modelling of non-premixed swirl burner flows using a reynolds-stress turbulence closure
DESCRIPTION
FreeTRANSCRIPT
-
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: [email protected] (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