In
engineering practice, the traditional method of spraying liquids is the use of
nozzles. The following types of nozzles are distinguished: jet, centrifugal,
pneumatic (two-phase), impact, mechanical, acoustic, etc. Commercial companies
often use their own terminology like slot, rotating, ultrasonic nozzles etc.
The process
of forming a fine spray is described quite well in the literature for various
types of nozzles [1-3]. In mechanical (jet, centrifugal) and pneumatic (air,
steam) nozzles, the fragmentation of the liquid sheet flowing from the nozzle
occurs under the action of hydrodynamic forces caused by the difference in the
speeds of the liquid sheet and the surrounding environment, with the formation
of individual clots in the form of threads and their subsequent breakup into
droplets. In some cases, multi-faceted secondary breakup of the droplets with
the carrier gas flow takes place.
The process
of liquid droplets breakup in nozzles causes the existence of a certain
distribution of droplets by diameter, and the range of droplet sizes can be
quite wide – from fractions to hundreds of micrometers. As numerous studies
have shown [4], in result of mechanical spraying of liquids by the most common
centrifugal nozzles, the range of droplet sizes is close to a lognormal
distribution.
Using the
properties of gas-droplet flows with a low mass concentration (up to 1%) of the
liquid phase can solve the problem of reducing aerodynamic heating. It is known
that when initially compressed gas expands in a channel, its thermodynamic
temperature decreases due to the transition of the internal energy of the gas
into the kinetic energy of the flow. The question arises: is it possible to
create conditions in the flow under which the streamlined wall temperature
would be close to the minimum temperature in the system – the flow
thermodynamic temperature. The solution to this problem is possible through the
use of the properties of gas-droplet flows. In the case of a low mass
concentration (up to 1%), the liquid phase has virtually no effect on the
properties of the carrier flow, while the droplets can cool down to the flow
thermodynamic temperature [5-8]. By organizing the precipitation of cooled
droplets on the wall, it is possible to achieve a decrease in the surface
temperature.
There are
both experimental and numerical works devoted to this issue in the literature.
In [9, 10] it was experimentally shown that the expansion of wet water vapor in
a nozzle (steam with water droplets with a humidity of up to 4,5%) leads to a
decrease in the nozzle wall temperature compared to the case of superheated
steam flow. In [9] the temperature recovery factor took the values
r = 0,7 in wet steam and
r = 0,9–0,8 in superheated steam depending on the
initial degree of superheating. In [10] it was shown that the adiabatic wall
temperature depends on both the initial humidity and the initial size
distribution of the droplets. For droplet diameters
d > 70 μm and an initial moisture content of more than 2%,
the droplets deposit on the wall, forming a liquid film with a temperature
equal to the saturation temperature. In [11-14] it is numerically shown that
the presence of even a small concentration of droplets (less than 3%) in the
main air flow can lead to a significant decrease in the adiabatic temperature
of the streamlined wall.
As a result
of previously conducted experimental studies [7, 15, 16], a system for
preparing and injecting liquid into a supersonic flow through a single- and
multi-nozzle system in the prechamber of the wind
tunnel was created and debugged. A series of thermal imaging measurements of
the cooling rate of a plate streamlined by supersonic air and air-droplet flows
were performed. The effects of ice build-up on the streamlined wall with a
temperature decrease of 10-13 C compared to a single-phase flow were detected.
Flow pattern visualization showed a preferential focusing of particles in the
central part of the channel after passing the wind tunnel nozzle. A method of
aerodynamic focusing of droplets along the shock wave front was tested when a
shock wave generator wedge was installed in front of the model. When varying
the Mach numbers of the incoming flow, a regime of maximum temperature decrease
of the entire surface of the streamlined plate was detected at Mach numbers
less than 2,5, while for higher Mach numbers, cooling of only the leading edge
of the plate was observed.
The aim of
this work is to study the dynamics of droplet breakup and histograms of droplet
size distribution in the critical section and in the expanding part of a
supersonic wind tunnel nozzle in the range of Mach numbers at the nozzle exit
section M∞ = 2,0-3,0.
Most modern
methods for determining the dispersion composition of particles/droplets
suspended in the gas phase, providing detailed information on their sizes, are
based on optical measurements. Optical methods are very common, as they are
contactless (they do not disturb the carrier medium and do not affect the
particles).
In this work, we used the panoramic shadow laser method SSP (shadow photography) [17-21], which includes: a flow illumination system based on a Beamtech dual-pulse Nd:YAG laser with a wavelength of 532 nm, a 7-joint arm for delivering laser radiation, a light-scattering screen for creating background illumination with an alcohol solution of rhodamine phosphor, a digital CCD camera with a frame rate at full resolution of up to 15 Hz, an Infinity K2 DistaMax microscope lens and a Polis SP-10.0PS synchronizing processor. Digital analysis of the shadow image of droplets allows us to determine the position and boundary of the object at the moment of background illumination by the laser (Fig. 1), which is important in the problems of thermal and gas dynamic state of a two-phase flow.
Fig. 1.
Methodology for measuring the size distribution of water droplets sprayed by a
centrifugal nozzle.
Experimental
studies were conducted on the supersonic continuous-action wind tunnel AR-2
(Fig. 2). The working channel of the wind tunnel has a rectangular
cross-section with dimensions of 70×98 mm. The supersonic nozzle is
formed by two flat flexible plates, providing the possibility of operation at
Mach numbers from 2,0 to 3,0 due to the compression of the critical section
using an electric drive.
Fig. 2. Scheme of the experimental installation: Ò0* – total temperature of the incoming flow, K; P0* – total pressure in the pre-chamber, Pa; P – static pressure on the wall, Pa.
In the
central part of the pre-chamber, at a distance of 300 mm from the beginning of
the narrowing zone, centrifugal nozzles were placed. The average size of water
droplets in the spray created by the nozzle (according to the manufacturer
information) was from 60 to 110 µm with a change in pressure drop from 1000 to
300 kPa, respectively. Distilled water was supplied
to the centrifugal nozzles through a separate system consisting of a tank with
distilled water under pressure (the water pressure in the tank was pumped and
maintained at a given level by a pneumatic system), a flow meter and connecting
tubes.
At the
first stage of research a series of measurements of the water droplet diameter
distribution during water spraying into the atmosphere by a centrifugal nozzle
were carried out. The obtained histograms were compared with the data from the
nozzle manufacturer Lechler. A series of images of
the instantaneous state of the droplets near the spraying nozzle edge (Fig. 3,
left) and at a distance of 30 mm (Fig. 3, right), as well as up to 100 mm from
the nozzle edge for comparison with the manufacturer's data were obtained using
the panoramic shadow method. The obtained images allow us to estimate the cone
angle of the spray torch being formed, the predominant mechanism of droplet
fragmentation, and the statistics collected from thousands of frames allow us
to construct histograms of the droplet size distribution (Fig. 4). For example,
with a pressure drop of 900 kPa, the average Sauter diameter of droplets during spraying into the
atmosphere was about 70 µm, while according to the manufacturer's data, it was
66 µm.
Fig. 3. Water
fragmentation into droplets and determination of the spray cone angle (left),
formed fine spray at a distance of 30 mm from the nozzle edge (right).
Fig. 4. Histogram
of droplet diameter distribution when spraying water into the atmosphere with a
centrifugal nozzle at a pressure drop of 900 kPa.
A series of
images of the instantaneous state of the air-droplet flow in the critical
section and in the expanding part of the wind tunnel nozzle were obtained (Fig.
5). The SSP method obtained a lognormal droplet size distribution with a
characteristic Sauter diameter of about 20 μm at the wind tunnel nozzle exit
section (Figs. 6, 7). In this case, the average droplet diameter and size
distribution were practically independent of the pressure drop on the
centrifugal nozzle in the studied wide range from 200 to 1300 kPa
and the change in the Mach number in the range from 2,0 to 3,0.
Fig. 5. SSP
visualization of the process of water droplet breakup during flow through a
Laval nozzle (X=0 mm corresponds to the critical nozzle section of the
wind tunnel).
Fig. 6.
Distribution of water droplets by diameter in a supersonic flow at a Mach
number M∞ and a water pressure drop at the centrifugal
nozzle
∆P: M∞ = 2.0, ∆
P = 1300 kPa;
M∞ = 2.5, ∆P = 1250 kPa;
M∞ = 3.0, ∆P = 1200 kPa.
Fig. 7. Comparison
of droplet diameter with changing water pressure drop at the centrifugal nozzle
∆P = 320; 650 and 1280 kPa.
A series of
images of the instantaneous state of droplets near the centrifugal nozzle edge
and at a distance of up to 100 mm from the edge were obtained using the panoramic
shadow method. The agreement with the nozzle manufacturer’s data was obtained
within 6% for water pressure drops at the nozzle up to 900 kPa.
The dynamics of the air-droplet flow in a flat supersonic wind tunnel nozzle
was studied. The SSP method established the average Sauter diameter of droplets at the nozzle exit section to be ≈20 μm. A series of images of the
instantaneous state of the air-droplet flow in the wind tunnel critical section
area and in the expanding part of the nozzle were obtained. The average droplet
diameter and size distribution histograms changed little with an increase in
the water pressure drop at the nozzle up to 1300 kPa and a change in the Mach number in a wide range from 2,0 to 3,0.
The work is
carried out within the framework of the state budget theme of
Lomonosov Moscow State University (N. AAAA-A19-119012990115-5).
SCXI – Signal Conditioning eXtensions for Instrumentation (National Instruments);
SSP – shadow photography;
CCD – charge-coupled device;
M – Mach number, -;
P – pressure, Pa;
T – temperature, Ê;
X, Y – coordinates, m.
Indexes:
0 – stagnation parameter;
∞ – free flow parameter.
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