AAE 439

Ch5 –1

5. COMBUSTION AND THERMOCHEMISTRY

AAE 439

Ch5 –2

Overview

 Definition & mathematical determination of chemical equilibrium,

 Definition/determination of adiabatic flame temperature,

 Prediction of composition and temperature of combusted gases as a function of initial temperature,

 Prediction of amounts of fuel & oxidizer,

 Thermochemical changes during expansion process in nozzle.

 Performance Parameters:

CF= 2γ 2

γ −12

γ +1

⎛⎝⎜

⎞⎠⎟

γ +1γ −1

1−p

e

p0

⎛

⎝⎜⎞

⎠⎟

γ −1γ

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥+

pe− p

a

p0

⋅ ε

c* =

RT0

γγ +1

2

⎡

⎣⎢

⎤

⎦⎥

γ +1γ −1

Performance depends on: T, MW, p0, pe, pa, γ

AAE 439

Ch5 –3

Overview

 Important Concepts & Elements of Analysis

 Conversion of Chemical Energy to Heat

 Simple Treatment of Properties of Gases

 Balancing Chemical Reactions - Stoichiometry

 Adiabatic Flame Temperature

 Chemical Equilibrium and Gibbs Free Energy

 Nozzle Expansion Effects

 Thermochemical Calculations

AAE 439

Ch5 –4

5.1 THERMODYNAMICS OF GAS MIXTURES

AAE 439

Ch5 –5

Perfect Gas

 Perfect Gas Law relates pressure, temperature and density for a perfect gas/mixture of gases :

 Universal Gas Constant:

 Gas Constant:

 Calorically Perfect Gas:  Internal Energy

 Enthalpy

 Specific Heat Relationships:

 Definition of “Mole”: A mole represents the amount of gas, which contains Avogadro’s number of gas

molecules: 6.02·1023 molecules/mol.

pV = nℜT = mRT ⇔ p v = RT

ℜ = 8.314

Jmol ⋅K

R = ℜ

M

du = cvdT u

2− u

1= c

v(T

2−T

1)

dh = cp

dT h2− h

1= c

p(T

2−T

1)

c

p− c

v= R γ =

cp

cv

AAE 439

Ch5 –6

Gibbs-Dalton Law

 Properties of a mixture is determined by the properties of constituents according to Gibbs–Dalton Law:

 The pressure of a mixture of gases is equal to the sum of the pressure of each constituent when each occupies alone the volume of the mixture at the temperature of the mixture.

 The internal energy and the entropy of a mixture are equal, respectively, to the sums of the internal energies and the entropies of its constituents when each occupies alone the volume of the mixture at the temperature of the mixture.

 Temperature

 Pressure

 Volume

 Energy

 Entropy

 Enthalpy

Tmix= T

1= T

2=…= T

N

p

mix= p

1+ p

2+ p

3…+ p

N= p

ii=1

N

∑

Vmix= m

mixv

mix= m

1v

1= m

2v

2=…= m

Nv

N

E

mix= m

mixe

mix= m

1e

1+ m

2e

2+…+ m

Ne

N= m

ie

ii=1

N

∑

Smix= m

mixs

mix= m

1s1+ m

2s2+…+ m

Ns

Nsmix

= Smix

nmix

Hmix= m

mixh

mix= m

1h

1+ m

2h

2+…+ m

Nh

Nh

mix= H

mixn

mix

AAE 439

Ch5 –7

Mixture of Gases

 Definitions by Mass Based Molar Based

 PG Law

 Pressure

 Fraction of Species

 Enthalpy

 Entropy

 Equivalent Molecular Weight

piV = m

iR

iT = n

iℜT pV

i= m

iR

iT = n

iℜT

p = p

ii=1

N

∑ V = V

ii=1

N

∑

Mmixequiv

= mn= m

mi

Mii=1

N

∑= 1

yi

Mii=1

N

∑ M

mixequiv

= mn=

niM

ii=1

N

∑n

= xiM

ii=1

N

∑

x

i=

ni

nmix

= yi

Mmix

Mi

xi

i=1

N

∑ =1 y

i=

mi

mmix

= xi

Mi

Mmix

yi

i=1

N

∑ =1

h

mix= y

ih

ii∑

h

mix= x

ih

ii∑

s

mix(T,p) = y

is

i(T,p)

i∑

smix

(T,p) = xisi(T,p)

i∑

s

i(T,p

i) = s

i(T,p

ref)−R ln

pi

pref

si(T,p

i) = s

i(T,p

ref)−ℜ ln

pi

pref

AAE 439

Ch5 –8

Mixture of Gases

 Definitions:

 Relationship

 Specific Heat

 Ratio of Specific Heat

Vi

V=

pi

p= x

i= y

i

Mmix

Mi

c

p,mix= c

p,iy

ii=1

N

∑

γ

mix=

cp,mix

cv,mix

=c

p,mix

cp,mix

−Rmix

AAE 439

Ch5 –9

5.2 1st LAW OF THERMODYNAMICS

AAE 439

Ch5 –10

1st LTD - Fixed Mass

 First law of thermodynamics embodies the fundamental principle of conservation of energy.  Q and W are path functions and occur only at the system boundary.

 E is a state variable (property), ∆E is path independent.

m, E

Q

W

System Boundary enclosing Fixed Mass

Q − W = ΔE1→2

Heat added to system in going from state 12

Work done by system on surrounding in

going from state 12

Change in total system energy in going from state 12

Q − W = dE dt

q − w = de dt

E = m u+ 1

2v2 + g z

⎛

⎝⎜

⎞

⎠⎟

AAE 439

Ch5 –11

1st LTD - Control Volume

 Conservation of energy for a steady-state, steady-flow system.

 Assumptions:  Control Volume is fixed relative to the coordinate system.

 Eliminates any work interactions associated with a moving boundary,

 Eliminates consideration of changes in kinetic and potential energies of CV itself.

 Properties of fluid at each point within CV, or on CS, do not vary with time.

 Fluid properties are uniform over inlet and outlet flow areas.

 There is only one inlet and one exit stream.

QCV WCV

Control Surface (CS) enclosing Control Volume (CV)

Q

CV− W

CV= m e

outlet− m e

inlet+ m p

ov

o− p

iv

i( )Rate of heat

transferred across the CS, from the

surrounding to the CV.

Rate of all work done by CV,

including shaft work but excluding flow work.

Net rate of work associated with pressure

forces where fluid crosses CS, flow work.

dmCV

dt= 0

dECV

dt= 0

Rate of energy flowing out

of CV.

Rate of energy flowing into

CV.

QCV

− WCV

= m ho− h

i( ) + 12

vo2 − v

i2( ) + g z

o− z

i( )⎡

⎣⎢

⎤

⎦⎥

m e + p v( )

inlet m e + p v( )

outlet

AAE 439

Ch5 –12

THERMODYNAMIC PROCESSES

 Energy Equation (1st Law of TD)

 Energy Change due to a process going from State 1 to State 2:

 Constant–Volume (Isochoric) Process:

 Constant–Pressure (Isobaric) Process:

E = U + Epotential

+ Ekinetic

= Q −Wshaft

−Wflow

ΔU = U2−U

1= Q −W

flow= Q − p V

ΔU = Q

ΔU = Q − pΔV

ΔU + pΔV = Q

ΔH = Q

AAE 439

Ch5 –13

5.3 THERMOCHEMISTRY BASICS

AAE 439

Ch5 –14

Energies in Chemical Reactions

 Enthalpy of Combustion (Reactions):

 Heat of Combustion:

– QCV

REACTANTS Stoichiometric fuel-oxidizer (air)

mixture at standard state conditions: Tref and pref.

PRODUCTS Complete combustion

at standard state conditions: : Tref and pref.

Hin= H

reactant Hout= H

product

Δhrxn

≡ qCV

= hprod

− hreac

ΔHrxn

= Hprod

−Hreac

ΔhC= −Δh

rxn

Graphical Interpretation