Simultaneous measurement of droplet velocity and size and gas phase velocities in a spray by combining ILIDS and PIV techniques

Transcription

1 Simultaneous measurement of droplet velocity and size and gas phase velocities in a spray by combining ILIDS and PIV techniques Yannis Hardalupas 1, Srikrishna Sahu 2, Alex M.K.P. Taylor 3, Konstantinos Zarogoulidis 4 1: Dept. of Mechanical Engineering, Imperial College, London, UK, y.hardalupas@imperial.ac.uk 2: Dept. of Mechanical Engineering, Imperial College, London, UK, s.sahu06@imperial.ac.uk 3: Dept. of Mechanical Engineering, Imperial College, London, UK, a.m.taylor@imperial.ac.uk 4: Dept. of Mechanical Engineering, Imperial College, London, UK, konstantinos.zarogoulidis@imperial.ac.uk Abstract A new approach for simultaneous measurement of droplet size and droplet-gas relative velocity is reported, which combines the out-of-focus imaging technique Interferometric Laser Imaging Droplet Sizing (ILIDS) for planar simultaneous droplet size and velocity measurements with the in-focus technique Particle Image Velocimetry (PIV) for gas velocity measurements in the vicinity of individual droplets. Discrimination between the gas phase and droplets is achieved in the PIV images by removing the glare points of focused droplet images by using the information of corresponding droplet position obtained through ILIDS processing. The combined optical arrangement results in a discrepancy between the detection of the centre of the same droplet, while imaging through ILIDS and PIV techniques, which may lead to erroneous identification of the glare points from droplets on the PIV images. The discrepancy was evaluated through a theoretical model for calculation of the apparent location of the droplet centre on images and quantified by measurements with stream of droplets issued from a monodispersed droplet generator. The discrepancy was found to be a function of position of the droplet on the CCD array and the degree of defocus, but almost independent of droplet size. Specifically, it varies linearly along the horizontal dimension of the image for a given defocus setting in ILIDS. This relationship is estimated by fitting a line through the measured resulting discrepancies. The experimental finding is supported by the theoretical analysis, which was based on geometrical optics for a simple optical configuration that replicates the optical system. The evaluated error from the measurements with monodispersed droplets is subtracted from the droplet centres identified in ILIDS images from a real spray without seeding particles. This resulted in reducing the discrepancy between PIV and ILIDS droplet centres from about 10 to 2 droplet diameters and hence increasing the probability of finding corresponding fringe patterns on the ILIDS image and glare points on the PIV image. An image processing algorithm is described for the detection of droplet centres in both images, the removal of glare points from PIV images and the processing to obtain gas velocity. Results are presented in a monodispersed droplet stream surrounded by a coflowing air seeded with aluminium oxide particles and in a real spray. In conclusion, it is shown that the proposed combined method can discriminate between droplets and seeding particles and is capable for two-phase measurements in real sprays. 1. Introduction In non-premixed liquid-fuelled combustion, the process of air fuel mixture formation is controlled by air entrainment, linked with the formation of coherent structures in the air flow and coupling between the dispersed and continuous phases. The interaction of a spray with the air flow field redistributes droplets due to differences in droplet inertia, momentum and drag. Because of the relative relaxation times of droplets of different sizes, interaction with various scales of eddies in turbulent flow field can lead to cluster formation (Sanchez et al. 2000; Zimmer et al. 2003). Centrifuging of larger droplets out of eddies may lead to local relative droplet void regions finally resulting in uneven spatial distribution of droplets and large temporal and spatial variation in local fuel - 1 -

2 vapour concentration. In this context, experiments on spray flows are essential not only for understanding the mechanisms of droplet-gas flow interaction but also for the development and evaluation of spray models. For a spray the turbulent kinetic energy equation for the carrier fluid contains terms, which include correlations of droplet concentration and velocity fluctuations of fluid and/or droplets and droplet-fluid velocity correlations (Hardalupas and Horender 2003). They represent an extra modification of turbulent kinetic energy of the fluid and depict the interaction, which needs to be modelled successfully. In this regard experiments need to characterize not only the droplet-gas relative velocity and associated spatial correlations but also the droplet size simultaneously, which is the ultimate aim of the present paper. Measurements in two phase flows have always been a difficult task, the most crucial aspect being the way the two phases are discriminated from each other. This is usually done either by acquiring images of both phases in a single camera followed by image processing to separate them out or by using two cameras each acquiring images of individual phases. The popular approach is to tag the gas phase with a fluorescent dye in conjunction with an adequate optical filter that attenuates the Mie scattering signal of the spray droplets. For example, Lindken and Merzkirch (2002) used only one camera for bubbly flow measurement based on combination of PIV with fluorescent tracer particles and shadowgraphy and digital phase separation with a masking technique. Similarly, Rottenkolber et al. (2002) acquired consecutively the images of the spray alone and of the induced gas flow alone using fluorescent seeding particles to trace the gas phase. They described two different algorithms for phase discrimination known as mask and peak separation techniques. In order to avoid the presence of the two phases on the same image, Kosiwczuk et al. (2005) tagged both phases, instead of only one, with two different fluorescent dyes. Two cameras were used one for each phase along with suitable optical filter set. They could obtain simultaneous and independent velocity fields of the two phases by processing each image containing only one phase by standard PIV or PTV algorithms. The systems described above lack either the droplet size information or simultaneous measurements of the two phases. Hence PIV alone is not sufficient for the task. Classical single-point techniques, though reliable, cannot easily address issues like preferential concentration and coherent flow structure identification in a spray. The fluorescence approach is always associated with the possibility of cross-contamination due to Mie scattering, which needs to be quantified, and more over it is expensive to use. Specifically it is unsuitable with respect to the work reported here (using a defocused technique for planar droplet sizing and velocity) in which finding the droplet centre location is a crucial factor for discriminating the two phases. This paper is an attempt towards simultaneous whole field measurements of droplet size and velocity along with the gas velocity in a spray by combining the out of focus imaging technique ILIDS (Interferometric Laser Imaging Droplet Sizing) for planar droplet size and velocity measurements with Particle Image Velocimetry (PIV) for gas phase velocity measurements (Fig.1). ILIDS is an optical technique for instantaneous measurements of the spatial distribution of individual droplet size and velocity in polydispersed sprays. It makes use of the spacing of the interference fringes formed due to reflected and first order refracted scattered light from individual droplets, when collected by defocused optics, to determine the droplet size (Glover et al. 1995). The incorporation of image compression optics by Maeda et al. (2000) could reduce fringe overlapping in dense sprays and avoided the complexity for the evaluation of fringe spacing (Damaschke et al. 2005) and thus extended the application of ILIDS to relatively dense spray. The advantage of the present technique lies in the fact that the position of droplets in a spray obtained by ILIDS beforehand helps in identifying the same droplets in the focused PIV image, thus making it possible to remove them from the PIV image. In this way the PIV image remains with only seeding particles, which follow the gas phase flow, and can be - 2 -

3 processed to obtain the gas velocity in the vicinity of each droplet. An unexpected difficulty with the combined technique is the presence of a discrepancy in droplet centres when calculated independently through ILIDS and PIV images. The objective of the paper is to reason out the cause and affect of this discrepancy and quantify the error. A theoretical analysis based on the optical configuration is performed to verify the experimental results. The application of the proposed method, including the image processing algorithm, is demonstrated for a stream of monosized droplets produced by a custommade droplet generator. The droplet generator is placed inside a coaxial slow moving air stream, seeded with particles for PIV measurements. Finally, preliminary results in sprays are presented. 2. Experimental set up for combined ILIDS with PIV measurements The fundamentals of combining the optical arrangements of ILIDS with PIV are considered by using geometrical optics. When a transparent spherical water droplet in a flow field is illuminated by a coherent laser source (Fig 1a), the reflected and first order refracted light scattered from the droplet dominate in the forward scatter region for angles between around 30 to 80 deg. On a defocused plane the reflected and refracted rays interfere to produce parallel fringes (Glover et al. 1995). The number of fringes present in each of the fringe pattern and the spacing is proportional to the diameter. The characteristic interferogram is observed with a far-field arrangement of receiving optics (Kawaguchi et al. 2000). With this optical system, bright spots called glare points, corresponding to focused reflected and refracted rays, appear when imaged on a focal plane (Fig. 1a). For the purpose of characterizing simultaneously the velocity of the air flow in the vicinity of individual droplets, the air surrounding the spray needs to be seeded with particles and the viewing area is imaged on the focal plane for PIV measurements. This is achieved by splitting a part of the incoming scattered light using a beam splitter and collecting it through a second camera placed at the focal plane (Fig. 1a). Hence, the same droplet is imaged as a rectangular region with a superimposed fringe pattern on the ILIDS camera and as distribution of two glare points on the PIV image. The defocused image from seeding particles appears on the ILIDS camera, but without any superimposed fringes. Traditionally, for both cases, the centre of a droplet is assumed to be the geometrical centre of the fringe pattern/glare points, which may not be the same as the actual droplet centre. (a) (b) Fig. 1 (a) Principle of the combined ILIDS and PIV technique (b) Experimental set-up - 3 -

4 An overview of the experimental rig is shown in Figure 1b. The present work employs a spray dryer rig for two phase measurements, the details of which can be found in Kavounides (2006). The rig allows coflowing air to enter from the top in the annulus around the atomiser, which was a custom built air assisted nozzle placed on the centreline of the rig. It produces a solid cone spray with a characteristic droplet diameter (SMD) of the order of µm at liquid feed rates of the order of kg/s. The coflowing air is seeded with aluminium oxide particles (diameter range 1-5 micron) before entering the rig. The coflowing air flowrate, carrying the seeding particles, is 200 lt/min, resulting in area-averaged air velocity m/s around the spray. A frequency-doubled, double pulse Nd:YAG laser (120 mj/pulse at 532 nm; New Wave Research) was used to illuminate the flow. Two identical cameras were used (PCO; Sensicam QE, 12bit, ) and positioned on the same side of the laser sheet. The scattered light from droplets was divided in to two parts by using a pellicle beam splitter (thickness 2µm) to avoid formation of ghost images. The light refracted through the pellicle beam splitter is directed at the defocused plane for measurements with ILIDS, while the reflected light is directed at the focal plane for PIV measurements. The purpose behind this configuration is that the reflected light is more sensitive to the alignment of the beam splitter than the refracted one. Since the ILIDS camera usually is operated with maximum aperture, the problem of image distortion will be more pronounced if the reflected light is used. Because of the issues related to optical aberrations of ILIDS images, both cameras are adjusted to provide a field of view of approximately 10 15mm, which is comparatively small with respect to that of usual PIV system operation. In all experiments, the scattering angle was set at θ = 69, which is the optimum scattering angle for a vertically polarised laser sheet. The collecting angle was set to 6.35, resulting in a resolution of 5.28 [µm/fringe] for the ILIDS system. Experiments are first performed with a custom built droplet generator, producing a single stream of monosized droplets. For this purpose, the droplet generator is supported inside the rig and seeded air is allowed to flow around it. The pinhole size at the exit of the monodispersed droplet generator was 100 µm. The injection pressure was set at 1.0 bar, while the water flow rate was 6.0 cm 3 /min. The resonance frequency of the piezoelectric elements of the generator was set to 20 khz. Under this condition, the diameter of the droplets is approximately 212µm with an accuracy of 97% (Pergamalis, 2002). The field of view of this system is not parallel to the CCD array due to the requirement of imaging at a scattering angle θ, which is different than 90. Hence, in order to avoid varying the degree of focus/defocus across the CCD array, both the cameras are set under Scheimpflug condition similar to Sugimoto et al. (2006). The system calibration is a crucial factor for the accuracy of the proposed optical arrangement. To ensure that the same area is imaged by both the cameras, a calibration plate with equally spaced crosses was used. The centres of the crosses are mapped to the respective pixels by fitting a mapping function, the coefficients of which are obtained through linear least square approximation. Thus, the real position in space can be obtained given a location on the image. 3. Theoretical prediction of droplet centre discrepancy It is usually expected that the centre of the same droplet obtained from ILIDS and PIV should coincide or the difference at most should be of the order of a droplet diameter. However, this is not correct. This is crucial for the simultaneous operation of ILIDS and PIV techniques, because it may lead to eliminating wrong droplets or seeding particles from the PIV image. In order to predict the cause of this effect and the order of the discrepancy, a theoretical analysis is performed, based on a simple optical arrangement using geometrical optics. Since defocusing is performed only in the - 4 -

5 horizontal direction of the compressed images of the ILIDS technique, the analysis is performed for one plane only, assuming that the droplet centres are situated in a single plane inside the laser sheet and the corresponding glare points remain on the same plane as well. Fig. 2 Schematic of the optical system for theoretical prediction of discrepancy in droplet centre between the focal and defocus plane As shown in Figure 2, the axis of the lens is at a forward scattering angle θ relative to the laser sheet direction. A droplet with diameter d is situated at a distance z from the point where the lens axis intersects the laser sheet. The distance of the glare points 1 and 2 formed by reflection and refraction at the droplet surface with respect to the centre can be calculated from the geometrical optics light scattering model (Golombokyz et al. 1998). Imaging planes are inclined to maintain the same degree of / / / focus/defocus across them. The glare points are imaged as 1 and 2 and the centre as 0 in the focal plane and are exactly located by using lens maker s formula. The geometrical centre (which is different / / / from the actual centre 0 ) is located in the middle between 1 and 2. In the defocus plane, the glare points become larger and interfere to produce a set of fringes. Again using the geometrical optics, the length of the defocused fringe pattern 1 // 2 // // and the position of both actual centre 0 and geometrical centre are obtained. Now the magnitude of discrepancy between fringe pattern centre and glare point centre ( 0 / 0 // ) is estimated as a function of various parameters, including the location of droplet ( z ) in the object plane, the degree of defocus and droplet size (d). The following conclusions are derived from the analysis. The results correspond to droplet size of 200µm. 1. For the case of glare points, the difference between actual and geometrical droplet centre (marked as * in Figure 3a) is always less than a droplet diameter and is almost independent of the position of the droplet in the object plane. 2. For the case of defocus fringe pattern, the difference between actual and geometrical droplet centre (marked as o in Figure 3a) can be more than a droplet diameter in the defocus plane and is proportional to the degree of defocus. Also it does not depend strongly on the droplet size and position on the image plane. 3. The discrepancy between droplet centres on the focal and defocus plane ( 0 / 0 // ) was found to be a function of degree of defocus (varies proportionally) and the position of droplet in the object plane/ccd array. For a given defocus plane, it varies almost linearly across the - 5 -

6 image plane from being negative at one side to positive at the other. The discrepancy is calculated using both the actual and geometrical centre of the droplet. Figure 3b shows the ratio of this discrepancy to the droplet diameter for the above two cases for a given defocus. It can be observed that the error is expected even if we detect the actual centre of droplet in the fringe pattern and glare points. 4. The magnitude of discrepancy of the droplet centre was found to be almost independent of droplet size. As shown in Figure 3c, the discrepancy for a droplet of size 200µm almost coincides with that of size 20µm. 5. The conclusions made above are true for all defocus planes. (a) (b) (c) Fig. 3 (a) Deviation of actual and geometrical droplet centres as a function of position in object plane. (b) Droplet centre discrepancy between focal and defocus plane as a function of position in the object plane. Results are for droplet diameter 200 µm. (c) Comparison of the discrepancy for two droplet sizes of 200µm and 20µm respectively. The theoretical results presented above provide useful information, but are limited to qualitative analysis only and can predict the trends and order of magnitude variation of the droplet centre discrepancy. This is due to the simplification of the calculations. In order to calculate the exact error we have to consider the thickness of the laser sheet and the actual optical arrangements, including the compression optics of the ILIDS arrangement, which makes the analysis quite cumbersome. We have to rely on experiments for the quantification of the error. However, the above theoretical analysis demonstrates that a large discrepancy can occur between the centre of the same droplet on the focused and defocused planes. 4. Quantification of droplet centre discrepancy 4.1 Detection of droplet centre Figure 4 shows the simultaneous defocused and focused images obtained with the optical set-up described in section 2 from a stream of water droplets issued from the monodispersed droplet generator with no coflowing air. Each droplet can be observed in Figure 4 as a set of vertical fringes within the horizontal stripes of light in the ILIDS image (left) and as a pair of glare points in the PIV image (right)

7 Fig. 4 Simultaneous defocused (left) and focused (right) images of droplets generated by a monodisperse droplet generator (droplets flow downward) Since the location of droplet centres plays a vital role in subsequent image processing, the first step is to detect the fringe patterns in ILIDS and glare points in PIV images. The algorithm employed in this work uses Continuous Wavelet Transform (CWT), as explained by Sugimoto et al. (2006). For the processing of ILIDS images, CWT was applied along each horizontal line of the image for two different scales of the mother wavelet or wavelet basis (Mexican Hat wavelet was chosen for this purpose due to its strong localisation properties). The transformation at larger scale (approximately equal to the fringe length) results in continuous wavelet transform with maxima almost at the centre of each fringe pattern, while the transformation at the smallest scale yields maxima corresponding to each intensity modulation of the individual fringes. Figure 5a shows a typical fringe pattern and the corresponding wavelet transforms at different scales. Considering the approximate centre identified by the large scale transform and maxima yielded from the transformation at smaller scale and using a suitable intensity threshold based on the mean intensity of the fringe, the fringe length is decided and thus the droplet centre is located at the geometrical centre of the fringe pattern. The droplet size is measured by employing the Fast Fourier Transform along a horizontal line of the fringe pattern to identify the fringe spacing from the power spectrum. Particle Tracking Velocimetry between two images, obtained at subsequent times, quantifies the droplet velocity from the corresponding droplet displacement. (a) (b) Fig. 5 (a) A typical intensity variation for a fringe pattern in the ILIDS image and its corresponding Continuous Wavelet Transform for two different scales (left) and (b) Intensity distribution of the Glare points in the PIV image and its corresponding wavelet transform

8 The glare points of each droplet in the PIV image are detected again by applying wavelet transform with a small scale along each line of the image using the same mother wavelet as before. As shown in Fig 5b, each maximum obtained from the wavelet transform corresponds to the location of a glare point. The geometrical centre between the two adjacent maxima (glare points) is assumed to be the actual centre of the droplet. The distance between glare points is proportional to the droplet size and can be a measure of droplet diameter. Since this distance can vary along the image plane (as predicted from theory) and spatial resolution of the camera is not good enough to image the glare points of smaller droplets, the determination of droplet diameter through this approach is not reliable. Hence, in this work, the glare points are used only to detect droplets on the PIV image. The corresponding droplet glare points at the subsequent time of the PIV images are found through Particle tracking velocimetry similar to the approach used for ILIDS. 4.2 Quantification of the centre discrepancy by droplet generator Once the droplets are detected in both ILIDS and PIV images, the next task is to identify the glare points in the PIV image corresponding to the appropriate fringe pattern in the ILIDS image, so that the glare points can be removed in order to proceed with PIV image processing for gas flow velocity measurement. However, the discrepancy of the droplet centre between the two images reduces the probability of identifying the correct glare points, especially for the case of a real spray. It is essential to quantify the error and eliminate it. Hence, experiments were performed with the droplet generator at five different positions along the horizontal dimension of the CCD array. The amount of defocus was kept the same for all cases. The corresponding images are shown in Figure 6 only for three different positions due to space restriction. In order to demonstrate the variation of droplet centre position, the focused and defocused images are shown together in Figure 6. The glare points seem to be moving from left to right with respect to the fringe centre along the CCD array. Two sets of images were processed for each position. At first, the location of droplet centres (geometrical centre) in ILIDS and PIV images are obtained by processing them separately. Then they are projected to the object plane using calibration coefficients. A fringe pattern is paired-up with a pair of glare points if the difference in their resulting droplet centre in the object plane is minimum in both horizontal and vertical direction. Since in this case the droplet number density is low and also there is no seeding around the droplets, the probability of identifying the corresponding glare points to a fringe pattern is almost 100%. The discrepancy between the centres is calculated for both horizontal and vertical direction. The droplet diameter estimated by ILIDS was 228µm, which is 7.5% off the theoretically calculated value for the operation of the monodispersed droplet generator. The ratio of the droplet centre discrepancy to droplet size as a function of horizontal position in the image plane is shown in Figure 7a. The droplet stream was inclined relative to the vertical direction during experiment, so that for each position of the CCD array a spread of the calculated error can be observed. The variation of the discrepancy follows a linear trend and the magnitude is greater than the droplet size (towards the edge of the CCD array), as predicted by the theoretical analysis (compare with Figure 3b). The overall trend of the error can be estimated through a linear fitting and finally can be eliminated from the original values. The remaining error is plotted in Figure 7b, which was found to be less than a droplet diameter in this case. The reason behind this remaining error can be attributed to the error involved in processing the images, especially while detecting fringe length in ILIDS. Improper alignment of the droplet stream causing droplet velocity in the third dimension can also be a reason behind this remaining error. In the vertical direction, the trend of the discrepancy was found to slightly increase from the top to the bottom of the CCD array with magnitude between 0.5d and 1.0d, which is - 8 -

9 relatively smaller than the former case and can be considered to remain constant. Since no defocusing occurs in this direction, this is attributed to a systematic error in the calibration of the optical arrangement with both cameras. Fig. 6 Fringe patterns and corresponding glare points for a stream of monodispersed droplets without seeding around it at three different positions along the CCD array, z = 1.0, 7.0 and 11mm respectively. Both the ILIDS and PIV images are superimposed on the same image Fig. 7 (a) Ratio of droplet centre discrepancy between ILIDS and PIV images in the horizontal direction normalised by droplet diameter as a function of CCD array position and estimated error (shown as a straight line obtained by a linear fit of the original data). (b) The remaining droplet centre discrepancy after subtracting the estimated error of Fig. 7(a). 4.3 Application to real spray with no seeding The detection of the corresponding fringe pattern and pair of glare points becomes more challenging for a spray, relative to the case of monodispersed droplets, because of the increase in droplet number density. The measurements in a spray were performed for a relatively dilute region at 50 cm below the nozzle centre and 25 cm away from the nozzle axis. The injection pressure was at bar and volume flow rate of water was m / s. The droplet sizes were from 80µm to 170µm as estimated from ILIDS. The corresponding ILIDS and PIV images are shown in Figure 8. In total 10 sets of images are processed to obtain droplet centres. In the focused image, detecting the pairs of glare points becomes more difficult because they tend to overlap as the droplet size reduces and may appear as a single bright spot instead of two. In such cases only one peak is obtained in the wavelet transform (refer to Fig 5b), the position of which is assumed to be the droplet centre. According to the theoretical analysis, the discrepancy between droplet centres from focused to defocused images is almost independent of droplet size. Therefore, the estimated error obtained for the monodispersed droplets (by linear fitting of the measured discrepancies) should be the same for a spray with a distribution of droplet sizes, since the degree of defocus of the ILIDS optics was not changed. The respective estimated errors, depending on the position on the CCD array, are subtracted from the position of droplet centre of each fringe pattern in the ILIDS images. For each of the fringe patterns, the corresponding pair of glare points is searched within a search area, defined on the object plane. The - 9 -

10 size of the searching window is decided by the final discrepancy in both directions obtained at the previous section using the monodispersed droplet stream. If more than one candidate is present, the one with minimum error in horizontal direction is chosen. In total 68 corresponding droplets were detected on the ILIDS and PIV images, out of which 59 had their corresponding glare points identified immediately. Since the defocusing causes a small change in the viewing area, there is a possibility that the droplets near the edges of the ILIDS images to disappear from the corresponding PIV images. In such cases a fringe pattern in the ILIDS image may not have its corresponding glare points on the PIV image. The final discrepancies of the droplet centres divided by individual droplet diameters are plotted in Figure 9a. In order to demonstrate the advantage of the present approach, the discrepancy without correction is also calculated and shown in Figure 9b. The droplet centre discrepancy with correction resulted in significant reduction from about 10 to 2 times the droplet diameter. Hence, the present approach is reliable in identifying matching fringe patterns and pairs of glare points. Fig. 8 Simultaneous ILIDS (top) and PIV (bottom) images of droplets in a spray without seeding particles 5. Combined ILIDS and PIV measurements Fig. 9 (a) Ratio of droplet centre discrepancy in horizontal direction over the droplet diameter as function of CCD array position for the spray. It is obtained after subtracting the estimated error (resulting from linear fitting the measured discrepancy for the monodisperse droplet stream) from droplet centres in the ILIDS image. (b) The same information as Fig. 9(a) without correction. In order to obtain gas velocity in the vicinity of droplets by PIV, air, seeded with aluminium oxide particles, are allowed to flow around the monodispersed droplet stream. In this section the data processing algorithm and the corresponding results are presented for one set of experimental images obtained from the combined measurements. The same operating conditions were maintained as before without seeding. The sequential images were collected with time interval of 40µs. The PIV image contains focused images of both seeding particles and droplets, out of which the glare points have to be identified and removed so that the resulting images can be processed to obtain the gas velocity

11 Figure 10 shows simultaneous ILIDS and PIV images for the case of a monodispersed droplet stream. The overall effect of the presence of seeding particles is to decrease the signal to noise ratio making the detection of droplets more difficult. In the ILIDS image, the seeding particles are defocused as well and so the image looks similar to that of a dense spray. Sometimes few seeding particles are detected along with droplets for both cases. This happens when the scattering intensity from a seeding particle exceeds the intensity threshold imposed by the algorithm. Fig. 10 Simultaneous ILIDS (left) and PIV (right) images corresponding to the monodispersed droplet stream surrounded with coflowing air seeded with aluminium oxide particles 5.1 Droplet filtering from PIV images Each pair of ILIDS and PIV images is first processed to obtain droplet centres, size (ILIDS only) and velocity. For each fringe pattern, corresponding glare points are detected, as described in the previous section, after incorporating the correction for droplet centre discrepancy. From geometrical optics, it can be proved that for each droplet the diameter is about 1.4 times the distance between glare points. Thus, around each centre determined by the glare points, a circular area with same diameter is removed. However, it is not always possible to detect perfectly the glare points for relatively small droplets. Figure 11a shows the method followed in this work based on the wavelet transform. As shown in the figure, each pair of glare points results in three negative peaks out of which the extreme ones contain the pair completely. A circular region with centre same as the middle of the distance between the glare points and with diameter equal to the distance between the two extreme negative peaks can be thought of as representative of the actual droplet. Hence the pixel values corresponding to this region are set to zero intensity. For overlapping glare points, the transform results in two negative peaks only instead of three and the droplet is removed based on those peaks. Since it is probable to detect seeding particles along with droplets in both ILIDS and PIV processing, the glare points that are removed from the PIV image are those that they have corresponding fringe patterns in the ILIDS image. Figure 11b shows a PIV image after removal of glare points

12 (a) (b) Fig. 11 (a) Demonstration of identification of glare points in PIV image using wavelet transform. (b) The PIV image after removing the glare points 5.2 Calculation of the gas velocity through PIV and integration of the result with ILIDS The focused PIV images with only seeding particles are now processed to obtain gas velocity. Use of a conventional PIV algorithm for this purpose is not preferable, because of non-uniform particle concentration due to droplet removal. Poelma et al. (2006) showed that the use of overlapping interrogation regions in images with a low image density can lead to biased results due to over sampling. This work uses an algorithm similar to Gui et al. (1998) in conjunction with non-overlapping windows. A digital mask is created with pixel values of zero for the coordinates corresponding to the circular region from where the glare points have been removed. Pixel value of one is assigned for the rest of the places, which correspond to the gas phase. This array is combined with the PIV algorithm during processing. The interrogation window size was chosen to be pixels. After calculating the gas velocity, the result has to be integrated with that of ILIDS. This is necessary in order to assign the droplet velocity and size at the appropriate locations of the PIV images, which correspond to the removed glare points. Though droplet velocity can be obtained both through ILIDS and PIV processing, the former includes diameter validation for the corresponding droplet at the two subsequent time instances. Since this is not always possible for the case of glare points, ILIDS processing is more reliable. However, there is one additional reason behind finding the corresponding glare points in the images at both time instances through particle tracking. Droplet size and velocity from ILIDS are assigned to only those glare points, which have corresponding fringe patterns in the images at both time instances. Figure 12 shows the simultaneous velocity vectors for gas and droplets corresponding to a given instant. As expected the gas velocity is almost negligible away from the droplet stream and gradually increases close to it. The average droplet size estimated from ILIDS was 228µm. Maximum droplet velocity was of the order of 10 m/s while that of gas in the vicinity of droplets was about 1 m/s. The application of the combined technique to a real spray (with seeded air surrounding it) is in progress. In such case the droplet number density increases and also there exists a chance of detection of seeding particles along with fringes and glare points. However, the current results demonstrated that the method described in this paper for eliminating the discrepancy between droplet centres on focused and defocused images increases the probability of identifying the glare points corresponding to each fringe pattern. The flow chart, presented in Figure 13, summarises the logic used for the measurement of simultaneous droplet size and both droplet and gas velocity with the combined ILIDS and PIV technique

13 Fig. 12 Simultaneous droplet and gas velocity vector plots for the case of the monosized droplet stream surrounded with seeding particles at a given instant. Thick vectors represent droplet velocity Quantify the droplet centre discrepancy using a monodispersed droplet generator and estimate the error by fitting a curve through the obtained discrepancies. Process the pair of ILIDS images to obtain droplet position, size and velocity. Process the pair of PIV images to detect the glare point centres and corresponding glare points at subsequent time instance. Correct the droplet centres location by subtracting the estimated error for each droplet. For each fringe pattern in ILIDS define a searching window to identify the corresponding glare points in PIV image. Remove the glare points from PIV images by identifying the extreme negative peaks in their corresponding wavelet transform. Process the PIV images with the modified PIV algorithm to obtain gas velocity. Assign the droplet size and velocity obtained from ILIDS to the corresponding region of the removed glare points in PIV image. Fig. 13 Flow chart for measurements of instantaneous droplet size and both droplet and gas velocity from simultaneously recorded individual pairs of ILIDS and PIV images

14 Conclusions For the study of droplet gas flow turbulence interaction in a spray, knowledge of droplet size is equally important as the droplet and gas velocities. Aiming at such investigations, we presented a new approach towards simultaneous two phase measurements in sprays by combining the out-of-focus imaging ILIDS technique with the in-focus imaging PIV technique. ILIDS provides planar droplet size and velocity, while the gas velocity in the vicinity of individual droplets is obtained by PIV. The advantage of the technique lies in its capability of identifying and removing the glare points, generated from the scattered light from droplets, from PIV images with the information of corresponding droplet position provided by ILIDS. Experiments with a stream of monosized droplets revealed that the defocusing of the ILIDS technique leads to a discrepancy between the centre location of the same droplet on the defocused and focused images. This can lead to erroneous removal of droplets or even seeding particles from PIV images during the attempt to measure the gas phase velocity. A theoretical analysis was performed by considering a simple optical configuration. Both the theory and measurements report that the discrepancy varies almost linearly with the CCD array position for a given degree of defocus. The estimated discrepancy is then subtracted from the centre of fringe patterns in the ILIDS images. This approach was shown to significantly enhance the probability of identifying corresponding pairs of fringe patterns and glare points in a real spray. A method for glare point removal from PIV images, based on wavelet transform was discussed. A modified version of the PIV algorithm was used to calculate the gas velocity field after the removal of droplets. Simultaneous ILIDS and PIV measurements and results are reported for a monodispersed droplet stream with air, seeded with particles, flowing around it. It is concluded that after elimination of the droplet centre discrepancy the combined ILIDS PIV technique can be applied in a real spray. References Damaschke N, Nobach H, Nonn TI, Semidetonv N, Tropea A (2005) Multi dimensional particle sizing techniques. Exp Fluids 39: Glover AR, Skippon SM, Boyle RD (1995) Interferometric laser imaging for droplet sizing: A method for droplet size measurement in sparse spray systems. Appl Opt 34: Golombokyz M, Morinyand V, Mounaim-Roussellex C (1998) Droplet diameter and the interference fringes between reflected and refracted light. J. Phys. D: Appl. Phys. 31:59 62 Gui L, Lindken R, Merzkirch W (1997) Phase-separated PIV measurements of the flow around systems of bubbles rising in water. ASME-FEDS M Hardalupas Y, Horender S (2003) A method to estimate gas-droplet velocity cross correlations in sprays. Atomization Spray 13: Kawaguchi T, Akasaka Y, Maeda M (2002) Size measurements of droplets and bubbles by advanced interferometric laser imaging technique. Meas Sci Technol 13: Kavounides C (2006) Particle Flows in Spray Dryers. PhD Thesis, Imperial College London

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