NUMERICAL STUDY OF SPRAY/PRECESSING VORTEX COREINTERACTION IN REALISTIC SWIRLING FLOWS

L. Guedot1, G. Lartigue1 and V. Moureau1

1 CORIA, CNRS UMR6614, INSA and University of Rouen,Saint-Etienne du Rouvray, France

lola.guedot@coria.fr

1 Background and motivationSwirling jet flows are widely used in combustion

devices for the stabilization of premixed or partiallypremixed flames. This stabilization is made possibleby the vortex breakdown that occurs when the geomet-ric swirl number, which measures the ratio of tangen-tial over axial momentum flux, is sufficient. In theseconditions, the vortex breakdown may lead to the for-mation of coherent structures such as the precessingvortex core (PVC) (Syred (2006)), single or multiplehelicoidal vortices. The PVC plays an important rolein the dynamics of the flame as it may wrinkle thepremixed flame front creating isolated flame pockets(Moureau et al. (2011a)). This leads to periodic fluctu-ations of the heat release rate, which is directly relatedto the total flame surface. In the case of spray flames,the PVC also influences the distribution of fuel massfraction as it leads to preferential segregation of fueldroplets (Sanjose et al. (2011)). The analysis of thislarge-scale feature is mandatory to improve the under-standing of the dynamics of swirling flows.

Large-Eddy Simulation is a powerful tool for theanalysis of coherent structures in turbulent flows. Thesteady increase in computational power leads to finerand finer mesh resolutions, which enables an accurateprediction of these important features. The extrac-tion of large-scale features in these well refined sim-ulations is particularly difficult because it requires toprocess either wide regions of the computational do-main or to perform some averaging of the flow. A so-lution is to use filters to remove the sub-filter scale mo-tions. To this aim, high-order filters, characterized bytheir good selectivity were implemented in the Large-Eddy Simulation (LES) solver YALES2 (Moureau etal. (2011b)), and applied in an aeronautical swirlburner.

2 Methodology for large-scale structuresidentification

Large scale structures in refined simulationsA convenient tool for the visualization of coherent

vortices is the Q-criterion, which is the second invari-

ant of the deformation tensor (Dubief and Delcayre(2000)). The Q-criterion is related to the Laplacianof the pressure field in incompressible flows. For ho-mogeneous isotropic turbulence, the scaling power ofthe Q-criterion with the wave number k is larger thanunity (Nabil et al. (2000)). As a result, the Q-criterionexhibits larger values for small vortices than for bigvortices. This issue is particularly annoying in wellrefined simulations that feature a large range of tur-bulent scales. In these simulations, the small vorticescompletely mask the large vortices when looking atQ-criterion iso-values (as shown with the iso-surfacesof unfiltered Q-criterion in Fig. 2). To circumvent theQ-criterion scaling issue, it is mandatory to developnumerical techniques able to separate the different co-herent structures such as spatial low-pass filters. Per-forming this scale separation is quite challenging asit requires to extract features from a large amount ofdata distributed across a large number of processors.This operation necessitates a good selectivity in orderto leave the large scale unaffected while damping allthe smallest scales.

High-order filtering

0

0.2

0.4

0.6

0.8

1

50 100 150 200 250 300

k

Cardinal Sine Filter

4th order filter

8th order filter

12th order filter

16th order filter

Figure 1: Damping functions of High order filters, fororder 4, 8 and 16, Gaussian filter, and low-pass filter.

The filtering of a scalar φ with high-order implicitfilters (HOF) (Raymond and Garder (1991)) can bewritten in a one-dimensional domain as

φ+ βpDpφ = φ with

βp =∆x2p

(−4)p sin2p(kc∆x/2)(1)

φ is the filtered value, D the second derivative opera-

Figure 2: Extraction of the PVC with high-order filters of the 12th order in the LES of the PRECCINSTA burner atvarious mesh resolutions from 3 million to 110 million tetrahedral elements. The vortices are colored by the axisdistance.

tor, 2p the order of the filter, kc the cut-off wave num-ber, and ∆x the homogeneous grid spacing.

This filter may be analyzed in the complex Fourierspace assuming a monochromatic signal and formingthe ratio of the filtered and unfiltered amplitudes A/A.This damping function is plotted in Fig.1 for variousorders. The higher is the order, the sharper is the fil-ter response. These efficient high-order implicit fil-ters, characterized by their good selectivity have beenadapted to three dimensional unstructured grids andoptimized (Guedot et al., 2013).

Extraction of the PVC in a swirling flowHigh-order filters are able to extract the PVC from

complex swirl burners as illustrated in Fig. 2 wherethe Q-criterion in isothermal LES of the PRECCIN-STA burner (Moureau et al. (2011)) has been filteredfor different mesh resolutions. Since they are highlyselective, they perform better than Gaussian filters forthe large scale feature extraction on fine grids as shownin Fig. 3. In this figure, the mesh features 878 milliontetrahedra and the Gaussian filter is not able to dampall the smallest scales as the high-order filters. To theauthors knowledge, this is the first time the PVC is vi-sualized on such massive grids.

A level set method was used to identify and iso-late the PVC among all the remaining large scale vor-tices. The segmentation algorithm consists of the fol-lowing steps. First, a level set function is definedbased on a Q-criterion iso-level. Then, all closed vol-umes within the level set function are identified, anda specific color is attached to each closed region. ThePrecessing Vortex Core can be isolated by removingthe level-set function everywhere the color is differentfrom the PVC color, so that only the PVC remains inthe level-set iso-surface.

The level-set function gives access to important

Figure 3: Comparaison of Gaussian filtering (left) and8th order filtering (right) for the extraction of the PVC.

Figure 4: Iso-surfaces of filtered and unfiltered Q-criterion for a mesh of 40 million cells. Only the smallstructures in the vicinity of the PVC are represented.

data such as the normals and the distance to the sur-face. It enables to plot simultaneously the large-scalestructure of interest (the PVC) and the smaller vorticesresolved on the mesh (with an iso-surface of raw Q-criterion) at a close distance of the PVC, in order tostudy the interaction between the large scale structuresand the small scale vortices (Fig. 4).

3 Application to a realistic swirling two-phase flow

Description of the MERCATO burnerThe MERCATO test-rig, dedicated to the study of

two-phase flows and in particular to the ignition ofaeronautic combustion chambers at high altitude, wasinvestigated at the French aerospace lab ONERA atFauga-Mauzac, providing detailed experimental dataon the combustion of either gaseous or liquid fuel.

The geometry of the MERCATO burner features aplenum, a swirler, and a square combustion chamberas illustrated in Fig.5, as well as a cylindrical exhaustwhich is not represented here but is taken into accountin the simulations. This semi-industrial injection sys-tem is very similar to the PRECCINSTA burner exceptthat liquid kerosene is injected at the swirler tip. Ithas been widely studied in the last few years, to studytwo-phase combustion (Franzelli et al. (2013)), igni-tion (Eyssartier et al. (2011), Bruyat et al. (2012)),or the effect of droplets diameter distribution (Han-nebique (2013)), but also to validate numerical modelsfor two-phase flows simulation (Sanjose (2009), Vie etal. (2013)), secondary atomization (Senoner (2010)),and evaporation (Sierra Sanchez (2012)).

Plenum  Inlet  

Swirler  

Chamber  

Figure 5: Description of the MERCATO burner.

The objective of this simulation is to study the roleof the PVC in the fuel droplet distribution and in thepreferential segregation of specific classes of droplets.

Numerical setupThe gaseous phase is solved using the LES solver

YALES2 for low Mach number flows. The resolu-tion of the incompressible Navier-Stokes equations isachieved with a projection method (Chorin (1968)).The momentum is first advanced with a 4th-orderfinite-volume scheme in space and a 4th-order Runge-Kutta like scheme in time. Then, from the predictedvelocity, a Poisson equation is solved to correct themomentum. The linear system for the Poisson equa-tion is solved with a highly efficient Deflated Pre-conditionned Conjugate Gradient (Malandain et al.(2013)). Sub-grid scale turbulence closure is achievedwith a dynamic Smagorinsky model (Germano et al.(1991)) and no-slip wall conditions are imposed on thechamber walls.

The dispersed phase is described with evaporatingLagrangian particles (Sirignano (1989)). The gas andthe particles are fully two-way coupled with mass, mo-mentum and energy exchanges.

Particular attention was paid to the particle injec-

R0  Ra  

θs  

Figure 6: Sketch of the atomization process and inputparameters of the injection model.

0 2e-05 4e-05 6e-05 8e-05 0.0001

Diameter (m)

PDF discrete - 50 classes of droplets diametersRosin-Rammler distribution

Figure 7: Discrete particle size distribution used in thesimulation (boxes) and Rosin-Rammler distributionwith the parameters used by Hannebique for the reac-tive simulation of MERCATO (Hannebique (2013)).

tion. In aeronautical burners, fuel is injected thanksto pressure-swirl atomizers: liquid under pressure isinjected tangentially in the injector, and then expelledin the combustion chamber as a conical liquid sheetwhich disintegrates into small droplets through pri-mary and secondary atomization processes. In thepresent work, the effect of atomization is neglected,and a developed spray is directly injected at the injec-tor exit orifice. Particles are injected in the injectionplane at a random radius betweenR0, the atomizer ori-fice radius, andRa, the radius of the air cone inside theinjector (see Figure 6). The ratio Ra/R0 is related tothe opening angle θs, and can be computed with theempirical correlation of Lefebvre (1988):(

RaR0

)2

=sin2 θs

1 + cos2 θs(2)

The velocity distribution prescribed at injection is setthrough an injection model inspired from the work ofSanjose et al. (2011). The present hollow cone modelsimply differs by the tangential velocity radial distri-bution. The axial velocity of the particles is recon-structed from the liquid mass flow rate, the radial ve-locity is set to zero, and the tangential velocity is spec-ified as a function of the radial position of the injectionpoint r. The opening angle of the spray is driven by the

swirl number (Gupta et al. (1984)), defined as:

S =

∫ R0uθuzr

2dr

R∫ R0u2zrdr

(3)

The tangential velocity must provide the right amountof orthoradial momentum to ensure the specified open-ing spray angle:

uz =m

ρπ(R20 −R2

a)

ur = 0

uθ(r) = r

√uz tan θsRs

(uz tan θsRs

+ 2) (4)

Rs is the mean radius (R0 − Ra)/2. The mass flowrate m, the radius of the atomizer orifice R0 and thespray angle θs are input parameters of the model.

Table 1: Parameters of the injection model.m R0 θs

(g/s) (mm) (◦)

1 0.25 40

The Lagrangian approach enables to handle eas-ily polydispersion of the spray. A discrete probabilitydensity function (PDF) of 50 classes of droplet diame-ters was used to reproduce a Rosin-Rammler distribu-tion. The diameter distribution used in the two-phasesimulation is plotted in Fig. 7.

The evaporation model assumes infinite thermalconductivity of the liquid (temperature is supposeduniform in the droplet), the evaporation rate is drivenby the thermal and species diffusion from the dropletsurface into the gas phase. The surface droplet temper-ature is then equal to the constant droplet temperature.The liquid/gas interface is assumed to be in thermo-dynamic equilibrium, the Clausius-Clapeyron equilib-rium vapor pressure relationship is used to computethe fuel mass fraction at the droplet surface. Ther-modynamic properties in the gas layer surroundingthe droplet are computed at a reference temperature(Tref ) and composition (Yk,ref ), defined as 2/3-1/3weighted interpolation of surface values and far-fieldvalues. The Nusselt (Nu) and Sherwood (Sh) numbersare modified following the Ranz-Marshall correlations(Ranz et al. (1952)) to take into account the fact thatevaporation is enhanced by the relative motion of thecarrier phase.

The kerosene is modeled by a single species com-posed (in volume) of 74% of C10H22, 15% of C9H12

and 11% of C9H18 (Franzelli et al. (2010)). Thermo-dynamics properties, computed as an average of indi-vidual kerosene component properties are summarizedin Table 2.

For this simulation, a mesh of 40 million tetrahedrawas used. Since the lagrangian particles are not ho-mogeneously scattered through-out the Eulerian grid,

Table 2: Thermodynamic properties of the kerosenespecies.

W Tboil Cp ρl Lv(g/mol) (K) (J/K/kg) (kg/m3) (J/kg)

137.195 445.1 2003 781 2.89 × 105

load-balancing was performed to make the domain de-composition sensitive not only to the number of cellsbut also to the number of particles. This enables to re-duce the computational cost of the Lagrangian solver.

Large-Eddy Simulation of the MERCATO burnerFor the operating conditions considered in the

study, cold liquid fuel is injected at the center of theswirler, in pre-heated air to enhance the evaporationprocess. The operating conditions are summarized inTable 3.

Table 3: Operating conditions.Tair Tfuel mair mfuel P(K) (K) (g/s) (g/s) (Pa)

463 300 15 0-2 101 300

First, the purely gaseous flow is simulated, to in-stall the flow topology and the recirculation zones. Forthis case, experimental mean and root mean square(RMS) velocity profiles are available in 5 measure-ment planes (z = 6mm, 26mm, 56mm, 86mm and116 mm, z being the axial distance from the injectionplane) as described in Fig. 8.

6mm

26mm

56mm

86mm

116m

m

Figure 8: Position of the measurement planes in theMERCATO burner.

Comparison between simulation and experimentsare shown in Figure 9. The velocity profiles are ingood agreement with the exprimental profiles, and alsowith the numerical simulation performed by Senoner(Senoner, (2010)) in the same operating conditions.

For this gaseous simulation, statistics were ob-tained by averaging over 400 ms. This averaging timemay be compared with the characteristic time scalesof the flow. The convective time is obtained by divid-ing the total length by the bulk velocity m/ρS. Whenconsidering the total length of the domain, the convec-tive time scale is about 30 ms, and based on the lengthof the measurements section, τconv = 4 ms. The PVC

2 4 6 8 10 12 14 16 18 20 2 3 4 5 6 7 8 9 10 11 12

RMS axial velocity (m/s) 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

-60

-40

-20

0

20

40

60

0 5 10 15 20 25

Rad

ial

dis

tan

ce (

mm

)

-20-10 0 10 20 30 40

z = 26mm

-10-5 0 5 10 15 20

Mean axial velocity (m/s)

z = 56mm

-10-5 0 5 10 15 20

z = 86mm

-10-5 0 5 10 15 20

z = 116mm

-60

-40

-20

0

20

40

60

-20-10 0 10 20 30 40 50

Rad

ial

dis

tan

ce (

mm

)

z = 6mm

-2 0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 4 5 6 7 8 9 10

RMS radial velocity (m/s) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 0.5 1 1.5 2 2.5 3 3.5

-60

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-20

0

20

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0 5 10 15 20 25

Rad

ial

dis

tan

ce (

mm

)

-8 -6 -4 -2 0 2 4

z = 26mm

-8-6-4-2 0 2 4 6 8

Mean radial velocity (m/s)

z = 56mm

ExperimentAVBP

YALES2

-8-6-4-2 0 2 4 6 8

z = 86mm

-8-6-4-2 0 2 4 6 8

z = 116mm

-60

-40

-20

0

20

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60

-20-15-10-5 0 5 10 15

Rad

ial

dis

tan

ce (

mm

)

z = 6mm

0 2 4 6 8 10 12 14 1 2 3 4 5 6 7 8 9

RMS orthoradial velocity (m/s) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 0.5 1 1.5 2 2.5 3 3.5

-60

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Rad

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mm

)

-25-20-15-10-5 0 5 10 15 20 25 30

z = 26mm

-10 -5 0 5 10 15

Mean orthoradial velocity (m/s)

z = 56mm

-10 -5 0 5 10 15

z = 86mm

-10 -5 0 5 10 15

z = 116mm

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-40

-20

0

20

40

60

-40-30-20-10 0 10 20 30 40

Rad

ial

dis

tan

ce (

mm

)

z = 6mm

Figure 9: Gaseous velocity profiles.

0 2 4 6 8 10 12 14 16

RMS axial velocity (m/s) 0 2 4 6 8 10 12

-60

-40

-20

0

20

40

60

0 2 4 6 8 10 12 14 16

Rad

ial

dis

tan

ce (

mm

)

-10 -5 0 5 10 15 20 25

Mean axial velocity (m/s)

z = 26mm

-10 -5 0 5 10 15 20

z = 56mm

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-5 0 5 10 15 20 25

Rad

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mm

)

z = 6mm

0 1 2 3 4 5 6 7 8 9

RMS radial velocity (m/s) 0 1 2 3 4 5 6

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60

0 2 4 6 8 10 12 14

Rad

ial

dis

tan

ce (

mm

)

-15 -10 -5 0 5 10 15

Mean radial velocity (m/s)

z = 26mm

-8 -6 -4 -2 0 2 4 6 8 10

z = 56mm

ExperimentAVBP

YALES2

-60

-40

-20

0

20

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60

-20-15-10 -5 0 5 10 15 20

Rad

ial

dis

tan

ce (

mm

)

z = 6mm

0 2 4 6 8 10 12 14

RMS orthoradial velocity (m/s) 0 1 2 3 4 5 6

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0 2 4 6 8 10 12

Rad

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ce (

mm

)

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Mean orthoradial velocity (m/s)

z = 26mm

-12-10-8 -6 -4 -2 0 2 4 6 8 10

z = 56mm

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-20

0

20

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60

-20-15-10 -5 0 5 10 15 20

Rad

ial

dis

tan

ce (

mm

)z = 6mm

Figure 10: Liquid velocity profiles.

Figure 11: Representation of the external recirculationzones in the injection plane in the experiments (left,Lecourt (2011)), in the Euler-Euler simulation of San-jose (center, Sanjose (2009)), and in the present simu-lation (right).

frequency, measured both experimentally and numeri-cally is around 800 Hz, leading to a caracteristic timescale τPV C = 1.25 ms. Another important time scaleis the time required to complete a rotation around thechamber axis. This swirl time scale can be estimatedas: τswirl = 2πR/uθ where uθ is the tangential veloc-

ity at the radial distance R. The swirl time scale wasmeasured close to the injection plane, and is aroundτswirl = 6 ms. The averaging time of 400 ms is one or-der of magnitude higher then the characteristic time-scales of the flow, ensuring a good convergence ofthe recirculation zones, where the very slow velocitieslead to higher convective time scales.

The flow features a long central recirculation zoneand four corner recirculation zones. This was alsoobserved in previous simulations and during the ex-periments. When impacting the chamber back wall,the fuel droplets trapped in the external recirculationzones tend to dilute the paint, making the recirculationzone clearly visible on the experimental device. Thefour recirculation zones (materialized by iso-lines ofuz = 0 axial velocity on the simulations and by lighterareas on the experiment are visible in Fig. 11.

In a second phase, liquid fuel is injected. PDA di-agnostics were performed to measure mean velocity

Figure 12: Instantaneous snapshots in the middleplane. From top to bottom: velocity, temperature,kerosene mass fraction and droplet diameter. Thewhite line in the top figure is the iso-level of zero meanaxial velocity.

profiles of the droplets. Under these conditions, mea-surements were possible only on the first three span-wise plans (z = 6mm, 26mm and 56 mm), due to thepresence of liquid fuel on the visualization window(Garcia Rosa (2008)). Figure 10 compares velocityprofiles for the dispersed phase to experiments andto the Euler-Lagrange simulation performed with theAVBP code (Senoner (2011)). Liquid velocity profilesare in good agreement with the experiment, especiallyclose to the injection plane, ensuring that the modelchosen for the injection is appropriate for this type ofsimulation.

Figure 12 shows instantaneous profiles of veloc-ity magnitude, temperature, evaporated kerosene massfraction, and particles (colored by their diameter)within a 2mm slice close to the mid-plane.

Analysis of the interactions between the PVC andthe spray

The post-processing tools presented in Section 2were used to isolate the PVC in the lagrangian simula-tion, by filtering Q-criterion with the homogeneous fil-tering size ∆ = 8mm at order 12, and plotting a filteredQ-criterion isosurface, as showned in Fig. 13. Hereagain, the filtering methodology enables to highlightthis structure characteristic of swirled flows.

Figure 13: Iso-surface of raw Q-criterion Q = 3 ×107 s−2 (left) and of the level-set function based onthe filtered Q-criterion iso-surface Qf = 3× 107 s−2.

Thanks to the level set distance function, the dis-tance to the PVC can be interpolated onto the parti-cles. Figure 14 shows the droplets in the chamber,colored by the distance to the PVC. The comparisonof the spray with and without the PVC shows that thespray topology is clearly impacted by the presence ofthe PVC, and the particles spatial distribution seemscorrelated with the position of the PVC.

Figure 14: Lagrangian particles colored by the dis-tance to the PVC seen from the combustor head. Inthe right figure, the PVC is superimposed to show itscorrelation with the droplet spatial distribution.

To get more insight into the correlation betweenthe spray and the PVC, the droplet spatial distributionin the radial direction to the PVC is computed for sev-eral classes of droplet diameter. Figure 15 (a) showsthe probability density function of the distance to thePVC for each diameter class. It is recalled that the dis-tance to the PVC is algebraic, i.e. the negative valuesare inside the chosen PVC iso-surface and the posi-tive values are outside. The spatial distribution of the

0

2

4

6

8

10

12

14

16

0 0.005 0.01 0.015 0.02

Distance to PVC [ m ]

(a)0-5 microns

5-15 microns15-25 microns25-35 microns35-45 microns45-55 microns55-65 microns

65-100 microns

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.005 0.01 0.015 0.02

Distance to PVC [ m ]

(b)0-5 microns

5-15 microns15-25 microns25-35 microns35-45 microns45-55 microns55-65 microns

65-100 microns

Figure 15: PDF of the distance to the PVC for all the droplet diameter classes (left) and droplet diameter PDF as afunction of the distance to the PVC (right)

smallest particles (in red) strongly differs from the dis-tribution of the biggest particles (in blue) in the vicin-ity of the PVC. While large droplets are able to crossthe inner core of the PVC leading to large values of thePDF for negative algebraic distances to the PVC, thesmall droplets are not present in the PVC and tend toaccumulate at the periphery of the PVC.

Figure 15 (b) shows the PDF of the droplet numberconditioned by the distance to the PVC. For instance,a value of 0.3 for the diameter class between 15 and 20microns indicates that 30 percents of the total numberof droplets found at this particular distance to the PVCare in this diameter class. The center of the PVC is pre-dominantly filled by medium to large droplets that areable to cross the inner core of the PVC, while the re-gion at 5 mm to the PVC is mainly populated by smallparticles. Away from the PVC, the PDF correspondsapproximately to the injected Rosin-Rammler PDF.

4 Conclusions and PerspectivesThe post-processing tools presented in this paper

enable to extract the PVC in aeronautical swirl burn-ers, and to study its impact on the spray topology andthe particles segregation. They will soon be extendedto have access to the local PVC tangential velocity.Averaging this tangential velocity will provide meanvelocity profiles of the PVC that will be compared toclassical vortex models. The combination of all theseresults should bring more insight into spray/PVC in-teractions, and will be a next step towards a better un-derstanding of the fuel mixing process in aeronauticalswirl burners.

AcknowledgmentsComputational time was provided by GENCI

(Grand Equipement National de Calcul Intensif), andall simulations were performed on the HPC ressourcesof IDRIS.

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