Experimental Thermal and Fluid Science 52 (2014) 164–173

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Experimental Thermal and Fluid Science

journal homepage: www.elsevier .com/locate /et fs

Three-dimensional organization of the flow structure in a non-reactivemodel aero engine lean burn injection system

0894-1777/$ - see front matter � 2013 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.expthermflusci.2013.09.007

Abbreviations: CSMART, camera-simultaneous multiplicative algebraic recon-struction technique; IRZ, inner recirculation zone; ISL, inner shear layer; LOR, loworder reconstruction; MLOS, multiplicative line of sight; ORZ, outer recirculationzone; OSL, outer shear layer; PIV, particle image velocimetry; POD, properorthogonal decomposition; PVC, precessing vortex core; rms, root mean square;SMART, simultaneous multiplicative algebraic reconstruction technique; TKE,turbulent kinetic energy.⇑ Corresponding author. Tel.: +39 0817683405.

E-mail address: giuseppe.ceglia@unina.it (G. Ceglia).

Giuseppe Ceglia a,⇑, Stefano Discetti a,b, Andrea Ianiro a,b, Dirk Michaelis c, Tommaso Astarita a,Gennaro Cardone a

a Dipartimento di Ingegneria Industriale – Sezione Aerospaziale, Università degli Studi di Napoli Federico II, via Claudio 21, 80125 Naples, Italyb Departamento de Bioingeniería e Ingeniería Aeroespacial, Universidad Carlos III de Madrid, Av. de la Universidad 30, 28911 Leganés, Spainc LaVision GmbH, Anna-Vandenhoeck-Ring 19, 37081 Goettingen, Germany

a r t i c l e i n f o

Article history:Received 24 May 2013Received in revised form 23 July 2013Accepted 11 September 2013Available online 20 September 2013

Keywords:Swirl flows, Tomographic PIVPrecessing vortex coreVortex breakdown

a b s t r a c t

An investigation of the three-dimensional flow field of a turbulent swirling jet at Re = 50 � 103 generatedby a non-reactive model aero engine lean burn injector is carried out in a water facility with tomographicParticle Image Velocimetry. This work is focused on the organization of the coherent structures arisingwithin the near field of the swirling jet both in free and confined configurations. The confinement causesan increase of the Swirl number: the measured values are equal to 0.90 and 1.27, respectively for free andconfined swirling jets. The effects of the confinement induce a larger spreading of the swirling jet promot-ing the enhancement of turbulence at the nozzle exit, but the expected upstream displacement of thereverse flow region is not observed. The instantaneous flow field is characterized by the presence ofthe precessing vortex core (PVC), of the outer helical vortex and of smaller turbulent structures perturb-ing the structure of the PVC. A three dimensional modal analysis of the velocity field using the ProperOrthogonal Decomposition (POD) highlights that the flow is dominated by the precessing vortex core.Using the first two POD modes a low order reconstruction of the velocity field is calculated. It is foundthat the small-scale structures shown in the instantaneous velocity field are not captured in the low orderreconstruction due to smoothing effects, but the precessing vortex core and the outer helical vortex areproperly represented.

� 2013 Elsevier Inc. All rights reserved.

1. Introduction jet axis itself, followed by a highly turbulent region of reverse flow

Swirling jets are widely used in gas turbine combustors to gen-erate an inner recirculation region near the jet nozzle to promotethe flame stabilization [1]. Moreover, swirling flows have demon-strated their capability in reducing the pollutants emissions [2]and improving the control of the combustion processes. The pres-ence of a recirculation region near the nozzle exit, commonly re-ferred as vortex breakdown [3], is a unique feature thatcharacterizes free and confined strongly swirling jets. This phe-nomenon is characterized by the transition from a jet-like to awake-like axial velocity profile, i.e., with a local minimum on thejet axis. This leads to the presence of a stagnation point on the

further downstream. The vortex breakdown occurs when the ratioof the intensity of azimuthal momentum with respect to axialmomentum exceeds a certain threshold, leading to strong radialpressure gradients coupled with an adverse axial pressure gradientalong the axis of symmetry [3].

The most common solutions adopted to generate a swirlingflow are probably radial swirl vanes [4] or axial-tangential fluid en-try [5]. Recently, multiple swirler systems in radial configurationare employed in gas turbine combustors [6] to obtain a furtherimprovement of the flame stability and reduction of the emissionof pollutants.

The wide application in industrial processes has stimulatedmany studies to understand the swirling flow organization. Theflow field is made complex by both the transition of the flow fromjet-like to wake-like (which induces the coexistence of inner andouter shear layers) and by the concomitant axial and azimuthalshear stresses; these features impose a challenge to both numericaland experimental investigations. The main issues in swirl flows arereported in a book [2] and several review papers that describe andsummarize all the numerous studies performed in the last 50 years(see e.g., [3,7]). Recent researches are mainly focused on the study

Nomenclature

D diameter of the swirler, mN number of snapshotsQ second invariant of the velocity gradient, s�2

Re Reynolds numberRij two-point temporal correlation matrix, m2/s2

S Swirl numberV [U, V, W] velocity vector, m/sVj bulk velocity, m/sVh azimuthal velocity component, m/sX [X, Y, Z] spatial position vector, man time coefficient, m/sf# focal ratio

r radial coordinate, mt time coordinate, sv0 [u0, v 0, w 0] velocity fluctuation vector, m/sU phase angle, degreesa half spreading angle, degreesh azimuthal coordinate, degreeski eigenvalue corresponding to i-th mode, m2/s2

v kinematic viscosity, m2/sun orthonormal basis function of the proper orthogonal

decompositionxr r-component of the vorticity, s�1

xh h-component of the vorticity, s�1

G. Ceglia et al. / Experimental Thermal and Fluid Science 52 (2014) 164–173 165

of the unsteady vortical features in swirling jets and of their effecton combustion processes [8–11]; other studies are focused on thedevelopment of numerical modeling tools for swirl flows that arestill a challenging application [12,13].

The swirling flow, under the condition of large swirl, exhibits ahelical vortical flow instability, commonly identified as precessingvortex core (PVC) [7] which is intimately associated with the vor-tex breakdown. The PVC appears as a helical structure and precess-es around the axis of symmetry with a frequency proportional tothe mass flow rate [3,7]. The PVC is characterized by a vorticitywith the same direction of the mean swirl vorticity while the pre-cession motion is counter-winding with the mean swirl motion[14]. The intensity of the PVC is stronger at the nozzle exit closeto the inner shear layer (ISL) between the jet and the reverse flowregion. The PVC extends with decaying intensity up to the bound-ary of the inner recirculation zone (IRZ) [9,15]. Additional coherentstructures can be found in the outer shear layer (OSL) between theexiting jet and the surrounding ambient. In particular, the PVC isaccompanied by a co-precessing vortex related to the convectivewaves through the inner and outer shear layer [9,16,17].

These flow features are significantly influenced by the effects ofthe confinement. The PVC is characterized by a higher frequencyand lower amplitude than that detected in free swirling jets. This ef-fect is caused by the reduced decay of the swirl velocity componentalong the axis of the chamber [7]. Along with this change, the sizeand strength of the IRZ increase. The ‘‘level’’ of the confinement isusually quantified with the ratio of the diameter of the confinementchamber and the diameter of the nozzle exit of the swirl burner. Thesmaller is this ratio, the more pronounced is the influence of theconfinement [7]. In this context, experimental investigations bySyred and Dahman [17] addressed the effects of high level of con-finement on the swirling jet: they found that the size of the IRZcan be increased by inserting bluff bodies into or near the exit ofthe swirl burner. Sheen et al. [18] investigated the flow field patternin the IRZ behind of the bluff body of a annular swirling jet for bothfree and confined configurations. Seven different regimes for IRZ areobserved, depending on the Reynolds and Swirl numbers: stableflow, vortex shedding, transition, prepenetration, penetration, vor-tex breakdown and attachment. Schefer et al. [19] investigated theeffects of the confinement on annular jets for variable blockage ra-tio (i.e., the ratio of the cross-sectional area of the inner bluff bodyand the duct). The results by Schefer et al. [19] highlight that at highlevel of the blockage ratio (equal to 0.83) the size of the IRZ in-creases, promoting the combustion stability.

Further experiments are focused on the near field of the swirl-ing jet where different strategies were adopted to reconstruct thethree-dimensional (3D) flow features from point-wise and planarmeasurements. Cala et al. [16] studied the unsteady precessingflow in a swirl burner for a Reynolds number Re = 15 � 103 and

Swirl number S = 1.01. From the analysis of the phase-averageddata, they identified three precessing helical vortex structures clas-sified as primary and secondary structures forming a 3D vortex di-pole. Using Proper Orthogonal Decomposition (POD), phase-averaging technique and azimuthal symmetry of the helical struc-tures, Oberleithner et al. [15] produced a 3D representation of thehelical vortices from uncorrelated 2D snapshots (obtained by Par-ticle Image Velocimetry (PIV) data) in the case of a swirling jet atRe = 20 � 103. The analysis highlighted that the dominant modesare associated with the PVC. Stöhr et al. [9,10] performed planarPIV measurements along streamwise and crosswise sectionalplanes in order to investigate the flow features of the swirling flowwith the presence of the flame. Following the approach proposedby van Oudheusden et al. [20], the 3D topology of the PVC is recon-structed from phase averaged measurements (the phase extractionis carried out using the first two POD modes, containing the bulk ofthe energy associated with the periodic PVC motion). The recon-struction of the PVC showed clearly that the evolution of the PVCalong the axial direction is coupled with a co-precessing vortexin the OSL. On top of this, a low order reconstruction (LOR) ofthe velocity field is performed using the first two POD modes.The representation of the velocity field provided by the LOR exhib-ited a pronounced smoothing effect with lesser detailed informa-tion than the phase average; however, the LOR is extremelyeffective in extracting information on the most energetic vorticalstructures.

Even though the POD analysis based on the 2D planar measure-ments might enable a three-dimensional reconstruction of theperiodic coherent structures, it does not allow an accurate descrip-tion of the intricate instantaneous 3D structures of the turbulentoutflow of swirling jets. Until now, to the author’s knowledge veryfew studies report about instantaneous 3D measurements in swirl-ing flows [21,22] and further investigations, especially at high Rey-nolds number, are needed. In the present study, the 3D coherentstructures organization of the turbulent swirling flow generatedby an aero engine lean burn injection system in cold (i.e., non-reacting) flow conditions is investigated using Tomographic PIV[23]. The effect of the confinement on both the instantaneousand statistical flow features is addressed. Moreover, a POD analysisis conducted to extract information on the most energetic coherentstructures.

2. Experiment setup and data analysis

2.1. Experiments configuration

Tomographic PIV experiments are conducted in a water tankfacility. A double radial swirl injector (with exit diameter D equalto 40 mm) designed by Avio S.p.A. is installed at the center of the

Fig. 2. Details of the measurement domain and coordinate systems.

166 G. Ceglia et al. / Experimental Thermal and Fluid Science 52 (2014) 164–173

bottom wall of a nonagonal Plexiglas tank (allowing full optical ac-cess for both illumination and camera imaging as in [24]) with cir-cumscribed diameter of 16D and height of 18D. A schematic viewof the experimental setup is shown in Fig. 1.

A stabilized water flow is provided using a centrifugal waterpump powered by an inverter and measured by means of a rota-meter. Subsequently, the flow passes through a series of gridsand honeycomb structures installed within a plenum chamber(with inner diameter equal to 2.5D and length equal to 10D) in or-der to reduce the free-stream turbulence anisotropy. Downstreamof the double radial swirl generator two co-swirling flows passthrough a central circular nozzle and a surrounding annular nozzle.The injector is sketched in Fig. 2 (the detailed geometry is coveredby a confidentiality agreement with Avio S.p.A). A closed-loop cir-cuit is completed by a siphon at the top of the tank, providingwater to the centrifugal pump.

The experiments are conducted in two different test conditions:free and confined outflow. In this last case, the swirling jet is con-fined in a Plexiglas hollow cylinder with inner diameter equal to3D. Both the experiments are performed with a flow rate equalto about 2.0 kg/s, corresponding to a bulk velocity Vj equal to about1.6 m/s. The accuracy of the rotameter is within the 5% of the mea-sured value. Consequently, the test Reynolds number is Re = VjD/v = 50 � 103, where v is the water kinematic viscosity (equal to1.3 � 10�6 m2/s in the present experiments).

2.2. Tomographic measurements

Neutrally buoyant polyamide particles with diameter equal to56 lm are inserted into the circuit upstream of the centrifugalpump; the turbulent mixing rapidly aids to achieve a reasonablyuniform seeding density within the circuit. The illumination is pro-vided by a double-cavity Gemini PIV Nd:YAG system (light wave-length equal to 532 nm, 200 mJ/pulse at 15 Hz , 5 ns pulseduration). The exit beam of about 5 mm diameter is shaped intoa parallelepiped volume using a three lenses system, i.e., a diverg-ing and a converging spherical lens (with focal length equal to�75 mm and 100 mm, respectively), and a diverging cylindricallens (with focal length equal to �50 mm); a knife edged mask isplaced along the laser path in order to set the volume thicknessto 46 mm and to suppress the tails of the Gaussian beam profile.

The light scattered by the particles is recorded by a tomographicsystem composed of four LaVision Imager sCMOS 5.5 megapixelscameras (2560 � 2160 pixels resolution, pixel pitch 6.5 lm,

Fig. 1. Schematic view of the illumination

16 bit intensity resolution). The cameras are equipped with100 mm EX objectives, set at f# = 16. Lens-tilt adapters are installedbetween the image plane and the lens plane to allow properly fo-cused particle images throughout the volume by achieving theScheimpflug condition. The particles image density is estimatedby counting the particles on the images. The measured image den-sity is 0.042 particles/pixel. However, considering that a certainpercentage of particles cannot be detected due to partially overlap-ping particles, it is reasonable to assume that the effective imagedensity is approximately 0.05 particles/pixel (in line with the oper-ative correspondence between measured and effective particle im-age density established by [25]). Considering that the depth of thevolume is equal to 46mm, this leads to a volumetric particles con-centration of about 0.3 � 0.35 particles/mm3.

The average magnification in the centre of the measurementvolume is approximately 0.11; the depth of field is of 62 mm andparticle image diameter is about 3.7 pixels according to the rela-tions reported in [26]. The details of the experimental settingsare summarized in Table 1.

Sequences of 500 couples of images are captured with acquisi-tion frequency equal to 10 Hz and time separation of 150 ls; thetime spacing between subsequent couples is large enough to en-sure that the samples are statistically independent. The field ofview covers a 3.2 � 3.2D2 area, corresponding to approximately

and imaging setup of the experiments.

Table 1Experimental parameters.

Tomo PIV

Seeding particles Diameter (lm) 56Concentration (particles/mm3) 0.3

Volume illumination Thickness (mm) 46Recording devices 4 LaVision Imager sCMOS (2560 � 2160 pixels at 10 Hz)Optical arrangement EX objectives (focal length (mm), f#) 100, 16

Field of view (D2) 3.2 � 3.2Magnification 0.11Acquisition frequency (Hz) 10Pulse separation (ls) 150Number of recordings 500

G. Ceglia et al. / Experimental Thermal and Fluid Science 52 (2014) 164–173 167

128 � 128 mm2. A schematic of the measurement domain andcoordinate systems is shown in Fig. 2.

For both experiments the calibration is performed without thepresence of the Plexiglas hollow cylinder; this additional difficultyin the case of the confined jet is due to physical access restrictions.An optical calibration procedure is performed using a double/planetarget imaged at 5 Z-locations covering the entire measurementdomain (±23 mm). The 3D mapping functions are generated usinga 3rd order polynomial function in X and Y, and 2nd order in Z witha root mean square (rms) calibration error equal to about 0.3 pix-els. For the free case, the calibration error is reduced up to 0.05 pix-els by means of the volume self-calibration technique proposed in[27].

Even if the refraction indices of water and Plexiglas are similar(about 1.3 and 1.5 respectively), the distortions of the optical pathsat the water-Plexiglas interface can cause significant modificationsof the mapping function with respect to the calibration previouslyperformed without the hollow cylinder. The mapping function isagain corrected with a volume self calibration [27] which is per-formed through ensemble average over 200 images in order toget well converged statistics. The initial not negligible errors (upto 3 pixels near the tube walls) are reduced to 0.07 pixels in orderto perform tomographic reconstruction. The background intensityon the raw images is eliminated by subtracting the historical min-imum based on the acquired sequence of 500 images. Subse-quently, the residual background (for example induced byfluctuations of the laser light intensity or of the seeding concentra-tion) is removed applying a sliding minimum subtraction over akernel of 31 � 31 pixels in space and using 5 samples in time.The volumetric light intensity reconstruction is performed combin-ing the MLOS technique with the CSMART algorithm (10 iterations)by LaVision software Davis 8. The algorithm CSMART is similar tothe SMART technique implemented in [28], with the basic differ-ence in the update process, involving each camera separately.The illuminated volume of 3.2 � 3.2 � 1.15D3 (i.e.,128 � 128 � 46 mm3) is discretized with 2298 � 2298 � 1004 vox-els (i.e., approximately 18 vox/mm; the reconstructed volumethickness is larger than that of the illuminated one in order to en-sure that all the particles will be enclosed within it). The recon-struction quality is improved by filtering the reconstructeddistributions in between each iteration using a Gaussian filter [29].

The accuracy of the reconstruction is assessed a posteriori bycomputing the sum of the intensity of the reconstructed particleson X–Y planes [23]. The ratio of the intensity of the reconstructedparticles (true and ghost) in the illuminated domain and the ghostparticles intensity in the immediate surrounding domain gives asignal to noise ratio �2, that is generally considered a value accept-able for three dimensional velocity measurements [23].

The 3D particle field motion is computed with the LaVision soft-ware Davis 8; the interrogation algorithm is based on a directsparse cross-correlation approach, as proposed in [30]. The final

interrogation volume is of 64 � 64 � 64 voxels (3.6 � 3.6 �3.6 mm3) with an overlap between adjacent interrogation boxesof 75%, leading to a vector pitch of about 0.9 mm in the X, Y andZ directions. The measurement uncertainty can be evaluated con-sidering physical criteria, for example the local mass conservationin the incompressible regime. The standard deviation of the diver-gence computed on raw data can be assumed as an estimation ofthe accuracy of measurement of the velocity spatial derivatives;in the present experiments the standard deviation of the diver-gence is about 7% of the typical value of the vorticity magnitudewithin the shear layer (0.24 voxels/voxel, equivalent to1.6 � 103 s�1).

2.3. Proper Orthogonal Decomposition implementation

The POD [31] is a mathematical procedure that uses anorthogonal transformation to convert a set of observations ofpossibly correlated variables into a set of values of linearlyuncorrelated variables referred as principal components. PODprovides an ‘‘energy-efficient’’ decomposition, i.e., the principalcomponents are sorted in terms of their contribution to the totalenergy; for the case of turbulent flows, the POD modes highlightthe most relevant contributions to the total turbulent kineticenergy.

In this section the POD analysis based on the method of snap-shots is briefly introduce in order to fix the notation (for a morerigorous formulation see [31,32]).

The starting point is a set of N uncorrelated and statisticallyindependent velocity fields V(X, t) (where X is the spatial positionvector, and t is the time coordinate), decomposed into a temporalaverage part VðX; tÞ (the overbar indicates the operation of time-averaging) and a fluctuating part v0(X, t):

VðX; tÞ ¼ VðX; tÞ þ v 0ðX; tÞ ð1ÞThe POD identifies a set of N orthonormal basis function un (X),

which is optimal in the least square sense in approximating thefluctuating velocity field, so that, by finding a proper set of timecoefficients an (t), it results:

v 0ðX; tÞ �XN

n¼1

anðtÞunðXÞ ð2Þ

In the formulation of the snapshot method [32] the POD modesare the eigenmodes of the two-point temporal correlation matrixRij ¼ v 0ðXi; tÞ � v 0ðXj; tÞ. The corresponding eigenvalues kn are repre-sentative of the energy associated with the modes un (X). In thecase of shedding or quasi-periodic phenomena, phase informationcan be inferred using a relatively low number of POD modes[20,33,34], enabling a LOR of the velocity field.

Fig. 3. Iso-contours with velocity vectors of the mean velocity maps W=Vj on theplane Z/D = 0 and iso-surface of axial mean velocity V=Vj ¼ �0:15 for the freeswirling jet (a) and the confined swirling jet (b).

Fig. 4. Iso-contour of TKE=V2j on planes Z/D = 0 and Y/D = 0.12 for the free swirling

jet (a) and the confined swirling jet (b).

168 G. Ceglia et al. / Experimental Thermal and Fluid Science 52 (2014) 164–173

3. Results and discussion

3.1. Statistical analysis

In Fig. 3a and b, the average velocity field of the free and con-fined swirling jets, is depicted by the iso-contours of W=Vj onthe plane Z/D = 0 (in this plane the vector representation of theU=Vj and V=Vj components is also reported) and by the iso-sur-faces of the axial mean velocity V=Vj ¼ �0:15.

For both cases, the sudden expansion of the flow at the nozzleexit induces strong velocity gradients that determine the presenceof an ISL and an OSL, as reported in [9,10]. High values of W=Vj aredetected near the nozzle exit, in agreement with the observationsof Stöhr el al. [9]. A cone-shaped reverse flow stream, extendingfrom the nozzle exit along the axial direction, is formed, promotingthe formation of an IRZ [3,7,9].

The confinement dramatically alters the size and shape of IRZ[7] (see Fig. 3b). The increased size of the IRZ is testified by thewider shape of the iso-surface of the negative axial velocity atthe nozzle exit. Furthermore, an Outer Recirculation Zone (ORZ)is formed between the OSL and the wall of the chamber due tothe step-like geometry that the jet encounters when expands atthe nozzle exit. In this condition, the flow undergoes the effect of

a radial pressure gradient due to the presence of the wall, promot-ing the Coanda effect [35].

In order to estimate the effects induced by the confinement, thehalf spreading angle a of the swirling jet [14] is measured as theslope of the linear regression of the radial position of the half-max-imum axial velocity (in the outer shear layer) versus Y and it isevaluated in the Y range 0.1 < Y/D < 0.3; the correlation coefficientbetween the data and the linear fit is equal 0.99. For the case of thefree swirling jet the measured half spreading angle is approxi-mately 18�, while in presence of confinement a is about 36�, i.e.,two times larger. Along with this different pattern, a larger Swirlnumber is expected in this latter case. The Swirl number S is eval-uated on the measured average flow fields in the plane located atY/D = 0.1 using the equation proposed in [36]:

S ¼2R D=2

0 r2VVhdr

DR D=2

0 r V2 � 12 V2

h

� �dr

ð3Þ

where Vh and r are the azimuthal mean velocity component and theradial coordinate, respectively. It is worth to note that the Swirlnumbers for the free and confined swirling jets are equal to 0.90and 1.27, respectively. Such an increase of the value of the Swirlnumber due to the confinement clearly reflects in the higherspreading angle (in agreement with Liang and Maxworthy [14])but, interestingly enough, it does not cause the expected upstreamdisplacement of the reverse flow region.

In Fig. 4a and b, the normalized turbulent kinetic energy(TKE=V2

j ) is shown for both the free and the confined configuration,respectively. The TKE is defined as:

TKE ¼ u0u0 þ v 0v 0 þw0w0

2ð4Þ

Local maxima of the TKE are achieved within the shear layers(ISL and OSL), while a relatively low level of turbulence occurs inthe neighborhood of the jet axis, i.e., in the IRZ. The confinementdetermines a higher TKE at the nozzle exit with respect to the caseof the free jet, but a lower TKE on the jet axis. In the horizontal slicepresented in Fig. 4 (i.e., the plane Y/D = 0.12), the ISL and OSL of the

Fig. 5. Profiles of the average velocity components for free swirling jet (a–c) and confined swirling jet (d–f) at Y/D = 0.04, 0.5, 1. � U=Vj , d V=Vj , NW=Vj . Symbols are placedeach 3 measured vectors.

Fig. 6. Radial profiles of the rms of the normalized turbulent fluctuations for free swirling jet (a–c) and confined swirling jet (d–f) at Y/D = 0.04, 0.5, 1. �ffiffiffiffiffiffiffiffiu0u0p

=Vj dffiffiffiffiffiffiffiffiffiv 0v 0p

=Vj ,N

ffiffiffiffiffiffiffiffiffiffiffiw0w0p

=Vj . Symbols are placed each 3 measured vectors.

G. Ceglia et al. / Experimental Thermal and Fluid Science 52 (2014) 164–173 169

Fig. 7. Instantaneous velocity field for the free (a) and the confined (b) swirling jet.Vortex visualization using Q criterion color-coded with the normalized radialvorticity xrD/Vj. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

Fig. 8. Energy distribution of the normalized eigenmodes for the first 10 modes fors free and D confined swirling jet.

Fig. 9. First POD mode describing the coherent streamwise development of PVChelix for the free (a) and confined (b) swirling jet. Iso-surface of positiveQD2=V2

j ¼ 0:7 color-coded with xhD/Vj. Contour of xhD/Vj with velocity vectors atplane Z/D = 0 blanked by imposing the �1.2 < xhD/Vj < 1.2 constraint. (For inter-pretation of the references to color in this figure legend, the reader is referred to theweb version of this article.)

170 G. Ceglia et al. / Experimental Thermal and Fluid Science 52 (2014) 164–173

jet are well discerned; further downstream the two shear layerstend to merge because of diffusion. The merging occurs at Y/Dapproximately equal to 0.44 and 0.30 for the free and confinedswirling jet, respectively; the abscissa of merging moves upstreamin presence of the confinement due to the improved turbulent mix-ing in proximity of the nozzle exit.

In Fig. 5 the profiles of the mean velocity components are re-ported for the free and confined cases at three longitudinal loca-tions (i.e., Y/D = 0.04, 0.5 and 1.0). For both cases, at Y/D = 0.04the profile of the axial velocity component V=Vj is wake-like, i.e.,two local maxima are detected while the velocity is nearly zeroin proximity of the jet axis. For the free case (Fig. 5a), the profileof the W=Vj component (which here corresponds to the tangentialvelocity component) is characterized by the presence of four localpeaks, which are due to the combination of the swirling flow issu-ing from the circular and annular nozzles. On the other hand, forthe confined case (Fig. 5d) the internal peaks disappear and theprofile exhibits two inflection points. A similar behavior is detectedfor the axial mean velocity profile V=Vj. For the free case, the stag-nation point is located on the axis of symmetry of the jet at Y/D = 0.04 (Fig. 5a), whereas at the same position the confined swirl-ing flow exhibits a weak positive axial mean velocity value (Fig. 5d)and the stagnation point is located further downstream from thenozzle exit.

The intensity of the U=Vj profiles (that is the radial velocity com-ponent for the considered profile) is weaker than that of the othercomponents for both the free and the confined configurations. Mov-ing downstream, the decay of U=Vj is lower for the confined

swirling jet, in particular at Y/D = 1 the values of the peaks of theU=Vj profile are of the same order of the normalized swirling veloc-ity component W=Vj. In Fig. 5d–f, the effects of the entrainment in-duced by the ORZ are testified by a non-zero values of the velocitycomponents in the region between the OSL and the wall.

The normalized root mean square of the velocity fluctuations(ffiffiffiffiffiffiffiffiu0u0p

=Vj,ffiffiffiffiffiffiffiffiffiv 0v 0p

=Vj andffiffiffiffiffiffiffiffiffiffiw0w0p

=Vj) are depicted in Fig. 6. Theturbulence intensity is larger in correspondence of the ISL andOSL regions. Even though the

ffiffiffiffiffiffiffiffiu0u0p

=Vj andffiffiffiffiffiffiffiffiffiv 0v 0p

=Vj decrease with

Fig. 10. Scatter plot of the time coefficients a1, a2 for free (a) and confined (b)swirling jets. The circumference with radius 1 is plotted for reference.

G. Ceglia et al. / Experimental Thermal and Fluid Science 52 (2014) 164–173 171

a local minimum on the jet axis, as reported in [8],ffiffiffiffiffiffiffiffiffiffiw0w0p

=Vj

reaches an additional local maximum value of 0.60 and 0.56 for

Fig. 11. Iso-contours with velocity vectors of the instantaneous velocity maps V/Vj (left)the normalized azimuthal vorticity xhD/Vj for free swirling jet (a and c) and confined sw

the free and confined swirling jets at the nozzle exit (Y/D = 0.04),respectively.

Moving downstream, the effect of the vortex breakdown deter-mines a rapid decay of the intensity of the turbulent fluctuationson the jet axis due to the improved mixing and turbulent dissipa-tion. At Y/D = 1.0 (Fig. 6c and f), the maximum values of the nor-malized velocity fluctuations are achieved much further awayfrom the jet axis for the confined case than for the free case. Thisbehavior is due to the spreading of the swirling jet that influencesthe shape of the IRZ.

Even though the U=Vj component is weak compared to theother velocity components (Fig. 5), the relatively high level offfiffiffiffiffiffiffiffi

u0u0p

=Vj indicates a fully 3D flow field in the ISL and OSL (Fig. 6)with a complex cross-talk between the principal directions of theturbulent fluctuations.

3.2. Instantaneous velocity field topology

The instantaneous organization of the flow field is illustrated intwo snapshots depicted in Fig. 7a and b. The vector representationof the U/Vj and V/Vj components on the plane Z/D = 0 shows a zig-zag pattern extending along the axial direction for the free swirlingjet, in agreement with [9]. On the other hand, for the confinedswirling jet a quiescent flow with a weak large recirculation regionis detected beyond Y/D = 1.2.

The Q criterion [37] (Q is the second invariant of the velocitygradient tensor) is used to visualize vortical features. Iso-surfacesof QD2=V2

j ¼ 50 (color-coded with the normalized radial vorticityxrD/Vj) reveal the presence of a 3D helical coherent structure,characterized by the PVC [7] and the outer helical vortex. Interest-ingly enough, the flow field is featured by the presence of smallerturbulent structures with significantly large radial vorticity. Thehelical vortex exhibits an azimuthal wavy shape in between the lo-cal peaks of radial vorticity. It can be hypothesized that thesestructures determine the azimuthal instability of the helical vortex

and of the LOR velocity (right) at plane Z/D = 0. Iso-surface of positive QD2=V2j with

irling jet (b and d).

172 G. Ceglia et al. / Experimental Thermal and Fluid Science 52 (2014) 164–173

before its dissipation about 0.8D and 0.5D downstream of the noz-zle exit for the free and confined case, respectively. However, thelimited spatial resolution of the present measurements does not al-low a more conclusive analysis on this regard.

3.3. POD analysis

The unsteady organization of the turbulent swirling flow is ana-lyzed by means of the POD analysis performed on the instanta-neous measurements of the 3D velocity field. The distribution ofthe energy of the POD modes, obtained as the ratio between eacheigenvalue and the sum of the entire set of eigenvalues, is illus-trated in Fig. 8. The energy distributions across the first 10 modeshighlight that the first two modes constitute the most relevantcontribution for both cases, in agreement with literature [9,10].For the free case, mode #1 and #2 contribute for the 5.2% and5.0% of the total TKE. For the confined case, the first pair of modesare less energetic (4.9% and 4.8%, respectively); this slightly largerspreading of the energy over the set of modes may be due to theenhanced mixing effects induced by the simultaneous presenceof the IRZ and the ORZ. Interesting enough all the other smaller tur-bulent features and the measurement noise represent 90% of theTKE.

The first mode is depicted in Fig. 9a and b for the free and con-fined swirling jets, respectively. The iso-surfaces of positiveQD2=V2

j color-coded with xhD/Vj (where xh is the azimuthal com-ponent of the vorticity), the contour of xhD/Vj and the vector rep-resentation of the U=Vj and V=Vj components are blanked byimposing the �1.2 < xhD/Vj < 1.2 constraint. Mode #1, as mode#2 (not shown for conciseness), describes the precessing motion,as it is characterized by two helical vortices located in the ISL, thatare phase shifted of p/2 on the crosswise plane and extend up to0.9D along the jet axis. The xhD/Vj contour reveals also the pres-ence of the outer helical vortices, placed in the OSL, that are statis-tically correlated with the PVC helix [9].

3.4. Low order reconstruction

The precessing motion of the PVC can be rebuilt by linearlycomposing a subset of modes carrying the bulk of the energy(see [38] for a detailed description). This is normally feasible whenthe flow field is dominated by a periodic/shedding phenomenol-ogy, for example the PVC observed for the flow under investigation.In this study the reconstruction of the flow field is achievedthrough a low-order model incorporating only the mean velocityfield and the first two POD modes:

VðX;UÞ � VðX; tÞ þ a1ðUÞu1ðXÞ þ a2ðUÞu2ðXÞ ð5Þ

The phase dependent coefficients a1 (U) and a2 (U) are relatedto the phase angle U and can be written as:

a1ðUÞ ¼ffiffiffiffiffiffiffiffi2k1

psinðUÞ ð6Þ

a2ðUÞ ¼ffiffiffiffiffiffiffiffi2k2

pcosðUÞ ð7Þ

Even though the time coefficients are statistically uncorrelatedby definition, they are not independent. In order to verify that thefirst two modes represent the coherent harmonics related to theprecession motion, in Fig. 10a and b, the scatter plots of the timecoefficients for the individual realization on the normalized plane(a1=

ffiffiffiffiffiffiffiffi2k1p

, a2=ffiffiffiffiffiffiffiffi2k2p

) are shown for the free and confined swirlingjets, respectively. The time coefficients are located in the neighbor-hood of a circle with unit radius, thus confirming the validity of theassumption in Eqs. (6) and (7). The scattering of the points aroundthe circle is due to the effects of turbulence or small-scale fluctua-tions, that are not represented in the first two modes.

Eqs. (6) and (7)can be used to extract the phase information, asin [38] and the animations obtained with the different phases ex-tracted with the LOR are available as Supplementary material mo-vie 1 and movie 2 respectively for the free and the confinedconfigurations. An instantaneous realization and the LOR relativeto the same phase (U � 0) are compared in Fig. 11 for the free (aand c) and for the confined (b and d) swirling jets, respectively.In order to identify the 3D coherent structures, the iso-surfacesof positive normalized QD2=V2

j are evaluated at two values equalto 50 and 5 for the instantaneous and LOR velocity field, respec-tively (in the latter case a lower value is adopted, as the LOR resultsin smoother velocity fields). The V/Vj contour plot and the in-planevelocity vectors for Z/D = 0 depict the flow field.

In both free and confined cases, the reconstructed velocity fieldreveals a more pronounced pattern of the coherent structures: therebuilt PVC and a counter-rotating and co-precessing outer helicalvortex are identified on the external boundary of the OSL, as re-ported in the literature [9,14,16,22]. The LOR is not able to capturesmaller coherent structures and azimuthal instabilities of the PVCthat indeed represent most of the 90% of the TKE.

4. Conclusions

The 3D organization of the flow structures of a free and a con-fined swirling jet issuing at Re = 50 � 103 from a double swirleraero engine lean burn injection system has been investigated inwater by means of Tomographic PIV. The vortex topological analy-sis shows different organization of the large-scale coherent struc-tures between the free and confined configuration.

In both cases, the flow field is dominated by the presence of thevortex breakdown, leading to a cone-shaped stream wrappedaround the jet axis, with a wide inner recirculation region.

The confinement dramatically alters the flow field topology,inducing an enhancement of turbulence at the nozzle exit and amore intense mixing. The spreading angle of the confined swirlingjet is about two times larger than for the free swirling jet, promot-ing an increasing of the size of the IRZ in the crosswise direction.This pattern influences the sudden expansion of the swirling flow;in particular the measured Swirl numbers for the free and the con-fined swirling jet are equal to 0.90 and 1.27, respectively. Eventhough the effects of the confinement induce a larger spreadingof the swirling jet, the expected upstream displacement of the re-verse flow stream is not detected.

The instantaneous flow field is characterized by the presence ofthe PVC and of the outer helical vortex. 3D measurements allowalso for the visualization of smaller turbulent structures of radialvorticity which are probably responsible of the development of azi-muthal instability of the PVC leading to its further dissipationdownstream. However, the limited spatial resolution does not al-low for a detailed inspection of the interaction between the smallturbulent structures and the PVC.

The application of the snapshot POD analysis to the velocityfield is used to investigate the organization of the large scale flow.The first two POD modes are the most energetics and contain 10.2%and 9.7% for the free and the confined swirling jet, respectively.These modes are representative of the 3D helical vortices, i.e., ofthe PVC, and are located between the ISL and the OSL. Subse-quently, a low order representation of the flow field has been cal-culated based on the first two POD modes. It is found that, usingthe low order reconstruction, the small-scale structures shown inthe instantaneous velocity field are not captured causing a smooth-ing effect, but the PVC and the outer helical vortex are well repre-sented. The results definitely highlight that 3D–3C measurementsare needed for a complete understanding of the turbulent featuresin swirling flows, even though the path towards the application ofTomo-PIV in large Reynolds number experiments is still steep.

G. Ceglia et al. / Experimental Thermal and Fluid Science 52 (2014) 164–173 173

Acknowledgments

The authors kindly acknowledge AVIO Group S.p.A. for provid-ing the swirling injector used in the experiments. The researchleading to these results is supported by the AFDAR project (Ad-vanced Flow Diagnostics for Aeronautical Research) funded bythe European Community’s Seventh Framework Programme (FP7/2007–2013) under Grant Agreement No. 265695.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.expthermflusci.2013.09.007.

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