Gas and hydrodynamic flows are present in many technical devices and
machines, in various scientific setups. Such phenomena occur, for example, when
air flows around transport vehicles in motion or when the ship's screw engines are
operating in water environment. The variety of similar effects has led to the
emergence of many methods for researching the patterns of vortex distribution
and turbulent flows in different kinds of objects. Flow spread conditions can
be quite harsh: high temperature (thousands of degrees) or high speeds (units
of km/s), therefore contactless optical methods which don't introduce any
disturbances into investigated process gain an advantage. So, one of these methods
is particle image velocimetry (PIV) [1].
Particle image velocimetry is applied to measure the velocity in the
selected two-dimensional section or three-dimensional flow volume in hydro- and
aerodynamic experiments [2 ‒ 4]. The method allows to register the field
of the instantaneous spatial distribution of velocities. PIV is used, for
example, to measure the speeds of gas turbine and aircraft engines, to optimize
the flow around aircraft [5 ‒ 10]. It has a number of advantages, such as
the absence of a disturbing effect on the flow and a wide dynamic range of
measured velocities [11 ‒ 13].
To date, PIV is widely used and in demand in various technical fields,
such as automobile and aircraft construction, power and mechanical engineering.
The method is also applied in a variety of scientific fields: for the study of
phenomena in ecology and meteorology. For example, PIV is used to model
processes of pollution of the ocean coastal zone by wastewater discharge systems,
to measure parameters of the air flow over the agitated surface [14], to investigate
flow characteristics in the nozzle of a gas turbine engine [15].
The rapid development of laser technology, electronics, and recording
equipment contributes in every possible way to the improvement of experimental
methods, allowing to measure instantaneous velocity fields with higher spatial
and temporal resolution and to automate the processing. The PIV method is
currently widely used in various fields of science and production, the
boundaries of its application are constantly expanding. However at the moment
its applicability to the study of the aerodynamics of combustion chambers and
boilers hasn't been investigated. In these objects, a special fuel-air mixture
is fed into a furnace and burns inside the chamber.
The research purpose is to determine the impact of surface roughness on
the air flowing around this surface. As a result of this study, the dependence
of changes occurring in air stream during the flowing of surfaces with
different degrees of roughness, depending on characteristic dimensions of
irregularities of this surface, can be revealed.
To measure the instantaneous flow rate, LaVision FlowMaster PIV flow
diagnostics system was used. It consisted of a pulsed Nd:YAG laser, operating
at wavelength of 532 nm (repetition frequency of pulses pairs is 6 Hz, pulse
duration is 6-9 ns with pulse energy of 150 MJ, delay between pulses in a pair
is 0.01 s). A CCD camera Imager pro SX 5M (resolution of 5 MP, bit depth of 12
bits) and a syncing processor acted as a radiation receiver. System control, data
collection, storage and processing were carried out using a computer with DaVis
software. The aerosol flow (average diameter of 1 microns) was illuminated by a
laser plane with a thickness of 3 mm. During recording images of particles
scattering laser radiation, an optical filter was used.
To ensure the possibility
of performing studies of air flow around a rough surface, an experimental setup
was developed (Figure 1). This installation allows using particle image velocimetry
to study flow around surfaces. A sample of the surface (3) is placed in a
plexiglass cube. An aerosol created by aerosol generator (5) is launched into the
cube. A laser plane (2) is formed by special optical system, which highlights
particles in the required cross-section. The air flow is created using an
industrial hair dryer. The stream flows around the surface in the direction
along the laser plane. Images of the stream are recorded by the digital video
camera (4). The resulting images are transmitted to the computer, where they
are processed. As a result of processing, vector fields of flow velocity can be
obtained.
1 – laser, 2 – optical
system, 3 – sample of surface, 4 – digital camera, 5 – aerosol generator, 6 –
syncing processor
Fig. 1. Scheme of
experimental setup
The
obtained images were subjected to cross-correlation processing in LAVISION
DaVis program [16]. The main processing parameters on which the visualization
result depends are the size and shape of the survey window, the overlap
percentage of the surveyed areas. As a result, vector velocity fields of the
flow have been obtained, and the average velocity profiles in the selected
plane have been calculated.
As a result of the experiments, images of the air flow around the
samples with various degrees of roughness have been obtained. An example of such
image is shown in Figure 2.
Fig. 2. Example of experimental
flow image
For each value of the flow rate five series of flow images were
recorded, each of which had ten double frames. As a result of cross-correlation
processing vector fields of the flow velocity were obtained in the section,
which has been located along the flow in a plane normal to the sample surface.
The processing was performed with the following parameters: the standard
cross-correlation method, the size of the survey area was 64 x 64 pixels, the
overlap was 50%.
Then, for each series of measurements, the obtained vector fields
were averaged. So the magnitude and direction of the resulting vector were
averaged for each survey area. This made it possible to significantly reduce
the influence of random emissions caused mainly by flow vortices that occurred
during the formation of the flow by an industrial hair dryer.
The averaged vector fields of the flow velocity for a rough surface
sample, which is a fragment of P100 sandpaper, at different values of the flow
velocity are presented in Figures 3 ‒ 7.
Fig. 3. Vector field for sample P100 at
flow velocity 1
Fig. 4. Vector field for sample P100 at
flow velocity 2
Fig. 5. Vector field for sample P100 at
flow velocity 3
Fig. 6. Vector field for sample P100 at
flow velocity 4
Fig. 7. Vector field for sample P100 at
flow velocity 5
The comparison of the
flow velocity vector fields obtained experimentally with the flow velocity
distributions obtained as a result of modeling can be carried out mainly
visually. Such a comparison is of an exclusively qualitative nature. Therefore
additional processing of the obtained data is required in order to move from
qualitative to quantitative analysis.
In order to perform a
quantitative comparison of the experimental results with the simulation
results, plots of the flow velocity dependence over the sample surface on the
longitudinal coordinate has been constructed. Then these graphs were averaged.
As a result, one plot was obtained for each velocity value, which took into
account all measurements made at the appropriate flow velocity.
Experimental results for a
case of a smooth surface flow were processed in a similar way. Vector fields of
the flow velocity obtained as a result of cross-correlation processing for the sample
of the smooth surface at different values of the flow velocity are shown in
Figures 8
‒
12.
Fig. 8. Vector field for sample of smooth
surface at flow velocity 1
Fig. 9. Vector field for sample of smooth
surface at flow velocity 2
Fig. 10. Vector field for sample of smooth
surface at flow velocity 3
Fig. 11. Vector field for sample of smooth
surface at flow velocity 4
Fig. 12. Vector field for sample of smooth
surface at flow velocity 5
For comparison, all the plots obtained experimentally and as a
result of modeling were transferred in pairs to one coordinate system. At the
same time, the approximation of the obtained plots was carried out, which made
it possible to reduce the influence of random outliers in data arrays on the
resulting plots. Comparative plots for the rough surface sample P100 at flow velocity
1-5 are shown in Figure 13.
Fig.13.
Dependence of flow velocity over the surface of the sample P100
at
flow velocities 1 (a), 2 (b), 3 (c), 4 (d), 5 (e)
In this case,
theoretical results were obtained by modeling the flow around the rough surface
with some simplifications. First, the surface model in the initial version was
set in a significantly simplified form, in which it had noticeable structural
differences from the real sample of the rough surface made of sandpaper.
Secondly, to simplify and, accordingly, to speed up the modeling process, only
a part of the air flow was considered, without taking into account the fact
that the samples used in the experiments had a certain thickness, which also
affected the results obtained. This revealed the need to improve the parameters
of the surface models and the air flow used in modeling.
Comparative plots
for the case of flow around the sample of the smooth surface were obtained in a
similar way, by transferring into a single coordinate system experimental plots
of the flow velocity dependence modeling plots. These plots are presented in
Figure 14.
Fig.14.
Dependence of flow velocity over the smooth surface
at flow
velocities 1 (a), 2 (b), 3 (c), 4 (d), 5 (e)
During the research,
the process of air flow around surfaces with different degrees of roughness has
been studied. The phenomenon was investigated both experimentally and theoretically,
which consisted of physical and mathematical simulations of the process.
In order to perform
aerodynamic studies using PIV method the experimental setup has been developed.
As the experiments results have shown, the setup allows us to successfully carry
out such experimental studies. However, to increase the accuracy of the
experimental results, it is desirable to use another method of creating an air
flow, in which the generated flow will be as close as possible to the laminar
in nature.
The result of
the experimental part was to obtain vector flow velocity fields for samples of the
smooth surface and four rough surfaces with different degrees of roughness at
different values of the flow speed. From the obtained vector fields,
information was extracted about the flow velocity over the surface of each of
the samples, depending on the coordinate along the flow.
In order to
verify the experimental data mathematical modeling of the process has been performed.
The modeling results are spatial distributions of the flow velocity in the
cross section normal to the sample surface, which are similar to the
experimentally obtained vector fields for visual comparison of flows, as well
as similar dependences of the flow velocity on the coordinate along the flow. When
modeling the flow around rough surfaces, a problem arose related to the need to
use large computing power, because the amount of required calculations depends
on the surface parameters.
This difficulty lies in the fact that with a decrease in the
degree of surface roughness, the average characteristic dimensions of surface
irregularities become smaller, and their number on the sample section of the
same length, respectively, increases. So creating sufficiently realistic models
of rough surfaces inevitably leads to a significant increase in the time spent
on calculations.
This
work was funded by Russian Foundation for Basic Research (project
19-07-00921A).
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