: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Fuel Enthalpies

RP e ie iP R

h n h n h Enthalpy of Combustion

For Example: A Control Volume at Steady State

cvcvf f f fe i e i e ie ie i e iP R P R P RF F

Q Wn h h n h h n h n h n h n h

n n

LHVRPh

LHV (Lower Heating Value): The enthalpy of combustion when the reactants and products are at the standard reference state and the water formed by combustion is a gas

HHV (Higher Heating Value): …water formed by combustion is a liquid

Page 16: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Adiabatic Flame Temperature

When no power produced, and combustion carried out adiabatically, Tp reaches a theoretical maximum.

When using tables, requires iteration to determine!

f fe ie iP R

n h h n h h

Page 17: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Adiabatic Flame Temperature

4

22 2

22 2

-

0

32210 Btu/lbmol(fuel)

2 7.52

169300 4028 2 104040 4258 7.52 3730

?

cvP R

F

fRCH

f fP ref ref refNCO H O

PNCO H O

P R

Qh h

n

h h

h h h T h T h h T h T h T h T

h h T h T h T

h h

T

Page 18: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Fuel Cells

Solid Oxide Fuel Cell Proton Exchange Membrane Fuel Cell

Page 19: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Third Law of Thermodynamics

The absolute entropy of a pure-crystalline substance at the absolute zero of temperature is

zero. Clip art courtesy of MS Office 2000

, ln ii ii

ref

y ps T p s T R

p Ideal Gas

, , , ,ref refs T p s T p s T p s T p

Page 20: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Entropy BalancesControl Volumes at Steady State, Reacting System

2 2 2 2 2

/0 3.76 3.76

4 4 2 4cvjj

F O N CO H O N

j F F

Q T b b b bs a s a s as s a s

n n

Closed, Reacting System

P Rb

QS S

T

1

P R bF F

Qns ns

n T n

Page 21: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Chemical ExergyTotal Exergy = Thermo-mechanical Exergy + Chemical Exergy

Thermo-mechanical Exergy found in Chapter 7

For a Hydrocarbon: CaHb

2

2 2 2

2 2

/ 4ech

0 0 0( ) / 2e ee , ln

4 2

a b

O

f O CO H O g a b

CO H O

yb bg a g ag g T p RT

y y

Page 22: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Chemical ExergyFor Carbon Monoxide: CO

2

2 2

2

1/ 2ech

0 0 0 e

1e , ln

2O

CO O CO

CO

yg g g T p RT

y

For Water: H2O 2 2

2

ch

0 0 0( ) ( ) e

1e , lnH O l H O g

H O

g g T p RTy

For N2, O2, CO2 ch

0 e

1e lnRT

y

For mixture of gas phases of Ideal Gases at T0, p0

ch

0 ee ln i

ii i

yRT y

y

Page 23: Chapter 13 Reacting Mixtures and Combustion Photo courtesy of

Exergy Summary

2

ch0 0 0 0 0e e

2

Vu u p v v T s s gz

2

chf 0 0 0e e

2

Vh h T s s gz