Application of Interferometric Laser Imaging Technique to a Transient Spray Flow.
by
Yukihiro AKASAKA, Tatsuya KAWAGUCHI, Masanobu MAEDA
Department of System Design Engineering, Keio University,
Hiyoshi 3-14-1, Kohoku-ku, Yokohama, Japan
Abstract
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. (2000) 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. (2000)). 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.
Velocity (m/s)
20
10
0
0
30
150
60
90 120
m)
Diameter( ƒ Ê
(c)
30
r (m m)
20
10
r
0
0
z
compression
10
calculate
20 z (m m)
30
(a)
(b)
40
(d)
Fig.1: Snapshot in a transient spray at t=4.2ms after the start of injection and fringe images for ILIDS:(a)classical
ILIDS,(b)present ILIDS,(c)correlation between the droplet diameter and velocity,(d)global velocity vector map at
the same time.
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. (2000) 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.1990) 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 30deg. to 80deg. 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
difference between two rays.
Laser sheet
Droplet
θ
Refraction light
α
Reflection light
∆θ
Interference image
Collecting lens
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.
d=
2λN
1
α
cos
θ
2
+
m sin
θ
(1)
2
m 2 + 1 − 2m cos
θ
2
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 >10-20, 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 (a). 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 (a) and our original technique (b). 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 (a) are transformed to compressed images
Fig.3 (b). These lenses can shift along the optical axis and enable to adjust the degree of horizontal defocusing. And to
adjust the aperture size and enhance the depth of focus , we added the rectangular mask in front of the collecting
lens(Fig.4 ).
(b)
(a)
Fig.3: example of the finge image measured by ILIDS(4mm×4mm), (a)classical ILIDS,(b)present ILIDS.
(a)
1
Particle(Droplet, Bubble,...)
2 Scattered light
1
2
3
4
6
5
7
30mm2
3 Rectangular mask: 5 ~
4 Collecting lens: Nikon Nikkor, 105mm, F2.5
5 Cylindrical lens: f=-100, 100mm
1008 pixels
6 CCD array: 1018 ~
7 Fringe image
(b)
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 30 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 (a) is the intensity profile on the
horizontal axis of circular image. On the other hand, Fig.5 (b) 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 2
Example 1
255
255
0
255
( b)
( a)
Intensity
Intensity
( a)
0
255
( b)
0
0
0
12 8
0
H orizontal P ixel
Fig.5: Measured interferograms and intensity profiles.
1 28
Horizo ntal Pixel
2.3 Image Processing
After capturing droplet image by the KODAK MEGAPLUS ES1.0 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.1990).
Pk
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 0.2% of the fundamental frequency. The
equation for adjusted Gaussian fitting is as follows:
Pk −1
P
) − log( k +1 )
Pk
Pk
1
∆k = ⋅
P
P
2
log( k −1 ) + log( k +1 )
Pk
Pk
(2)
f * = K peak + 0.9169a + 0.336a 3
(3)
log(
N=
L
×f*
PFFT
(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, PFFT 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 (R12) and present
method(R’12). Correlation map R’12 indicates the clear single peak around δx = −5,δy = −10(Fig.7 (b)), but R12 gives the
multiple peaks of the correlation function (Fig.7 (a)). 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
Wind ow 2
Interferogram
R12
Cross correlation
coefficient
R ’ 12
20
20
10
10
0
0
-10
-10
-20
(a)
-20
-20
-10
0
10
20
δx
(b)
-20
-10
0
10
20
δx
Fig.7: Comparison between convential particle tracking (R12) correlated with many particles (a) and
the present method (R12’) considering the diameter difference which provide a unique correlation with
well corresponding particle (b).
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.
Top View
Chamber
Laser1
Laser2
Window
Laser Head
Receiving optics
The laser source is double--pulsed Nd:YAG laser at 532nm in
CCD Camera
wavelength with the maximum output power of 100mJ/pulse,
the repetition frequency of 30Hz and duration time of the laser
Nd:YAG Laser
Power Supply
pulse is 3 to 5ns and the thickness of the laser sheet at the test
Timing Pulse
Generator
section is 0.5mm. But the system is insensitive for the imaging
Injec tor
D river
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
Side View
Injector
r
Laser head
CCD camera which acquires and transfers the progressive
z
Fuel Tank
N2
image sequence to a computer's memory directly. The CCD
camera has 1008×1018 pixels, each pixel is a 10bit grayscale
Fig.8: Experimental apparatus of the transient
accuracy and the size of each pixel is 9µm×9µm. The viewing
spray measurement.
area of the receiving optics is 10mm×10mm. The distance of the
objective lens and the test section in tank was 170mm, scattering was 73deg. that gives the maximum visibility of
interference signal. The collecting angle was set to 10deg., 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 0.75mm, 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 0.5MPa and 0.1MPa,
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=0.5ms 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
15
20
Injector
50 mm
30
z (mm)
r (mm)
25
15
40
diameter
20 µm
40 µm
60 µm
velocity
3.0 m/s
50
z (mm)
Fig.9: Comparison of Particle diameter and velocity distribution from a instantaneous frozen
image viewing z=25mm, 45mm of r=20mm from the nozzle at t=4.2ms after the start of
injection.
Fig.9 is the example of the measured results in z=25mm,
Injector
45mm of r=20mm from the nozzle at t=4.2ms after the start
10mm
20mm
of injection. The rectangular in the picture represents the
r = 0mm
0.1
viewing area of the receiving optics of 10mm ×10mm.
0
0.2
ILIDS gives the instantaneous droplet locations, individual
0.1
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.
0
20mm
0.2
Probability
diameters and velocity vectors.
z=0mm
0.2
Tdelay = 4.2 ms
0.1
0
0.2
0.1
40mm
0
0.2
Fig.10 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=0mm to 25mm
and z=0mm to z=60mm. On the center axis at r=0mm, no
0.1
0
0.2
0.1
0
0
30
60
90
120
150 0
30
60
90
120
150
0
30
60
90
120
150
60mm
drastic change of size distribution is found except z=15mm
Diameter(µm)
region. The PDF at r=10mm, 20mm showed that the mean
Fig.10:Probability Density Function of droplet
diameter in the downstream region was lager than that of
diameter in 10mm×10mm region and their spatial
upstream, i.e. larger droplets have reached to the
distribution of droplets at t=4.2ms after the start of
downstream region rapidly and smaller droplets remained in
injection.
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.10. In the region of z>30mm, 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
Injector
understand the spatial structure of the flow fields. Fig.12
20mm
illustrates the global velocity vector field and their diameter
10mm
r = 0mm
z=0mm
20
dependency. It is important that these velocity vectors in Fig.12,
Tdelay = 4.2 ms
13 are all evaluated from the pictures for the different particle
10
0
20
sizes. The viewing area is 0<r<30mm and 0<z<40mm from the
10
nozzle. The time was frozen at after the start of injection
0
20
and the flow regime was compared. Each velocity vector was
0
20
Velocity (m/s)
t=4.2ms. Diameter range was selected to d<30µm and d>50µm
10
obtained by calculating the mean velocity vector of droplets
detected within the 4mm×4mm, 50% overlapped small
subregion. The vector maps give us a significant knowledge that
20mm
10
0
20
40mm
10
0
20
the velocity of the smaller droplets is comparatively slow
10
throughout the given area in contrast with the high velocity of
0
0
30
60
90
120 150
the larger droplets.
0
30
60
90
120 150 0
30
60
90
120 150
60mm
Diameter (µm)
Fig.11: Correlation between droplet diameter and the
velocity at t=4.2ms after the start of injection.
r
r (mm)
30
Diameter range :
20
d < 30 µm
r (mm)
10
0
30
20
10
0
0
0
10
10
20 z (mm)
20
30
30
40
40
z
z (mm)
50 µm < d
Fig.12: Global velocity vector map of smaller(d<30µm)and larger(50µm<d) droplet.
Viewing area is 0<r<30mm and 5<40mm, t=4.2ms after the start of injection.
Fig.13 illustrates the velocity vector maps in the magnified area at r=10mm, z=15mm in the previous Fig.12.
Simultaneously the PDF of the droplet diameter at the corresponding area is shown in Fig.13. Diameter range was
(a)20µm<d<30µm, (b)30m<d<40µm, (c)40µm<d<50µm}, (d)50µm<d<75µm. Each vector was given by the mean
velocity of the droplets within the 3mm×3mm, 80% overlapped subregion. The velocity of the smaller droplet (a) and
(b), 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
0.15
(a) (b) (c)
(d)
PDF
0.10
0.05
5
0
0
10
20
30
40
50
60
70
80
90
100 110 120 130 140 150
Diameter (µm)
15
(a)
5
r
15
(b)
Diameter range : 20 < d < 30 µm
r (mm)
5
z
30 < d < 40 µm
10
10
z (mm)
20
15
(c)
5
20
15
(d)
40 < d < 50 µm
5
50 < d < 75 µm
10
10
20
20
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=10mm,z=20mm 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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