Research paper

23rdNational Conference on I. C. Engine and Combustion (NCICEC 2013)

SVNIT, Surat, India 13-16, December 2013

Numerical Simulations of Turbulent Non-premixed Flames

S. Sreedhara and R. N. Roy

Department of Mechanical Engineering, Indian Institute of Technology, Bombay, India.

Abstract

Non-premixed flame plays a major role in the performance and emission characteristics of gas turbines, internal

combustion engines and industrial furnaces. Accurate modelling is necessary to capture turbulence-chemistry

interaction and to predict the temperature and species mass fractions. Further, stringent emission norms

demand higher accuracy of these predictions. In this article, necessity of advanced combustion models to

capture experimental data obtained at higher turbulence levels, has been highlighted. Two test cases, a bluff-

body flame and a lifted turbulent flame have been chosen to demonstrate the superiority of the advanced

combustion models. Conditional Moment Closure (CMC) is a promising combustion model which solves the

governing equations in the mixture fraction field. Closure model is not required for the reaction rate term, which

is one of the major advantages of this model. In the first test case, CMC predictions are benchmarked against the

experimental data obtained through bluff-body flame at very high turbulence levels. Improved predictions are

obtained using CMC compared to that obtained from basic models based on average values. The gap between

the predictions from CMC and basic models were more prominent at higher turbulence levels where extinction

and re-ignition occur. The second test case, a turbulent lifted flame in a vitiated coflow, is a more complex

flame to model as the flame lifts off from the nozzle tip, resulting in a partially premixed scenario. In this case,

even the CMC model on its own could not capture the behavior of the lifted flame. Hence, to improve the

predictions from CMC, an extinction model has been included, referred to as CMCE. In the CMCE model, the

flame is assumed to be extinguished when the ratio of flow time scale to the chemical time scale falls below a

critical value. Predicted lift-off height by the CMCE model agrees very well with the experimental results. There

is a significant improvement in temperature and species distributions in both axial and radial directions with the

implementation of the CMCE model. Further, the model is extended to predict the flame lift-off height for

various coflow temperatures and jet velocities by using scaling ratios.

Keywords: Non-premixed flame; Turbulence-chemistry interaction; Conditional moment closure; Bluff-body

flame; Lifted flame; Extinction model.

1. Introduction

Combustion process in gas turbine or internal

combustion engine involves non-premixed flames

subjected to high turbulence. In some cases the

flame is anchored on to the fuel nozzle and in some

other cases the flame gets stabilized further

downstream of the nozzle exit. Lifted flame

enhances the life of the nozzle, by reducing thermal

stresses on the nozzle tip. Turbulent lifted jet

diffusion flame can generally be observed when the

velocity of the fuel jet discharging into surrounding

hot or cold air surroundings exceeds beyond a

critical value. Turbulence-chemistry interaction

cannot be neglected in these situations and some of

the existing combustion models generally fail to give

good predictions of these flame structures. Hence,

advanced combustion models are needed to model

non-premixed flame existing at high turbulence

levels. Various modelling approaches have been

proposed previously to capture the behavior of these

types of flames [1]. With basic combustion models,

accurate prediction of flame structure, such as radial

and axial distributions of temperature and species

mass fractions becomes difficult [2].

Two flames are considered here for benchmarking

the combustion models. They are the bluff-body

flame and the lifted flame as shown in Fig. 1.

(a) (b)

Figure 1. Schematic of (a) bluff-body flame and (b) lifted

flame in a vitiated coflow CMC has been recognized as a promising method

with sound theoretical background and accuracy at a

reasonable cost in diverse engineering problems [3,

4]. Conditionally averaged equations, in the mixture

fraction field, require modelling of some conditional

terms such as conditional velocity and scalar

dissipation rate, but do not invoke any arbitrary

assumption regarding the structure of a local flame.

Thus the reaction rate term becomes a closed term in

the mixture fraction field. The first-order closure

Corresponding author: S. Sreedhara

E-mail address: [email protected]



(CMC I) evaluates the conditional mean reaction

rate in terms of the conditional average species mass

fractions and temperature, whereas in the second-

order closure (CMC II), conditional variance and

covariance equations are also solved to account for

higher conditional fluctuations.

Conditional moment closure models have

successfully been employed in a wide range of

problems including a highly transient autoignition

phenomenon in a non-premixed medium [5-7]. The

behaviors of turbulent jet flames were well captured

by parabolic first-order CMC in the axial direction

[8-13]. Second-order CMC was implemented for a

few rate-limiting steps of methane in a one-

dimensional parabolic formulation [14, 15]. Kim and

Huh [14] applied the second-order corrections to

study Sandia Flames D, E, and F [16] and obtained

significant improvement for OH, NO, and

intermediate species, CO and H2, as well.

Lifted flame in a vitiated coflow has been modelled

by many researchers. Premixed model was proposed

by Vanquickenborne and Tiggelen [17] consisting of

balance between local turbulent burning velocity and

local time averaged axial velocity which leads to

stabilization of a lifted flame. Ignoring the partial

premixing of air and fuel upstream of the flame

base, Peters and Williams [18] argued that

quenching of laminar diffusion flamelets results in

stabilization of lifted flame. The reaction zones

shifts to the downstream locations where the value

of scalar dissipation rate is not high enough to

extinguish the flame. Later, Peters [19]

acknowledged the fact that stabilization at the lift-off

height occurs due to premixed flame propagation

theory and not by diffusion flamelet quenching. To

support this Watson et al. [20] carried out

measurements of scalar dissipation rate for lifted

flame using laser Rayleigh scattering for wide range

of Reynolds numbers. It was found that

instantaneous scalar dissipation rates were not high

enough to cause extinction. Chen and Bilger [21]

found that scalar dissipation rates at the lifted flame

base along the stoichiometric mixture fraction were

1/s for propane flame and 0.24/s for methane flame.

These values were far below the calculated

extinction scalar dissipation rate.

Broadwell et al. [22] formulated the stabilization

mechanisms and blowout criteria for turbulent

diffusion flames based on large eddy theory. Due to

entrainment of hot combustion products and air into

the fuel-rich jet by large scale structures,

stabilization of lifted flame takes place; a blowout

criterion was deduced for various fuels based on

these large scale structures. A new variant of this

large eddy model was examined by Kelman et al.

[23] using simultaneous laser imaging of Rayleigh

scattering, Raman scattering and OH-LIF. These

large scale turbulent structures draw air into the jet,

around the base of the reaction zone which makes

the mixture too lean to sustain reaction at the flame

base and extinction begins to occur.

Experimental tests using cinema-PIV were carried

out by Upatnieks et al. [24] on methane jet diffusion

flames for low Reynolds numbers (4300-8500) to

identify the dominant mechanisms for flame

stabilization. Turbulent intensities at the flame base

were measured and suggested that it was not a

dominant parameter for flame stabilization. The

large eddy theory also does not fall in line with the

experimental results.

An extinction model, based on the assumption of

quenching of flame where Damkӧhler number (Da)

is less than unity was proposed by many researchers

[25-26] and was tested for different fuels. Devaud

and Bray [27] implemented first-order radially

averaged CMC on lifted hydrogen-air flame. The

study does not include the effect of heat release on

turbulent flow field. The first-order radially

averaged CMC can provide satisfactory results for

lifted jet flames. This work was extended by Kim

and Mastorakos [28] by implementing two-

dimensional first-order CMC to calculate lift-off

height and found a reasonable agreement with the

experimental data. Patwardhan et al. [29] carried out

CMC simulations of lifted turbulent jet flame

(H2/N2) in a vitiated coflow. The prediction obtained

from CMC for the reactive scalars and the

temperature were better than that from PDF

combustion model. The study suggests that for high

coflow temperatures, flame gets stabilized by auto-

ignition phenomena, as the convection-diffusion-

reaction (CDR) budgets indicate a balance between

convection and reaction terms at the upstream of the

flame base. Whereas, for low coflow temperatures,

flame gets stabilized by the turbulent flame

propagation theory, as the principal balance was

between convection and diffusion terms. Numerical

simulations of lifted methane-air flame in a vitiated

coflow based on RANS solvers for flow field,

coupled with PDF modelling [30, 31] indicate that

auto-ignition is the controlling mechanism for the

flame stabilization. Results of LES based unsteady

flamelet/progress variable model, developed by

Ihme and See [32] supports the autoignition theory

for the flame stabilization. Recent LES-CMC studies

[33, 34] on series of lifted flames indicate that flame

gets stabilized by auto-ignition phenomena for high

coflow temperature. It is claimed in Ref. [33] that

RANS based models fail to capture the flame base

dynamics and information on the temporal variation

of lift-off height is lost whereas unsteady effects

may be modelled accurately using LES. Devaud et

al. [35] carried out CMC simulations of lifted

turbulent methane-air flame and found that the lift-

off heights were highly underpredicted. Second-

order CMC resulted in improved predictions of lift-

off height, but only by around 10% [36].

The major objective of this article is to test the

applicability of CMC for modelling a bluff-body



flame and a lifted methane flame in a vitiated coflow

[37] using the detailed kinetic mechanism. In case of

a bluff-body, it was intended to obtain improved

predictions for species mass fractions at high

turbulence level compared to that obtained from the

basic combustion models [2]. For the lifted flame,

several investigators [for e.g. 19-21] suggested that

scalar dissipation rates were not high enough to

cause extinction at the flame base. So the authors

wanted to include an extinction criterion based on

the ratio of mixing to chemical time scale, motivated

by the previous attempt [26], to the conventional

CMC model to capture the lift-off height accurately.

The study was then extended to characterize the lift-

off height for different coflow temperatures and jet

velocities by proposing certain scaling ratios.

2. Mathematical formulations

Governing equations used in CMC calculations are

given in this section. The conditional mean mass

fraction Qi of species i is defined as

, , , ,i iQ x t Y x t x t (1)

Angular brackets in Eq. (1) denote ensemble

averaging subject to the condition to the right of the

vertical bar. Yi is mass fraction of species i, η the

sample space variable for the mixture fraction ξ. x is

spatial coordinate and t is time. The instantaneous

mass fraction is decomposed into its Favre

conditional mean and its fluctuation, given as in [4]

'', , , , ,i i iY x t Q x t x t Y x t (2)

The governing equation for conditional mean

quantity is written as [4]

'' ''

2

2

1

1

2

i ii i i

i i

ii

Q Qu P u Y

t x xP

Q

(3)

''

iu and "

iY are conditional fluctuations of velocity and

mass fraction of the ith species respectively. The

PDF ( )P is assumed to have a β-function form. The

conditional velocity is approximated as [38]

" "

''2

i

i i

uu u

(4)

The conditional scalar dissipation rate is modelled

by amplitude mapping closure [39]

2

-10.5 exp 2 erf 2 1

(5)

1

2-1

0

0.5

exp 2 erf 2 1 d

(6)

The mean chemical source term is approximated

using first-order CMC. The conditional mean

radiative loss is estimated using the optically thin

assumption [40, 41].

3. Extinction model coupled with CMC

In this section, an extinction model incorporated into

the conditional moment closure model for the

improved prediction of lift-off height has been

proposed. The model consists of two time scales,

flow and chemical time scales. Flow time scale is

defined as the reciprocal of the scalar dissipation

rate and is given by

1

f

(7)

Chemical time scale depends on the reaction rates

and in this paper, it is taken as reciprocal of the

reaction rate of a particular species.

ci

(8)

Where i is the mean reaction rate of the ith

species.

According to this model, in the computational

domain, local flame extinction is said to be occurred

when the local flow time scale in the flow field is

smaller than the chemical time scale by a factor. The

unconditional mean reaction rate for a specific

species in the physical domain i , was obtained by

Favre PDF weighted conditional reaction rate

i and is given by,

1

0

i i P d (9)

The reaction rates, thus obtained, were utilized to

determine the chemical time scales. The computed

chemical time scale for a particular species is then

compared with the flow time scale at each of the

physical grid points. The conditional reaction rates

''i for all species are set to zero if

if c c fCS S .

Here Sc and Sf are the scaling ratios to accommodate

the change in coflow temperature and jet velocity

respectively. Constant C is taken as 0.68 by

matching the lift-off height for a particular test case

by keeping both scaling ratios as unity. About 5%

variation in the value of C has changed the lift-off

height by around 10%. The flame lift-off height is

quite sensitive to the model constant C. The reaction

rate of CO is considered here for obtaining the

chemical time scale as it is one of the important

intermediate species. An attempt was made to define

the chemical time scale based on the species OH; the

methodology works well but with a different value

of C. On the other hand if /if c c fCS S then the

conditional reaction rates are calculated as per the

CMC approach.



The approach taken in this study to predict lift-off

heights for change in coflow temperature is similar

to the model proposed by Kumar et al. [26]. As the

coflow temperature decreases, the lift-off height

increases because of changed reaction rate due to

change in temperature. However, this increase in

lift-off was much smaller than that observed in the

experimental data. Therefore, a scaling factor was

needed to capture the variations in lift-off height

with decreased coflow temperature. The scaling

ratio for change in coflow temperature is calculated

from the following equation

,

,

/

/

a u stoich base

a u stoich new

E R T

cE R T

eS

e

(10)

where Tstoich,base and Tstoich,new are the temperatures at

the stoichiometric mixture fraction corresponding to

base and new case respectively. Temperatures at the

stoichiometric mixture fraction are estimated from

the equilibrium solution. The coflow temperature of

1350 K is taken as the base case. The effect of

change in coflow temperature is accounted by the

exponential terms. The term Ea (activation energy) is

considered for the reaction which is having slowest

CO oxidation rate in the reaction mechanism. The

reaction is given as

2 2O CO O CO (11)

The activation energy for the above reaction is 200

MJ/kmol. The above reaction is very slow and hence

the chemical time scale becomes important.

With an increase in the jet velocity, the flame lift-off

height does not increase in the same proportion, as

overprediction of the lift-off height at lower jet

velocities and underprediction at higher velocities

were observed by Kumar et al. [26]. Similar

observations were found in our preliminary

simulations. Hence, to determine a flow time scale

for change in jet velocity turbulent parameter should

be included in the extinction model [26]. So in the

present study, change in maximum mixture fraction

variance in the whole domain has been taken into

account for the change in jet velocity. Therefore, the

scaling ratio for change in jet velocity is determined

by the following relationship.

''2max

''2max

base

f

new

S

(12)

where ''2max base and

''2max new are the maximum

mixture fraction variance corresponding to the base

and a new case respectively. The jet velocity of 100

m/s is considered as the base case velocity. In the

rest of the sections, the extinction model in the CMC

is referred as CMCE model.

4. Numerical simulation and boundary conditions

Simulations were carried out to investigate the

CH4/H2 bluff-body flames with different jet

velocities. The diameter (DB) of the bluff-body is 50

mm and that of the fuel jet is 3.6 mm. CH4 and H2

are mixed in the volume ratio of 1:1, which results in

the stoichiometric mixture fraction of 0.0498. The

jet velocities are 118, 178, and 214 m/s,

respectively, for the flames HM1, HM2, and HM3.

The coflow air velocity is 40 m/s. The Reynolds

numbers based on the jet diameter and inlet jet

velocities are 15,800, 23,900, and 28,700,

respectively, for HM1, HM2, and HM3. Inlet

boundary conditions are given as reported in Dally

et al. [42]. The steady-state flow and mixing fields

were calculated by a program based on the SIMPLE

algorithm with the k–ε model. To compensate for

excessive diffusion by the standard k–ε model the

constant, Cε1, was modified to 1.6 from its standard

value of 1.44. The numbers of control volumes were

taken as 70 and 50, respectively, in the axial and

radial directions. The resulting steady flow field was

used in CMC simulation to obtain the steady-state

solution for local conditional flame structures.

Weaker spatial dependence of conditional mean

quantities allows a coarser spatial grid of 20 × 10 in

the axial and radial directions. Sensitivity on grid

resolution was checked with no noticeable

difference in the results with a finer spatial grid of

40 × 10. Detailed kinetic mechanism of GRI Mech

2.11 was used to calculate reaction rates. The

upwind technique is used in transport steps, whereas

the stiff solvers of CHEMKIN are called during

chemical reaction steps.

In case of a lifted flame, the experimental data

obtained by Cabra et al. [37] is used for the

modelling purpose. In their setup, a fuel jet

consisting of a CH4/air (d = 4.57 mm) was issued

into a hot surrounding consisting of products from

lean premixed H2/air flame. Fuel jet was having a

bulk velocity of 100 m/s and that of coflow was 5.4

m/s.

The flow and mixing fields were treated as

axisymmetric in nature and were calculated by fully

implicit finite-volume method using SIMPLE

algorithm incorporated in a 2-D in-house code.

Again, a variant of k-ɛ turbulence model was used to

predict the turbulence mixing accurately. To reduce

the rate of decay of turbulent kinetic energy, Cε2 was

changed from 1.92 to 1.8 in the modified k-ɛ

turbulence model as done previously by Kumar and

Goel [25].

In the flow solver, the Favre-averaged form of

momentum, pressure, turbulent kinetic energy, eddy

dissipation, mixture fraction and its variance

equations were solved. The closure of mean density

term was achieved using β-PDF. The details of

computational domain are shown in Fig. 2.



At the jet inlet (nozzle exit) fully developed velocity

profile [37] was supplied to the solver, where the

velocity distribution is assumed to be related to the

bulk velocity via 1/7th

power law.

Figure 2. Diagram of the computational domain

where y is the distance in the radial direction and r is

the radius of the jet. Uniform velocity profile was

considered for coflow boundaries. The turbulent

intensity was set equal to 15% of the inlet flow

velocity. Adiabatic wall boundary was provided at

the outer part of the domain. Numbers of control

volumes taken in the computational domain were

315 and 150 respectively in axial and radial

direction, based on the grid independent study. No

significant differences were observed with further

refinement of grids.

The solution methodology as given in Fig. 3 is

described below. Principal reaction mechanism for

CH4 combustion used here is GRI1.2 mainly to

reduce the computational effort. Steady flamelet

equations were solved for the boundary condition

given in Ref. [37]. The mixture fraction space in

SLFM solver was divided into 50 grid points with

denser grids around stoichiometric mixture fraction.

Fully burnt solutions, corresponding to near zero

scalar dissipation rate, obtained by solving steady

flamelet equations were used as initial conditions for

CMC simulations. Flow field information was

passed onto the CMC solver to obtain steady

conditional flame structure as shown in Fig. 3. The

effect of density variation on the flow-field is taken

into account. Flow simulations were started with

cold density, but updated densities at each grid

points were provided using CMC solutions. Flow

and CMC simulations were coupled by running them

one after the other for several cycles till the steady

state results were obtained as shown in Fig. 3.

Figure 3. Schematic of solution methodology

The physical space in the CMC solver was

discretized into 50 and 38 grids in axial and radial

direction respectively. Each physical grid point

consists of 50 mixture fraction grids concentrated

near the stoichiometric mixture fraction. Both CMC

and CMCE models were initialized using fully burnt

solutions obtained by solving Flamelet equations.

The fractional step method was used to solve CMC

equations, where the terms for transport and

chemical reaction were solved in a separate

fractional step. The stiff ODE solver VODE was

employed for chemical reaction steps.

5. Results and Discussion

Results obtained from basic combustion models on

bluff-body flames were compared and discussed in

the TNF workshop [2]. The numerical results

obtained showed a significant discrepancy with

experimental data [42, 43], particularly for the flame

with the highest jet velocity (HM3) as shown in Fig.

4. Huge deviation from the data may be observed

particularly for NO mass fraction. Post-processed

data [43] showed significant local extinction in HM3

which is having highest Reynolds number among the

three flames tested. The basic combustion models

based on the averaged values could not capture the

experimental data very well because of this local

extinction.

Figure 4. Predictions from basic combustion models

compared against experimental data

Sreedhara and Huh [44], applied CMC second-order

method to model bluff-body flame and to obtain

improved results for the above said species

concentrations. Initially mixing field was compared

against the experimental data by comparing mean

and variance of mixture fraction at various locations

of the flame. Two locations (x/Db=1.8 and 2.4),

where the local extinction is more, were chosen for

the comparison purpose. Mean and variance of

mixture fractions at these locations matched

reasonably well with the experimental data as shown

in Fig. 5. This comparison may be improved by

implementing a better mixing model, for e.g. LES.

Flamelet solver

"2, , , , , ,u v p k

Flow Solver

Combustion model

(CMC)

, iT Y

Steady state

, ,iT Y

Initial

condition

0

2

4

6

0.0 0.3 0.6 0.9 1.2

YC

O (%

)

r/Rb

Expt

TNF[2]

TNF[2]

x/Db = 1.8

0

2

4

6

0.0 0.3 0.6 0.9 1.2

YC

O (%

)

r/Rb

Expt

TNF[2]

TNF[2]

x/Db = 2.4

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.3 0.6 0.9 1.2

YN

O (

%)

r/Rb

Expt

TNF[2]

TNF[2]

x/Db = 1.8

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.3 0.6 0.9 1.2

YN

O (

%)

r/Rb

Expt

TNF[2]

TNF[2]

x/Db = 2.4



Figure 5. Comparison of radial distributions of Favre

mean and root mean square fluctuation of mixture fraction

with measurements (symbol: measurement; line:

prediction)

These parameters are crucial in calculating the

probability density function (PDF) of the mixture

fraction field. PDF in turn required for converting

CMC results, obtained in the mixture fraction field,

into physical space results.

Some of the results are given here, but for the details

of other results readers are directed to refer

Sreedhara and Huh [44]. Improved predictions of

NO from CMC compared to that from the basic

combustion models given in TNF proceedings [2], at

two axial locations, are shown in Fig. 6. It may be

seen clearly from the Fig. 6 that the NO predictions

from CMC are very close to the experimental data. It

may also be observed from Fig. 6 that a significant

amount of improvement is obtained in the

predictions compared to that from the basic models.

This may attributed to the fact that turbulence-

chemistry interaction is captured well in CMC.

Figure 6. Comparison of radial distributions of NO mass

fractions by CMC and basic combustion models with

measurements

Improved results are obtained for the species mass

fractions of CO and OH also and are shown in Figs.

7 and 8. The minor deviations in the predictions of

mass fractions from the experimental data observed

in Figs. 6-8 may be attributed to the inaccurate PDF

obtained from the mixing field. PDF may be

improved by incorporating a better mixing model.

Figure 7. Comparison of radial distributions of CO mass

fractions by CMC model with measurements

Figure 8. Comparison of radial distributions of OH mass

fractions by CMC model with measurements

As a next step, the CMC has been employed to

model the lifted methane flame existing in a vitiated

coflow. Lift-off heights predicted by CMC for

different jet velocities underpredicted the

experimental results by a huge factor as shown in

Fig. 9. However, lift-off height is increasing with the

increase in jet velocity i.e. CMC is capturing the

trend of lift-off height but fails to capture the

absolute value of the lift-off height by a large factor.

In CMC simulations, the flame extinguishes because

of very high scalar dissipation rate. As observed by

many researchers [19-21] at the flame base of the

lifted flame, scalar dissipation rates are not high

enough to cause extinction; hence the lift-off height

is underpredicted in Fig. 9. To overcome this issue,

it was planned to incorporate an extinction model in

the CMC to take care of extinction even when the

scalar dissipation rates are not so high. Extinction

model coupled with CMC is referred here as CMCE.

Figure 9. Comparison of lift-off heights for different cases

with CMC

Results obtained from both the CMC and the CMCE

models are presented below. Prediction of the

turbulent mixing field accurately is important in

modelling turbulent combustion because it has a

strong influence on turbulence-chemistry

interactions. Fig. 10 shows the Favre mean and root

mean square (r.m.s) mixture fraction along the

centreline predicted by both SKE and MKE

turbulence models. The figure includes both the

experimental [37] and the computational results.

Mean mixture fraction is underpredicted by the SKE

model, it also results in large overprediction of r.m.s

mixture fraction in the range 0 < x/d < 24.

Calculated mean mixture fractions and r.m.s mixture

fraction obtained from the MKE model are in good

agreement with the experimental data as shown in

Fig. 10. Thus, an excellent agreement is achieved for

the mixing field by changing the k-ɛ modelling

constants appropriately.

0.00

0.05

0.10

0.15

0.20

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.3 0.6 0.9 1.2

rms

mix

ture

fra

ctio

n

Mix

ture

fra

ctio

n

r/Rb

x/Db = 1.8

0.00

0.05

0.10

0.15

0.20

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.3 0.6 0.9 1.2

rms

mix

ture

fra

ctio

n

Mix

ture

fra

ctio

n

r/Rb

x/Db = 2.4

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.3 0.6 0.9 1.2

YN

O (

%)

r/Rb

Expt

TNF[2]

TNF[2]

CMC

x/Db = 1.8

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.3 0.6 0.9 1.2

YN

O (

%)

r/Rb

Expt

TNF[2]

TNF[2]

CMC

x/Db = 2.4

0

2

4

6

0.0 0.3 0.6 0.9 1.2

YC

O (%

)

r/Rb

Expt

CMC

x/Db = 1.8

0

2

4

6

0.0 0.3 0.6 0.9 1.2

YC

O (%

)

r/Rb

Expt

CMC

x/Db = 2.4

0.00

0.05

0.10

0.15

0.0 0.3 0.6 0.9 1.2

YO

H (

%)

r/Rb

Expt

CMC

x/Db = 1.8

0.00

0.05

0.10

0.15

0.0 0.3 0.6 0.9 1.2

YO

H (

%)

r/Rb

Expt

CMC

x/Db = 2.4

0

20

40

60

80

Case1 Case2 Case3

Lif

t-off

hei

ght

(h/d

)

Expt

CMC



Figure 10. Comparisons of centerline Favre mean and

root mean square fluctuation of mixture fraction with

measurements

In Fig. 11 a comparison of the predicted Favre

average centerline temperature and species mass

fractions using the CMC and the CMCE models

with the experimental data are provided. One of the

important parameters of the lifted jet flame is the

centerline temperature. The temperature profile is

overpredicted in the range 10 < x/d < 60 by the

CMC model. However, predicted temperature from

the CMCE model matches well with the

experimental data as seen from Fig. 11. Further

downstream, for x/d > 60 both the models yield

almost identical results. The prediction for centerline

CH4 mass fraction from the CMCE model matches

well with the experimental data. The prediction of

the CMC model is good up to an axial location of

x/d = 10 and then drops suddenly. In the

experiments, it is observed that CO2 mass fractions

are very low up to x/d = 45 then increase abruptly.

Both CO2 and O2 mass fractions are predicted well

by the CMCE. Mean temperature contours obtained

using the CMC and the CMCE models are shown in

Fig. 12. The temperature field can clearly show the

lift-off height of the flame. Lift-off height obtained

using the CMC model is 2.5d and that using the

CMCE model is 34.5d. It may be noted that the

shape of the flame has not changed even after

implementing the extinction model. Smooth

centerline profiles and unchanged flame shape in

Figs. 11 and 12 ensure that no numerical issues

caused due to the inclusion of the extinction model.

Figure 11. Centerline profiles for temperature and species

mass fractions

Figure 12. Mean temperature field (in K) for base case by

CMC and CMCE models

Favre average statistics are obtained by averaging

the conditional statistics with the β-PDF over the

entire mixture fraction space. Therefore, the

predicted accuracy of Favre averaged statistics

depends on the accuracy of both the PDF of the

mixture fraction and the conditional statistics. The

quantities, Favre mean temperature and species mass

fractions are compared with the experimental data in

Fig. 13 for the axial location x/d = 30. Figure 13

shows that the mean temperature profile obtained

using the CMC model is overpredicted by a

significant amount. On the other hand, the

predictions of the temperature profile in the pre-

flame zone from the CMCE model are considerably

much better. Further, the CMC model predicts rapid

consumption of CH4 and O2 mass fractions at this

axial location, resulting in increase in production of

CO2 mass fraction. The radial distributions of all

scalar quantities are well captured by the CMCE

model. The predictions of conditional mean values

by the CMCE model for temperature and reactive

scalars and Favre average statistics at other axial

locations are provided in Roy et al. [45].

Figure 13. Comparison of Favre mean temperature and

mass fractions of CH4, CO2 and O2 with measurements at

x/d = 30

The variation of lift-off height with coflow

temperature and jet velocity were investigated and

compared with the experimental measurements.

With the change in coflow temperature, reaction

0.00

0.20

0.40

0.60

0.80

1.00

0 20 40 60 80 100

Mix

ture

Fra

ctio

n

x/d

ExptMKESKE

0.00

0.04

0.08

0.12

0.16

0 20 40 60 80 100

r.m

.s m

ixtu

re f

ract

ion

x/d

ExptMKESKE

0

500

1000

1500

2000

2500

0 20 40 60 80 100

Tem

per

atu

re (

K)

x/d

ExptCMCCMCE

0

5

10

15

20

25

0 20 40 60 80 100

CH

4(%

)

x/d

Expt

CMC

CMCE

0

2

4

6

8

10

0 20 40 60 80 100

CO

2(%

)

x/d

Expt

CMC

CMCE0

5

10

15

20

25

0 20 40 60 80 100

O2

(%)

x/d

Expt

CMC

CMCE

h/d

h/d

0

500

1000

1500

2000

2500

0 3 6 9 12 15

Tem

per

atu

re (

K)

r/d

ExptCMCCMCE

0

2

4

6

8

0 3 6 9 12 15

CH

4(%

)

r/d

Expt

CMC

CMCE

0

2

4

6

8

10

0 3 6 9 12 15

CO

2(%

)

r/d

Expt

CMC

CMCE

0

4

8

12

16

20

0 3 6 9 12 15

O2

(%)

r/d

Expt

CMC

CMCE



rates change and hence the lift-off. Changed coflow

temperature changes the value of scaling ratio (Sc)

and this enables the CMCE model to capture the

change in lift-off height. The flame shifts towards

downstream locations with decrease in coflow

temperatures, indicating the higher flame lift-off. To

demonstrate the quality of prediction of flame lift-

off heights with change in coflow temperature by the

proposed model, present results are compared, in

Fig. 14, with the measured lift-off heights. Results

from other numerical models available in the

literature are also shown in Fig. 14. Cabra et al. [37]

carried out PDF calculations with M-Curl and Well-

Mixed (W-M) mixing models to predict the flame

lift-off height at different coflow temperatures. The

lift-off heights were underpredicted by Well-Mixed

model, whereas the M-Curl model predicted the lift-

off height very close to experimental data. The

model proposed by Kalghatgi [46] also significantly

underpredicts the lift-off heights. However, earlier

numerical predictions by PDF [31] and LES-CMC

[33] models show a good agreement with

experimental data. It may be observed from Fig. 14

that the lift-off heights predicted by the CMCE

model match very well with the experimental data

and other predictions [31, 33] both qualitatively and

quantitatively.

Figure 15 shows the comparison of the lift-off

heights predicted by the CMCE model, at different

jet velocities (varied from 100 m/s to 250 m/s) with

measured and predicted results from M-Curl model

[37]. In the CMCE model, value of scaling ratio (Sf)

changes with change in jet velocities, which enables

the model to capture the change in lift-off height.

The predicted trend obtained for the lift-off height

by the proposed CMCE model compares well with

the experimental data. From Figs. 14 and 15 it may

be concluded that the new model can predict the lift-

off height very accurately for large variations of

coflow temperatures and jet velocities.

Figure 14. Comparisons of measured and predicted lift-off

height with change in coflow temperature

Figure 15. Comparisons of measured and predicted lift-off

height with change in jet velocity

6. Conclusions

In the present article, Conditional Moment Closure

(CMC) model has been benchmarked against the

experimental data related to bluff-body flame and

lifted flame. Mixing field is obtained using a

modified k- model. CMC predictions of bluff-body

flame structure were found to be superior to that

from the basic combustion models. For modelling

the lifted methane flame in a vitiated coflow, flow

and scalar fields are fully coupled. The original

CMC model is modified by including an extinction

model to accurately capture the lift-off height.

Capabilities of CMC and CMCE models to predict

the scalar field and lift-off height are compared

against the experimental data. The CMC model

overpredicts the centerline temperature field by a

large amount resulting in an underprediction of the

lift-off height. The predicted lift-off height with the

CMCE model is found to be in good agreement with

the experimental measurements. As a result,

significant improvement in centerline and radial

profiles of various scalars has been observed with

the CMCE model. Further investigations related to

the effect of change in coflow temperature and

change in jet velocity on the lift-off height reveal

that the proposed model, CMCE, can capture the

experimental data of lift-off heights, both

qualitatively and quantitatively for large variations

of coflow temperatures and jet velocities.

Acknowledgment

The authors are grateful to the Aeronautics Research

and Development Board (AR&DB), Govt. of India

for funding this research work.

References

1. T. Poinsot, D. Veynante, Theoretical and

numerical combustion, Edwards, Second edition,

2005.

2. R.S. Barlow, J.C. Oefelein (Eds.), Proceedings of

the Seventh TNF Workshop, Chicago, IL, 2004, pp.

73–108.

0

20

40

60

80

1260 1280 1300 1320 1340 1360

Lif

t-off

hei

gh

t (h

/d)

Coflow Temperature (K)

ExptM-Curl [37]W-M [37]Kalghatgi [46]LES_CMC [33]PDF [31]CMCE

0

20

40

60

80

50 100 150 200 250 300

Lif

t-o

ff h

eig

ht

(h/d

)

Jet velocity (m/s)

Expt

M-Curl [37]

CMCE



3. R.W. Bilger, Conditional Moment Closure for

Turbulent Reacting Flow, Physics of Fluids A 5

(1993) 436–444.

4. A.Y. Klimenko, R.W. Bilger, Conditional

moment closure for turbulent combustion, Progress

in Energy and Combustion Science 25 (1999) 595-

687.

5. E. Mastorakos, R.W. Bilger, Second-order

conditional moment closure for the auto-ignition of

turbulent flows, Physics of Fluids 10 (1998) 1246–

1248.

6. S.H. Kim, K.Y. Huh, R.A. Fraser, Modelling

autoignition of a turbulent methane jet by the

conditional moment closure model, Proceedings of

Combustion Institute 28 (2000) 185.

7. S. Sreedhara, K.N. Lakshmisha, Assessment of

conditional moment closure models of turbulent

autoignition using DNS data, Proceedings of

Combustion Institute 29 (2002) 2069–2077.

8. R.S. Barlow, J.H. Frank, Effects of turbulence on

species mass fractions in methane/air jet flames,

Proceedings of Combustion Institute. 27 (1998)

1087–1095.

9. P.J. Coelho, N. Peters, Numerical Simulation of a

Mild Combustion Burner, Combustion and Flame

124 (2001) 444–465.

10. Q. Tang, J. Xu, S.B. Pope, Probability density

function calculations of methane/air flames,

Proceedings of Combustion Institute 28 (2000) 133–

139.

11. R.S. Barlow, N.S.A. Smith, J.Y. Chen, R.W.

Bilger, Nitric oxide formation in dilute hydrogen jet

flames: isolation of the effects of radiation and

turbulence-chemistry submodels, Combustion and

Flame 117 (1999) 4–31.

12. M.A. Roomina, R.W. Bilger, Conditional

moment closure (CMC) predictions of a turbulent

methane-air jet flame, Combustion and Flame 125

(2001) 1176–1195.

13. M. Fairweather, R.M. Woolley, First-order

conditional moment closure modelling of turbulent,

non-premixed hydrogen flames, Combustion and

Flame 133 (2003) 393–405.

14. S.H. Kim, K.Y. Huh, Second-order conditional

moment closure modelling of turbulent piloted Jet

diffusion flames, Combustion and Flame 138 (2004)

336–352.

15. S.H. Kim, C.H. Choi, K.Y. Huh, Second-order

conditional moment closure modelling of a turbulent

CH4/H2/N2 jet diffusion flame, Proceedings of

Combustion Institute 30 (2005) 735–742.

16. R.S. Barlow, J.H. Frank, Effects of Turbulence

on Species Mass Fractions in Methane/Air Jet

Flames, Proceedings of Combustion Institute 27

(1998) 1087–1095.

17. Vanquickenborne, A.V. Tiggelen, The

stabilization mechanism of lifted diffusion flames,

Combustion and Flame 10 (1966) 59-72.

18. N. Peters, F.A. Williams, Lift-off characteristics

of turbulent jet diffusion flames, AIAA J 21(1983)

423-429.

19. N. Peters, Turbulent combustion, Cambridge

University Press, 2000.

20. K.A. Watson, K.M. Lyons, J.M. Donbar, C.D.

Carter, On scalar dissipation and partially premixed

flame propagation, Combustion Science and

Technology 175 (2003) 649-664.

21. Y.C. Chen, R.W. Bilger, Stabilization mechanis-

ms of lifted laminar flames in axisymmetric jet flows,


22. J.E. Broadwell, W.J.A. Dahm, M.G. Mungal,

Blowout of turbulent diffusion flames, Proceedings

of Combustion Institute (1984) 303-310.

23. J.B. Kelman, A.J. Eltobaji, A.R. Masri, Laser

imaging in the stabilization region of turbulent lifted

flames, Combustion Science and Technology 135

(1998) 117-134.

24. A. Upatnieks, J.F. Driscoll, C.C. Rasmussen, S.L.

Ceccio, Liftoff of turbulent jet flames-assessment of

edge flame and other concepts using cinema-PIV, Combustion and Flame 138 (2004) 259-272.

25. S. Kumar, S.K. Goel, Modelling of lifted

methane jet flames in a vitiated coflow using a new

flame extinction model, Combustion Science and

Technology 182 (2010) 1961-1978.

26. S. Kumar, P.J. Paul, H.S. Mukunda, Prediction

of flame lift-off height of

diffusion/partially premixed jet flames and modellin

g of mild combustion burners, Combustion Science

and Technology 179 (2007) 2219-2253.

27. C.B. Devaud, K.N.C Bray, Assessment of the

applicability of conditional moment closure to a

lifted turbulent flame: first order model, Combustion

and Flame 132 (2003) 102-114.

28. I.S. Kim, E.Mastorakos, Simulations of

turbulent lifted jet diffusion flames with two-

dimensional conditional moment closure,

Proceedings of Combustion Institute 30 (2005) 911-

918.

29. S.S. Patwardhan, S. De, K.N. Lakshmisha, B.N.

Raghunandan, CMC simulations of lifted turbulent

jet flame in a vitiated coflow, Proceedings of

Combustion Institute 32, (2009) 1705-1712.

30. R.L. Gordon, A.R. Masri, S.B. Pope, G.M.

Goldin, Transport budgets in turbulent lifted flames

of methane autoigniting in a vitiated coflow,


31. K. Gkagkas, R.P. Lindstedt, Transported PDF

modelling with detailed chemistry of pre- and auto-

ignition in CH4/air mixtures, Proceedings of

Combustion Institute 31 (2007) 1559-1566.

32. M. Ihme, Y.C. See, Prediction of autoignition in

a lifted methane/air flame using an unsteady

flamelet/progress variable mode, Combustion and

Flame 157 (2010) 1850-1862.

33. S. Navarro-Martinez, A. Kronenburg, LES-CMC

simulations of a lifted methane flame, Proceedings

of Combustion Institute 32 (2009) 1509-1516.

http://www.sciencedirect.com/science/article/pii/S0082078400802106
































34. S. Navarro-Martinez, A. Kronenburg, Flame

stabilization mechanisms in lifted flames, Flow

Turbulence Combust. 87 (2011) 377-406.

35. C.B. Devaud, J.H. Kent, R.W. Bilger,

Conditional moment closure applied to a lifted

turbulent methane-air flame, The Third

Mediterranean Combustion Symposium. Marrakech,

Morrocco, 2003.

36. C.B. Devaud, A second-order conditional

moment closure method for the simulation of a lifted

turbulent flame, ANZIAM J 45 (E) (2004) 419-434.

37. R. Cabra, J.Y. Chen, R.W. Dibble, A.N.

Karpetis, R.S. Barlow, Lifted methane-air jet flames

in a vitiated coflow, Combustion and Flame 143

(2005) 491-506.

38. V.R. Kuznetsov, V.A. Sabel’nikov, in: P.A.

Libby (Ed), Turbulence and Combustion, English ed,

Hemisphere, New York, 1990.

39. N.Peters, Laminar diffusion flamelet models in

non-premixed turbulent combustion, Progress in

Energy and Combustion Science 10 (1984) 319-339.

40. http://www.sandia.gov/TNF/radiation.html.

41. Grosshandler, W. L., RADCAL: A Narrow-

Band Model for Radiation Calculations in a

Combustion Environment, NIST Technical Note

1402, 1993.

42. R.B. Dally, A.R. Masri, R.S. Barlow, G.J.

Fiechtner, D.F. Fletcher, Instantaneous and mean

compositional structure of bluff-body stabilised non-

premixed flames, Combustion and Flame 114

(1998) 119–148.

43. http://www.ca.sandia.gov/TNF.

44. S. Sreedhara, K.Y. Huh, Modelling of turbulent,

two-dimensional non-premixed CH4/H2 flame over a

bluff-body using first- and second-order elliptic

conditional moment closures, Combustion and

Flame 143 (2005) 119-134.

45. R.N. Roy, S. Kumar, S. Sreedhara, A new

approach to model turbulent lifted CH4/air flame

issuing in a vitiated coflow using conditional

moment closure coupled with an extinction model,

Combustion and Flame (2013, in press).

46. G.T. Kalghatgi, Lift-off heights and visible

lengths of vertical turbulent jet diffusion flames in

still air, Combustion Science and Technology 41

(1984) 17-29.

http://www.sciencedirect.com/science/article/pii/036012858490114X

http://www.sciencedirect.com/science/article/pii/036012858490114X

http://www.sandia.gov/TNF/radiation.html

http://www.ca.sandia.gov/TNF

http://scholar.google.co.uk/citations?view_op=view_citation&hl=en&user=KKfji7QAAAAJ&citation_for_view=KKfji7QAAAAJ:u9iWguZQMMsC



Research paper

Documents

Transcript of Research paper