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Journal of Scientific & Industrial ResearchVol. 65, November 2006, pp. 921-934

Flow characteristics of an annular gas turbine combustor model for

reacting flows using CFD

S N Singh*, V Seshadri, R K Singh and T Mishra

Department of Applied Mechanics, IIT Delhi, New Delhi 110 016

Received 16 March 2005; revised 28 June 2006; accepted 18 July 2006

Computational Fluid Dynamics (CFD) approach can reduce the expenses as well as time to provide an insight into thecharacteristics of flow and combustion process inside combustion chamber at design stage. Geometry of combustor

simulated for present investigation is a 45 sector of an annular combustor. Primary, secondary and dilution holes aresimulated on the inner and outer liner walls with swirler being placed at the center of the liner dome. Flow has beenanalyzed in the annulus region. The results are fed as input for the flow analysis in the liner. Uniform velocity distribution is

obtained in the annulus passage around the liner. For the liner flow, it is observed that on moving axially from nozzle tooutlet, velocity and temperature contours become more uniform and symmetric in circumferential plane. Mass fraction ofCH4and O2decreases whereas concentration of CO2, NO and H2O increases in the axial direction (nozzle to outlet).

Keywords:Annular gas turbine combustor, Computational fluid dynamics, Liner holes, Species concentration, Temperature

contours

IPC Code: F15D1/00; G09B23/08

IntroductionAnnular combustors, which offer maximum

utilization of available volume, fewer requirements of

cooling air and high temperature application1are one

class of combustors most commonly used. A well-

designed gas turbine combustor2 should have

complete combustion and minimal total pressure loss

over a wide range of operating conditions. Flow

characteristics3in the annulus passage surrounding the

liner is equally important as the flow is fed into the

liner through the annulus passage. Bharani et al4have

shown that the bulk of the flow remains close to the

outer liner wall between the rows of primary and

dilution holes while it shifts towards the liner mid

plane after the row of dilution holes. Bharani et al5,

using a prototype reverse flow combustor, have

shown that swirl has no significant effect on the flow

split through primary holes while the split through

dilution holes decreases for Swirl number up to 0.55.

Ahmed & Nejad6 have carried out experimental

investigation of turbulent swirling flow in a

combustor model for coaxial swirling jets with dump

diffusers. Green & Whitelaw7have suggested that the

standard k-model gives better results than the otherturbulence models in turbulence combustion

prediction. Mongia8 has shown the difficulty in the

specification of boundary conditions, inferior

resolution of which hampers the ability of

computational models to predict combustor

characteristics. Mohan et al9 have numerically

investigated annuli flow and effect of inlet swirl on

the flow split through the liner holes of annular

reverse flow combustor model. Garg et al10

and

Singh et al10

have reported the effect of height of

inner and outer annuli for an elliptical dome shape

combustor for cold flow simulation using

computational fluid dynamics (CFD).

Cadiou & Grienche12

have conducted hot flow

studies on the liner with and without primary holes for

a reverse flow annular combustor. John & Torel13

have investigated the temperature profile and

concentration of CO, CO2, O2 and Nox for can type

combustor. Murthy14has developed an algorithm for

one-dimensional analysis for flow and heat transfer in

straight tubular, tubo-annular and annular combustors.Present analysis is an attempt to study reacting flow in

the annular combustor geometry suggested by

Garg et al10and Singh et al11 using CFD.

MethodologyA commercial available CFD code FLUENT

15

has been used for the analysis. The details of the

mathematical models are given in the manual of the

code. Brief discussion of the model is as follows:

__________

*Author for correspondence

E-mail: [email protected]

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J SCI IND RES VOL 65 NOVEMBER 2006922

The governing equations for mean flow in reducedform for steady incompressible turbulent flows are,

( ) mii

Sux

= (1)

Mass conservation equation is valid for both

incompressible and compressible flows. Sm is mass

added to continuous phase from dispersed phase.

Momentum conservation equation for turbulent flow

is written as,

2

3

ji i i

j ij

j i j j i i

uu u upu

x x x x x x

= + + +

( )' 'i i jj

F u ux

+ +

(2)

These equations are of the same general form as

the original equations except for some additional

terms. The additional terms are the Reynolds stresses

and these need to be modeled for closure solutions.

The Boussinesq hypothesis16

is used to relate the

Reynolds stresses to the mean velocity gradient as

iji

i

ti

j

j

i

tji x

uk

x

u

x

uuu

+

+

=

3

2''

(3)

where k is the turbulent kinetic energy and ij is theKronecker delta and t is the eddy viscosity.

For reacting flow, energy equation also needs to be

solved, which is given as

( ) hk

iik

ip

b

i

i

i

Sx

u

x

H

c

k

xHu

x+

+

=

' (4)

Sh is the heat of chemical reaction, H is the total

enthalpy and is computed as sum of each mass

fraction from Eqs 5 and 6

='

''j

jjHmH (5)

)( ,'',' jrep

T

T

ojjpj ThdTCH

j

+= (6)

Reynolds stresses in the time averaged momentumequations need to be approximated and represented by

additional equations, which are required to be solved

for closure solution of fluid flow problem. In presentinvestigation, two-equation turbulence model

(standard k-)17has been used.

Standard k-Model

Equations for k-model are

Mk

ik

t

ii

i YGx

k

xx

ku ++

+

=

(7)

KCGkCxxxuk

i

t

ii

i

2

21

+

+

=

(8)

Gk is generation term for turbulent kinetic energy

due to mean velocity gradient and is given by

i

j

jikx

uuuG

= '' (9)

Eddy or turbulent viscosity, tis computed from

2

t

kC= (10)

where C is constant.

Dilatation dissipation (YM) is modeled as per

Sarkar and Balakrishnan18

and is given as

2

t

2

M MY = (11)

where, Mtis turbulent Mach Number, defined as

RT

kMt = (12)

For incompressible flow YMis normally neglected.

Values of the empirical constants used are C1= 1.44,

C2 = 1.92, C = 0.09, k = 1.0 and = 1.3. Thesevalues have been found to work fairly well for a wide

range of wall bounded and free shear flows.

Reaction Modeling

Combustion is the major energy release mechanism

and it always gives off heat and gases as a product.

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SINGH et al: FLOW CHARACTERISTICS OF ANNULAR COMBUSTOR USING CFD 923

Combustion reaction is assumed to be single step,irreversible reaction following finite rate chemistry.

CH4+ 2O2CO2+2H2O (13)Heat formations (or standard state enthalpy) for the

fuel species can be calculated from the known heating

value, and are computed as

( ) ==

N

ikiki

o

ihH

1',',', (14)

where, oi,h is the standard state enthalpy (J/kg) for each

chemical species.ki ,' is the stoichiometric coefficient

for reactant 'i in the reaction k andki ,'

is the

stoichiometric coefficient for product 'i .

Species Transport Equation

CFD approach is based on the transport

equation for each species. The local massfraction of each species, mi, through the solution

of convection diffusion for the ith species is

expressed as

( ) i,'ii,'ii,'ii

'ii

i

SRjx

mux

++

=

(15)

where,iiR ,' is mass rate of creation or depletion of

species 'i by chemical reaction andiiS ,' is the mass

rate of creation or depletion by addition from the

dispersed phase plus any user defined source.

Mass Diffusion in Turbulent Flow

For turbulent flow, mass diffusion of species 'i iscomputed as

(16)

iij ,' is diffusion flux of species 'i , which arises due to

concentration gradient. Dim is the diffusion

coefficient for species 'i in the mixture. tSc is the

turbulent Schmidt number and is expressed as

t

tt

DSc

= (17)

Reaction Rate Calculation (Finite Rate Chemistry)

Most traditional way to model the reaction rate isthe approach of finite rate chemistry where chemical

reaction is defined as

oductPrk'Ri

ttancaRe EE (18)

The source of chemical species i due to reaction

rate 'iR is computed as the sum of the reaction

sources over the NR reactions that the species may

participate in

==

RN

1kk,'i'i'i RMR (19)

'iM is the molecular weight of species 'i andR ki ,' is the molar rate of creation/destruction of

species 'i in reaction k computed as

( )', ',

', ', ', , ' , '' 1 ' 1

j k j kN N

i k i k i k f k j b k jj j

R k C k C

= =

=

(20)

where, Cj,r = molar concentration of each reactant and

product species j in reaction R (kgmol/m3), k,'j =

forward rate exponent for each reactant and product

species j in reaction R, and k,'j = backward rateexponent for each reactant and product species j inreactionR.

represents the net effect of third bodies on thereaction rate and is calculated as

= N

'j'jk,j c (21)

kj , is the third body efficiency of the jthspecies in

the chemical reaction.

In the present reacting flow analysis, the reactionrate is controlled by the mixing of the turbulent eddies

containing fluctuating species concentration namely

eddy dissipation model (EDM). Reaction is assumed

to be in continuous phase for the continuous species

only.

Eddy- Dissipation Model (EDM)

EDM is based on a detailed description of the

dissipation of turbulent eddies on the concept of

interaction between turbulence and chemistry of

flame. The total space is subdivided into reaction

i

'i

t

t

i

'i

m,'ij,'i x

m

Scx

m

Dj

+

=

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space (fine structure) and surrounding fluid. All

reactions in the gas phase component are assumed to

take place within the reaction space, which represents

the smallest turbulent scale where all turbulent energy

isdissipated into heat.Influence of turbulence on thereaction rate is taken into account by employing

Magnussem & Hjertager model19, which gives the rate

of reaction ', ,i kR which is given by the smaller of

the following two expressions

', ', ' '

,

' Ri k i k i

R k R

mR M A

k M

= (22)

', ', ' ''

,'

'pP

i k i k i N

R k Rj

mR M A B

k M

=

(23)

where,pm and Rm are mass fraction of product

species (P) and reactant (R) respectively. A and B are

empirical constants having values of 4.0 and 5.0respectively.

EDM relates the rate of reaction to the rate of

dissipation of the reactant and product containing

eddies. (k/) represents the time scale of the turbulenteddies. The model is useful for the prediction of

premix and diffusion problems as well as for partially

premixed reacting flows.

Validation of the Code

CFD code FLUENT 5.014

was validated against

experimental results of three-dimensional swirlingreacting turbulent flow inside the Can combustor20,

which consists of fuel nozzle with swirler (Fig. 1). In

addition, there are six dilution holes equally spaced on

the circumference of the combustor wall. Henceprediction was made in 60-sector model byconsidering 3D problem with symmetric boundary

conditions. The 60-sector model consists of only onedilution hole on the wall. Flow in the sector model

was solved for various degree of fineness of

computational mesh for checking the grid

independency and finally the number of meshing

element was found to be 78,000. The changes in

results were negligible for further increase in meshing

elements. Simulations were also carried out with

different turbulence models (RNG K-, K- model

and RSM model) to validate the results. Standard K-model gave the best results. The two-equation

turbulence model (K-) has also been used foreconomical reasons. For sake of brevity, results of

only standard K- model are presented. Thecombustion has been simulated with the generalizedfinite rate chemistry model and is modelled using

one-step reaction mechanism, assuming complete

conversion of fuel to CO2 and H2O. Reaction rate is

determined on the basis of assumption that turbulent

mixing is the rate limiting process with the turbulent

Fig. 1 Geometry of the combustor used for validation20

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Geometry and Boundary Conditions

Combustor consists of 8 annular swirlers and 56

holes along the inner and outer circumference for

primary, secondary and dilution zones (Fig. 4). For

prediction, a 45o sector model is simulated with a

coaxial jet arrangement in the center of liner domeand 7 holes each for primary, secondary and dilution

zones on the inner and outer circumference of the

liner. Combustor model consists of a pre-diffuser

followed by a dump diffuser, straight annularconfinement and liner. The liner dome is elliptical

with major axis perpendicular to the liner axis.

Coaxial jet arrangement has fuel in the central jet and

non-swirling or swirling annular jet for the oxidizer. It

also shows the plane selected for presentation of theresults inside the annulus. Mass fraction between the

two annuli is given as S = mo/mi, Dimensions of

various holes and coaxial jet are: Diam of primary andsecondary holes, 8; Diam of dilution hole, 12; Inner

diam of coaxial jet, 10; Outer diam of coaxial jet,30 mm.

A 3-D 45o sector model (Fig. 5) was developed

from 2-D geometry using GAMBIT package of the

FLUENT code. The geometry was meshed with both

structured as well as unstructured mesh. Near the wall

region, boundary layer meshing scheme was opted

whereas in the rest of the region, tetrahedral meshing

scheme (hybrid grid) was employed. Boundary layer

meshing scheme is used, as it is useful forcomputation of viscosity-dominated near wall regions

for turbulent viscous flows. Optimum numbers of

cells was arrived by checking the grid independence

with respect to the velocity vector and velocity

profile. Finally, total number of mesh was arrived tobe 78,000. In the 3-D geometry, one mesh element

contains 4 nodes, therefore the total number of nodesare approx 300000.

Prediction has been carried out for air-fuel

mixture as working fluid. The flow in annulus andliner have been analyzed separately. For solving the

annulus part, a flat velocity profile is fed upstream of

the pre diffuser having a velocity magnitude of

26 m/sec, which corresponds to an inlet Reynolds

number of 4.96105 based on the inlet diam.Atmospheric pressure conditions are specified at

different holes of the liner as outlet boundary

Fig. 4 Plane representation of annulus geometry: A) 2-D Axisymmetric geometry of annular combustor; B) 3-D geometry of a

45sector of annular combustor

Fig. 5 3-Dimensional geometry of liner and orientation ofplanes: a) 3-D geometry of liner; b) Orientation of vertical crosssectional planes; c) Orientation of horizontal and vertical centralplanes

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conditions at the holes and the coaxial jetarrangement. Symmetry condition is imposed on both

the sidewalls. Outlet velocity profile obtained at

different holes was fed as input for the flow analysisin the liner. For the liner flow, velocity profile

through the annular jet and uniform velocity for thefuel jet was also specified as the input. At the outlet of

the liner, pressure outlet (atmospheric conditions)

boundary condition is specified. In the circumferential

direction for a 45-sector model, symmetric boundaryconditions at the sides of the sector model were

specified.

Calculation for Air Fuel ratio

For complete combustion and better efficiency of

methane (CH4, density 0.668 kg/m3), fuel to air ratio

is given as21

F/A = 0.02929 (24)

For reaction modeling in the combustion chamber,

mass flow rate of air (A) is taken as 0.2329 kg/sec.

Substituting the value of A in Eq. (24), mass flow rate

of the fuel (F) works out to 0.00668 kg/sec. Fuel

velocity has been calculated as

fuelfuelfuel VAF = (24)

Substituting the value of F, Afuel and fuel in above

expression, a value of Vfuel = 130 m/sec (Re= 2.4105

based on the fuel jet diam) was obtained for fuel.

Flow analysis has been carried out for the above-calculated air and fuel velocities with no swirl

condition. Velocity vectors as well as contours,

temperature contours and velocity profiles are plotted

for each case.

Orientations of planes for analysis (Fig. 5) are Mid1 Plane (Mid Vertical Plane of the liner), Mid 2 Plane

(Mid Horizontal Plane of the Liner), Plane 1 (Vertical

cross-sectional Plane before 25 mm from Dilution

Holes) and Plane 2 (Vertical cross-sectional Plane at

the exit of the Liner).

Results and Discussion

Flow Analysis in the Annulus

Velocity (Fig. 6a) decreases gradually as the flow

progresses through the pre-diffuser (magnitude of

velocity at inlet of pre-diffuser is 26 m/sec and at

outlet it is 19.42 m/sec). After pre-diffuser, flow

enters into the dump diffuser where velocity further

reduces due to sudden enlargement of flow area

resulting in the formation of wall recirculation zone.

Velocity profile is almost same for both the annuli

except that the magnitude is slightly higher in the

inner annuli, perhaps due to reduced flow area as

compared to the outer annuli. Fig. 6b shows the

velocity vectors in the mid vertical plane for better

visualization of the flow. Flow apart from entering the

liner from the annuli, it also enters the liner through

the coaxial jet configuration where flow is nearly

axial and hence more flow enters the liner through

this jet. Maximum velocity of air in the annular jet is

61.52 m/sec.

Velocity Profiles at Primary, Secondary and Dilution Holes

Magnitude of velocity in inner annular holes is

slightly higher than outer annular holes (Figs 7 & 8),

whereas nature of profiles is nearly identical for

primary and secondary holes. Maximum velocitymagnitude for primary and secondary inner liner holes

is 58.28 m/sec, whereas it is 55.04 m/sec for outer

annuli. Magnitude of velocity at dilution holes is

higher than that in primary and secondary holes

(61.52 m/sec for inner, 58.28 m/sec outer). Velocity

entering the liner through these holes is nearly

uniform.

Flow Analysis in the Liner

Flow analysis for the liner is carried out by feeding

the air velocities (130 m/sec) obtained through the

Fig. 6 Vector contours and vector plot for the annulus atcentral mid Plane: a) Vector contours; b) Vector plot

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Fig. 7 Velocity profiles at inner wall holes: a) Primary hole;b) Secondary hole; c) Dilution hole

Fig. 8 Velocity profiles at outer wall holes: a) Primary hole;b) Secondary hole; c) Dilution hole

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annular jet and various liner holes along with fuel inthe central jet.

Analysis of Velocity Field

Recirculation zone is formed just at the downstream of the primary and secondary holes for both

inner and outer walls (Fig. 9). There is no formation

of reverse flow down stream of dilution holes on the

outer wall but a reverse flow is found near the dilution

holes on the inner wall, which suggests the need for

modification of liner geometry.

Fuel velocity coming out from the nozzle at the

mid 1 plane (Fig. 10a) has a magnitude of 130 m/sec.

Air coming through the annular jet to the liner has a

maximum velocity of 65.01 m/sec and this flow

spreads in the radial direction occupying whole spacewithout formation of recirculation zone. This is due to

the blockage effect created by the primary jets forcing

the annular jets and fuel jet to spread in radial

direction. Velocity of air fuel mixture suddenly

reduces as it enters the liner to a value of 71.51/m/secat the center of the liner and again decreases to a low

value of 6.50 m/sec in the radial direction (close to the

wall). Air entering the liner through primary,

secondary and dilution holes helps to achieve a better

air-fuel mixture with uniform velocity profile at theexit of the liner. Velocity contours at Mid 2 plane

(Fig. 10b) clearly shows a faster spread rate for the

flow that may be results in combustion process

completeness. The value of velocity (78.02 m/sec) at

the exit of liner is nearly uniform with slightly higher

value in the center. In plane 1, effects of primary and

secondary holes are seen and flow becomes more

uniform in circumferential direction due to better

mixing of air fuel mixture (Fig. 10c). The velocity in

the central zone decreases gradually from 65.01 m/sec

to 6.50 m/sec. In plane 2, velocities are high at the

center, which reduce gradually away from the center

(Fig. 10d). The velocity contours are symmetrical and

uniform a desirable feature for improved performance

of gas turbine.

Analysis of Temperature Contours

At nozzle and annular jet, temperature of inlet air

and fuel was taken as 300 K. Temperature contours at

mid 1 plane (Fig. 11a) of the liner shows the reactionrates to be quite slow in this region resulting in low

temperature rise. After the initial region, temperature

increases gradually from 300 K to a maximum value

of 1948 K in the central region due to efficient

combustion of air fuel mixture. High temperature

zone is around 1948 - 2039 K and forms as a circularband around the central region as a result of complete

combustion (Fig. 11b). Air fuel mixture flows axially

after the reaction and it diffuses away from the centerto ensure entrainment of more air along the centerline

of the combustor thereby reducing the temperature inthis region. Temperature contours depict a spread in

the circumferential direction with the shape change

from circular to elliptical for Plane 1 (Fig. 11c). The

reaction also intensifies at the down stream of the

secondary jet, forcing high temperatures (2039 K) dueto better mixing of air and fuel. Outlet temperature

contours are more uniform and flatter in the central

region, which may result in better performance of

turbine stage. In this plane (Fig. 11d), contours are

wider and completely elliptical in shape.

Analysis of Species Concentration

Mass concentration of different species (CH4, O2,

CO2, NO and H2O) is analyzed for mid-1-Plane.

Mass fraction of CH4

Mass fraction of CH4(Fig. 12a) decreases in axial

direction (0.99 at the inlet and 0.05 at the outlet of

liner) due to efficient mixing of fuel with air.

Inspection of contour levels also indicates that large

fraction of the fuel is consumed in the initial region of

the liner.

Mass fraction of O2

Mass fraction of O2(Fig. 12b) also reduces in theaxial direction because it is also involved in

combustion process. At the inlet, O2 coming through

holes and swirler was around 23% whereas at the

outlet of the liner it was found to be only 1.1%.

Mass fraction of CO2

Mid 1 plane (Fig. 12c) shows that concentration of

CO2 increases in the axial direction (0 at the inlet and

around 13% at the exit). CO2 is generated as a by-

product of the chemical reaction. Mass fraction

contours are symmetric due to proper combustion and

mixing of jets.

Mass fraction of H2O

Mass fraction of H2O is almost (Fig. 12d) same as

CO2 as it is also generated as a by-product of chemical

reaction. Differences are only in magnitude (0% at

inlet and maximum value of 10.9% at exit).

Analysis of Pollutant

Pollution emission level from a combustor depends

upon the interaction between the physical and

chemical process and is strongly temperature

dependent. Dominant component of the pollutant is

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Fig. 9 Vector plot at the Mid 1 plane of the liner

Fig. 10 Vector contours at the different selected planes of the liner: a) Mid 1 plane; b) Mid 2 plane; c) Plane 1; d) Plane 2

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Fig. 11 Temperature contours at the different selected planes in the liner: a) Mid 1 plane; b) Mid 2 plane; c) Plane 1; d) Plane 2

Fig. 12 Mass fraction contours of different species in the liner at Mid 1 plane: a) Mass fraction of CH4; b) Mass fraction of O2

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Fig. 12 Mass fraction contours of different species in the liner at Mid 1 plane: c) Mass fraction of CO2; d) Mass fraction of H2O;e) Mass fraction of NO

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nitrogen monoxide (NO) and evaluation of NO as

pollutant is based on thermal model. In thermal

model, temperature controlled oxidation of N2leads to

formation of NO (Fig. 12e) whose emission level

changes with axial distance. As temperature increasesin the axial direction, oxidation of N2 increases

leading to increase in NO concentration (1e-06 at

inlet, 6e-06 at outlet).

Mass Split through Liner Hole

Mass split through dilution holes is found to be

maximum from both annulus spaces (Table 1). The

higher velocity through annulus passage deflects the

fluid core towards casing wall. Due to higher flow

momentum, fluid jumps the initial liner holes andmore fluid enters the liner through dilution holes.

It is also observed that the flow splits through primaryand secondary holes are nearly same for both inner

and outer annulus, whereas flow splits through

dilution holes is higher from the inner annulus

passage.

ConclusionsAn attempt has been made to simulate the

phenomenon of reacting three-dimensional turbulent

flow in the combustion chamber using CFD.

Methodology allows parameteric investigation for

optimizing the design of combustion chamber. Mass

splits of the total flow through the outer annuli andinner annuli respectively have been found to be:

primary, 23.06, 22.51; secondary, 23.17, 22.93; and

dilution hole, 53.77, 54.56%. Recirculation zone

forms just downstream of the primary and secondary

holes at both the inner and outer wall. There is no

flow reversal at downstream of the dilution holes at

the outer wall; however, a large reverse flow is seen at

the inner wall. This phenomenon suggests the

necessity for modification of the liner shape. The flow

spreads uniformly in the axial direction and velocity

contours change from circular to elliptical shape inthe circumferential plane quantifying the spread rate.

The temperature contours are circumferentially more

uniform and symmetric. Temperature was found to bemaximum at the outlet of the liner. The mass fractions

of CH4 and O2decrease whereas concentration of CO2and H2O increases as combustion products move from

the inlet to the outlet.

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Table 1 Mass split through different liners holes

Liner holes Inner holeskg/sec

Outer holeskg/sec

Primary 0.0212 0.0217

Secondary 0.0216 0.0218

Dilution 0.0514 0.0506

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Nomenclature

C1, C2, C,k, Constants of turbulence model

Gk Generation term (kinetic energy)

K Turbulent kinetic energy

M Number of dependent variable

P Static pressure

Ri Sum residual for a dependent variable

Sm Mass added to the continuous phase

SN Normalizing factor

Tij Stress Tensor

Uavi Mass average inlet velocity

u Mean velocity

u Velocity perturbation

ub Bulk velocity

V Cell volume

Vf Mass flux (velocity) through the face

X Longitudinal coordinate

Under relaxation factor

Turbulence dessipation rate

Density of fluid Dynamic viscosity

t Turbulence viscosity (Eddy viscosity)

Kinematic viscosity

Subscript

i,j Indices of tensorial notation as 1,2,3

00 b 4952 b 1441209340000000

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