LAMINAR PREMIXED
FLAMES
OVERVIEW
Applications:
 Heating appliances
 Bunsen burners
 Burner for glass product manufacturing
Importance of studying laminar premixed flames:
 Some burners use this type of flames as shown by
examples above
 Prerequisite to the study of turbulent premixed
flames. Both have the same physical processes
and many turbulent flame theories are based on
underlying laminar flame structure.
PHYSICAL DESCRIPTION
Physical characteristics
 Figure 8.2 shows typical flame temperature profile,
mole fraction of reactants,R, and volumetric heat
release, Q
. 
 Velocity of reactants entering the flame, u = flame
propagation velocity, SL
 Products heated  product density (b) < reactant
density (u). Continuity requires that burned gas
velicity, b >= unburned gas vel., u
u u A = b b A
(8.1)
 For a typical hydrocarbon-air flame at Patm,
u/b  7  considerable acceleration of the
gas flow across the flame (b to u).
A flame consists of 2 zones:
 Preheat zone, where little heat is released
 Reaction zone, where the bulk of chemical energy
is released
Reaction zone consists of 2 regions:
 Thin region (less than a millimeter), where
reactions are very fast
 Wide region (several millimeters), where reactions
are slow
 In thin region (fast reaction zone), destruction of the fuel
molecules and creation of many intermediate species
occur. This region is dominated by bimolecular reactions to
produce CO.
 Wide zone (slow reaction zone) is dominated by radical
recombination reactions and final burnout of CO via CO +
OH  CO2 +H
Flame colours in fast-reaction zone:
 If air > stoichiometric proportions, excited CH radicals
result in blue radiation.
 If air < stoichiometric proportions, the zone appears bluegreen as a result of radiation from excited C2.
 In both flame regions, OH radicals contribute to
the visible radiation, and to a lesser degree due to
reaction CO + O  CO2 + h.
 If the flame is fuel-rich (much less air), soot will
form, with its consequent blackbody continuum
radiation. Although soot radiation has its maximum
intensity in the infrared (recall Wien’s law for
blackbody radiation), the spectral sensitivity of the
human eye causes us to see a bright yellow (near
white) to dull orange emission, depending on the
flame temperature
Figure 1. Spectrum of flame colours
Typical Laboratory Premixed Flames
 The typical Bunsen-burner flame is a dual flame: a
fuel rich premixed inner flame surrounded by a
diffusion flame. Figure 8.3 illustrates a Bunsen
burner.
 The diffusion flame results when CO and OH from
the rich inner flame encounter the ambient air.
 The shape of the flame is determined by the
combined effects of the velocity profile and heat
losses to the tube wall.
 For the flame to remain stationary,
SL = normal component of u = u sin (8.2).
Figure 8.3b illustrates vector diagram.
 Example 8.1. A premixed laminar flame is
stabilized in a one-dimensional gas flow where the
vertical velocity of the unburned mixture, u, varies
linearly with the horizontal coordinate, x, as shown
in the lower half of Fig. 8.6. Determine the flame
shape and the distribution of the local angle of the
flame surface from vertical. Assume the flame
speed SL is independent of position and equal to
0.4m/s (constant), a nominal value for a
stoichiometric methane-air flame.
 Solution
 From Fig. 8.7, we see that the local angle, , which
the flame sheet makes with a vertical plane is (Eqn.
8.2)
 = arc sin (SL/u), where, from Fig. 8.6,
u (mm/s) = 800 + (1200 – 800)/20 x (mm) (known).
u (mm/s) = 800 + 20x.
So,
 = arc sin (400/(800 + 20x (mm))
and has values ranging from 30o at x = 0 to19.5o at x
= 20 mm, as shown in the top part of Fig. 8.6.
 To calculate the flame position, we first obtain an
expression for the local slope of the flame sheet
(dz/dx) in the x-z plane, and then integrate this
expression with respect to x find z(x). From Fig.
8.7, we see that

dz
 tan   
dx

2
u
 x  S
2
L
S L2
1/ 2



,which, for u=A + Bx,
becomes
1/ 2

dz  A  Bx 
 
  1
dx  S L 


2
Integrating the above with A/SL = 2 and B/SL =
x
0.05 yields z(x)   dz  dx  (x 2  80x  1200) 0.5  x  1 


  dx 
40
0



-10 ln[(x2+80x+1200)1/2+(x+40)]
-203+10 ln(203+40)
 The flame position z(x) is plotted in upper half of
Fig. 8.6.

SIMPLIFIED ANALYSIS
Turns (2000) proposes simplified laminar flame
speed and thickness on one-dimensional flame.
Assumptions used:
 One-dimensional, constant-area, steady flow.
One-dimensional flat flame is shown in Figure 8.5.
 Kinetic and potential energies, viscous shear work,
and thermal radiation are all neglected.
 The small pressure difference across the flame is
neglected; thus, pressure is constant.
 The diffusion of heat and mass are governed by
Fourier's and Fick's laws respectively (laminar
flow).
 Binary diffusion is assumed.
– The Lewis number, Le, which expresses the
ratio of thermal diffusivity, , to mass diffusivity,

kis unity,
D, i.e.,
Le  
D C p D
k

u C p
 The Cp mixture ≠ f(temperature, composition).
This is equivalent to assuming that individual
species specific heats are all equal and
constant.
 Fuel and oxidizer form products in a single-step
exothermic reaction. Reaction is
1 kg fuel +  kg oxidiser  ( + 1)kg products
 The oxidizer is present in stoichiometric or
excess proportions; thus fuel is completely
consumed at the flame.
 For this simplified system, SL and  found are
1/ 2

(8.20)

m 
S L   2   1 F 
u 

 and
 2 u 
 




1
m
 F 


 or
2
 
SL
(8.21)
where is m  volumetric mass rate of fuel and  is
thermal diffusivity. Temperature profile is assumed
linear from Tu to Tb over the small distance, as
shown in Fig. 8.9.
F
FACTORS INFLUENCING FLAME
SPEED (SL) AND FLAME THICKNESS ()
1. Temperature (Tu and Tb)
 Temperature dependencies of SL and  can be
inferred from Eqns 8.20 and 8.21. Explicit
dependencies is proposed by Turns as follows
k (T )
 
(8.27)
0.75
1
 T Tu P
u C p (T )
 where  is thermal diffusivity, Tu is unburned gas
temperature, T  0.5 Tb  Tu  , Tb is burned
gas temperature.

n Tu

 / u
 F  .  Tb n P n1Tu exp( E A /( RuTb ) (8.28)
mF
P
where the exponent n is the overall reaction order,
Ru = universal gas constant (J/kmol-K), EA =
activation energy (J/kmol)
 Combining above scalings yields and applying
Eqs 8.20 and 8.21
  EA  ( n 2) / 2
0.375
n / 2
 SL  T TuTb
(8.29)
exp 
P
 2 RuTb 
 
T
0.375
Tb
n/2
 EA   n / 2
exp 
P
 2 RuTb 
(8.30)
 For hydrocarbons, n  2 and EA  1.67.108 J/kmol
(40 kcal/gmol). Eqn 8.29 predicts SL to increase by
factor of 3.64 when Tu is increased from 300 to
600K. Table 8.1 shows comparisons of SL and 
 The empirical SL correlation of Andrews and
Bradley [19] for stoichiometric methane-air flames,
SL (cm/s) = 10 + 3.71.10-4[Tu(K)]2
(8.31)
which is shown in Fig. 8.13, along with data from
several experimenters.
 Using Eqn. 8.31, an increase in Tu from 300 K to
600 K results in SL increasing by a factor of 3.3,
which compares quite favourably with our estimate
of 3.64 (Table 8.1).
 Table 8.1 Estimate of effects of Tu and Tb on SL
and  using Eq 8.29 and 8.30
Case
Tu (K)
Tb (K)
SL/SL,A
/A
A (ref)
300
2,000
1
1
B
600
2,300
3.64
0.65
C
300
1,700
0.46
1.95
 Case A: reference
 Case C: Tb changes due to heat transfer or
changing equivalent ratio, either lean or rich.
 Case B: Tu changes due to preheating fuel
Pressure (P)
 From Eq. 8.29, if, again, n  2, SL  f (P).
 Experimental measurements generally show a
negative dependence of pressure. Andrews and
Bradley [19] found that
SL (cm/s) = 43[P (atm)]-0.5
(8.32)
fits their data for P > 5 atm for methane-air flames
(Fig. 8.14).
Equivalent Ratio ()
 Except for very rich mixtures, the primary effect of
 on SL for similar fuels is a result of how this
parameter affects flame temperatures; thus, we
would expect S L,max at a slightly rich mixture and
fall off on either side as shown in Fig. 8.15 for
behaviour of methane.
 Flame thickness () shows the inverse trend,
having a minimum near stoichiometric (Fig. 8.16).
Fuel Type
 Fig. 8.17 shows SL for C1-C6 paraffins (single
bonds), olefins (double bonds), and acetylenes
(triple bonds). Also shown is H2. SL of C3H8 is used
as a reference.
 Roughly speaking the C3-C6 hydrocarbons all
follow the same trend as a function of flame
temperature. C2H4 and C2H2‘ SL > the C3-C6 group,
while CH4’SL lies somewhat below.

H2's SL,max is many times > that of C3H8. Several
factors combine to give H2 its high flame speed:
i. the thermal diffusivity () of pure H2 is many
times > the hydrocarbon fuels;
ii. the mass diffusivity (D) of H2 likewise is much >
the hydrocarbons;
iii. the reaction kinetics for H2 are very rapid since
the relatively slow CO CO2 step that is a major
factor in hydrocarbon combustion is absent.
 Law [20] presents a
compilation of laminar
flame-speed data for
various pure fuels and
mixtures shown in
Table 8.2.
 Table 8.2 SL for
various pure fuels
burning in air for  =
1.0 and at 1 atm
Fuel
SL (cm/s)
CH4
40
C2H2
136
C2H4
67
C2H6
43
C3H8
44
H2
210
FLAME SPEED CORRELATIONS
FOR SELECTED FUELS
 Metghalchi and Keck [11] experimentally
determined SL for various fuel-air mixtures over
a range of temperatures and pressures typical of
conditions associated with reciprocating internal
combustion engines and gas turbine
combustors.
 Eqn 8.33 similar to Eqn. 8.29 is proposed


Tu   P  (1 – 2.1Y ) (8.33)
SL = SL,ref 
dil

 

 Tu , ref   Pref 

 

for Tu  350 K.
 The subscript ref refers to reference conditions
defined by
Tu,ref = 298 K, Pref = 1 atm and
SL,ref = BM + B2( - M)2 (for reference conditions)
where the constants BM, B2, and M depend on
fuel type and are given in Table 8.3.
 Exponents of T and P,  and  are functions of ,
expressed as
 = 2.18 - 0.8( - 1) (for non-reference conditions)
 = -0. 16 + 0.22( - 1) (for non-reference conditions)
 The term Ydil is the mass fraction of diluent present
in the air-fuel mixture in Eqn. 8.33 to account for
any recirculated combustion products. This is a
common technique used to control NOx in many
combustion systems
 Table 8.3 Values for BM, B2, and M used in Eqn
8.33 [11]
Fuel
M
BM (cm/s)
B2 (cm/s)
Methanol
1.11
36.92
-140.51
Propane
1.08
34.22
-138.65
Iso octane 1.13
26.32
-84.72
RMFD-303 1.13
27.58
-78.54
Example 8.3
Compare the laminar flame speeds of gasoline-air
mixtures with  = 0.8 for the following three cases:
i. At ref conditions of T = 298 K and P = 1 atm
ii. At conditions typical of a spark-ignition engine
operating at wide-open throttle: T = 685 K and P
= 18.38 atm.
iii. Same as condition ii above, but with 15 percent
(by mass) exhaust-gas recirculation
Solution
 RMFD-303 research fuel has a controlled
composition simulating typical gasolines. The
flame speed at 298 K and 1 atm is given by
 SL,ref = BM + B2( - M)2
 From Table 8.3,
 BM = 27.58 cm/s, B2 = -78.38cm/s, M = 1. 13.
 SL,ref = 27.58 - 78.34(6.8 - 1.13)2 = 19.05 cm/s
 To find the flame speed at Tu and P other than the
reference state, we employ Eqn. 8.33
 SL(Tu, P) = SL,ref  Tu   P  

 

 Tu , ref   Pref 
where
 = 2.18-0.8(-1) = 2.34
 = -0.16+0.22(-1) = - 0.204
Thus,
SL(685 K, 18.38 atm) =
19.05 (685/298)2.34(18.38/1)-0.204 =73.8cm/s
With dilution by exhaust-gas recirculation, the
flame speed is reduced by factor (1-2.1 Ydil):
SL(685 K, 18.38 atm, 15%EGR) =
73.8cm/s[1-2.1(0.15)]= 50.6 cm/s
QUENCHING, FLAMMABILITY,
AND IGNITION
 Previously  steady propagation of premixed
laminar flames
 Now  transient process: quenching and ignition.
Attention to quenching distance, flammability
limits, and minimum ignition energies with heat
losses controlling the phenomena.
1. Quenching by a Cold Wall
 Flames extinguish upon entering a sufficiently
small passageway. If the passageway is not too
small, the flame will propagate through it. The
critical diameter of a circular tube where a flame
extinguishes rather than propagates, is referred to
as the quenching distance.
 Experimental quenching distances are determined
by observing whether a flame stabilised above a
tube does or does not flashback for a particular
tube diameter when the reactant flow is rapidly
shut off.
 Quenching distances are also determined using
high-aspect-ratio rectangular-slot burners. In this
case, the quenching distance between the long
sides, i.e., the slit width.
 Tube-based quenching distances are somewhat
larger (20-50 percent) than slit-based ones [21]
Ignition and Quenching Criteria
Williams [22] provides 2 rules-of-thumb governing
ignition and flame extinction.
 Criterion 1 -Ignition will only occur if enough
energy is added to heat a slab thickness steadily
propagating laminar flame to the adiabatic flame
temperature.
 Criterion 2 -The rate of liberation of heat by
chemical reactions inside the slab must
approximately balance the rate of heat loss from
the slab by thermal conduction. This is applicable
to the problem of flame quenching by a cold wall.
Simplified Quenching Analysis.
 Consider a flame that has just entered a slot
formed by two plane-parallel plates as shown in
Fig. 8.18. Applying Williams’ second criterion:
heat produced by reaction = heat conduction to
the walls, i.e.,

(8.34)

Q V  Qcond ,tot
Q is volumetric heat release rate
 Q   m h
F
c
(8.35)
where mF is volumetric mass rate of fuel,
hc is heat of combustion
 Thickness of the slab of gas analysed = .
Find quenching distance, d.
Solution
dT

Q  kA
cond
dx
(8.36)
in gas  wall
 A = 2L, where L is slot width ( paper) and 2
accounts for contact on both sides (left and
right). dT
is difficult to approximate. A
dx
dT =
reasonable lower bound of
Tb  Tw 
dx
d /b
(8.37)
where b = 2, assuming a linear distribution of T
from the centerline plane at Tb to the wall at Tw.
In general b > 2.
 Quenching occurs from Tb to Tw.
 Combining Eqns 8.35-8.37,

Tb  Tw
( mF hc )( dL))  k (2 L)
d /b
 or
2kb Tb  Tw 
2
d 

mF hc
(8.38a)
(8.38b)
 Assuming Tw = Tu, using Eqn 8.20 (about SL), and relating
 . hc  (  1)c p (Tb  Tu ) , Eqn 8.38b becomes

d = 2b /SL
(8.39a)
 Relating Eqn 8.21 (about ), Eqn 8.39a becomes

d = 2b 
 Because b  2, value d is always > . Values of d for fuels
are shown Table 8.4.
 Table 8.4 Flammability limits, quenching distances
and minimum ignition energies
Flammability limit
min
max
Quenching distance, d
Stoich-mass For =1
Absolute
air-fuel ratio
min, mm
C 2H 2
0.19

13.3
2.3
-
CO
0.34
6.76
2.46
-
-
C10H22
0.36
3.92
15.0
2.1
-
C 2H 6
0.50
2.72
16.0
2.3
1.8
C2H4
0.41
> 6.1
14.8
1.3
-
H2
0.14
2.54
34.5
0.64
0.61
CH4
0.46
1.64
17.2
2.5
2.0
CH3OH
0.48
4.08
6.46
1.8
1.5
C8H18
0.51
4.25
15.1
-
-
C 3H 8
0.51
2.83
15.6
2.0
1.8
Fuel
Minimum ignition energy
For =1 (10-5 J)
Absolute
minimum (10-5 J)
C 2H 2
3
-
CO
-
-
C10H22
-
-
C 2H 6
42
24
C 2H 4
9.6
-
H2
2.0
1.8
CH4
33
29
CH3OH
21.5
14
C8H18
-
-
C 3H 8
30.5
26
Example 8.4.
 Consider the design of a laminar-flow, adiabatic,
flat-flame burner consisting of a square
arrangement of thin-walled tubes as illustrated in
the sketch below.
 Fuel-air mixture flows through both the tubes and
the interstices between the tubes.
 It is desired operate the burner with a
stoichiometric methane-air mixture exiting the
tubes at 300 K and 5 atm


Determine the mixture mass flowrate per unit
cross-sectional area at the design condition.
Estimate the maximum tube diameter allowed so
that flashback will be prevented.
Solution
 To establish a flat flame, the mean flow velocity must equal
the laminar flame at the design temperature and pressure.
From Fig. 8.14,
 SL (300K, 5atm) = 43/P (atm) = 43/5 = 19.2cm/s.
 The mass flux, , m is
 m = m / A
= uu = uSL
 Assuming an ideal-gas mixture, where
 MWmix = CH4MWCH4 + (1 - CH4)MWair

= 0.095(16.04) + 0.905(28.85)

= 27.6 kg/kmol =5.61kg/m3
 (Stoichimetric mass ratio air/ methane = 17.2, see Table
8.4)
 Thus, the mass flux is m
= uSL = 5.61(0.192)= 1.08
kg/(s.m2)
 We assume that if the tube diameter < the quench
distance (d), with some factor-of-safety applied,
the burner will operate without danger of
flashback.
 Thus, we need to find the quench distance at the
design conditions.
 Fig. 8.16 shows that dslit 1.7 mm. Since dslit = dtube
– (20-50%), use dslit outright (our case) with factor
of safety 20-50%. Data in Fig 8.16 is for slit,
design is of tube.
 Correction for 5 atm:
 Eqn. 8.39a, d  /SL
 Eqn 8.27,   T1.75/P

d2 = d  2 S L,1  d P1 S L,1
1
1 S L,2
1
P2 S L,2
 d(5atm) =1.7mm. 1 atm 43 cm / s
5 atm 19.2 cm / s
 ddesign  0.76 mm
 Check whether d=0.76 mm gives laminar flow (Red
< 2300).
u ddesign SL 5.61(0.00076)(0.192)
Red 

 51.5
6

15.89.10
 Flow is still laminar
2. Flammability Limits
 A flame will propagate only within a range of
mixture the so-called lower and upper limits of
flammability. The limit is the leanest mixture ( <
1), while the upper limit represents the richest
mixture ( > 1).  = (A/F)stoich /(A/F)actual by mass
or by mole
 Flammability limits are frequently quoted as %fuel
by volume in the mixture, or as a % of the
stoichiometric fuel requirement, i.e., ( x 100%).
Table 8.4 shows flammability limits of some fuels
 Flammability limits for a number of fuel-air
mixtures at atmospheric pressure is obtained from
experiments employing "tube method".
 In this method, it is ascertained whether or not a
flame initiated at the bottom of a vertical tube
(approximately 50-mm diameter by 1.2-m long)
propagates the length of the tube.
 A mixture that sustains the flame is said to be
flammable. By adjusting the mixture strength, the
flammability limit can be ascertained.
 Although flammability limits are physico-chemical
properties of the fuel-air mixture, experimental
flammability limits are related to losses from the
system, in addition to the mixture properties, and,
hence, generally apparatus dependent [31].
Example 8.5.
 A full C3H8 cylinder from a camp stove leaks its
contents of 1.02 lb (0.464 kg) in 12' x 14' x 8' (3.66
m x 4.27 m x 2.44 m) room at 20oC and 1 atm.
After a long time fuel gas and room air are well
mixed. Is the mixture in the room flammable?
Solution
 From Table 8.4, we see that C3H8-air mixtures are
flammable for 0.51 <  < 2.83. Our problem, thus,
is to determine  of the mixture filling the room.
Partial pressure of C3H8 by assuming ideal-gas
behaviour
PF 






mF  Ru / MWF  T
Vroom
0.464(8315/44.094)(20  273)

3.66(4.27)(2.44)
= 672.3 Pa
Propane mole fraction =
F = PF/P = 672.3/101,325 = 0.00664
and
air = 1 - F = 0.99336
The air-fuel ratio of the mixture in the room is
(A/F)act =  MW
0.99336 (28.85)
air
air

 97.88
 fuel MW fuel 0.00664 (44.094)
 From the definition of  and the value of (A/F)stoich
from Table 8.4 (i.e. 15.6 by mass ratio), we have
 = (A/F)stoich /(A/F)act = 15.6/97.88 = 0.159
 Since  = 0.159 < lower limit (= 0. 51), the mixture
in the room is not capable of supporting a flame.
Comment
 Although our calculations show that in the fully
mixed state the mixture is not flammable, it is quite
possible that, during the transient leaking process,
a flammable mixture can exist somewhere within
the room.
 C3H8 is heavier than air and would tend to
accumulate near the floor until it is mixed by bulk
motion and molecular diffusion.
 In environments employing flammable gases,
monitors should be located at both low and high
positions to detect leakage of heavy and light
fuels, respectively.
3. Ignition
 Most of ignition uses electrical spark (pemantik
listrik). Another means is using pilot ignition (flame
from very low-flow fuel).
Simplified Ignition Analysis
 Consider Williams’ second criterion, applied to a
spherical volume of gas, which represents the
incipient propagating flame created by a point
spark. Using the criterion:
 Find a critical gas-volume radius, Rcrit, below
which flame will not propagate
 Find minimum ignition energy, Eign, to heat critical
gas volume from initial state to flame temperature
(Tu to Tb).
Critical radius, Rcrit, and Eign

(8.40)
QV  Qconduction
(propagation)
  mh 4 R 3 / 3  k 4 R 2 dT
(8.41)
F
c
crit
crit
dr Rcrit
where is mass flowrate/volume
 Heat transfer process is shown in Figure 8.20

dT
dr
Tb  Tu 


Rcrit
(8.42)
Rcrit
 Substitution Eqn 8.42 to 8.41 results in
 .
Rcrit
3k Tb  Tu 

mFhc
(8.43)
 Rcrit is therefore determined by the flame propagation
 If R < Rcrit, it would require exothermic heat > hc
 Substituting from Eqn 8.20 into Eqn 8.43 will give


(8.44)
Rcrit  6
 6/2 
SL


 Ignition is aimed to increase fluid from Tu to Tb at
the onset of combustion to replace hc (ignition)
 E  m c T T
(8.45)
ign
crit p

b
u

where Eign is minimum ignition energy
 Substitution mcrit=b.4Rcrit3/3 and b using gas
ideal formulae to Eqn 8.45 results in
3

(8.47)
 c p  Tb  Tu   
Eign  61,6 P  
 
 Rb  Tb   S L 
 where Rb = Ru/MWb and Ru = gas constant
4. Dependencies on Pressure, Temperature
and Composition
 Using Eqn 8.27 and 8.29 on Eqn 8.47
demonstrates effect of pressure to be
Eign  P-2
(8.48)
(see comparison with experimental result in Fig
8.21)
 Eqn 8.47 implies that in general, Tu Eign (see
Table 8.5).
 Eign vs %fuel gives U-shaped plot (Figures 8.22
and 8.23). This figure indicates that Eign is
minimum as a mixture composition is
stoichiometric or near it.
 If the mixture gets leaner atau richer, Eign
increases first gradually and then abruptly. %fuel
at Eign =  to be ignited are flammability limits
Figure 8.22. Effect of %fuel on Eign
Figure 8.22. Effect of %fuel on Eign
Figure 8.23. Effect of methane composition on Eign
Table 8.5 Temperature influence
on spark-ignition energy
Fuel
n-heptane
Iso-octane
n-pentane
Initial temp (K)
298
373
444
298
373
444
243
253
Eign (mJ)
14.5
6.7
3.2
27.0
11.0
4.8
45.0
14.5
Fuel
n-heptane
Initial temp (K)
298
Eign (mJ)
7.8
propane
373
444
233
4.2
2.3
11.7
243
253
298
331
9.7
8.4
5.5
4.2
356
373
477
3.6
3.5
1.4
References:
 Turns, Stephen R., An Introduction to
Combustion, Concepts and Applications, 2nd
edition, McGrawHill, 2000