Corso di Laurea Magistrale in Ingegneria Chimica/
Ingegneria Energetica
Formazione e Controllo di Inquinanti nella
Combustione
Impianti di trattamento effluenti
Combustion Theory
2: premixed and diffusion flames
Prof. L.Tognotti
Dipartimento di Ingegneria Civile e Industriale
Anno Accademico 2014-2015
Introduction
Basic Flame Types:
•
Premixed flames: fuel and oxidizer are homogeneously mixed before reaction occurs.
Laminar and turbulent premixed flames
•
Non premixed flames: fuel and oxidizer come into contact during combustion process.
Laminar and turbulent diffusion flames
Combustion Theory
2
1. Laminar premixed flames
1. Laminar premixed flames
A premixed flame is a self-sustaining propagation of a localized combustion zone
at subsonic velocities (deflagration regime)
The classical device to generate a laminar premixed flame is the Bunsen burner:
Typical Bunsen burner flame
Combustion Theory
4
Example: Typical Bunsen-burner CH4/Air flame
Outer diffusion flame
Outer cone (luminous zone):
reaction and heat transfer
Preheating region
containing fuel and air
Inner cone (dark zone):
fuel rich flame
Typical Bunsen-burner flame is a dual flame:
•
a fuel-rich premixed inner flame
•
a diffusion outer flame: CO and H2 from inner flame encounter ambient air
Combustion Theory
5
•
Experimental evidence for the presence of a cool inner preheating region
A wire to reveal the presence of a cool preheating region containing unburned CH4 and O2
A match in preheating region does not ignite until it is moved to the inner cone
Combustion Theory
6
• Basic features of laminar premixed flames
Fuel/Air Ratio
Flame colour,
i.e. colour of the
outer cone
Fuel lean
Stochiometric
Deep Violet
Blue
due to large
concentrations
of excited CH
radicals
Fuel rich
Very fuel rich
Green
Yellow
due to large
concentrations
of C2 species
due to carbon
particles
High-T burned
gases usually
show a reddish
glow due to
radiation from
CO2 and H2O
Flame characteristics for hydrocarbon-air stochiometric mixtures
•
The flame is ~1 mm thick and moves at ~0.5 m/s
•
Pressure drop through the flame is very small: ~1 Pa
•
Temperature in reaction zone is ~2200-2600 K
•
Density ratio of reactants to products is ~7
•
2 sub regions exist: a fast chemistry zone, dominated by bimolecular
reactions, and a slow chemistry zone (CO+OH=CO2+H)
Combustion Theory
7
• Kinematic balance for a steady oblique flame
Thermal expansion through the flame front
•
Normal component of velocity vector
  v n u
•
   v n b
v n ,b  v n ,u
u
b
Tangential component of velocity vector
v t ,u  v t ,b
•
At steady-state the burning velocity equals
the flow velocity of the unburnt mixture
normal to the flame front
S L , u  v n , u  v u sin 
Combustion Theory
8
• Laminar flame theory: What do we particularly feel
interested in?
Laminar burning velocity, SL: It is the velocity with which the flame front
propagates normal to itself into the unburned mixture
Steady combustion wave propagation
Various flame theories attempt to predict the laminar flame propagation from physical and
chemical properties:
•
Thermal theory (Mallard and Le Chatelier; Zeldovich, Frank-Kamenetsky and
Semenov): the mixture is heated by conduction to the point where the reaction is
sufficiently rapid to become self-propagating
•
Diffusion theory (Tanford and Pease): diffusion of active species, such as atoms and
radicals, from the reaction zone into the unreacted mixture causes reaction to occur
REALITY: Diffusion Of Heat And Active Radicals
Combustion Theory
9
• Thermal theory of Mallard and Le Chatelier:
The flame consists of two zones:
•
Pre-heat zone: the unburned gases are
heated by conduction and reach ignition
•
Reaction zone: chemical enthalpy is
converted into sensible enthalpy
Energy balance on preheat zone:
m c p T i  Tu   
Tb  Ti 
m   u S L
r
Laminar flame-front thickness:
 r  S L r  S L
1
w is a mean reaction rate, evaluated at Ti
w
Laminar flame speed:
SL 
 

 c
 u p
 T  T 
i
 b
w 
 T  T 
u
 i

T b  T i 
w
Ti  T u 
Combustion Theory
10
Example: Evaluate SL for a n-th order homogeneous chemical reaction:
The reaction rate for species i (reactant) is ginen by:
w
dC i
dt
dX
 kC i
n
 kX i p
i
dt
n
or, in terms of molar fractions:
being
n 1
Ci  X i
p
R T
The laminar flame speed dependence on pressure is then:
SL 
1

p
n 1

p
n2
u
•
For 2-nd order reactions, laminar flame speed is not affected by pressure
•
Most of elementary reactions are second order reactions
Combustion Theory
11
• Comprehensive theory of Zeldovich, Frank-Kamenetsky
and Semenov
This theory is based on Mallard and Le Chatelier’s idea but takes into account:
•
Species conservation
•
Energy equation
Basic assumptions of the theory
•
1-D and steady flame
•
The pressure is constant
•
Specific heat and thermal conductivity are constant
•
•
Unity lewis number Le 
i
c p Di

thermal diffusivit y
mass diffusivit y
Lean-fuel conditions and first order reaction rate
w F  AT
•


Species
Lei
H2
0.3
OH
0.7
H2O
0.9
CH4
1
O2
1.1
CO2
1.4
E 

exp  
 F  Y F
RT


Ti is replaced with Tb in the estimation of reaction rates
Combustion Theory
12
Species and energy conservation
T  Tb 

Y F  Y F ,b 

x0
x  
 d YF
2
uSL
dY F
dx
c p dx
uSL
dT
 d T
x
dx

2
2

c p dx
2

 wF
wF Qr
cp
What do we get?: Laminar flame speed
SL 
2  A  Tu

 u c p  Tb
  RT b2

 E

 exp   E / RT b 

Tb  Tu 2

2
H2 is characterized by the maximum flame speed:
•
•
Species
Flame speed (cm/s)
CO
29
CH4
43
H2 diffusivity is much greater than that of
C2H6
44
hydrocarbon fuels.
C4H10
45
LeH2<<LeCH4
C3H8
46
H2 kinetics is very fast compared to that of
C6H6
48
hydrocarbon fuels which includes CO oxidation step
C2H2
144
H2
170
(slowest step in fuel oxidation)
Combustion Theory
13
• Factors influencing flame velocity and thickness
Effect of Equivalence Ratio
Flame speed peaks occur at stochiometric or
slightly fuel-rich mixtures
(highest burned gases temperatures)
SL 
  w Tb 
Effect of Fuel Molecular Structure
Flame speed is proportional to S 
L
w

and, thus, it depends on Mw,:   f M w , F
Combustion Theory
1
14

Factors influencing flame velocity and thickness
Effect of temperature and pressure
SL
Laminar flame speed for stochiometric methane-air mixtures as a function of pressure
and reactants’ temperature
Laminar flame speed correlation for stochiometric methane-air mixtures
S L cm / s   10  3 . 71  10
4
T u  K  2  43  p  atm  0 .5
Combustion Theory
15
Turbulent flames
•
Most of combustion devices operate in turbulent
flow regime, i.e. internal combustion or aircraft
engines, industrial burners and furnaces. Laminar
combustion applications are almost limited to
candles, lighters and some domestic furnaces.
Turbulence increases the mixing processes thus
enhancing combustion.
•
Also combustion influences turbulence. Heat
release due to combustion causes very strong flow
accelerations through the flame front (flamegenerated turbulence). Moreover, huge changes in
kinematic viscosity associated with temperature
changes may damp turbulence leading to flow relaminarization
Combustion Theory
16
Turbulence
Turbulent shear flows
• Fundamental aspects of turbulence
Turbulence is the most complex phenomena in non reacting fluid mechanics. Various time
and length scales are involved and the structure and description of turbulence remain an
open question
Re
Streamlines at a cross-section through pipe flow for three different Reynolds numbers
The flow behaves chaotic in an ”eddy-like” pattern. With increasing Reynolds number the range
of scales present in the flow also increases. Since the macro-structures are confined by the
geometry of the flow, the broadening of the scales can only be achieved by introducing smaller
scales.
Combustion Theory
19
• Phenomenological description of turbulence
Energy cascade theory (Rischardson, 1922)
1. Turbulence is organised as an hierarchy of eddies of various scales.
2. The biggest eddies, which are anisotropic and have the size of the flow geometry,
break up in smaller eddies which on their turn break up in even smaller eddies. Kinetic
energy is transferred from larger to smaller eddies, without any dissipation
3. This process continues until viscous forces can no longer be neglected. At the smallest
scales the incoming energy is dissipated into heat.
Kolmogorov (1941) hypothesis:
1. During the cascade process the anisotropy is gradually lost and from a certain eddy
size the scales are homogenous and isotropic. So, a range of scales exist where the
flow is locally homogeneous and isotropic. This regime is universal, independent of
the type of flow, and determined by only two parameters, i.e. the energy dissipation
rate and the coefficient of viscosity.
1
  4
   3/4
  Re
 
  k  

  1 / 4
  

k  

Combustion Theory
uk
'
3
k




k
1/ 3

4/3
1
20
• Phenomenological description of turbulence
•
Energy dissipation may be defined as
the ration of turbulent kinetic energy
(u’2) and the characteristic energy
transfer time in the larger eddies (l/u’):
 
k

tL
u
'2
u
•

l
u
'3
l
'
The macroscopic Reynolds number is:
'
Re l 
ul

.
•
The relation between large and small scales:
l
k
 Re l
3
u
4
uk
 Re l
1
4
l
k
1
 Re l 2
With increasing Reynolds number, turbulence develops an even finer structure, which is very
difficult to model.
Combustion Theory
21
• Turbulence effect on transport processes
1. Turbulent diffusion (Taylor diffusion): as a consequence of the energy transfer from
larger to smaller scales, scalar quantities gradients (temperature, species
concentration) are reduced from a macro to a micro scale
2. Molecular diffusion: fluid volumes deformation due to turbulent whirls leads to a
strong increase of contact surface area between regions of fluid with different
properties, thus enhancing mixing.
Deformation of a fluid element subject
to turbulent scales (a) larger and (b)
smaller than characteristic element size
Combustion Theory
22
• Turbulence/Combustion interactions
 Combustion enhancement
Turbulence enhances mixing processes and combustion rate, leading to an
increase of flame front area per unit cross sectional area. Typical turbulent
flame speed are 5-10 m/s (laminar flame speed ranges between 0.2-2 m/s)
 Re-laminarization
Kinematic viscosity of air increases roughly as T1.7. For a flame with
temperature ratio Tb/Tu=8 the Reynolds number is about 40 times smaller in
burnt than in fresh gases. Flow may become laminar after ignition
 Flame-generated turbulence:
The flow acceleration due to heat release through the flame front may be
significant. For typical hydrocarbon flames, the speed difference through the
flame front is of order of 4 m/s (considering Tb/Tu=8 and SL=0.5).
vb  S L
Tu
Tb
Combustion Theory
23
T
• Turbulent premixed flames combustion regimes: Borghi’s diagram
What do we need? Some definitions:
•
Damköhler number, Da: This number compares the turbulent time scale, τT, and the chemical
time scale, τT:
Da 
T
C

l /u
'
r / SL
In the limit of high Damköhler numbers (Da>>1), the chemical time is short compared to the
turbulent time, corresponding to a thin reaction zone distorted and convected by the flow field.
The internal structure of the flame is not affected by turbulence and may be described as a
laminar flame element, called flamelet, wrinkled and strained by the turbulence motions.
On the other hand, a low Damköhler numbers (Da=1) corresponds to a slow chemical reaction.
Reactants and products are mixed by turbulent motion before reaction and reaction rate is
dominated by chemistry. This represents the limit of a perfectly stirred reactor, in which flame
speed is independent of Reynolds number.
Most practical situations correspond to high to medium values of the Damköhler numbers
Combustion Theory
24
• Turbulent premixed flames combustion regimes: Borghi’s diagram
What do we need? Some definitions:
2.
Karlovitz number, Ka: This number refers to the smallest scales of the flow and compares the
chemical time scale to the Kolmogorov time, τk:
Ka 
1
Da  k


C
k

 / SL
 k / u  k 
'
Combustion Theory
1
  2


 
k  
25
Borghi diagram
u'
sl

Intesità della turbolenza
Damkohler =
Velocità di fiamma laminare
 T u rb o le n za
 C h im ico
lK=microscala della
turbolenza
Il n.o di Karlovitz è una misura
della curvatura e non stazionarietà
della superficie della fiamma
L
l
Combustion Theory
J.F.Griffiths, J.A.Barnard ‘Flame and Combustion’ Blackie Academic London 1994

Macroscala della turbolenza
spessore del fronte di fiamma
27
• Turbulent premixed flames combustion regimes
Wrinkled laminar-flame regime
Combustion Theory
•
Flame regimes:
•
(a) Wrinkled flames
•
(b) Thin reaction sheets
•
(c) Flamelets in eddies
•
(d) Distributed reactions.
28
1. Ka<1. The chemical time scale is shorter than any turbulent time scale and the flame
thickness is smaller than the smallest turbulent length scale, the Kolmogorov scale.
The flame front is thin, has an inner structure close to a laminar flame and is wrinkled
by turbulent motions. This regime is called “thin flame regime” or “flamelet regime”
and is divided in two sub-regions, depending on the ratio u’/SL
Wrinkled laminar-flame regime
•
Chemical reactions occur in thin
sheets (thinner than Kolmogorov
scale)
•
Damkohler number always greater
than 1. Fast chemistry
•
Flame becomes wrinkled increasing
flame surface
•
Flame speed 3~5 times laminar
burning velocity
Combustion Theory
29
2. Da>1 Ka>1. The turbulent integral time scale is still larger than chemical time scale
but Kolmogorov scales are smaller than the flame thickness and are able to modify
the inner structure of the flame. The structure of the flame is no longer laminar but it
is still wrinkled.
3. Da<1. Turbulent motions have shorter characteristic times than chemical reaction:
mixing is fast and the overall reaction rate is limited by chemistry. This regime is
known as perfectly stirred reactor regime
Combustion Theory
30
Thin reaction zone regime
Broken reaction zone regime
• Turbulent flame speed
Damkohler analysis (1940): ST as a function of turbulent Reynolds number
•
Re < 2300: flame speed is independent of Reynolds number
•
2300 < Re < 6000: turbulent flame speed is proportional to the square root of
Reynolds number. Turbulent eddies are much smaller than the flame thickness. Thus,
the increase of flame speed is mainly due to the enhancement of transport processes
within the combustion wave
•
Re > 6000: flame speed is proportional to the Reynolds number. Turbulent eddies are
much larger than the flame thickness and they distort the otherwise smooth laminar
flame front. The flame front surface per unit cross section increases and the flame
speed raises
Flame front images obtained by LIF at various turbulence
intensities. Numbers under the images indicate the
magnitude of the normalized turbulence intensity, i.e. u’/SL
Combustion Theory
35
• Turbulent flame speed calculation
1. 2300 < Re < 6000. The molecular transport processes are enhanced. SL
evaluation formula may be recalled:
ST 
T w
thus
ST

SL
T

if both the turbulent Prandtl number (Pr=νT/αT) and the molecular Prandtl
number (Pr=ν/α) are approximately equal to unity, then we obtain:
ST
SL

T

For pipe flow νT/ν=0.01Re:
ST
1
 0 . 1 Re
2
SL
2. Re > 6000. The inner structure of the flame is not altered (molecular transport
properties remain the same) but flame surface is wrinkled. The laminar flame
speed remain contsant and, thus, flame surface depends on flow velocity, u’:
ST  S L  u
'
Combustion Theory
36
• Turbulent flame speed calculation
3. Some correlations for turbulent flame speed in the limit of high Reynolds
number (Re>6000):
Schelkin Analysis: surface are distorted into cones
1
ST

 2u
 S L 1  

 SL
'




2



2
whose base area is proportional to the square of the
average eddy diameter, l.
1




S T  S L  0 . 5 1 




•
2
2 
 
 
 

1

 1  8u
2

S
L

'2
Clavin e Williams Analysis
Turbulent flame speed: state of the art
1. Definition of turbulent burning velocity is not uniform and universal
2. Experimental data scatter is significant between different experimental
rigs
3. Numerical simulation, i.e. flamelets models, turbulent burning velocity
closure, direct numerical simulation
Combustion Theory
37
Premixed flames ignition and stabilization
Two ways exist to cause ignition:
•
Self-ignition. Reactants’ temperature and pressure are such that combustion is selfsustained
•
Induced ignition. The reactants’ mixture is ignited locally by means of sparks, piloted
flames, hot wires
Ignition criteria:
•
Chemical-diffusive theory (Tanford and Pease). Ignition is caused by radicals
recirculation in the preheating region
•
Thermal theory. The heat provided to the fluid in the preheating region is enough to
initiate oxidation processes
 Ignition occurs when the heat generated in the reaction zone equals heat losses
to surrounding (Jost)
 Ignition occurs when the cooling time of reactant’s mixture, heated up to
adiabatic flame temperature, is greater than chemical reaction time (Zeldovich)
 Ignition occurs when a portion of fluid as thick as a laminar propagating flame is
heated up to adiabatic flame temperature (Lewis e Von Elbe)
Combustion Theory
38
Ignition process schematization with thermal ignition criterion
Combustion Theory
39
• Important design criteria
Avoid flash back and lift-off
•
Flashback: flame enters and propagates through the burner upstream without
quenching (Safety Hazard)
•
Lift-off: flame is not attached to burner tube but is stabilized at some distance from
the tube. Further increase in incoming flow velocity causes blowoff, i.e. flame
extinguishing.
Flames stabilization:
•
Laminar Flames: The fluid flow is adjusted in order to generate a region upon the
burner rim where the burning velocity equals the gas flow velocity
•
Turbulent Flames: Creation of a strong recirculation zone of hot products close to the
burner exit. This provides a constant ignition source for the incoming mixture and
generates a zone where local turbulent flame speed match local flow velocity (bluffbody flame holders, swirl or jet-induced recirculating flows, rapid increase in flow area
creating recirculating separated flow)
Combustion Theory
40
Bunsen flame stabilization at burner rim
Hypothesis: flow velocity equals flame velocity at location 2 and maximum SL is reached at location 3
•
If the flame is moved to location 3, SL>v and flame returns to location 2
•
If the flame is moved to location 1, v>SL and flame returns to location 2
Location 2 is then a stable operation point
Combustion Theory
41
Stability diagram for methane-air mixtures
Combustion Theory
42
Premixed vs diffusion flames
Laminar diffusion flames
A very difficult flame: the candle flame
•
The solid fuel is first heated by heat
transfer induced by combustion. The
liquid fuel reaches the flame by
capillarity along the wick and is
vaporized.
•
Fuel oxidation occurs in thin blue
layers (the color corresponds to the
spontaneous emission of the CH
radical)
•
Unburnt carbon particles are formed
because the fuel is in excess in the
reaction zone. The this soot is the
source of the yellow light emission.
•
Flow (entrainment of heavy cold
fresh air and evacuation of hot light
burnt gases) is induced by natural
convection
Combustion Theory
45
Example: gas lighter
Diffusion flames
•
In a diffusion flame combustion occurs at the interface between the fuel and
the oxidizer. Fuel burning rate depends more on reactants’ diffusion than on
chemical reaction rates.
•
It is more difficult to give a general treatment of diffusion flames, largely
because no simple, measurable parameter, analogous to laminar burning
velocity (SL) in premixed flames, can be defined.
Typical concentration profiles for diffusion flames:
•
Diffusion flames equivalence ratio varies
locally (Φ>1 and Φ<1 regions)
•
Real flame front is no zero-thickness
layer
Combustion Theory
47
Diffusion flame regimes
Flame height evaluation
•
Diffusion process is
rate-determining: the
reaction rate is directly
related to the amounts
of fuel and oxidizer
diffusing into the
reaction zone.
H
f

QF
 D
•
Laminar diffusion flames: flame height is proportional to fuel flow rate
•
Turbulent diffusion flames: flame height is independent of fuel flow rate. The fuel oxidized per unit
time increases (combustion enhancement due tu turbulent motion)
•
Transition region: ….
•
Very high fuel flow rates cause flame lift-off
Combustion Theory
48
Turbulent jet diffusion flame
Combustion Theory
50
Methane air diffusion flames at high pressure
Combustion Theory
51
Combustion Theory
52
http://sydney.edu.au/engineering/aeromech/thermofluids/database.htm
Combustion Theory
53
Single droplet combustion
Burnout time
Spray combustion