Stereoscopic particle image velocimetry measurements of a turbulent axisymmetric jet

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1 Stereoscopic particle image velocimetr measurements of a turbulent aisetric jet M. G. Crane, D. M. Deutscher, D. Sumner Department of Mechanical Engineering, Universit of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, Canada, S7N 5A9, david.sumner@usask.ca Stereoscopic particle image velocimetr (PIV) was used to stud the developing region of a turbulent aisetric jet at a Renolds number of Re = Measurements of the jet velocit field were obtained using two configurations of the laser light sheet and cameras. The in-plane configuration was similar to the setup for a conventional, two-dimensional PIV sstem, where the aial flow direction was within the plane of the light sheet. In the out-of-plane configuration, the jet ais was oriented normal to the plane of the laser light sheet. A comparison of the data from the two light sheet configurations, and additional data obtained from a conventional, two-dimensional PIV sstem, showed good agreement in the mean aial and RMS velocit profiles, the Renolds stress profiles, the mean aial momentum flu and the volume flow rate, based on an ensemble average of 800 instantaneous three-dimensional vector fields. 1. INTRODUCTION Stereoscopic particle image velocimetr (PIV) is an etension of the conventional twodimensional PIV technique that allows measurement of the third velocit component within the plane of the laser light sheet [1,2]. The stereoscopic PIV technique uses two digital cameras to image a coon field of view within a flow from two different perspectives (Fig. 1). This allows the velocit component normal to the laser light sheet to be measured. B using the Scheimpflüg configuration for the two cameras, which introduces an angular offset between the image plane of each camera and the principal plane of its lens, the plane of best focus can be made to coincide with the plane of the laser light sheet [2]. From a calibration procedure, mapping functions are obtained that relate the camera images to phsical positions in the flow field. The mapping functions account for the perspective distortion and the varing magnification introduced b the camera positions. Using the twoframe spatial cross-correlation method [2,3], a two-dimensional velocit vector field is obtained for each camera. The pair of two-dimensional velocit vector fields is then combined, using the mapping functions, to give an instantaneous, three-dimensional velocit vector field. In the present stud, the performance of a stereoscopic PIV sstem was evaluated b acquiring some preliminar measurements in the developing region of a turbulent aisetric jet. The performance assessment was the first part of a stud of the behaviour of a turbulent aisetric jet, under conditions of lateral and aial confinement, using stereoscopic PIV. This flow was previousl studied in the same facilit with conventional, two-dimensional PIV [4], but the use of stereoscopic PIV would allow more spatial information on the turbulent flow field to be obtained. For eample, other studies of turbulent jets have used stereoscopic PIV to eamine the small-scale three-dimensional structures within the flow [5], the role of coherent structures [6], and the influence of elliptical eit geometr [7]. To assess the performance of the stereoscopic PIV sstem, the laser light sheet was oriented in two directions (Fig. 2), the first being parallel to the jet ais (the in-plane configuration, corresponding to measurements in the - or -z plane in Cartesian coordinates, where the -coordinate is in the aial flow direction), and the second being normal to the jet ais (the outof-plane configuration, corresponding to the -z plane in Cartesian coordinates). Measurements of the velocit field (u, v, w in Cartesian coordinates, where u is the aial velocit component, see Fig. 2), for the same jet flow conditions, obtained from the two different light sheet configurations, were compared to assess the sstem s performance. This comparison included the mean and RMS aial velocit profiles, the Renolds stress profiles, and the mean aial momentum flu and flow rate. CSME 2004 Forum 1

2 Flow Light Sheet Area of Interest Seeding Particles Laser Optics Laser Left Camera Included Angle Right Camera Snchronizer Computer Figure 1: Components of a stereoscopic PIV sstem. 2. EXPERIMENT SET-UP The eperiments were conducted in water using a glass-walled jet tank with a height of m and a m square cross-section (Fig. 3). The jet entered the tank through a 9- diameter nozzle on the tank floor, which produced a tophat jet eit velocit profile of low turbulence intensit [4]. The jet eperiences lateral confinement from the side walls of the tank and aial confinement b the free surface at the top of the tank. The rising fluid spills over the top of the tank and is collected in an overflow gutter before being pressurized and sent to a constant head tank which feeds the nozzle. The flow is controlled and metered after leaving the constant head tank b means of a valve and a digital turbine flow meter. This same apparatus and configuration was used b Shinneeb et al. [4]. The flow was seeded with 8-12-µm silver-coated hollow glass spheres. A TSI stereoscopic PIV sstem was used to measure the flow. The laser light (532 nm) was supplied b a 120-mJ/pulse dual Nd:YAG Gemini PIV 15 from New Wave Research, which had a maimum pulse frequenc of 15 Hz. The two orientations of the laser light sheet and cameras are shown in Fig. 3. The out-of-plane configuration, where the dominant flow velocit was normal to the light sheet, proved to be the most challenging to image with the stereoscopic PIV sstem. The light sheet optics included a -15- clindrical lens and a 500- spherical lens. A variable-position light arm was used as the beam deliver sstem. The cameras were one-megapiel PIVCAM models manufactured b TSI, fitted with either Nikon 28- f/2.8 lenses or Sigma f/2.8-4 zoom lenses (depending on the light sheet and camera configurations). Each camera bod could be rotated with respect to the lens in order to make possible the adjustment of the Scheimpflüg angle. The images were captured via frame grabbers (90 MB/s TSI model High-Speed Camera Interfaces) on a dual-processor (Intel Pentium III, 1-GHz) computer. The timing of the lasers, cameras, and frame grabbers was controlled b a TSI LaserPulse snchronizer and b the TSI Insight 5 software. A dual-plane, fied calibration target was used to focus the cameras, adjust the Scheimpflüg angles, and find the mapping functions between the image planes and the area of interest in the flow, using the reconstruction algorithm described in [1,2]. CSME 2004 Forum 2

3 JE Areas of Interest Jet Eit z, w, u d d, v u Profiles u Profiles - - (In- Configuration) -z -z (Out-of- Configuration) Figure 2: Aisetric jet coordinate sstem and areas of interest used in the present stud (with aial coordinate direction,, lateral coordinate directions, and z, and aial velocit component, u), showing iso-velocit (aial component) contour lines in the two measurement planes. Image pairs from each camera were processed with a recursive (multiple-pass) Nquist grid algorithm, a FFT correlation algorithm, and a Gaussian peak detection algorithm. The pulse separation time ranged from 125 to 900 µs (depending on the eperiment setup), the primar interrogation window was piels, and the sub-correlation window was piels. For the in-plane configuration, the field of view was approimatel close to the jet eit (56 51 vectors), and further awa (59 56 vectors). For the out-of-plane configuration, the field of view was approimatel at /D = 10 (38 33 vectors), at /D = 20 (46 32 vectors), and at /D = 30 (50 25 vectors). 3. RESULTS AND DISCUSSION The Renolds number based on the jet eit diameter and the mean eit velocit (2.44 m/s) was Re = Stereoscopic PIV measurements were confined to the developing region of the jet, within 30 diameters from the jet eit (for 10 /d 30, where d is the jet eit diameter). For each light sheet configuration, an ensemble average of 800 instantaneous three-dimensional velocit vector fields was used to compute the mean velocit field and the turbulence statistics. The image pairs (one pair for each camera) were acquired at a rate of 15 Hz; eperiments were also conducted with a frequenc of 1 Hz but the showed the sampling rate had no effect on the mean velocit field and other time-averaged statistics. Eamples of the mean aial (u) velocit field from the in-plane configuration (Fig. 3a), for two different vertical positions of the laser light sheet, are shown in Fig. 4. Eamples of the mean aial (u) velocit field from the out-ofplane configuration (Fig. 3b), at three different positions from the jet eit, are shown in Fig. 5. Both figures show the aial development of the CSME 2004 Forum 3

4 Jet Tank Cameras Laser Laser AOI Light Sheet AOI Flow Cameras Jet Flow Jet Light Sheet Figure 3: Eperiment set-up: in-plane configuration of the laser light sheet (light sheet parallel to the jet ais); out-of-plane configuration of the laser light sheet (light sheet normal to the jet ais). Figure 4: Mean aial velocit [m/s] distribution in the turbulent aisetric jet (ensemble average of 800 instantaneous velocit fields), in-plane stereoscopic PIV configuration: field of view /d = 0.6 to 19.5, where in this figure = 0 corresponds to 100 from the jet eit; field of view /d = 18.4 to 36.6, where in this figure = 0 corresponds to from the jet eit. jet (in the -direction), the lateral spread of the jet (in the - and z-directions), and the setr of the jet about its centreline. Comparisons of the lateral profiles of mean aial velocit, u, RMS aial velocit, u, and Renolds stress, -u v or -u w (depending on the configuration), are shown in Figs. 6, 7, and 8, respectivel. For the out-of-plane stereoscopic PIV data, profiles are presented from two perspectives, namel the - plane (u(), u (), and - u v () data along the line z = 0) and the -z plane (u(z), u (z) and -u w (z) data along the line = 0). In order to full show the agreement between the different light sheet configurations, the data were not presented in dimensionless form, where the collapse of the data might obscure differences from the two configurations. CSME 2004 Forum 4

5 z z z Figure 5: Mean aial velocit [m/s] distribution in the turbulent aisetric jet (ensemble average of 800 instantaneous velocit fields), out-of-plane stereoscopic PIV configuration: /d = 10; /d = 20; (c) /d = 30. (c) The mean velocit data (Fig. 6) show the reduction in centreline velocit and the lateral spread of the jet with increasing aial distance from the eit. The mean velocit data are higher for the in-plane configuration of the stereoscopic PIV sstem, but this ma have been caused b a small error in the measured mass flow rate. The RMS aial velocit data (Fig. 7) show a reduction in turbulence intensit with increasing distance from the jet eit. At /d = 10 (Fig. 7a), the RMS aial velocit profile shows two peaks on either side of the jet centreline. These peaks diminish within increasing /d as the aial turbulence intensit profile flattens (Figs. 7b,c). There is a reduction in the peak Renolds stress with increasing /d, as shown in Fig. 8. In general, the results in Figs. 6-8 show good agreement between the stereoscopic PIV data and the conventional two-dimensional PIV data from Ref. [4], and also between the two light sheet configurations of the stereoscopic PIV sstem. The agreement in the RMS aial velocit profiles and Renolds stress profiles is least satisfactor closest to the jet eit, /d = 10 (Figs. 7a, 8a), but this ma improve with a larger ensemble average of instantaneous velocit fields. Overall, the results demonstrate the capabilit of the stereoscopic PIV sstem for resolving the out-of-plane (normal to the light sheet) velocit component in an equivalent manner to the inplane velocit components resolved b conventional, two-dimensional PIV. For the out-of-plane configuration of the stereoscopic PIV sstem, there is good agreement for the mean aial velocit, RMS aial velocit, and Renolds stress profiles between the - and -z planes (Figs. 6-8). In these eperiments (Fig. 3b), the perspective distortion and varing magnification of the images was greatest in the -direction, and was most severe for /d = 30 where the included angle between the cameras was the greatest. The results indicated that neither the calibration mapping functions nor the eperiment set-up introduces a directional bias to the velocit field measurements. Calculations of the mean aial momentum flu, J, volume flow rate, Q, and centreline velocit, u CL, are shown in Table 1 (based on an CSME 2004 Forum 5

6 is agreement between the in-plane and out-ofplane configurations of the stereoscopic PIV sstem and the results from the two-dimensional PIV sstem from Ref. [4]. u [m/s] u [m/s] u [m/s] , z [] (c), z [] 4. CONCLUSIONS Preliminar measurements of the velocit field of a turbulent aisetric jet at Re = were obtained with a stereoscopic PIV sstem using two different laser light sheet configurations. The measurements were obtained to assess the performance characteristics of the stereoscopic PIV sstem, prior to using the technique for further stud of the jet s turbulence structure. In the first configuration, the light sheet was oriented parallel to the jet ais, and the dominant aial velocit component was in the plane of the light sheet, similar to conventional twodimensional PIV. In the second configuration, the light sheet was oriented normal to the jet ais, so that the dominant aial velocit component was out of the plane of the light sheet. Using an ensemble of 800 instantaneous vector fields, good agreement was obtained between the different eperiment configurations for the mean and RMS aial velocit profiles, the Renolds stress profiles, the mean aial momentum flu and the volume flow rate. The eperiments demonstrated the capabilit of the stereoscopic PIV technique to properl resolve the out-ofplane velocit component., z [] Figure 6: Mean aial velocit profile (ensemble average of 800 instantaneous velocit fields: /d = 10; /d = 20; (c) /d = 30., Stereoscopic PIV, out-of-plane, -z plane;, stereoscopic PIV, out-of-plane, - plane;, stereoscopic PIV, in-plane, - plane;, conventional, two-dimensional PIV, - plane, from [4]. ensemble average of 800 instantaneous velocit fields). The aial momentum flu remains nearl constant along the jet ais, there is an increase in the aial volume flow rate with /d due to entrainment, and there is a gradual streamwise deca of the centreline aial velocit. Again, there 5. ACKNOWLEDGMENTS The authors acknowledge the support of the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Canada Foundation for Innovation (CFI), the College of Graduate Studies and Research, and the Department of Mechanical Engineering. The assistance of A. Shinneeb and Engineering Shops is appreciated. 6. BIBLIOGRAPHY [1] Willert, C., Stereoscopic digital particle image velocimetr for application in wind tunnel flows, Measurement Science and Technolog, 8: , CSME 2004 Forum 6

7 u' [m/s] u' [m/s] u' [m/s] (c), z [] , z [], z [] -u'v' or -u'w' [m 2 /s 2 ] -u'v' or -u'w' [m 2 /s 2 ] -u'v' or -u'w' [m 2 /s 2 ] (c), z [] , z [] -4, z [] Figure 7: RMS aial velocit profile (ensemble average of 800 instantaneous velocit fields): /d = 10; /d = 20; (c) /d = 30. Smbols as in Fig. 6. Figure 8: Renolds stress profile (ensemble average of 800 instantaneous velocit fields): /d = 10; /d = 20; (c) /d = 30. Smbols as in Fig. 6. [2] Raffel, M., Willert, C. E., Kompenhaus, J., Particle Image Velocimetr: A Practical Guide, New York: Springer, [3] Willert, C. E., Gharib, M., Digital particle image velocimetr, Eperiments in Fluids, 10: , [4] Shinneeb, A., Bugg, J. D., Balachandar, R., PIV measurements in a confined jet, Proceedings of FEDSM 02, 2002 ASME Fluids Engineering Division Suer Meeting, Montréal, Canada, Paper. No. FEDSM , [5] Ganapathisubramani, B., Longmire, E. K., Marusic, I., Investigation of three dimensionalit CSME 2004 Forum 7

8 Table 1: Mean aial momentum flu, volume flow rate, and centreline aial velocit results for the turbulent aisetric jet, Re = /D J [kg/ms 2 ] Q [m 3 /s] u CL [m/s] Stereoscopic PIV Stereoscopic PIV Stereoscopic PIV In- Out-of- (-z plane) Conventional PIV, Ref. [4] In- Out-of- (-z plane) Conventional PIV, Ref. [4] In- Out-of- (-z plane) Conventional PIV, Ref. [4] in the near field of a round jet using stereo PIV, Journal of Turbulence, 3: 1-12, [6] Alkislar, M. B., Krothapalli, A., Lourenco, L. M., Structure of a screeching rectangular jet: a stereoscopic particle image velocimetr stud, Journal of Fluid Mechanics, 489: , [7] Yoon, J.-H., Lee, S.-J., Investigation of the near-field structure of an elliptic jet using stereoscopic particle image velocimetr, Measurement Science and Technolog, 14: , CSME 2004 Forum 8