ILASS Americas, 20 th Annual Conference on Liquid Atomization and Spray Systems, Chicago, IL, May 2007 Measurement of Spatially Resolved Mean Velocities in a Transient Spray using Statistical Image Correlation Velocimetry Jongmook Lim * and Yudaya Sivathanu En Urga Inc. 1291-A Cumberland Avenue West Lafayette, IN 47906 and Ariel Muliadi and Paul E. Sojka Maurice J. Zucrow Laboratories School of Mechanical Engineering Purdue University West Lafayette, IN 47907 and Yong Chen, Nitin Sharma, and Prabodh Varanasi S.C. Johnson & Son, Inc. 1525 Howe Street Racine, WI 53403 Abstract Statistical Image Correlation Velocimetry (SICV) was used to obtain mean velocity information in the spray issuing from a consumer fragrance injector. Statistical Image Correlation Velocimetry consists of obtaining several ensembles of the entire transient spray event at 1000 Hz. The spatial correlation coefficient between all the pixels in the image plane is then calculated from the ensemble of images. Based on the magnitude of the spatial correlation coefficient at different locations in the image plane, the mean velocity distribution is obtained. These velocities can be estimated from spatial correlation of streaklines in the images, without needing to resolve individual droplets. Furthermore, it is also not necessary to have well defined streaklines to estimate the velocity because the correlation is based on the statistics of the successive images, rather than on a single set of successive shots. The velocities obtained using SICV were compared with those obtained using a conventional Phase Doppler Anemometer (PDA). The mean velocities estimated from the fragrance dispenser compare reasonably well with those obtained using conventional PDA. * Corresponding author
Introduction Single point velocity measurements in particleladen flows can be readily obtained using Laser Doppler Velocimetry [1], hot wire anemometry [2], and Ultrasound Doppler Velocimetry [3], and a variety of other techniques. Since these measurements are obtained at a single point, it is difficult and time consuming to estimate velocities over a plane with any significant spatial resolution. For obtaining planar velocities in particle-laden flows, several methods are currently employed. These include Particle Imaging Velocimetry [4,5], Particle Tracking Velocimetry [6], Optical Interferomety [7], Molecular Tagging Velocimetry [8], Holographic PIV [9], and a host of other techniques. A review of the different planar velocity estimation methods is provided by Pereira and Gharib [10]. For particle-laden flows, Particle Image Velocimetry (PIV) is the most commonly used method to estimate velocities. PIV estimates the velocity of the flow by measuring the displacement of particles for a fixed time interval. Therefore, PIV requires a high resolution camera to capture distinct and unambiguous images of the particles in the flow. More recently, Image Correlation Velocimetry (ICV) has been used to estimate planar velocities in flows that have distinct visible structures (such as smoke streaks or vortices created with dyes) embedded in the image [11, 12]. The technique can be used even when the camera cannot resolve the individual particles. ICV uses only two shots, or a few shots, to find the pixel-to-pixel correlation, and therefore can be used only when the patterns are very distinct. In a general particulate flow, such as a transient spray, such distinct patterns are difficult to discern. Therefore, we developed a statistical correlation method, Statistical Image Correlation Velocimetry (SICV), that relies on having a very large ensemble of images, but does not require them to have distinct patterns. In addition, the method proposed is reasonably straight forward to implement in an industrial setting. Based on the above arguments, the objective of the present study is to evaluate SICV by comparing results obtained in a transient flow with an alternative diagnostic (Phase Doppler Anemometry). Experimental and Theoretical Methods The transient particle laden flow was generated using two consumer aerosol fragrance dispensers. One is referred to as Device 1 and the other as Device 2. Both devices are battery operated and dispensed commercially available fragrances. A photograph of one of the them mounted on the test bench for SICV measurements is shown in Fig. 1. Figure 1. Photograph of experimental arrangement used for Statistical Image Correlation Velocimetry. The aerosol emitted by the device was illuminated using a white light source. The data for SICV were obtained high speed digital camera operating at 1000 Hz. The camera had a 64 x 64 pixel resolution. The camera/lens system limited the interrogation area to a small square approximately 6 mm on each side. The aerosol dispenser releases a small quantity of fragrance during a time interval of approximately 10 ms. Each dispensation event (called a puff) was repeated approximately every seven seconds. A typical time trace of the absorptance profile (obtained using a SETScan optical patternator) is shown in Fig. 2. Figure 2. Transient path-integrated absorptance measured using the optical patternator. As Fig. 2 shows, the peak of the absorptance profile occurs within 2 ms of the dispenser actuation. During the next 7 ms, the absorptance profile remains near the peak value as the fragrance continues to be ejected from the dispenser. As Fig. 2 also shows, the puff has ended by about 40 ms. Therefore, the camera was triggered to collect data for approximately 50 ms following the start of each puff. Since the data was
collected at 1000 Hz, each puff produces a video that has 50 images. An ensemble of fifty such videos was used to estimate the mean velocity of the particles during the first 5 ms after the initiation of the puff. The method of estimating the velocity from the images is as follows. For each pixel in the array denoted by the coordinate (i, j), the intensity of light j Vk was obtained for a period of 50 ms. The cross correlation coefficient of intensity between the two pixels is defined as: Similarly, the intensities obtained 4 ms after the beginning of a puff are shown in Fig. 4. N V i (t) V i j (t) V (t ) V j k k (t) S k ij 1 (1) N i (t) j(t) where (t-t ) is the time lag between the images, and N is the total number of pixels. V i (t) is the mean intensity obtained at pixel i at the specified time t from the ensemble of images, and i is the variance. The velocity U (x,y,t) is estimated from the peak displacement of the intensity of each specific pixel. The peak displacement of the intensity is in turn estimated by searching the entire field of pixels for the pair of pixels (i, j) that provides the highest correlation coefficient. For the highest correlation pair, the displacement distance is divided by the time lag to give the mean velocity. Mean velocities for evaluation purposes were also measured from a sample of 20 puffs using Phase Doppler Anemometry. Figure 4. Intensities obtained 4 ms after the beginning of the puff from device 1. Consider a pixel located at the co-ordinate location (2.5 mm, 1mm). The cross-correlation coefficient between the intensities at this pixel at t and all other pixels at t is calculated and shown in Fig. 5. Results and Discussion The intensities obtained from device 1 at 3 ms after the beginning of the puff are shown in Fig. 3. Figure 5. Correlation coefficients obtained for the puff from device 1 (i = (2.5, 1), j = entire field). Figure 3. Intensities obtained 3 ms after the beginning of a puff from device 1. It can be immediately seen that a peak correlation coefficient of approximately 0.85 is obtained at a coordinate given by (2.37 mm, 2.89 mm ) at a time t. From this peak displacement and time interval, the velocity is directly obtained. It should be noted that the success of the method depends on obtaining sufficiently high correlation coefficients so that the peak
displacement can be unambiguously determined. The peak correlation coefficients obtained over the entire field of interrogation for device 1 (for t of 3 ms) is shown in Fig. 6. velocities at one axial location, 5 mm above the exit orifice of the dispenser. This was the closest location that the PDPA was capable of measuring due to the geometry of the device. The PDPA mean velocities were obtained by averaging over the entire duration of twenty puffs. The comparison of the mean velocities obtained from PDPA and SICV is shown in Fig. 8 Figure 6. Peak correlation coefficients obtained for the entire field from device 1 For a majority of locations, the peak correlation coefficient is over 0.8. At the edges of the puff, the correlation coefficients are too low to reliably estimate the mean velocities. The mean velocities obtained from the displacements are shown in Fig. 7. Figure 7. Estimated velocities at 3 ms for the entire flow field from device 1. The velocities obtained using SICV were evaluated against convention Phase Doppler Anemometry measurements. The PDPA was used to obtain Figure 8. Comparison of velocities estimated using SICV and PDA for device 1. There are several observations that can be made from this comparison. The first is that the overall agreement is within 30%. This is well within the experimental uncertainties of the two techniques. The second is that the SICV technique can be improved significantly with a higher resolution and faster camera. For this study, a 64 x 64 pixel array with a 1000 Hz framing rate was used. Therefore, the velocity resolution of the SICV is approximately 0.09 m/s, and the spatial resolution is approximately 0.2 mm. It is conjectured that the agreement would be much higher if the resolution of the camera (both spatial and temporal) were increased. The third observation is that the velocities estimated by SICV agree with the PDPA data even when the peak correlation coefficient is as low as 0.50. This implies that the current SICV technique is robust and can be used to estimate velocities in a majority of the locations within the spray. The SICV method was then applied to device 2. The instantaneous intensities obtained for device 2, 2 ms after the beginning of a puff, are shown in Fig. 9. They already show substantial development of the aerosol flow when compared with device 1 data. This implies that the mean velocities of the aerosol from device 2 should be higher than those obtained from device 1. Similar to device 1, there is a high degree of asymmetry in the instantaneous intensities recorded. It is possible that the ensemble averaged intensities recorded over the fifty puffs are more sym metric.
Figure 9. Intensities obtained 2 ms after the beginning of the puff from device 2. The peak correlation coefficients obtained for device 2 are shown in Fig. 10. Figure 11. Velocities estimated using SICV for the entire field from device 2. The mean velocities at an axial location of 5 mm above the dispenser exit were obtained using SICV and PDA; they are shown in Fig. 12. Figure 10. Peak correlation coefficients obtained for the entire field from device 2. The peak correlation coefficients are over 0.8 for a majority of the locations within the interrogation domain implying that the velocities estimated at these locations should be accurate. The peak displacements obtained were used to compute the velocity for the entire field. The mean velocities obtained for device 2, 2 ms after the initiation of the puff, are shown in Fig. 11. The velocity scale for Fig. 9 is identical to that used in Fig. 5. It is clear that the mean velocities at many locations are much higher for device 2 than for device 1. In addition, there is an asymmetry in the velocity field. Figure 12. Comparison of velocities estimated using two methods for device 2. The agreement is not as good for device 2 as it was for device 1. In particular, the velocities at the centerline are different by a factor of 1.6. This is outside the bounds of uncertainty of both methods. There are two potential reasons for this disagreement. It is possible that the number of puffs averaged for the PDA or the SICV techniques is not sufficient. The mean velocities during the entire period of the puff obtained using PDPA could be potentially higher than the mean velocities obtained at a specific time of 2 ms provided by the SICV technique. It is also clear that the SICV technique requires further refinement in terms of spatial and temporal resolution. Despite these
reservations, the SICV method is a promising technique for obtaining velocities in particle-laden flows and should be investigated further. Conclusions The following conclusions were obtained from the present study. 1. Conventional image correlation velocimetry was successfully extended to obtain temporally resolved velocities in particle laden flows. 2. The velocities obtained using statistical image correlation velocimetry (SICV) are in reasonable agreement (within 30 to 60%) with values obtained using Phase Dopler Anemometry. Acknowledgement Partial support for this project was provided by a SBIR matching grant from the Indiana 21st Century Fund. References 1. Somerscales, E. F. C., 1981, Methods of Experimental Physics: Volume 18, Fluid Dynamics, Part A, R. J. Emrich, ed., Academic Press, New York, p. 93 (1981). 2. Blackwelder, R. F., 1981, Hot-Wire and Hot-Film Anemometers, Methods of Experimental Physics: Volume 18, Fluid Dynamics, Part A, R. J. Emrich, ed., Academic Press, New York, p.259-314. 3. Takeda, Y., 1986, Int. J. Heat Fluid Flow, vol. 7, p. 313. 4. Adrian, R. J., Ann. Rev. Fluid Mech., 22:261-268 (1991). 5. Guezennec, Y. G., Brodkey, R. S., Trigui, N., and Kent, J. C., "Fully Automated Three-Dimensional PIV Technique", 1994, Exp. Fluids, vol. 17, p. 209. 6. Racca, R. G., and Dewey, J. M., A Method for Automatic Particle Tracking in a Three- Dimensional Flow Field, 1988, Exp. Fluids, vol. 6, p. 25-32. 7. Goldstein, R. J., 1983, Fluid Mechanics Measurements, Hemisphere, Springer, Washington. 8. Miles, R. B., Connors, J. J., Markovitz, E. C., Howard, P. J., and Roth, G. J., Instantaneous Profiles and Turbulence Statistics of Supersonic Free Shear Layers by RELIEF Velocity Tagging of Oxygen, 1989, Exp. Fluids, vol. 8, p. 17. 9. Green, S. I., and Zhao, Z., Reconstructed Doublepulsed Holograms: A System for Efficient Automated Analysis, 1994, Appl. Opt., vo. 33, p. 761. 10. Pereira, F., and Gharib, M., Defocusing Digital Particle Image Velocimetry and the Threedimensional Characterization of Two-phase Flows, 2002, Meas. Sci. Technol., vol. 13, p. 683-694. 11. Hwang, K.S., Cui, G. X., Zhang, Z. S., Feng, B. C., Quantitative visualization of the near-wall structures in a turbulent pipe flow by image correlation velocimetry, Experiments in Fluids, 32: 447 452 (2002). 12. Apps, C. P., Chen, T., Sigurdson, L., Image correlation velocimetry applied to discrete smokewire streak lines in turbulent pipe flow, Experiments in Fluids, 35: 288 290 (2003).