TURBULENCE
Schloesing and Montdesir first observed the influence of turbulence on the combustion of a
gaseous mixture in a closed vessel in 1883. Clerk, in 1912, carried out experiments in a
reciprocating engine that clearly showed the importance of intake gas motion on the nature of
the pressure development. D.W. Lee, in 1939, was perhaps the first to look at the fluid
motion inside the engine cylinder through photographs in the glass cylinder of a motored
research engine. In 1958, the first experiment to quantitatively measure the gas velocities
inside an engine was reported by Semenov. He used a temperature compensated Hot Wire
Anemometer on a motored engine. The problems associated with this type of instrument are
1.
response to flow direction,
2.
response to complex heat transfer mechanisms, and
3.
inability to use it with combustion.
The Laser Doppler Velocimeter (LDV) which overcomes all the shortcomings of the
Hot Wire Anemometer was first used in 1978 and reported by P. Hutchinson, A.P. Morse and
J.H. Whitelaw.
Definition
Turbulence is defined as the fluctuating velocity component superimposed on the mean
velocity of viscous flow. The most essential characteristic of a turbulent flow is that at any
point within the flow, the velocity and pressure are not constant in time but exhibit irregular,
high frequency fluctuations1.
According to Witze et al2, quoting Semenov”…for unsteady flow in an engine
cylinder, the magnitude and direction of the directional velocity for a given point on the cycle
may vary considerably from cycle to cycle.” The essence of the problem is that the time
scales of the unsteadiness of the engine cycle are of the same order of magnitude as the time
scales of the turbulence.
Andrews et al3 state that, qualitatively, the effects of turbulence upon combustion
have been known since 1883, that turbulence increased both energy transfer and flame
surface area and also formed new centers of inflammation.
It has been recognized that shear flow past the inlet valve is the major source of
turbulence in engine cylinders. The size of the turbulent structure decreases with increase in
engine speed, that is, increasing Reynolds number, since the turbulent intensity is
proportional to engine speed4.
An increase in the turbulent velocity initially increases the mass of the gas burned in a
given time in a gasoline engine. Too great an increase can lead to unacceptably high pumping
losses.
1
Lancaster et al, SAE Paper No. 760160, who had taken from Schlicting’s book, 1968
SAE Paper No. 840377
3
Combustion and Flame, Vol. 24, p 285-304, 1975
4
Tabaczynski, I.Mech.E Paper C51/83, p 51, 1983
2
Flame speeds can be increased many times by turbulence. The area of the flame front
is greatly distorted while the unburned mixture is swept bodily into the reaction zone.
Turbulence changes the mode of heat transfer and diffusion to include highly convective
mixing which also carries active particles into the unburned region.
For a laminar flame, it is possible to define the burning velocity, which is independent
of the measuring apparatus within reasonable limits. This is not yet possible with turbulent
flames. Values of turbulent burning velocity depend not only on the apparatus used, but also
on the concept of the turbulent flame assumed. In turbulent flow, the stream velocity
fluctuates at random and consequently the flame in such a stream is continuously subjected to
random distortions as it conforms to the fluctuations of the stream.
Turbulent Flame Propagation
In a non-turbulent mixture, flame propagation is laminar and the flame has a smooth surface
and a relatively thin reaction zone. The flame speed, or the speed, with which the reaction
zone moves relative to the unburned mixture, is determined by the chemical and
thermodynamic properties of the mixture. When turbulence is present, the flame front is no
longer smooth and the reaction zone is thicker than that in the laminar case. In addition, the
flame speed, when turbulence is present, is several times the laminar value depending on the
intensity of turbulence.
There are two mechanisms, which have been used to explain the increase in flame
speed due to turbulence.
First Mechanism
The first mechanism considers the effects of turbulent eddies of a scale less than the thickness
of the laminar flame front. These eddies are assumed to increase the local heat and mass
transfer rates along the flame front thereby increasing the local rate of flame propagation. A
characteristic expression, developed from this approach by Damköhler, for the ratio of
turbulent to laminar flame speed, based on the transport properties in the unburned gas ahead
of the flame, is
ST/SL = (D/)½
where D is the total turbulent diffusivity and the other symbols are given below.
Second Mechanism
The second mechanism, which is generally accepted as more important, considers the effects
of turbulent eddies of a scale larger than the thickness of the flame front. These eddies are
assumed to have no effect on the local flame velocity but to distort the flame front so that its
area is increased. The increase in flame speed is then proportional to the increased area of the
flame front. The ratio of the turbulent to laminar flame speed is given by
ST/SL = AT/AL
where A is the flame front area.
The expression of Shelkin5 is typical of the “large scale” theories. He assumed that
the flame front was broken into cones with characteristic dimensions which depended on both
the turbulent intensity, u’, and the turbulent scale. His resulting expression
ST/SL = [1 + (2u’/SL)2]½
is dependent only on the turbulent intensity, and shows an almost linear dependence of
turbulent flame speed on turbulent intensity for u’ » S L. Shelkin suggested the substitution of
an empirical constant  for the factor 2 in the equation to account for actual geometries.
It is generally found that the turbulent burning velocity is directly proportional to the
laminar burning velocity; the ratio of the two velocities is independent of the initial
temperature6.
The increase in the rate of burning of the turbulent flame compared to the laminar
flame may be due to
1.
wrinkling of the flame so that the surface area is markedly increased,
2.
increase in the rate of transport of heat and active species thereby increasing the actual
burning velocity normal to the flame surface and/or
3.
stirring of the unburned and burned gas in such a way that the flame becomes
essentially a homogeneous reaction whose rate depends on the ratio of burned to
unburned mass in the mixing process.
Stages of Combustion of a Pre-mixed Charge in a Constant Volume Bomb
Consider the events occurring when a pre-mixed charge is spark ignited in a constant volume
bomb. The events occurring in the chamber can be broadly classified into four stages. There
is an accelerating and decelerating trend in flame propagation from the beginning to the end.
First Stage
Between the time of ignition up to the point of perceptible pressure rise, chemical reactions
begin at the spark plug. It accelerates at a rate primarily dictated by fuel-air ratio,
temperature, density, and heat loss. This is the delay period and in this stage the first small
element burns essentially at constant pressure, since it can expand and compress the unburned
mixture. The flame movement is extremely slow. Flame velocities are essentially laminar.
Second Stage
In this stage the flame starts to sweep outwards from the source. A high expansion (gas)
velocity is added to the small laminar burning velocity to yield the flame velocity. The flame
accelerates and the pressure rises throughout the chamber continuously because both the
unburned mixture and the burned products are compressed and the temperature rises.
5
6
NACA, TM 1110, 1947 (Taken from Lancaster et al, SAE Paper No. 760160
S.P. Sharma and Chander Mohan, Fuels and Combustion, Tata McGraw-Hill Co. Ltd., 1984
Third Stage
A fully developed turbulent flame propagates into the chamber. There is only a slight change
in burning velocity because the change in flame area with flame radius is the least.
Fourth Stage
This stage is characterized by a decrease in the burning velocity. The flame approaches the
walls of the chamber. The expansion or gas velocity must necessarily approach zero; hence
the flame velocity decreases to approach the burning velocity. The flame is wall-quenched.
Figure 1 shows a plot of flame radius versus the turbulent burning velocity and clearly
indicates the four stages of combustion.
Definition of Turbulence Parameters in Engines
The engine flow processes are quasi-periodic because of the cyclic nature of the engine
operation. The period of the engine is short; thus a statistical description of turbulence is
difficult to define. However, ensemble (or phase) averaging techniques may be employed7.
Consider the turbulent jet flow into the cylinder during the inlet process. The
instantaneous flow structure may be different from cycle to cycle partly due to the nature of
the breakdown of the jet. It is therefore necessary to distinguish between fluctuations which
arise because of cyclically different flow structures (cycle-to-cycle variations) and those
fluctuations due to turbulence within any one of the flow structures, corresponding to a given
cycle. There are basically two approaches to defining flow characteristics: ensemble analysis
and cycle-to-cycle analysis. These approaches are explained by Daneshyar and Hill7.
Normally, turbulence is characterized as the turbulent intensity, u’, which at a point, is
the root mean square (RMS) value of the velocity fluctuation at the given point. This is
believed to be a stronger characteristic influencing flame speed than the ones explained
below probably because the energy of turbulent flow is not contained in a single eddy size but
distributed over a continuous range of eddy sizes.
The structure of small-scale turbulence originally proposed by Tennekes8 involves the
concept of eddies for which the various scales need to be defined. Among these is the
turbulent integral scale or the Taylor integral.
This denotes the size of the turbulent eddies, representing the overall characteristics
dimension of the eddy9. Measurement of turbulent velocity made at any 2 locations should
correlate if they were made inside an eddy. The integral length scale lI or L is a measure of
the largest-size eddy.
From the engine point of view, the characteristic length represents the largest possible
eddy size that the confining geometry of the walls of an enclosure will allow, for example,
the cylinder bore or the clearance height.
7
Daneshyar and Hill, Progress in Energy and Combustion Science, vol.13, p 47-73, 1987
Physics of Fluids, Vol.1, p 3, 1968
9
Tabaczynski et al, SAE paper No. 770647
8
For a cylindrical combustion chamber, near the top dead center, the characteristic
length is the clearance height, h. Near the bottom dead center, it is approximately the cylinder
bore. For a cylindrical cup in the piston, near top dead center, it is the cup diameter.
The Kolmogorov micro scale, LK or lK, also denoted by , is a measure of the smallest
size eddy where small-scale kinetic energy is dissipated via molecular viscosity. It is also the
smallest size eddy viscous damping will allow. This is given by the following relation
 = LK  [(3LI/(u’)3]1/4
where  is the kinematic viscosity, m2/s
u’ is the turbulent intensity.
The Kolmogorov microscale defines the dissipation length scale – the characteristic
diameter of the spaghetti-like vortex tubes that divide each tube into numerous laminarburning zones. Dissipation due to high frequency turbulent fluctuations is most important on
this scale. This scale has been linked to the luminous zone of reaction in a turbulent flame9.
The Taylor microscale, , is defined as the spacing of the spaghetti-like structure of
the vortex tubes of Kolmogorov thickness6. It is useful in estimating the mean strain rate of
the turbulence. Figure 2 shows the different length scales.
The Taylor microscale can be obtained from the relation
/L = (15)½(u’L/)-½ = (15)½(ReL)-½ = (15)-1Re
or from the relation
/ = (15) ½(ReL)-¼ = (15)¼(Re)½
Andrews et al3 gave the following relation for /L
/L = (48.64) -1Re
A turbulent Reynolds number based on the turbulent intensity and integral scale is
given by the relation
ReL = u’L/
and based on the turbulent velocity ST is given by
Re’L = STL/
Since Re = LV/ = V2/V/L = inertia forces/viscous forces, a large ReL indicates
inertia forces dominating over dissipative effects of molecular viscosity. Re L is a measure of
how larger eddies are damped by viscosity.
For turbulence to occur at all, ReL > 1. Often, in practice, ReL » 1. For a hot gas
flowing at 1 atm pressure,  = 1 cm2/s, and L  1 mm and u’ = 100 cm/s,
ReL = 10.0
At a pressure of 100 atm, ReL = 1000.
Empirical correlations for turbulent flame speed have sometimes successfully used
ReL as the correlating parameter.
For an internal combustion engine, taking the inlet valve diameter to be 20 mm (= L,
typically), u’ to be 1 m/s at tdc,  = 6 x 10-6 m2/s at 8 atm and 580K, we get a value of Re
equal to about 400.
Now
Re  (L /u’)(/u’)
where L/u’ is the time scale for large eddies and /u’ is the time scale for small fluctuations
or the time scale for small eddies. As Re increases the time scale for large eddies decreases
but the time scale for small eddies decreases even more. There is an indication from
experimental data that the ratio ST/SL correlates with Re3. According to them combustion
will occur where Re and the rate of strain are the highest and no flame propagation will
occur where Re is the lowest.
According to Daneshyar and Hill7
 = (u’)3/L
where  is the rate of disappearance of turbulent kinetic energy per unit mass due to viscosity,
then
 = 15(u’/)2 = v2/2
where v = ()¼ and is called the Kolmogorov velocity.
Length and Velocity Scales Typical of Spark Ignition Engine Combustion
For this discussion we assume the following:
1.
The integral scale L during the combustion period is of the order of the combustion
chamber height. Daneshyar and Hill7 have taken this to be about one-fifth of the
minimum clearance height at tdc.
2.
The laminar burning velocity for the mixture near the compression period is about 0.5
m/s.
3.
The kinematic viscosity in the unburned mixture towards the end of compression is
about 6 x 10-6 m2/s.
4.
The laminar flame thickness may be estimated to be about 0.01 mm (/u’).
5.
The quench distance may be taken as q  10 = 0.1 mm.
6.
The spark gap will be approximately 1 mm.
They7 took the turbulence intensities in the ranges
1 < u’ < 2 m/s for unshrouded valve
4 < u’ < 6 m/s for shrouded valve
This range, the various correlations for the turbulence terms and the above
assumptions have been used to construct Table 1.
Table 1. Typical Length and Velocity Scales for Engine Turbulence7
u’ m/s
1
3
6
ReL = u’L/
1700
5,000
10,000
u’/SL
2
6
12
(u’/SL)/(/)
0.02
0.1
0.3
L mm
10
10
10
 mm
1
0.6
0.4
 mm
0.038
0.017
0.01
 mm
0.01
0.01
0.01
q mm
0.1
0.1
0.1
Abdel-Gayed et al10 have defined a flame stretch factor, K as
K = 0.157(u’/SL)2ReL-0.5
Other correlations are based on the ratio of turbulent to laminar burning velocities,
ST/SL and the most commonly used ratio, that of u’/SL. Some correlations use the Lewis
number, defined as
Le = k’/cpD
where k’ is the thermal conductivity and
D is the diffusion coefficient.
The Karlovitz flame stretch factor Kk, is defined as
Kk = (u’/)(1/SL)
where 1 = /SL
Based on the Kolmogorov scale we have
Re = u’/
Based on the Taylor microscale we have
Re = u’/
10
21st Symposium on Combustion, p 497-504, 1986
If the integral scale is determined, the other scales can be obtained.
As the turbulent Reynolds number increases, the smaller microscales (Taylor and
Kolmogorov) decrease in size. Now, turbulence in an engine increases with increase in piston
speed. Integral scale is independent of the engine speed; so as the engine speed goes up,
microscales of turbulence go down. Micro-shadow-graphs of flames11 confirm this
prediction.
We define a chemical reaction time R, given by
R = /u’
ZR =  / VL (VL=Laminar flame speed)
where  is the laminar flame thickness, and an eddy turn over time (or the eddy “life time”) as
to = L/u’ For the largest eddies
which is a useful turbulent time scale. The ratio of the two times is called the Damköhler
number, DaL given by
DaL = (R/to)-1 = (L/u’)(u’/) = L/ =
L
u'
VL  L   VL 
=  

δ  δ  u' 
For high values of DaL, (103 to 104), the chemistry is very fast compared with the
turbulence. Under these conditions, reaction sheets are observed.
Now we have
ReLDaL = (u’L/)(L/), hence
( ReLDaL)  L/
so sheets are associated with large values of L/.
Now, we can obtain a Damköhler number based on the Karlovitz microscale, thus
Da = /
= Lk/
and if this quantity is greater than 1, then all eddies will be greater than the laminar flame
thickness and the reaction sheet will wrinkle. The laminar flame thickness will be smaller
than the smallest turbulent eddy, and so
u’  SL
Turbulence will wrinkle and distort the laminar flame front. In the flow field, the
turbulent vortices spread the ignition sites via a ragged edge emerging from the spark plug.
If the laminar flame thickness, , is greater than the Kolmogorov microscale, , but
less than the characteristic length, L, that is
L>>
11
Smith, SAE Paper No. 820043
then we get flamelets in the eddies and
u’ » SL
When turbulence is higher and the flame becomes wrinkled, the flame area increases;
that is, it becomes larger than that of a similar laminar flame. It becomes thick.
ST/SL = Af
ST/SL = 1 + C(u’/SL)
where C  1 – 2. This has been used by Checkel and Ting (SAE Paper No. 930867). In their
case, C varied between 0.6 and 1.01, the smaller values being applicable for smaller flames.
Their studies were carried out on propane-air and methane-air mixtures.
Flame velocity is less dependent on the laminar flame velocity and so less dependent
on the fuel-air ratio and fuel type. Velocity is 3-5 times (according to Borman and Ragland12
and 3-30 times according to Ferguson and Kirkpatrick13) the laminar flame velocity. The
flame is brush-like.
The fact that turbulent flames are wrinkled with a relatively thick flame brush (of
thickness 5-6 mm) means that measuring the flame velocity is more difficult than for laminar
flames.
High-speed direct photographs show small flamelets14. These small tongues of flame
fluctuate, thus making a simple area measurement difficult.
This happens at higher engine speeds because turbulent intensity is proportional to
engine speed. Hence the transition from wrinkled sheet to flamelets in the eddies regime.
Since  is larger, Damköhler number is now reduced so burning rate is controlled by
the turbulent mixing rate.
Distributed Reaction Zones.
Wrinkling increases flame area, but intense wrinkling may also cause small pockets of
reactants to be entrained into the reaction zone.
Entrainment of small turbulent eddies and wrinkling caused by large eddies give rise
to the observation that turbulence burning velocity is not sensitive to laminar burning velocity
or turbulence scale.
The flame is not a coherent structure but a thick zone of reactant eddies embedded in
products. In this region, an increase of turbulence scale can cause a decrease in burning
velocity. Energy from combustion goes into motion of the eddies as well as directed motion
of the flame.
ST/SL = 6.44(u’/SL)(SL/u’)¾
12
Combustion Engineering, WCB/McGraw-Hill, Boston, 1998
I.C. Engines-Applied Thermosciences, Wiley, 2001
14
Bracco, Combustion, Science and Technology, vol. 58, p 209-230, 1988
13
Since there is a decrease in the burning velocity, u’/ S L is high (highly turbulent
combustion under conditions where products mixed with reactants cause SL to be low). This
occurs in an automobile engine under conditions of rapidly closing throttle while the engine
speed is still high (driver takes his foot off the accelerator when the car is at high speed or
going down-hill12.
Tabaczynski et al9 obtained an expression for the eddy burn up time b for a given
eddy diameter L (the integral length scale) of a spherical mass given by u(4/3)(L/2)3
b = (1/2)( b/u)2/3(L/(u’ + SL)
They have correlated this expression to the ignition delay. If L is increased, spark will
occur earlier in the compression stroke and so delay will increase. Also as u’ increases, the
delay would reduce. They believed that this equation would probably yield correct results
near stoichiometric air-fuel ratios.
Turbulent Burning Velocity
It has been shown why the turbulent burning velocity (or turbulent flame speed) is higher
than the laminar burning velocity (or flame speed). As a rule, the working mixture in the
engine cylinder is in sufficiently turbulent motion, consisting of directed vortices and random
pulsations of velocities of the gas streams. Because of these factors the flame speed is
accelerated.
Bouchard et al15 measured flame speed in a spark ignition engine as a function of
engine speed. They found that flame speed was nearly a linear function of engine speed. This
relationship between engine speed and flame speed was one of the first pieces of evidence
that turbulence and flame speed in the engine were related, since mixture turbulence increase
with engine speed.
A number of relationships exist relating the laminar flame speed to the turbulent
burning velocity. In many such relations, the turbulent intensity plays a prominent part.
One line of thinking indicates that turbulent burning velocity ST is obtained by adding
a certain terms St to the laminar burning velocity, SL , this
ST = S L + St
This term St may be called the turbulent velocity factor. According to Karlovitz, this turbulent
velocity factor depends on the turbulent intensity, u’ (which is defined on the root mean
square value of the velocity fluctuations about the mean velocity)
u´ = û 2
Under certain conditions St also depends on laminar burning velocity. Thus
For
u´/SL <<1,
For
u´/SL >>1
For
u´/SL 1
15
St = u´ and SL=ST
St =(2u´SL)1/2
St =(2u´SL)1/2[1-SL/u´{1-exp(-u´/SL)}]
SAE Journal, vol.41, no. 5, November 1937
According to Mizutovi16, Karlovitz et al gave the following relation for the ratio of
turbulent to laminar burning velocity
ST/SL=1+2[u´/SL + exp(-u´/SL) – 1]1/2
Daneshyar and Hill7 quoting one reference (Libby et al) gave the following relation
for ST/SL
ST/SL = 1 + 1.14(u’/SL)[1 + (126 – 8.33)(u’/SL)2(1/ReL)]
This predicts a departure from linear dependence of ST on u’ which decreases with
Reynolds number. They, however, give their own relation for the same quantity, namely
ST/SL = 1 + d(u/b)0.5(u’/SL)
where d  (2/3)
According to Khovac17
St = K u´
where K is a coefficient directly proportional to the rate of reaction at the flame temperature
Tb, that is
K= þN exp(-E/RT)
An increase in pressure has a positive effect on the turbulent flame speed. The initial
temperature and composition have a greater effect on the turbulent burning velocity than on
the laminar burning velocity.
Lancaster et al1 developed the concept of flame speed ratio (FSR), the ratio of
turbulent to laminar burning velocity. According to their hypothesis, the maximum flame
speed ratio
FSRmax=C1u´
Where C1 is a constant. This, according to Gat and Kauffman18, applies when u´ is very large.
The flame speed at any reaction of the flame front r (distance from the spark plug)
was given as
FSR(r) = FSRmax(r/3.0)0.5
where r is in cm.
This equation is taken to be valid for the period of flame development. As the
equation indicates, it assumes linear relationship with the turbulent intensity.
16
Combust. Flame vol. 19, 203-212, 1972
Motor Vehicle Engines, Mir Publishers, Moscow, 1971 Translated by A. Troitsky
18
Gat and Kauffman Combust. Sci. Technol. Vol. 23, p 1-15, 1980
17
For the second stage of flame development, beyond a value of r = 3 cm, the above
expression may be increased by a factor k which is equal to 1.0719.
Mattavi et al20 found that the flame speed ratio is strongly affected by engine speed.
They obtained a value of unity flame speed ratio for a value of u´/S L of zero. The relation for
flame speed they have reported is as follows
FSR)T.S = 1.0 + 4.01(u´/SL)
Mathur et al21 used this relation for the third stage of flame propagation and used this
relation for the second stage as follows
FSR)max =FSR)T.S(r/3)0.5
Groff and Matekunas22 obtained relations, which were different from Mattavi et al20.
Their relation for the third stage takes into account the effect of spark timing on the flame
speed ratio. They obtained the following relation for flame speed ratio
FSR = 2.00 + 1.21(u´/SL)(p/pm)0.82s
Where
p is the pressure, kPa
Pm is the corresponding motoring pressure, kPa
S is the spark advance factor given by
s = 1.0 + 0.050.4
where  is the spark advance, crank angle degrees before top dead centre.
This equation was used by Subrahmanyam et al23 for the third stage. This expression was
multiplied by (r/3)0.5, for the first stage and by 1.07(r/3)1.04 for the second stage of
combustion.
Heikal et al24 used the following relation for the ratio of turbulent to the laminar
burning velocity
ST/SL = {1 + b/Prt[r(ST + c Spd)/]a}1/2
where a, b, c, and d are constants. a = 1.42, b = 1.833x10-8, c = 12, and d = 1.75
 is the molecular diffusivity given by /cp [ = ratio of specific heats]
Prt is the Turbulent Prandl number.
19
JPS Ph.D. Thesis report, 1984
Mattavi et al, GMR-2866,1978
21
SAE Paper No. 830333
22
SAE Paper No. 800133
23
Ph.D. Thesis, 1984
24
I.Mech.E. Paper No. 115/79, p 195-200
20
An early correlation for the turbulent burning velocity was a linear one with the
laminar burning velocity without the concept of the turbulent intensity. This correlation took
the form
ST = kff SL
This was justified on the ground that turbulence increased the speed of combustion
due to the wrinkling of the flame front.
Benson et al25 called it the flame factor. They found that it non-dependent on the level
of turbulence, running conditions, and engine type and was obtained experimentally. If no
experiment data was available, the value of the flame factor was adjusted so that the pressurecrank angle diagram gave a symmetrical curve about the top dead centre. Benson et al
obtained a value of 3.15 for kff.
Lucas and James26 and Hiroyasu and Kadota27 obtained the following correlation for
the flame factor as a function of engine speed
Kff = 1+C1*N
where N, is the engine speed in rev/min.
Lucas and James26 assumed a value of 0.00197 while Hiroyasu and Kadota’s27 value
was not much different at 0.002 for C1. Lucas and James reported values for C1 as 0.0017 and
for other researchers.
This relation has the drawback that it assumes a constant nature of turbulence
throughout the period of combustion. It implies that the turbulent burning velocity can vary
only through the laminar burning velocity for a given engine speed. It does not take into
account the effect of flame development at the early stages of combustion.
Annand28 had used a multiplication factor (presumably the flame factor as defined
above) which was dependent on the turbulence parameters. The factor was an “ arbitrary
multiplication factor” and was not clearly specified.
Girgis and Tidmarsh29 called the quantity C1 as the flame velocity function. They
found this quantity to be relatively constant for a given combustion configuration.
Lancaster et al1 used the relation for turbulent burning velocity by applying the
concentration of mass to the moving flame front (mass continuity equation). This gives the
rate at which the fuel is engulfed by the advancing front.
dmb/dt = u Af ST
where dmb/dt is the mass burning rate or the fuel engulfment rate, kg/s,
25
Proc I Mech. E 191(1977) paper 32/77, Proc I Mech. E 189(1975), Int. Journal Mech Sci.
17(1975), and SAE 780663
26
SAE Paper No. 730053
27
15th comb symposium, 1974.
28
Proc I Mech. E Vol. 185, p 119, 1971
29
I Mech. E Conf C114/79,1979
u is the density of unburned mixture ahead of the flame front or that of the fuel in the
unburned mixture, kg/m3,
Af is the area of the flame front, m2
They called ST as the turbulent flame speed or the burning velocity of the flame
relative to the unburned gases, m/s
The mass burning rate may be obtained from the combustion model typically Krieger
and Borman30 from which the density of unburned charge may also be obtained. The area of
the flame front may be obtained from the geometry of the flame.
Hamamoto et al31 gave the following relation for the ratio of turbulent to laminar
burning velocity.
ST/SL = 1.0+5.6(u´/SL)1.80
They used Lavoie’s32 relation for SL. They reported that this equation (above) is
useful for turbulence intensity greater than about 0.3m/s.
Gat and Kauffman18 used Shelkin’s5 relation for the ratio of laminar to turbulent
burning velocity. For a wrinkled flame front
ST/SL = [1 + (u´/SL)2]1/2
They found the equation was superior to a linear to parabolic equation. They also
found that of all the turbulent characteristics, the ratio of turbulent to laminar burning
velocity best correlates with the turbulence intensity, u´. They also found that the basic
relationship between the burning velocity and the turbulence characteristics do not change
with the increase in dilution of the fresh charge by recirculation of exhaust gas.
Factors Affecting Turbulence Burning Velocity
Factors affecting turbulence burning velocity are the same as those affecting laminar-burning
velocity and essentially in the same manner.
1.
Equivalence Ratio
Ohigashi and Hamamato33 studying the effect of equivalence ratio on burning velocity with
propane-air mixture found that the burning velocity reached a maximum at mixture slightly
richer than stoichiometric. In a companion paper Ohigashi et al34 indicated that with weak
turbulence, the maximum burning velocity occurred around stoichiometric air-fuel ratio
whereas with strong turbulence the burning velocity is independent of the mixture strength
over a fairly wide range of equivalence ratios (0.88 to 1.27). But in all cases the burning
velocity decreases if the mixture is very lean or rich.
JPS 23 and Lancaster et al21 have predicted a similar trend.
30
ASME 66 WA/DGP-4,1966
JSME Int. J 30(1987):1995-2002
32
Lavoie, SAE Paper No. 780229
33
Bull JSME 13(1970):1232-39
34
Bull JSME 14(1971):849-858
31
2.
Spark Timing
Increasing spark advance increases burning velocity. This is probably because peak
temperatures are higher when the spark is advanced. Lancaster et al21 and JPS23 have showed
this. The higher temperatures increase the laminar burning velocity and the reaction rate.
3.
Swirl
Chaibongsai et al35 obtained higher burning velocities by using a modified shrouded inlet
valve (perforated with large holes).
4.
Engine Speed
According to Lancaster et al1, speed is the engine variable, which has the greatest effect on
engine flame speed. The increase in burning velocity due to higher engine speeds is primarily
due to higher mixture turbulence. Higher speeds also probably increase temperatures due to
reduced heat losses as a result of reduced time available .A similar trend was obtained by
Chaibongsai et al35.
5.
Compression Ratio
Lancaster et al1 reported a slight decrease in turbulent burning velocity with higher
compression ratios. A more substantial decrease in burning velocity with increase in
compression ratio was shown by JPS19. This was apparently due to small changes in the
turbulence characteristics. Chaibongsai et al35 found that the burning velocity is not sensitive
to variation in compression ratio.
6.
Laminar Flame Speed
Lancaster et al1 has reported from literature that the turbulent burning velocity remains
constant with varying laminar burning velocity if the combustion temperature remains
constant. This was shown at a constant equivalence ratio by varying the composition of the
inert diluent in the mixture. It was concluded that it was the reaction rate and not the laminar
burning velocity which influenced the turbulent burning velocity.
Turbulent Intensity
The turbulent intensity has been earlier defined as the root mean square value of the velocity
fluctuation about the mean velocity.
The calculation of turbulent burning velocity requires the knowledge of turbulence
intensity. Karlovitz gave the following formula for turbulent intensity
u´ = SL/3(u/b – 1)
in which u and b are densities of the unburned charge and burned products respectively. In
this equation, the turbulent intensity is assumed to depend on the laminar burning velocity
and independent of mechanical factors, which affect the turbulence in the engine.
Lienesch36 found that the motored turbulent intensity was a function of engine speed,
crank angle and inlet swirl. By non-dimensionalising the turbulent intensity with the mean
35
36
SAE Paper No. 800860
GMR-3206, FISITA Proc, 1980
piston speed, Vp, he was able to plot the quantity u´/Vp as a function of crank angle and get a
single curve indicating that the intensity is nearly linear with engine speed. According to him,
this curve may be adjusted up or down by a constant multiplier and can be used for
determining the turbulent intensity at various crank angles.
Mathur et al21 used this data to obtain a polynomial curve for u´ as follows:
u´ = Vp(C50+ C51 + C522+------C577)
where  is the crank angle in degrees with zero degrees at bottom dead centre of the intake
stroke. When  greater than 185
u´ = Vp(C60+C61+C622+---------C677)
They used a correction factor c as follows
u´(actual)= u´/C
where C was taken to be 3.0 to 3.4 which was obtained by matching experimental data at a
baseline condition.
JPS et al19 used the same equation with C equal to 1.2 to 1.5.
The drawback of using this data is that the turbulent intensity has been obtained from
motoring tests. It has been seen that while turbulence accelerates the flame velocity
markedly, the flame arguments the intensity of turbulence (Mizutani16). Witze et al2 have
indicated that there is an increase in turbulence in the post flame gases.
At the flame front, the kinetic energy of the gas increases because of the rapid
acceleration and the energy of the turbulence also increases simultaneously. It seems,
therefore, to be quite natural to assume that the increment in the turbulent energy across
combustion wave is closely related to the increment in the kinetic energy. Experiments
indicate that the increase in the turbulence level also depends upon the energy of turbulence
in the approach flame, that is the motored value.
Mizutani16 has given a relation for the amplifying effect of the flame on the turbulent
intensity. This relation gives a correction factor to be added to the value turbulent intensity
prior the passage of the flame, that is, the motored value.
(uf´ / SL )2 = ( u1´/SL) + K2(u1´/ SL)(ST/SL)m Un SL(l+m-1) [(u / b)2 –1] (m+n)/2
where K2=2(1-) K1
l=2
m=2a
n=2(1-a)
U is the gas velocity
a is a constant
The values of l, m and n depend on the type of flame.
Rao and Bardon37, quoting various references, state that turbulence in engines is
isotropic and does not vary greatly from location to location within the cylinder. They also
state that intensity of turbulence at the commencement of the compression stroke (closure of
the intake valve) varies between 20-50 per cent of the mean piston speed. So they assume
that, at the start of compression
u’ivc/Vp = 0.288
and therefore, we have
u’/ u’ivc = (Vivc/V)1/3
where subscript ivc indicates inlet valve closing.
It is thus possible to estimate the instantaneous values of turbulence intensity in the
charge as it varies over the closed part of the cycle from inlet valve closure in the
compression stroke to exhaust valve opening in the expansion stroke.
Factors Affecting Turbulent Intensity
A number of engine variations affect the turbulent intensity, The various studies have been
carried out, however, on a motored engine only.
1.
Engine Speed
It appears that turbulent intensity at the top dead centre increase almost linearly with increase
in engine speed. This has been shown by Lancaster et al1, Cole and Swords 38, Wakisaka et
al39, Groff and Matekunas22, Grasso and Bracco40 and Mattavi et al41.
Mattavi et al20 measured the turbulent intensity for a 45o crank angle interval before
tdc at the spark plug location. As shown in Fig. 3, these intensities increase with engine speed
for the wedge and open chambers. Lancaster1 also demonstrated similar behavior, for a disc
chamber. Trends were similar for measurements away from the spark plug. The flow field in
the wedge chamber appears to be anisotropic with a higher turbulent intensity in the vertical
direction due to higher swirl. The open chamber results, like those of the disc chamber, are
close to being isotropic.
2.
Volumetric Efficiency
Lancaster et al1 showed that the turbulent intensity increases linearly with increase in engine
volumetric efficiency but to a lesser extent when compared with engine speed. Grasso and
Bracco39 have obtained a similar trend.
3.
Throttle opening
Lancaster et al1 obtained a parameter called the relative inlet volume flow rate obtained by
dividing the intake mass flow rate at each condition by the mass flow rate at the baseline
37
Proc. I.Mech.E., vol. 199, no. D3, p 221-226, 1985
17th Symposium on Comb,
39
I.Mech.E Proc., C91/79, 1979
40
AIAA Journal, Vol. 21, no. 4, p 601-607, 1983
41
I.Mech.E Conf. Publ., 1979
38
condition and correcting this mass flow rate for changes in intake manifold charge density
relative to baseline. Thus
Relative Mass flow Rate (RMFR) =Mass flow rate /Mass flow rate at baseline condition.
Relative Volume Flow Rate,
RVFR =RMFR*(Intake manifold charge density at baseline condition/Intake manifold charge
density).
They obtained a straight-line relation indicating that for a given geometry the intensity
can be expressed as a constant multiplied by the intake volume flow rate. The correlation
implies that piston generated velocities are an insignificant contribution to the turbulent
intensity in a disc chamber.
Throttling decreases the intake pressure and hence inlet charge density thereby
increasing the relative volume flow rate. From the correlation above the turbulence intensity
would thereby increase. Cole and Swords38 have indicated a slightly higher turbulent intensity
at part throttle compared to full throttle operation. Lancaster et al1 indicated that throttling
influences the intake charge density more than the intake jet velocity.
4.
Compression Ratio
Lancaster1could not obtain a clear trend of variation of intensity with changes in
compression. It appears that the intensity increases slightly with small increase in
compression ratio and subsequently decreases. Grasso and Bracco40 indicate that the intensity
“ is rather insensitive to compression ratio”.
4.
Inlet Swirl
Inlet swirl introduced by means of a shroud is a popular method. Lancaster1, Wakisaka et al39
and Groff and Matekunas22 have studied the effect of using a shrouded inlet valve. They have
obtained a larger value of turbulent intensity as is to be expected, especially at higher engine
speeds. Groff and Matekunas22 indicated an average 42 percent higher intensity for the
shrouded valve.
5.
Squish
Davis and Borganakke42 indicated a small reduction in turbulence intensity, of the order of
about 10 percent as the squish area was reduced from 75 percent to zero. Mattavi et al20
indicated a higher level of intensity for a wedge chamber (higher squish compared to open
chamber (low squish).
6.
Dilution
Davis and Borganakke42 studied the effect of turbulent intensity as a function of exhaust gas
recirculation. The turbulent intensity was estimated at the top dead centre. It was reported that
only small changes in turbulent intensity occurred over the range of recirculated exhaust gas
levels considered. The turbulent intensity showed a slight decrease as the dilution was
42
Davis and Borganakke, SAE Paper No. 820045
increased. The decrease was greater if the spark plug was located at the cylinder head/wall
interface (corner location) compared to the centrally located spark plug.
7.
Flame Speed Ratio
Lancaster et al1 found that the flame speed ratio is a linear function of turbulent intensity. It is
found to correlate well with both shrouded and non-shrouded valves, for various volumetric
efficiencies and engine speeds. This indicates a linear correlation of flame speed ratio with
turbulence intensity similar straight-line relations was obtained by Groff and Matekunas22 for
flame speed ratio and turbulent intensity non-dimensionalised with the laminar burning
velocity.
Lancaster et al1 concluded that the turbulent flame speed was dependent on the
turbulent intensity and independent of turbulent scale.
According to Lancaster (SAE Paper No. 760159), in the stationary analysis (as shown
in the Figure 4 below), it was assumed that turbulence was stationary during the measurement
interval (which was 45o in one cycle). The velocity corresponding to each anemometer
measurement was computed. The mean velocity was computed as the average of the
measured velocities in the record. The turbulent intensity was computed as the RMS variation
about this mean.
Lancaster found that there was a significant variation in mean velocity during the
measuring interval. This variation in mean velocity distorted the time-averaged intensity and
scales computed by the stationary analysis. The stationary analysis was based on the
conventional definition of turbulence, which considers all fluctuations about a mean velocity
as turbulence. This definition includes as turbulence the time-varying component of the
ensemble-averaged mean velocity, an inclusion, which is inconsistent with the concept of
turbulence being irregular, high frequency fluctuations. This inconsistency was resolved by
redefining turbulence and applying a non-stationary analysis to the data. The turbulence was
redefined by including a time-varying mean velocity.
Figures 5 and 6 have been taken from Cole and Swords38 showing mean and RMS
turbulent velocity versus engine speed for two different locations in the combustion chamber.
The engine was motored. Figure 7 shows the mean and RMS turbulent velocity at a particular
location as a function of throttle position, at a given speed.