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

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5.2 Future Directions and Applications of Lean Premixed Combustion 393

Figure 5.22. DNS of Bell et al. [77] of the slot Bunsen experiment of Filatyev et al. [63]:

(a) Computed 1684 K isotherm; (b, c) measured and computed mean reactedness contours

(black line: reactedness = 0.5); (d) measured and computed turbulent burning velocities of

the experiments of Filatyev et al. [63].

compare computations with experiments only if the burner geometry is the same

for both. Similarly, it is best to correlate turbulent burning velocity data only from

burners of similar geometry. This fairly obvious rule has not been followed in the

past. For example, a spherical ﬂame becomes more wrinkled in time; Bunsen and V-

ﬂames become more wrinkled as the distance from the anchoring location increases.

Bunsen and V-ﬂames have an imposed mean velocity of the reactants, whereas

spherical ﬂames do not. Therefore it does not seem logical to expect that burning

velocities that are measured for different types of burners will correlate, even if the

turbulence level and integral scales of the reactants are matched (see Section 2.3 for

recent developments.)

LES and RANS simulations also have accurately predicted values of the turbu-

lent burning velocity, but unlike DNS, some modelling constants must be speciﬁed.

LES predictions of Charlette et al. [78] appear in Fig. 5.19(a), while the RANS result

of Peters [ 79] and Duclos et al. [80] appear in Figs. 5.23(b) and 5.23(c). It is noted

that all three sets of curves display a ‘bending’ that is seen in many experiments,

u′/S

u′(m’s)

CFM 2b

Experiment of

Abdel-Gayed et al.

50101520

04812

0.0

10.0

(a)

(b) (c)

0.0

10.0

20.0

experiment

of Bradley

(dashed lines)

LES (solid lines)

for different filter size

Figure 5.23. Comparisons of turbulent burning velocities predicted by (a) the LES of

Charlette et al., [77] (b) the RANS/G-Equation approach of Peters [78] (dashed line), and

the RANS–coherent ﬂamelet model of Duclos et al. [79] with measurements of Abdel-Gayed

et al. [80].

394 Future Directions

and all three models yield values that are similar to experiments of Bradley and co-

workers [81]. The LES of Charlette et al. assumed that subgrid turbulent diffusion

is represented by a Smagorinsky relation (see Chapter 1), and the mean volumetric

reaction rate

˙ω was s et equal to

˙ω = ρ

0,SG



. (5.10)

To model 

the ﬂame surface density balance was considered and the diffusion

and convection of 

were neglected, so the production and destruction terms were

equated. Equation (5.10) becomes:

˙ω = ρ (1 − c) exp



−E



1 +









, (5.11)

where

c and T are the resolved progress variable and temperature, respectively.

Another relation was included to relate subgrid turbulent velocity u





to the resolved

vorticity ﬁeld, and the exponent β was set to 0.5 to achieve best agreement with

measurements. A is the Arrhenius pre-exponential constant, F is a thickening factor,

and 

is the stretch efﬁciency function [67, 78]. A different LES subgrid model was

developed by Hawkes and Cant [82], who included Eq. (5.10) but used the surface

density balance equation instead of Eq. (5.11). Their computed values of S

were

as large as 2.6 for turbulent ﬂame in a box.

Another LES subgrid model involves the G equation, as described by Pitsch

et al. [72]. The height of a Bunsen ﬂame was computed, and it differed by only 6%

from a corresponding experiment. Because ﬂame height is inversely proportional

to turbulent burning velocity, and because the LES does predict the correct ﬂame

height, this implies that the LES does accurately predict the experimental burning

velocity. The resolved-scale wrinkled interface is thicker and less wrinkled than

the true interface, which cannot be resolved. The resolved interface is forced to

propagate at a speed of S

T,SG

, assumed to be equal to

T,SG

= 1 + b





1 +









−1



1/2

, (5.12)

where D

and D are the turbulent and molecular diffusivities, respectively,  is the

LES ﬁlter scale, and b

and b

are constants. It was argued that this function behaves

properly at the thin-ﬂamelet limit where the laminar ﬂame thermal thickness, δ

is much smaller than  and S

T,SG

should be proportional to (u





). It was also

argued that it behaves properly at the thick-ﬂamelet limit, where δ

is larger than 

and S

T,SG

should be proportional to (D

/D)

1/2

Another unresolved question is related to the limits of the ﬂamelet regime; these

limits have not been measured accurately, and current information is based only on

theoretical scaling arguments. It would be useful to know the range of conditions

over which ﬂamelet models are applicable. Peters [83] deﬁnes a laminar ﬂamelet to

be a layer that contains a preheat and reaction zone, has gradients in the normal

direction that are signiﬁcantly larger than gradients in the tangential direction, and

has a molecular diffusivity within it that is much larger than its turbulent diffusivity.

Peters also deﬁnes another regime that occurs when the preheat zone is broadened

but there is no broadening of the reaction zone. I n this regime small eddies ﬁt in the

5.2 Future Directions and Applications of Lean Premixed Combustion 395

preheat zone but do not ﬁt into the reaction zone. This regime has been called the

regime of the ‘broadened preheat zone/thin reaction zones’ or ‘thickened layers’.

There is experimental evidence that preheat layers of turbulent ﬂamelets vary

from about 0.5 to about 4 times the thickness of the unstretched laminar preheat

layer; a number of studies are reviewed in [72]. Unfortunately there has been no

experimental veriﬁcation that turbulence is the cause of the few cases of layer broad-

ening that have been recorded. This would require the imaging of vortices that are

smaller than the layer thickness, which is not yet possible. Measurements that simply

show that the layer is thicker than the unstretched ﬂame thickness are not conclusive

evidence that turbulence is the cause of the broadening. A laminar ﬂamelet may

be 3–4 times thicker than an unstrained laminar ﬂame, not because of turbulence,

but because of the strain rate that is applied, because of the orientation of the layer

with respect to a laser light sheet, or because several layers have merged together

to give the appearance of a thick reaction zone. There is almost no hard evidence

that turbulence alone can cause distributed reaction zones. Documented examples

of distributed reactions usually involved the rapid heating of reactants in rapid-

compression devices such as HCCI engines and shock tubes. In these cases it is the

rapid compression (and not the large turbulence level) that raises the temperature of

the reactants above the ignition temperature and thus is the cause of the distributed

reactions. However, improved spatial resolution of measurement techniques is ex-

pected to provide measurements of the limits of the ﬂamelet regime in the future.

This can be achieved by applying PLIF and Rayleigh scattering imaging diagnostics

that have thinner laser sheets and have optics that zoom in to resolve smaller scales.

5.2.5 Summary

New designs of practical combustion devices are taking advantage of the beneﬁts

of partial premixing, but there remains a gap in our ability to model these types

of ﬂames. In real devices the fuel and air often are introduced in separate streams;

examples are fuel jets introduced into cross-ﬂowing or co-ﬂowing airstreams. A mix-

ing region is followed by a downstream partially premixed combustion region. This

avoids ﬂashback problems and results in low levels of NO

, CO, and soot. However,

partial premixing increases the probability of ﬂame blowout and the occurrence of

acoustic instabilities compared with conventional non-premixed combustion. LESs

and DNSs have made impressive progress in simulating some important basic con-

cepts, including the wrinkling of ﬂame sheets, the local propagation of the interface

where the premixed ﬂames exists, and the unsteady ﬂamelet modelling of the inter-

face region where the non-premixed ﬂames exist. However, proper assessment of

models still requires new experimental information. Measurements are needed of

the instantaneous structure of the reaction layers, the ﬂame index (which indicates

whether the local combustion is premixed or non-premixed), and the stretch efﬁ-

ciency function (which is in the source term of the ﬂame surface density equation in

LES subgrid models). One new research direction is the effort to achieve improved

experimental spatial resolution in order to zoom in and image the ﬁne-scale ﬂame

structure including scalar gradient, and the eddy–ﬂame interactions. Another new

direction is the development of kilohertz PLIF and PIV imaging methods to record

high-speed movies of combustion instabilities and eddy–ﬂame interactions. Some

396 Future Directions

DNS results were presented to show that DNS has successfully simulated the exper-

imental data that was obtained in laboratory-scale turbulent premixed V-ﬂames and

Bunsen ﬂames.

5.3 Future Directions in Modelling

By K. N. C. Bray and N. Swaminathan

The balance between the various different energy sources that will be in use globally

in the years ahead cannot be predicted with conﬁdence. We do not know what frac-

tion will be produced from biofuels or from tar sands, for example, or the nature of

the fuels to be derived from these sources, or the extent to which electric vehicles will

take over road transport, or the means by which the resulting increased demand for

electrical power will be met. What is apparent is that, although combustion processes

will continue to provide a major source of heat and power for the foreseeable future,

the speciﬁcations of future fuels are likely to be more variable than at present, creat-

ing a range of issues [84], such as ﬂame position, stabilisation, ﬂashback, combustion

oscillations, etc., for gas turbines and engine knock and misﬁres for reciprocating

engines, to deal with while optimising combustors or engine designs. At the same

time, growing legislative and ﬁnancial pressures must be anticipated, which will en-

courage more efﬁcient use of fuel and will further constrain emissions of pollutants

and greenhouse gases. In these uncertain circumstances, designers and operators of

combustion systems will require the most accurate and reliable ways to predict the

inﬂuence of changes in fuel speciﬁcation, operating procedure or plant design on the

performance of their equipment, and such predictions must be provided by models

and computer codes that are based on a fuller understanding of the physics and

chemistry of combustion and the amount of empiricism involved in the modelling

must be minimised. Furthermore, the choices made by designers of combustion sys-

tems are strongly inﬂuenced by policy on energy and environment for which sound

scientiﬁc advice is imperative [85].

In this closing section, we ﬁrst identify some developments of turbulent com-

bustion modelling capabilities that appear to be desirable. Strengths and potential

weaknesses of existing models are then discussed, in order to assess the ability of

each model to meet the challenge of these future requirements and, ﬁnally, some

unsolved problems are identiﬁed and indications of future directions are proposed.

Inevitably these conclusions are based on the personal judgement of the present

authors; other recent reviews of the present and future status of the subject may be

found in [86 –90].

5.3.1 Modelling Requirements

1. Chemical Kinetics: A detailed and accurate chemical kinetic mechanism, appro-

priate for the fuel–oxidiser system under consideration, is an essential feature

of any model that aims to predict pollutant emissions, auto-ignition, extinction,

or ﬂashback phenomena. Practical fuels may contain heavy hydrocarbon com-

ponents or biofuel fractions for which appropriate data is not always available,

and validated mechanisms are often too large to be directly included in tur-

bulent combustion simulations. On the other hand, numerically stiff algebraic

5.3 Future Directions in Modelling 397

rate expressions of reduced mechanisms available for simple fuels, for ex-

ample, despite involving fewer chemical species, present their own issues for

simulations.

The accurate prediction of NO

concentrations is a continuing challenge,

partly because of the strong sensitivity to temperature of relevant reaction rates,

so it may sometimes be necessary to take account of heat losses that are due

to radiation, as well as temperature and composition ﬂuctuations that are due

to incomplete mixing. If pockets of fuel-rich combustion can occur, which is in-

evitable in practical engines, then the kinetics of soot formation and oxidation is

relevant. Processes of auto-ignition and the quenching of combustion that is due

to heat losses must also be included in a complete chemical kinetic speciﬁcation.

An accurate and reliable prediction of CO also remains challenging, as noted

in Subsection 4.2.9. The formation of nanoparticles [91] and polyaromatic cyclic

hydrocarbons [92, 93] must also be included in view of the impact of combus-

tion on human health [94, 95] and environment [85, 96]; see Section 4.1 for the

importance of particulate matters in automobile engine emissions legislation.

2. Flows with Non-Uniform Composition: As discussed in earlier sections of this

Chapter and Chapter 4, most practical applications of lean premixed combus-

tion are expected to involve incomplete fuel–air mixing, and partial mixing with

cooled combustion products is also common. An important special case is the

preparation of a combustible mixture through liquid-droplet evaporation, mix-

ing, and the possibility of its simultaneous autoignition.

3. Inﬂuence of Liquid Spray: Although a liquid fuel spray can be expected to

be fully evaporated by the time it reaches a combustion zone, its atomisation,

evaporation, and mixing can have a strong inﬂuence on auto-ignition and ﬂash-

back (see Subsections 4.2.9, 4.3.8, 4.3.9, and 5.1.3), and also on the degree of

inhomogeneity of combustion.

4. Flows with Heat Losses: It may become necessary to take account of radiation

heat losses in some systems in order to improve the accuracy of NO

predictions,

particularly if regions of fuel-rich combustion can occur in considerable portions

of the combusting ﬂow. Modelling of turbulence–radiation interaction is also of

interest, and recent developments on this topic can be found in [97–101]. The

quenching of combustion at cold walls and resulting in emissions of unburned

hydrocarbon species are also of interest, as explained in Subsections 4.1.3 and

4.1.4.

5. Unsteady Effects: Difﬁculties in simulating the development of certain com-

bustion instabilities were referred to in Section 3.1. The possible occurrence

of auto-ignition, ﬂashback, or blowout of combustion is of obvious concern in

gas turbine design, as described in Subsection 4.2.8. Auto-ignition is also cen-

tral to the modelling of HCCI reciprocating engines (see Section 5.1) and mild

or ﬂameless combustion (see Subsection 5.1.3). Predictions of ﬂame acoustics–

combustion dynamics require knowledge of the ﬂuctuating heat release rate,





as noted in Subsection 3.3.1.

6. Non-Conventional Processes: Given a high probability for variability in future

fuels, non-conventional methods such as catalytic combustion may become more

widely used in order to improve combustion characteristics and stability over a

range of operating conditions. The application of catalytic combustion for gas

398 Future Directions

turbines running on syngas/hydrogen is explored in [102]. Catalytic combustion

is an important topic although its treatment does not belong within the scope of

this book as it involves heterogeneous reactions and catalysis. Interested readers

can ﬁnd a detailed treatment of the subject in other references, for example

[103–105].

5.3.2 Assessment of Models

It seems safe to assume that the speed and power of computing systems will continue

to increase, while the unit cost of calculations will go on falling, as Moore’s law pre-

dicts [106]; in these circumstances, the attractions of LES are likely to grow as time

passes. Nevertheless, many issues [107] in LES remain unanswered, for example the

suitability of LES to predict the law of the wall in wall-bounded ﬂows [108, 109] and

the non-trivial inﬂuence of grid [110], all of which will be resolved eventually. How-

ever, we must acknowledge that RANS calculations will remain substantially less

expensive than LES, so a continuing signiﬁcant demand for both types of simulation

is anticipated. The high cost of DNS, particularly with realistic reaction-rate mech-

anisms, will continue to rule out its use for practical problems for the foreseeable

future, although its value for model development is widely recognised. We discuss

RANS models ﬁrst, and then LES.

A. RANS Models

1. Laminar Flamelet Models: Here we include the ﬂame surface density models

and G-equation formulations, introduced in Section 2.2,aswellassimplepre-

sumed PDF models, introduced in Sections 1.7.2 and 2.1, all of which can take

account of detailed chemical reaction-rate mechanisms in tabulated form; see

Subsection 2.2.3. An advantage of these models is that they are relatively in-

expensive to run, although cost and complexity are increased if non-gradient

turbulent transport processes are to be taken into account, as described in

Section 2.1. Predictions of these models are sensitive to the SDR, 

. Their

extension to describe partial premixing is not straightforward, particularly if

regions of fuel-rich burning can occur in diffusion ﬂamelets, and auto-ignition

and quenching do not belong within this framework. The prediction of CO us-

ing these methods is not as good as one would wish. However, these methods

work well for species with fast time scales. Additional modelling strategies

must be sought for these methods to improve the prediction of species with

slow time scales.

2. SDR Models: These models, described in Section 2.3, can be applied in sev-

eral different ways. At sufﬁciently large values of the Damk

ohler number,

the mean reaction rate

˙ω

is proportional to the scalar dissipation 

[see

Eqs. (1.36) and (2.9)], and the algebraic approximations for

, introduced in

Subsection 2.3.5, then lead directly to algebraic models for

˙ω

. Alternatively,

the 

transport equation derived and modelled in Subsection 2.3.4 can be

interpreted as an equation for

˙ω

or  [111]. Used in these ways, SDR mod-

els can be implemented in conjunction with chemical-reaction-rate data in

tabulated form, and have the same advantages and limitations as the laminar

ﬂamelet models previously discussed. Some success of this approach is shown

5.3 Future Directions in Modelling 399

in [112] and [113]. More generally, SDR models provide a promising route to

a more accurate and physically based description of scalar dissipation phe-

nomena, central physical processes in turbulent combustion, as an input to

other combustion models (see [114]).

3. Transported PDF Models: A great advantage of this approach, described in

Section 2.4, is its ﬂexibility. Chemical reaction terms are included in closed

form, and detailed mechanisms can be included; auto-ignition and quenching

processes can be simulated, as can the effects of incomplete mixing and radia-

tion. If velocity components are represented as additional stochastic variables,

both gradient and counter-gradient scalar transport can be predicted. Models

of this type are more expensive to run in comparison with ﬂamelet mod-

els, and cost constraints usually lead to the imposition of simpliﬁed reaction

rate mechanisms. Transient processes would also be expensive to follow. A

more fundamental modelling challenge is met at sufﬁciently large values of

the Damk

ohler number, when reaction zones resemble laminar ﬂames, as the

scalar dissipation and pressure gradient ﬂuctuation terms in Eq. (2.145)are

then linked to chemical reaction rates.

4. Other RANS Models: The CMC approach is well advanced for non-premixed

ﬂames. Its development for premixed ﬂames is hindered mainly by issues

related to the modelling of the conditional SDR of the progress variable, as

noted in Chapter 1. A preliminary calculation using CMC with a classical

SDR model [115] seems encouraging, especially for slow time-scale species.

Similarly to transported PDF models, the CMC method can be used to predict

auto-ignition and ﬂame quenching with additional second-order modelling.

However, this method can be computationally expensive as it involves (N +1)

CMC equations, each with four independent variables for a 3D turbulent

ﬂame involving (N + 1) scalars. However, the computational expense can

perhaps be reduced by using cross-stream averaged CMC equations, as has

been done for non-premixed ﬂames [116], but the applicability of this strategy

for premixed combustion has yet to be studied.

B. LES Models

1. As noted in Subsection 1.7.3, RANS modelling can be extended to LES

and thus the preceding comments apply equally to the LES approach. If

sufﬁciently ﬁne numerical grids with small ﬁlter widths are used, then LES

solutions are found to be relatively insensitive to subgrid scale models, which

is clearly attractive. Also, transient ﬂame processes such as auto-ignition,

ﬂashback, and lift-off height can be predicted, and details of combustion os-

cillations can be obtained, as discussed in Section 3.3. However, the numerical

discretisation scheme and the nature of the solver can affect the details of the

simulated ﬂow and ﬂame, and the high computational cost of LES limits its

regular use in industry. This implies that there can be a strong incentive to

improve subgrid closures, so that larger ﬁlter scales and coarser meshes can

be used. Signiﬁcant advances have yet to be made on this front. A review [87]

of industry-standard approaches to the numerical simulation of gas turbine

combustion has identiﬁed that the unsteady RANS (URANS) methodology

has the potential to predict combustion-induced oscillations at a moderate

computational cost. It is also unclear how well dynamic LES models perform

400 Future Directions

in predicting the SDR in premixed ﬂames. Issues relating to the recovery of

law-of-the-wall behaviour [108, 109] in LES also raise uncertainties in circum-

stances in which the heat and momentum ﬂuxes through the combustor walls

need to be evaluated as design variables.

5.3.3 Future Directions

Turbulent combustion is a socioeconomically important topic, and its modelling will

continue to be an active area of research as long as we go on burning fuel to meet

society’s energy needs in a controlled manner. All established combustion models

will continue to be developed to improve their accuracy, reliability, and capabilities.

The following are some of the topics that are believed to need immediate attention

in order to assist the development of lean premixed combustion equipment.

1. Detailed chemical kinetic mechanisms applicable to present and future fuels are

required. These mechanisms must be able to accommodate variability in fuel

composition.

2. There is an immediate requirement to identify ways to improve CO predictions

because ﬂamelets and transported PDF approaches give similar results whose

agreement with experimental data is only marginal [113].

3. Practical lean-burn systems often involve ﬂow regions with both high and low

Damk

ohler numbers, and thus models with a wider range of applicability are re-

quired. Speciﬁcally, the combustion submodel and the chemical kinetics should

be able to accommodate both fuel-lean and fuel-rich combustion because prac-

tical lean premixed combustion almost always include both lean and rich regions

involving different physics.

4. Reliable and accurate models capable of simulating auto-ignition, ﬂashback,

blowout, and quenching processes are needed.

5. Radiative heat loss and its interaction with turbulence need to be addressed. The

formation rates of oxides of nitrogen are very sensitive t o temperature, and thus

their accurate prediction can sometimes require reliable models for radiation

and its interaction with turbulence.

6. In situations in which liquid fuels are burned, models are needed to simulate

atomisation and droplet evaporation and their interaction with turbulence and

turbulent mixing of the fuel and air, in order to correctly predict the composition

of the mixture entering the combustion zone. Can the modelling of atomisation

and evaporation be decoupled from thermochemistry in spray combustion? If

so, under what conditions would this decoupling be acceptable?

There is a real need to capture the complex geometries of practical combustors in

CFD simulations, and the most computationally expensive combustion models may

not be attractive for regular use in these circumstances. There will be a continuing

need for both LES and RANS models. Also, the level of conﬁdence to be placed in

model predictions must be established. One way to achieve this is through a posteriori

validation of the models using as much experimental data as possible. There is an

urgent need for carefully designed experiments for model validation, both fully and

partially premixed, with comprehensive scalar and velocity ﬁeld information and

covering the widest possible range of burning regimes. In particular, experiments are

References 401

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valuable insights, together with a tool to test model hypothesis and data for model

validation, Reynolds numbers remain unrealistically low. A few test cases at the

highest possible Reynolds numbers would enable the inﬂuence of this parameter to

be explored.

To conclude, we would like to suggest this: Nature is usually kind to us. Simple

modelling methods based on a very good understanding of the underlying physics is

generally adequate and it is seldom necessary to complicate our approach.

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