Recently,
quite
various types of injectors have
found
a
broad
application in a number of industries, for instance in chemical technologies,
in fuel production, in heat and power engineering, etc. [1, 2]. Injectors are
also used in fluid rocket engines, vortex combustion chambers, cooling systems
and burner devices [3 ‒ 5].
The
injectors
based
approach assumes that the
information
about stream structure and its main parameters such as speed and droplets sizes
should first be taken into account. The lack of information about main nozzles
parameters can lead to incorrect device operation and possibly to harmful
consequences. For example, in the case of cooling systems, this can cause an
unequal distribution of the coolant over the object surface and lead to
decommission.
The operating
principle of most existing systems for measuring the velocity of gas-fluid
flows is based on optical methods. The main advantage of such techniques is
non-invasiveness, remoteness and non-inertia. Notable among them are methods
involving the use of laser radiation [6 - 8]. These techniques include
Laser Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV).
Laser Doppler
Velocimetry relies on the determination of frequency shift of radiation
scattered
by the studied
medium. The method also
has
some
other
unique properties including
high spatial
resolution and ability to measure three components of the velocity vector.
However, LDV allows
obtaining
the velocity values only at one point of space. In contrast to
LDV, Particle Image Velocimetry allows the two components of flow velocity
vectors to be measured simultaneously in a plane. For PIV measurements,
investigated flow is illuminated by a laser sheet and the radiation scattered
by particles is recorded. By the way, the most complete information about the
flow can be obtained by PIV modifications such as stereo, tomography and
multi-color PIV.
This paper
discusses the possibility of using multi-color Particle Image Velocimetry
(MPIV) to diagnose flows from injectors.
Multicolor
Particle Image Velocimetry significantly differs from the other existing PIV
modifications. This method allows the vector velocity field in several planes
simultaneously to be obtained. Based on this concept, it will be enough to use
only one camera to obtain information about three-dimensional flow structure.
From the assumption that when the experimental image is decomposed into color
channels, the response from the corresponding laser plane will correspond to a
certain color channel. To illuminate the flow volume, it is more expedient to
use a laser radiation source than a natural one. However, it may also be
difficult to find a laser that would generate light with the required
wavelength range.
Results of
measuring by multicolor PIV may not always be true, because at present there is
no direct correspondence between the information contained in any color channel
obtained by decomposing an experimental image into color components by digital
methods and the information transmitted by an optical signal of the
corresponding color. This is due to the use of a color digital camera as a
detector, namely, its sensitivity
property. The typical
camera response curve is usually unequal. Figure 1 shows the method measurement
scheme.
Fig. 1. MPIV measurement scheme
The principle
operation illuminates the
measured
region by three RGB laser sheets and registers
particles
positions in scattered light at short time intervals.
Seeding
particles must move at the flow speed and not introduce any disturbance. For
this purpose, particles should be small, and their density should be close to
the flow density. In the MPIV, red, green and blue laser planes located at a
small distance from each other are used as probing radiation. Laser modules are
selected in such way that when the experimental image is divided into three
colors, the signal from each plane is present only in one of three color
channels. Registration is carried out by a color digital camera. In turn, each
image recorded will have three main colors. As a result, by applying the
cross-correlation to processed images pairs for each color channel, it is
possible to get information about velocities distributions in three planes. On
the basis of this data, it is capable to visualize a flow three-dimensional
velocity field.
The accuracy
of
MPIV measurements
can be affected by several factors. The three most important ones are
the
adjustment
accuracy,
the
cross-correlation processing accuracy and
the
parameters of
an experimental setup. The first factor doesn’t strongly influence the accuracy
of experimental data.
Compared to
other PIV modifications, the
technique
is quite simple to implement and doesn’t require
a
complex
precision adjustment.
Thus,
it is possible to minimize the adjustment error. The same is true for
the
second factor. The processing error in PIVview program is less than 3%.
However,
the measurements accuracy can be significantly affected by the
installation parameters, such as the wavelength
of the radiation
source. Therefore, necessary requirements for the component base
of the setup for MPIV measurements is the separation of the detected scattered
radiation of red, green and blue colors according to the corresponding color
receiving channels of the digital camera. Ideally,
the scattered radiation from particles of one of the probing
components should be registered for
each of
the
three color components
of an experimental
image,
for
example, there should be no signal
for
the other two
colors in the red color channel. To fulfil this requirement,
we should
take into
account the spectral sensitivity of the photodetector when choosing radiation
sources. Otherwise, there will be no
correspondence between the physical process and
experimental data.
The accuracy
of MPIV measurements can also be affected by
the
ratio of
radiation intensities of laser planes.
The
spectral
sensitivity of the photodetector selected as the receiving equipment may be
unequal. Then, as a result of the MPIV measurements,
the
response
from
the receiver
for each plane to the radiation scattered by the same object will be different.
A large
difference in values of the receiver response
for
each of three
laser planes can lead to incorrect experimental results. For example, let the
radiation intensities of three RGB laser planes be equal, spectral sensitivity
of the photo
detector is uneven, in such way the response of the receiver to
two laser planes will be much less than the response to the third plane. In
this case, the receiver will not be able to register the entire signal from the
first two laser planes
The camera matrix is very likely to be illuminated
when registering a signal from the third plane.
As a result, the signal from this plane will be present not in
one channel, but in all three.
Diagnosing vortex structures by MPIV method
also
requires
choosing the
correct
distance between laser planes. For example, in case of diagnostics of the flow
shown in Figure 2, it is advisable to arrange laser planes as follows (Figure
3).
Fig. 2. Border of vortex structure
Fig. 3. Correct location of laser planes
Otherwise, if
laser planes are located at a small distance (Figure 4), the flow structure
will not be fully visualized, because the selected area doesn’t cover the
entire flow structure.
Fig. 4. Incorrect location of laser planes
Also,
choosing the
distance between laser planes
requires
taking
into account
a depth of camera field. If laser planes aren’t located completely within the
depth
of the camera
field, then part
of the
signal
will be lost.
The other
problem that occurs during
the
experimental setup is
the
incorrect
configuration.
Reconstructed coordinates of
the particle's
positions
along Z axis
may not
correspond to their actual positions at a large (relative to
diameter of particles) thickness. The obtained data indicate that the
information about positions of tracer particles along Z axis
within the thickness
of
a
laser plane isn’t taken into account when performing MPIV
measurements. Therefore, when developing an experimental setup, it is advisable
to strive for a minimum thickness of laser planes.
The developed
setup has been tested on air bubbles inside the glass. During testing, the
glass was previously fixed on a two-coordinate table with a micrometer screw.
Positions of bubbles
were
recorded
as
the glass
was
moved in different directions.
In the first
experiment, the glass was moved along the x axis with the same step equal to
0.5 mm from the position
x
= 0 mm to the position
x
= 9 mm
(Figure 5).
Fig. 5. Direction of glass displacement in first experiment
During
processing, experimental images were first decomposed into three color
channels. Figure 6 shows an example of one of
the
received
images. The numbers indicate the air bubbles that
were
used for
further analysis.
Fig. 6. Example of experimental image
Then, using
the PIVview2CDemo program,
we applied
the
cross-correlation processing to
each pair of decomposed images and a vector field of displacements was
constructed. According to processing results for each pair of experimental
images, the value of displacement of selected air bubbles was determined for
each color channel.
To assess the
accuracy of data obtained, relative measurement error was calculated for each
color channel using the following formula
|
|
(1)
|
where
xm
is the displacement value measured by a micrometer screw,
xt
= 0.5 mm;
x
is the displacement value measured by MPIV method.
The
calculation results are presented in Table 1.
Table 1.
Relative measurement errors for three channels
|
Blue color
channel
|
Red color
channel
|
Green color
channel
|
|
6,861% ≈ 7%
|
7,325% ≈ 7%
|
7,163% ≈ 7%
|
During the
second experiment, the glass was moved strictly along the z axis, and only one
air bubble was recorded (Figure 7).
Fig. 7. Direction of glass displacement in second experiment
Figure 8
shows examples of experimental images.
|
|
|
|
Red laser plane
|
Green laser plane
|
|
|
|
Blue laser plane
|
Fig. 8. Experimental images
To restore
the object trajectory, a corresponding program was developed in MathCad. The
algorithm is as follows. At the first stage,
the
experimental
images are loaded into the program in the form of matrices with quantized pixel
brightness values. Next,
the
center coordinates of the registered object are calculated for
each of them.
For
this,
we calculate
the sum of the pixels brightness in the image
with
the following
formula
|
,
|
(2)
|
where
m
is the number of rows of the image matrix,
n
is the number of columns,
Mi,j
is the brightness value of the corresponding pixel.
After that,
we compute the
x,
y
coordinates
with the
formulas
below
|
.
|
(3)
|
Z coordinate
is determined from experimental conditions.
The trajectory of the object is constructed with
the obtained coordinates (x, y, z).
Figure 9
shows the reconstructed trajectory of the object for the second experiment.
Fig. 9. Reconstructed trajectory of air bubble movement
To assess the
results accuracy, the standard deviation (RMS) of the displacement value of the
object center determined by MPIV method from the displacement value of the
object center determined using a micrometer screw was calculated according to
the following formula
|
,
|
(4)
|
where
Sm
is the displacement value of the object center, measured by a micrometer screw,
S is the displacement value of the object center, measured using MPIV
As a result,
RMS was
|
mm.
|
|
During
investigation, an experimental setup was developed. Its principle scheme is
presented
in
Figure 10.
The setup
includes a set of three laser modules with wavelength 450 nm, 520 nm and 650
nm; an optical system and a digital camera with color matrix.
Fig. 10. Principle
scheme
of experimental setup
As a research
object, the jet formed by the sprayer has been considered. Figures 11, 12 show
one of the experimental images and its inverted version.
Fig. 11. Experimental image
Fig. 12. Inverted experimental image
By applying
Particle Tracker Velocimetry (PTV) processing to images from each color
channel, information about velocities of spray droplets in each laser plane can
be obtained. Figure 13, 14 and 15 shows the result of processing.
Fig. 13. Blue channel
Fig. 14. Green channel
Fig. 15. Red channel
After that,
the calculated speed values can be output from the program in form of a text
file, and based on them, a three-dimensional velocity field can be constructed.
The
subject of this research work is the
multicolor particle image velocimetry.
Compared to the in contrast to other PIV modifications, t
he main advantage of
the method proposed, is the ability to fix vector velocity fields simultaneously in
several planes.
This work
investigates such important features of the process as
the influence of wavelengths, the radiation intensity of laser
planes, their thickness and the distance between them on the accuracy of MPIV
measurements.
The developed
setup allows measuring all three components of flow velocity vector in the
range from 47.4·10-6 m/s to 8.6·10-3 m/s and visualizing its three-dimensional
structure. The measurement accuracy is 7-11%. It should be noted that this
speed range is due to the characteristics of the camera Nikon 1 J5.
For the other
camera
used
as the
receiving optical system, for example, a high-speed camera, the speed range
will be increased.
The setup can
be widely used to solve problems in the field of aero-and hydrodynamics,
visualization of fast-flowing processes and study of complex vortex structures.
The final consumers of the proposed product are various rocket engineering
enterprises, factories for cooling systems production, enterprises engaged in
the development of fuel purification systems, aircraft engine manufacturers,
research institutions.
The work was
carried out within the framework of the project «Development of optical
electronic setup for complex diagnostics of gas-liquid flows» with the support
of the grant from the National Research University «MPEI» for the
implementation of research programs «Electronics, radio engineering and IT» in
2020-2022.
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CenterDetroit; United States.
