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

MULTI-SCALE ANALYSIS ON 3D FLOW STRUCTURES BEHIND A WALL-MOUNTEDSHORT CYLINDER CONTROLLED BY USING A FRONT INCLINED HOLE
Hiroka Rinoshika
Department of Mechanical Systems Engineering
Yamagata University
4-3-16 Jonan, Yonezawa-shi, Yamagata, Japan

Akira Rinoshika
Department of Mechanical Systems Engineering
Yamagata University
4-3-16 Jonan, Yonezawa-shi, Yamagata, Japan

Masato Akamatsu
Department of Mechanical Systems Engineering
Yamagata University
4-3-16 Jonan, Yonezawa-shi, Yamagata, JapanABSTRACTThis paper deals with the three-dimensional (3D) wakestructures of a wall-mounted short circular cylinder, which arecontrolled by the flow issuing from a front inclined hole (FIH)
drilled from the front side surface to the free end surface in theshort cylinder. The 3D velocity fields are instantaneously
measured at a Reynolds number of 10720 based on highresolution tomographic particle image velocimetry (Tomo-PIV)
in a water tunnel. A 3D W-type arch vortex is observed behindthe short FIH cylinder. Compared with the standard cylinder, the3D W-type arch vortex exhibits a large peak or convex at centerof the horizontal part and collapses more rapidly at thedownstream for the FIH cylinders. The flow from the FIH may
increase the rear recirculation region, and its height may
effectively control the vortical structures. A 3D wavelet
multiresolution analysis is employed to decompose theinstantaneous 3D velocity fields measured by the Tomo-PIV.
The large-scale streamwise vortices in the FIH cylinder wakes
are smaller than those in the standard cylinder wake, and thisbecomes more evident as the hole height increases. However, 3D
time-averaged large-scale arch vortical structures becomesstronger.

applications in drag control for the design of offshore structuresand increasing the efficiency of thermofluid systems, such asbuildings, heat sink compounds, and the control surfaces on
automobiles, aircraft, and underwater vehicles. Recently, thedrilling of a front inclined hole (FIH) passing from the front side
to the free end surface induces the increases of the rear
separation region and Reynolds shear stress, and results in theincrease of drag although it reduces the separation region on thefree end surface (Rinoshika and Rinoshika, 2019). Such FIH
short cylinders may be applied to control the offshore(breakwater) structures for reducing wave and Tsunami energies.
However, how the flow that issues from the FIH affects the 3D
wake structures of wall-mounted short cylinders remains unclear.
This is the motivation for the present investigation.
In this paper, to clarify how the flow issuing from an FIH
drilled from the front side to the free end of a wall-mounted shortcylinder affects the 3D flow structures behind the cylinder, theinstantaneous 3D velocity fields around the FIH and standard
cylinders are first measured by Tomo-PIV. Then 3D orthogonal
wavelet multiresolution analysis is used to decompose theinstantaneous 3D velocity fields of the Tomo-PIV data, allowing
their various scale 3D flow structures to be analysed.

INTRODUCTION
Wall-mounted ﬁnite-length circular cylinders originate astrongly three-dimensional (3D) complex wake flow, which
differs from that of an inﬁnite circular cylinder (Rinoshika andZhou, 2005). Due to the existence of the free end of the cylinder
and the connection between the cylinder and the wall, such 3D
flow structures are greatly influenced by the aspect ratio (theratio of height to diameter) of the cylinder. The details on finiteheight cylinders were described by Sumner (2013). Zhu et al.
(2017) first measured the 3D flow structures behind a wallmounted cylinder with an aspect ratio of 2 by tomographic PIV(Tomo-PIV), and found an instantaneous and mean 3D M-shapearch vortex. Recently, the 3D multiscale wake structures of awall-mounted circular cylinder having an aspect ratio of 1 were
investigated by Rinoshika et al. (2020) based on Tomo-PIV anda 3D wavelet transform; they found a strong 3D W-type archvortex behind the short cylinder, and this was also observed in
the time-averaged intermediate-scale structures.
Even though many investigations have revealed the flow
structures behind short cylinders, few studies have focused oncontrolling the vortex-induced drag of a wall-mounted shortcylinder. This would have wide-ranging engineeringydx

LHzoxhDFigure 1 Model of wall-mounted short circular cylinder.

EXPERIMENTAL SETUP AND METHODS
A short circular cylinder of diameter D = 70 mm and height
H = 70 mm (aspect ratio H/D = 1), as shown in Fig. 1, was placedon the bottom wall of a circular open water tunnel. This
experiment was performed at a free stream velocity of U = 0.162
m/s, corresponding to a Reynolds number Re = 10720. To
control the complex 3D wake structures, an inclined hole ofdiameter d = 10 mm (d/D = 0.14), as shown on the right side ofFig. 1, was drilled from the front side to the free end of a wallmounted short cylinder, which generates a flow issuing from the112th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
free end. To evaluate the effect of the FIH position on the wakestructures, three kinds of FIH cylinders were constructed withdifferent heights of h = 20 mm, 35 mm, and 50 mm(corresponding to h/D = 0.29, 0.5, and 0.71) from the flat plateon the front side of cylinder; these are referred to as FIH20,
FIH35, and FIH50, respectively.

issuing from the FIH of the cylinder increases the rearrecirculation region and is related to increasing drag force. It
may be used as an important application in the offshore
structures and heat exchangers, especially suppressing Tsunami
energy.
Figure 4 shows the comparison of the 3D time-averaged
isosurfaces of Q/(U/D)2 =0.7 colored by the streamwise vorticity
𝜔 𝐷/𝑈 between the standard and FIH cylinders. The archvortex shape of the standard cylinder wake, as shown in Figure4(a), changes from a W shape to an M shape along the flow
direction due to the strong downwash flow near the central plane.
However, since the issuing flow from the hole of free end
induces a large separation flow and unsteady flow (Rinoshikaand Rinoshika 2019), the arch vortex shapes of the FIH cylinders
collapses easily at the downstream. As the height of the FIH
decreases, the destruction of the M-shape head becomes moreevident, because the hole issuing flow from the free end forms alarge angle with the main flow direction, and produces aseparation flow on the free end. Moreover, the shape of arch
structure gradually recovers to that of the standard cylinder as
increasing the height of front hole (i.e., the angle decreases).
These results indicate that the flow from the FIH cylinder may
break down and control the large-scale vortical structures of theshort cylinder wake. This result may be applied to the dragcontrol.

Figure 2 Tomo-PIV setup.
Figure 2 shows the experimental apparatus of the Tomo-PIV
measurements. A dual-head Nd:YAG laser (500 mJ/pulse)
having a 120-mm-thick light sheet was used. Four highresolution (6600×4400 pixels) double-exposure charge-coupleddevice cameras recorded the measurement domain
simultaneously. A synchronizer controlled the laser and cameras
and produced a sampling frequency of 0.25 Hz. In this study, themeasurement volume covered the domain of 235 × 140 × 100
mm3 behind the cylinder. By using a multipass correlation
analysis with a deforming interrogation window, the 3D vector
field was calculated. The interrogation volume was 32 × 32 × 32
voxels with 50% overlap in the final pass, resulting in a 3D
velocity vector field of 101 × 57 × 40 and giving a spatial
resolution of 2.4 mm and a vector pitch of 2.4 mm.

RESULTS AND DISCUSSION
Time-averaged 3D flow structures
The 3D isosurfaces of 𝑢/𝑈 = 0 behind the FIH cylinders andthe standard cylinder are shown in Figure 3. Here two contoursof the streamwise velocity in the (x, y) of z/D = 0.04 and (y, z) ofat x/D = 0.7 are also plotted in Figure 3. The isosurface of 𝑢/𝑈= 0, averaged over 400 Tomo-PIV snapshots, shows a 3D rearrecirculation zone. A top concavity isosurface is clearlyobserved near the plane of y/D = 0 in the standard cylinder[Figure 3(a)], generated by the downwash flow from the free end.
The separation region gradually contracts along the main flow
direction, and comes to an end downstream at around x/D = 1.6
because of the interaction of the vortex generating from the sideand free end of the cylinder. In the case of the FIH cylinders, as
shown in Figures. 3(b)–3(d), a large top concavity isosurface
appears near the plane of y/D = 0 by the flow issuing from theFIH in the short cylinder. The separation region in thestreamwise direction of FIH cylinders is larger than that of thestandard cylinder because the issuing flow from the hole of free
end increases the separation region. The isosurface heights ofFIH cylinders are also slightly higher than that of the standard
cylinder since the issuing flow from the FIH prevents downwash
flow. As the height of front hole becomes higher, the height ofseparation region increases slightly. It is clear that the flow(a) Standard(b) FIH20

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022(c) FIH35(c) FIH35(d) FIH50
Figure 3 Mean isosurface of 𝑢/𝑈 = 0 with the contours of thestreamwise velocity in the (x, y) of z/D = 0.04 and (y, z) of x/D =0.7.

(d) FIH50
Figure 4 Mean isosurface of Q/(U/D)2 = 0.7 colored by thestreamwise vorticity 𝜔 𝐷/𝑈.

Instantaneous 3D multiscale wake structures
Figure 5 shows the 3D distribution of the instantaneous Q
criterion with the isosurface of Q/(U/D)2 = 5.5 colored by thestreamwise vorticity 𝜔 𝐷/𝑈 around the standard and FIH
cylinders. This figure shows the complexity of 3D instantaneous
vortical structures of various scales. Large-scale streamwise
vortices (Zhu et al. 2017) (indicated by 3 and 4) near the cylinder
are clearly observed, and the W-type arch vortex rapidly breaks
down into several fragments (indicated by 2) downstream.
Figure 6 shows the instantaneous 3D Q1/(U/D)2 = 1.0
isosurface of large-scale structures, colored by the streamwise
vorticity 𝜔 𝐷/𝑈 in the standard and FIH cylinder wakes, basedon the 3D wavelet multiresolution analysis. A large-scale archvortex, corresponding to the vortical structure labelled 2 inFigure 5, is clearly observed in the standard and FIH cylinders.
Meanwhile, large-scale streamwise vortices (labelled by 3 and4) are also extracted, which match the instantaneous flow
structures in Figure 5. They go through the center of the archvortex and develop downstream, dominating the flow structures
downstream. Compared to the large-scale arch structure(labelled 2) of standard cylinder, more large-scale arch structures(labelled 1 and 2) are observed in the FIH cylinders. As theheight of the FIH decreases, the size of large-scale streamwise
vortex decreases because the hole issuing flow from the free end
forms a large angle with the main flow direction, which induces
a strong upwash flow and limits to the generation of streamwise
vortex near the cylinder. These results indicates that the flow
issuing from the FIH dominates and controls the large-scale flow
structures including the large-scale streamwise vortex.

(a) Standard(b) FIH20

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022(a) Standard(a) Standard(b) FIH20(b) FIH20(c) FIH35(c) FIH35(d) FIH50
Figure 5 Instantaneous 3D isosurface of Q/(U/D)2 = 5.5 coloredby the streamwise vorticity 𝜔 𝐷/𝑈 around various cylinders.

(d) FIH50
Figure 6 Instantaneous 3D large-scale isosurface of Q1/(U/D)2= 1.0 colored by the streamwise vorticity 𝜔 𝐷/𝑈 aroundvarious cylinders.

412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
Time-averaged 3D multiscale wake structures
The time-averaged 3D large-scale isosurface Q1/(U/D)2 = 0.7of large-scale structure (level 1) based on the 3D wavelet
multiresolution analysis, as shown in Figure 7, exhibits a largescale 3D arch vortex behind the standard cylinder and FIHcylinders. A pair of tip vortices near two convex parts of thehorizontal part of the arch vortex can be clearly seen based on
the contour of time-averaged streamwise vorticity 𝜔 𝐷/𝑈. TheQ1/(U/D)2 isosurfaces of the FIH cylinders are slightly larger
than that of the standard cylinder, which implies stronger largescale structures in the FIH cylinders.

(d) FIH50
Figure 7 Time-averaged 3D large-scale isosurface of Q1/(U/D)2= 0.7 colored by the streamwise vorticity 𝜔 𝐷/𝑈 aroundvarious cylinders.
CONCLUSIONSThis paper has addressed the applications of Tomo-PIV
measurements and 3D wavelet analysis to reveal the 3D
multiscale flow structures behind wall-mounted FIH shortcylinders. Compared with a wall-mounted standard shortcylinder, the main results are as follows.
(1) A large rear recirculation region and a strong 3D Wtype arch vortex appear behind FIH cylinders, which increases
with decreasing the height of the FIH.
(2) An instantaneous W-type arch vortex and streamwise
vortices are also observed in the near-wake region, and break
down more quickly into several fragments downstream.
(3) Based on the 3D wavelet analysis, the size of large-scalestreamwise vortex decreases with decrease of the FIH height.
Moreover, 3D time-averaged large-scale arch vortical structures
become stronger, the intermediate-scale arch vortices are moreactive.

(a) Standard

REFERENCES
Rinoshika, A. and Zhou, Y., 2005, “Orthogonal wavelet
multi-resolution analysis of a turbulent cylinder wake”, J. Fluid
Mech., Vol.524, pp. 229-248.
Rinoshika, H. and Rinoshika, A., 2019, “Passive control ofa front inclined hole on flow structures around a surfacemounted short cylinder”, Ocean Eng., Vol.189, 106383.
Rinoshika, H., Rinoshika, A., and Wang, J. J., 2020, “Threedimensional multiscale flow structures behind a wall-mounted
short cylinder based on tomographic particle image velocimetry
and three-dimensional orthogonal wavelet transform”, Phys. Rev.
E, Vol.102, 033101.
Sumner, D., 2013, “Flow above the free end of a surfacemounted finite-height circular cylinder: A review”, J. Fluids
Struct., Vol.43, pp. 41-63.
Zhu, H. Y., Wang, C. Y., Wang, H. P., and Wang, J. J., 2017,“Tomographic PIV investigation on 3D wake structures for flow
over a wall-mounted short cylinder”, J. Fluid Mech., Vol.831,
pp. 743-778.

(b) FIH20(c) FIH355