ftc kempf swirl paper
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detail about swirling combustionTRANSCRIPT
Loughborough UniversityInstitutional Repository
Recirculation and vortexbreakdown in isothermal
and reacting swirling flows:insights from two different
large eddy simulationprograms [Published as:
Large eddy simulations ofswirling non-premixedflames with flamelet
models: a comparison ofnumerical methods]
This item was submitted to Loughborough University’s Institutional Repositoryby the/an author.
Citation: KEMPF, A..... et al., 2008. Large eddy simulations of swirling non-premixed flames with flamelet models: a comparison of numerical methods.Flow, Turbulence and Combustion, 81(4), pp. 523-561
Additional Information:
• This article was published in the journal, Flow, Turbulence and Com-bustion [ c© Springer Verlag]. The original publication is available atwww.springerlink.com
Metadata Record: https://dspace.lboro.ac.uk/2134/5580
Version: Accepted for publication
Publisher: c© Springer Verlag
Please cite the published version.
2
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Recirculation and Vortex Breakdown in Isothermal
and Reacting Swirling Flows: Insights from two
different Large Eddy Simulation Programs
A. Kempf1, W. Malalasekera2, K.K.J.Ranga-Dinesh2
and O. Stein1
1Department of Mechanical Engineering, Imperial College London, SW7 2AZ, UK
2Wolfson School of Mechanical and Manufacturing Engineering, Loughborough Univer-
sity, Loughborough, LE11 3TU, UK
Keywords: LES, Turbulence, Swirl, Vortex Breakdown, Recirculation, Precession, Non-
Premixed, Combustion
Abstract
This work investigates the application of Large Eddy Simulation (LES) to se-
lected cases of the turbulent non-premixed Sydney swirl flames. Two research
groups (Loughborough University, LU and Imperial College, IC) have simulated
these cases for different parameter sets, using two different and independent LES
methods. The simulations of the non-reactive turbulent flow predicted the exper-
imental results with good agreement and both simulations captured the recircu-
lation structures and the vortex breakdown without major difficulties. For the
reactive cases, the LES predictions were less satisfactory, and using two indepen-
dent simulations has helped to understand the shortcomings of each. Furthermore
one of the flames (SMH2) was found to be exceptionally hard to predict, which
1
was supported by the lower amount of turbulent kinetic energy that was resolved
in this case. However, the LES has identified modes of flame instability that were
similar to those observed in some of the experiments.
1 Introduction
1.1 Motivation
Powerful geophysical flows such as tornados, dust devils or waterspouts are dominated by
swirl and may affect our lives. Swirl flows are also ubiquitous in turbo-machinery, propul-
sion systems and chemical reactors; and they are commonly used in process engineering.
Around the tips of wings, strong swirl flows cause drag but are vital for creating lift.
The present paper focuses on swirl in combustion systems, and how swirl-phenomena can
alter a flame. A typical combustor is designed to achieve a completed chemical reaction
in the smallest, lightest and cheapest enclosure possible. By creating regions of reverse
flow through swirl, the reactants are kept inside the combustor for an enhanced residence
time, allowing for better mixing and complete reaction. This helps to stabilise the flame
and to control the emission of pollutants. An improved understanding of swirl flows and
their interaction with flames will help devise strategies to enhance the performance and
safety of a given combustor, to reduce its size, weight and cost, and to minimise the
emission of pollutants. These targets are of paramount importance for a global economy
that obtains approximately 90% of its primary power from the combustion of fossil and
non-fossil fuels1 [35].
1In 2000, energy was supplied from fossil fuels (79.5%), nuclear fuels (6.8%), hydropower (2.3%),non-fossil fuels (11.0%) and other sources (0.5%)
2
1.2 Swirl Flow
Turbulent swirl flows have been investigated for many years, and some of the work was
reviewed by Hall [33], Leibovich [49], Gupta et al. [31], Escudier [23] and others. In gen-
eral, swirl flows encounter similar shear-layer instabilities as axial jets, with the additional
presence of an azimuthal shear layer due to the radial gradient in circumferential velocity.
An additional source of instability is the centrifugal force, which is only balanced if the
flow profile corresponds to a potential vortex, where vorticity is only encountered on the
centreline. Taken together, these instabilities can lead to highly unstable, transient flow
patterns such as vortex breakdown (VB) or precessing vortex cores (PVC).
PVC occur when the vortex region is unstable and starts to precess about the axis of
symmetry. PVC are usually found on the boundary of the reverse flow zone [85]. In
combustors, the periodical motion of vortex precession can enhance the mixing between
fuel and oxidiser and thus stabilise the flame. Interestingly, Anacleto et al. [6] found that
a PVC’s precessing frequency and core circulation only depend on the vortex generation
as encountered in isothermal flow, and are not altered by combustion. Even more complex
flow patterns than PVC are observed with VB, which will be described in the next section.
1.3 Vortex Breakdown
Vortex breakdown (VB) is a phenomenon that occurs in swirl flows if the swirl surpasses
a critical level: centrifugal forces will reduce the pressure on the swirl-axis far enough
to create a significant adverse pressure gradient in axial direction. The flow is hence
decelerated and eventually reversed, creating a semi-stable recirculation zone (RZ) if the
swirl was strong enough. The flow encountered with VB is generally asymmetric and
variable in time [15, 24, 85] but there are no general criteria to predict the occurrence or
the type of VB. Swirl flows must be considered as highly sensitive and are influenced by
many parameters, but for single swirling jets, a critical swirl number of 0.6 is typically
3
accepted for the onset of breakdown [31].
1.3.1 Types of Vortex Breakdown
One typically distinguishes four distinct modes of VB [11, 74]; double helix breakdown,
spiral breakdown, axisymmetric bubble breakdown, and axisymmetric conical breakdown.
These breakdown modes are best explained using a visualisation technique that injects
dye on the vortex axis. For very low Reynolds numbers, the double helix mode [74]
can occur, where the dye introduced on the vortex axis is decelerated and expanded
into curved triangular sheets. Each half of the sheet is then wrapped around the other,
effectively forming the double helix. At higher Reynolds numbers, spiral breakdown can
occur [74], where a rapid flow deceleration to stagnation is followed by the swirl axis
leaving the symmetry axis, resulting in a corkscrew-shaped spiral structure. This spi-
ral breaks up into turbulent vortices after several rotations. Vortices can also break
down in an axisymmetric bubble [74] that forms at the stagnation point. The bubble
continuously exchanges fluid with the environment, leading to simultaneous filling and
emptying through vortex rings that are caused by pressure instabilities in the wake of the
bubble. A fourth breakdown mode, the axisymmetric conical breakdown [11], appears
similar to the bubble breakdown, but has an open conical sheet after the expansion. The
sheet breaks down into turbulent structures, and only a weak RZ is observed but no
contraction. Leibovich [49] describes further types of VB which result from variations
and combinations of the classical modes.
1.3.2 Studies of Vortex Breakdown
At this point, we have provided a sketch of the phenomenon of VB, and the following
paragraphs outline some significant studies.
At high angles of attack, most of the lift created by a delta wing results from vortex lift,
which is limited by VB [63]. Even worse, VB close to an aircraft’s wings or control sur-
4
faces can lead to buffeting, with very high loads on the airframe. The first investigations
of VB hence tried to identify the basic patterns of breakdown and to find criteria which
determine its appearance. Harvey [34] simplified the problem by conducting experiments
on swirling flows inside a tube, with a sudden transition to breakdown. More quantitative
results were provided by Chanaud [15], who studied the breakdown position in swirling
jets as a function of the Reynolds number and of swirl levels. Sarpkaya [74] altered Har-
vey’s experiment by using a slightly diverging conical tube and provided charts on the VB
position depending on the same parameters. These charts show that the vortex core size
decreases with increasing Reynolds number and that the length of the RZ increases with
growing strength of swirl. Sarpkaya and co-workers also describe how more than one VB
can exist in the divergent pipe-flow if the swirl is strong enough. Buckley et al. [14] and
Farokhi et al. [25] showed that the behaviour of swirling flows depends strongly on the
distribution of the axial and circumferential velocity, which strongly varies with different
swirl generation methods. Naughton et al. [59] examined compressibility effects on the
swirl induced growth of a jet, and found no significant influence, supporting the validity
of the low-mach number assumption. Theoretical studies on VB were attempted to find
simple descriptions of the causes and mechanisms based on inviscid model vortices [48]
or wave theory [8, 9, 47, 70, 81]; and hydrodynamic instability theory on VB [50, 52, 53]
was developed to find criteria for instability.
Numerical simulations of swirl flows were originally limited to axisymmetric, steady,
laminar and incompressible situations [30, 46] before unsteady axisymmetric simulations
made it possible to predict axisymmetric breakdown with periodic flow behaviour [77].
Laminar axisymmetric simulations made it possible to predict the multiple breakdowns [32]
that had been experimentally observed by Harvey [34] and Sarpkaya [74]. The bubble
type breakdown was captured by Spall & Gatski [80] who carried out three dimensional
unsteady simulations of a laminar swirl flow. Turbulent swirl flows were simulated from
the 1990s based on the k − ǫ model, algebraic Reynolds stress models (ARSM), and full
Reynolds stress models (RSM) [91] but k − ǫ models generally require further modifica-
5
tions to accurately predict swirling flows, as they cannot capture anisotropy or strong
streamline curvature. Later simulations of swirl flows with recirculation and VB used
DNS to investigate the flow in great detail [27, 45, 72].
Very recently, several LES investigations have been carried for cases as complicated as
swirl stabilised combustors. For example, Wang & Bai [89] performed LES calculations
of non-reacting swirling flow fields and captured complex phenomea such as recircula-
tion, VB and precessing motion. DiMare et al. [19], Kim et al. [42], and Mahesh et
al. [55] carried out LES of combustion and simulated set-ups like simplified aero-engines.
Sankaran & Menon [73] obtained encouraging results for non-premixed swirling spray
combustion, and Oefelein [61] applied LES to propulsion and power systems. Pierce &
Moin [65] examined complex gas turbine combustors and Wang et al. [90] managed to
accurately predict the swirling flow from a gas turbine injector. Recently, the group
of Poinsot has started to publish ”frontier simulations” that apply LES to systems as
complicated as ramjet combustors [71].
At this end, the present paper attempted to show the success of LES in the application
to turbulent combustion. The configuration considered for this study is an unconfined,
swirling flow configuration known as the Sydney swirl burner, which is an extension of
the Sydney bluff-body burner (Dally & Masri [16]) to swirling flames. Applications of
LES to the Sydney bluff-body burner have been carried out by Kempf et al. [40], Raman
& Pitsch [69], Navarro-Martinez & Kronenburg [60] and Drozda et al. [21] and good
agreement with experimental measurements was obtained. In this paper, we present
the efforts of two independent groups from Loughborough University (LU) and Imperial
College (IC) to model selected cases of the Sydney swirl flame series with LES. This effort
is part of a major drive to enhance combustion calculations using generic burners as a
platform (TNF workshop series [86]). The Sydney burner was chosen here as a model
problem because of its well-defined boundary conditions, its capability to hold flames
where finite-rate chemistry effects are high, even though some flames possess modes of
flow instability and because of the existence of extensive data on reactive and non-reactive
6
flows. The swirl burner has been experimentally investigated by Masri et al. [58], Kalt et
al. [37], Al-Abdeli & Masri [2–4] and Masri et al. [57]. LES simulations of Sydney swirl
burner reacting and non-reacting test cases were carried out by Malalasekera et al. [56],
Stein & Kempf [83], El-Asrag & Menon [22], James et al. [36] and encouraging results
with different combustion models were obtained.
2 Experimental Configuration
2.1 Burner Set-Up
This work examines the Sydney swirl burner that is shown in fig. 1. The configuration
is relatively simple featuring a fuel jet (diameter 3.6mm) surrounded by a bluff-body of
50mm diameter. An annular gap (5mm wide) around the bluff-body provides the swirled
primary air. Swirl is introduced aerodynamically by using tangential ports 300mm up-
stream of the burner exit. Two diametrically opposed ports, located on the periphery
of the burner but upstream of the tangential inlets, supply the axial air to the swirling
stream. The swirled air passes through a tapered neck section that ends 140mm up-
stream of the burner exit plane. This promotes uniform boundary conditions at the exit
plane by combining axial and tangential streams to form a uniform swirl flow stream.
The burner is installed in a wind tunnel which provides a coflow of un-swirled secondary
air. Two different wind tunnel configurations were used as the velocity measurements
were performed by Sydney University [2] in a tunnel of 130 × 130 mm cross section,
whereas the species measurements were taken at Sandia National Laboratory in a tunnel
of 310 × 310mm [57].
Swirl flames are strongly affected by the swirl number S, which is defined in eq. (1) as
the ratio of the axial flux of the angular momentum Gφ to the axial flux of the axial
7
momentum Gx:
S =Gφ
RGx=
∫ R
0ρ <U><W> r2dr
R∫ R
0ρ <U>2 rdr
(1)
In this equation, <U> and <W> are the mean axial and tangential velocities at the
exit plane, ρ is the density and R is a characteristic length. However, for this burner the
experimentalists chose to characterise the level of swirl by the geometric swirl number Sg,
which is defined as the ratio of bulk tangential to bulk axial velocity <W>s / <U>s above
the annulus [1]. The Reynolds number of the flow from the annulus Res(= Us × rs/ν) is
defined in terms of bulk axial velocity Us and the outer radius rs of the annulus [1]. The
Reynolds number for the central jet, Rej(= Uj × dj/ν), is based on the nozzle diameter
dj, the bulk jet velocity Uj and the viscosities of the relevant gases at 293K (air or fuel
mixture).
The flow characteristics of the swirl burner are controlled by four parameters: the bulk
velocity of the central jet Uj , the bulk axial and tangential velocities Us and Ws of the
primary air stream, and the mean co-flow velocity Ue of the secondary air stream in the
wind tunnel. For the swirl flames investigated, Ue was maintained at 20ms−1.
2.2 Non-Reacting Test Case
In the Sydney swirl burner configuration, a number of non-reacting cases at relatively
high Reynolds numbers were investigated. These flows exhibit various recirculation and
flow field regimes that have been discussed in detail by Al-Abdeli & Masri [2]. They
found the typical upstream RZ introduced by the bluff-body, and eventually the oc-
currence of a downstream recirculation region due to VB. Al-Abdeli & Masri [4] also
examined precession and recirculation and found that precession frequency depends on
the swirl number, as well as the Reynolds number of both the central jet and the swirling
annulus. The main conclusion of their studies was that the addition of swirl to bluff-
body flows leads to more complex flow patterns, which may include the secondary RZ,
8
flow instabilities and precession. They also found that VB does not necessarily occur at
higher swirl numbers; a VB bubble occurs only when axial momentum (Reynolds num-
ber) of the swirling annulus provides the right conditions [2]. The successful simulation
of such a sensitive configuration can hence be considered as an important milestone for
a computational technique. In the present study, we first consider the LES of the non-
reacting case N29S054 (cf. table 1) to understand the flow field and the limitations of
our methods in the absence of turbulence/chemistry interactions.
2.3 Reacting Swirling Cases
Al-Abdeli & Masri [3] and Masri et al. [57] conducted detailed measurements of the flow
field, temperature, species distribution and stability characteristics for flames burning
three different fuel compositions. The flames were identified as “Swirl Methane” flames
SM, “Swirl Methane-Air” flames SMA (1:2 vol.), and “Swirl Methane-Hydrogen” flames
SMH (1:1 vol.). Single-point Raman-LIF and Rayleigh techniques were applied at San-
dia National Laboratories to obtain the temperature and species concentrations. The
velocities were measured by Laser Doppler Velocimetry (LDV) at Sydney University,
where methane was replaced with cheaper compressed natural gas that consists of 90%
methane. The flow features and stability characteristics of all these flames have been
described in detail in [3] and [57]. Due to their relatively high jet velocities, the SMH
flames were longer than the SM and SMA flames. The flames (except some SMA flames)
showed a necking region just downstream of the bluff-body before spreading radially
further downstream. Some flames operated close to the blow-off limits and showed large
temperature fluctuations, considerable local extinction, re-ignition, and in some cases
even acoustic instabilities. For the LES investigations, we have chosen the flames SM1,
SMH1 and SHM2, which are free from combustion instabilities. Table 1 shows the op-
erating parameters of the flames investigated in this study. Important features of these
flames (VB, upstream & downstrean RZ, highly-roating parcels of fluids, etc.) that were
9
Table 1: Parameters of the investigated casesCase Fuel fs Ue Us Ws Ujet Rejet Res Sg Lf
(vol.) m/s m/s m/s m
N29S054 – – 20 29.7 16.0 66 15,700 59,000 0.54 –
SM1 CH4 0.054 20 38.2 19.1 32.7 7,200 75,900 0.50 0.12SMH1 CH4/H2(1:1) 0.050 20 42.8 13.8 140.8 19,300 85,000 0.32 0.37SMH2 CH4/H2(1:1) 0.050 20 29.7 16.0 140.8 19,300 59,000 0.54 0.40
found experimentally are discussed jointly with the corresponding LES data in the results
section.
3 Modelling and Mathematical Formulations
This section describes the mathematical background and the models that were used for
the simulations performed by the groups involved in this work.
3.1 Filtered Governing Equations
To compute the temporal development of large scale flow features, the modelled transport
equations for mass, momentum and mixture fraction are solved. In the present work,
Schumann’s implicit filtering [76] is used with a kernel based on the computational cell,
which naturally fits into the finite volume formulation.
The filtered transport equations for mass (2), momentum (3), and mixture fraction (4)
read:
∂ρ
∂t+
∂
∂xjρui = 0 (2)
10
∂
∂t(ρui) +
∂
∂xj(ρuiuj) = −
∂p
∂xi+
∂
∂xj
(2ρ(ν + νt)
[Sij −
1
3δijSkk
])
+1
3
∂
∂xj[ρδijτkk] + ρgi (3)
with the strain rate Sij =1
2
(∂ui
∂xj+∂uj
∂xi
)
∂
∂t(ρf) +
∂
∂xj(ρf uj) =
∂
∂xj
(ρ
[ν
σ+νt
σt
]∂f
∂xj
)(4)
In these equations, ρ denotes the density, ui is the velocity component in the xi direction,
ν and νt the laminar and turbulent viscosity, τkk is the isotropic part of the SGS tensor,
p is the pressure, gi is the gravitational acceleration and f is the mixture fraction. The
laminar and turbulent Schmidt numbers σ and σt were set to 0.7 and 0.4 [68] respectively.
3.2 Turbulence Models
The filtered momentum equation (3) contains unclosed terms. In the above model the
sub-grid scale (SGS) contribution to the momentum fluxes is modelled via the eddy
viscosity νt and the isotropic part of the SGS stress tensor τkk. The turbulent viscosity
νt is determined from Smagorinsky’s [79] eddy viscosity model, with the model parameter
Cs, the filter width ∆, and the strain rate tensor Sij according to equation (5):
νt = Cs∆2 |Sij| = Cs∆
2
∣∣∣∣1
2
(∂ui
∂xj+∂uj
∂xi
)∣∣∣∣ (5)
The isotropic part of the stress tensor τkk is absorbed into the pressure correction equation
such that P = p − 13τkk. Germano’s procedure [28] is used to calculate the Smagorin-
sky model coefficient Cs dynamically from the local instantaneous flow conditions. Ger-
mano’s original method required averaging in homogeneous directions to achieve stability,
11
but Ghosal et al. [29] and Piomelli & Liu [66] developed extensions that do not require
such averaging. The latter model (localised dynamic procedure) was used by group LU.
Germano’s procedure can result in negative eddy viscosity which is usually clipped off.
3.3 Combustion Models
The chemical reactions in non-premixed combustion occur at the smallest scales that
cannot be resolved in LES. The combustion process hence occurs on the SGS level and
must be modelled completely. As the chemical state must be determined for every
single time step, the computational cost depends strongly on the efficiency of the applied
chemistry model.
In this study the steady state laminar flamelet approach was used with comprehensive
chemistry to describe thermo-chemical coupling. Variables such as density, temperature
and species concentrations are obtained as functions of the mixture fraction f (as defined
by Bilger [10]) and its dissipation rate χ. To generate laminar flamelet relations, the
steady state flamelet equations for unity Lewis number are solved for the species mass
fractions ψi [64]:
ρχ
2
∂2ψi
∂f 2+ ωi = 0 (6)
In this equation the chemical source term ωi depends on the instantaneous scalar dissi-
pation rate χ = 2 ν/σ|∇f |2. In the LES context, only the filtered values f and χ of
the mixture fraction and scalar dissipation are known, and hence any non-linear func-
tion of f and χ will depend on its SGS distribution. The SGS distribution of mixture
fraction is modelled by a β-function parameterised by the filtered mixture fraction f
and its variance f ′′2. The groups used different approaches to compute the SGS vari-
ance f ′′2 of the mixture fraction. Group LU used the model by Branley and Jones [13]:
f ′′2 = C∆2(∇f)2. Group IC applied the approach by Forkel & Janicka [26] to calculate
the mixture fraction variance through the resolved variance based on a test filter cell.
12
Table 2: Comparison of the combustion modellingGroup LU Group IC
Chemical Mechanism: GRI 2.11 Lindstedt, Sick et al. [78]Species: 49 97Reactions: 279 629Flamelets: single flamelet multiple flameletsStrain Rates: 500 s−1 variable
Group LU used a single steady flamelet for a strain rate of 500 s−1 generated from
the chemical mechanism GRI 2.11 [12], which includes 49 species and 279 reactions,
solved using the Flamemaster code [67]. Group IC used a mechanism by Sick, Hilden-
brand and Lindstedt [78] with 97 species and 629 reactions and modelled the filtered
scalar dissipation rate with the eddy viscosity approach proposed by deBruyn et al. [18]:
χ = 2 (ν/σ + νt/σt) (∇f)2. The SGS distribution of the scalar dissipation (which is
typically assumed to be log-normal) is then approximated by a Dirac δ function. Group
IC uses a pre-integrated look up table to calculate all dependent scalars φ as a function
of f, χ and f ′′2. A comparison of the combustion models applied by both groups can be
found in table 2.
4 Numerical Description
4.1 Discretisation Methods
4.1.1 PUFFIN – Loughborough University (LU)
The PUFFIN code was developed by Kirkpatrick [43] at the University of Sydney (Aus-
tralia) and extended by Ranga-Dinesh [20] at Loughborough University (UK). PUFFIN
computes the temporal development of large scale flow structures by solving the trans-
port equations for the spatially filtered density (2), momentum (3), and mixture fraction
(4). The equations are discretised in space with a finite volume formulation (FVM) using
Cartesian coordinates and a non-uniform staggered grid. Second order central differences
13
(CDS) are used for the spatial discretisation of the momentum equation and the pressure
correction equation, which minimises the projection error and ensures convergence with
an iterative solver.
The diffusion terms of the scalar transport equation (4) are discretised using a second or-
der CDS scheme. However, a CDS discretisation of convection would cause non-physical
oscillations of the mixture fraction field, which is coupled with the momentum field
through density. This means that wiggles in the mixture fraction would de-stabilise the
solution of the velocity field. To overcome this problem, PUFFIN uses Leonard’s [51]
“Simple High Accuracy Resolution Program” (SHARP) for the convection of mixture
fraction. The SHARP scheme considers the curvature CRV and computes the face value
φf from the values φC and φU in the cell C and in its upwind neighbour U shown in
fig. 2:
φf = [(1 − θ)φC + θφU ] −1
8CRV × ∆x2
U (7)
The weighting factor for the interpolation depends on θ = ∆xf/∆xU , where ∆xf and
∆xU are the distances from the node C to the face centroid f and to the upwind neigh-
bour node U respectively. The upwind biased curvature term CRV is also affected by
the cell UU upstream of the upwind neighbour (u < 0) and the downwind neighbour
cell D (u > 0):
CRV =
φU−2φC+φD
∆x2
U
: u > 0
φC−2φU+φUU
∆x2
U
: u < 0
(8)
For variable density calculations, an iterative time advancement scheme is used. First,
the time derivative of the mixture fraction is approximated from a Crank-Nicolson
scheme, and the flamelet library yields the new density at the end of each time step. This
density is then used to advance the momentum equations through a second order hybrid
scheme. Advection terms are calculated explicitly with second order Adams-Bashforth,
while diffusion terms are calculated implicitly using second order Adams-Moulton. Fi-
14
nally, mass conservation is enforced by projecting the approximated velocity field onto a
divergence free field, using the method of VanKan [88] and Bell & Collela [7].
4.1.2 FLOWSI – Imperial College (IC)
The FLOWSI code was originally developed by Schmitt [75] at TU-Munchen (Germany)
for the LES of turbulent pipe and channel flows, and has been extended by Forkel [26],
Kempf [39] and others at TU Darmstadt. The program solves the filtered transport
equations for mass (2), momentum (3) and mixture fraction (4) for a cylindrical reference
frame using FVM and a staggered grid. The momentum equation is discretised by second
order CDS, possible oscillations are limited by the continuity equation. However, scalar
transport is not constrained by continuity, but oscillations in the scalar field must be
avoided. A total variation diminishing (TVD) scheme is used for the advection of scalars,
which combines the accuracy of CDS with the robustness of an upwind differencing
scheme (UDS). In the finite volume context, TVD schemes interpolate the value on the
cell-face φf from the corresponding upwind value φU , local value φC , and downwind value
φD with a limiter function B(r):
φf = φC +B(r)(φC − φU)
2(9)
In the present work, the non-linear CHARM limiter [92] was used, which is second order
accurate away from sharp gradients. The CHARM limiter-function B(r) depends on the
gradient ratio r as follows:
B(r) =
r(3r+1)(r+1)2
: r > 0
0 : r ≤ 0
with r =ΦD − ΦC
ΦC − ΦU(10)
Time integration is described with an explicit three-step low-storage Runge-Kutta scheme
that is third-order accurate for linear problems. To increase the time-step width, diffusive
15
fluxes in circumferential direction were treated through sub-steps. For further details on
the discretisation in FLOWSI, the reader is referred to [38, 40].
4.2 Grid and Boundary Conditions
4.2.1 Group LU (PUFFIN )
The computational domain of group LU has a cross-section of 300 × 300 mm2 and a
length of 250mm. It is discretised by a Cartesian grid of 100 cells in each dimension,
resulting in a total of 1 million cells. The non-equidistant grid is refined to better
resolve the fuel jet, the primary annulus and the bluff-body wall. The mean axial inflow
velocity of the jet is specified using the power law profile provided by Masri et al. [58]
(<U>= C0Uj(1 − r/(1.01 · rj))1/7, C0 = 1.218, rj = 1.8mm), with the bulk velocity
Uj , the distance from the centreline r, and the radius of the central nozzle rj . The
coefficient C0 is set to obtain the correct mass flow rate at the inlet. In the annulus, the
mean axial and swirl velocity are specified by the same power law. Velocity fluctuations
are generated from a Gaussian distribution such that the turbulent kinetic energy on the
inflow plane is identical to the experimental values. The instantaneous inflow velocity
is then computed by superimposing the fluctuations on the mean velocity. At solid
walls, a no-slip condition is applied. At the outflow, a convective boundary condition
(∂uj/∂t + Ub∂uj/∂n = 0) is used for the velocity components uj with the bulk axial
velocity Ub across the boundary, which allows for convection of structures out of the
domain with minimal distortion [62]. On the inflow plane, the mixture fraction is set to
unity in the jet and to zero everywhere else. On the outflow plane, the mixture fraction
is treated with a zero gradient condition.
16
4.2.2 Group IC (FLOWSI )
Group IC uses a cylindrical computational domain with a length of 250mm and a di-
ameter of 440mm. In a preceding study, the length of the domain was doubled and its
radius increased. This did not result in any major changes of the flow behaviour, which
suggested that the domain was sufficiently large. A grid resolution of 500 cells in axial,
94 cells in radial and 64 cells in circumferential direction results in more than 3 million
cells.
At the inflow boundary, transient Dirichlet velocity conditions are set, while zero velocity
gradient Neumann conditions are applied on the outflow plane. A simplified momentum
equation at the lateral boundary allows for entrainment of ambient air. For the mixture
fraction, a Dirichlet condition is applied to the inflow plane (1 in the fuel jet, 0 elsewhere)
and Neumann conditions are set at all other boundaries. Inflow and outflow pressure
result from Neumann conditions, whereas ambient pressure is set at the lateral boundary.
Since a computational domain beginning at the exit plane of the burner may yield strong,
unphysical vortex shedding at the edge of the bluff-body [40], group IC uses immersed
boundary conditions with a computational domain shifted upstream of the burner face.
Unfortunately, no inflow data is available at this position so that the following technique
had to be applied to generate transient inflow conditions: Mean velocity profiles from
experiments and DNS of fully-developed turbulent pipe flow [87] are superimposed with
artificially created turbulent fluctuations. For the central jet, (mean) turbulent pipe flow
profiles are scaled to match the jet bulk velocity <Uj>. In the annulus, the axial and
radial component of the flow field are assumed to be channel-flow-like and the available
pipe flow profiles are taken as an acceptable approximation of such channel flow. Hence,
the pipe flow data is scaled to yield the bulk axial velocity in the annulus <Us>. To
account for the additional swirling velocity component in the annulus, which does not
exist in turbulent channel- or pipe flow, the shape of a mean axial profile is taken as a
good approximation, scaled to match <Ws> and applied to the (mean) circumferential
17
Table 3: Comparison of the DiscretisationGroup LU Group IC
Spatial Discretisation
ρui, p O(2) CDS O(2) CDSf -diffusion O(2) CDS O(2) CDS, sub-steps in
circumferential directionf -convection O(2) SHARP ≈ O(2) TVD (CHARM)
Temporal Discretisation
ρui O(2) hybrid Adams-Bashforth/-Moulton ≈ O(3) expl. low-stor. Runge-Kuttaf O(2) hybrid Crank-Nicolson ≈ O(3) expl. low-stor. Runge-Kutta
velocity component.
The pseudo-turbulent velocity fluctuations are generated by a method developed by
Kempf et al. [41] that works on arbitrary grids and was based on an approach by Klein
et al. [44]. The method diffuses random noise to generate transient velocity fields with
a realistic integral length-scale L(x0, r, φ). For the present study, the length-scale is
determined as L = min(0.4·∆y, Lmax), which means that L is scaled with the distance
∆y to the closest wall, but limited by a maximum integral length scale Lmax of 2 mm
(considering the swirl burner geometry). Three independent fields of fluctuations are then
scaled and combined with a procedure by Lund et al. [54] to satisfy the Reynolds stress
tensor Rij(x0, r, φ). More detailed information on the generation of pseudo-turbulent
initial and boundary conditions is provided in [41].
4.3 Differences between the computational techniques
The key differences between the approaches of group LU and group IC are summarised
in table 3.
A significant difference between the codes lies in the discretisation of mixture fraction
convection; group LU uses Leonard’s SHARP [51], whereas group IC applies a TVD
scheme (CHARM) [92]. For time integration FLOWSI (IC) uses an explicit Runge-
Kutta method while PUFFIN (LU) relies on a second order hybrid scheme, in which the
advection terms of the momentum equations are treated explicitly (Adams-Bashforth)
18
Table 4: Comparison of Dimensions & ResolutionGroup LU Group IC
Coordinate System Cartesian Cylindrical
Direction Dim. [mm] Res. [-] Dim. [mm] Res. [-]
X / X 250 100 250 500Y / Φ 300 100 - 64Z / D 300 100 440 95
1,000,000 3,040,000
and diffusion terms are treated implicitly (Adams-Moulton). The advection terms in the
mixture fraction transport equation are non-linear, and PUFFIN uses iterations with
the Crank-Nicolson scheme to retain second-order accuracy.
Group LU uses a Cartesian grid but IC relies on a cylindrical mesh, which means that
LU’s method should achieve a better grid resolution far away from the axis, whereas IC
has finer cells in the central jet. The number of cells varies by a factor of three (106
cells by LU and 3 · 106 cells by IC), however, group IC’s domain extends upstream of the
burner exit plane.
The inflow velocity conditions of group LU were determined with superimposed Gaus-
sian noise. Group IC’s approach is more complex, using mean velocity profiles from
experiments and DNS of pipe flows together with artificially created turbulence [41].
An interesting difference lies in the treatment of the lateral boundaries, where group IC
allows for entrainment while group LU applies a free slip condition.
Both groups use a steady flamelet model and LU applied GRI 2.11 for a single flamelet
of relatively high strain (a = 500 s−1), whereas IC uses a more recent mechanism by
Sick, Hildenbrand and Lindstedt [78] with multiple flamelets. Furthermore, the groups
use different models for the SGS variance of the mixture fraction.
19
Table 5: Comparison of Boundary ConditionsGroup LU Group IC
inflow plane burner exit plane upstream of burner exit plane(immersed boundaries)
inflow generation power law + random fluct.: exp./DNS + turb. generation:stress tensor: trace specified stress tensor: fully specifiedlength scale: ∆ length scale: realistic
inflow b.c. (ρui) trans. Dirichlet (Gaussian) trans. Dirichlet (Kempf et al. [41])inflow b.c. (f) f = 1 in fuel stream, f = 1 in fuel stream,
f = 0 elsewhere f = 0 elsewhere
outflow b.c. (ρui) convective b.c. zero gradient Neumann,clipping of u < 0
outflow b.c. (f) zero gradient Neumann zero gradient Neumann
lateral b.c. (ρui) no slip allows entrainmentlateral b.c. (f) Dirichlet (f = 0) Dirichlet (f = 0)
solid wall b.c.(ρui) no-slip b.c. no-slip b.c. (immersed)
5 Results and Discussion
5.1 N29S054
This section discusses the isothermal case N29S054 with a central jet velocity of 66m/s
and a geometric swirl number of Sg = 0.54. Figures 3–8 present comparisons of exper-
imental LDV data and the simulations of both groups. The computations of group LU
(Cartesian grid, 1 million cells) required about 2 weeks on a single-processor Pentium
4 workstation, while the simulations of group IC (cylindrical grid, approx. 3 million
cells) were run over a period of approximately 3 months on one AMD Opteron core.
The simulation data presented here was averaged over a physical time interval of 30ms
after the initial transients (≈ 30ms) including approximately 1000 statistical samples.
Simulations over a total physical time of up to 150ms were carried out by both groups
on coarser grids, but the results were independent of the increased sampling time.
Figure 3 shows the comparison of radial profiles (normalised by the bluff-body radius
Rb) of the mean axial velocity at different axial positions (normalised by the bluff-body
diameter D) from LES and LDV. The agreement between LES and experiments is good
at all axial locations, particularly with the finer grid used by group IC. Group LU predicts
20
slightly broader profiles close to the burner exit plane along with earlier jet break-up,
indicated by the drop in the mean axial velocity. The axial velocity fluctuations are
compared in fig. 4, showing a good agreement with noticeable deviations only close to
the centreline.
Figure 5 shows the mean radial velocity data. Apart from x/D = 0.4 and x/D = 2.0 the
computed and measured profiles agree well, considering obvious difficulties to accurately
predict this quantity of much lower magnitude than the two other velocity components.
Furthermore, the LES data at x/D = 2.0 for r → 0 seem to be more reasonable than
the LDV results, since the mean radial velocity of an axisymmetric set-up is expected
to reduce to zero at the axis of symmetry. The profiles of the radial velocity fluctua-
tion (fig. 6) show a good accordance between experiment and simulation, with a better
prediction of the outer shear layers on the finer grid of group IC. At the same time, the
singularity of the central axis in the cylindrical coordinate system in group IC’s data
is apparent at r = 0 where the coarser Cartesian grid prediction of group LU is more
accurate.
In fig. 7 the radial profiles of the mean circumferential velocity are plotted. While the
Cartesian grid already yields a good agreement, the predictions on the finer cylindrical
grid are excellent. At x/D = 0.2, both LES predict the expected zero mean circumferen-
tial velocity on the axis, while the non-zero LDV value is likely a result of experimental
uncertainties. Figure 8 compares the circumferential velocity fluctuations. Both LES
profiles agree reasonably well with the LDV data, but the better prediction of the outer
shear layers on the fine grid points to the requirement of a high resolution, particularly
with respect to the mixing processes occurring in non-premixed combustion.
Further analysis of the main flow features of case N29S054, as documented by Al-Abdeli
& Masri [2] yields:
The upstream recirculation zone (RZ) in the calculation of group LU stagnates at about
x = 20 mm, whereas group IC predicts a stagnation point at 25 mm, which corresponds to
21
the location that was observed in the experiment. In the LES, the upstream zone can be
subdivided radially into an inner (3 mm < r < 7 mm) and an outer (12 mm < r < 22 mm)
RZ, which can also be observed in the vector plots from LDV [2]. The LES capture VB
and downstream recirculation, with a downstream RZ between 50 mm < x < 110 mm
and a maximum width of 16 mm, which corresponds to the experimentally found values.
Despite this exact match of position and size of the RZ, the peak value of the negative
axial velocity is lower (-3m/s) and slightly shifted upstream (x ≈ 80 mm, compared to
x ≈ 85 mm from LDV). The fine grid LES (IC) predicts the “collar-like” fluid structure
with a peak circumferential velocity of Wmax = 26m/s at r = 16 mm and x = 42 mm.
This result is in excellent agreement with the LDV data, as well as the resulting maxi-
mum rotation rates 245s−1 (LU) and 259s−1 (IC) (LDV 265s−1). Additionally, the LES
predicts jet precession, which can be seen in animated visualisations of e.g. the instan-
taneous mixture fraction [82]. Further comparisons by group IC of the Reynolds shear
stresses (not shown) and an estimation of the resolved contribution to the turbulent ki-
netic energy (fig. 31, [17, 40]) give further evidence of the good agreement between LES
and experimental data.
Overall, a good quantitative agreement between experiments and LES has been found
for the isothermal case N29S054. In spite of their lower resolution, the results of group
LU show a good agreement, while some difficulties to accurately capture the shear layers
above the annulus are apparent. The higher resolution of group IC yields a small ad-
vantage for their simulations, that show better prediction of the shear layers, while some
discrepancies due to the cylindrical grid are noticeable in the fluctuation profiles on the
centreline. The results of this isothermal study confirm the ability of LES to predict
VB, downstream recirculation and precessing behaviour and are taken as a sound base
for the LES of the flame series.
22
5.2 SM1
The methane flame SM1 has a jet velocity of 32.7m/s and a swirl number of 0.5.
The measurements found the upstream RZ stagnating at about 43 mm downstream
of the bluff-body face and the second downstream RZ extending from x = 65 mm to
110 mm [37]. The second RZ is centred around x = 85 mm and forms a VB bubble on
the geometric centreline. A collar-like flow feature is observed at about 60 mm down-
stream of the burner face. Furthermore, the measurements revealed an irregular motion
of the central jet over a broad range of frequencies [1]. The LES results shown here are
taken from statistics well away from the initial transients and comprise a similar number
of samples as for case N29S054.
Figure 9 shows the comparison of the mean axial velocity. Both groups have captured
the upstream bluff-body stabilised RZ, as well as the downstream swirl-induced RZ due
to VB. The agreement between measurements and predictions is quite good at all axial
locations. The axial velocity fluctuations are shown in fig. 10, and there are some notable
discrepancies apparent. Group LU’s prediction is reasonable but misses out on the radial
inward movement of the two shear layer peaks at x/D = 0.8. Group IC’s prediction from
the finer grid shows less discrepancies, apart from x/D = 1.4 and 0.4 < r/Rb < 0.9,
where the axial fluctuation from LES shows a local maximum. The analysis of animated
visualisations from the LES of group IC indicates that this predicted peak is a result of
the interaction of the unsteady central jet with the swirling annulus stream. Figure 31
reveals that this location also corresponds to the only part of the flame region, where
less than 86% of the turbulent kinetic energy are resolved.
The comparison of the mean circumferential velocity is shown in fig. 11. Group LU’s
results are generally slightly over-predicted, whereas group IC’s results compare well,
apart from the nozzle region where the level of swirl is over-predicted. Figure 12 shows
the comparison of the circumferential velocity fluctuations. The agreement between mea-
surements and predictions is reasonable, but group LU under-predicts the fluctuations
23
at x/D=0.8 and 1.4 while group IC’s calculation overestimates the turbulence level at
the same axial locations. The peak in group IC’s data at x/D=1.4 is consistent with the
results for the axial velocity fluctuations and has already been discussed in the context
of fig. 10.
The comparison of the mean mixture fraction is shown in fig. 13. The centreline pre-
diction of group LU overestimates the mixture fraction at x/D = 0.4 and x/D = 1.1,
indicating a late jet break-up, while the prediction of group IC matches the experimen-
tal profiles reasonably well at most axial locations. Earlier coarse grid studies of group
IC (not shown) revealed that a high grid resolution is crucial to accurately capture the
steep axial gradient of the mean mixture fraction of flame SM1. Figure 14 shows the
comparison of the mixture fraction variance and group LU’s predictions are underesti-
mated at the first four axial locations. Again, group IC’s predictions compare well to
the experimental data, but the overestimated velocity fluctuations (x/D = 1.4) do not
show in the mixture fraction fluctuations at x/D = 1.5.
The mean temperature is shown in fig. 15. At x/D = 0.2 temperature is clearly over-
predicted, which is a direct result of the slight under-prediction of the mean mixture
fraction (fig. 13) and the strong non-linear coupling of T and f on the lean side of
stoichiometry. Further downstream, the agreement of LES and experiment is better,
allowing for a better temperature prediction.
Further comparisons of LES and the data by Kalt et al. [37] show that the simulations
have captured both the toroidal shaped upstream and downstream RZs. The predictions
of the extension and locations of the RZs show a reasonable agreement with experimental
data (not shown).
Overall, the LES of SM1 yield a good qualitative agreement with experimental observa-
tions, while some quantitative discrepancies are apparent. Due to the high sensitivity
of the chemical state to an accurate prediction of the mixing, precise predictions of the
chemical species could not be achieved.
24
5.3 SMH1
Flame SMH1 has a CH4/H2-fuel jet with a velocity of 141m/s and a swirl number
of 0.32. The experimental measurements by Al-Abdeli & Masri [3] reveal that flame
SMH1 – despite its relatively low swirl number – features two RZs. The upstream RZ
has a peak negative mean axial velocity of -10m/s for 20mm < x < 40mm and extends
approximately to 45 mm downstream of the burner exit plane. The downstream RZ (VB
bubble) is formed on the centreline in the region 125mm < x < 150mm and extends
radially to about r=5–7mm. In between the two RZs SMH1 shows strong necking and
a collar-like flow feature of high rotation at around 60mm < x < 80mm.
Figure 16 shows a volume-rendered visualisation of OH-chemiluminescence from the
LES of group IC. A visual comparison of the flame luminescence from LES and ex-
periments [57] shows a good qualitative agreement for the upstream flame region, where
flame necking is captured by the LES. Further downstream, the predicted LES flame is
thin and long, whereas the experimental photograph (not shown) shows a stronger radial
spread, possibly resulting from VB.
Figures 17–22 show the comparisons of experimental measurements and LES predictions
that were obtained on the same grids that were used for the isothermal case. Group LU
used 1 million cells and required approximately 3 weeks on a Pentium 4 single worksta-
tion. Group IC investigated the transient development of flame SMH1 for different grid
resolutions for up to 6 months of CPU time and concluded that fine grid data taken from
a physical time interval of 40ms < t < 60ms, including approximately 1000 samples were
required for accurate statistics.
The comparison of the mean axial velocity at different axial locations is shown in fig. 17.
The agreement between predictions and measurements is acceptable at the first four
axial locations and both groups captured the upstream RZ. However, the predictions
show several discrepancies on the centreline, especially, at x/D = 2.5 and 3.5. Both
simulations failed to capture the downstream VB bubble observed in the experiment. It
25
is noted that the velocity field in the upstream jet region is unknown due to a limitation
of the LDV set-up [3], which additionally complicates the LES predictions. Figure 18
shows the axial velocity fluctuations and the agreement is reasonable.
The radial profiles of the mean circumferential velocity (fig. 19) show a good agreement
with experimental measurements for the fine grid, only the over-predicted velocity at
x/D = 2.5 points to the missing recirculation bubble as the strongly swirled flow is
deflected in radial direction. Figure 20 compares the circumferential velocity fluctuations,
and both group achieved acceptable agreement.
The mean mixture fraction predictions are compared in fig. 21. The agreement looks good
for most axial locations, with a clearly better prediction of the central fuel jet at x/D = 0.2
from group IC, while further downstream some predictions of group LU are closer to the
experimental data. The comparison of the mixture fraction variance is shown in fig. 22.
The mixture fraction variance shows steep gradients near the central jet at x/D = 0.2,
which may result from the interaction of the jet with the upstream RZ and which is well
captured by group IC. Overall, the mixture fraction variance is in reasonable agreement
with experimental evidence. However, when comparing mixture fraction plots, one must
bear in mind that the temperature, density and hence momentum are sensitive non-linear
functions of the mixture fraction. For example, a mixture fraction error of 5% on the
lean side of the mixture fraction density relationship can cause a density error in excess
of 500%. This sensitivity is a significant conceptual problem of the mixture fraction
approach that becomes very obvious in fig. 23, which shows the mean temperature. The
upstream temperature predictions show some large discrepancies from the experimental
data, and especially at x/D = 0.8, both groups failed to capture the peak temperature.
The downstream predictions compare well with experimental data.
The overall agreement between the LES predictions and experimental measurements for
flame SMH1 is found to be reasonable, considering the complex interaction of a bluff-
body, a high-momentum axial jet and a low-swirl annular flow. It is noted that the low
26
swirl number (0.32) and the high axial velocity of the fuel jet (141m/s) result in a very
sensitive VB behaviour and render flame SMH1 a difficult test case for LES validation.
Figure 31 shows that the overall amount of resolved turbulent kinetic energy of flame
SMH1 is high, but it is possible that the regions close to the jet, where less than 84% of
the kinetic energy is resolved negatively affect the predictions. An even higher resolution,
inclusion of compressibility effects, as well as a less sensitive chemistry model may help
to improve future predictions of flame SMH1.
5.4 SMH2
Flame SMH2 has the same fuel mixture and the same jet velocity as SMH1 (CH4/H2,
141 m/s), but a higher swirl number of 0.54. The flow field of this flame was experimen-
tally studied by Al-Abdeli & Masri [3] and it was found to exhibit only one (upstream)
RZ, despite its higher swirl number compared to SMH1. This was explained by the
relatively low mass flow from the annulus, as the axial velocity Us of the swirling air
was only 29.7m/s, compared to 42.8m/s for case SMH1 [3], so that flame SMH2 may be
more strongly dominated by the central jet.
The upstream RZ in SMH2 extends to approximately 50 mm from the burner exit
plane. Weak necking was observed in the same region and no collar-like flow feature
was found. Further experimental investigations have shown the central jet of SMH2 to
precess strongly [1].
Visual inspection and comparison of the 3D-rendering of OH-chemiluminescence in SMH2
(fig. 16, right panel) to the photographs in [3] shows a good qualitative agreement, with
a weakly necking flame. However, animated visualisations from group IC reveal that
the LES does not capture precession of the central jet and shows a dominating, straight
central jet instead. This may make group IC’s predictions similar to the experimental
findings for flame SMH3, which has higher jet-velocity and for which Abdeli et al. [5]
have not described any jet precession. Interestingly, group IC predicts a puffing motion of
27
flame SMH2, which is very similar to the experimental findings for the very flame SMH3
[5]. Group LU also did not predict any jet precession, but their predictions appear more
realistic for this flame.
Figures 24–30 show the comparison of mean and fluctuating quantities from LES and
experiments. For the LES of SMH2 the same grids and computational domains as for
flame SMH1 (section 5.3) were used, and sampling was also comparable to sampling for
SMH1.
Figure 24 shows the experimental data and predictions for the mean axial velocity. Here,
as well as for other quantities, the results of both groups show different trends. The
predictions of group LU agree well with the LDV measurements at all axial locations,
with slight over-predictions at x/D = 2.5 and 3.5. The fine grid results of group IC
clearly over-predict the velocity of the fuel jet at x/D = 0.8, 1.2 and 1.7, indicating that
jet precession is not captured. Unfortunately, limitations of the LDV set-up resulting in
missing experimental data in the upstream nozzle region do not allow for an assessment
of the upstream jet behaviour. However, predictions of the annular flow (x/D = 0.2),
as well as the downstream radial profiles of group IC are very good. The fluctuations of
the axial velocity are shown in fig. 25. At x/D = 0.2, a trend consistent with the mean
axial velocities is apparent. While group LU captures the fluctuation profile for r → 0,
group IC predicts very high fluctuations near the fuel jet and a sharp gradient to very
low turbulence levels in the bluff-body region, again representing a dominating central
jet. This is in line with the simulation of the non-reactive case N29S054 and for flames
SM1 and SMH1, where group IC predicted a later break up of the jet, which is more
realistic for those cases. Further downstream the agreement between LDV and both LES
is good.
Figure 26 shows the comparison of mean circumferential velocities. At x/D = 0.2 group
IC predicts higher values near the centreline. Analysis of animated visualisations shows
that circumferential velocity (momentum) accumulates in the vicinity of the jet, but
28
does not trigger jet precession. Group LU does not over-predict the peak velocity here,
but shows some deviations in the annulus region. Further downstream, both groups
show different trends with LU’s predictions being better at x/D = 0.8 and IC’s at the
last four downstream locations. The circumferential velocity fluctuations are shown in
fig. 27. Again, IC does not show the correct trend close to the central jet, but obtains
good predictions of the annular flow, while LU shows good overall agreement except at
x/D = 1.7, where the circumferential velocity is overpredicted near the centreline.
The comparison of the mean mixture fraction is shown in fig. 28. Group LU predicts
jet break-up too early but finds a good downstream agreement with the experimental
mixture fraction values. The mixture fraction results of group IC are consistent with
the velocity data and show a dominance of the central jet resulting in an over-prediction
of f for r = 0 at all downstream locations. The low mixture fraction results of group
IC at x/D = 0.2 for 0.2 < r/Rb < 1.0 are probably a direct result of the lack of jet
precession, which would have led to a redistribution of fuel from the jet to the upstream
RZ. Figure 29 shows the mixture fraction variance. Both groups demonstrate similar
deviations, with reasonable agreement in the downstream region of the flame.
The mean temperature is shown in fig. 30. Deviations of the temperature field are a
direct result of imprecise mixture fraction predictions and hence the agreement is only
good where the mixing field was well predicted (e.g. x/D = 1.6, group LU).
The overall comparison between LES and experiment for flame SMH2 is not satisfactory.
Both groups capture the upstream RZ, the length of which is consistent with experi-
mental measurements. Concurrently, jet precession which seems to dominate the flame
structure is not captured, resulting in some strong deviations. Figure 31 shows that
there are noticeable flow regions in the LES of group IC, where less than 80% of the
turbulent kinetic energy are resolved, demonstrating the relatively challenging character
of the SMH2 flame.
29
6 Conclusions
The present work examined the LES of the flow and structure of non-premixed turbulent
flames stabilised on the Sydney swirl burner. This burner has been target of the TNF
workshop series [86], where the challenging character of the flow has already been estab-
lished. In the present work, two LES programs (FLOWSI and PUFFIN ) with different
SGS models and numerical techniques were applied by groups from Imperial College
(IC) and Loughborough University (LU) to obtain code-independent insights into these
flames.
The approaches were tested by simulating a non-reacting test case with moderate swirl,
and both approaches successfully predicted the RZs, the VB bubble and the jet pre-
cession observed in the experiments. Furthermore the first and second moments of the
calculated velocities agreed well with the experimental values. To support the validity of
the results, the group from Imperial College has also performed preceding studies [83, 84]
to investigate the effect of grid-resolution, domain-size, inflow-boundary conditions and
sampling time. Group IC also found that in the non-reactive case, less than 10% of the
total turbulent kinetic energy was contributed by their SGS model.
In the main part of this work, three different flames from the Sydney flame series were
simulated by both groups. The methane flame SM1 and the high-speed hydrogen-
methane flames SMH1 & SMH2 feature a challenging combination of RZs from the
bluff-body and from VB, and even jet precession and precessing vortex cores are encoun-
tered. All three flames have very different properties, and the SMH flames were found
much harder to predict than SM1. For flame SM1, both groups captured the upstream
RZ and the downstream VB, and good predictions were achieved for the mean velocities,
their fluctuations and the mixture fraction statistics. However, the temperatures ob-
tained from LES suffer from error propagation due to the (relatively small) deviations in
mixture fraction, as temperature depends on mixture fraction in a highly non-linear way
(For the SMH flames, the temperature can drop from the adiabatic flame temperature
30
to ambient if the mixture fraction is underpredicted by 5% only (fstoic = 0.05)).
In addition to flame SM1, the high-speed methane-hydrogen flames SMH1 and SMH2
were also simulated, but the results were less good, although extensive and time-consuming
parameter studies have been performed by both groups to understand the relatively poor
predictions. Parts of the difficulties with the SMH flames resulted from the lack of exper-
imental velocity data close to the nozzle, so that the validity of the inflow-data could not
be checked. This problem is immediately obvious in the different axial velocity profiles
obtained by groups IC and LU close to the inflow plane (figs. 17 & 24, x/D = 0.2).
Furthermore, the complex interaction of various RZs with the high momentum fuel jet
turns these flames into a very challenging and sensitive test case. For the SMH flames,
further work is needed to improve the predictions, and additional and more detailed
experiments would help to obtain much deeper insights.
Many of the findings in this paper were supported by the two independent simulations,
and some of the information could not be obtained from a single simulation only: Without
a second simulation, no model-independent validation of numerics and no insight into
sensitive regions of the flow would have been possible. The analysis of experimental
errors and the non-linear dependency of mixture fraction, temperature, density and
hence momentum would have been more difficult.
Acknowledgements
The authors gratefully acknowledge the support by the EPSRC (EP/D03258X/1). We
would further like to thank Salah Ibrahim, Peter Lindstedt, Assaad Masri, and Magnus
Persson for many helpful discussions.
31
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Figure 1: Schematic of the Sydney swirl burner.
41
Figure 2: Arrangement of computational cells that contribute to the interpolation of thevalue φf on the face of cell C.
42
-10
0
10
20
30
40
50x/D = 0.2
Exp.LES-LULES-IC
x/D = 0.4
010203040 x/D = 0.6 x/D = 0.8
010203040
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 1.4
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.0
Figure 3: N29S054: Mean Axial Velocity U [m/s]
0 5
10 15 20 25 30 35
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.4
0
5
10
15 x/D = 0.6 x/D = 0.8
0
5
10
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 1.4
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.0
Figure 4: N29S054: Axial Velocity RMS Urms [m/s]
43
-10
-5
0
5
10 x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.4
-10
-5
0
5 x/D = 0.6 x/D = 0.8
-10
-5
0
5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 1.4
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.0
Figure 5: N29S054: Mean Radial Velocity V [m/s]
0 2.5
5 7.5 10
12.5 15
17.5 20
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.4
0
2
5
8 x/D = 0.6 x/D = 0.8
0
2
5
8
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 1.4
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.0
Figure 6: N29S054: Radial Velocity RMS Vrms [m/s]
44
0 5
10 15 20 25 30
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.4
0 510152025 x/D = 0.6 x/D = 0.8
-5 0 510152025
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 1.4
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.0
Figure 7: N29S054: Mean Circumferential Velocity W [m/s]
0
2.5
5
7.5
10
12.5
15
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.4
0 2 5 810 x/D = 0.6 x/D = 0.8
0 2 5 810
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 1.4
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.0
Figure 8: N29S054: Circumferential Velocity RMS Wrms [m/s]
45
-20
0
20
40
60
80
x/D = 0.136Exp.
LES-LULES-IC
x/D = 0.4
-20 0204060 x/D = 0.8 x/D = 1.4
-20 0204060
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
Figure 9: Flame SM1: Mean Axial Velocity U [m/s]
0
5
10
15
20
x/D = 0.136Exp.LES-LULES-IC
x/D = 0.4
0
5
10
15 x/D = 0.8 x/D = 1.4
0
5
10
15
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
Figure 10: Flame SM1: Axial Velocity RMS Urms [m/s]
46
-10
0
10
20
30
40
x/D = 0.136Exp.
LES-LULES-IC
x/D = 0.4
-10 0102030 x/D = 0.8 x/D = 1.4
-10 0102030
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
Figure 11: Flame SM1: Mean Circumferential Velocity W [m/s]
0
4
8
12
16
x/D = 0.136Exp.
LES-LULES-IC
x/D = 0.4
0
4
8
12 x/D = 0.8 x/D = 1.4
0
4
8
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
Figure 12: Flame SM1: Circumferential Velocity RMS Wrms [m/s]
47
0.0
0.2
0.4
0.6
0.8
1.0
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.4
0.00.10.20.30.4 x/D = 0.8 x/D = 1.1
0.0
0.1
0.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 1.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.0
Figure 13: Flame SM1: Mean Mixture fraction F
0.000.040.080.120.160.200.240.28
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.4
0.000.040.080.120.16 x/D = 0.8 x/D = 1.1
0.000.020.040.060.08
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 1.5
0.00 0.20 0.40 0.60 0.80 1.00 1.20r/Rb
x/D = 3.0
Figure 14: Flame SM1: Mixture Fraction Variance Frms
48
0
500
1000
1500
2000
2500 x/D = 0.2Exp.LES-LULES-IC
x/D = 0.4
0
500
1000
1500x/D = 0.8 x/D = 1.1
0500
100015002000
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 1.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.0
Figure 15: Flame SM1: Mean Temperature T
49
Figure 16: Flames SMH1 (left) and SMH2 (right): 3D rendering visualisation ofOH-chemiluminescence, group IC. Corresponding snapshots from the experiments [57]can be found at http://www.aeromech.usyd.edu.au/thermofluids/main frame.htm in theswirling flames database.
50
-20 0
20 40 60 80
100 120 140 160 180
x/D = 0.2Exp.LES-LULES-IC
x/D = 0.8
-20 020406080 x/D = 1.2 x/D = 1.6
-20 020406080
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 17: Flame SMH1: Mean Axial Velocity U [m/s]
0 5
10 15 20 25 30 35 40 45
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.8
0 51015202530 x/D = 1.2 x/D = 1.6
0 5101520
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 18: Flame SMH1: Axial Velocity RMS Urms [m/s]
51
0 5
10 15 20 25 30 35 40 45
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.8
0 51015202530 x/D = 1.2 x/D = 1.6
0 5101520
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 19: Flame SMH1: Mean Circumferential Velocity W [m/s]
0 5
10 15 20 25 30 35
x/D = 0.2Exp.LES-LULES-IC
x/D = 0.8
0
5
10
15 x/D = 1.2 x/D = 1.6
0
5
10
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 20: Flame SMH1: Circumferential Velocity RMS Wrms [m/s]
52
0.0
0.2
0.4
0.6
0.8
1.0
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.8
0.00.10.20.30.4 x/D = 1.1 x/D = 1.6
0.0
0.1
0.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 21: Flame SMH1: Mean Mixture fraction F
0.00
0.04
0.08
0.12
0.16
0.20
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.8
0.000.040.080.120.16 x/D = 1.1 x/D = 1.6
0.000.020.040.060.08
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.00 0.20 0.40 0.60 0.80 1.00 1.20r/Rb
x/D = 3.5
Figure 22: Flame SMH1: Mixture Fraction Variance Frms
53
0
500
1000
1500
2000
2500 x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.8
0
500
1000
1500x/D = 1.1 x/D = 1.6
0500
100015002000
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 23: Flame SMH1: Mean Temperature T
54
-20 0
20 40 60 80
100 120 140 160 180
x/D = 0.2Exp.LES-LULES-IC
x/D = 0.8
-20 020406080 x/D = 1.2 x/D = 1.7
-20 020406080
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 24: Flame SMH2: Mean Axial Velocity U [m/s]
0 5
10 15 20 25 30 35 40 45
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.8
0 51015202530 x/D = 1.2 x/D = 1.7
0
5
10
15
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 25: Flame SMH2: Axial Velocity RMS Urms [m/s]
55
0 5
10 15 20 25 30 35 40 45
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.8
0 51015202530 x/D = 1.2 x/D = 1.7
0 5101520
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 26: Flame SMH2: Mean Circumferential Velocity W [m/s]
0 5
10 15 20 25 30 35
x/D = 0.2Exp.LES-LULES-IC
x/D = 0.8
0
5
10
15 x/D = 1.2 x/D = 1.7
0
5
10
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 27: Flame SMH2: Circumferential Velocity RMS Wrms [m/s]
56
0.0
0.2
0.4
0.6
0.8
1.0
x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.8
0.00.10.20.30.4 x/D = 1.1 x/D = 1.6
0.0
0.1
0.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 28: Flame SMH2: Mean Mixture fraction F
0.00
0.04
0.08
0.12
0.16
0.20x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.8
0.000.040.080.120.16 x/D = 1.1 x/D = 1.6
0.000.020.040.060.08
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.00 0.20 0.40 0.60 0.80 1.00 1.20r/Rb
x/D = 3.5
Figure 29: Flame SMH2: Mixture Fraction Variance Frms
57
0
500
1000
1500
2000
2500 x/D = 0.2Exp.
LES-LULES-IC
x/D = 0.8
0
500
1000
1500x/D = 1.1 x/D = 1.6
0500
100015002000
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 2.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2r/Rb
x/D = 3.5
Figure 30: Flame SMH2: Mean Temperature T
58
Figure 31: Resolved contribution to the turbulent kinetic energy as estimated [40] fromthe model by Deardorff [17] on the fine grid of group IC. The left half of each panelshows the original grid resolution, while the right half was smoothed by a Gaussian filterfunction. The black lines delimit regions where less than the noted amount of kineticenergy is resolved.
59