ix

ess

n, T

ntal a

form

e 18 N

models are now increasingly being used for the evaluation turbulent transport of momentum and scalar quantities is

Fuel 84 (2005)0016-2361/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.In this computational study, the performance of a differential Reynolds-stress turbulence model has been assessed in predicting a turbulent,

non-premixed combusting swirling flow of the type frequently found in practical combustion systems. Calculations are also performed using

the widely employed eddy-viscosity based k3 turbulence model in order to examine the relative performances of these two closure models.

The predictions are compared against the experimental data of mean axial and tangential velocities, turbulence quantities, gas temperatures

and oxygen concentration collected in a 400 kW semi-industrial scale combustor fired with coke-oven gas using an industry-type swirl burner

at the International Flame Research Foundation [17]. Computations of a corresponding non-combusting flow are also carried out and the

predictions are compared with limited data available. The overall agreement between the measurements and the predictions obtained with

both the k3 and Reynolds-stress turbulence models are reasonably good, in particular, the flame properties. However, some features of the

isothermal and combusting flow fields, and the flame are better predicted by the Reynolds-stress model. The subcritical nature of the

isothermal flow and the effects of combustion on the size and shape of the swirl-induced internal recirculation zone in the corresponding

combusting flow are well simulated by this model. The k3 model fails to reproduce the subcritical nature of the isothermal flow. The

predictions of this model erroneously show a general trend of the mean tangential velocity distribution to assume a forced-vortex profile. The

levels of gas temperature and oxygen concentration in the internal recirculation zone and the enveloping shear region are on the whole better

predicted by the Reynolds-stress model.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Combusting swirling flow modelling; Combustion modelling; Second-moment closure modelling

1. Introduction

Swirling flows are widely used in industrial burners

employed, for example, in power-station furnaces and gas-

turbine combustors to provide stable and high-intensity

flames. Flame structure and stability, and pollutant emis-

sions strongly depend on the aerodynamic and mixing

characteristics of the fuel and swirling combustion air jets in

the near burner region. Over the last two decades, significant

progress has been made in the development of compu-

tational fluid dynamics (CFD) based models to simulate the

performance of practical combustion systems. These

of the performance, and to assist in the design and

development of such combustors. Reliable predictions of

the combustion and pollutant formation processes occurring

in the near burner region critically depend on the accuracy

of the turbulent flow field calculation. The eddy-viscosity

based k3 turbulence model is generally employed for flow

calculations. The limitations of this model for predictions of

both non-combusting (isothermal) and combusting strongly

swirling flows, in particular, the size and strength of the

swirl-induced internal recirculation zone (IRZ), are well

known [14]. For improved predictions of the properties of

swirling flows, a more detailed representation of theModelling of non-prem

using a Reynolds-str

A.E. Germa

Department of Chemical Engineering, School of Process, Environme

Received 30 March 2004; received in revised

Available onlin

Abstracted swirl burner flows

turbulence closure

. Mahmud*

nd Materials Engineering, University of Leeds, Leeds LS2 9JT, UK

27 October 2004; accepted 27 October 2004

ovember 2004

583594

www.fuelfirst.commoment closures based on the solutions of modelled

differential transport equations. Although more advanced

methods, such as large-eddy simulation, are available, they

doi:10.1016/j.fuel.2004.10.015

* Corresponding author. Tel.: C44 113 343 2431; fax: C44 113 3432405.

E-mail address: t.mahmud@leeds.ac.uk (T. Mahmud).required. This can be achieved through the use of second-

the various sub-models embodied in the prediction pro-

cedure, such as the turbulent combustion and radiation heat

v r ~u ~k Z v mt v~k

CP K r~3 (5)

d / Ftransfer models. It is therefore important to validate the

turbulence models directly against flow measurements.

In the present computational study, the performance of a

Reynolds-stress turbulence (RST) model, based on the

modelled differential transport equations for stresses, has

been evaluated against that of the standard k3 turbulence

model [15] by simulating isothermal and combusting

turbulent flows produced by an industry-type, non-premixed

swirl burner with a divergent quarl. This study focuses on

the issue of turbulence modelling. The widely used eddy-

dissipation combustion model [16] has been adopted for the

modelling of non-premixed combustion. The experiments

were carried out in a semi-industrial scale combustor fired

with coke-oven gas at the International Flame Research

Foundation (IFRF), Holland [17]. The predictions obtained

with the two turbulence models are compared against the

experimental data of mean axial and tangential velocities,

turbulence quantities, gas temperatures and oxygen

concentration.

2. Modelling of combusting flow

Mathematical modelling procedure for turbulent com-

busting flow involves numerical solutions of the time-mean

conservation equations for mass, momentum, chemical

species and thermal energy. Supplementary equations are

solved to determine the turbulent momentum (Reynolds

stresses) and scalar fluxes, the rate of combustion reaction,

and the radiation heat transfer in the combustor. An

overview of the aerodynamic and combustion calculation

procedure employed in the present study is provided here.

2.1. Conservation equations for fluid flow

The Favre-averaged equations for conservation of mass

and momentum for a steady, variable-density turbulent flowrequire prohibitively large computing resources even for

relatively simple flows.

In the past, substantial efforts were made on the

development and validation of second-moment differential

Reynolds-stress turbulence models for a range of flows (see

reviews in Refs. [5,6]) including confined, isothermal

swirling flows [3,711]. However, their evaluation for the

calculation of combusting swirling flows, particularly in

geometries relevant to industrial burner configurations, has

been remarkably limited [1214]. Because of the scarcity of

reliable mean velocity and turbulence data for combusting

swirl burner flows, the performance of the turbulence

models has generally been assessed indirectly against the

gas temperature and species concentration measurements.

This is not an entirely satisfactory approach as the

predictions of such quantities are influenced strongly by

A.E. German, T. Mahmu584can be expressed in concise forms in terms of Cartesianvxjj

vxj sk vxj

~3-transport equation

v

vxj r ~uj ~3 Z v

vxj

mt

s3

v~3

vxj

CC31

~3~k

P KC32r~32

~k(6)

where P is the rate of production of turbulence energy and is

given by:

P ZKru00i u00jv ~uivxj

(7)

The model constants are assigned the following standard

values [15]: CmZ0.09, C31Z1.44, C32Z1.92, skZ1.0 ands3Z1.3.

RST model. The Reynolds-stress turbulence model

employed in this study is based on the modelled partial

differential equations for transport of the individual stressestensor notation as:

v

vxj r ~uj Z 0 (1)

v

vxjr ~ui ~uj

Zv

vxjm

v ~uivxj

Cv ~ujvxi

K

v P

vxiK

v

vxj ru00i u00j

(2)

where ~ui and u00i are the Favre-averaged (density-weighted

mean) and fluctuating velocity components respectively in

the xi direction, P and r are the unweighted mean(conventional time-averaged) pressure and density of the

mixture, and m is the laminar viscosity. The Reynolds

stresses, ru00i u00j , are obtained using two different closuremodels: the eddy-viscosity based k3 model [15] and the

RST model [5,18].

2.2. Turbulence models

k3 model. The Reynolds stresses are related to the rate

of strain based on the Boussinesq hypothesis as:

ru00i u00j ZKmtv ~uivxj

Cv ~ujvxi

C

2

3dij r ~k (3)

The isotropic turbulent viscosity, mt, is given by the Prandtl

Kolmogorov relation

mt Z Cm r ~k2=~3 (4)

where ~kZ 1=2u00i u00i is the turbulent kinetic energy, ~3 is therate of dissipation of ~k, and Cm is an empirical constant. Theturbulent kinetic energy and its dissipation rate are

determined by solving their modelled transport equations.~k-transport equation:

uel 84 (2005) 583594[5,18]. The transport equations for the Reynolds stresses,

strain redistribution, viscous dissipation and additional

ud / Fproduction of the stresses.

The convection and production terms are exact, while the

remaining terms are modelled. The production term, Pij, can

be expressed as:

Pij ZKru00i u

00k

v ~ujvxk

K ru00j u00kv ~uivxk

(9)

The diffusion term is modelled by a simple gradient-

diffusion approximation [19] using the isotropic turbulent

viscosity. The stress dissipation process is assumed to be

isotropic and is modelled in terms of the rate of dissipation

of turbulent kinetic energy as:

~3ij Z2

3dij ~3 (10)

The pressurestrain redistribution term, Pij, consists of

two components: the return-to-isotropy term [20] and the

Rapid or isotropization-of-production term [21]. It should

be noted that the contribution of the wall reflection term,

effect of which is confined in the proximity of the walls, is

not included. Thus, the Pij term can be expressed as:

Pij ZKC1 r~3~k

u00i u00j K2

3dij ~k

KC2 r Pij K

1

3dijPkk

(11)

where C1 and C2 are model constants, and their values are

taken [22] as 3.0 and 0.3, respectively.

The Gij term represents the interaction between the mean

pressure gradients and the density-weighted fluctuating

velocities, and appears only in the density-weighted stress

transport equations. The contribution of this term is small

compared to other terms of Eq. (8) [23], and is neglected in

the present calculation. The dissipation rate, ~3, is determinedby solving a transport equation compatible with the RST

model and the turbulent kinetic energy, ~k, is obtaineddirectly from the normal stresses.

2.3. Scalar transport equations

The density-weighted transport equations for scalar

quantities, such as chemical species and gas enthalpy, for

a steady, turbulent flow can be written in general form using

Cartesian tensor notation as:

v r ~ui ~f ZK v ru00i f00 C Sf (12)ru00i u00j , are expressed in general form as:

v

vxk r ~uku00i u00j K

v

vxkmt

vu00i u00jvxi

!Z Pij CPij K r~3ij CGij

(8)

where the various terms from left to right represent,

respectively, convection, diffusion, production, pressure

A.E. German, T. Mahmvxi vxi2.4. Combustion model

A suitable turbulent combustion model is required in

order to determine the mean reaction rate of fuel, which

allows the calculations of the source terms in the species and

enthalpy transport equations. In the present calculation, the

coke-oven gas is represented by a single chemical species in

order to reduce the number of species transport equations.

The measurements [17] show that the concentrations of

carbon monoxide are rather small, in the range of 104

105 ppm. Hence, the fuel is assumed to burn by a single-step

chemical reaction to produce the final combustion products

(carbon dioxide and water vapour)

Fuel1 kg

COxidants kg

0Products1Cs kg

(14)

where s is the stoichiometric oxygen requirement, and is

determined from the fuel composition given in Table 1.

The turbulent non-premixed combustion process is

simulated using the widely employed eddy-dissipation

combustion model [16]. According to this model, the

mean reaction rate of fuel is proportional to the inverse of

the time-scale of the large-scale eddies characterised by the

ratio ~k=~3, and to the smallest of the fuel, oxygen or productsconcentrations. The mean reaction rate is given by:

Rfu Z A r~3

min ~mfu;~mox

;B~mpr

(15)where ~f and f 00 represent the Favre-averaged andfluctuating components of an instantaneous scalar quantity.

In the present calculation, transport equations for the mass

fraction of fuel ~mfu, oxidant ~mox and products ~mpr, andgas enthalpy ~h are solved. Sf stands for the time-averagedsource term representing the mean rate of formation or

destruction Ri of a chemical species in the speciestransport equations, and the rate of heat generation by

combustion (DH Rfu, where DH is the calorific value of thefuel) and net heat gained due to thermal radiation QR in theenthalpy transport equation.

The turbulent scalar fluxes, ru00i f00 , can be determined bytwo different types of closure models: a gradient-diffusion

model based on the eddy-viscosity approach and a second-

moment scalar flux model based on the transport equations

for scalar flux components analogous to Eq. (8). The latter

model leads to a significant increase in computing time and

storage requirement. Hence in the present calculation, in

common with previous studies [13,14], the turbulent scalar

fluxes are modelled using the gradient-diffusion approach

[15] as

ru00i f00 ZKmt

st

v ~f

vxi(13)

where st(Z0.7) stands for the turbulent Prandtl or Schmidtnumber.

uel 84 (2005) 583594 585~k s 1 Cs

2.5. Thermal radiation model

2.6. Numerical solution procedure

velocities is used. In order to improve numerical stability

when the RST model is employed, a staggered arrangement

d / FThe computational procedure for combusting swirling

flow is based on finite-volume numerical solutions of theThe radiation heat transfer is simulated by means of the

non-equilibrium diffusion radiation model [24]. This model,

which has been used before for the simulation of pulverised-

coal [25,26] and natural gas [27] flames, is easy to apply,

computationally efficient and compatible with the finite-

volume solution method of the governing transport

equations. The radiative transfer equation for an absorbing

and emitting medium is expressed as:

v

vxi

1

3k

vT4Rvxi

Z kT4R K ~T4 (16)

where T4R and ~Tare the radiation and mean gas temperatures,respectively, and k is the gas absorption coefficient. The

above transfer equation is solved for T4R which allows the

calculation of the radiation source term, QR, in the enthalpytransport equation:

QR Z ksT4R K ~T4 (17)where s is the StefenBoltzman constant.where A and B are constants which take the values of 4 and

0.5, respectively.

Table 1

Fuel composition and the burner operating conditions

Coke-oven gas analysis (vol.%) Burner operating conditions

CH4 22.4 Fuel flow rate (kg/h) 38.4

Higher hydrocarbons 3.6 Air flow rate (kg/h) 1200

H2 62.6 Air temperature (K) 300

CO 5.5 Thermal input (kW) 400

CO2 1.2 Air swirl number 1.4

O2 0.2 Air velocity (m/s) 19.2

N2 4.5 Fuel velocity (m/s) 33.6

DensityZ0.4142 kg/m3; calorific valueZ40 MJ/kg; stoichiometric airZ13.4 kg/kg of fuel.

A.E. German, T. Mahmu586governing transport equations for the mean axial ~U, radial ~V and tangential ~W velocities; ~k, ~3 and six components ofthe Reynolds stress (u002 , v002 , w002 , u00v00 , u00w00 , v00w00); meanscalar quantities ( ~mfu, ~mox, ~mpr, ~h); and the radiation heattransfer. The combustor simulated in this study is

cylindrical and is fired along its axis, which allows the

flow to be modelled as two-dimensional and axisymmetric.

The basic CFD code adapted for the calculations has

been described in a number of references, see, for example,

Refs. [25,26]. This code is based on the k3 turbulence

model and the hybrid (central/upwind) and QUICK [28]

differencing schemes. In the present study, the RST model

and a higher-order boundedness preserving differencingfor the shear stresses is adopted as suggested in Ref. [30].

The rest of the variables are stored at the scalar grid nodes. In

recirculating flow calculation, numerical diffusion errors

resulting from the use of a first-order convective differencing

scheme may be significant when the flow-to-grid skewness is

large. The use of a higher-order scheme such as the QUICK

scheme [28] can minimise numerical diffusion. However,

this scheme does not possess the boundedness property and

may generate physically unrealistic solutions. Consequently,

the convective terms of the transport equations have been

approximated by a third-order boundedness preserving

scheme, known as the curvature-compensated convective

transport (CCCT) algorithm [29]. The diffusion terms are

discretised by the central-difference scheme.

The solutions of the elliptic transport equations require

specification of boundary conditions on the four sides of the

computational domain. The inlet boundary conditions

employed in the computations are described below. At the

symmetry axis, the values of the radial and tangential

velocities, shear stresses, and the cross-stream gradients of

all other variables are set to zero. No-slip boundary

conditions and log-law based wall functions are applied

along the solid walls. Diffusion of u00i u00j normal to the wall isset to zero. At the outlet boundary, the zero streamwise

gradient conditions are imposed for all variables except for

the axial velocity, which is adjusted to satisfy the overall

mass continuity.

Finally, the discretised momentum equations coupled

with a Poisson-type pressure correction equation are solved

iteratively for the velocity components and pressure using

the PISO algorithm [31]. Solution of the discretised

equations for all other variables and updating of the

physical properties are also performed in each iteration.

The discretised equations are solved using the tridiagonal

matrix algorithm (TDMA).

3. Application of the model

3.1. The experimental case

The combustor used at IFRF [17] was cylindrical with an

internal diameter of 0.44 m and a length of 2.0 m, and was

fired by an industry-type swirl burner. The burner consisted

of two concentric nozzles with a cylindrical bluff bodyscheme [29] have been incorporated into the original code,

and the validation results are presented in this paper.

The transport equations (presented in Cartesian tensor

notation in the preceding sections) in their two-dimensional,

axisymmetric form in cylindrical coordinates are discretised

by integrating over control volumes covering one half-plane

of the flow domain. A conventional staggered arrangement of

the control volumes associated with the axial and radial

uel 84 (2005) 583594inserted in the primary nozzle and fitted with a divergent

of the

A.E. German, T. Mahmud / Fuel 84 (2005) 583594 587quarl of 208 half-angle. This combustor is illustratedschematically in Fig. 1. The fuel (coke-oven gas) was

introduced through the primary nozzle and the combustion

air through the secondary nozzle. Swirl in the combustion

air was imparted by a tangential-entry swirl generator

located upstream of the burner throat which produced solid-

body rotation flows in the secondary nozzle. The burner

quarl and the cylindrical walls were refractory lined. The

confinement ratio, defined as the ratio of the cylindrical

chamber diameter to the quarl exit diameter, was 1.15.

The semi-industrial swirling flame simulated in this

study is of 400 kW thermal input. The coke-oven gas

composition and the operating conditions of the burner are

given in Table 1. In the experiment, a short and intense non-

premixed swirling flame in the vicinity of the burner quarl

was produced. The fuel jet did not penetrate into the IRZ as

it was rapidly entrained by the swirling air stream and

combustion occurred on the boundary of the IRZ [17].

According to the IFRF classification, this flame is referred to

as type-2 non-premixed flame. Measurements of the mean

axial and tangential velocities, and the components of

normal stresses (u002 and w002) were obtained using aLDA system. Gas temperatures were measured using

Fig. 1. Geometrya conventional intrusive suction pyrometer and species

concentrations by analysing gas samples obtained using a

water quenched probe. The measurement stations were

Fig. 2. Computational grlocated at 0.19, 0.373, 0.543 and 1.623 m from the burner

inlet.

3.2. Computational details

The calculations were carried out using the measured

inlet flow conditions where available. The measured profiles

of mean axial and tangential velocity, and the normal

stresses (u002 and w002) at the quarl inlet were employed asthe inlet boundary conditions. In the absence of experimen-

tal data, the mean radial velocity was set to zero and the

normal stress v002 was assumed [32] to be 0:5u002 . The threecomponents of shear stresses (u00v00 , u00w00 , v00w00) were takento be zero. The measured profiles of normal stresses at the

quarl inlet were used to calculate the inlet turbulent kinetic

energy ~kin. The inlet energy dissipation rate ~3 wasestimated from ~k

1:5in =[, with a constant mixing-length, [,

taken as 0.33 times the nozzle dimension (annular widths of

the primary and secondary nozzles). As mentioned above,

the IFRF combustor walls were refractory lined. The heat

losses through the walls were less than 5% of the thermal

input [17]. Consequently, the combustor was treated as

adiabatic.

IFRF combustor.The computations were performed on a 54 (axial)!30(radial) grid. The computational grid in the near burner

region is shown in Fig. 2. The grid lines were uniformly

id near the burner.

in Figs. 3 and 4, respectively. For the isothermal flow, the

k3 model predicts a swirl-induced closed IRZ anchored to

rns us

A.E. German, T. Mahmud / Fuel 84 (2005) 583594588the bluff body and a forward flow in the downstream region,

which approaches the fully developed conditions near the

exit of the combustor. In contrast, the RST model predicts a

long IRZ, surrounded by an annular forward flow, extending

to the exit of the combustor. The high confinement of thespaced in the radial direction and expanded in the axial

direction, downstream of the burner quarl. The inclined wall

of the quarl was represented by a series of steps.

Calculations were also performed on a 32!24 grid withvirtually identical results.

4. Results and discussion

4.1. Effect of combustion on the flow pattern

The predicted combusting and corresponding flow

patterns in the form of non-combusting (isothermal)

velocity vectors using the k3 and RST models are shown

Fig. 3. Predicted combusting flow pattecylindrical chamber suppresses flow separation at the quart

Fig. 4. Predicted isothermal flow patterns usexit, and as a consequence a very small reverse flow is

predicted at the corner by both models of turbulence. The

predicted and measured boundaries of the IRZ for

isothermal and combusting flows are compared in Fig. 5.

The isothermal flow measurements show a long IRZ

extending up to the combustor exit without closing, which

reveals the subcritical nature of this strongly swirling flow

[17]. This is correctly captured by the RST model, whereas

the k3 model fails to reproduce the basic feature of the

flow. The failure of the k3 model in predicting subcritical

features of cold swirling flows has also been observed in

previous calculations [3,8,10].

Comparison of the experimental data [17] presented in

Fig. 5(a) and (b) reveals the effects of combustion on the flow

pattern. The main effects are the reduction of both the size

and the strength of the IRZ. The subcritical flow in the

isothermal condition becomes supercritical when combus-

tion takes place, resulting in the formation of a smaller and

closed IRZ. Figs. 3 and 5(b) show that for the combusting

flow both the k3 and RST models predict a closed IRZ in

agreement with the experimental data. However, the RST

ing (a) k3 model and (b) RST model.model predictions correctly show the forward flow near

ing (a) k3 model and (b) RST model.

rmal and (b) combusting flow (C, experimental; - - -, k3 model; , RST model).

ud / Fuel 84 (2005) 583594 589the axis of the combustor at xZ0.543 m (where x is the axialdistance measured from the burner throat). The reduction of

the size and strength of the IRZ in the combusting flow is

due to the decrease of the level of swirl in the combustor.

The measurements show that the axial velocities in

the forward flow region increase significantly due to

combustion-induced flow acceleration while the tangential

velocities are slightly altered. Consequently, the ratio of the

tangential to axial momentum fluxes decreases substantially,

resulting in a marked reduction of the inlet swirl number in

the near burner region. The swirl number is defined as the

ratio of the tangential momentum flux to axial momentum

flux, as:

Sn Z

R2R1

r ~U ~Wr2 dr=R2

R2R1

r ~U2r dr (18)

where R1 and R2 are the inner and outer radii of the

annular duct of the combustion air for the burner inlet

swirl number, and for the swirl number at a downstream

Fig. 5. Comparisons of measured and predicted IRZ boundaries for (a) isothe

A.E. German, T. Mahmlocation, R1 is taken as zero and R2 is the quarl/combustor

wall radius.

The variations of the swirl numbers in the combusting

flow, obtained using the RST model calculated and

measured velocity distributions, along the length of the

combustor are shown in Fig. 6. The values of the swirl

number calculated using the k3 model predicted velocities

are similar to those based on the RST model. As can be seen,

the inlet swirl number of 1.4 is reduced to about 0.3 within

the burner quarl and then it slowly increases in the

downstream region where an experimental value of about

0.5 and calculated 0.4 are reached. The values of the swirl

number in the near burner region are very close to the

minimum swirl level required in the experiment to establish

a reverse flow [17]. It is important to note that measure-

ments of a range of combusting swirling flows carried out in

the IFRF combustor [17] reveals that the effects of

combustion on the IRZ properties depend on the extent of

reduction of the initial swirl level, which in turn depends onthe location of the flame front and the degree of flow

acceleration.

4.2. Comparison of predicted and measured flow fields

The predicted and measured radial profiles of mean axial

and tangential velocity for the combusting flow at four

stations are shown in Figs. 7 and 8, respectively. The first

station, xZ0.19 m, is within the burner quarl and the rest ofthe stations, xZ0.373, 0.543 and 1.623 m, are in thecylindrical chamber. Predictions are shown for the k3 and

RST models. At the first station (xZ0.19 m), significantdiscrepancies exist between the predicted and measured

axial and tangential velocities. The predicted widths of the

IRZ are much too small compared to the measurement

resulting in a wider shear layer enveloping this zone.

Consequently, the steep gradients of the measured velocity

profiles are not reproduced in the predictions. The predicted

flow development immediately downstream of the burnerFig. 6. Comparisons of measured and predicted swirl number (6,

experimental; , RST model).

d / FA.E. German, T. Mahmu590inlet is strongly influenced by the specified inlet values of

the radial velocity and energy dissipation rate (3), as

demonstrated in previous computational studies [33,34].

The discrepancies between the predictions and measure-

ments at this station are believed to be due to the use of zero

radial velocity and 3 estimated from an assumed mixing-

length as the inlet boundary conditions in the calculations.

At the second station (xZ0.373 m), the axial velocitiespredicted by the k3 and RST models are in reasonably good

agreement with the experimental data. However, differences

between the predictions of two turbulence models are

evident in the IRZ. It is difficult to draw a definite

Fig. 7. Comparisons of measured and predicted mean axial velocity profiles

(6, experimental; - - -, k3 model; , RST model).uel 84 (2005) 583594conclusion with regard to their performance in this region.

As can be seen in Fig. 8, the tangential velocities are

significantly underpredicted by both the turbulence models

at this station. At the third station (xZ0.543 m), bothmodels of turbulence fail to reproduce the measured trend of

the axial velocity profile in the forward flow region. It is

interesting to note that at this station, the shape of the

measured axial velocity profile resembles that of an

unconfined flow and the measured tangential velocity

profile shows an unexpected peak near the wall. However,

the axial and tangential velocities predicted by the RST

Fig. 8. Comparisons of measured and predicted mean tangential velocity

profiles (6, experimental; - - -, k3 model; , RST model).

response to the swirl.

the neglect in the calculation of the effect of soot on

the radiation heat transfer from the flame. The production of

soot in the near burner region influences the local gas

temperature through its effect on the absorption coefficient

of the medium. A previous modelling study [2] of swirling

natural gas flame has demonstrated the smoothing effect of

radiation from soot on the temperature distributions. The

formation and oxidation of soot is a complex process and no

attempt has been made in the present study to include this in

Fig. 9. Comparisons of measured and predicted axial turbulence intensity

profiles (6, experimental; - - -, k3 model; , RST model).

ud / FIn the absence of detailed measurements of turbulence

quantities, the predicted levels of axial,u002

p,

and tangential,w002

p, turbulence intensities obtained

using the k3 and RST models are compared against the

data in Figs. 9 and 10, respectively. As can be seen, the RST

model predicted turbulence intensities are lower and

generally in better agreement with the measurements

compared to those obtained from the k3 model. Previous

studies [8,9] also reported that the k3 model overestimated

the levels of stresses in confined, isothermal swirling flows,

while the RST model correctly returned reduced levels of

stresses in response to the swirl.

4.3. Comparison of predicted and measured

flame properties

The predicted radial profiles of gas temperature based on

the flow calculations using the k3 and RST models are

compared with the measurements in Fig. 11. As can be seen,

the general features of the measured temperature profiles are

reasonably well predicted by both the turbulence models. At

the first station (xZ0.19 m) within the burner quarl, thepredictions are in good agreement with the data in the

central region inside the IRZ. It should be noted that at this

station the width of the IRZ is significantly underpredicted

by both the models of turbulence (see Fig. 7). The peaks in

the predicted temperature profiles at a radial distance (r) of

about 0.1 m, reveal that combustion occurs in the shear layer

surrounding the IRZ, which is a typical feature of type-2

non-premixed flames [17]. Although this is not evident from

the measured temperature profile, the measured carbon

dioxide concentration distribution (not presented here)

shows a peak near the quarl wall. The predicted highmodel near the axis of the combustor are in better agreement

with the data compared to that of the k3 model predictions.

At the last station (xZ1.623 m), both the k3 and RSTmodels, in agreement with the data, predict flat axial

velocity profiles. The predicted tangential velocity distri-

bution using the RST model at this station is in much better

agreement with the data compared to that predicted by the

k3 model. The latter model erroneously predicts a forced-

vortex profile. The k3 model predictions in general show a

tendency of the tangential velocity distribution to approach

the forced-vortex profile, which has also been reported by

previous investigators for computations of isothermal [1,8]

and combusting [2] flows. This has been attributed to

deficiencies in the 3-transport equation in Ref. [1] and to the

overestimation of the diffusive transport of momentum in

the radial direction by the k3 model in Ref. [8]. The latter

has also been revealed by the predicted levels of shear

stresses (not shown here) by the two turbulence models in

our calculations. The comparison clearly shows the

reduction in stress levels produced by the RST model in

A.E. German, T. Mahmtemperatures in the shear layer are presumably due touel 84 (2005) 583594 591the radiation model. Downstream of the quarl, at xZ0.373

A.E. German, T. Mahmud / F592and 0.543 m, the predictions are again in good agreement

with the data. At these stations, the peaks in the measured

temperature profiles are evident near the combustor wall. At

xZ0.375 m, although the predicted value of the temperaturepeak is in good agreement with the data, its radial location is

further away from the wall. At the last station (xZ1.623 m),which is located in the post-flame region far downstream of

the IRZ, both models underpredict temperatures by about

250 8C, probably due to uncertainty in the wall heat transfer

boundary conditions employed in the calculation. In

general, the predicted levels of temperature obtained with

Fig. 10. Comparisons of measured and predicted tangential turbulence

intensity profiles (6, experimental; - - -, k3 model; , RST model).uel 84 (2005) 583594the k3 and RST models are qualitatively similar (with

a maximum difference of about 175 8C) although in the IRZand the enveloping shear region the latter model predictions

are in better agreement with the measurements.

Comparison between the predicted and measured radial

profiles of oxygen concentration is shown in Fig. 12. At the

first two stations (xZ0.19 and 0.373 m), both modelspredict, in agreement with the measurements, virtually zero

oxygen concentration in the IRZ. In the region outside the

IRZ dominated by the combustion air flow (see Fig. 3), the

predicted and measured oxygen concentrations increase

to a maximum value near the wall. As can be seen,

Fig. 11. Comparisons of measured and predicted gas temperature profiles

(6, experimental; - - -, k3 model; RST model).

A.E. German, T. Mahmud / Fthe predictions obtained from both the turbulence models

are identical at the first station, and at xZ0.373, the RSTmodel returns slightly better predictions. At the third station

(xZ0.543 m), the k3 model significantly overestimatesoxygen concentration in the IRZ whereas the RST model

predictions are in better agreement with the data. At the last

station (xZ1.623 m), both models overpredict oxygenconcentration near the axis of the combustor, but the

predictions are in good agreement with the experimental

Fig. 12. Comparisons of measured and predicted oxygen concentration

profiles (6, experimental; - - -, k3 model; , RST model).5. Concluding remarks

The performance of the standard eddy-viscosity based

k3 and RST turbulence models in predicting combusting

swirling flow has been assessed against the LDA flow and

combustion data [17], collected in a gas fired semi-industrial

combustor at IFRF. Calculations of a corresponding non-

combusting (isothermal) flow are also performed in order to

examine the effect of combustion on the flow field and the

predictions are compared with a limited amount of data

available.

Although the k3 turbulence model reasonably well

predicts the overall flow and combustion characteristics in

the combustor, some features of both the isothermal and

combusting flow fields, and the flame are better predicted by

the RST model. The subcritical nature of the isothermal flow

and the effects of combustion on the size and shape of the

swirl-induced IRZ in the corresponding combusting flow are

well simulated by the RST model. The k3 model fails to

reproduce the subcritical nature of the isothermal flow. The

predictions of this model erroneously show a general trend

of the mean tangential velocity distribution to assume a

forced-vortex profile. The predicted turbulence intensities

using the RST model are generally in better agreement with

the measurements compared to those obtained from the k3

model. The levels of gas temperature and oxygen concen-

tration in the IRZ and the enveloping shear region are on thedata further away from the axis (rO0.08 m). In general, thepredicted oxygen concentration profile at this station is

relatively flat compared to the measured one presumably

due to the overestimation of the diffusive transport of mass.

The use of a second-moment closure for the calculation of

the turbulent scalar fluxes in the transport equations

(Eq. (12)) would probably enhance the quality of predic-

tions. On the whole, the prediction of oxygen concentration

distributions with the RST model is better than that given by

the k3 model.

In general, the predictions of the swirling flow field and

flame properties in the present combustor obtained with the

RST model are in better agreement with the data compared

to that of the standard k3 model predictions. However, for

the present flow with a high inlet swirl number of 1.4, it is

expected that the differences between the predictions of the

k3 and RST models should be greater than that displayed

in previous figures. This, unexpected, performance of the

turbulence models may be explained in terms of the effect

of combustion on the swirl level. As revealed in Fig. 6,

there is a drastic reduction of the initial level of swirl from

1.4 to about 0.3 in the near burner region resulting from the

increase of the axial momentum due to combustion-

induced flow acceleration. Consequently, the effects of

swirl on the mean flow and turbulence fields are

significantly reduced.

uel 84 (2005) 583594 593whole better predicted by the RST model.

For the type-2 non-premixed flame considered in this

study, the combustion front is located in the vicinity of

the burner as observed experimentally [17], which drasti-

cally reduces the swirl number from 1.4 at the burner inlet to

about 0.3 in this region due to the increase in axial

momentum. As a consequence, the effect of swirl on the

flow field is significantly reduced. The experiments carried

out at IFRF demonstrated that the effect of combustion on

the swirling flow field depends on the location of the flame

front and the degree of flow acceleration. This suggests that

the difference between the performances of these two

turbulence models will depend on the flame types.

Acknowledgements

The financial support provided by Lagoven S. A. of

Venezuela to A. German to undertake this research is

gratefully acknowledged.

References

[5] Launder BE. Int J Heat Fluid Flow 1989;10:282.

[6] Hanjalic K. Int J Heat Fluid Flow 1994;15:178.

[7] Nikjooy M, So RMC. Int J Numer Meth Eng 1989;28:861.

[8] Hogg S, Leschziner MA. J AIAA 1989;27:57.

[9] Jones WP, Pascau A. J Fluids Eng, Trans ASME 1989;111:248.

[10] Weber R, Visser BM, Boyan F. Int J Heat Fluid Flow 1990;10:225.

[11] Nikjooy M, Mongia HC. Int J Heat Fluid Flow 1991;12:12.

[12] Hogg S, Leschziner MA. In: Proceedings of the third international

conference on computational combustion, Antibes, France 1989.

[13] Lockwood FC, Shen B. Proc Combust Inst 1994;25:503.

[14] Landenfeld T, Kremer A, Hassel EP, Janicka J. In: Proceedings of the

eleventh symposium on turbulent shear flows, Grenoble 1997.

[15] Launder BE, Spalding DB. Comput Meth Appl Mech Eng 1974;

3:269.

[16] Magnussen BF, Hjertager BH. Proc Combust Inst 1978;17:719.

[17] Weber R, Dugue J. Prog Energy Combust Sci 1992;18:349.

[18] Launder BE, Reece GJ, Rodi W. J Fluid Mech 1975;68:537.

[19] Shir CC. J Atmos Sci 1973;30:1327.

[20] Rotta JC. Z Phys 1951;29:547.

[21] Naot D, Shavit A, Woifshtein M. Israel J Technol 1970;8:259.

[22] Gibson MM, Younis BA. Phys Fluids 1986;29:38.

[23] Jones WP. In: Kolimann W, editor. Prediction methods for turbulent

flows. London: Hemisphere; 1980. p. 379.

[24] Arscott JA, Gibb J, Jenner R. In: Weinberg FJ, editor. Proceedings of

the European symposium. Sheffield, UK: The Combustion Institute;

1973. p. 675.

[25] Lockwood FC, Mahmud T. Proc Combust Inst 1988;22:165.

A.E. German, T. Mahmud / Fuel 84 (2005) 583594594[1] Sloan DG, Srnith PJ, Smoot LD. Prog Energy Combust Sci 1986;12:

163.

[2] Boardman RD, Eatough CN, Germane GJ, Smoot LD. Combust Sci

Technol 1993;93:193.

[3] Benim AC, Nahavandi A. In: Hanjalic K, Nagano Y, Tummers M,

editors. Proceedings of turbulence, heat and mass transfer 4, 2003.

p. 715.

[4] Van Maele K, Merci B, Dick E. In: Hanjalic K, Nagano Y,

Tummers M, editors. Proceedings of turbulence, heat and mass

transfer 4, 2003. p. 931.[26] Lockwood FC, Mahmud T, Yehia MA. Fuel 1998;77(12):1329.

[27] Costa M, Costen P, Lockwood FC, Mahmud T. Proc Combust Inst

1990;23:973.

[28] Leonard BP. Comput Meth Appl Mech Eng 1979;19:59.

[29] Gaskell P, Lau A. Int J Numer Meth Fluids 1988;8:617.

[30] Pope SB, Whitelaw JH. J Fluid Mech 1976;73:9.

[31] Issa RI. J Comput Phys 1986;62:40.

[32] Habib MA, Whitelaw JH. Numer Heat Transfer 1982;5:145.

[33] Sturgess GJ, Syed SA, McManus KR. AIAA paper 83 1983 p. 1263.

[34] Leschziner MA, Rodi W. J AIAA 1984;22:1742.

Modelling of non-premixed swirl burner flows using a Reynolds-stress turbulence closureIntroductionModelling of combusting flowConservation equations for fluid flowTurbulence modelsScalar transport equationsCombustion modelThermal radiation modelNumerical solution procedure

Application of the modelThe experimental caseComputational details

Results and discussionEffect of combustion on the flow patternComparison of predicted and measured flow fieldsComparison of predicted and measured flame properties

Concluding remarksAcknowledgementsReferences