Swaminathan N., Bray K.N.C. (eds.) Turbulent Premixed Flames

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5.2 Future Directions and Applications of Lean Premixed Combustion 383

A challenge is to correctly model and measure the residence times in post-ﬂame

gases. RANS predictions of residence times often are unrealistically small because

the actual path of a ﬂuid element in a recirculation zone, for example, is longer than

that predicted from the time-averaged ﬂow ﬁeld. One motivation for applying LES

is to achieve realistic predictions of residence times. Another challenge is to develop

methods to account for strain rate on the turbulent premixed ﬂamelets. The leading

edge of the premixed main ﬂame in an LPP device is lifted to a position within a

strong shear layer, where strain rates are large. Images of the ﬂamelet thicknesses

in LPP devices would help to determine if a thickened ﬂamelet model or a strained

laminar ﬂamelet model is more appropriate.

Another issue is that models are needed to predict ﬂame-stability limits. Better

models would assist in achieving operation of LPP devices closer to the lean limit.

To maintain safety margins, a non-premixed pilot ﬂame often is used, so additional

reductions in pollutant levels should be possible if there is better understanding of

how to minimise the pilot fuel yet still stabilize the main ﬂame. An acoustic com-

bustion instability that is called growl can occur if LPP devices are operated outside

of their operating margins. This instability has been linked to several factors: the

shedding of shear layer vortices, the precessing of recirculation zones, the movement

of the premixed ﬂame anchoring position, and the time lag introduced by droplet

evaporation. Current industry practice relies heavily on trial-and-error methods to

avoid growl, such as varying the location and number of fuel injector ports, the gas

velocities, and the fuel-drop diameter.

5.2.2 Reliable Models that Can Predict Lift-Off and Blowout Limits

of Flames in Co-Flows or Cross-Flows

A major challenge is to develop models that can correctly predict ﬂame-blowout

limits. These limits determine the operating envelope of many practical combustion

devices. For safety reasons, fuel and air often are introduced in separate streams

in gas turbines, scramjets, rockets, direct-injection internal combustion engines, and

industrial burners. Mixing often occurs in the lift-off distance that exists between the

fuel injector and the downstream ﬂame, parts of which consist of partially premixed

combustion. The fundamental physics of lift-off was studied extensively for the

case of a lifted simple jet ﬂame. The ﬂame-base region was observed to consist

of a ‘triple ﬂame’ by Bray and co-workers [43]. Both a lean premixed reaction

layer and a rich premixed layer exist, and they create products that come into

contact to form a central diffusion ﬂame. When the ﬂow remains laminar the lift-off

heights of several laminar jet ﬂames have been predicted accurately by the highly

resolved CFD solutions of Smooke and co-workers [47], which include complex

chemistry and buoyancy forces. However, practical devices introduce complexities

associated with turbulence, swirl, and co-ﬂowing or cross-ﬂowing air. An extensive

set of measurements was reported that quantiﬁes the blowout and lift-off limits for

all of these cases [48–53], but reliable computations of blowout limits are still in the

developmental stage.

To identify the information that is still needed to properly model blowout limits,

some scaling arguments can be of help. For a lifted, initially non-premixed jet ﬂame,

the basic criterion that controls lift-off height is that the gas velocity incident upon

384 Future Directions

the lifted base region (U

) must equal the propagation speed of the ﬂame base (S

)

[54]. The propagation speed of the base is the product of the strained laminar ﬂame

speed (S

) and an enhancement factor that is due to turbulence (S

)so

= S

), (5.1)

where S

is the turbulent burning velocity of an edge ﬂame. To proceed, estimates

of the quantities in Eq. (5.1) are needed. When a simple jet is considered, the

gas velocity U

everywhere along the stoichiometric contour is argued to be nearly

constant and approximately equal to (U

), where U

is the jet exit velocity and Z

is the stoichiometric mixture fraction. Thus at any location along the stoichiometric

contour the mean velocity U

is nearly equal to the stoichiometric value (Z

)of

the conserved scalar. The next step is to estimate the strained burning velocity S

One proposed idea [55]istouse

= S



1 +

K ˆα



−1

, (5.2)

where K is the strain rate, ˆα is the thermal diffusivity, S

is the unstretched laminar

ﬂame speed, and c

is a constant. This relation states that S

decreases from S

to zero as the ﬂame is strained. It is not the conventional relation among burning

velocity, Markstein number, and Karlovitz number that often is applied in the limit

of zero strain. Instead, only the limit of a large strain rate is considered; at this limit

approaches zero for any value of Markstein number. In some models the strain

rate (K) is replaced with the scalar dissipation-rate (SDR) [55], but strain-rate and

dissipation-rate concepts are similar. For a simple jet, strain rate K is proportional to

the jet centreline velocity divided by the jet width; the former scales as U

/x),

whereas the latter is proportional to x. Combining these relations with Eq. (5.1),

while neglecting the term that is equal to unity in Eq. (5.2), and setting x equal to

the lift-off height h, leads to

/ ˆα

= Z

−1/2

B, (5.3)

where

B = c





1/2



ˆα



−1/2

. (5.4)

Equation (5.3) is in agreement with measured lift-off heights [48], provided

that the quantity B deﬁned by Eq. (5.4) is a constant. More research is needed to

evaluate B as well as the turbulent burning velocity S

of an edge ﬂame. It would

be attractive to replace S

with a formula that was measured in a Bunsen ﬂame,

for example, but this may be erroneous because the triple ﬂame may not undergo

the same wrinkling and straining process as does a Bunsen ﬂame. The previous

arguments that lead to Eq. (5.3) are somewhat speculative, but they do identify the

idea that the straining of the ﬂame base can explain the measured values of lift-off

heights. Note that the left-hand side of Eq. (5.3)isaninverseDamk

ohler number,

which often has been found to correlate ﬂame lift-off and blowout data. Blowout

must occur when the lift-off height (h) exceeds the length of the region within which

5.2 Future Directions and Applications of Lean Premixed Combustion 385

THEORY

BlowoutStable

100

20,000

10,000

FUEL VELOCITY (m/s)

FUEL VELOCITY U

(m/s)

Fuel jet velocity / jet diameter (s

-1

)

0510 1015 20 20 30 0 200

Cross flow air velocity/jet diameter (s

-1

)COAXIAL AIR AXIAL VOLOCITY U

(m/s)

COAXIAL AIR VELOCITY (m/s)

(a) Coaxial jet

(b) Coaxial air with swirl

EXCESSIVE FUEL

(RICH) BLOWOUT

ZERO SWIRL

BLOWOUT LIMIT

S =0.38

0.25

0.15

OVERALL

LEAN

EXCESSIVE AIR

(LEAN) BLOWOUT

400 600

Stable

Blow

out

Blowout

Figure 5.16. Measured ﬂame blowout limits for the (a) coaxial jet of Dahm and Mayman

[51]; circles = 5-mm inner-tube diameter, squares = 3-mm diameter. (b) Swirling coaxial jet

of Driscoll and co-workers [52]; swirl number is largest for the curve on the right. (c) Jet in a

cross-ﬂow of Kalghatgi [50].

the gases are ﬂammable. For a simple jet this length is proportional to (d

). Thus

if h in Eq. (5.3) is replaced with (d

) and if U

is replaced by the jet blowout

velocity U

, then

/ ˆα

= c

−3/2

B, (5.5)

which is also in reasonable agreement with experimental data [49] if the quantities

B and c

remain constant. For example, for a typical methane–air ﬂame, the product

of the constants c

and B in the preceding relation, is 0.024.

A more complex case is that of a coaxial jet ﬂame. Consider a central fuel tube

that is surrounded by a larger-diameter tube that contains a coaxial stream of air.

This geometry is of practical importance because if coaxial air is forced across the

diverging boundaries of the central fuel stream, then the fuel–air mixing process will

be more intense and a shorter combustion zone will result. For the coaxial geometry

some measurements of ﬂame blowout limits were correlated in [51]by

∗

/ ˆα

∗

, (5.6)

where the parameters d

∗

, U

∗

, and Z

∗

are the effective diameter, jet exit velocity at

blowout, and stoichiometric mixture fraction of jet ﬂuid for an equivalent single jet

that has the same momentum ﬂux and mass ﬂux as the coaxial jet. Simple relations

for d

∗

and Z

∗

are given in [51] in terms of the diameters and gas velocities of

the inner and outer coaxial jets; for example,

∗

= d





−1/2

1 + ρ

− d

)/(ρ

)



1 + ρ

− d

)/(ρ

)



1/2

. (5.7)

The quantity c

is the only empirical constant that was required to achieve good

agreement between Eq. (5.6) and the measured blowout limits that are seen in

Fig. 5.16(a). This ﬁgure shows that coaxial air (with no swirl) always is destabilising.

The blowout curve always is below the location where the curve intersects the

y axis, which corresponds to a jet with no coaxial air. The coaxial air does signiﬁcantly

386 Future Directions

shorten the ﬂame, but care must be taken to limit the coaxial air velocity to avoid

blowout.

When swirl is added to the outer coaxial air ﬂow, a stable region is measured

[52] to have the same general shape as the zero-swirl case, but the stable region is

seen in Fig. 5.16(b) to become much larger and taller than the zero-swirl case. The

stable region extends far above the point on the y axis that identiﬁes the blowout

limit with zero swirl. Therefore swirl usually is very stabilising for two reasons. Swirl

creates a central recirculation zone that transfers heat to the reactants upstream of

the ﬂame base, and this increases the burning velocity S

. It also creates low-velocity

regions, which reduces U

in Eq. (5.1), and this also is stabilising, providing that the

mixture within the low-velocity region is ﬂammable. For the case of a jet ﬂame in

a cross-ﬂow, the measured blowout curves [50] are shown in Fig. 5.16(c); the stable

region has a shape that is similar to those of the last two examples. However, the

cross-ﬂow of air is very destabilising because the blowout limits are lower than the

case of zero-cross-ﬂow velocity, which is the extrapolated intersection of the upper

part of the curve with the y axis. A fuel jet in a cross-ﬂow occurs in lean premixed

gas turbine combustors as well as in scramjets. Scramjets typically inject fuel from a

port in the wall jet to avoid the melting of fuel injector struts if struts were placed in

the hot airstream.

Several models can correctly predict the blowout limits of a simple turbulent

jet ﬂame, but more research is required to make such models robust enough to

correctly predict blowout limits when coaxial air, swirl, or cross-ﬂow is added. The

RANS model of Bradley and Gu simulates the strained premixed turbulent ﬂame

that occurs at the base of a lifted jet ﬂame [56]; their approach is consistent with

experimental observations. Their model does correctly predict a linear increase in

the lift-off height as the jet velocity is increased. Devaud and Bray [57] simulate

lifted jet ﬂames by employing the conditional moment closure (CMC) method,

whereas in other studies DNS [58] and LES [59] were applied. However, there are

few systematic studies that predict the measured values of lift-off height as the fuel

velocity or injector diameter is systematically varied, which is needed for model

validation. The preceding scaling analysis suggests that the ﬂame base will lift to a

downstream location where the strain rate is sufﬁciently reduced; a realistic model

should be expected to predict that the strain rate decreases in the downstream

direction in a manner that is consistent with experiments. Proper validation will also

require measurements of strain rates on the lifted base such as those of [60] and

[61]. Some other theories are reviewed in [61] that do not assume that the strain rate

governs lift-off. Instead they assume that the ﬂame lifts off in order to ﬁnd a location

where the integral scale is larger [49] or where the ﬂame is less likely to be subjected

to coherent vortices in the shear layer.

5.2.3 New Technology in Measurement Techniques

New measurement technology is now making it possible to visualise the individual

premixed ﬂamelets, the individual turbulent eddies, and the interactions that occur

between the two. The eddy–ﬂamelet interaction represents the fundamental building

block of premixed turbulent combustion, and it is important to measure it for several

reasons. This interaction determines the rate of stretching of the ﬂame surface, and

5.2 Future Directions and Applications of Lean Premixed Combustion 387

Figure 5.17. Reaction layers and HRRs within a turbulent counterﬂow ﬂame imaged by

Ayoola et al. [46] using simultaneous formaldehyde–OH PLIF diagnostics.

thus it controls the amount of the surface area of the reaction layers as well as the

amount of local extinction that may occur. Because eddy–ﬂamlet interactions control

the rate of strain that is exerted, they affect the NO

and CO chemistry. In addition,

acoustic instabilities (see Chapter 3 for ﬂame instabilities) often are associated with

premixed combustion processes; these instabilities can be triggered when a periodic

stream of shed vortices causes periodic oscillations in both the ﬂame surface area and

the heat release rate (HRR). Therefore there is a strong motivation to improve the

spatial and time resolution of current imaging techniques in order to better image

and quantify the eddy–ﬂamelet interactions.

A quantitative measure of the strength of each reaction layer is the HRR, which

now can be recorded using simultaneous formaldehyde–OH PLIF diagnostics [46].

This is an important advance because the local HHR quantiﬁes the local ﬂamelet

chemistry as well as the degree of local extinction. The HRR was demonstrated to be

proportional to the product of the concentrations of formaldehyde and OH, as these

two species react to form HCO in the major chemical pathway that releases heat.

The HRR can be measured by recording PLIF signal intensities (I) for formaldehyde

(CH

O) and OH and applying

HRR = I

f (T ). (5.8)

In general the function f (T ) is a complicated function of gas temperature; however,

this function was shown in [46] to be a constant when the proper ﬂuorescence excita-

tion and emission wavelengths were selected. Figure 5.17 illustrates some images of

the OH, formaldehyde (CH

O), HRR, and OH* chemiluminescence in a turbulent

premixed counterﬂow burner. A different way to image ﬂamelets is to record CH

ﬂuorescence [62, 63] because CH is a short-lived radical that exists only within the

thin reaction layers.

Another advance is the use of phase-locked diagnostics to simultaneously im-

age the 2D velocity ﬁeld and ﬂame structure in combustors that undergo periodic

oscillations. A combustion instability occurs in the partially premixed gas turbine

388 Future Directions

(a)

(b)

(c)

Intensity [a.u.]

Pressure [a.u.]Volumetnic discharge [a.u.]

90 135 180 225 270 315 90 135 180 225 270 315045

0 45 90 135 180 225 270 315 90 135 180 225 270 315045

Phase angle [°]

0.8

0.6

0.4

0.2

0.5

–0.5

–1

0.8

0.6

0.4

0.2

OH*

Intensity

Pressure

Plenum

Pressure

Chamber

h=10mm

h=5mm

h=20mm

- Q

h=5mm

h=20mm

-40 -30 -20 -10 0 10 20 30

-30 -20 -10 0 10 20 30

x (mm)

velocity m/s

10 m/s

VelocityOH PLIF

OH* Chemiluminescence

ϕ=0°

ϕ=90°

ϕ=180°

ϕ=270°

Figure 5.18. Simultaneous phase-locked measurements of velocity ﬁeld, ﬂame properties,

and gas pressure by Stohr et al. [64] to understand acoustic instabilities in a partially premixed

gas turbine model combustor.

model combustor of [64]. Lasers are repeatedly pulsed at one particular phase angle

ϕ of the sinusoidal pressure signal, and the ﬂuorescence signal is phase averaged.

Some results are plotted in Fig. 5.18. In this ﬁgure a gaseous fuel jet issues upwards

and is surrounded by coaxial swirling air. The velocity ﬁeld contours show that a

strong central recirculation zone is formed. Simultaneous images were recorded of

OH PLIF (to quantify the HRR), the velocity ﬁeld using PIV, and the gas pressure.

The sinusoidal curves in Fig. 5.18 provide the phase-lag and time-response infor-

mation that is needed to model the combustion instability. Another recent study

[65] demonstrated that simultaneous PLIF and PIV images can be recorded at a

exceptionally high framing rate of 12 000 frames/s using a diode-pumped YAG laser.

Biacetyl vapour was seeded into the fuel to act as a fuel marker and was excited

5.2 Future Directions and Applications of Lean Premixed Combustion 389

at a wavelength of 355 nm. It also was shown that OH PLIF could be imaged at

1000 frames/s using an Nd:YLF laser [66].

Improved diagnostics also can provide answers to important questions that ini-

tially were raised by Damk

ohler, Markstein, and other pioneering researchers many

decades ago. For conditions that fall within what is now called the laminar ﬂamelet

regime, they proposed the idea that the primary role of turbulence is to increase the

turbulent burning rate by increasing the surface area of the reaction surface. They

assumed that the wrinkled surface continues to convert reactants to products locally

at a rate (per unit surface area) that is similar to that of a laminar ﬂame. Markstein

proposed a relation between the curvature of the reaction surface and its local prop-

agation speed. Several of these ideas were incorporated into the balance equation

for the ﬂame surface density. However, this equation requires a model for the source

term that describes the basic way by which eddies stretch the ﬂame. A relation for

this source term was proposed, but it is based on theoretical speculation and not

on hard experimental evidence. The eddy–ﬂamelet interaction is described by the

stretch efﬁciency function (

) that relates the mean stretch rate (K) to the local

turbulence intensity (u

rms

) and the integral scale of turbulence () in the following

way:

K = 

rms



(5.9)

Computations were performed [67] to estimate 

by ﬁrst assuming that turbu-

lence can be represented by an ensemble of vortex pairs that have different sizes.

The axis of each canonical vortex pair is assumed to be always perpendicular to

the ﬂame surface, and all vortices are counter-rotating such that the vortex pair

exerts only a positive stretch rate. Numerical simulations of many laminar canoni-

cal vortex-pair–ﬂame interactions were ensemble averaged to estimate the stretch

efﬁciency function, and these computed values of 

are used in several LES and

RANS models.

Only recently has it been possible to observe eddy–ﬂame interactions within

fully turbulent premixed combustion. Steinberg et al. [68–70] were able to image

eddy–ﬂamelet interactions; their goal was to provide measured values of 

that

do not require any assumptions about the eddy structure. It was shown that the

geometry of the actual eddies often did not correspond to that of the canonical

vortex pair that was assumed to occur in previous calculations. Cinema-stereo PIV

diagnostics provided high-speed movies of the eddy–ﬂamelet interactions that were

recorded at 1100 frames/s. One interaction is shown in Fig. 5.19. Eddies are identiﬁed

by contours of vorticity; these eddies move to the right and upwards across the ﬂame,

which is the black line. Exceptionally good time resolution (0.66 ms/frame) and a

spatial resolution of 280 μm were achieved, which resolves the Taylor scale, which

was 0.9 mm.

3D movies of the interactions also were reported in [69], but for reduced spatial

and temporal resolution. To obtain 3D images of the vorticity ﬁeld, two simulta-

neous cinema–PIV systems were employed that required horizontal and vertical

laser sheets, respectively. Taylor’s hypothesis was applied as eddies moved verti-

cally upwards throught the horizontal sheets. Measurements from the vertical sheets

indicated that the frozen-ﬂow Taylor hypothesis was an accurate assumption. Typical

390 Future Directions

Figure 5.19. High-speed movies of eddy–ﬂamelet interactions in the fully turbulent premixed

Bunsen ﬂame of Steinberg et al. [69]. Time between images is 0.66 ms. Field of view is

4mm× 8 mm. The Black line is the ﬂame surface. Contours of vorticity vary from −1000 s

−1

(blue) to 1000 s

−1

(red). Flow is from bottom to top. (See colour plate.)

3D results are seen in Fig. 5.20, which indicate that horseshoe-shaped vortical struc-

tures are common. The toroidal structure shown on the right also occurs, but is less

common.

Several efﬁciency functions now have been measured [70] that are useful inputs

for LES subgrid models that include the ﬂame surface density balance equation.

The mean stretch rate (K) is separated into two components: the subgrid strain rate

on the ﬂame (a

t,sg

) and the component associated with ﬂame curvature (K

c,sg

). The

measured relations that represent these subgrid quantities are given in Table 5.1.

The subgrid strain rate on the ﬂame was found to correlate best with the resolved

scale ﬂuid dynamic strain rate of the reactants (S





5.2.4 Unresolved Fundamental Issues

It is clear that some fraction of future research in the ﬁeld of turbulent premixed

combustion will be devoted to resolving a number of lingering questions that were

studied extensively in the past, but have not yet been answered. The reason why

additional research now might be expected to be fruitful is because of recent advances

in DNS and time-resolved laser diagnostics and a new understanding of complex

chemistry. If we were to list some fundamental questions that still need answers,

5.2 Future Directions and Applications of Lean Premixed Combustion 391

Table 5.1. Measured relations [70] for subgrid stretch rate (K

), which is the sum of subgrid strain rate

t,sg

) and the component of stretch that is associated with ﬂame curvature (K

c,sg

)

Notes: The constants in the relations are given in [70]. S



is the subgrid ﬂuid dynamic strain rate, A is the ﬂame area,

and  is the ﬁlter scale. P is the measure probability, $ is the strain-rate transfer function, ϒ is the ﬂame curvature

transfer function, δ

is the unstretched laminar ﬂame thermal thickness, and  is the wrinkling factor.

the list might include these: How well can we predict the turbulent burning velocity

of fully premixed (see Section 2.3 for recent developments) and partially premixed

ﬂames with DNS, LES, or CMC models? What are the measured limits to the ﬂamelet

regime, that is, over what range of conditions can ﬂamelet-based LES submodels be

expected to remain valid? Does the turbulent burning velocity vary as the square

root of the integral scale of the turbulence, as has been postulated in the past? Can

we observe and understand the physical process by which turbulent eddies strain

and wrinkle the reaction layers in order to apply concepts that are sometimes called

the theory of ﬂame stretch [71] to turbulent ﬂames? Can we correctly simulate

Figure 5.20. High-speed cinema PIV movies that record 3D vorticity contours during an

eddy–ﬂamelet interaction in the fully turbulent premixed Bunsen ﬂame of Steinberg et al.

[69]. Two cinema PIV systems are used that employ vertical and horizontal laser sheets,

respectively. Field of view is 4 mm × 8 mm. The contours of vorticity shown corresponds to

700 s

−1

392 Future Directions

100

-40 -20

0.0 0.2 0.4

0.6 0.8 1.0

Simulation

Experiment

Half V Angle (degrees)

Brush Thickness (mm)

20 40 60 80 100 120

x (mm)

z (mm)

(a) (b) (c) (d)

z (mm)

Figure 5.21. DNS of Bell et al. [76] of the V-ﬂame experiment of Cheng and Shepherd: (a)

Computed instantaneous reactedness, (b) computed mean reactedness contours, (c) computed

and measured half-angle of the mean contour, where reactedness is 0.5, which is proportional

to the turbulent burning velocity, (d) computed and measured brush thicknesses.

these eddy–ﬂame interactions using LES subgrid models that employ, for example,

a stretch efﬁciency function [72]. How do turbulent burning velocities depend on

elevated gas pressures and very large Reynolds number conditions? A review of

some of these questions is contained in [73–75].

To begin such a discussion, it is ﬁrst noted that DNS results of Bell et al. [76, 77]

demonstrated that, using no modeling constants, it is now possible to predict accurate

values of the turbulent burning velocity of the V-ﬂame experiment of Cheng and

Shepherd [76] and the 2D slot Bunsen experiment of Filatyev et al. [63] for realistic

(but moderate) Reynolds numbers. In [63] the reactants were methane and air, and

the Bunsen burner exit dimensions were 50 mm × 25 mm; the mean velocity of

the reactants was 3 m/s. The conditions in [63] and [76] represent fully turbulent

ﬂames, because the burning velocities (S

) varied between 2.5 and 4.0, but the

turbulence level was only of moderate intensity, because values of u

rms

were

1.1 and 0.8. The spatial resolution of 60 μms of the adaptive mesh in the DNS

was sufﬁcient to resolve the Kolmogorov scale of both experiments, and the DNS

included a 20-species, 84-reaction chemistry mechanism.

Results of the DNS for the V-ﬂame are seen in Fig. 5.21. The computed half-angle

(θ/2) of the brush agrees with the experiment, as does the turbulent burning velocity

), which is (U/S

)sin(θ/2), where U is the velocity of the reactants. The

normalised burning velocity of the V-ﬂame is 3.95 for the DNS and 3.62 cm/s for the

experiment. Figure 5.22 displays some DNS results for the 2D slot Bunsen ﬂame. The

thick line represents the

c = 0.5 contour, from which the turbulent burning velocities

) were determined to be 2.45 and 2.55 for the DNS and the experiment,

respectively. The brush thicknesses of the Bunsen experiment and the DNS were

also in agreement.

It is now generally understood that turbulent premixed combustion is geometry

dependent, because turbulent burning velocity depends on the amount of ﬂame

surface wrinkling, and this wrinkling process differs for each burner geometry. It is

useful to deﬁne the following categories of turbulent premixed combustion: Bunsen

ﬂames, V-ﬂames, counterﬂow ﬂames, and spherical ﬂames. The best practice is to