Short-time FFT based laser Doppler velocimetry for bubbly...
Transcript of Short-time FFT based laser Doppler velocimetry for bubbly...
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Short-time FFT based laser Doppler velocimetry for bubbly two-phase turbulent boundary layers
H. J. Park1,* , K. Toda2, Y. Oishi3, Y. Tasaka1, Y. Murai1
1: Faculty of Engineering, Hokkaido University, Japan 2: Graduate School of Engineering, Hokkaido University, Japan
3: College of Design and Manufacturing Technology, Muroran Institute of Technology, Japan * Correspondent author: [email protected]
Keywords: Laser Doppler Velocimetry, Bubble, Turbulent Boundary Layer
ABSTRACT
Bubbly drag reduction (BDR) technique has been recently applied to low speed vessels for actual use. Despite to
applications on progress, we do not clearly understand microscopic mechanisms hidden complicatedly in BDR. Here,
we focus velocity distribution in a turbulent boundary layer, especially a viscous sublayer, because wall shear stress
is directly evaluated from velocity profiles in this layer. To investigate velocity modification by bubbles injected into
the boundary layer, we developed a laser Doppler velocimetry (LDV) with a high spatial resolution enough to access
the layer. A data processing using a short-time FFT analysis and a statistical analysis was devised to calculate
velocities automatically from beat signals including low frequency noises generated by an inverter in experimental
facility. Velocity distributions with a single-phase flow and a two-phase flow were investigated by the LDV with the
data processing, and were evaluated using statistical values, such as average, standard deviation, skewness and
kurtosis. By these analyses, it is confirmed that the bubbles have a big potential to modify characteristics of the
velocities even with a low void fraction.
1. Introduction
Bubbles injected into a turbulent boundary layer modify completely its characteristics. For
example, they are possible to reduce wall friction on a turbulent boundary layer and the maximum
drag reduction rate by bubble injection is up to 80% [1]. Since bubbly drag reduction (BDR)
reported by McCormick and Bhattacharyya [2], it has researched to improve energy efficiency of
sailing large vessels by reducing frictional drag occupying approximately 80% of total drag of the
vessels. Although many researches on BDR have been performed for over 40 years, we do not
clearly understand this phenomenon yet. Ceccio [3] reviewed many previous researches on BDR
and summarized a relationship between BDR rate and void fraction. According to this review
article, variance of the rate has a trend that basically it becomes larger as the void fraction increases.
When the void fraction is lower than a critical void fraction, however, frictional drag is increased
by adding bubbles. Although this trend appears at the all previous researches summarized in
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Ceccio [3], the BDR rate is not summarized by the void fraction because it is greatly affected by
experimental conditions and facilities. Also, Murai [4] summarized effects by adding bubbles in
flows and their conduciveness on the drag reduction at his review paper and made a map of main
effect of bubbles according to a flow speed and a bubble size. Unfortunately, this transition map
is not perfect because the effect and its conduciveness are influenced by other factors such as void
fraction [3], wall roughness [5] and entrance distance from a bubble injector [6, 7]. Summarizing
these, BDR is affected by several factors associated with flows and investigation of effects of the
bubbles with considering these all factors is required to understand BDR. Unfortunately, it is
actually impossible to grasp influences of the all factors. Besides, even if we have clear information
of each factor, it is hard to understand BDR because of a non-linearity occurring by mutual
interactions between the factors.
For deeper understanding of BDR, as the first step, we focus modification of velocity
distribution in a turbulent boundary layer, especially a viscous sublayer, by bubble injection
because a velocity gradient in the viscous sublayer is linked directly with wall shear stress (τw),
which is defined as
𝜏w = 𝜌𝜈 |𝑑𝑢
𝑑𝑦|𝑦=0
. (1)
Here, ρ, ν, u and y are density of fluid, viscosity of fluid, velocity and depth from the wall.
Assuming that ρ and ν in the viscous sublayer are not changed by the bubbles because thin liquid
film exists between the bubbles and the wall [8], the velocity gradient has to be decreased by the
bubbles when BDR occurs. Modification of the velocity gradient means that turbulent flow
structures are changed by the bubbles. To achieve our purpose, we designed a laser Doppler
velocimetry with a high spatial resolution to access the turbulent boundary layer without any
interference on velocity distribution by measurement instrument and estimated effects of the
bubbles on the turbulent boundary layer by investigating velocity fluctuation in the layer.
2. Experimental facilities and conditions
A horizontal channel with a water circulating system is adopted for the investigation. Figure 1
shows the schematic diagram of experimental facilities. The channel is made of transparent acrylic
resin and is 40 mm in height (H = 2h), 160 mm (W = 8h) in width and 6000 mm in length,
respectively. The tap water including fine loam soil is employed as a working fluid. Temperature,
density (ρ), viscosity (ν) and refractive index (n) of the water are 17 °C, 999 kg/m3, 1.08×10–6 m2/s,
1.33, respectively. The loam soil (JIS Test Powders 1: Class 11, APPIE) is adopted as tracer particles,
and its specific gravity and mean diameter are 3.0 and 2.2 μm, respectively. The water is supplied
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
to the channel by a pump and its liquid flowrate (Q) is measured by a flowmeter. To inject bubbles
into the channel, a syringe is installed on the upper wall of the channel at x/h = 64 and z/h = 1.5.
Here, x, y, and z directions are defined to be the streamwise, vertical and spanwise directions. The
origin of the coordinate system corresponds to inlet, upper wall and nearside wall of the channel.
Injected bubbles are removed in a water tank located at the end of the channel and only the water
is circulated to the channel. As seen in the figure, a camera and a laser Doppler velocimetry system,
which is composed by a laser source and an optical receiver, is located at x/h = 70 for the
investigation. The laser source is tilted away towards the upper wall with 4° and emits two laser
beam having 655 nm in wavelength (λ) with a crossing angle (θ = 16°). The beams are crossed at
z/h = 1.5, reflected at the upper wall, and finally reached to the optical receiver. Interference
fringes to make beat signal for measuring a flow velocity are formed in the beam crossing area
with 19 μm in the vertical direction, 19 μm in the streamwise direction and 150 μm in the spanwise
direction. The optical receiver converts a variance of laser beam to an electronical signal and send
it to a data logger (NR-500, KEYENCE) connected to the receiver. The data logger has 1 MHz in a
temporal resolution and record the signal for 2.5 s. The laser source and the optical receiver are
moved by traversers which are possible to make move them at intervals of 12.5 μm in the vertical
direction. By these traversers, location of the measurement point, i.e., the beam crossing area, in
the vertical axis is controlled.
Fig. 1 Schematic diagram of experimental facilities, where h and θ are a half-height of the channel
and a crossing angle, and red lines indicate pass line of laser beams; (a) overall view of the facilities,
(b) top view around the measurement point and (c) cross sectional view at the measurement point.
In the paper, we performed experiments in two different flow conditions, a single-phase
flow and a two-phase flow. In the two-phase flow, air was supplied by the injector to become a
line of bubbles, having 5–12 mm in diameter, passing the measurement point as seen in figure 2.
Reynolds number (Re) in the experiments is defined as
Horizontal channelDiverging converter
Liquid flowmeter PumpWater tank
Injector Measurement point
Two phaseLiquid phase
64h 6h150h
a b
cCamera
Lasersource
Opticalreceiver
zy g
xy g
2h
zx
8h Lasersource
Opticalreceiver
1.5h2θ
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
𝑅𝑒 =𝑈ℎ
𝜈=
𝑄
2𝑊𝜈 (2)
and is fixed at 7000, where U is a bulk mean velocity in the channel. Measurements at each location
were performed 5–10 times to secure statistical validity of data.
Fig. 2 Snap picture taken by the camera located above the measurement point.
3. Data processing of the beat signal
Figure 3 shows a sample of a signal recorded by the data logger. We can observe wave with a low
frequency, electric noise generated by an inverter of the pump, and small fluctuations with a high
frequency on the wave, the beat signal. Generally, a laser Doppler velocimetry uses a hardware
system, composed by a frequency counter with a band pass filter, to automatically detect a
frequency of the beat signal. In the measurements, however, it is hard to use the hardware system
because of too much strong intensity of the noise. Besides, it is expected that a range of frequencies
of the beat signal occurred in the viscous sublayer is overlapped that of the noise, because
velocities in the layer are very low and a frequency of the beat signal is proportional to the velocity.
Therefore, we tried to detect the frequency of the beat signal from the signal of the data logger by
data processing.
Fig. 3 Sample of laser intensity variation, where wave with a low frequency are occurred by electric
noise and small fluctuations with a high frequency on the wave are beat signals.
At the first, we performed short-time FFT every 256 μs to the signals obtained from the data
logger. Figure 4(a) shows a sample of time series of linear spectra for the laser intensity variation
with a single-phase flow calculated by short-time FFT analysis, where temporal resolution is 3.9
xz
10 mm
Bubbles
Bubble
Measurement point
0 100 200 300 400 500
100
50
0
-50
-100
Time (t) [μs]
Va
riat
ion
of
lase
rin
ten
sity
[mV
]
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
kHz (= 1/256 μs). We supposed that three peaks having different frequencies appear at each time
domain by the analysis; they are respectively a low frequency of the noise, a high frequency of the
beat signal and a middle frequency caused by fluctuations of beat signal intensity [9]. However,
range of frequencies of the noise lies in broadband and overlaps sometimes that of frequencies of
the beat signal. Therefore, detection of the frequencies of the beat signal is hard to use only the
maximum intensity in the spectra without any filtering. Here, Laplacian filter in each frequency
domain is employed to emphasis only a peak in the domain occurred by the beat signal. A result
of this filtering is shown in figure 4(b). Although high intensities until remain in a low frequency
region, f < 25 kHz, we can clearly recognize single peak which continuously exists in 100 kHz < f
< 200 kHz in all time domain. In this paper, a frequency of the maximum intensity (fmax) of linear
spectra with the Laplacian filter in f > 25 kHz is distinguished as a frequency of the beat signal.
Fig. 4 Sample of time series of linear spectra for the laser intensity variation with a single-phase
flow calculated by short-time FFT analysis, where data interval for the FFT analysis is 256 μs; (a)
original spectra and (b) spectra processed Laplacian filter in the frequency dimension.
Velocity (uy) is determined as
𝑢𝑦 =𝑓max𝜆
2𝑛 sin𝜃 (3)
in laser Doppler velocimetry systems [9] and figure 5 shows a time series of velocity calculated
using this equation and obtained fmax from figure 4(b). Although the Laplacian filter is applied to
reduce the noise, a lot of erroneous velocities are concentrated near f = 44 mm/s, corresponding
to the lowest fmax = 25 kHz. Fortunately, even if the erroneous velocities are eliminated in figure 5,
0 1.56Intensity [μV]
Time (t) [ms]250.0200.0150.0100.050.00
0
500
300
200
100
400
Fre
qu
ency
(f)
[k
Hz
]
Time (t) [ms]250.0200.0150.0100.050.00
0
500
300
200
100
400
Fre
qu
ency
(f)
[k
Hz]
a
b
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
we can confirm that correct velocities in 150 mm/s < uy < 400 mm/s are varied continuously in
the time domain.
Fig. 5 Time series of velocity obtained from Laplacian filted spectra in figure 4(b).
Figure 6 shows a probability density function (PDF) of velocities in figure 5. Two groups
are in the PDF; one is a group of the error velocities in uy < 100 mm/s and the other is a group of
the correct velocities in 180 mm/s < uy. A threshold velocity is calculated by Otsu method to
classify them automatically and the calculated value is indicated as a gray dashed line in the figure.
Assuming that velocities slower than the threshold velocity are error, in all measurements, the
correct velocities survive only approximately 15% in all data. In this paper, the erroneous velocities
are deleted and instead velocities estimated by linear interpolation are supplemented as seen in
figure 7.
Fig. 6 Probability density function (PDF) of the velocities in figure 5, where a gray dashed line
indicates a threshold velocity (uth) calculated by Otsu method.
Fig. 7 Time series of velocity removed error velocities in figure 5, uy < uth, and supplemented by
linear interpolation.
Time (t) [ms]250.0200.0150.0100.050.00
0
300
200
100
400
Vel
oci
ty (
uy)
[mm
/s]
Velocity (uy) [mm/s]4003002001000
0
90
10
100
PD
F [
s/m
m]
20
Threshold velocity (uth)
Time (t) [ms]250.0200.0150.0100.050.00
0
300
200
100
400
Vel
oci
ty (
uy)
[mm
/s]
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Until here, data processing to obtain time series of velocity from beat signals with low
frequency noises were explained using the beat signal with a single-phase flow. Basically,
velocities with two-phase flows are obtained using the same data processing. Figure 8(a) shows
time series of linear spectra for the laser intensity variation calculated by the short-time FFT
analysis. When bubbles are passing through the measurement point, the laser beam cannot arrive
at the optical receiver by interruption at the gas-liquid interface. As a result, the beat signal does
not exist at that time. It is confirmed by comparing the linear spectra and a line-scanned image
taken by a camera synchronized with the data logger. In the paper, velocities when the bubbles
exist at the measurement point are supplemented by linear interpolation and time series of
velocity performed all data processing is shown in figure 8(b).
Fig. 8 Case of a two-phase flow; (a) time series of the linear spectra and (b) time series of the
velocity with all data processing.
4. Results and discussions
Figure 9(a) shows averaged velocity distribution near the upper wall, where error bars indicate
standard deviations, and yw is a distance between the upper wall and the nearest measurement
point from the wall. In the experiments, y of a measurement point is unclear because distance
between measurement points is only given from the traversers. To define the distance between the
upper wall and a measurement point, it is assumed that the first and the second measurement
points in the single-phase flow are located in the viscous sublayer. It is known that the viscous
sublayer has a linear velocity distribution as
0 1.56Intensity [μV]
b
Time (t) [ms]250.0200.0150.0100.050.00
0
500
300
200
100
400
Fre
qu
ency
(f)
[k
Hz
]a
Time (t) [ms]250.0200.0150.0100.050.00
0
300
200
100
400
Vel
oci
ty (
uy)
[mm
/s]
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
𝑢𝑦̅̅ ̅̅
𝑢𝜏= 𝑦+, (4)
where wall unit (y+) and friction velocity (uτ) are defined as respectively
𝑦+ =𝑦𝑢𝜏
𝜈 (5)
and
𝑢𝜏 = √𝜏w
𝜌. (6)
Calculating yw using equations (1) and (4)–(6) with the assumption, it is approximately 44 μm.
Figure 9(b) shows the velocity distribution expressed using y+ and uτ. It is normally known that
the linear velocity distribution in the viscous sublayer is located in y+ < 5. In the figure, however,
the linear velocity distribution keeps only in y+ < 4. It is because too low velocities in the layer are
deleted by the threshold velocity to neglect erroneous velocities.
Fig. 9 Average velocity distribution near the upper wall, where error bars indicate standard
deviations; (a) when distance between the upper wall and the nearest measurement point from
the wall (yw) is unknown, and (b) when it is assumed that the second measurement point is located
in the viscous sublayer having linear velocity distribution, where uτ is friction velocity.
Although this error exists in the measurements, it is allowable to discuss modification of
velocity distribution in the boundary layer by the bubbles. Average and standard deviation of the
velocity fluctuations are hardly modified by injecting bubbles into the turbulent boundary layer.
In this experimental condition, it is supposed that the wall shear stress is slightly increased by the
bubble injection because the linear velocity distribution with the two-phase flow is steeper
inclination than that with the single-phase flow. This result, i.e., shear stress increased by the
bubbles with a low void fraction, is corresponding with previous researches [3]. Also tendency of
skewness of the velocity fluctuations in figure 9(a) is maintained in spite of the bubble injection.
Skewness values in y+ ≤ 3 are positive and higher than others, because the lower velocities are
Distance from the upper wall (y) [μm]yw+ 150.0yw+ 100.0yw+ 50.0yw
0
200
100
50
350
Mean v
elo
city
(uy)
[m
m/s
]
150
300
250
a
W all unit (y+ )9531
0
4
2
1
6
uy/
uτ
3
5
b
742 106 8
uy/uτ = y+
Sing le-phaseTwo-phase
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
deleted together with error velocities when the data processing is performed. Even if we consider
skewness values in y+ > 4, obvious modification of skewness is not observed. However, tendency
of kurtosis in figure 9(b) is dramatically modified by the bubble injection. In the figure, the kurtosis
is defined as kurtosis of Gaussian distribution becomes zero. In the single-phase flow, the kurtosis
decreases when location of the measurement point becomes closer to the upper wall. Contrary to
this, the kurtosis with two-phase flow increases. By these statistical analyses, it is confirmed that
even if bubbles in the turbulent boundary layer are with a low void fraction, characteristics of
velocities in the layer are modified by them.
Fig. 10 Statistical analysis for time series of velocities near the upper wall; (a) skewness and (b)
kurtosis, where the kurtosis is defined as kurtosis of Gaussian distribution becomes zero.
5. Conclusions
We developed a laser Doppler velocimetry system with a high spatio-resolution, 19 μm in the
vertical direction, to access a turbulent boundary layer in a horizontal channel flow and estimated
effects of bubbles injected into the layer on the velocity distribution in the layer. In the
measurements, the system was influenced by electric noise generated by an inverter system of a
pump which is to control a flowrate in the channel. Because beat signals used for calculating
velocities in the system are corrupted by the noise with relatively lower frequencies than that of
the beat signals, a frequency counter with a band pass filter, which is normally used to a laser
Doppler velocimetry, is not useable for detecting automatically a frequency of the beat signals.
Therefore, we also devised a data processing to calculate velocities automatically from the beat
signals with the noise using a short-time FFT analysis and a statistical analysis. Velocity
distributions with a single-phase flow and a two-phase flow were investigated by the laser
Doppler velocimetry system with the data processing, and were estimated using statistical values,
such as average, standard deviation, skewness and kurtosis. In spite of bubble injection, other
statistical values excepting the kurtosis are keeping their values before the bubble injection
W all unit (y+ )
-0.5
0.5
1.5
skew
ness
0
1.0
a
W all unit (y+ )
100-1.0
0
-0.5
0.5
kurt
osi
s
b
42 126 8100 42 126 8
Sing le-phaseTwo-phase
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
because injected bubbles had too low void fraction. However, the kurtosis with a condition of the
bubble injection shows distinctly different tendency comparing with that with a single-phase flow.
In the single-phase flow, the kurtosis, which defines that Gaussian distribution is zero, has
negative values and decreased when a measurement point becomes close to the wall. In the two-
phase flow, on the contrary, it increases when the measurement point becomes close to the wall,
and has finally positive values. By these analyses, it is confirmed that although bubbles in a
turbulent boundary layer are with a low void fraction, they have a potentiality enough to change
characteristics of velocities in the layer.
Acknowledgment
This work was supported by Grant-in-Aid for JSPS Fellows No. 15J00147 and JSPS KAKENHI
Grant Nos. 24246033 and 23760143. The authors would like to express their appreciation for these
supports.
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