measurements of droplets spatial distribution in spray by

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 09-12 July, 2012

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Measurements of Droplets Spatial Distribution in Spray

by Combining Focus and Defocus Images

Kentaro HAYASHI1*, Mitsuhisa ICHIYANAGI2, Koichi HISHIDA3

1: Dept. of System Design Engineering, Keio University, Yokohama, Japan

2: Dept. of Engineering and Applied Sciences, Sophia University, Tokyo, Japan 3: Dept. of System Design Engineering, Keio University, Yokohama, Japan

* correspondent author:, [email protected] Abstract: The measurement accuracy of droplets’ position, size and velocity in a spray flow was improved by combining interferometric laser imaging for droplet sizing (ILIDS) with glare-points technique (GPT). For the combination of ILIDS and GPT, we have developed the advancing optical measurement system, called as Double-planes Particle Imaging (DPI). DPI has an advantage to simultaneously capture both focus images (glare-points) and defocus images (interferometric fringes) by using only one imaging device. For the determination of droplets’ position, the center position of glare-points was adopted as the actual droplet position. For the calculation of droplets’ sizing, we need to multiply the spatial frequency of fringe pattern with the fringe length. For reducing the ambiguity of the fringe length, the estimation technique for the fringe length was proposed, which was calculated from the vertical distances between the focus and defocus images. The relationship between fringe length and vertical distance was estimated by the ray tracing method. The velocity was calculated by PTV with the aid of droplet information by ILIDS. The measurement accuracy of droplets’ sizing for the DPI system was validated by evaluating the diameter of monodispersed droplets. Compared with ILIDS and DPI, the bias error was extremely improved. Furthermore, DPI was applied to the actual spray flow, and the spatial distributions of droplets’ position, size and velocity were measured. These results indicate that the histogram of droplet diameter was similar to the chi-squared distribution, because the probability of large size droplets was reduced by improving the measurement accuracy of droplets’ sizing especially in the droplet size area of more than 150 µm. 1. Introduction

A liquid spray is widely used for many industrial fields, such as fuel injections in engines,

inhalers in medical applications, ink-jet printers and so forth. For further enhancement of industrial devices using sprays, the size and velocity distribution of droplets in a spray are required, because this information enables us to understand the unsteady behavior of droplets and surrounding flow structure. Various optical measurement techniques have developed to investigate the flow structure of sprays. One of the most common measurement techniques is Phase Doppler Anemometer (PDA). This technique gives the accurate data of droplet size and velocity by extracting information from the scattered light. However, the PDA is a pointed measurement technique, so that it is difficult to obtain droplets’ spatial distributions in unsteady spray flows. Interferometric laser imaging for droplet sizing (ILIDS) is a promising technique to provide the spatial distribution of droplets’ position, size and velocity simultaneously. This technique captures the interference patterns generated from the reflected and refracted lights in the forward scattering regions (Glover et al. 1995), because the angular frequency of the interference pattern or the number of fringe depends on the size of particles (Hesselbacher et al. 1991). Maeda et al. (2000, 2002) and Kawaguchi et al. (2002) developed the optical system to compress interference images, which can dramatically increase the droplets’ number density per an image, in order to solve the problem to overlap fringe


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pattern images in dense particle areas. In addition, they measured the droplets’ diameter and velocity simultaneously by combining ILIDS with Particle Tracking Velocimetry (PTV).

Recently, several researchers pointed out that ILIDS has two problems about the measurement accuracy of droplets’ position and sizing. Hardalupas et al. (2010) noted that the droplet center discrepancy is found between focus and defocus planes, which was made clear by using the geometrical optical method. The center discrepancy is several times larger than droplet diameter, which causes the calculation errors of droplets’ velocity and mass flux. Our previous work (Shigeta et al. 2010, 2012) presented that ILIDS has the error of droplet size detection, because of the ambiguity of the fringe length in interference patterns. To solve the above two problems, Shigeta et al. (2012) developed a new measurement technique called DPI (Double-plane Particle Imaging). DPI combined ILIDS with glare-points technique (GPT), which simultaneously captures focus images (glare-points) and defocus images (interferometric fringes) by using only one imaging device. The errors of droplets’ position and sizing were corrected by using the droplets’ diameter and the center position obtained from GPT, respectively. This technique has a powerful tool to overcome the problems of ILIDS. However, the measurement accuracy of droplets’ sizing of GPT is lower, because the distance between glare-points is proportional to droplets’ diameter, and its accuracy dominates the spatial resolution of the imaging device such as a CCD camera.

The objective of this work is to develop the new analytical algorithm of interference patterns from the DPI system for the estimation of droplets’ position, sizing and velocity. For the determination of droplets’ position, the center position of glare-points was adopted as the actual droplet position. For the calculation of droplets’ sizing, we need to multiply the spatial frequency of fringe pattern with the fringe length. For reducing the ambiguity of the fringe length, the estimation technique for the fringe length was proposed which was calculated from the vertical distances between the focus and defocus images. The relationship between fringe length and vertical distance was estimated by the ray tracing method. The velocity was calculated by PTV with the aid of droplet information by ILIDS. The measurement accuracy of droplets’ sizing was confirmed to measure a monodispersed droplets’ diameter by ILIDS and DPI. Furthermore, DPI was applied to the actual spray flow, and the spatial distributions of droplets’ position, diameter and velocity were measured at several points in an air atomizing spray. 2. Improvement of ILIDS 2.1. Principles of ILIDS and GPT

When light illuminates a spherical transparent droplet, the intensity of the reflected and the first order refracted light from the droplet are stronger than that of higher order refracted light in the forward region for the scattering angle between around 30 to 80 degrees. In the focal plane, two bright spots, which are derived from these two lights and known as glare points, are observed (van de Hulst and Wang 1991). On the other hand, in the defocus plane, these two lights interfere with each other, and a parallel interferometric fringe is observed as shown in Fig. 1. A measurement technique using focus images is called Glare-Points Technique (GPT), and a technique using defocus images is called as Interferometric Laser Imaging for Droplet Sizing (ILIDS).

In GPT, a diameter of spherical transparent droplet, D, is calculated from the following


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equation, which was derived from the geometrical optics,

2D GP E= ⋅ , where

1122cos sin 1 2 cos

2 2 2E m m mθ θ θ

−−⎡ ⎤⎛ ⎞⎢ ⎥= + ⋅ + −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

, (1)

where GP is the distance of glare-points, m is the relative refractive index of the liquid droplet, and θ is the scattering angle. Equation (1) is available when qualifying the following condition.

20>=λπ p

p

dx , (2)

where dp is the particle diameter, λ is the laser wavelength. The planar positions of droplets are defined as center positions between these two bright dots, and the planar velocity-vectors are determined by calculating the deviation of center positions of glare-points in a short time. The advantage of this measurement system is that the mid-points of the glare-points correspond closely to the actual droplets’ center positions, and their discrepancies were estimated to be only 0.1D (Hardalupas et al. 2010). However, GPT has the difficulty to detect the diameter of droplets of the order of 10 µm, because the distances between glare-points are narrow to need the sub-pixel evaluation in images.

On the other hand, ILIDS measures the diameter of a spherical transparent droplet from the pattern frequency or number within the interferogram. The relationship between the droplets’ diameter and frequency of interferometric fringe is derived from the phase difference between reflected and the first order refracted light originated from one droplet. The droplet diameter, D, is obtained by the following equation, which is derived from the geometric optics,

2 ND Eλα

= ⋅ , (3)

where N is the number of fringe, λ is the wavelength of the laser light source, m is the relativerefractive index of the liquid droplet, θ and α are scattering and collecting angles,

Focus plane

Droplet

θ

Collecting lens

Defocus plane

Interferometric fringe

Glare-Points

Laser sheet

Y

Z

X

α

Fig. 1. Principle of glare-points and interferometric fringe pattern.


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respectively. Droplet planar position is determined as the center of the fringe pattern. The two-dimensional velocity is calculated from consequent frames by using the cross-correlation method. In conjunction with the cross-correlation coefficient, the validity of the planar displacement estimation can be validated by comparing the droplet size obtained in the first frame with the size of the candidate droplets inside the predefined interrogation window. Maeda et al. (2000) improved the ILIDS technique by developing the optical compressed system in order to overcome the circular interferograms overlapping problem in high particle concentration regions.

Hardalupas et al. (2010) pointed out that the droplet center discrepancy is found between interferometric fringe and glare-points by the geometric optics method. Figure 2 illustrates the horizontal center discrepancy at two droplet location. Their results indicate that the discrepancy depends on not only horizontal droplet position but also vertical and depth droplets’ position and degree of defocus. Shigeta et al. (2010, 2012) noted that ILIDS has the error of droplet size detection. For the calculation of droplets’ sizing, we need to multiply the spatial frequency of fringe pattern with the fringe length. As shown in Fig. 3, the full length of fringes includes fringes from noise areas, which causes the ambiguity of the fringe length in interference patterns. 2.2 Present system based on DPI

In order to overcome the above two problems, a new algorism was developed using the Double-planes Particle Imaging (DPI) system. DPI combined ILIDS with GPT, and simultaneously can capture both focus image (glare-points) and defocus image (interferometric fringe) by only one imaging device. Figure 4 shows the overview of the present algorithm using the DPI system, and the detailed procedure of the algorithm is summarized in chapter 3. The droplets’ position was corrected by adopting the position data of glare-points’ image center. The measurement accuracy of droplets’ sizing of ILIDS was improved by reducing the ambiguity of the fringe length detection, which corrects the number of fringe pattern. The droplets’ velocity was calculated from the displacement of glare-points’ image center. A pair of droplets’ images in subsequent photos was matched with the aid of the interferometric fringe pattern from ILIDS.

Ray axisDroplet

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Defocus plane

Y

Z

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Droplet center discrepancy

Fringe’s centerGlare-Points’ fringe

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Captured imageon focus and defocus plane

0 20 40 60 80 100 120 140

Actual length [pixel]

Full length in an image [pixel]

Inte

nsity

[-]

Fig. 2. Problem of droplets’ position detection by

ILIDS. Fig. 3. Relationship between actual and

full length of fringe pattern.


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3. Optical Arrangement and Image Processing 3.1. Configuration of optical system

For the combination of ILIDS and GPT, the receiving optical system called as DPI system was developed as shown in Fig. 5(a). The optical glass ((1) in the figure) and two cylindrical lenses ((2): curvature radius = ±51.9 mm) were equipped at the positions between the collecting lens (Nikon Corp., focal length = 105 mm) and the imaging device ((3): CCD camera (Imperx ICL 2520 SC, 2058 × 2456 pixels, 30 fps)). As shown in Fig. 5(b), the imaging device was set with sheimpflug arrangement, and the scattering angle and collecting angle were set as 73 degrees and 6.53 degrees, respectively. The total length of this system (the length from optical axis to imaging device) was 412 mm. The distance from optical axis to the optical lens was 219 mm. The distance from the center of laser sheet to collecting lens was 185 mm. The degree of defocus was 11.0 mm. The refracted and first-order refracted scattered lights from droplets can transmit two ray paths guided by the apertures, as shown in Fig. 5(c). In the top circular aperture (diameter = 3.5 mm), both scattered lights pass through the optical glass and produce two glare-points in a focus plane. On the other hand, in the middle rectangular aperture (3 mm × 25 mm), both scattered lights go through two cylindrical lenses and provide interferometric fringe patterns in a defocus plane, whose images are vertically compressed. The outside dimension of the optical glass is equal to that of the cylindrical lenses, which gives that the optical path lengths of focus images are the same as those of defocus images. Thus, focus and defocus images from droplets, illuminated by a laser sheet, can be captured by using only one camera, as shown in Fig. 5(d). In this study, the measurement area was 10 × 10 mm, and the thickness of laser sheet was approximately 2 mm.

t =t1

t =t1+Δt Position: GPT Diameter: ILIDS

0 20 40 60 80 100 120 140

To adopt Glare-points center as a droplet position

To calculate fringe number Nby ray tracing

Fig. 4. Overview of present algorithm using Double-planes Particle Imaging (DPI) system.


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3.2. Algorithm of image processing

The algorithm of image processing of the DPI system is shown in Fig. 6. Firstly, fringe patterns and glare-points are individually detected from an image. Secondly, the center positions are calculated from fringe patterns and glare-points, and its fringe frequencies are obtained from fringe patterns. Thirdly, as shown in Fig. 7, a fringe length, L, is proportional to a vertical distance, s, between a fringe pattern and glare-points (Willert and Gharib 1992). The calibration curve between L and s was estimated by using the ray tracing method, as shown in Fig. 8. The actual fringe length was estimated by calculating the vertical distance from the image processing and using the calibration curve in Fig. 8. Fourthly, the droplets’ position, size and velocity were calculated. The droplets’ position was determined as the center position of glare-points, because discrepancies between glare-points and actual droplets’ positions are less than 5%, compared to the droplet size. For the droplets’ sizing, the fringe number was calculated by multiplying a fringe length and a fringe pattern frequency, and the droplets’ size was calculated by substituting the fringe number for equation (3). The droplets’ velocity was calculated from the displacement of center positions of glare-points which was based on the PTV method with the aid of fringe patterns. Finally, the droplets’ position and velocity-vectors were transformed into actual coordinate by using the calibration curve between the camera’s and actual coordinates.

DropletY

XZ

(2) Cylindrical lens

(1) Optical glass

(3) CCD with sheimpflug arrangement

Aperture + Collecting lens

(3)

X

Y

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(1)

(2)

Ray axisDroplet

(1)

YZ

X

(3)

(2)

Receiving optical system

(a)

(b)

(c) (d)

Focus image

Defocus image

Collecting angle

Scattering angle

Fig. 5. (a) Schematic of DPI system. (b) Top view and (c) side view of optical path lines by DPI

system. (d) One sample image including glare-points (focus image) and interferometric fringe pattern (defocus image) captured by DPI system.


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Glare -pointsFringe pattern

Center positionCenter positionFringe frequency

Calculate fringe length by estimating depth position

Ray tracing

Calculate position, droplet size and velocity

Coordinate transformation

Fig. 6. Flow chart of algorithm of image processing of DPI system.

X

YZ

Aperture Imaging planeObject plane Collecting lens

s1

s2

s: Vertical image distance [mm]

L1

L2

L: Fringe length [mm] Fig. 7. Relationship between fringe length, L, and vertical distance, s, between fringe pattern and

glare-points.

1.51.61.71.81.9

22.12.2

0.15 0.2 0.25 0.3 0.35 0.4

Frin

ge le

ngth

L[m

m]

Vertical disance s [mm]

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020040060080010001200

fringe

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1800

Fig. 8. Procedure to obtain calibration curve between fringe length, L, and vertical distance, s.


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3.3. Experimental condition

The measurement accuracy of droplets’ sizing using the DPI system was validated by measuring the diameter of monodispersed droplets. The droplets were generated by using the mono disperse generator as shown in Fig. 9(a), and their true diameter was measured by GPT and evaluated to be 179 µm. In order to clarify the availability of the proposed system, the results from DPI were compared with those of DPI.

The DPI system was applied to measure the spatial distributions of droplets’ position, size and velocity in an air atomizing spray, and compared with ILIDS. The spray was generated by an air atomizing nozzle (H. Ikeuchi & Co., Ltd, BIMJ2022), and the water and air pressure was set to be 0.5 bar and 0.1 bar, respectively. The spatial distributions of droplets were measured at (X, Y) = (0 mm, 30 mm), (0 mm, 40 mm), and (0 mm, 50 mm) in Fig. 9(b). 4. Results and Discussion 4.1 Validation of measurement accuracy of droplet sizing

For the validation of measurement accuracy of droplets’ sizing, the droplets with the diameter of 179 µm were measured by using ILIDS and DPI. Figure 10 shows the histograms of droplets’ diameter from ILIDS and DPI. The result indicates that the peak value of histogram from DPI is significantly close to the true value, compared with ILIDS. Furthermore, the measurement uncertainty of droplets’ sizing of ILIDS and DPI was evaluated and summarized in Table 1. It was obvious that the bias index of DPI was drastically improved. This was caused by reducing the ambiguity of the fringe length from the area of image noise.

4.2 Application to actual spray

The spatial distributions of droplets’ position, sizing and velocity in an actual spray flow were measured by ILIDS and DPI. Figure 11 shows the histograms of droplets’ diameter at (x, y) = (0

x

ySpray

Air atomizing nozzleDroplets

Z

YX

Collecting lens （f =105 mm）and apertureCCD camera

Cylindrical lenses

Mono disperse generator

Optical glass

(a) (b)

Fig. 9. Experimental set up for (a) validation of droplet sizing and (b) application to actual spray.


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mm, 30 mm), (0 mm, 40 mm), and (0 mm, 50 mm). The origin was located at the nozzle exit. It was found that the histogram of droplet diameter form DPI was similar to the chi-squared distribution, because the probability of large size droplets, especially more than 180 µm, was reduced by improving the measurement accuracy of droplets’ sizing. Figure 12 indicates the spatial distribution of droplets’ position, sizing and velocity, located at (x, y) = (0 mm, 40 mm). The droplets’ positions from ILIDS corresponded to those from DPI at x-location ranging from x = 1.0 mm to x = 2.0 mm. On the other hand, the droplets’ positions from ILIDS were deviated away from those from DPI at around x = −2.5 mm or 5.0 mm. Thus, the droplets’ position error from ILIDS was improved by using the DPI system. 5. Conclusions

A new measurement technique called as Double-plane Particle Imaging (DPI) was developed by combining ILIDS and GPT, for the improvement of measurement accuracy of droplets’ position, size and velocity. The system enables to simultaneously capture focus and defocus images by using only one CCD camera. The center position in focus image was determined as the actual droplets’ position, which causes to improve the droplets’ position error of ILIDS. The ray tracing method was

0

0.05

0.1

0.15

0.2

0.25

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10 30 50 70 90 110130150170190210230250270290

ILIDSPresent work

D = 179[µm] ( validated by GPT)

Diameter [µm]

Prob

abili

ty[-

]

Fig. 10. Histograms of droplets’ diameter measured by ILIDS and DPI. Table 1. Measurement uncertainty in 95% confidence level of droplets’ sizing of ILIDS and DPI

ILIDS DPI Averaged diameter [µm] 226 178 Bias index [µm] 47 1 Precision index [µm] 31.2 21.1 Measurement uncertainty in 95% confidence level [µm]

77.1 41.3


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employed to estimate fringe lengths in defocus images, which causes to improve the measurement accuracy of droplets’ sizing. The DPI system was applied to measure the diameter of the monodispersed droplets and the spatial distribution of droplets in a spray flow. The important conclusions obtained from this work are summarized below.

(1) The measurement accuracy of droplets’ sizing of DPI was validated by measuring the diameter of monodispersed droplets. The bias index of DPI was significantly reduced, compared with ILIDS. This was caused by reducing the ambiguity of the fringe length from the area of image noise and improving the measurement accuracy of droplets’ sizing.

(2) The DPI system was applied to measure the spatial distributions of droplets’ position, size

and velocity in a spray flow, and compared with ILIDS. The histogram of droplet diameter form DPI was similar to the chi-squared distribution, because the probability of large size

X

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(0,50)(0,40)(0,30)

Diameter [µm]

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abili

ty[-

]

(X , Y ) =

ILIDS

DPI

Fig. 11. Histograms of droplet diameter measured by ILIDS and DPI.

42

43

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46

47

48

49

-2.5 2.5 5.00

X [mm]

Y [m

m]

250 [µm]1.0 [m/sec]

DPI

ILIDS

Fig. 12. Spatial distribution of droplets’ position, diameter and velocity at (x, y) = (0 mm, 40 mm).


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droplets was reduced by improving the measurement accuracy of droplets’ sizing. Furthermore, the droplets’ position error from ILIDS was improved.

Acknowledgements

This work was subsidized by Grant-in-Aid for Scientific Research (S) (No. 21226006) of Japan Society for the Promotion of Science. References Glover AR, Skippon SM, Boyle BD (1995) Interferometric laser imaging for droplet sizing

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measurements of droplets spatial distribution in spray by

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