10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13 Delft, The Netherlands, July 2-4, 2013
Tomographic PIV measurements of the flow at the exit of an aero engine
swirling injector with radial entry
Giuseppe Ceglia1, Stefano Discetti1, Andrea Ianiro1, Dirk Michaelis2, Tommaso Astarita1 and Gennaro Cardone1
1 Dipartimento di Ingegneria Industriale – Sezione Aerospaziale, Università degli studi di Napoli Federico II,
Naples, Italy giuseppe.ceglia@unina.it
2 LaVision GmbH, Goettingen, Germany
ABSTRACT
An investigation of the three-dimensional flow field of a turbulent swirling jet at generated by an aero-engine injector for lean premixing prevaporized burner is carried out with tomographic particle image velocimetry. This work is focused on the organization of the coherent structures arising within the near field of the swirling jet both in free and confined configurations. The confinement causes an increase of the swirl number: the measured values are equal to 0.90 and 1.27, respectively for free and confined swirling jets. The effects of the confinement induce a larger spreading of the swirling jet promoting the enhancement of turbulence at the nozzle exit, but the expected upstream displacement of the reverse flow stream is not observed. The instantaneous flow field is characterized by the presence of the Precessing Vortex Core (PVC), of the outer helical vortex and of smaller turbulent structures developed both in the inner and in the outer shear layer. A three dimensional modal analysis of the velocity field using the Proper Orthogonal Decomposition (POD) highlights that the flow is dominated by the precessing vortex core.
NOMENCLATURE
D Diameter of the swirler, m number of snapshots
second invariant of the velocity gradient, s-2
Re Reynolds number
two-point temporal correlation matrix, m2/s2
S Swirl number
velocity vector, m/s
bulk velocity, m/s
azimuthal velocity component, m/s spatial position vector, m
focal ratio
radial coordinate, m
t time coordinate, s
velocity fluctuation vector, m/s half spreading angle, degrees azimuthal coordinate, degrees
eigenvalue corresponding to -th mode, m2/s2
kinematic viscosity, m2/s
orthonormal basis function of the proper orthogonal decomposition -component of the vorticity, m/s
ABBREVIATIONS
CSMART Camera-Simultaneous Multiplicative Algebraic Reconstruction Technique IRZ Inner Recirculation Zone
ISL Inner Shear Layer
ORZ Outer Recirculation Zone OSL Outer Shear Layer
PIV Particle Image Velocimetry POD Proper Orthogonal Decomposition PVC Precessing Vortex Core
rms Root Mean Square
SMART Simultaneous Multiplicative Algebraic Reconstruction Technique TKE Turbulent Kinetic Energy
INTRODUCTION
Swirling jets are widely used in gas turbine combustors to generate an inner recirculation region near the jet nozzle to promote the flame stabilization [1]. Moreover, swirling flows have demonstrated their capability in reducing the pollutants emissions [2] and improving control of the combustion processes. The presence of a recirculation region near the nozzle exit (commonly referred as vortex breakdown [3]) is a unique feature that characterizes free and confined strongly swirling jets. This phenomenon is characterized by the transition from a jet-like axial velocity profile to a wake-like velocity profile, i.e. with a local minimum on the jet axis. This leads to the presence of a stagnation point on the jet axis itself, followed by a highly turbulent region of reverse flow further downstream. The vortex breakdown occurs when the ratio of the intensity of azimuthal momentum with respect to axial momentum exceeds a certain threshold, leading to strong radial pressure gradients coupled with an adverse axial pressure gradient along the axis of symmetry [3].
Different solutions have been adopted in order to generate a swirling flow. Harvey [4] employed radial swirl vanes in order to deflect the flow passing through a long pipe, Rose [5] made use of a rotating pipe, Chigier and Chervinsky [6] performed experiments using an axial-tangential fluid entry obtaining different degree of swirl. Billant et al. [7] used a hollow cylinder with an inner co-axial cylinder in rotation. Recently, multiple swirler systems in radial configuration are employed in gas turbine combustors [8] to obtain a further improvement of the flame stability and reduction of the emission of pollutants.
The wide application in industrial processes have stimulated many studies to understand the swirling flow organization. The transition of the flow from jet-like to wake-like, inducing the coexistence of inner and outer shear layers, and the concomitant axial and azimuthal shear stresses complicate the flow field, thus imposing a challenge to both numerical and experimental investigations. The main issues in swirl flows are reported in a book and several review papers that describe and summarize all the numerous studies performed in the last 50 years [2, 3, 9]. Recent researches are mainly focused on the study of the unsteady vortical features in swirling jets and of their effect on combustion processes [10, 11, 12, 13]; other studies are focused on the development of numerical modeling tools for swirl flows that are still a challenging application [14, 15].
The swirling flow, under the condition of large swirl, exhibits a helical vortical flow instability, commonly identified as precessing vortex core (PVC) [9] which is intimately associated with the vortex breakdown. The PVC appears as a helical structure and precesses around the axis of symmetry with a frequency proportional to the mass flow rate [3, 9]. The PVC is co-rotating and counter-winding with the mean swirl motion [16]. The intensity of the PVC is stronger at the nozzle exit close to the inner shear layer (ISL) between the jet and the reverse flow region. The PVC extends with decaying intensity up to the boundary of the inner recirculation zone (IRZ) [11, 17]. Additional coherent structures can be found in the outer shear layer (OSL) between the exiting jet and the surrounding ambient. In particular, the PVC is accompanied by a co-precessing vortex related to the convective waves through the inner and outer shear layer [11, 18, 19].
These flow features are significantly influenced by the effects of the confinement. The PVC is characterized by a higher frequency and lower amplitude than that detected in free swirling jets. This effect is caused by the reduced decay of the swirl velocity component along the axis of the chamber [9]. Along with this change, the size and strength of the IRZ increase. The “level” of the confinement is usually quantified with the ratio of the diameter of the confinement chamber and of the diameter of the nozzle exit of the swirl burner. The smaller is this ratio, the more pronounced is the influence of the confinement [9]. In this context, experimental investigations by Syred and Dahman [19] addressed the effects of high level of confinement on the swirling jet: they found that the size of the IRZ can be increased by inserting bluff bodies into or near the exit of the swirl burner. Sheen et al. [20] investigated the flow field pattern in the IRZ behind of the bluff body of a annular swirling jet for both free and confined configuration. Seven different regimes for IRZ are observed, depending on the Reynolds and Swirl numbers: stable flow, vortex shedding, transition, prepenetration, penetration, vortex breakdown and attachment. Schefer et al [21] investigated the effects of the confinement on annular jets for variable blockage ratio (i.e. the ratio of the cross-sectional area of the inner bluff body and the duct). Their
Figure 1 Schematic view of the illumination and imaging setup of the experiments.
results highlight that at high level of the blockage ratio (equal to 0.83) the size of the IRZ increases, promoting the combustion stability processes.
Further experiments are focused on the near field of the swirling jet where different strategies were adopted to reconstruct the three-dimensional (3D) flow features from point-wise and planar measurements. Cala et al. [18] studied the unsteady precessing flow in a swirl burner for a Reynolds number and Swirl number S=1.01. From the analysis of the phase-averaged data, they identified three precessing helical vortex structures classified as primary and secondary structures forming a 3D vortex dipole. Using Proper Orthogonal Decomposition (POD), phase-averaging technique and azimuthal symmetry of the helical structures, Oberleithner et al [17] produced a 3D representation of the helical vortices from uncorrelated 2D snapshots (obtained by Particle Image Velocimetry (PIV) data) in the case of a swirling jet at . The analysis highlighted that the dominant modes are associated with the PVC. Stöhr et al. [11, 12] performed planar PIV measurements along streamwise and crosswise sectional planes in order to investigate the flow features of the swirling flow with the presence of the flame. Following the approach proposed by van Oudheusden et al. [22], the 3D topology of the PVC is reconstructed from phase averaged measurements (the phase extraction is carried out using the first two POD modes, containing the bulk of the energy associated with the periodic PVC motion). The reconstruction of the PVC showed clearly that the evolution of the PVC along the axial direction is coupled with a co-precessing vortex in the OSL.
Even though the POD analysis based on the 2D planar measurements might enable a three-dimensional reconstruction of the periodic coherent structures, it does not allow an accurate description of the intricate instantaneous 3D structures of the turbulent outflow of swirling jets. In the present study, the 3D coherent structures organization of the turbulent swirling flow generated by an aero-engine lean premixing prevaporized burner in isothermal flow conditions is investigated using Tomographic PIV [23]. In particular, the effect of the confinement on both the instantaneous and statistical flow features is addressed. Moreover, a POD analysis is conducted to extract information on the most energetic coherent structures.
EXPERIMENT SETUP AND DATA ANALYSIS Experiments configuration
Tomographic PIV experiments are conducted in a water tank facility. A double radial swirl injector (with exit diameter D equal to 40mm) designed by Avio S.p.A. is installed at the center of the bottom wall of a nonagonal Plexiglas tank (allowing full optical access for both illumination and camera imaging as in [24]) with circumscribed diameter of 16 D and height of 18 D. A schematic view of the experimental setup is shown in Fig. 1.
A stabilized water flow is provided using a centrifugal water pump powered by an inverter and measured by means of a rotameter. Subsequently, the flow passes through a series of grids and honeycomb structures installed within a plenum chamber (with inner diameter equal to 2.5 D and length equal to 10 D) in order to reduce the free-stream turbulence anisotropy. Downstream of the double radial swirl generator, two co-swirling flows pass through a central circular nozzle and a surrounding annular nozzle. The injector is sketched in Fig. 2. A closed-loop circuit is completed by a siphon at the top of the tank, providing water to the centrifugal pump.
Figure 2 Details of the measurement domain and coordinate systems.
The experiments are conducted in two different test conditions: free and confined outflow. In this last case, the swirling jet is confined in a Plexiglas hollow cylinder with inner diameter equal to 3 D. Both the experiments are performed with a flow rate equal to about 2.0kg/s, corresponding to a bulk velocity equal to about 1.6m/s. Consequently, the test Reynolds number is ⁄ , where is the kinematic viscosity coefficient of water (equal to 10-6m2/s
in the present experiments).
Tomographic measurements
Neutrally buoyant polyamide particles with diameter equal to 56µm are homogeneously distributed in order to achieve a uniform concentration approximately of 0.3particles/mm3. The illumination is provided by a double-cavity Gemini PIV
Nd:YAG system (light wavelength equal to 532nm, 200mJ/pulse@15Hz, 5ns pulse duration). The exit beam of about 5mm diameter is shaped into a parallelepiped volume using a three lenses system, i.e. a diverging and a converging spherical lens (with focal length equal to -75mm and 100mm, respectively), and a diverging cylindrical lens (with focal length equal to -50mm); a mask is placed along the laser path in order to set the volume thickness to 46mm and to suppress the tails of the Gaussian beam profile.
The light scattered by the particles is recorded by a tomographic system composed of four LaVision Imager sCMOS 5.5 megapixels cameras (2560 x 2160 pixels resolution, pixel pitch 6.5µm, 16bit intensity resolution). The cameras are equipped with 100mm EX objectives, set at f#=16. Lens-tilt adapters are installed between the image plane and the lens
plane to allow properly focused particle images throughout the volume by achieving the Scheimpflug condition. The particles image density obtained for the chosen illumination and imaging configuration is about of 0.05 particles/pixel. The average magnification in the centre of the measurement volume is approximately 0.1, which corresponds to a spatial resolution of about 18 pixels/mm; the depth of field is of 62mm and particle image diameter is about 3.7 pixels according to the relations reported in [25]. The details of the experimental settings are summarized in Table 1.
Sequences of 500 couples of images are captured with acquisition frequency equal to 10Hz and time separation of 150µs; the time spacing between subsequent couples is large enough to ensure that the samples are statistically independent. The field of view covers a 3.2 x 3.2 D2 area, corresponding to approximately 120 x 120mm2. A schematic
of the measurement domain and coordinate systems is shown in Fig. 2.
For both the experiments the calibration is performed without the presence of the Plexiglas hollow cylinder; this additional difficulty in the case of the confined jet is due to physical access restrictions. An optical calibration procedure is performed using a double/plane target imaged at 5 Z-locations covering the entire measurement domain (±23mm). The 3D mapping functions are generated using a 3rd order polynomial function in X and Y, and 2nd order in Z with a root
mean square (rms) calibration error equal to about 0.3 pixels. For the free case, the calibration error is reduced up to 0.05 pixels by means of the volume self-calibration technique proposed in [26].
TOMO PIV
Seeding particles Diameter [µm] Concentration [particles/mm3]
56 0.3
Volume illumination Thickness [mm] 46
Recording devices 4 LaVision Imager sCMOS (2560 x 2160pixels@10Hz) Optical arrangement EX objectives (focal lenght [mm], f#) 100, 16
Field of view [D2] 3.4x3.4
Magnification 0.1
Acquisition frequency [Hz] 10
Pulse separation [µs] 150
Number of recordings 500
Table 1 Experimental parameters.
For the experiment in confined conditions it is needed to correct the mapping functions reducing the effect of the optical distortions across the interface between the working fluid and the hollow cylinder. Despite of the very similar values of the refraction index of water and Plexiglas, the optical distortions can cause significant errors (up to about 3 pixels near the tube walls) since the viewing angle on the cylinder surface varies across the image. The corrections are obtained through ensemble average on 200 images in order to get well-converged statistics. After the self-calibration procedure, the rms of calibration error is reduced up to 0.07 pixels.
The background intensity on the raw images is eliminated by subtracting the historical minimum based on the acquired sequence of 500 images. Subsequently, the residual background (for example induced by fluctuations of the laser light intensity or of the seeding concentration) is removed applying a sliding minimum subtraction over a kernel of 31 x 31 pixels in space and using 5 samples in time. The volumetric light intensity reconstruction is performed combining the MLOS technique with the CSMART algorithm (10 iterations) by LaVision software Davis 8. The algorithm CSMART is similar to the SMART technique implemented in [27, 28], with the basic difference in the update process, involving each camera separately. The illuminated volume of 3.2 x 3.2 x 1.2 D3 (i.e. 130 x 130 x 46mm3) is discretized with 2298
x 2298 x 1004 voxels (i.e. 18vox/mm). The reconstruction quality is improved by filtering the reconstructed distributions in between each iteration using a Gaussian filter [29].
The accuracy of the reconstruction is assessed a-posteriori by computing the sum of the intensity of the reconstructed particles on X-Y planes. The ratio of the intensity of the reconstructed particles (true and ghost) in the illuminated domain and the ghost particles intensity in the immediate surrounding domain gives a signal to noise ratio 2, that is generally considered a value acceptable for three dimensional velocity measurements.
The 3D particle field motion is computed with the LaVision software Davis 8 software; the interrogation algorithm is based on a direct sparse cross-correlation approach, as proposed in [30]. The final interrogation volume is of 64 x 64 x 64 voxels (3.5 x 3.5 x 3.5mm3) with an overlap between adjacent interrogation boxes of 75%, leading to a vector pitch
of 0.8mm. The measurement uncertainty can be evaluated considering physical criteria, for example the local mass conservation in the incompressible regime. The standard deviation of the divergence computed on raw data is about 7% of the typical value of the vorticity magnitude within the shear layer (0.24 voxels/voxel, equivalent to 1.6 x 103s-1). Proper Orthogonal Decomposition implementation
The POD [31] is a mathematical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables referred as principal components. POD provides an “energy-efficient” decomposition, i.e. the principal components are sorted in terms of their contribution to the total energy; for the case of turbulent flows, the POD modes highlight the most relevant contributions to the total turbulent kinetic energy.
In this section the POD analysis based on the method of snapshots is briefly introduce in order to fix the notation (for a more rigorous formulation see [32]).
Figure 3 Iso-contours with velocity vectors of the mean velocity maps ̅̅̅ ⁄ on the plane Z/D=0 and iso-surface of axial mean velocity ̅ ⁄ for the free swirling jet (a) and the confined swirling jet (b).
The starting point is a set of N uncorrelated and statistically independent velocity fields ( ) (where is the spatial position vector, and t is the time coordinate), decomposed into a temporal average part ( )̅̅̅̅̅̅̅̅̅ (the overbar indicates the operation of time-averaging) and a fluctuating part ( ):
( ) ( ) ( ) (1)
The POD identifies a set of N orthonormal basis function ( ), which is optimal in the least square sense in approximating the fluctuating velocity field, so that, by finding a proper set of time coefficients , it results: ( )≈∑ ( ) (2)
In the formulation of the snapshot method [32] the POD modes are the eigenmodes of the two-point temporal correlation matrix ( ) ( ) . The corresponding eigenvalues are representative of the energy associated with the modes ( ). In the case of shedding or quasi-periodic phenomena, phase information can be inferred using a relatively low number of POD modes [22, 33, 34].
RESULTS AND DISCUSSION Statistical analysis
In Fig. 3a and 3b, the average velocity field of the free and confined swirling jets, is depicted by the iso-contours of ̅ ⁄ on the plane (in this plane the vector representation of the ̅ ⁄ and ̅ ⁄ components is also reported) and by the iso-surfaces of the axial mean velocity ̅ ⁄ .
For both cases, the sudden expansion of the flow at the nozzle exit induces strong velocity gradients that determine the presence of an ISL and an OSL, as reported in [11, 12]. High values of ̅ ⁄ are detected near the nozzle exit, in agreement with the observations of Stöhr el al. [11]. A cone-shaped reverse flow stream, extending from the nozzle exit along the axial direction, is formed, promoting the formation of an IRZ [3, 9, 11].
The confinement dramatically alters the size and shape of IRZ [9] (see Fig.3b). In particular, the increased size of the IRZ is testified by the wider shape of the iso-surface of the negative axial velocity at the nozzle exit. Furthermore, an Outer Recirculation Zone (ORZ) is formed between the OSL and the wall of the chamber due to the step-like geometry that the jet encounters when expands at the nozzle exit. In this condition, the flow undergoes the effect of a radial pressure gradient due to the presence of the wall, promoting the Coanda effect [35].
In order to estimate the effects induced by the confinement, the half spreading angle α of the swirling jet, defined as the angle between the line joining the half-maximum axial velocity (in the outer shear layer) and the line parallel to the axis of symmetry [16], is measured. For the case of the free swirling jet the measured half spreading angle is approximately 18°, while in presence of confinement α is about 36°, i.e. two times larger. Along with this different pattern, a larger swirl number is expected in this latter case. The swirl number is evaluated on the measured average flow fields using the equation proposed in [36]:
∫
Figure 4 Iso-contour of on planes and for the free swirling jet (a) and the confined swirling jet (b).
where and r are the azimuthal mean velocity component and the radial coordinate, respectively. It is worth to note that the swirl numbers for the free and confined swirling jets are equal to 0.90 and 1.27, respectively. Such an increase of the value of the swirl number due to the confinement clearly reflects in the higher spreading angle (in agreement with Liang and Maxworthy [16]) but, interestingly enough, it does not cause the expected upstream displacement of the reverse flow region.
In Fig. 4a and 4b, the normalized Turbulent Kinetic Energy ( ) is shown for both the free and the confined configuration, respectively. The TKE is defined as:
̅̅̅̅̅̅ ̅̅̅̅̅̅ ̅̅̅̅̅̅̅ (4)
Local maxima of the TKE are achieved within the shear layers (ISL and OSL), while a relatively low level of turbulence occurs in the neighborhood of the jet axis, i.e. in the IRZ. The confinement determines a higher TKE at the nozzle exit with respect to the case of the free jet, but a lower TKE in the jet axis. In the horizontal slice presented in Fig. 4 (i.e. the plane ), the ISL and OSL of the jet are well discerned; further downstream the two shear layers tend to merge because of diffusion. The merging occurs at approximately equal to 0.44 and 0.30 for the free and confined swirling jet, respectively; the abscissa of merging moves upstream in presence of the confinement due to the improved turbulent mixing in proximity of the nozzle exit.
Figure 5 Profiles of the average velocity components for free swirling jet (a,b,c) and confined swirling jet (d,e,f) at ⁄ . ⁄ , ● ⁄ , ▲ ⁄ . Symbols are placed each 3 measured vectors.
In Fig. 5 the profiles of the mean velocity components are reported for the free and confined cases at three longitudinal locations (i.e. ⁄ ). For both cases, at ⁄ the profile of the axial velocity component ⁄ is wake-like, i.e. two local maxima are detected while the velocity is nearly zero in proximity of the jet axis. For the free case (Fig. 5a), the profile of the ⁄ component is characterized by the presence of four local peaks, which are due to the combination of the swirling flow issuing from the circular and annular nozzles. On the other hand, for the confined case (Fig. 5d) the internal peaks disappear and the profile exhibits two inflection points. A similar behavior is detected for the axial mean velocity profile ⁄ . For the free case, the stagnation point is located on the axis of symmetry of the jet at ⁄ (Fig. 5a), whereas at the same position the confined swirling flow exhibits a weak positive axial mean velocity value (Fig. 5d) and the stagnation point is located further downstream from the nozzle exit.
Figure 6 Radial profiles of the rms of the normalized turbulent fluctuations for free swirling jet (a,b,c) and confined swirling jet (d,e,f) at ⁄ . √ ̅̅̅̅̅ ⁄ ● √ ̅̅̅̅̅ ⁄ ▲ √ ̅̅̅̅̅̅̅ ⁄ . Symbols are placed each 3
measured vectors.
The intensity of the ̅ ⁄ profiles (that is the radial velocity component for the considered profile) is weaker than that of the other components for both the free and the confined configurations. Moving downstream, the decay of ̅ ⁄ is lower for the confined swirling jet, in particular at ⁄ the values of the peaks of the ̅ ⁄ profile are of the same order of the normalized swirling velocity component ̅ ⁄ . In Fig. 5d-e-f, the effects of the entrainment induced by the ORZ are testified by a non-zero values of the velocity components in the region between the OSL and the wall.
The normalized root mean square of the velocity fluctuations (√ ̅̅̅̅̅̅ , √ ̅̅̅̅̅ and √ ̅̅̅̅̅̅ ) are depicted in Fig. 6. The turbulence intensity is larger in correspondence of the ISL and OSL regions. Even though the √ ̅̅̅̅̅ and √ ̅̅̅̅̅ decrease with a local minimum on the jet axis, as reported in [10], √ ̅̅̅̅̅̅ reaches an additional local maximum value of 0.60 and 0.56 for the free and confined swirling jets, respectively.
Moving downstream, the effect of the vortex breakdown determines a rapid decay of the intensity of the turbulent fluctuations on the jet axis due to the improved mixing and turbulent dissipation. At (Fig. 6c and 6f), the maximum values of the normalized velocity fluctuations are achieved much further away from the jet axis for the confined case than for the free case. This behavior is due to the spreading of the swirling jet that influences the shape of the IRZ.
Even though the ̅ ⁄ component is weak compared to the other velocity components (Fig. 5), the relatively high level of √ ̅̅̅̅̅̅ indicates a fully 3D flow field in the ISL and OSL (Fig. 6) with a complex cross-talk between the principal directions of the turbulent fluctuations.
Figure 7 Instantaneous velocity field for the free (a) and the confined (b) swirling jet. Vortex visualization using Q criterion (red) and iso-surfaces =12 (blue).
Instantaneous velocity field topology
The instantaneous organization of the flow field is illustrated in two snapshots depicted in Figs. 7a and 7b. The vector representation of the ⁄ and ⁄ components on the plane ⁄ shows a zig-zag pattern extending along the axial direction for the free swirling jet, in agreement with [11]. On the other hand, for the confined swirling jet a quiescent flow with a weak large recirculation region is detected beyond ⁄ .
Iso-surfaces of positive Q (shown in red) reveal the presence of a 3D helical coherent structure, i.e. the PVC [9]. Coupled with the PVC also an outer helical vortex is visualized in the outer shear layer. Moreover the flow field is characterized also by the presence of smaller turbulent structures evidenced by the normalized radial vorticity shown in blue in Fig. 7.
These structures determine the azimuthal instability of the helical vortex before his breakup about 0.8 D and 0.5 D downstream of the nozzle exit for the free and confined case, respectively.
The presence of these complex vortical structures clearly explains the strong three dimensional turbulent features presented in Fig. 7.
Figure 8 Energy distribution of the normalized eigenmodes for the first 10 modes for ○ free and ∆ confined swirling jet.
POD analysis
The unsteady organization of the turbulent swirling flow is analyzed by means of the POD analysis. The distribution of the energy of the POD modes, obtained as the ratio between each eigenvalue and the sum of the entire set of eigenvalues, is illustrated in Fig.8. The energy distributions across the first 10 modes highlight that the first two modes constitute the most relevant contribution for both cases, in agreement with literature [11, 12]. For the free case, mode #1 and #2 contribute for the 5.2% and 5.0% of the total TKE. For the confined case, the first pair of modes are slightly less energetic (4.9% and 4.8%, respectively); this slightly larger spreading of the energy over the set of modes may be due to the enhanced mixing effects induced by the simultaneous presence of the IRZ and the ORZ. Interesting enough all the other smaller turbulent features represent the 90% of the TKE.
The first mode is depicted in Fig. 9a and 9b for the free and confined swirling jet, respectively. The iso-surfaces of positive Q color-coded with ⁄ (where is the azimuthal component of the vorticity) and the contour of ⁄ and the vector representation of the ̅ ⁄ and ̅ ⁄ components are blanked by imposing the ⁄ 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, that are phase shifted of π/2 on the crosswise plane and extend up to 0.9 D along the jet axis from the nozzle exit. A detailed inspection of the ⁄ contour reveals the presence of the outer helical vortices, placed in the OSL, that are statistically correlated with the PVC helix [11].
CONCLUSIONS
The 3D organization of the flow structures of a free and a confined swirling jet issuing at from a double swirler aero-engine lean premixing prevaporized burner has been investigated by means of tomographic PIV. The vortex topological analysis using Q criterion shows different organization of the large-scale coherent structures between the free and confined configuration.
In both cases, the flow field is dominated by the presence of the vortex breakdown, leading to a cone-shaped stream wrapped around 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 a more intense mixing. The spreading angle of the confined swirling jet is about two times larger than for the free swirling jet, promoting 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 confined swirling jet are equal to 0.90 and 1.27, respectively. Even though the effects of the confinement induce a larger spreading of the swirling jet, the expected upstream displacement of the reverse flow stream is not detected.
The instantaneous flow field is characterized by the presence of the PVC the outer helical vortex and the smaller turbulent structures of radial vorticity. The PVC is characterized by azimuthal waves before his breakdown.
The application of the snapshot POD analysis to the velocity field 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. of the PVC, and are located between the ISL and the OSL. The results definitely highlight that 3D-3C measurements are needed for a complete understanding of the turbulent features in swirling flows.
Figure 9 First POD mode describing the coherent streamwise development of PVC helix for the free (a) and confined (b) swirling jet. Iso-surface of positive Q color-coded with ⁄ . Contour of ⁄ with velocity
vectors at plane ⁄ blanked by imposing the ⁄ constraint.
ACKNOWLEDGEMENTS
The authors kindly acknowledge LaVision GmbH for contributing the tomographic hardware the cameras used in the experiments and AVIO Group S.p.A. for the design of the swirling injector. The research leading to these results is supported by the AFDAR project (Advanced Flow Diagnostics for Aeronautical Research) funded by the European Community’s Seventh Framework programme (FP7/2007-2013) under grant agreement no 265695.
REFERENCES
[1] Lilley DG “Swirl flows in combustion: a review” AIAA J. 15 (1977) pp. 1063–1078.
[2] Gupta AK, Lilley DG and Syred N “Swirl Flows” Abacus Press, Tunbridge Wells, Kent, England, 1984. [3] Lucca-Negro O and Doherty TO’ “Vortex breakdown: a review” Prog. Energ. Combust. 27 (2001) pp. 431–481. [4] Harvey JK “Some observations of the vortex breakdown phenomenon” J. Fluid Mech. 14 (1962) pp. 585–592.
[6] Chigier NA and Chervinsky A “Experimental investigation of swirling vortex motion in jets” J. Appl. Mech.-T. ASME 34 (1967) pp. 443–451.
[7] Billant P, Chomaz JM and Huerre P “Experimental study of vortex breakdown in swirling jets” J. Fluid Mech. 376 (1998) pp. 183–219. [8] Huang Y and Yang V “Dynamics and stability of lean-premixed swirl-stabilized combustion” Prog. Energ. Combust. 35 (2009) pp. 293–
364.
[9] Syred N “A review of oscillation mechanisms and the role of the precessing vortex core (PVC) in swirl combustion systems” Prog. Energ. Combust. 32 (2006) pp. 93–161.
[10] Moeck JP, Bourgouin JF, Durox D, Schuller T and Candel S “Nonlinear interaction between a precessing vortex core and acoustic oscillations in a turbulent swirling flame” Combust. Flame 159 (2012) pp. 2650–2668.
[11] Stöhr M, Sadanandan R and Meier W “Phase-resolved characterization of vortex-flame interaction in a turbulent swirl flame” Exp. Fluids 51 (2011) pp. 1153–1167.
[12] Stöhr M, Boxx I, Carter CD and Meier W “Experimental study of vortex-flame interaction in a gas turbine model combustor” Combust. Flame 159 (2012) pp. 2636–2649.
[13] Fröhlich J, García-Villalba M and Rodi W “Scalar mixing and large-scale coherent structures in a turbulent swirling jet” Flow, Turbulence Combust. 80 (2008) pp. 47–59.
[14] García-Villalba M, Fröhlich J and Rodi W “Identification and analysis of coherent structures in the near field of a turbulent unconfined annular swirling jet using large eddy simulation” Phys. Fluids 18 (2006) pp. 055103.
[15] Roux S, Lartigue G, Poinsot T, Meier U and Bérat C “Studies of mean and unsteady flow in a swirled combustor using experiments, acoustic analysis, and Large Eddy Simulations” Combust. Flame 141 (2005) pp. 40–54.
[16] Liang H and Maxworthy T “An experimental investigation of swirling jets” J. Fluid Mech. 525 (2005) pp. 115–159.
[17] Oberleithner K, Sieber M, Nayeri CN, Paschereit CO, Petz C, Hege HC and Wygnanski I “Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction” J. Fluid Mech. 679 (2011) pp. 383–414. [18] Cala CE, Fernandes EC, Heitor MV and Shtork SI “Coherent structures in unsteady swirling jet flow” Exp. Fluids 40 (2006) pp. 267–
276.
[19] Syred N and Dahman KR “Effect of high levels of confinement upon the aerodynamics of swirl burners” J. Energy 2 (1978) pp. 8–15. [20] Sheen HJ, Chen WJ and Jeng SY “Recirculation zones of unconfined and confined annular swirling jets” AIAA J. 34 (1996) pp. 572–
579.
[21] Schefer RW, Namazian M, Kelly J and Perrin M “Effect of Confinement on Bluff-Body Burner Recirculation Zone Characteristics and Flame Stability” Combust. Sci. Technol. 120 (1996) pp. 185–211.
[22] van Oudheusden BW, Scarano F and van Hinsberg NP, Watt DW “Phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence” Exp. Fluids 39 (2005) pp. 86–98.
[23] Scarano F “Tomographic PIV: principles and practice” Meas. Sci. Technol. 24 (2013) pp. 012001.
[24] Violato D, Ianiro A, Cardone G and Scarano F “Three-dimensional vortex dynamics and convective heat transfer in circular and chevron impinging jets” Int. J. Heat Fluid Fl. 37 (2012) pp. 22–36.
[25] Adrian RJ and Westerweel J “Particle Image Velocimetry” Cambridge University Press (2010).
[26] Wieneke B “Volume self-calibration for 3D particle image velocimetry” Exp. Fluids 45 (2008) pp. 549–556.
[27] Atkinson C and Soria J “An efficient simultaneous reconstruction technique for tomographic particle image velocimetry” Exp. Fluids 47 (2009) pp. 553–568.
[28] Mishra D, Muralidhar K and Munshi P “A robust mart algorithm for tomographic applications” Numer. Heat Tr. B-Fund. 35 (1999) pp. 485–506.
[29] Discetti S, Natale A and Astarita T “Spatial Filtering Improved Tomographic PIV” Exp. Fluids 54 (2013) pp. 1505–1517. [30] Discetti S and Astarita T “Fast 3D PIV with direct sparse cross-correlation” Exp. Fluids 53 (2012) pp. 1437–1451.
[31] Sirovich L “Turbulence and the dynamics of coherent structures. Part 1: Coherent structures” Q. Appl. Math. 45 (1987) pp. 561–571. [32] Berkooz G, Philip H and Lumley JL “The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows” Annu. Rev. Fluid
[33] Legrand M, Nogueira J and Lecuona A “Flow temporal reconstruction from non-time-resolved data part I: mathematic fundamentals” Exp. Fluids 51 (2011) pp. 1047–1055.
[34] Legrand M, Nogueira J, Tachibana S, Lecuona A and Nauri S “Flow temporal reconstruction from non time-resolved data part II: practical implementation, methodology validation, and applications” Exp. Fluids 51 (2011) pp. 861–870.
[35] Wille R and Fernholz H “Report on the first European Mechanics Colloquium, on the Coanda effect” J. Fluid Mech. 23 (1965) pp. 801– 819.
