Influence of number of cameras and preprocessing for thick volume Tomographic PIV. Yuichi Fukuchi

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1 Influence of number of cameras and preprocessing for thick volume Tomographic PIV Yuichi Fukuchi Fundamental technology research center division 3, Honda R&D, Saitama, Japan Abstract To apply Tomographic PIV to industrial flow, ex. flow around rain gutter, 5 mm volume thickness and.1 ppp particle density, at least, are necessary. In such experimental conditions, signal to ghost ratio of object images and accuracy of vectors are problems. To tackle these problems, influence of number of cameras, image pre-processing and vector post-processing to the accuracy of Tomographic PIV are experimentally investigated at different measurement volume thickness and particle densities. This investigation reveals that time-series minimum subtraction at each pixel without any spatial filter is suitable for image pre-processing for such conditions. Although this filter results in lower signal to ghost ratio, better vector field without less spurious vectors than a traditional one. This signal to ghost ratio is improved linearly by increasing the number of camera up to 8 and accuracy of velocity vectors also increasing up to 8 at any particle density and volume thickness conditions. This improvement by increasing the number of camera is experimentally proved as a first time. Obtained velocity vectors are filtered by spatial filter in physical domain and frequency domain to reduce measurement noise. Filtered velocity profile of thick volume measurable domain, 135 x 23 x 5 mm 3 in air, is well coincident with previous experiments even in velocity fluctuation and Reynolds stress. To resolve turbulent fine scale vortex and large scale vortex simultaneously, more than 6-camera are needed for the case of.12 ppp particle density and 5 mm volume thickness. For the case of.45 ppp and 5 mm volume thickness with 8-camera has also enough accuracy to access velocity fluctuation and Reynolds stress. This paper achieves the large measurable domain, 16 x 22 x 8 mm 3, at the particle density of.53 ppp. 1. Introduction Recently in the research of automotive flow analysis, RANS and LES are used. Although, the mesh number of these CFDs and the quality of meshes are sometimes not sufficient to resolve fine scale turbulent vortex, therefore validation of CFDs by experiments become much important. Especially for the separated flow, like mirror-wake flow or flow around rain gutter, these fine scale turbulent vortexes are sensitive to the total performance of aero-acoustic which are difficult to predict accurately. To treat with these difficulties, large-scale PIV technique in 2D2C (2-dimensional and 2-components) or 2D3C PIV were developed (Hoshino 21). This technique is effective for aerodynamics but for the case of aero-acoustic research, unsteady 3D3C measurement, Tomographic PIV, is needed. Although Tomographic PIV has resolution in measurement depth direction, thicker measurable depth, for example more than 5 mm thickness is necessary. Typical measurable depth of Tomographic PIV in air is about 1 mm. This depth is not enough to understand 3-dimensional vortex structure for the industrial application. The reason of this limited depth is mainly two-folds; the insufficiency of brightness of particle image and the influence of ghost particles at high particle density (particle per pixel, ppp). Multi-pass laser amplification technique (Andreas 26) improves the former problem. By using this amplification technique, measurement depth achieved up to 19 mm (Andreas 29). For the latter problem, signal to ghost ratio is affected by particle density and spatial resolution in measurement depth direction. Moreover thicker volume measurement brings in higher particle density and much number of voxels voxel number in depth direction. Motion tracking enhanced - 1 -

2 MART (MTE) allows almost 3-times higher particle density condition than MART (Michaelis 21). This technique can be adapt to the flow even if the shear rate is sufficiently strong (Elsinga 29) and give Tomographic PIV flexibility of experimental condition. However, at the point of practical view for the industrial application of Tomographic PIV, more flexibility concerning on particle density and spatial resolution in depth is needed especially for experiments in air because to control particle density is more difficult than in water. The number of cameras can also improve signal to ghost ratio and its effect is studied by using numerical simulation (Thomas 21, Elsinga 26). These previous studies show that there is less advantage to increase cameras more than 5-camera. These method based on numerical simulation has advantage of quantitative assessment for particle image and velocity field, however it is difficult to evaluate all of experimental effects like camera noise, laser profile, optical transfer function and etc. In this study, the effect of number of cameras is experimentally investigated by using 8-camera at several particle densities for thick measurement volume conditions. 2. Experimental setup and conditions The effect of the number of cameras is assessed by measurement of cylinder wake flow, which is conducted in a 1-meter wind tunnel, open-jet and Göttingen type, of DLR at a free-stream velocity of 3.6m/s (See Figure 1). A circular cylinder of 2 mm diameter is placed horizontally (Figure 1) and coordinate system is also shown in Figure 1. The corresponding Reynolds number based on the diameter and free stream velocity is 48. The flow is seeded with 1 m DEHS droplets by using Laskin nozzle seeder, which is illuminated by a 9 mj/pulse Nd:YAG laser. For the amplification of laser power, double-pass and multi-pass laser bounce technique are used for 5 mm and 1mm measurement thickness. This means all of camera can use forward scattering and backward scattering. An aperture is located in the pass of laser illumination. This aperture is set to 2 x 5 mm 2 and 2 x 1mm 2 for each case. In addition to this aperture, removable 1 mm thickness slit is mounted just before the aperture. By using this removable slit during a start and end of recording, illuminated volume is reduced to 1 mm and it become easier to count particle number. Particle density is estimated by these filtered images. The particle images are recorded at 7. pixels/mm resolution using 8 CCD cameras (PCO 4) in a circular configuration. These cameras are equipped with Nikon f = 15 mm lenses and Scheimplug adapters. The Scheimplug adapter is fixed to the gear head camera mounting. The z y x Figure 1: Experimental setup in the open jet wind tunnel

3 Scheimplug axes are aligned horizontally on concentric circles around the center of the measurement volume. F# is set to 11 for 5 mm volume thickness and 16 for 1 mm thickness. To allow lager permissive circle of confusion of particle image and to get high intensity of particle image, hardware 2 x 2 binning is applied. The calibration target is a 3 x 3 mm 2 dual layer plate (LaVision type 31). A single position at the center of the measurement volume is calibrated by this calibration target. Remaining calibration error is eliminated by volume self calibration and reduced to a maximum of.8 pixel and rms of.3 pixel. Measurements are performed for two particle densities (.12 and.45 ppp) at 5 mm volume thickness. To assess the effect of thickness of volume, measurements are also performed for two light sheet thickness (5 mm and 1 mm). 1-shots are averaged for statistic values. 7-iterations of MART are applied for the reconstruction. Reconstructed volume sizes are 999 x 1873 x 46 voxel for 5 mm thickness and 129 x 1859 x 745 voxel for 1 mm thickness. For the cross-correlation, interrogation volume sizes are respectively 32 x 32 x 32 and 4 x 4 x 4 with 75% overlap. Vector grid numbers are 17 x 183 x 4 and 14 x 136 x 56 each, and spacing between vectors are 1.28 mm and 1.61 mm each. Davis8. (LaVision) is used for these analysis. 3. Calculation of seeding density A straightforward way to calculate the particle density is to count the number of particles in the recorded images. This method has a problem, i.e. the more the number of particles increases, the more difficult counting correctly is, because of the overlapped particles. Figure 2 shows the relationship of the measured particle density by particle counter and the true particle density calculated from synthetic data. It is clear that particle counting method only work at low particle densities (up to.3 ppp). For the condition of.12 ppp, 1 mm removable slit is used to analyze particle density. To take into account of Gaussian laser profile, counted particle density,.267ppp, is multiplied by 4.5 for the 5 mm thickness condition. For the other conditions, particle density is estimated from image intensity in the illuminated area. In this assumption, particle density is proportional to particle image intensity. As shown following equation, background intensity is subtracted and image data of.12 ppp is used as a reference image. Where, I is the intensity of the image obtained by CCD camera. Iilluminated_area I background ppp.12 (1) I I illuminated_area, ppp.12 background, ppp.12 Measured particle density [ppp] True particle density [ppp] Figure 2: Relationship between true particle density and measured particle density

4 4. Image preprocessing and signal to ghost intensity ratio Before the reconstruction of 3-dimensional object image, signal conditioning has some importance for Tomographic PIV experiment. In the previous studies of image preprocessing (Elsinga 25), effective image pre-processing algorithm for background intensity removable is a combination of pixel wise time-series minimum subtraction and a local neighborhood (in this study 5 x 5 pixels) minimum intensity subtraction. In addition to this preprocessing, Gaussian smoothing and sharpen filter are also used to clean up particle image profile. These spatial noise reduction filters are mainly studied and are effective in sparse particle density (Elsinga 25). In Figure 3, the overwrap of particle image can be seen in these experimental conditions and particle images are not isolated, therefore effect of spatial filter of image preprocessing is investigated. Figure 4 shows the effect of image pre-processing to laser profile in z-direction. Traditional filter, with spatial filter, contains the subtraction of time-series and local minimum, Gaussian smoothing filter and sharpen filter, normalization of local intensity averaged over 1 pixels. Ts-min filter, without spatial filter, includes the subtraction of time-series and normalization of local intensity average. Traditional filter results in flat laser profile and higher signal to ghost ratio (SGR). SGR of traditional filter is about 45 %. Here, signal to ghost ratio is defined by following equation. Where, I is the intensity of the object image. SGR I illuminated _ area dark _ area (2) I I dark _ area On the other hand, Ts-min filter results in skewed profile and lower SGR. For the case of time-series minimum subtraction filter, intensity of dark area is averaged in left and right side. SGR of this is about 75%. To compare with both of SGRs, it can be seen that traditional filter is better, but concerning on vector map Figure 4 (d) and 4 (e), traditional filter results in noisier velocity vector map. The reason of this is that traditional filter eliminates not only noise but also real particles in such a high particle density condition (See Figure 4 and 4 (c)), thus strong image pre-processing is not suit for thick volume or high particle density Tomographic PIV ppp.45ppp 3 Intensity x [pixel] Figure 3: 1-dimensional distribution of particle image

5 Intensity Traditional filtered image(left) Ts min filtered image(right) z [mm] Intensity (c) (d) (e) Figure 4: Distribution of intensity profiles in depth direction, object image by traditional filter at z=-2.7mm, located at centerline of measurement depth, for.12ppp, object image by Ts-min filter (c), velocity map of traditional filter (d), velocity map of Ts-min filter (e). Figure 5 shows laser profile along z-direction of.45 ppp condition. These profiles are the results of Ts-min filter. In this figure, the intensity is normalized by the intensity at centerline of laser profile. These laser profiles are skewed and SGR goes to worse along minus z-direction, but it is clear that SGR becomes better when the number of cameras increase. Although data is not shown in this paper due the page limitation, this skewness is more emphasized in the case of 1 mm volume thickness and less emphasized in the case of.12 ppp condition. Although, the further research is necessary, there is some possibility that overlap of particle image at the edge is the reason of this skewed profile. Figure 5 shows the relationship of SGRs to number of cameras for each experimental condition. In the case of.12 ppp and.45 ppp at 5 mm volume - 5 -

6 thickness, SGR rise up linearly and for the case of.53 ppp at 1 mm volume thickness, SGR do not rise up until 6-camera. To compare with difference of particle density and volume thickness, difference of volume thickness has bigger effect to SGR. There are three reasons for this. First one is the number of voxel along z-direction. Second one is the effect of Gaussian laser intensity profile. For the case of 1 mm volume thickness, laser is expanded compared to 5 mm volume thickness, however, laser profile filtered by aperture is not so much compare to the condition of 5 mm volume thickness. Therefore, at the edge of laser profile in measured particle image is not so clear compared to that of 5 mm one. Third one is the effect of skewed laser profile. This laser profile shows that SGR is better at the near camera side and worse at the far side, therefore if volume thickness is increased, SGR is affected this skewed profile effect and goes worse. From these results, there is an advantage to increase number of cameras up to 8 in these thick volume and high particle density conditions. Normalized intensity cams 5cams 6cams 7cams 8cams Signal to ghost ratio[%] [ppp].45[ppp].53[ppp](1mm thickness) z [mm] Number of cameras Figure 5: Laser profile along z-direction of.45ppp, SGR vs. number of cameras for varying particle density and measurements depth. 5. Assessment of velocity vectors In this section, quality of velocity vectors is assessed. Figure 6 shows 1-dimensional power spectrum of v-component along y-direction. In here, k is a spatial wave number. Power spectrum is averaged all over the measured domain that ranges from x/d = 1.7 to 8.5. Figure 6 shows the comparison of spatial filter for the case of.45 ppp and 5 mm thickness. In the case of Raw data, spurious velocity vectors are removed and no smoothing methods are applied. Top-hat filter and Gaussian filter means 3 x 3 x 3 grid smoothing and 3 x 3 x 3 grid Gaussian smoothing respectively. Polynomial filter uses 2 nd order polynomial fitting for 5 x 5 x 5 grid. There is a large difference between Raw data and filtered data but less difference between various kinds of filters. Figure 6 shows the comparisons of number of cameras. These spectrums are the results of Polynomial filter. There is no visible difference between the spectrum of 7-camera and 8-camera, but there is a large difference from 4-camera to 6-camera. Even for the case of more than 7-camera for.45 ppp condition, measurement noise is still remained at high frequency region. Spatial low-pass filter is used to eliminate this noise (Tanahashi 23). For y-direction, cut-off wave number is set to 55 in this case and suitable cut-off wave number is selected for other directions. This limit of spatial resolution is not changed in case of.45 ppp with 24 x 24 x 24 voxel interrogation volume size, therefore spatial resolution is dominated by the quality of object image. This is a smoothing effect of ghost particles (Elsinga 211). Figure 7 is the instantaneous velocity vector profile at.12 ppp and.45 ppp condition. Polynomial filter and low-pass filter are adapted to filtered data. The deviation from 8-camera is - 6 -

7 still remained in filtered data. Moreover, the deviation in case of.45 ppp condition is larger than that of.12 ppp condition. Only at the region of peak and valley of velocity profile, the deviation is large. The location of fine scale vortex is well correlated with second variant of velocity tensor, thus many cameras Tomographic PIV is desirable for the analysis of fine scale turbulent structure. Deviation from 8-camera is shown in Figure 8. It is clear that deviation is decrease with increasing of number of cameras. The improvement is large at from 4-camera to 5-camera and it is linear from 5-camera to 8-camera for each case. Volume self-calibration is conducted during the recording by using removable 1 mm slit and remaining calibration error is reduced to.3 voxel, but cameras are vibrating during a recording therefore remaining calibration error increase up to.98 voxel at the end of recording. To take into account of this calibration error and cross-correlation error, deviation of.2 voxel from 8-camera is reasonable accuracy for this experiment. The case of.12 ppp with 7-camera is the only case within.2 voxel deviation from 8-camera. Moreover, instantaneous velocity profile of 7-camera and 8-camera for.12 ppp (Figure 7) shows good agreement. However, deviation from 8-camera is not absolute error, therefore quality of results are assessed by using SGR, deviation from 8-camera and comparison of previous experiment. According to several experiments, SGR should be larger than 5 % for the reliable result. In Figure 5, SGRs of more than 6-cameras for.12 ppp and 8-cameras for.45 ppp exceed 5 %. These cases are assessed moreover in the following section E(k) Raw data Top-hat filter Gaussian filter Polynomial filter E(k) cams 5cams 6cams 7cams 8cams k = k k Figure 6: Comparison of spatial filter for vector post-processing for 8-camera, comparison of number of cameras for.45 ppp..5.5 Displacement [voxel] ppp,7cams,raw.12ppp,8cams,raw.12ppp,7cams,filtered.12ppp,8cams,filtered y/d Displacement [voxel] Figure 7: Comparison of span-wise instantaneous v-velocity profile for raw data and filtered data for.12 ppp condition, for.45 ppp condition at x/d = ppp,7cams,raw.45ppp,8cams,raw.45ppp,7cams,filtered.45ppp,8cams,filtered y/d - 7 -

8 Rms. deviation from 8cams [voxel] ppp.45ppp.53ppp(1mm thickness) Number of cameras Figure 8: Deviation of the calculated vector field from it s of 8-camera reconstruction. The SGRs of 1 mm thickness is considerably low, but deviation from 8-camera is not so large compared to SGRs of 5 mm one. There is some possibility of skewed laser profile in z-direction for this reason. For the further study, velocity profiles are compared with previous experiments. Figure 9 is a u-velocity profile along center line. This profile is averaged through y-direction. To compare with other experiments, results of the case for.45 ppp with 4-camera has larger difference especially in high velocity gradient region and variability of the other results for 5 mm volume thickness are within that of previous experiments. Figure 9 shows u-velocity profile along z-direction. There is an asymmetric diversity for every case. Setting error of cylinder or calibration target is the reason of this. The difference is also seen in the case of.45 ppp with 4-camera around center line. For the case of 1 mm volume thickness, there is some discrepancy from other results, but to take into account of lower SGR of this condition, the discrepancy of velocity profile is comparatively small u/u.6 Cantwell(Re=14) Lourenco(Re=39).4 Ong(Re=39).12ppp,4cams.12ppp,6cams.12ppp,8cams.2.45ppp,4cams.45ppp,6cams.45ppp,8cams.53ppp,1mm,8cams x/d u/u Ong(Re=39).12ppp,4cams.8.12ppp,6cams.75.12ppp,8cams.45ppp,4cams.7.45ppp,6cams.45ppp,8cams.53ppp,1mm,8cams z/d Figure 9: Velocity profile of u-component for x-direction at the center line, for z-direction at x/d=

9 u'/u Ong(Re=39).12ppp,4cams.12ppp,5cams.12ppp,6cams.12ppp,7cams.12ppp,8cams.45ppp,4cams.45ppp,5cams.45ppp,6cams.45ppp,7cams.45ppp,8cams.53ppp,1mm,8cams w'/u Ong(Re=39).12ppp,4cams.12ppp,5cams.12ppp,6cams.12ppp,7cams.12ppp,8cams.45ppp,4cams.45ppp,5cams.45ppp,6cams.45ppp,7cams.45ppp,8cams.53ppp,1mm,8cams z/d z/d Figure 1: Velocity fluctuation profile of u-component for z-direction at x/d=3., fluctuation velocity profile of w-component for z-direction at x/d=3.. u'w'/u Ong(Re=39).12ppp,4cams.12ppp,5cams.12ppp,6cams.12ppp,7cams.12ppp,8cams.45ppp,4cams.45ppp,5cams.45ppp,6cams.45ppp,7cams.45ppp,8cams.53ppp,1mm,8cams z/d Figure 11: Reynolds stress profile of u-component for z-direction at x/d=3.. Figure 1 and Figure 11 shows velocity fluctuation profile and Reynolds stress profile respectively. The effect of the number of cameras to the results of velocity fluctuation and Reynolds stress is clearer than that of mean velocity profile. Ghost particles tend to decrease velocity fluctuation because ghost particles moves over mean velocity (Elsinga, 211). In the case of fewer cameras, there is a tendency that the fluctuation and Reynolds stress become smaller value at the peak or valley. From these fluctuation profiles, the case of.12 ppp with more than 6-camera,.45 ppp with 8-camera for 5 mm volume thickness is suitable to assess turbulent fine scale structure. The case of.53 ppp with 8-camera for 1 mm volume thickness, mean and fluctuation velocity is comparatively coincident with other results

10 (c) Figure 12: Instantaneous flow field visualization of 3-vorticity vector components for the case of.45ppp and 5mm volume thickness with 8-camera, stream-wise vorticity for the case of.45ppp and 5mm volume thickness with 8-camera, for the case of.53ppp and 1mm volume thickness with 8-camera (c). Figure 12 shows the iso-surface of instantaneous vorticity, red and blue color means span-wise vortex and yellow and green means stream-wise vortex. Difference of color, like blue and red, shows difference of rotational direction. These stream-wise vortexes, it is called as a finger structure, are smaller structure compared with span-wise vortex, both of flow structure is well resolved. It is clear that counter-rotating finger structure interact with roller structure. The Resolved wave number for each direction in x, y, and z are 1-45, 1-55 and 1-13 respectively. This wide range of resolved wave number enabled to measure fine-scale and large-scale vortex interaction. Figure 12 and (c) shows stream-wise vortex for 5 mm volume thickness and 1 mm volume thickness respectively. In the case of 1 mm volume thickness, whole of turbulent structure is qualitatively captured in the measured domain. Usable region of 1 mm volume thickness is 16 x 22 x 8 mm 3, at the point of conservative view

11 6. Conclusions The effect of number of cameras, image pre-processing and vector post-processing are studied for thick volume measurement depth conditions at different particle densities and volume thickness. Image pre-processing: In these particle density conditions (.12 ppp,.45 ppp and.53 ppp), particle image overlaps frequently, therefore spatial filter for particle image induced higher SGRs but noisier velocity vector map to compare with the result of time-series minimum subtraction filter without any spatial filter. This effect of overlap at the edge of particle image produce ghost particles and SGR become worse toward to minus z-direction. This effect increases when volume thickness is increased. Vector post-processing: Spatial filter in physical domain and low-pass filter in frequency domain for velocity vector are effective to reduce measurement error and the difference of each spatial filter in physical domain is negligible small. By using these filters, resolved wave number for each direction in x, y, and z are 1-45, 1-55 and 1-13 respectively, vector grid is 17 x 183 x 4, for the case of 5 mm volume thickness. This limit is not dominated by the number of signal particle or interrogation volume size, but the smoothing effect by ghost particles. Effect of number of cameras to velocity vector: Vector profiles are compared with previous experiments and to understand velocity fluctuation and Reynolds stress, more than 6-camera are needed for.12 ppp and 5 mm volume thickness condition and 8-camera is needed for.45 ppp. The SGRs of these conditions are more than about 5 % and those deviations from 8-cameras are about.2 voxel. To take into account of calibration error and cross-correlation error, the deviation of.2 voxel is reasonable accuracy for this experiment. The results of 5 mm volume thickness can visualize 135 x 23 x 5 mm 3 and resolve the interaction of roller structure and finger structure. The results of 1 mm volume thickness with 8-camera are comparatively coincident with other results, in spite of its low SGR. This is the effect of skewed laser profile and ghost particles along z-direction. Further study is needed to improve this effect. Results of this study show the performance of thick volume or high spatial resolution of Tomographic PIV in air and also show flexibility of experimental condition. This result will encourage the application of Tomographic PIV to industrial flow. 7. Acknowledgments This experiment was supported by Dr. Dirk Michaelis from LaVision GmbH and Dr. Andreas Shröder, Dr. Daniel Schanz, Dr. Reinhard Geisler from DLR, and analysis was also supported by Dr. Dirk Michaelis. Prof. Scarano gave the valuable suggestions. Their supports are greatly acknowledged. 8. References [1] G. Hoshino, T. Yoshino, Y. Fukuchi and M. Teramura. Development of Large-scale PIV Measurement technique, Honda R & D technical review. October, 21. [2] A. Shröder, R. Geisler, G.E. Elsigna, F. Scarano, U. Dierksheide. Investigation of a turbulent spot using time-resolved tomographic PIV, 13 th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal,

12 [3] A. Shröder, R. Geisler, A. Seiverling, B. Wieneke, A. Henning, F. Scarano, G.E. Elsigna and C. Poelma. Lagrangian aspects of coherent structures in a turbulent layer flow using TR-Tomo PIV and PTV, 8 th Int. symp. PIV, Melbourne, AU, 29. [4] D. Michaelis, M. Novara, F. Scarano and B. Wieneke. Comparison of volume reconstruction techniques at different particle densities. 15 th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, 21. [5] G.E. Elsigna, J. Westerweel, F. Scarano, M. Novara. On the velocity of ghost particles. In proc. Of PIV9, Melborune, Australia, 29. [6] G.E. Elsigna, B.W. van Oudheusden, F. Scarano. Experimental assessment of Tomographic-PIV accuracy. 13 th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, 26. [7] L. Thomas, R. Vernet, B. Tremblais, L. David. Influence of geometric parameters and image preprocessing on tomo-piv results, 15 th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, 21. [8] G.E. Elsigna, J. Westerweel, F. Scarano, M. Novara. On the velocity of ghost particles and the bias errors in Tomographic-PIV. Exp. Fluids (211) 5: [9] M. Tanahashi, Y. Fukuchi, G.-M. Choi, K. Fukuzato and T. Miyauchi (23). High spatial resolution time-series PIV for turbulence measurement, Turbulence, Heat and Mass Transfer 4, pp ,