Application of Interferometric Laser Imaging Technique to a Transient Spray Flow.

Transcription

1 Application of Interferometric Laser Imaging Technique to a Transient Spray Flow. by Yukihiro AKASAKA, Tatsuya KAWAGUCHI, Masanobu MAEDA Abstract Department of System Design Engineering, Keio University, Hiyoshi , Kohoku-ku, Yokohama, Japan This paper describes the planar measurement technique for size and velocity distribution of spherical droplets and the experimental investigation of a transient spray. In the field of spray analysis, various kinds of measurement technique have been proposed. Interferometric Laser Imaging for Droplet Sizing (ILIDS) provides the planar diameter distribution of transparent spherical droplet. Fig.1 shows the snapshot of the conventional interferometric image of liquid droplets in a transient spray flow. This technique has been improved by Maeda et al. (2) and their optical image compression technique has overcome the fringe overlapping issue of conventional interferometric techniques. The number of fringes or fringe spacing of individual droplets is simply proportional to the particle diameter. The accuracy of this system on the diameter was about 4% using monodisperse droplet generator (Maeda et al. (2)). And they added the device of measuring Velocity of individual particles by Particle Tracking Velocimetry (PTV) technique. The accuracy of this on the velocity was about 9% in the high number density of droplets position using LDV. Finally, we measured the particle location, diameter and velocity in a transient spray flow. compression Velocity (m/s) 2 1 calculate Diameter(ƒÊm) 3 (c) r (m m) 2 r 1 1 z 2 z (mm) 3 4 (d) Fig.1: Snapshot in a transient spray at t=4.2ms after the start of injection and fringe images for ILIDS:classical ILIDS,present ILIDS,(c)correlation between the droplet diameter and velocity,(d)global velocity vector map at the same time.

2 1. Introduction This paper describes the planar measurement technique for size and velocity distribution of spherical droplets and the experimental investigation of a transient spray. In the field of spray analysis, various kinds of measurement technique have been proposed. The phase-doppler anemometry (PDA) is one of the successful techniques to measure the diameter and velocity of individual particles through the probe volume with high spatial resolution. Such point measurement techniques, however, have a difficulty understanding the spatial structure of unsteady flow fields and the interaction between particles and surrounding fluid. Interferometric Laser Imaging for Droplet Sizing (ILIDS) observes the spatial interference pattern of scattered light on an out-of-focused plane of receiving optical system. The relation between fringe spacing and particle diameter was derived by noting the angular phase difference of external reflection and direct refraction of a spherical particle illuminated by a coherent laser source. The number of fringes or fringe spacing of the interferogram is simply proportional to the particle diameter. Previous ILIDS techniques, which observe the circular interferogram, have still difficulties in discriminating the neighboring particle s image. The intensity distribution within the fringe overlapping region gives the complicated interferential signal and their irregular-frequency components is not connected with the particle diameter. The present imaging technique has been improved by Maeda et al. (2) and their optical image compression technique has overcome the fringe overlapping issue of conventional interferometric techniques. The improved technique observes the linear interferogram which can be easily detected by scanning the horizontal pixels of the recorded digital image in the computer's memory. Particle diameter is determined by estimating the accurate spatial frequency of the interferogram by using Discrete Fourier Transform and Adjusted Gaussian fitting interpolation technique (Kobashi et al.199) in order to reduce the bias error of estimated frequency. And, we improved the ILIDS to be able to measure the Velocity of individual particles by PTV with particle interferometric image correlation technique. The present study attempts to examine the transient spray analyzing spatial distribution of the droplets. 2. Principle 2.1 Theoretical background The laser sheet illuminated the spherical droplets in the flow-field. The reflected and refracted light from the droplet is dominant in the wide-angle forword-scatter region, around 3deg. to 8deg. ILIDS is based on counting the number of fringes in the interference image, made by these scattering lights. At a view angle in off-axis alignment θ, two components of the scattered light appear to emanate from small spots. The two spots are observed as glare points (Fig.2) on the focal plane. From the spacing between the spots, the droplet diameter is determined. However, because of the lack of resolution and the necessity of magnification, it was not effective for real flows. On the non-focal plane, the two rays interfere with each other and the regular fringes are clearly observed and their origin can be understood in terms of a simplified geometric theory. The fringe spacing is proportional to the droplet diameter, and if a set of fringes can be observed for individual droplets, they provide a potentially accurate measurement of droplet diameter. Gréhan et al. (1998) calculated the adequate defocus length, since defocus length is necessary for doing image plane far-field. König et al. (1986) describe a method for measuring the size of single droplet and the angular fringe spacing as a function of droplet size so that the particle size measurement might become independent of the absolute light intensity and only the real part of the refractive index has to be taken into account. The function (provided below) relates the number of fringes and particle diameter. It is easily expressed via the phase

3 difference between two rays. Laser sheet Droplet α θ Refraction light Reflection light θ Collecting lens Interference image Non focal plane Focal plane Glare points (Not to scale) Fig.2: Basic configuration of the ILIDS imaging system Pajot et al. (1998) described the relationship between particle diameter d and the number of fringes. 2λN d = α θ cos + 2 m 1 θ msin 2 (1) + 1 2mcos 2 2 θ where; d is the droplet diameter, N is the number of fringe, θ is the scattering angle, α is the collecting angle(equal to N θ), θ is the angular inter-fringe space, λ is the wave length of the incident laser and m is the refractive index of the liquid droplet. Eq. (1) is derived from geometric analysis. Van de Hulst (1957) showed that reasonable agreement between the geometric analysis and the full Lorenz-Mie theory is generally obtained for values of χ=πd/λ >1-2, provided that the refractive index of the droplet differs significantly from its surroundings and that rays close to grazing incidence and those close to the rainbow angles are not involved. In our case, for λ=532nm, the lower limit is approximately d=2µm. If a set of fringes can be observed and this number can be measured, droplet size can be obtained from Eq. (1). 2.2 Fringe image compression for denser sprays A conventional picture taken ILIDS is presented in Fig.3. The number of fringes on each circle image determines the droplet size. But the evaluation of the individual droplet images is difficult because these images of droplets overlap each other. We designed the original receiving optics to overcome droplet overlapping. Fig.3 is a comparison of the fringe image between the conventional ILIDS technique and our original technique. Fig.4 illustrates the simplified schematic of the present receiving optics that consists of a rectangular mask, a circular collecting lens, a pair of cylindrical lenses and CCD array. The most important feature of the present technique was to add a compression unit in the receiving optics. This unit is mounted between the collecting lens and the CCD array and consists of two cylindrical lenses(fig.4). By using this compression unit, circular fringe images Fig.3 are transformed to compressed images Fig.3. These lenses can shift along the optical axis and enable to adjust the degree of horizontal defocusing. And to

4 adjust the aperture size and enhance the depth of focus, we added the rectangular mask in front of the collecting lens(fig.4). Fig.3: example of the finge image measured by ILIDS(4mm 4mm), classical ILIDS,present ILIDS Particle(Droplet, Bubble,...) Scattered light Rectangular mask: 5 ~3mm 2 Collecting lens: Nikon Nikkor, mm, F2.5 Cylindrical lens: f=-1, 1mm CCD array: 118 ~18 pixels Fringe image Fig.4: Details of the receiving optics with cylindrical lenses. By using this optical device, the droplet overlapping can be avoided and the spatial resolution is increased 3 times compared with the conventional method. The signal within fringe is sometimes not simple. Especially in the dense spray location, fringe image is distorted (Fig.5, Example 1) due to the secondary scattering or internal oscillation. In the number of Example 1, the fringe is not related to the diameter. Example 2 in Fig.5 shows a typical fringe image. Fig.5 is the intensity profile on the horizontal axis of circular image. On the other hand, Fig.5 is the intensity profile of the compressed fringe image. It shows that the numbers of the broken fringe image are not counted. In this study, it filters optically and the interference fringes which are unrelated to the diameter of a particle are rejected automatically by image processing. Example 1 Example Intensity 255 Intensity H orizontal Pixel Fig.5: Measured interferograms and intensity profiles. 1 Horizontal Pixel 28

5 2.3 Image Processing After capturing droplet image by the KODAK MEGAPLUS ES1. CCD camera, the image analysis is carry out with an original code written in C. In the beginning, the position of compressed fringe image is searched by several imaging filter. The signals obtained images are similar to Doppler burst signals. The concept of the image processing to evaluate the fringe spacing is the same of as an FFT based LDV/PDA technique by which the accurate frequency is calculated with adjusted Gaussian fitting of the discrete Fourier power spectrum, as shown in Fig.6 (Maeda et al.1988, Kobashi et al.199). P k k-1 k k+1 f Frequency Fig.6: Fine peak detection and frequency determination by Discrete Fourier Transform with Gaussian fitting. The interpolation technique is effective in reducing the bias error to less than.2% of the fundamental frequency. The equation for adjusted Gaussian fitting is as follows: Pk log( 1 Pk k = 2 Pk log( P k Pk + 1 ) log( ) Pk Pk + 1 ) + log( ) P f * = K peak a +.336a 1 1 k 3 (2) (3) N = L P FFT f * (4) Where k is the frequency corresponding to the maximum power in the discrete spectrum, f* is the adjusted frequency, N is the fringe number, L is fringe image length, P FFT is the FFT point number. Thus, if N is known, Eq. (1) shows droplet s diameter. Next, the velocity measuring method is explained. The velocity is calculated by the same method as a Particle Tracking Velocimetry (PTV) technique. S and t are the particle displacement and time interval between two images, respectively. The velocity of an individual particle is given as follows. v S t = (5) However the conventional PTV technique has difficulty in determining the corresponding particle in denser spray flow. Fig.7 is a comparison of the correlation maps between a conventional cross correlation method (R 12 ) and present method(r 12 ). Correlation map R 12 indicates the clear single peak around δ x = 5, δy = 1(Fig.7 ), but R 12 gives the

6 multiple peaks of the correlation function (Fig.7 ). The present technique has significant advantages to determine the corresponding particles by using the information of the individual diameter measured by ILIDS. In the end it provides higher correlations. Window 1 Window 2 Interferogram R 12 R Cross correlation coefficient δ x δ x Fig.7: Comparison between convential particle tracking (R 12 ) correlated with many particles and the present method (R 12 ) considering the diameter difference which provide a unique correlation with well corresponding particle. 3. Experiments and Results The experimental setup is shown in Fig.8. The measurement equipment consisted of a high power laser light source, receiving optics (explained above section.), timing controller, high resolution CCD camera, and personal computer. The laser source is double--pulsed Nd:YAG laser at 532nm in wavelength with the maximum output power of 1mJ/pulse, the repetition frequency of 3Hz and duration time of the laser pulse is 3 to 5ns and the thickness of the laser sheet at the test section is.5mm. But the system is insensitive for the imaging depth because the technique is basically on the defocused images and the ratio of image diameter and its fringe spacing. The Fringe images are captured by a high resolution digital CCD camera which acquires and transfers the progressive image sequence to a computer's memory directly. The CCD camera has pixels, each pixel is a 1bit grayscale accuracy and the size of each pixel is 9µm 9µm. The viewing area of the receiving optics is 1mm 1mm. The distance of the Top View Side View objective lens and the test section in tank was 17mm, scattering was 73deg. that gives the maximum visibility of interference signal. The collecting angle was set to 1deg., which is calculated from the ratio between the distance to the droplet and the effective diameter of the objective lens. Fuel injection system consists of a pressure pump, a fuel tank, a swirl-type injector and a driver. N-heptane is used as a fuel. The nozzle diameter is.75mm, while the spray cone angle is 55deg. Under atmospheric pressure and room temperature condition.fig.9 is the frozen photographs of a transient spray flow by a swirl-type fuel injector. The injection pressure and ambient pressure are.5mpa and.1mpa, Laser1 Laser2 Laser Head Nd:YAG Laser Power Supply Laser head Timing Pulse Generator Injector Driver Chamber Window Injector z r Receiving optics Fuel Tank CCD Camera Fig.8: Experimental apparatus of the transient spray measurement. N2

7 respectively. The most important set up was the timing controller to catch up the preferable coincidence of spray timing and illumination. The time delay after the start of injection is t=.5ms to 4ms. In the transient spray flow, local droplet concentration and diameter, velocity distributions are a function of both time and location. r (mm) 25 2 Injector 5 mm r (mm) 25 3 z (mm) 4 Fig.9 is the example of the measured results in z=25mm, 45mm of r=2mm from the nozzle at t=4.2ms after the start of injection. The rectangular in the picture represents the viewing area of the receiving optics of 1mm 1mm. ILIDS gives the instantaneous droplet locations, individual diameters and velocity vectors. The result shows the difference that the upper region contains the dense smaller particle and the lower contains larger droplets, which were injected earlier period. Fig.1 shows the Probability Density Function (PDF) of the particle diameter distribution at t=4.2ms after the start of injection. The measurement area is from r=mm to 25mm and z=mm to z=6mm. On the center axis at r=mm, no drastic change of size distribution is found except z=mm region. The PDF at r=1mm, 2mm showed that the mean diameter in the downstream region was lager than that of upstream, i.e. larger droplets have reached to the downstream region rapidly and smaller droplets remained in 5 z (mm) diameter velocity Fig.9: Comparison of Particle diameter and velocity distribution from a instantaneous frozen image viewing z=25mm, 45mm of r=2mm from the nozzle at t=4.2ms after the start of injection. Probability 2 µm 4 µm 6 µm 3. m/s mm T delay = 4.2 ms mm Diameter(µm) Injector r = mm z=mm 2mm 4mm 6mm Fig.1:Probability Density Function of droplet diameter in 1mm 1mm region and their spatial distribution of droplets at t=4.2ms after the start of injection.

8 the upstream area floating downstream slowly. Fig.11 is the correlation plot of the droplets size and velocity at the corresponding area shown in Fig.1. In the region of z>3mm, residual droplets by the previous injection were simultaneously observed and gave the bimodal distribution of both size and its correlation to the velocity. One of the novel feature of the present technique is to understand the spatial structure of the flow fields. Fig.12 illustrates the global velocity vector field and their diameter dependency. It is important that these velocity vectors in Fig.12, 13 are all evaluated from the pictures for the different particle sizes. The viewing area is <r<3mm and <z<4mm from the nozzle. The time was frozen at after the start of injection t=4.2ms. Diameter range was selected to d<3µm and d>5µm and the flow regime was compared. Each velocity vector was obtained by calculating the mean velocity vector of droplets detected within the 4mm 4mm, 5% overlapped small subregion. The vector maps give us a significant knowledge that the velocity of the smaller droplets is comparatively slow throughout the given area in contrast with the high velocity of the larger droplets. Velocity (m/s) mm T delay =4.2ms Diameter (µm) Fig.11: Correlation between droplet diameter and the velocity at t=4.2ms after the start of injection. r 2 1 1mm 2 1 Injector r = mm z=mm 2mm 4mm 6mm r (mm) r (mm) z z (mm) 2 z (mm) Diameter range : d <3µm 5 µm < d Fig.12: Global velocity vector map of smaller(d<3µm)and larger(5µm<d) droplet. Viewing area is <r<3mm and 5<4mm, t=4.2ms after the start of injection. Fig.13 illustrates the velocity vector maps in the magnified area at r=1mm, z=mm in the previous Fig.12. Simultaneously the PDF of the droplet diameter at the corresponding area is shown in Fig.13. Diameter range was 2µm<d<3µm, 3m<d<4µm, (c)4µm<d<5µm}, (d)5µm<d<75µm. Each vector was given by the mean velocity of the droplets within the 3mm 3mm, 8% overlapped subregion. The velocity of the smaller droplet and, which contain the peak of the PDF of diameter, flow direction significantly changes in the attractive region from the left side toward the downstream due to the entrainment of spray. In contrast with the results of smaller particle, velocity

9 . (c) (d).1 PDF Diameter (µm) r r (mm) 5 5 Diameter range : 2 < d <3µm 3< d <4µm 1 1 z z (mm) 2 2 (c) 5 4 < d <5µm 1 (d) 5 5 < d <75µm Fig.13: Probability density function of droplet diameter in the upper diagram. Velocity vector maps below show the size dependency of the velocity fields at the same location,r=1mm,z=2mm and at t=4.2ms after the start of injection. distribution of larger droplet(c) and (d) gives the higher and almost homogeneous direction of the velocity vector. The comparison of the velocity maps demonstrate the remarkable difference of the absolute velocity and flow direction. 4. Conclusion We added the device of measuring velocity of individual particles and original receiving optics to the conventional ILIDS. By using the original receiving optics of a image compression technique, the spatial resolution for diameter was improved and the optical signal to noise ratio of the captured interferential image were enhanced. And it was able to reject automatically the signals with distorted or inclined fringes by wrong incident light in the dense spray flow. The significant advantage of the present technique is the precise diameter determination. Using this feature the cross correlation was carried out and high correlation was obtained between two images. The technique was further applied to the transient dense spray of N-heptane and provided an instantaneous spatial distribution of particle diameter, velocity vector of individual particles successfully. The comparison of the unique velocity vector map by the present technique demonstrates the remarkable difference of the velocity fields depending on the particle diameter even in the same area.

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