12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Effects of energetic large-scale coherent structures on wall mass transfer rate of
turbulent flow behind orifice in round pipe
Feng Shan
School of Energy and Power Engineering
Huazhong University of Science and Technology
Wuhan, 430074, China
shanfeng@hust.edu.cn

Zhiqiang Yu
School of Energy and Power Engineering
Huazhong University of Science and Technology
Wuhan, 430074, China
onoryu@foxmail.com

Kano Masashi

Yoshiyuki Tsuji

Department of Energy Engineering and Science Department of Energy Engineering and Science
Nagoya University
Nagoya 464-8603, Japankanomashshi@ees.nagoya-u.ac.jp

Nagoya University
Nagoya 464-8603, Japan
c42406@cc.nagoya-u.ac.jp

ABSTRACTThis paper first uses a low-speed stereoscopic particle image
velocimetry (SPIV) system to measure the convergent statisticalquantities of the flow field and then simultaneously measure thetime-resolved flow field and the wall mass transfer rate by ahigh-speed SPIV system and an electrochemical system,
respectively. We measure the flow field and wall mass transfer
rate under the upstream pipe Reynolds numbers between 25000
and 55000 at three specific locations behind the orifice plate.
Moreover, we apply proper orthogonal decomposition (POD),
stochastic estimation, and spectra analysis to study the propertiesof the flow field and the wall mass transfer rate. More
importantly, we investigate the large-scale coherent structures’
effects on the wall mass transfer rate. The collapse of the wallmass transfer rates’ spectra by the corresponding time scales at
the three specific positions of orifice flow suggests that thephysics of low-frequency wall mass transfer rates are probably
the same, although the flow fields away from the wall are pretty
different. Furthermore, the spectra of the velocity reconstructedby the most energetic eigenmodes agree well with the wall masstransfer rate in the low-frequency region, suggesting that the first
several energetic eigenmodes capture the flow dynamics
relevant to the low-frequency variation of the wall mass transfer.
Stochastic estimation results of the velocity field associated withlarge wall mass transfer rate at all three specific locations further
reveal that the most energetic coherent structures are correlatedwith the wall mass transfer rate.

of the thinnest pipe wall location. Consequently, pipe rupture
usually occurs in the thinnest pipe wall location, which has
caused many serious accidents worldwide. Although thedecrease of pipe wall thickness behind an orifice is combinedwith material, chemistry, and hydrodynamic conditions, theorifice plate's strongly turbulent flow field is believed toaccelerate the decrease of the pipe wall thickness, which
motivates the present study.
So far, many researchers believe that the position of the
maximum wall mass transfer rate is close to the position of the
maximum streamwise velocity fluctuation (or the maximum
turbulent kinetic energy) in orifice flow, and some further argue
that it should be located near the reattachment point. However,
we find this is not true, at least in the Reynolds number region
25000~55000. Furthermore, how the large-scale energetic
coherent structures evolve in this strongly developing flow is
missing in previous studies of this rapidly developing separated
internal flow. The effects of the large-scale energetic coherent
structures on the wall mass transfer rate are also missing in theliterature. Understanding these effects helps reveal themechanisms of wall mass transfer augmentation and theappearance of the large wall mass transfer rate position in thenear field of orifice flow, which is beneficial for preventing FAC
problems. The coherent structures are also expected to playessential roles in macro-characteristics of the flow and processes
such as scalar and momentum transport, chemical mixing, andnoise generation. Trying to understand these structures’ spatial
and temporal evolution has become paramount to understanding
the process by which heat, mass, and momentum are transferredthrough the mean flow (Tinney et al., 2008).
In the current study, we rely on the mixed Fourier and POD
techniques to extract the large-scale energetic coherent
structures in orifice flow. We adopt this method is mainly
because of its successful use in a pipe flow and a sudden pipe
expansion (Tinney et al., 2006), which is another typical
separated internal flow and shares many similar characteristicsof the flow field. In general, our research aim is twofold. The
first aim is to extract the large-scale coherent structures at three
typical locations in the near field of orifice flow to understandthe evolution of the coherent structures in orifice flow, and thesecond aim is to find out the possible role of these large-scalecoherent structures on the wall mass transfer rate.

INTRODUCTION
Orifice plates widely exist in many piping systems in theenergy and chemical industry. The turbulent flow field behind acircular orifice plate in a round pipe (hereafter referred to as
orifice flow in short) is a typical separated internal flow, where
flow separation and reattachment occur with strong threedimensional complex properties, as shown in figure 1. It is ofimmense importance in many practical fields; for instance, flowaccelerated corrosion (FAC), also known as flow-assisted
corrosion, usually occurs in the near field. FAC isa corrosion mechanism in which an ordinarily protective oxide
layer on a metal surface dissolves in fast-flowing water. As aresult, the pipe wall thickness decreases because of FAC.
Moreover, the pipe wall thickness in the near fielddownstream of the orifice plate is not even with the appearance

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
EXPERIMENTAL SETUP
In the present study, we carried out two sets of experiments,
one was the measurements of independent instantaneous
velocity fields by a low-speed SPIV system, and another was thesimultaneous measurements of the time-resolved velocity field
and the wall mass transfer rate by the combination of a highspeed SPIV system and an electrochemical system. Using thelow-speed SPIV system, we measured the independent velocity
fields for a sufficiently long time to get convergent orifice flow
statistics. We simultaneously measured the velocity field andwall mass transfer rate at a relatively high speed for a shortperiod. In this case, we can analyze the flow field’s dynamical
properties and the relationships between the flow field and thewall mass transfer rate.
Figure 2 shows the sketch of the flow recirculation loop formeasurements of the velocity field and the wall mass transfer
rate. A gas container filled with high-pressure nitrogen isconnected to the water tank to remove the oxygen in the flow
recirculation loop before the simultaneous velocity field andwall mass transfer rate measurements. A centrifugal pump drove
the working fluid in the tank to recirculate inside a piping system
of inner diameter 46 ± 0.1mm. There is a square-edged orificeplate with a thickness of 5 mm located inside the piping system.
The orifice to pipe diameter ratio 𝛽 ≡ 𝑑/𝐷 = 0.62, where 𝑑 and𝐷 are the orifice and pipe diameters, respectively. We measured
the flow fields at two upstream pipe Reynolds numbers 𝑅𝑒𝐷 =𝑈𝑏 𝐷⁄ν = 25000 and 55000, where 𝑈𝑏 is the bulk velocity andν is the kinematic viscosity. The straight pipe’s length upstreamof the orifice plate was approximately 74𝐷; and the length of thestraight pipe downstream of the orifice was approximately 15𝐷,
as can be seen in figure 2. The flow achieves a fully developed
pipe flow far upstream of the orifice plate.
We specially designed a test section in figure 3 to measure
the velocity field and the wall mass transfer rate simultaneously.
A handcrafted trigger box (not shown here) triggered thesimultaneous measurements of the velocity field and the wallmass transfer rate. An acrylic water jacket and two prisms filledwith water were adopted to minimize the optical distortion due
to refraction through the pipe wall. The test section housed
several electrodes, separated into three groups: the working
electrodes, the counter electrode, and the reference electrode. All
electrodes were mounted flush with the pipe wall; therefore, noabrupt change of the hydrodynamic conditions occurred in theconnection region between the electrodes and the pipe wall.
The working electrodes were constructed by inserting acylindrical gold wire with a diameter of 1 mm into the pipe wall.
There are 20 working electrodes evenly distributed from𝑥⁄𝐷 = 0.1~2 ; thus, the distance between two neighboring
electrodes is 0.1𝐷, as shown in Figure 3. The counter electrode
was a nickel circular ring with a length of 5 mm. The much larger
size of the counter electrode than the working electrodes was
selected to ensure that the current flowing into the circuit wascontrolled by the working electrode’s surface reactions. The
counter and reference electrodes were located approximately
five and eight times the pipe diameter away from the orifice’s
downstream surface, respectively. The original coordinate
system of the raw PIV data is Cartesian coordinate with theorigin in the center of the orifice plate’s downstream surface, as
shown in figure 3. Vz, Vy, and Vx represent the instantaneous
spanwise, vertical, and streamwise velocities, respectively.
However, to use the mean velocity field’s axisymmetric property
in the azimuthal direction, the original velocity field isinterpolated into a cylindrical coordinate system using Vr, Va,
and Vx to represent the instantaneous radial, azimuthal, andstreamwise velocity components, respectively.

In the present study, one working electrode was selected withthe counter electrode to form a current circuit to measure thelocal wall mass transfer rate. The working electrodes act as thecathode. The counter electrode acts as the anode and requires a
known potential to balance the charge added or removed by theworking electrode. The reference electrode was used as an anodewith a known reduction potential. Its only use was to act as areference when measuring and controlling the working
electrode’s potential; it did not pass any current.
A carefully configured chemical solution with thefluorescent particles was used as working fluid in the flow
recirculation loop, as shown in Figure 2. The fluorescentparticles Fluostar with a mean diameter of 15 μm and density of
1.1 g⁄cm3 is commercially available from Kanomax Company.
The use of fluorescent particles was aimed at reducing the strong
laser reflection from the pipe wall. To record only the fluorescentlight reflected by the fluorescent particles, two long-pass filters(𝜆𝐿 > 580 nm) were mounted in front of the two lenses in the
SPIV measurement.
The test solution was an equilibrium mixture of potassium
ferricyanide ( 𝐾3 𝐹𝑒(𝐶𝑁)6 ) and potassium ferrocyanide(𝐾4 𝐹𝑒(𝐶𝑁)6 ) with potassium sulfate (𝐾2 𝑆𝑂4 ) as the supporting
electrolyte, whose ions were not involved in the electrodereactions. De-ionized water and high purity chemicals(analytical reagent) were used to make up 90 𝐿 solutions. The
temperature of the electrolyte was maintained at 20 ℃
throughout the measurements. Precautions were taken to avoid
contamination of both electrolyte and electrode surfaces. Morespecifically, the solution was protected as much as possible fromexposure to daylight, and the solution was de-aerated and kept
under a blanket of inert nitrogen gas. For more details of themass transfer measurement, please refer to Tong et al. (2018).

DATA ANALYSIS METHOD
The mixed Fourier and POD process in the present study isvery similar to those used in many previous studies, see, forinstance, Hellstrom and Smits (2014). The determination of thelarge wall mass transfer rate is subjective. Since we are
discussing the fluctuations of wall mass transfer below, we
define the condition of the large wall mass transfer rate thefluctuation of wall mass transfer rate larger than five times its
root mean square. Stochastic estimation can estimate theconditionally averaged velocity field with much less data.
Adrian (1977)first proposed its application to extract coherent
motion in turbulent flows. Since then, it has been widely used in
the community of fluid dynamics, where the velocity field orpressure has been primarily used as the condition to perform thestochastic estimation.

RESULTS AND DISCUSSIONS
Based on the experimental data(Shan et al., 2013), we replot
the mean streamline pattern in the radial-streamwise plane andthe mean wall mass transfer rate profile as shown in Figure 4.
One can observe the secondary and primary recirculation regions
from the mean streamline patterns shown in the sketch of orificeflow in Figure 1. The four red lines represent the location atwhich the mean streamwise velocity 𝑉̅𝑥 = 0. These lines can beconsidered the mean reattachment lines separating the positive
and negative mean streamwise velocities. Quantitatively, thetwo mean reattachment lengths of this flow are locatedapproximately at 𝑥𝑟1 = 3.64𝑅 and 𝑥𝑟2 = 0.26𝑅 , respectively.
The three bold green lines illustrate the positions of the threecross-sections in the present study. We selected the three crosssections 𝑥1 = 0.2𝑅 , 𝑥2 = 2𝑅 and 𝑥3 = 4𝑅 , locating at three212th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
typical positions of this separated internal flow. Morespecifically, the three locations are located in the secondary
recirculation, the primary recirculation and the redevelopment
regions, respectively.

collapse of the wall mass transfer spectra in the low-frequency
region suggests that it probably follows the same physics in thewall region though the flow fields at these three locations far
from the wall are pretty different.

1

y/R

0.5
0

-0.5
-1

0

1

2

3

4

x/R
(a)
Figure 5. Normalized spectra of wall mass rate at the three
typical positions.
To analyze the relationship between the velocity field andthe wall mass transfer rate statistically, we calculate the velocity
and wall mass transfer rate spectra. The spectra for both theoriginal velocity and the velocity reconstructed by the mostenergetic POD eigenmodes are compared with the wall masstransfer rate spectrum. The velocity spectra for all threecomponents are normalized by the corresponding variances andthe typical time scales of the wall mass transfer rate, and thevelocity spectra are averaged in the azimuthal direction.
Figure 6 shows the power spectra density of the wall masstransfer rate and the azimuthal velocities for different radial
positions at the cross-section 𝑥⁄𝑅 = 0.2. The original velocity
spectra shown in figure 6 (a) can be divided into three groups,
i.e., the spectra in the core, shear layer, and recirculation regions,
respectively. The black and green solid lines representing thevelocity spectra in the recirculation region have similar profiles.
The cyan line represents the velocity in the shear layer region
and has a small peak around non-dimensional frequency 20,
probably the typical frequency of the vortex shedding in theshear layer region. Note that this peak is more evident in the
spectra of the radial and the streamwise velocities 6. The velocity
spectra in the core and shear layer regions (the red and blue solidlines) are very different from the wall mass transfer rate
spectrum (the black dashed line) since they are relatively far
away from the wall mass transfer rate measurement sensor.
However, velocity spectra in the recirculation region (the solid
green and black lines) are similar to the wall mass transfer rate
spectrum in the low-frequency region, suggesting that the low
frequency (large time scale) flow structures probably have arelationship with the wall mass transfer rate. However, theprofile of the wall mass transfer spectra starts to differ from thatof the velocity in the non-dimensional frequency region f∆𝑡0 >2.
Figure 6 (b) shows the spectra of the wall mass transfer rate
and the velocity reconstructed by the ten most energetic POD
eigenmodes, accounting for approximately 33 % of the turbulent
kinetic energy. The reconstructed velocity spectra can still be
divided into three groups similar to the original velocity spectra.
However, noticeable differences between the original andreconstructed velocity spectra also appear. For instance, thereconstructed velocity spectra in the core and shear layer regions
have small peaks around non-dimensional frequency 20. We
assume that this frequency is related to the large-scale coherent
structures in the secondary recirculation region. Although the(b)
Figure 4. (a) mean streamline pattern and (b) profile of mean
wall mass transfer downstream of orifice flow normalized by
the value of fully developed pipe flow: the three green lines
illustrate the laser sheet positions; 𝐾 and 𝐾0 represent the mean
wall mass transfer rate in the orifice flow and the fully
developed pipe flow, respectively.
The profile of the mean wall mass transfer rate downstreamof the orifice plate shown in Figure 4 (b) shows that the wallmass transfer rate is far from uniform in the near fielddownstream of the orifice, which would result in a non-uniform
pipe wall thickness. Moreover, the wall mass transfer rate in the
primary recirculation region downstream of one pipe radius(~1< 𝑥⁄𝑅 < ~3.5 ) is enhanced compared with that of fully
developed pipe flow (𝐾⁄𝐾0 > 1), and the maximum mean wallmass transfer rate position is located near 𝑥⁄𝑅 = 2 . The
maximum mean wall mass transfer rate position agrees very wellwith the thinnest pipe wall location in the industry.
We measured the wall mass transfer rate corresponding to theabove three positions in the simultaneous measurements of thevelocity field and the wall mass transfer rate. Figure 5 shows the
spectra of the wall mass transfer rate fluctuations normalized by
the typical time scale ∆𝑡0 , which is defined based on the autocorrelation function of the wall mass transfer rate,〈𝑘(𝑡)𝑘(𝑡 + ∆𝑡)〉c(∆t) =.
(1)
𝜎2
The typical time scale ∆𝑡0 is given by the zero-crossing of the
autocorrelation curve∆𝑡0 = ∆𝑡|𝑐(∆𝑡)=0 .
(2)
One can observe that the spectra at three different positions
match very well in the low-frequency region (f∆t < 10) whennormalized by the corresponding time scales. The wall masstransfer rate may be contaminated by high-frequency electricalnoise; therefore, the wall mass transfer rate fluctuation was
filtered by a low-pass filter (Tong et al., 2018). However, we are
only interested in the low-frequency wall mass transfer
fluctuation; thus, no filter was used in the present study. The

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
original velocity spectra in the shear and core regions (the red,
blue, and cyan lines) do not agree with the wall mass transfer
rate spectrum, all the spectra of the velocity reconstructed by themost energetic POD eigenmodes agree reasonably well with thewall mass transfer rate spectrum in the low-frequency region(f∆𝑡0 < 2), especially the reconstructed velocity spectra in therecirculation region (the black and green solid lines). This result
reveals that the low-frequency wall mass transfer rate fluctuation
is probably related to the large-scale energetic coherent
structures.

17, which we assume is probably related to the vortex shedding
property in the shear layer region.
One can also observe from figure 8 (a) that the solid blackline representing the original velocity spectrum in the near-wallregion at the cross section 𝑥⁄𝑅 = 4 agrees with the wall masstransfer spectrum in the low-frequency region ( f∆𝑡0 < 2 ).
Moreover, this spectrum can be reconstructed by the large-scaleenergetic POD eigenmodes if one compares figures 8 (a) and (b).
Note that the red and blue lines in figure 8 (a) representing theoriginal azimuthal velocity spectra show a small peak aroundf∆𝑡0 ≈ 2. However, the original streamwise velocity spectra do
not have this peak. We assume that this peak is probably related
to the shear layer reattachment process.

(a)
v

(a)
v

(b)
v

(b)
v

Figure 6. Spectra of the wall mass transfer rate and azimuthal
velocity for different radial positions (r/R = 1 is the pipe wall) at
the streamwise position x/R = 0.2: (a) wall mass transfer andoriginal velocity; (b) wall mass transfer rate and reconstructedvelocity using ten most important eigenmodes. The superscript“rec” represents the reconstructed velocity.

Figure 7. Spectra of the wall mass transfer rate and the azimuthal
velocity at different radial positions (r/R = 1 is the pipe wall) at
streamwise position x/R = 2: (a) wall mass transfer and original
velocity; (b) wall mass transfer rate and reconstructed velocity
using 80 most important eigenmodes.

Figures 7 and 8 show the spectra of the wall mass transfer
and the azimuthal velocity at the cross-sections 𝑥⁄𝑅 = 2 and𝑥⁄𝑅 = 4 , respectively. The selection of different numbers of
POD eigenmodes to reconstruct the velocity field is based on theenergy profile of the POD eigenmodes. The solid black line
representing the original velocity spectrum in the near-wallregion at the cross section 𝑥⁄𝑅 = 2 has similar profiles as thatof the wall mass transfer rate in the low-frequency region(f∆𝑡0 < 2) as shown in figure 7(a), which suggests that the
dynamical properties of velocity field in the low-frequency
region at the cross section 𝑥⁄𝑅 = 2 are similar to that of the wallmass transfer rate. Additionally, the low-frequency region of thevelocity spectra can be reconstructed by the large-scale energetic
eigenmodes (80 modes in the present case), as shown in figure 7(b). The blue and red lines representing the original velocity
spectra in the shear layer regions peak around f∆𝑡0 ≈ 3 in figure

(a)
v

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022(b)v

Figure 8. spectra of wall mass transfer rate and azimuthal
velocity at different radial positions (r/R = 1 is the pipe wall) at
streamwise position x/R = 4: (a) wall mass transfer and original
velocity; (b) wall mass transfer rate and reconstructed velocity
using 50 most important eigenmodes.
We find out from the above discussions that the wall masstransfer rate spectra agree reasonably well with the spectra ofvelocity reconstructed by the most energetic eigenmodes in the
low-frequency region at all three specific cross-sections. We
thus assume that the large-scale energetic coherent structures'
frequency properties are related to those of the wall mass rate. In
other words, the energetic coherent structures are probably
related to the low-frequency variation of the wall mass transfer
rate in the near field of orifice flow.
Figure 9 shows the quadratic stochastic estimation of theconditionally averaged flow field associated with the large wallmass transfer rate (𝑘 > 5 𝑘𝑟𝑚𝑠 ) at all three cross-sections, where
𝑘 is the wall mass transfer rate fluctuation and 𝑘𝑟𝑚𝑠 is the root
mean square of the fluctuation. One can observe from figure 19(a) that large-scale azimuthal velocity patterns with opposite
directions appear in the conditional averaged flow field. In
addition, the background contour shows the high-speed fluid
flanked by low-speed fluid. If we compare figure 9 (a) with thesamples of the several most energetic POD eigenmodes shownin figure 10, we can observe that the first three most energetic
POD eigenmodes show similar velocity patterns. The differenceis that the scale of the velocity patterns in the azimuthal direction
may be different. Figures 9 (b) and (c) show similar counterrotating vortex pairs in the conditional averaged velocity fields
associated with large wall mass transfer rates. All the mostenergetic POD eigenmodes at the cross-sections 𝑥⁄𝑅 = 2 and𝑥⁄𝑅 = 4 show counter-rotating vortex pairs of different radial
and azimuthal scales. In addition, the distribution of thestreamwise velocity shown as the background contour is alsosimilar. More specifically, there are high-speed regions flanked
by low-speed regions for both two cross-sections. We believethat comparing the stochastic estimation results in figure 19 andthe most energetic POD eigenmodes reveals evidence of thestrong effects of the large-scale energetic coherent structures on
the wall mass transfer rate at all three specific cross-sections in
the near field orifice flow. Note that the counter-rotating vortex
pairs enhancing the wall mass transfer rate here in figures 19 (b)and (c) are very similar to the flow structures enhancing the wall
shear stress (Tong et al., 2020) in a pipe flow and the sketch oflarge-scale coherent flow motions in the boundary layer of wallbounded flow (Marusic et al., 2010).

Figure 9. Stochastic estimation of the conditional averaged flow
structures associated with large wall mass transfer rate at: (a)cross section x/R =0.2; (b) cross section x/R=2; (c) cross section
x/R = 4.
REFERENCES
Adrian, R. J. (1977). On the role of conditional averages in turbulence theory.
Hellstrom, L., & Smits, A. (2014). The energetic motions in turbulent pipe
flow. Physics Of Fluids [P], 26(12), 1-10.
Marusic, I., Mathis, R., & Hutchins, N. (2010). Predictive model for wallbounded turbulent flow. Science, 329(5988), 193-196.
Shan, F., Fujishiro, A., Tsuneyoshi, T., & Tsuji, Y. (2013). Particle image
velocimetry measurements of flow field behind a circular squareedged orifice in a round pipe. Experiments in fluids, 54(6), 1553.
Tinney, C., Glauser, M., Eaton, E., & Taylor, J. (2006). Low-dimensionalazimuthal characteristics of suddenly expanding axisymmetricflows. Journal of Fluid Mechanics, 567, 141-155.
Tinney, C. E., Glauser, M. N., & Ukeiley, L. S. (2008). Low-dimensional
characteristics of a transonic jet. Part 1. Proper orthogonal
decomposition. Journal of Fluid Mechanics, 612, 107-141.
https://doi.org/10.1017/S0022112008002978
Tong, T., Bhatt, K., Tsuneyoshi, T., & Tsuji, Y. (2020). Effect of large-scale
structures on wall shear stress fluctuations in pipe flow. PhysicalReview Fluids, 5(10), 104601.
Tong, T., Tsuneyoshi, T., Ito, T., & Tsuji, Y. (2018). Instantaneous masstransfer measurement and its relation to large-scale structures inpipe flow. International Journal of Heat and Fluid Flow, 71, 160169.

512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 1. Sketch of orifice flow and FAC problem.

Figure 2. Sketch of the flow recirculation loop for measurements of the flow field and the wall mass transfer rate.

Figure 3.Test section for simultaneous measurements of the velocity field and the wall mass transfer rate.

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