Politecnico di Torino
Dipartimento Energia
Chemically reactive systems
Dipartimento Energia
Politecnico di Torino
Fluid machinery
1
Prof. D. Misul
1
Politecnico di Torino
Dipartimento Energia
Introduction
Chemical reaction
Let’s introduce the possibility that the interatomic bonds of the molecules of
some or all the original chemical components of the mixture system may
break, thus leading to the formation of new chemical componenents.
The original mixture components whose molecules undergo disintegration
are reffered to as the reactants.
The new components whose molecules are formed as the atoms of the
original reactants change partners are recognized as the products.
A chemical reaction is the process by which the mole number of the mixture
changes, from reactants to products.
A combustion process is a fast exothermic gas-phase reaction (where
oxygen is usually one of the reactants).
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Prof. D. Misul
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1
Politecnico di Torino
Dipartimento Energia
Introduction
Flame
A flame is a combustion reaction which can propagate sub-sonically through
space; motion of the flame relative to the unburned gas is an important
feature, since it implies that the reaction is confined to a zone which is small
in thickness compared to the dimensions of the apparatus (e.g. the engine
combustion chamber). The reaction zone is usually called the flame front.
This flame characteristic of spatial propagation is the result of the strong
coupling between:
- chemical reaction;
- the transport processes of mass diffusion;
- heat conduction;
- fluid flow.
The generation of heat and active species accelerate the chemical reaction;
the supply of fresh reactants, governed by the convection velocity, limits the
reaction. When these processes are in balance, a steady-state flame results.
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Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Introduction
Flame classification
Flames are usually classified according to three main overall characteristics.
• The composition of reactants as they enter the reaction zone: if the fuel
and the oxidizer are essentially uniformly mixed together, the flame is
designated as premixed (SI engines). If the reactants must mix together in the
same region where reaction takes place, the flame is called a diffusion flame
(CI engines) because the mixing must be accomplished by a diffusion process.
• The time steadiness of the phenomenon: if the flame structure and motion
change with time the flame is said to be steady, otherwise it is unsteady.
• The basic character of the gas flow through the reaction zone: in laminar
(or streamlined) flow, mixing and transport are done by molecular processes.
Laminar flows only occur at low Reynolds number. In turbulent flows, mixing
and transport are substantially enhanced by the macroscopic relative motion of
eddies or lumps of fluid which are the characteristic feature of a turbulent (high
Reynolds number) flow.
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Prof. D. Misul
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2
Politecnico di Torino
Dipartimento Energia
Energy and enthalpy balance
Application of FLT to combustion
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.
Nonetheless, the first law of thermodynamics can be used to relate the end
states of mixtures undergoing a combustion process; its application does not
require the details of the process to be known.
The FLT relates changes in internal energy (or enthalpy) to heat and work
transfer interactions. In applying the FLT to a system whose chemical
composition changes, care must be taken in relating the internal energy (or
enthalpy) reference states for each species or groups of species. When
chemical reactions occur, it is not possible to choose independently the
reference states of the involved chemical substances.
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Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Energy and enthalpy balance
Application of FLT to combustion
Consider a system of mass m which changes its composition from reactants
(R) to products (P) by a chemical reaction.
Products
Reactants
ti
Fluid machinery
tf
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Prof. D. Misul
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3
Politecnico di Torino
Dipartimento Energia
Energy and enthalpy balance
Application of FLT to combustion
Applying the first law to the system between its reactants, R (or initial, i) and
products, P (or final, f) states gives
Q + L e = U +  Ek + Eg  E
The overall energy change is composed by macroscopic forms of energy
(kinetic, gravitational, centrifugal) and by internal energy, which depends on
temperature and chemical composition. We will suppose that change in
macroscopic forms of energy are negligible, therefore:
Q + Le = U = UP  t f  - UR  ti 
Recall that the internal energy can be splitted into a chemical and a thermal
component:
U = Uch + Uth
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Prof. D. Misul
7
Politecnico di Torino
Dipartimento Energia
Energy and enthalpy balance
Sample processes
Let’s now consider a series of special processes. Let’s start with a constant
volume process where the initial and final temperature is the same (T’):
Le = 0
Q = UP  T  - UR  T  =  U V,T
Combustion processes are exotermic. Therefore in order to keep the final
temperature equal to the initial one in a constant volume process, heat must
be substracted:
Q =   U V,T  < 0
Let’s now consider a constant pressure process where the initial and final
temperature is the same (T’):
Q - p  VP - VR  = UP  T  - UR  T 
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Prof. D. Misul
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4
Politecnico di Torino
Dipartimento Energia
Energy and enthalpy balance
Sample processes and heat of reaction
The previous equation can be rearranged as:
Q = UP  T  + pVP - UR  T  + pVR 
Therefore, enthalpies can be introduced:
Q = HP  T  - HR  T 
Again, since combustion processes are exotermic, heat must be
substracted:
Q =  H p,T < 0
The quantities -  U V,T and -  H p,T are called heat of reaction at constant
volume and pressure, respectively, and they depend on the temperature T’;
moreover, remember that the energy balance is written per mole of fuel.
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Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Energy and enthalpy balance
Internal energy and enthalpy plots
These processes can be displayed on the internal energy or enthalpy
versus temperature plots, respectively:
R
U
U0
P
P
-  U  V,T
-  H p,T
H0
-  U  V,T
-  H p,T
0
0
T0
Fluid machinery
R
H
T’
T
T0
10
T’
T
Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Energy and enthalpy balance
Internal energy and enthalpy plots
If the internal energy (or enthalpy) for the reactants is arbitrarily
assigned a value U0 (or H0 ) at some reference temperature T0,
then the value of -  U  V,T (or -  H p,T ) fixes the relationship
between U  T  (or H  T  ) for the products and the reactants.
Note that the slope of these lines increases with increasing
-  H p,T )
temperature; also, the magnitude of -  U  V,T (or
decreases with increasing temperature (cv or cp pattern).
It is also worthwhile recalling that:
 H p,T -  U V,T = p  VP - VR 
Therefore, if P and R are ideal gases:
 H p,T -  U V,T = R nP - nR  T
Fluid machinery
Prof. D. Misul
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11
Politecnico di Torino
Dipartimento Energia
Energy and enthalpy balance
Internal energy vs temperature plot
From the internal energy versus temperature plot it is also apparent that:
R
U
P
-  U  V,T
U0
-  U  V,T
0
T’
T0
T
-  U  V,T + UR  T  - UR  T0   = -  U  V,T + UP  T  - UP  T0  
0
T
-  U V,T = -  U  V,T - m   c v,P - c v,R  dT
0
Fluid machinery
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T0
Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Energy and enthalpy balance
Enthalpy vs temperature plot
Similarly from the enthalpy versus temperature plot:
H
R
P
-  H p,T
H0
-  H p,T
0
T’
T0
T
-  H p,T + HR  T   - HR  T0   = -  H p,T + HP  T  - HP  T0  
0
T


-  H p,T = -  H p,T - m  c p,P - c p,R dT
0
Fluid machinery
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T0
Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Energy and enthalpy balance
H2O effect
With an hydrocarbon fuel, one of the products, H2O, can be in gaseous or
liquid phase. Therefore, the internal energy (or enthalpy) in the constant
volume (or constant pressure) process will depend on the relative amount of
water in each phase.
R
R
H 2O
H 2O
U
H
vapour
vapour
P
P
-  U  V,T
-  H p,T
U0
A
-  U  V,T
0
Fluid machinery
T0
B
-  H p,T
0
H2O liquid
T’
H0
H2O liquid
T
14
T0
T’
Prof. D. Misul
T
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Politecnico di Torino
Dipartimento Energia
Energy and enthalpy balance
H2O effect
The highlighted differences can be explicated in the following way:
A =  U V,T,H Oliq -  U V,T,H O vap = mH2OuH2O,P
2
2
B =  H p,T,H Oliq -  H p,T,H Ovap = mH2OhH2O,P
2
2
Where mH2O is the mass of water in the products, and uH20,P (or hH20,P) are
the internal energy (or enthalpy) of vaporization of water at the temperature
and pressure of the products.
-  U  
= -  U  V,T 
+ mH2OuH2O,P
V,T H O liq


H2O vap
2
-  H  
= -  H  V,T 
+ mH2OhH2O,P
p,T H O liq

H2O vap

2
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Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Enthalpies of formation
Definition
For fuels where the exact composition is known, the internal energies or
enthalpies of the reactants and the products can be related through the
so-called enthalpies of formation of the reactants and products.
The enthalpies 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 (p=1 atm) at the given temperature.
Since thermodynamic calculations are made as a difference between an
initial and a final state, it is necessary to select a datum state (the most
common is p = 1 atm; T0 = 298.15 K) to which all other thermodynamic
states can be referred. Elements at their reference state (i.e., the stable
standard state of the elements) are arbitrarily assigned zero enthalpy at
datum temperature (e.g., for oxygen at 298.15 K the reference state is O2
gas, whose formation enthalpy is therefore zero).
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Prof. D. Misul
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8
Politecnico di Torino
Dipartimento Energia
Enthalpies of formation
Definition
Enthalpies of formation will be labeled as h sf , where the superscript s
denotes the thermodynamic standard state, the subscript f stands for
formation, and the “tilde” indicates that it is the enthalpy increase associated
with the reaction of forming one mole of the given compound
For a given reaction, the enthalpy of reactants and products at the
standard state relative to the enthalpy datum is then given by:
HRs =  ni his
HPs =  ni his
reactants
products
The enthalpy increase is then obtained from:
 H p,T = HPs - HRs
whereas the internal energy increase can be obtained with:
 U   =  H p,T - R nP - nR  T
V,T
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Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Enthalpies of formation

State (at 298.15 K and
1 atm)
O2
Gas
0
N2
Gas
0
H2
Gas
0
C
Gas
0
CO2
Gas
-393.52
H2O
Gas
-241.83
H2O
Liquid
-285.84
CO
Gas
-110.54
CH4
Gas
-74.87
C3H8
Gas
-103.85
CH3OH
Gas
-201.17
CH3OH
Liquid
-238.58
C8H18
Gas
-208.45
C8H18
Liquid
-249.35
18

l
o
m
k
J
M
Fluid machinery
sf
h
Δ
Typical values
Species

Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Example
Calculate the enthalpy of the products and reactants, and the enthalpy
increase and internal energy increase of the reaction, of a stoichiometric
mixture of methane and air at 298.15 K:
CH4 + 2O2 + 2 N2 = CO2 + 2H2 0 + 2 N2
 = 3.773
 Rs =  -74.87 + 2  0 + 7.546  0 MJ kmolCH = -74.87 MJ kmolCH
H
4
4
H20 liquid
 Ps = -393.52 + 2   -285.84  + 7.546  0  MJ kmolCH = -965.20 MJ kmolCH
H
4
4
 H  = H - H = -965.20 -  -74.87  MJ kmol = -890.33 MJ kmol
 U  =  H  - R n - n  T

= -885.4 MJ kmol
  8.546 -10.546   298.15  MJ kmol
 U  = -890.33 - 8314.3
10

p,T
s
P
s
R
P
p,T
V,T
CH4
R
CH4
6
V,T
CH4
Fluid machinery
CH4
Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Example
H20 vapour:
 Ps = -393.52 + 2   -241.83  + 7.546  0  MJ kmolCH = -877.18 MJ kmolCH
H
4
4
 H  = H - H = -877.18 -  -74.87  MJ kmol = -802.31MJ kmol
 U  =  H  - R n - n  T

= -802.31MJ kmol
 10.546 -10.546   298.15  MJ kmol
 U  = -802.31- 8314.3
10

p,T
V,T
V,T
s
P
p,T
s
R
CH4
P
CH4
R
CH4
6
CH4
All quantities were indicated with the “tilde” so as to highlight that the
considered combustion reaction involves one mole of fuel, i.e. the
calculated enthalpy and internal energy increases correspond to the
heats of reaction at constant pressure and volume, respectively.
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Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Heating values
Definition
For fuels whose exact composition is not known, the internal energies
or enthalpies of the reactants and products cannot be determined from
the enthalpies of formation. Therefore, the so-called heating value (or
calorific value) of the fuel is measured directly.
The heating value H of a fuel is the heat of reaction required at constant
pressure or at constant volume at a standard temperature (usually 298.15
K) for the complete combustion of a unit mass of fuel.
Complete combustion means that all carbon is converted to CO2, all
hydrogen is converted to H2O and any sulfur present is converted to SO2.
It is unnecessary to specify how much oxidant was mixed with the fuel,
though this must exceed the stoichiometric requirement. It is immaterial
whether the oxidant is air or oxygen.
 U 
Fluid machinery
V,T
0
HV  = =T0
mmole,f
Heating value at constant volume:
 U V,T
0
mf
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Politecnico di Torino
Dipartimento Energia
Heating values
Definition
 

H
 H p,T0
p,T0
Heating value at constant pressure: Hp  = =T0
mmole,f
mf
mmole,f is the mass of a mole of fuel, mf is the mass of fuel involved in the
combustion. If P and R are ideal gases:
 H p,T -  U V,T
0
0
mf
HV T
0
= HP T +
0
R
mf
=
R
mf
nP - nR  T0 =
HV T
nP - nR  T0
0
m
RP - RR  T0
mf
= HP T +
0
m
RP - RR  T0
mf
where m is the mass (of reactants or products) involved in the combustion.
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Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Heating values
H2O effect
For fuels containing hydrogen, the phase of H2O in the products (liquid or
gaseous phase) affects the value of the heat of reactions. The term higher
heating value or gross heating value (HHV or HHp) is used when the H2O
formed is all condensed to the liquid phase. The term lower heating value or
net heating value (HLV or HLp) is used when the H2O formed is all in the
vapour phase.
Constant volume heating value:
-  U 

V,T0 

H2O liq
mf
HHV T
0
=
 -  U 

V,T0 

H2O vap
mf
= HLV T +
mH2O
0
Fluid machinery
mf
+
mH2O
mf
uH2O,P
uH2O,P
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Politecnico di Torino
Dipartimento Energia
Heating values
H2O effect
Constant pressure heating value:
 -  H  
p,T0 
H O liq

2
mf
=
 -  H  
p,T0 
H O vap

2
mf
+
mH2O
mf
hH2O,P
mH O
HHp  = HLp  + 2 hH2O,P
T0
T0
mf
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Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Heating values
Continuous flow calorimeter
Heating values of fuels can be measured in calorimeters according to
specifically defined standard procedures.
For gaseous fuels, the continuous-flow atmospheric pressure
calorimeter is used.
The entering fuel is saturated with water vapour and mixed with sufficient
saturated air for complete combustion at the reference temperature T0.
The mixture is burned in a burner and the combustion products are cooled
with water-cooled metal tube coils down to a value close to the inlet
temperature.
The heat transferred to the cooling water is calculated from the measured
water flow rate and the water temperature rise. The H determined by this
process is therefore the higher heating value at constant pressure HHp.
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Prof. D. Misul
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Politecnico di Torino
Dipartimento Energia
Heating values
Bomb calorimeter
For liquid and solid fuels, it is more effective to burn the fuel with oxygen
under pressure at constant volume in a bomb calorimeter.
A sample of fuel is placed in a bomb apparatus, which is a stainless steel
container immersed in cooling water at the standard temperature T0.
Sufficient water is placed in the bomb to ensure that the water produced in
the combustion process will condense.
Oxygen at a pressure of about 25-30 atm is admitted to the bomb, so as to
guarantee the rapid and complete combustion of the fuel sample. The fuel
is ignited by means of an electric current.
The T rise of both the bomb and the cooling water is hence measured. The
heating value determined by this process is the higher heating value at
constant volume HHV.
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Politecnico di Torino
Dipartimento Energia
Heating values
JANAF tables
HHp [MJ/kg]
HLp [MJ/kg]
stech
Gasoline (l)
47.3
44
14.6
2.83
Light diesel oil (l)
44.8
42.5
14.5
2.74
Heavy diesel oil (l)
43.8
41.4
14.4
2.76
50
45
14.5
2.9
55.5
50
17.17
2.75
Fuel
Natural gas (g)
Methane (CH4) (g)
HLp/(1+stech) [MJ/kg]
Propane (C3H8) (g)
50.4
46.4
15.67
2.75
Isooctane (C8H18) (l)
47.8
44.3
15.13
2.75
Cetane (C16H34) (l)
47.3
44
14.82
2.78
Benzene (C6H6) (l)
41.9
40.2
13.27
2.82
Methanol (CH3OH) (l)
22.7
20.0
6.47
2.68
Ethanol (C2H5OH)
29.7
26.9
9.00
2.69
Carbon (s)
33.8
33.8
11.51
2.70
Carbon monoxide (CO) (g)
10.1
10.1
2.467
2.91
Hydrogen (H2) (g)
142
120
34.3
3.40
The difference between Hp and HV is usually small. The heating value at constant pressure is the
most commonly used. Mostly often the qualification “at constant pressure” is omitted.
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Politecnico di Torino
Dipartimento Energia
Heating values
Graphical meaning
Recalling the heating values definition, they can be easily highlighted on
the specific internal energy or specific enthalpy plots:
R
U
R
h
P
P
HV T
Hp 
T
m mf
m mf
HV T
Hp 
TO
O
m mf
Fluid machinery
m mf
T0
T’
T
T0
28
T’
T
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Politecnico di Torino
Dipartimento Energia
Heating values
Temperature effect
The effect of temperaure on H can be taken into account as shown here:
-  U  V,T
mf
=
-  U  V,T
0
mf
HV T = HV T
0
-
m
mf
-
m
mf
T
  Cv,P - Cv,R  dT
T0
T
  Cv,P - Cv,R  dT
T0
T


-  H p,T = -  H p,T - m  Cp,P - Cp,R dT
0
m
Hp  = Hp  T
T0 m
f
Fluid machinery
T0
T
  Cp,P - Cp,R  dT
T0
Prof. D. Misul
29
29
Politecnico di Torino
Dipartimento Energia
Example
Calculate the heating values and the fuel energy factor HLp/(m/mf) for the
stoichiometric combustion of methane at T0 = 298.15 K:
CH4 + 2O2 + 2 N2 = CO2 + 2H2 0 + 2 N2
 = 3.773
 H 
 H 
p,T
= -890.33 MJ kmolCH4
p,T0
 -890.33 
HHp  = =  MJ kg = 55.51MJ kg
T0
mmole,f
 16.04 
mH2O =  2  18.02 kg/kmolCH4 = 36.04 kg/kmolCH4
hH2O,P = 2442 kJ/kg  at 25°C 
mH O
36.04


HLp  = HHp  - 2 hH2O,P = 55.512.442 MJ kg = 50.02 MJ kg
T0
T0
mf
16.04


HHV T
0
= HHp 
T0
+
R
mf
nP - nR  T0
8314.3

= 55.51+
 8.546 -10.546   298.15  MJ kg = 55.20 MJ kg
6
16.04
10



Fluid machinery
30
Prof. D. Misul
30
15
Politecnico di Torino
Dipartimento Energia
Example
HLV T
0
= HLp 
T0
+
R
mf
nP - nR  T0
8314.3

= 50.02 +
10.546 -10.546   298.15  MJ kg = 50.02 MJ kg
16.04  106


m = mf + mair = 16.04 + 2  32 + 7.546  28.01 kg/kmolCH4 = 291.40 kg/kmolCH4
mf = 16.04 kg/kmolCH4
m mf =
HLp 
T0
m mf
mf + mair
m
291.40
= 1+ air = 1+  = 1+  st =
= 18.167
mf
mf
16.04
=
HLp 
T0
1+  st

50.02
MJ kg = 2.75 MJ kg
18.167
Fluid machinery
Prof. D. Misul
31
31
Politecnico di Torino
Dipartimento Energia
Adiabatic combustion processes
Constant volume combustion
ti
Ti
reactants (R):
mair (air)
mf (fuel)
mr (residual gas)
products (P)
tf
mR = mair + mf + mr = mP = m
Q + L e = UP  t f  - UR  ti  = 0
UP  t f  = UR  ti 
mPUP  t f  = mRUR  ti 
UP  t f  = UR  ti 
Fluid machinery
32
Prof. D. Misul
32
16
Politecnico di Torino
Dipartimento Energia
Adiabatic combustion processes
Constant volume combustion
UP  Tf  - UP  Ti  = UR  Ti  - UP  Ti 
R
U
Tf
 Cv,P dT =
P
HLV T
i
m mf
Ti
=
Ui = Uf
mair
mf
=
HLV T
i
1+  +  
 =
mr
mf
Assuming C’v to be the average
value of Cv,P in the interval [Ti,Tf]:
HLV T
i
HLV T
m mf
i
Ti
m mf
T
Tf
= Cv  Tf - Ti 
Tf = Ti +
Fluid machinery
1 HLV Ti
Cv m mf
Prof. D. Misul
33
33
Politecnico di Torino
Dipartimento Energia
Adiabatic combustion processes
Constant pressure combustion
F
F
ti
Ti
reactants (R):
mair (air)
mf (fuel)
mr (residual gas)
products (P)
tf
mR = mair + mf + mr = mP = m
Q - p  VP  t f  - VR  ti   = UP  t f  - UR  ti 
HP  t f  = HR  ti   hP  t f  = hR  ti 
Fluid machinery
34
Prof. D. Misul
34
17
Politecnico di Torino
Dipartimento Energia
Adiabatic combustion processes
Constant pressure combustion
hP  Tf  - hP  Ti  = hR  Ti  - hP  Ti 
R
h
Tf
 Cp,P dT =
P
Ti
=
hi = hf
HLp 
Ti
m mf
mair
mf
=
HLp 
Ti
1+  +  
 =
mr
mf
Assuming C’p to be the average
value of Cp,P in the interval [Ti,Tf]:
HLp 
Ti
m mf
HLp 
Ti
Ti
m mf
T
Tf
Tf = Ti +
Fluid machinery
= Cp  Tf - Ti 


1 HLp  Ti
Cp m mf
Prof. D. Misul
35
35
Politecnico di Torino
Dipartimento Energia
Steady state combustion processes
Gas turbine burner
 f ; Tf
m
G
 air ; T2
m
 + L i =  m
 jh j
Q
j
Fluid machinery
 air + m
 f ; T3
m
 j > 0 outlet ports
m

 m j < 0 inlet ports
36
Prof. D. Misul
36
18
Politecnico di Torino
Dipartimento Energia
Steady state combustion processes
Gas turbine burner
 f ; Tf
m
 = m
 air + m
 f  hP  T3  - m
 air hair  T2  - m
 f hf  Tf 
Q
 = m
 air + m
 f  hP  T3  - m
 air hair  T2  - m
 f hf  Tf 
Q
 f hf  T2  + m
 f hf  T2 
-m
 = mh
 P  T3  + m
 f hf  T2  - hf  Tf  
Q
 air hair  T2  - m
 f hf  T2 
-m
 air ; T2
m
 =m
 air + m
 f ; T3
m
 f hf  T2  + m
 air hair  T2  =  m
 f +m
 air  hR  T2  = mh
 R  T2 
Considering that: m
 = mh
 P  T3  - mh
 R  T2  + m
 f hf  T2  - hf  Tf  
Q
Fluid machinery
Prof. D. Misul
37
37
Politecnico di Torino
Dipartimento Energia
Steady state combustion processes
 m
 f
Q
Gas turbine burner
h  T  - hf  Tf   = hP  T3  - hR  T2  
 m
  f 2
m
= hP  T3  - hR  T2  + hP  T2  - hP  T2  
R
h

P
 cp,P dT -
T2
HLp 
T2
=
 m
 f
m
Fluid machinery
T3
T2
 air
m
 f
m
HLp 
T2
 m
 f
m
1+  =

m
 f
m
T
38
Prof. D. Misul
38
19
Politecnico di Torino
Dipartimento Energia
Steady state combustion processes
Gas turbine burner
Assuming C’p to be the average value of Cp,P
in the interval [Ti,Tf]:
R
h
HLp 
T2
1+ 
P
HLp 
T2
= Cp  T3 - T2  -
b
 m
 f
m
T2
Fluid machinery
1
+
h  T  - hf  Tf  
 1+   f 2
m
HLp 
T2
1+ 
= cp  T3 - T2 
Burner efficiency
T
T3

Q
Prof. D. Misul
39
39
Politecnico di Torino
Dipartimento Energia
Steady state combustion processes
Steam generator
 v ; TO
m
G
 a ; Tair,in
m
 f ; Tf,in
m
 v ; TM
m
 =m
 air + m
 f ; Texh
m
 > 0 outlet ports
m
 + L i =  m
 jh j  j
Q
j
Fluid machinery
 j < 0 inlet ports
 m
40
Prof. D. Misul
40
20
Politecnico di Torino
Dipartimento Energia
Steady state combustion processes
Steam generator
 =m
 v hv,O - m
 v hv,M +  m
 air + m
 f  hP  Texh  - m
 air hair  Tair,in  - m
 f hf  Tf,in 
Q
 =m
 v hv,O - m
 v hv,M
Q
 v ; TO
m
 air + m
 f  hP  Texh  - m
 air hair  Tair,in 
+ m
 f hf  Tf,in  + m
 f hf  Tair,in  - m
 f hf  Tair,in 
-m
 =m
 v hv,O - m
 v hv,M
Q
 a ; Tair,in
m
 f ; Tf,in
m
 air + m
 f  hP  Texh  -  m
 air + m
 f  hR  Tair,in 
+ m
 f hf  Tf,in  + m
 f hf  Tair,in 
-m
Fluid machinery
 =m
 air + m
 f
m
 v ; TM
m
41
Texh
Prof. D. Misul
41
Politecnico di Torino
Dipartimento Energia
Steady state combustion processes
Steam generator
 =m
 v hv,O - m
 v hv,M +  m
 air + m
 f  hP  Texh  -  m
 air + m
 f  hR  Tair,in 
Q
 air + m
 f  hP  Tair,in  -  m
 air + m
 f  hP  Tair,in  - m
 f hf  Tf,in  - hf  Tair,in  
 m


 =m
 v hv,O - hv,M  +  m
 air + m
 f  hP  Texh  - hP  Tair,in  
Q


 air + m
 f  hR  Tair,in  - hP  Tair,in   - m
 

- m

 f hf  Tf,in  - hf  Tair,in  
 =m
 v hv,O - hv,M  +  m
 air + m
 f  hP  Texh  - hP  Tair,in  
Q


 air + m
 f  hR  Tair,in  - hP  Tair,in   - m
 

- m

 f hf  Tf,in  - hf  Tair,in  
 =m
 v hv,O - hv,M  +  m
 air + m
 f  hP  Texh  - hP  Tair,in  
Q



 air + m
 f 
- m
HLp 
Tair,in
 m
 air + m
 f

Fluid machinery

 -m
 h T - h T

 f  f  f  f,in  f  air,in  
m

42
Prof. D. Misul
42
21
Politecnico di Torino
Dipartimento Energia
Steady state combustion processes
Steam generator
 +m
 f HLp 
Q

T
air,in
 f hf  Tair,in  - hf  Tf,in   -  m
 air + m
 f  Cp  Texh - Tair,in  =
-m


 v ; TO
m
 v hv,O - hv,M 
m
 f HLp 
bm


Tair,in
 a ; Tair,in
m

= mv hv,O - hv,M  m
 f ; Tf,in
Fluid machinery
 =m
 air + m
 f
m
 v ; TM
m
Steam Generator efficiency
Texh
Prof. D. Misul
43
43
Politecnico di Torino
Dipartimento Energia
Combustion in IC engines
Power balance
 - L i =  m
 air + m
 f  hP  Texh  - m
 air hair  Tair,in  - m
 f hf  Tf,in 
Q
 f ; Tf,in
m
 - L i =  m
 air + m
 f  hP  Texh 
Q
 air ; Tair,in
m
 air hair  Tair,in  - m
 f hf  Tf,in 
-m
 f hf  Tair,in  - m
 f hf  Tair,in 
+m
 =m
 air + m
 f
m
Texh
 - L i =  m
 air + m
 f  hP  Texh 
Q

Q
 air + m
 f  hR  Tair,in 
- m
 f hf  Tair,in  - hf  Tf,in  
+m


Fluid machinery
i
L
44
Prof. D. Misul
44
22
Politecnico di Torino
Dipartimento Energia
Combustion in IC engines
Power balance
 - L i =  m
 air + m
 f  hP  Texh  +  m
 air + m
 f  hP  Tair,in  -  m
 air + m
 f  hP  Tair,in 
Q
 air + m
 f  hR  Tair,in  + m
 f hf  Tair,in  - hf  Tf,in  
- m


 - L i =  m
 air + m
 f  hP  Texh  -  m
 air + m
 f  hP  Tair,in 
Q
 HLp 

 Tair,in
 air + m
 f 
- m
 m
 air + m
 f m
 f


Q
 air + m
 f
m
Fluid machinery
-

 +m
 f hf  Tair,in  - hf  Tf,in  




 HLp 

 Tair,in
= hP  Texh  - hP  Tair,in  - 
 m
 air + m
 f
 +m
 f m
 f
m
 air
 f
m
h T
+
-h T 
mair + m
 f  f  air,in  f  f,in  
i
L
45




Prof. D. Misul
45
Politecnico di Torino
Dipartimento Energia
Combustion in IC engines
Power balance
 HLp 
 Tair,in
 
 m
 air + m
 f m
 f


i

L
Q
 = h T  - h T
+
P
exh
P  air,in  
 air + m
 f m
 air + m
 f
m

+
 HLp 
 Tair,in
 
 m
 air + m
 f m
 f

Fluid machinery
 f
m
h T
-h T 
 air + m
 f  f  air,in  f  f,in  
m

i

L
Q
  C T - T
+
p  exh
air,in  
 air + m
 f m
 air + m
 f
m

46
Prof. D. Misul
46
23
Politecnico di Torino
Dipartimento Energia
Combustion in IC engines
Power balance
 HLp 
 Tair,in
 
 m
 +m
 f m
 f
 air
h

i

L
Q
  C T - T
+


p
exh
air,in

 air + m
 f m
 air + m
 f
m

R
P
HLp 
Tair,in
 air + m
 f m
 f
m
T
Tair,in Texh
Fluid machinery
Prof. D. Misul
47
47
Politecnico di Torino
Dipartimento Energia
Combustion in IC engines
Premixed charge engine
IVC (Inlet Valve Closing):
mR = mair + mf + mr = m
TIVC
EVO (Exhaust Valve Opening):
mP = mR = m
TEVO
Q - L = mUP  TEVO  - mUR  TIVC 
Q - L = mUP  TEVO  - mUR  TIVC  + mUP  TIVC  - mUP  TIVC 
 HLV T
IVC
= UP  TEVO  - 
m m
 m mf
Q L
-
Fluid machinery
48

 - UP  TIVC 

Prof. D. Misul
48
24
Politecnico di Torino
Dipartimento Energia
Combustion in IC engines
Premixed charge engine
 HLV T
IVC
= UP  TEVO  - 
m m
 m mf
Q L
-
R
U
 HLV T
IVC

 m mf
P

 - UP  TIVC 


Q L
 = Cv  TEVO - TIVC  - +
m m

HLV T
IVC
m mf
TIVC TEVO
T
Fluid machinery
49
Prof. D. Misul
49
Politecnico di Torino
Dipartimento Energia
Chemical equilibrium and dissociation
The working fluids in internal combustion engines and gas turbines are
mixture of gases. Chemical reactions may be:
• so slow that they have a negligible effect on the mixture composistion
(i.e., the mixture composition is essentially “frozen”);
• so rapid that the mixture state changes and the composition remains in
chemical equilibrium;
• one of the rate-controlling processes that determine how the composition
of the mixture changes with time.
In this context, the mixture composition of the reactants will be considered
to be “frozen”, whereas the burned gases produced by the combustion of
fuel and air will be regarded as a chemical equilibrium. This also means
that, at high temperatures (T > 1850 K), some molecules of burned gas
(namely, CO2 and H2O) might dissociate.
CO2
1
CO + O2
2
Fluid machinery
 68000 kcal kmolCO2 H2 O
50
H2 + O  58000 kcal kmolCO2
Prof. D. Misul
50
25
Politecnico di Torino
Dipartimento Energia
Chemical equilibrium and dissociation
Premixed charge engine
R
U
 HLV T
IVC

 m mf

Q L
2
 = Cv  TEVO - TIVC  - + +Di  TEVO -1850 
m m

P
P
-
Q
m
L
HLV T
m
IVC
m mf
Di  TEVO -1850 
TEVO
TIVC
TEVO
T
1850 K
2
Fluid machinery
51
1850 K
Ing. D. Misul
51
Politecnico di Torino
Dipartimento Energia
Combustion with rich mixtures
For rich mixtures, the reactants cannot complete their oxidation due to
the lack of available oxygen. Thus:
  HLV T 
Q L
2

 = Cv  TEVO - TIVC  - + +Di  TEVO -1850 
IVC
U
R
 st  m mf 


m m
P
 HLV TIVC
 st m mf
TEVO
TIVC 1850 K
Fluid machinery
T
52
With reference to the premixed
charge engine and considering
dissociation, TEVO can be evaluated
as reported in the figure. We assume
the portion of fuel corresponding to
the available oxygen alone to take
part to the reactions.
Prof. D. Misul
52
26