Tomographic PIV measurements in a swirling jet flow

10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13 Delft, The Netherlands, July 1-3, 2013

Tomographic PIV measurements in a swirling jet flow

1

Kutateladze Institute of Thermophysics, Siberian Branch of Russian Academy of Sciences, 1 Lavrentyev Avenue, 630090, Novosibirsk, Russia

*dmark@itp.nsc.ru 2

Department of Physics, Novosibirsk State University, 2 Pirogova Street, 630090 Novosibirsk, Russia

ABSTRACT

The present work is devoted to the application of the Tomographic PIV technique to study coherent structures in a swirling turbulent jet. The aim of the paper is to study the possibilities of caring out tomographic PIV measurements with the large depth of a volume configuration in the swirling jet setup. It is recognized that an extension of the Tomo PIV technique to a large depth of view along light deficiency gives a set of problems linked with the optical opacity limit, the uncertainty of reconstruction by few projections and the increasing of the ghost particles number. Thus, the paper reports results of comparative study of the mean flow characteristics by Tomo PIV and Stereo PIV. The measurements were carried out by Tomo PIV and Stereo PIV techniques for the same object and under the same experimental conditions.

From the analysis of the obtained results, the volumetric to planar comparison showed acceptable correspondence through all common measurement points for mean velocity and satisfactory correspondence of the velocity fluctuations intensity. The comparison of coherent structures detected by proper orthogonal decomposition (POD) analysis of 3D velocity distributions with large-scale vortices in a set of the instantaneous velocity fields with the decent spatial resolution (1.5 mm) was performed. The instantaneous data revealed the presence of the double vortex helix at the inner shear layer and appearance of an additional secondary helical vortex in the outer mixing layer. The phase-averaged vortex structure from POD data resolves only one vortex helix in the outer shear layer and a thick screw or drill like structure at the axis of the jet without resolving distinct double helix of vortex filaments, detected in the instant 3D velocity distributions.

1. INTRODUCTION

The study is devoted to comparative application of tomographic and stereoscopic PIV to a swirling jet flow with breakdown of vortex core. With vortex breakdown and appearance of the central recirculation zone, the jet flow represents an annular swirling jet with strong gradient of the axial and azimuthal velocity. Usually, because of a high swirl, the global flow instability [1] results in a pair of the most powerful coherent structures, viz., precessing vortex core and secondary vortex helix induced in the outer mixing layer. These structures are resolved with planar PIV technique by using a phase-averaging or proper orthogonal decomposition. Among these vortices, intensive eddies of smaller size are formed (in the present paper turbulent swirling jet flow with Re = 30 000 was studied). Such vortices are important, since they affect mixing and flame quenching in swirl combustors.

At the moment, the spatial resolution of small-scale vortex structures in Tomo PIV method is two times lower than that of the planar analogues PIV and Stereo PIV. This is caused by a number of reasons, including imperfection of the known methods of tomographic 3D reconstruction over a limited number of projections. A reconstructed volume contains a certain amount of non-physical reconstruction artifacts or ghost particles [2]. These ghost particles increase the noise level when evaluating velocity in a measurement domain, particularly for large depth volumes where the particle concentration on projections is high. From an analysis of the literature it was found that the maximum measurement depth using Tomo PIV up to now does not exceed 40-50 mm [3], [4], [5]. It should be noted that recently proposed effective algorithm MTE MART (Motion Tracking Enhanced MART) can increase the accuracy of the reconstruction by suppressing the intensity of ghost particles [6]. The principle of the algorithm is based on the assumption that there is no correlation between the registered ghost particles at different times.

In the literature there are only a few studies on a swirling jet by using Tomo PIV technique. In the paper [7], [8] authors provided measurements in swirling impinging jets at five different swirl numbers, including zero. An impingent plate was located at two calibers from the nozzle exit, D = 19.7 mm. The volume depth was equal to 1.2 D Three-dimensional flow structures that formed at Re = 10,000 were studied. Registration of the measurement volume was performed by three 4-megapixel high-speed cameras at a frame rate equal to 500 Hz. The cameras observed the measurement area from the top cover of the test rig. It was shown that the helical swirl generator produces the flow

reversal region in the center of the jet and instantaneous velocity fields have ring vortices that after impingement breakup into smaller structures. Also swirling jets were characterized by higher turbulence levels in the jet core.

Next work [5] concerns an application of the tomographic PIV technique for diagnostics of the swirled jet flow created in a model of an engine injector. The large depth of the measurement volume equal to the nozzle diameter D = 40 mm and the Reynolds number was equal to 60,000. The presence of helical vortices and a pronounced recirculation zone were cased by the vortex breakdown phenomenon at the exit of the nozzle.

And finally the studies [8], [9] of the swirling flow past a sudden expansion were devoted to analysis of the turbulent jet flow at Re = 150,000 issued from the 20 mm nozzle into a transparent tube with inner diameter D = 100 mm. The depth of the volume was chosen equal to D/4. Several features were found for the swirled jet: presence of the precessing jet mode which exists even for the low swirl rate and self activated precession in the case of no swirl, the jet attachment to the inner tube wall. The precessing motion with frequency near to 1 Hz was resolved in time by 10 Hz registration rate of the system. Analysis of the dominating flow structures was performed by POD technique. It was shown that the most energetic modes determined by the precession motion.

The purpose of the present paper is to analyze the spatial 3D structure of large eddies in a turbulent swirling jet flow. The Reynolds of the flow was chosen be 30 000 to provide data relevant for validation of CFD codes used simulation of unsteady turbulent flows. The question addressed in the study is the ability Tomo PIV technique to resolve features of such complex turbulent flow. This was tested by coupled planar Stereo PIV measurements at the center plane of jet and comparison of the statistical characteristics of velocity. The aim is also to study the possibility of using Tomo PIV method for measuring the volume with increased depth up to 40 mm. This depth was necessary for the diagnostics of a swirling jet in order to extract full (not clipped) flow structure. Expanding the field of application of Tomo PIV on volumes with the larger measurement depth along with the lack of light there is a lot of problems associated with the limit of optical transparency and low accuracy of the reconstruction over the limited number of projections due to the increase in the number of ghost particles affecting the quality of obtained velocity distributions.

EXPERIMENTAL SETUP

(a) (b)

Working section top view

Camera observation direction -45 -15 15 45 Calibration and plane position laser sheet Volume illumination area 2.5D Reconstruction area Z X D

Figure 1 Photograph of the experimental setup (a), the scheme of the measurement section from top view (b)

The experimental setup represented a hydrodynamic loop equipped with a pump, flowmeter and temperature stabilizing device. Average flow rate was maintained constant by means of the pump with feedback from the flow meter. All

measurements were carried out in a Plexiglass rectangular working section with the size of 200×200×400 mm3_{. The}

object of research is a circular turbulent jet formed by a nozzle with a diameter D = 15 mm. A swirl generator, same as that used in [10], [11], produced the strongly swirling flow. The swirl rate was S = 1 (see [10] for definition). Reynolds number defined on a basis of a bulk velocity Vb = 1.7 m/s and diameter D of the nozzle was equal to 30,000.

The flow was seeded by 50 µm polyamide particles. The concentration of the particles on the projections in

three-dimensional and planar measurements Nppp were equal to 0.063 ppp and 0.047 ppp correspondingly or Ns = 0.45 and Ns = 0.33 in terms of a source density. An average particle diameter on projections was near 3 px (M0 = 0.17, f# = 16). The registered particle concentration in the measurement area was controlled by particle identification procedure based on the particle mask correlation method [12], [13] . The particle volume concentration was assessed from Nppp and

equaled to C ~ 1.13 particles per mm3_{. Prior to the planar PIV measurements the volumetric concentration was}

increased by adding more particles.

The measurement volume with the size of 2.5D×4D×2.5D was recorded by four low speed 4 Mpx CCD cameras with the pixel size of 7.4 um and operated at 1 Hz. Cameras were arranged in a single horizontal plane (see Fig. 1). For illumination a pulsed dual Nd:YAG laser with 70 mJ per pulse was utilized and operated with ∆t = 120 us between the pulses. At first tomographic measurements were done, and after that the test stereoscopic PIV recording was performed

for the same object under the same experimental conditions. Switching from volumetric measurements to planar one was done by changing geometry of the illumination area. Laser sheet thickness for Stereo PIV technique was near to 1 mm. The position of the cameras and their focus remained unchanged; therefore, the same calibration data was utilized for both experiments.

Camera calibration was performed by a plane calibration target 80x80 mm with reference circles on the Cartesian grid and a 3 mm step between the circles. The target was moved by 25 mm in depth by the traverse equipped with a micrometer actuator. Experiment management and data processing was carried out by home-made software ActualFlow with the volumetric processing extension [14].

DATA PROCESSING

Tomo PIV experimental data were processed by hybrid CPU-GPU realizations of the processing algorithms including SMART and MTE. The server station with 2x16 AMD Opteron processors 6274, 2200 MHz (32 cores in total) with the graphics processor NVIDIA Tesla C2075 was used for the calculations.

Self-calibration procedure was done to align all camera models directly by final experimental particle images to get perfect multiple ray correspondence throughout the measurement volume. The maximum disparity was obtained at the level of four pixels. The residual disparity after three iterations of self-calibration procedure was below 0.2 pixels. Correction of a misalignment of the calibration target and the laser sheet was performed for stereoscopic measurements as well. Normal-to-measurement plane shift of the order of one millimeter was corrected.

Also the recorded projections were preprocessed by subtracting the median statistical intensity by 11x11 pixel stencil that was separately calculated for each view. This type of the image filter was use in order to get bigger zero intensity domains in the projections to reduce particle streaks along the pixel LOS in xz planes and to suppress the ghost particles formation.

The number of vectors in 3D velocity field was 54×41×54, with a resolution of 1.5 mm for a single velocity vector. The reconstructed volume was sampled at 1100×850×1100 voxels. The level of the sampling in the horizontal and vertical directions was determined by the near equal sampling rate of a volume and a projection, the preferred size of the volume in mm and the available 4.2 GB memory to run on the GPU device. The size of the cubic voxel was set equal to

0.036 mm. The chosen final size of the interrogation domain was 403 _{voxels with 50% overlap factor.}

RESULTS AND DISCATION

In this paper the comparison of the results obtained by comprehensively tested and widely accepted nowadays Stereo PIV technique [15] with the tomographic results to assess the quality of the volumetric measurements in a swirling turbulent flow. This kind of flow becomes a popular object for Tomo PIV application as it has an inherent complex structure and also used in various technical devices.

Figure 2 shows the comparison of the results of assessment the mean velocity spatial distributions in the central vertical plane of the jet by the tomogarphic (in the left column) and the reference stereoscopic (in the right column) PIV technique. The mean velocity distributions appear to be quite similar except that Tomo PIV data are noisier than reference data because of lower statistics since MTE processing takes much time and due to a lower accuracy of the tomographic measurements per se. The shift of the laser sheet plane position towards positive z values was observed inspecting the nonzero radial velocity component at the center of the recirculation bubble. Comparison of the velocity fluctuations intensity by the normalized square root of the turbulent kinetic energy (includes all three measured velocity components) spatial distribution in the center plane gives less similarity than the mean velocity due to less statistics and lower accuracy of tomographic measurements. The maximum velocity fluctuation near the nozzle is rather high and corresponds to 60% of the bulk velocity.

The impact of the velocity gradients on the degradation of the estimated velocities near the nozzle was investigated. Figure 3 shows profiles of the gradient of the mean displacements at the distance y/D = 0.25 from the nozzle. Gradient maximum values for mean velocities reach 0.05 mm/mm (see Figure 3); however, as it was observed for instantaneous fields, gradient of the instantaneous displacement was up to 0.15 mm/mm. This is near to ~0.2 mm (±0.1 mm) displacement difference within an interrogation volume (IV of 1.5 mm in size) with maximum displacement by “one quarter rule” [16] equal to 0.375 mm. The detected signal peak can be biased due to peak broadening and multiple peak generation in case of a strong displacement gradient.

In the book [16] the model dependency of the displacement error on the displacement gradient value was presented. For the maximum gradient 0.15 pixel/pixel the uncertainty reached 1 px. Therefore the gradients in the crosswise direction of the flow near the nozzle are rather extreme and a local region with the small displacement values surrounded by higher velocity values, like the recirculation zone, can be easily smoothed out. This effect is demonstrated in Figure 2-a. The detected mean shape of the recirculation bubble is spheroid with the lateral size near to 0.5D and the center at 0.75D for Re = 30,000, S = 1. Booth planar and volumetric data show that the recirculation zone extends into the nozzle by its bottom part.

(a) x/D y/ D -1 -0.5 0 0.5 1 0 0.5 1 1.5 2 Vy/Vb 0.80 0.69 0.58 0.47 0.36 0.25 0.15 0.04 -0.07 -0.18 -0.29 -0.40 (b) x/D y/ D -1 -0.5 0 0.5 1 0 0.5 1 1.5 2 (c) x/D y/ D -1 -0.5 0 0.5 1 0 0.5 1 1.5 2 Vz/Vb 0.70 0.57 0.45 0.32 0.19 0.06 -0.06 -0.19 -0.32 -0.45 -0.57 -0.70 (d) x/D y/ D -1 -0.5 0 0.5 1 0 0.5 1 1.5 2 e) x/D y /D -1 -0.5 0 0.5 1 0 0.5 1 1.5 2 (TKE^0.5)/Vb 0.60 0.55 0.49 0.44 0.38 0.33 0.27 0.22 0.16 0.11 0.05 0.00 f) x/D y/ D -1 -0.5 0 0.5 1 0 0.5 1 1.5 2

Figure 2 Comparison of the mean axial velocity component (a)-(b); the mean azimuthal velocity component (c)-(d) and

normalized square root of the turbulent kinetic energy (TKE) (e)-(f) distributions at the central plane obtained by Tomo PIV (left column) and Stereo PIV (right column) techniques for the swirling turbulent jet for S = 1, Re = 30,000. Statistics is calculated through 100 and 350 velocity snapshots for Tomo and Stere PIV, correspondingly

Next valuable parameter is a signal to noise ratio (SNR) which depends upon the number of true particles inside IV (NI) and the ghost to actual particle fraction. The average number of particles per IV was NI = 5 and estimation of the ghost fraction gives Ng/Np = 26 times (M0 = 0.17, f# = 16) according to [8] for four camera measurement system and current source density. Also using this estimation it can be shown that eight cameras are needed to decrease the ghost factor to unity for the current Nppp and fixed other parameters. The current IV size is the compromise between low SNR and high velocity gradients in the flow.

(a) x [mm] D y [m m/ dt ], dD y /dx [1 /d t] -15 -10 -5 0 5 10 15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 (b) x [mm] D z [m m/ dt ], dD z /dx [1 /d t] -15 -10 -5 0 5 10 15 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Figure 3 Mean profiles of the axial (a) and azimuthal (b) displacements (square symbols, data is in mm per time delay

∆t) in the central plane at y/D = 0.25 of Stereo PIV data. Gradient profiles of the mean axial and azimuthal displacements are shown by triangles.

Figure 4 presents the mean velocity distribution in 3D plots. The iso-surface of the axial velocity at Vy/Vb = -0.1 on the left and the closed streamlines on the right corresponds to the recirculation zone. The helical streamlines demonstrates the swirl effect on the mean jet flow.

(a) (b)

Figure 4 Vector field for the normalized mean velocity with the iso-surface Vy/Vb = -0.1 in the recirculation zone (a);

the mean axial velocity distribution at the section y/D = 0.6 and examples of streamlines (b) for the swirling turbulent jet S = 1, Re = 30,000

In general, the accuracy of the velocity estimation in the studied swirling jet can be expressed as follows. The half-width of symmetric distributions with respect to zero transverse displacement components vx and vz was about 10 voxels. The PDF of the longitudinal component of the particle displacement vy was asymmetric and shifted to positive values with an average of 1.3 voxel, the typical positive values in the jet core about 5 voxels and negative values in the center of the recirculation zone are near to -1.5 voxel. Since the typical value of the absolute instantaneous displacement estimation error is about 0.3 voxel, the minimum relative velocity error of the rate in areas with large displacements was 6%, and the error of the longitudinal component of an instantaneous velocity at the axis of the jet, where there is a reverse flow can be evaluated equal to 20%.

In order to reduce the error amplification during the calculation of the derivatives by the estimated velocity distributions, the original velocity fields were smoothed by the isotropic Gaussian filter through blocks over 5×5×5 vector blocks. The width of the filter at a half maximum was chosen equal to 3 mm that is two times larger than IV size. Values of the detected outliers in the original velocity fields were not used during the smoothing.

Figure 5 shows iso-surfaces of λ2 criterion [17] for the instantaneous velocity distribution. They visualize a pair of

helical vortexes generated in the outer shear layer and a pair of helical vortex filaments in the inner region. At the current spatial resolution of the tomographic measurements the branching of vortex filaments were observed.

(a) (b)

Figure 5 Spatial distribution of the normalized instantaneous velocity field in the vertical plane x/D = 0 and an

instantaneous large scale vortex structure at r/D < 1 in a strongly swirling turbulent jet (S = 1, Re = 30,000). The color denotes the value of the axial velocity component, iso-surfaces show the normalized λ2 criterion at the level of -3.8. The detailed view of inner helical vortexes at r/D < 0.5 (b).

a) 1 10 100 i 0 0.01 0.02 0.03 0.04 0.05 ηi /ηη k b) -2 -1 0 1 2 a1i/(2ς1)0.5 -2 -1 0 1 2 a2 i/(2ς 2 ) 0. 5

Figure 6 Normalized eigenvalues versus POD mode number for a swirling turbulent jet (a) and scatter plot of POD

correlation coefficients of two the most energetic modes for the obtained 3D velocity distributions

POD was applied to the obtained hundred of the 3D velocity fields. The analysis of 3D data confirmed earlier observations (performed by planar Stereo PIV measurements, e.g., [11]) that the two most coherent modes are present in the flow (see Figure 6). They are expected to referto the precession in the swirling jet core. Next Figure 7 shows the

low order reconstruction performed by using the mean velocity distribution V and the two most energetic POD modes

1, 2

ϕ ϕ :v_{L O. .}( , )φ x = +V 2 sin( ) ( )λ₁ φ ϕ₁ x + 2λ₂cos( )φ ϕ₂( )x , where λ λ are the eigenvalues of the POD modes, ₁, ₂

and φ is the phase of the quasi-periodic process. Rotation of the overall structure with phase changing can be observed. Sense of rotation of the outer spiral is the same as the direction of the jet swirl, while the winding is in opposite sense. In general, the analysis of 100 velocity fields by the snapshot POD showed that the phase-averaged flow pattern of a swirling jet with the bubble-type vortex breakdown is in consistence with the literature: the vortex core of the jet takes

the form of a helix with an increased radius in the region of flow expansion, where the recirculation zone is formed.The

helix precesses around the axis of symmetry of the jet and results in formation of secondary spiral vortex in the outer shear layer, which moves around the jet at the same angular velocity. Most importantly, the Tomo PIV method allows

to measure the 3D instantaneous velocity fields, and hence to analyze the structure of the 3D vortexes actually present in the flow (in contrast to the phase-averaged structures). Thus, Tomo PIV reveals smaller eddies due to strong shear induced by the coherent structures and due to breakup (splitting) phenomenon of helical vortices.

(a) (b)

Figure 7 Low order reconstruction of coherent structures in a strongly swirled turbulent jet from the mean velocity

distribution and two the most energetic POD modes, φ π= / 4 (a) and φ=0 (b). The iso-surfaces correspond to Q criterion at the level 245 and are colored by the normalized axial velocity.

CONCLUSION

The paper describes the results of the Tomographic PIV measurements in a strongly swirled turbulent jet at Re 30,000. The swirl generator with S = 1 and the nozzle with the diameter D =15 mm at the exit were used to form the jet. The size of the reconstructed measurement domain is 2.5D×2D×2.5D starting from the edge of the nozzle. Projections of the measurement volume were registered by four low-speed 4 Mpx CCD cameras. The seeding density upon the projections was 0.45 in terms of the source density. This allowed getting velocity fields with the spatial resolution 1.5 мм and the size of 54×41×54 vectors. Tomo PIV experimental data were processed by hybrid CPU-GPU realizations of the processing algorithms including SMART and MTE. The results demonstrate the possibility of the large depth (40 mm or 1100 voxels) Tomo PIV measurements to capture the full (not clipped in z direction) velocity distribution.

The measurements were carried out by Tomo PIV and Stereo PIV techniques for the same object and under the same experimental conditions. Successive Tomo PIV and Stereo PIV measurements with the same optical arrangement were performed in order to validate the obtained volumetric data via comparison of the statistical velocity characteristics with planar measurements. From the analysis of the obtained data, the volumetric to planar comparison showed acceptable correspondence through all common measurement points for mean velocity and satisfactory correspondence of the velocity fluctuations due to lower accuracy of the tomographic technique and limited amount of statistics.

The analysis of the large-scale vortices in the swirling jet from a set of 3D instantaneous velocity fields showed the presence of the double helix vortex in the inner shear layer of the jet and presence of the strong helical vortex in the outer mixing layer. POD analysis of the 3D velocity distributions gives two pronounced modes corresponded to the jet core precession. The low-order reconstruction of the phase-averaged 3D flow pattern by these modes gives the same structures obtained in other studies by means of POD of Stereo PIV data. It is shown that the phase-averaged vortex structure is different from the instantaneous velocity field. It resolves one helical vortex in the outer shear layer and a single thick screw- or drill-like structure at the axis of the jet, without distinct double helix of vortex filaments which are found in the instantaneous 3D velocity distributions. The 3D flow structure obtained by the low-order reconstruction shows the position of the dominating flow structures in average and hides or smoothes the less statistically significant, low-energy structures although they have an important contribution to the turbulent mixing and energy dissipation.

ACKNOWLEDGEMENTS

This work was supported by the AFDAR (#265695) project of the 7th Framework Programme of EC and the Russian Foundation for Basic Research (grants №№ 12-08-33149, 13-08-01356). The authors are also grateful for support by the ‘Scientific and scientific-pedagogical personnel of innovative Russia for 2009–2013’ program of the Ministry of Education and Science of RF agreement №8233.

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