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

TURBULENT BOUNDARY LAYER OVER STRUCTURED POROUS SURFACE
Zhixiang Feng
Institute of Fluid Engineering
Zhejiang University
Hangzhou, 310027, China
fzx1998@zju.edu.cn

Qingqing Ye
Institute of Fluid Engineering
Zhejiang University
Hangzhou, 310027, China
qingqing_ye@zju.edu.cn

ABSTRACT
Porous media is a widely used passive flow control device,
which shows potential in reducing skin friction and mitigating
flow introduced noise. In the present study, structured porous
media is applied to a flat plate to investigate its interaction
with turbulent boundary layer. Cylindrical pores are uniformly
distributed over the porous surface. The two-dimensional andthree-dimensional flow field over the porous surface wererespectively measured using planar and tomographic PIV at
the momentum-based Reynolds numbers of 719. The flow
field over smooth surface was also measured for comparison.
The porous media induced momentum transport close to thewall, leading to the generation of alternative low- and highspeed regions. The streamwise velocity fluctuations decreases
and the turbulence near the wall tends to be isotropic. Whilethe coherence of streamwise velocity streaks reduced. Most
streaks are located at the side of pores and migrate
downstream.

Recent studies found that structured porous media hassimilar drag and noise reduction effect to the unstructured type
(like ceramic and metal foam) (Carpio et al., 2020). The
porosity and interior pattern of the structured is easier tocontrol and design. In the present study, we used structured
porous media with uniformly distributed circular pores on
zero-pressure gradient flat plate. The porous media has arraysof circular through pores, with the diameter of 1 m. Timeresolved planar and tomographic PIV to capture theinstantaneous flow features. The statistical and coherent
structural analysis of the flow are performed.

EXPERIMENT SETUP
The experiments were carried out at the closed-loop windtunnel in the Institute of Fluids Engineering, Zhejiang
University. The wind tunnel has a cross-sectional area of
0.4×0.5 m2. The contraction ratio of the tunnel is 6.2:1,
resulting a maximum velocity of 35m/s.
A flat plate of 630 mm×400 mm×20 mm is installed overthe symmetry plane of the test section, as shown in Figure 1.
In order to inhibit flow separation, the leading-edge of theplate is designed using super-elliptical shape. The trailingedge of the plate ends with 12°inclination angle. The porous
media of 100 mm×50 mm is installed at 378 mm downstreamof the leading edge. Boundary layer trip is applied at 100 mm
from the leading edge, achieving fully turbulent boundary
condition before reaching the porous surface. The x, y, z axis
corresponds to the streamwise, wall-normal and spanwise
directions, originating from the start location of the porous
media. The incoming velocity is 10 m/s. The Reynolds
number based on momentum thickness of the boundary layer(Reθ) at the porous location is 719.

INTRODUCTION
Porous media exists widely in nature, such as river beds,
forest canopies and bird feathers. Inspired by the silent flightof owls, the porous media shows large potential in reducing
flow induced noise, which is used as passive method for noise
mitigation in aerospace and wind energy industry (Kroeger etal., 1971). In addition, the possibility of drag reduction is also
found through the study of anisotropic porous media (Gómezde-Segura and García-Mayoral, 2019).
In order to make better use of porous media to achievenoise and drag reduction and more optimized design, it isnecessary to fully understand the influence of porous media
on the boundary layer.
Suga et al. (2017) performed an experimental study on
two-dimensional flow characteristics of turbulent boundary
layer over metal foam in a rectangular pipe flow, and foundthat with the increase of permeability Reynolds number, thestreak structures tend to fade. Ali et al. (2018) found that theuse of porous media greatly changed the energy cascade
distribution in the turbulent boundary layer, increased thepressure fluctuation on the wall and reduced the spanwise
coherence length. Kim et al. (2018) studied the interaction of
the flow across interface of porous media, using refractiveindex matching and PIV technique to capture the flow
overlying and within porous media. The results showed thatthe flow on both sides of the interface is negatively correlated.
The crest region for the 5-layer case reduces stress close to thewall. However, the evolution of coherent structures over the
porous surface is not fully understand yet, due to its threedimensional intermittency nature.

(a)1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022(b)using optical lens. The snapshots were acquired at 1.5 kHzwith ensemble size of 500.

TIME-AVERAGED FLOW TOPOLOGY
The time-averaged flow topology is investigated toprovide the first inspection on the interaction between porous
surface and turbulent boundary layer. The cross-plane contourin x-y plane non-dimensional streamwise velocity and wallnormal velocity ( 𝑢/𝑢∞ and 𝑣/𝑢∞ , respectively) wereobtaining by averaging 4000 snapshots, as shown in Fig. 3.
Contours of mean velocity difference (Δu/u∞) by subtracting
the result over smooth surface is also presented in Fig. 3. The
grey areas at the bottom of the image represent solid walls andthe white areas represent pores. Streamlines are superimposedin the zoomed area to visualize the vortical structures. The
influence of porous surface is actively present in the near wallregion of y < 1mm. The mean velocity in the near wall region
exhibits strong streamwise inhomogeneity over the porous
surface. The pores induce strong upwash and downwash
motion at the upstream and downstream half of each pore,
respectively, shown by the wall-normal velocity in Fig. 3(b).
The momentum transport of fluid leads to the formation ofalternative high- and low-speed regions (Fig. 3(a)), which
exist from the most upstream of pore centered at x = 1mm andsustains until the most downstream of the measurement
domain. These phenomenon over the porous surface isconsistent with previous researches (Kim et al., 2020). The
intensity of downwash motion is remarkably higher than the
upwash, leading to higher near wall streamwise velocity
compared with smooth surface case (Fig. 3(c)). The results
indicate the weakening of wall blocking effect (Breugem et al.,2006). The relaxation of the no-slip boundary condition leads
to surface shear stress reduction. The magnitude of wallnormal velocity grows from 𝑣/𝑢∞ = 0.07 to 0.2 fromupstream to downstream, revealing the enhancement of
momentum transport across the porous surface.

Figure 1. Schematic illustration of experimental setup.
(a) Tomo-PIV and (b) Planar PIV.
Structured porous media are porous media with arrays ofcircular pores was used. One pore size of 2mm diameter wasstudied. The details of porous media arrangements are shownin Fig. 2 and Table 1. In addition, a solid surface insert wastested under the same flow conditions for comparison.

Figure 2. Porous media (diameter d, streamwise distance
between adjacent pores t and streamwise distance between
adjacent pores h)

SmoothPorousTable 1. Porous media detail parameters
h/mm
t/mm
d/mm
——
——
——
4.6
4.2
2

(a)

The instantaneous velocity field is measured with timeresolved planar and tomographic PIV (Tomo-PIV). For the
Planar-PIV (Fig. 1(b)), the measurement domain of 50×22
mm2 (x×y) starts from 5 mm upstream of the porous media.
Images were captured using a high-speed camera at thefrequency of 2 kHz (Photron FASTCAM Mini AX100,
1024×1024 pixels). The illumination was provided by
Beamtech Vlite-Hi-527-50 high speed laser (Nd:YLF, 527nm,
50 mJ/pulse at 1 kHz). The laser beam is converted into lightsheet with a thickness of about 1 mm using an optical lensarray. An ensemble size of dataset of 4000 was obtained.
For the tomo-PIV (Fig.1 (a)), the measurement domain of
40×4×40 mm3 (x×y×z) locates in the range of x = [-8, 32] mm
adjacent to the surface. Images are recorded using four highspeed cameras (two Photron FASTCAM SA4 and two Photron
FASTCAM Mini AX100, 1024×1024 pixels) with crossarrangement. Each camera is equipped with objective of
105mm focal length and Scheimpflug adapters. The samelaser device is used to provide the illumination and the laser
beam is turned into light sheet with a thickness of 4 mm by

(b)

(c)

Figure 3. Time-averaged velocity field over the porous
surface at x-y plane. (a) streamwise velocity (𝑢/𝑢∞ ), (b) wallnormal velocity ( 𝑣/𝑢∞ ), (c) mean streamwise velocity
difference (Δu/u ∞ ), (d) mean wall-normal velocity change.
The flow topology is shown by the zoomed red rectangle area
superimposed with streamlines. The grey areas represent solid
walls and the white areas represent pores.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
To further understand the influence of the porous media
on the turbulent boundary layer, the three-dimensional timeaveraged flow field closed to porous surface is illustrated inFig. 4. For each pore, a pair of counter-rotating streamwise
vortices locate at the side flank (Fig. 4(a)), leading to themodification of mean boundary layer in not only streamwise
but also spanwise directions. The intensity of the counterrotating vortice increases when developing downstream.
Besides the downwash motion over the pores, the vortex pair
induce strong upwelling motion between spanwise
neighboring pores, which cause the low-momentum fluid tomove away from the wall and generate low-speed regions, as
shown by the y-z plane in Fig. 4(b). The low-speed area
extends in the streamwise direction over the entire
measurement domain due to the successive upwash motion,bounding the high-speed regions over the pores, as shown in
Fig. 4(c). This phenomenon has also been observed in themean flow field over rough surfaces, which is caused by largescale secondary flows (Barros et al., 2014). Mejia-Alvarez andChristensen (2013) refers to the low-speed elongated area after
time average as the low-momentum pathway (LMP), differingfrom the low-momentum region (LMR) detected ininstantaneous velocity field of wall turbulence. The LMR is
associated to the growth of Kelvin-Helmholtz (K-H)
instability, leading to the formation of large scale-hairpin
structures. The latter will be discussed in the remaining study.

et al., 2010) over the permeable walls comprised of regularly
packed spheres (Kim, 2019). Manes et al. (2011) speculated
that the reduction of <𝑢′ >/𝑢∞ is related to the suppression of
streaks near the wall over porous surface. This is confirmedby the absence of streaks over porous surface in the
instantaneous 3D flow filed, which will be analyzed in detailbelow.
The decrease of the amplitude of <𝑣 ′ >/𝑢∞ over porous
surface is observed in the range of 0.15 < 𝑦/𝛿99 < 0.5 (Fig.
5(b)). This phenomenon was reported by Bhat et al. (2021)
who performed a micro-cavity array to control the near-wall
turbulence. It is worth mentioning that 𝑣𝑟𝑚𝑠 /𝑢∞ directly
above the pores is bigger than that over smooth surface near
the wall (0 < 𝑦/𝛿99 < 0.15) due to the momentum exchange inthe vertical direction (Kim et al., 2018). This result is inagreement with the near-wall intensity increase for the rms
wall-normal velocity over porous media (metal foam) (Manes
et al., 2011; Suga et al., 2010).
(a)

(a)

(b)

(c)

(b)

Fig 5 Profiles of streamwise and wall-normal velocity
fluctuations. The black line represents smooth surface; the redand blue lines represent the pore location at x = 21mm anddownstream interval at x = 23.1mm, respectively.

Figure 4. Three-dimensional time-averaged flow fieldnear the porous surface. Iso-surfaces represent the timeaveraged streamwise vorticity (𝜔𝑥 = ±300 1/𝑠). Cross
planes contours of the time-averaged streamwise velocity are
shown at y-z plane (b) and x-z plane at y = 0.15 mm (c).

QUADRANT ANALYSISThe sweep and ejection events induced by the porous
surface by the quadrant analysis. The distribution of the joint
probability density of the velocity fluctuations (𝑢′ , 𝑣 ′ ) at y =0.45 mm (𝑦 + ≈ 12) is depicted Fig 6. The density distribution
above and the pore at x = 42mm and the interval directly
downstream are shown in Fig 6(b) and (c) respectively. The
solid red ellipse is the distribution profile with a confidence
level of 95%. The shape profile of the joint probability density
distribution yields ellipse for both the porous and the smoothsurface. Both Q2 (ejection) and Q4 (sweep) events dominate
the production of turbulence, while Q1 and Q3 events aresecondary. However, compared with slender elliptical shapeof the probability density distribution on the smooth surface(Fig 6a), the shape on the porous surface becomes ‘roundshaped’ and tilted (Fig 6b). This change in the shape indicatesthat the porous surface leads to the decrease of streamwise

TURBULENT FLUCTUATIONSIn order to quantitatively analyze the effect of momentum
transport induced by the porous surface to the turbulent
fluctuations, R.M.S. of the streamwise and wall-normal
velocity fluctuations (<𝑢′ >/𝑢∞ and <𝑣 ′ >/𝑢∞ ) are extracted atselected location, corresponding to pore, pore interval, andsmooth surface, as shown in Fig. 5.
Compared with the smooth surface case, the streamwise
velocity fluctuations (< 𝑢′ >/ 𝑢∞ ) decreases over the entire
boundary layer for the porous surface case (Fig. 5(a)). The
maximum reduction establishes close to the wall due to therelaxation of no-slip boundary condition over porous surface.
This phenomenon has been observed in many studies ofturbulent structures over metal foam (Manes et al., 2011; Suga3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
velocity fluctuations (𝑢′ ) and slight increase of wall-normal
velocity fluctuations (𝑣 ′ ) due to the momentum transport. The
phenomenon is consistent with results of <𝑢′ >/𝑢∞ (Fig 5(a))
and <𝑣 ′ >/𝑢∞ (Fig 5(b)) near the wall. Manes et al. (2011)
observed similar change of velocity fluctuations in the nearwall of the porous surface. Moreover, the distribution of theprobability density over the pore interval (Fig. 6(c)) is still
slender elliptical shape. However, the amplitudeof<𝑢′ >/𝑢∞ decreases, while the amplitude of <𝑣 ′ >/𝑢∞ has littlechange. Similar results can be found in profiles of <𝑢′ >/𝑢∞(Fig. 5(a)) and <𝑣 ′ >/𝑢∞ (Fig. 5(b)) over the pore interval. The
block effect of the pore interval of porous surface prevents theflow from penetrating into the wall and causes the near-wall𝑣 ′ /𝑢∞ to return to the same level as in the smooth surface
condition. The change in shape into round over porous surface
indicates that the porous treatment turns the anisotropic
turbulence over smooth surface into the less anisotropic
turbulence, which is similar to observation of Suga et al.
(2011).

identified as negative and positive streamwise velocity
fluctuations. Iso-surfaces of streamwise velocity fluctuations(𝑢′ /𝑢∞ = ±0.1) are shown in Fig. 7, where green and blue
represent the high- and low-speed streaks, respectively. Abovethe smooth surface, the streamwise elongated streaky
structures with alternating sign along spanwise direction are
clearly observed, which is consistent with the typicalstructures in a zero-pressure-gradient boundary layer (Kline etal., 1967). Although there are streamwise elongated streaks
over the porous surface, the number of streaks is reduced andthe quasi-periodic variation of streaks along the spanwise
direction is suppressed. This phenomenon can be observed on
both low-permeability surface (Suga et al., 2017) and highpermeability surface (Kuwata & Suga, 2019). The enhanced
wall-normal upwash and downwash motion over porous
surface (Fig. 3(b)) leadind to the growth of the K-H instability.
The latter interrupts the streak formation. Notably, there are
no apparent lager-scale spanwise rolls over the porous surface,which are generated by the K-H instability. The reason for thisis that low wall-normal permeability and streamwise
impermeability prevent development of the streamwise
perturbation by the K-H instability. Another explanation is theinstantaneous streamwise fluctuations can not well reflect the
spanwise structure over porous surface and instead thepressure fluctuations might be a better option to show
spanwise structures (Kuwata & Suga, 2016).

(a)

(a)

(b)

(b)

(c)

Figure 7. Iso-surfaces of instantaneous streamwise velocity
fluctuations (u’/u∞ = ±0.1). (a) smooth surface and (b) porous
surface. The green and blue represent high- and low-speed
streaks.
Figure 6. Quadrant analysis at y = 0.45 mm (𝑦 + ≈ 12),coloured by the joint density distribution. The red circle
highlights the profile of overall density distribution. (a)smooth surface, porous surface (b) at x = 42 mm and (c) at x
= 44.1 mm.

In order to quantitatively discuss the change of streak
structure observed above, the two-point correlation analysis ofstreamwise velocity fluctuations at y = 0.31 mm (𝑦 + ≈ 10) is
performed, as shown in Fig. 8. The profile of correlation
coefficient is obtained by global averaging. For two surfaces,
the spanwise correlation coefficient drops to a negative peakat 𝛥𝑧 + ≈ 93, which is the mean spanwise length between
neighboring high- and low-speed streaks. The streaks spacingof 93 wall units is close to that of 100 wall units over a smooth

COHERENT STRUCTURESThe evolution of three-dimensional coherent structures isrepresented by the streasmwise velocity streaks, which are412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19-22, 2022
surface by Kim et al. (1987). It can be inferred that the porous
surface has little effect on the statistical spatial size of streaks,
which is inconsistent with results for flow over an anisotropic
porous surface with drag reduction (Li et al., 2020; Rosti et al.,2018). However, for the spanwise correlation coefficient, themagnitude of the negative peak over porous surface is smaller
than that over smooth surface. The phenomenon shows thatstreamwise streaks over porous surface are less-organized(Suga et al., 2017), that is, the coherence between the lowspeed streak and its adjacent high-speed streak is weakened.

field. Vanderwel et al.’s (2019) explanation for this is that thelarge-scale secondary flow structures in the mean field are thetime-averaged result of small-scale counter-rotating vortex
pairs with stronger vorticity in the instantaneous flow fields.
Moreover, very large-scale low-speed regions withsurrounding vortical structures are convected downstream
along the side of pores. That is to say, the vortical structures
are concentrated on one side of pores, which is different fromposition of vortical structures over smooth surface. Similar
distributions of vortical structures are observed in flows oversmooth surfaces with spanwise heterogeneities (Ni et al.,2018).
(a)Figure 8. Two-point correlation of streamwise velocity
fluctuations along spanwise.
(b)

LOW ORDER RECONSTRUCTION OF VELOCITY
FIELDThe proper orthogonal decomposition (POD) is aneffective method to extract the large-scale structure of the flowfrom turbulent flow. The background noise from PIV
measurements and the influence of small-scale structures canbe better removed, so that the spatial distribution
characteristics of the large-scale coherent structures in theflow can be observed more clearly. In order to further study
the effect of porous media on the turbulent boundary layer,
low-order modes with cumulative energy reaching 90% ware
selected to reconstruct the large-scale flow for threedimensional velocity fields, as shown in Fig. 9. Since the highspeed streaks are not the main structure over the porous
surface, only the low-speed strip structure is shown in the Fig.
9 for the sake of clarity. Fig 9(b) shows vortical structures in
the red box area in Fig. 9(a).
Although the coherency of velocity streaks is reduced by
the porous surface, there are still large-scale low-speed streaks
in streamwise direction. Vortical structures surrounding lowspeed streaks are also clearly captured, as shown in Fig. 9(b).
By comparing the position of pores and low-speed streaks, it
can be found that streaks appear on one side of pores. Thisphenomenon exists for both large-scale and relatively smallscale low-speed streaks. The instantaneous low-speed regions
distribution is consistent with the time-averaged low-speed
regions distribution (Fig. 4). This finding supports theprevious hypothesis that the low-momentum pathways (LMPs)
could be preferential pathways for instantaneous large-scale
motions (LMRs) (Mejia-Alvarez & Christensen, 2013). The
streamwise elongated streaks become less curvy over porous
surface compared with that over smooth surface, which isconsistent with flow over an anisotropic porous wall with dragreduction (Li et al., 2020). The arrangement of the pores inthis paper induces large-scale secondary flow, which is
responsible for the less curved streaks in the streamwise
direction. However, the large-scale secondary flow that exists
in the mean field is not observed in the instantaneous flow

Figure 9. Iso-surfaces of instantaneous streamwise
velocity fluctuations (𝒖′ /𝒖∞ = -0.1) and vortical structures(𝜆𝑐𝑖 = 900) over porous surface reconstructed by low-ordermodes. (a) Top view of low-speed streaks and (b) vorticalstructures. The red iso-surface 𝜆𝑐𝑖 of represents vorticalstructures; the blue is low-speed streaks. The yellow circle
highlights the coherent structures.

CONCLUSION
Structured porous media have great potential in noise anddrag reduction. In order to study the mechanism of thesefunctions, the instantaneous flow structures of turbulent
boundary layer over porous surface are obtained by timeresolved planar and tomographic PIV. The porous surface
with cylindrical pores is applied. The results show that theporous surface has resulted in the increase of the streamwise
velocity near the wall and reduction of the turbulent intensities
in the range of 0.15 < 𝑦/𝛿99 < 0.5. The joint probability
density analysis of velocity fluctuation shows that the
turbulence in the near-wall region of the porous surface tend
to be isotropic. For the coherent structures, the streamwise
velocity streaks over the porous surface are significantly
suppressed and the distribution of the pores introduces thesecondary flow, which causes the streaks less curevd andmigrating downstream along the side of pores.

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