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

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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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40

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