13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
Near wall organization of a turbulent boundary layer over a twodimensional rough wall
Lyazid Djenidi1, Robert A. Antonia1, Muriel Amielh2 and Fabien Anselmet2
1
: School of Engineering, University of Newcastle, Newcastle, Australia,
lyazid.djenidi@newcastle.edu.au , robert.antonia@newcastle.edu.au
2
: IRPHE, Marseille, France: amielh@irphe.univ-mrs.fr , fabien.anselmet@irphe.univ-mrs.fr
Abstract Particle Image Velocimetry (PIV) measurements and Planar Laser Induced Fluorescence (PLIF)
visualizations have been made in a turbulent boundary layer over a rough wall. The roughness consists of
square bars placed transversely to the flow at a pitch to height ratio of 11. The near wall region flow is
dominated by coherent structures associated with the shear layers which originate at the downstream edge of
a roughness element and reattach on the wall upstream of the subsequent element. Shear layer vortices shed
downstream a roughness elements impact on the consecutive element producing intermittent form drag and
strong turbulence production.
1. Introduction
The relatively slow progress that has been made, especially in understanding how the roughness
affects the turbulence structure, reflects, by and large, the extra parameters involved, by comparison
to the smooth wall case, and the general difficulty of making reliable measurements in the vicinity
of a rough surface. Nevertheless, there has recently been a renewal of interest in rough wall flows
e.g. [1] . Djenidi et al. [2] reported Laser Doppler Velocimetry (LDV) measurements and flow
visualizations (with the PLIF technique) for a turbulent boundary layer over a surface consisting of
square bars (height = width = k) attached to the wall where the steamwise pitch λ is equal to 2k (λ
is the streamwise separation between two consecutive roughness elements, and k the height of the
roughness elements). These techniques proved to be quite helpful in gaining insight into the nearwall flow organization. In particular, they confirmed and extended the earlier observations, over the
same surface [3].
Direct numerical simulations (DNSs [4, 5]) and large eddy simulations (LESs, [6]) have been
carried out for fully developed turbulent channel flows with a rough wall made up of 2D
transverse elements (of various cross-sectional geometries). While these studies show that DNS
data bases provide much new information, the results remain limited to relatively small Reynolds
numbers. This in itself is not too worrisome given that the form drag is the dominant contributor to
the total drag under fully rough conditions. However, there is the possibility that differences exist,
at least in the outer region, between a channel flow and a boundary layer. It is therefore important to
study turbulent boundary layers over 2-D rough walls.
The present work is part of a more extensive programme aimed at studying in detail a rough wall
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
boundary layer with variable λ/k. This paper reports Particle Image Velocimetry (PIV) and PLIF
measurements in a turbulent boundary layer over a wall on which two-dimensional square bars are
attached with λ/k =11. The main objective is to describe the flow structure and compare it with that
previously reported for smaller λ/k. The focus is on the near-wall region of the boundary layer. This
work extends that of [2] and [7].
2. Experimental set up
Two complementary experiments were carried out in two different water tunnels, one at Newcastle
for the PLIF visualizations, and the other at Marseille for the PIV measurements.
PLIF Setup:
The PLIF visualizations were made in a constant-head closed circuit vertical water tunnel with a
2 m long square (250mm × 250mm) Perspex test section. One of the working section walls is used
as the rough wall. The roughness elements consist of square bars (height k = 3mm) fixed to the wall
and spanning the full width of the test section, with a separation between the roughness elements λ
equal to 33mm. The boundary layer is tripped with 4.5 mm high pebbles glued over the wall span,
30mm upstream of the first roughness element. The roughness elements extend over a streamwise
distance of 1.8m downstream of the trip. Detailed flow visualizations are made at a distance of 1m
downstream of the first element; at this location, the boundary layer thickness δ is about 20k. The
Reynolds number Rθ based on the momentum thickness θ ( θ is estimated midway between
two roughness elements), is approximately 2100.
To implement the PLIF method, fluorescein dye is injected through a transverse slit (0.25mm ×
240mm) machined flush with the wall at a distance of about 2k downstream of a roughness element.
The dye is injected continuously using a small pump at a flow rate low enough to avoid any
perturbations to the flow. A 4 W multimode Argon-Ion laser is used as a light source ( ≈ 2 W) for
the PLIF. The reflection of the laser beam onto a cylindrical mirror causes the expansion of the
beam into a planar light sheet. The 250 µ m thick light sheet was placed either parallel or normal to
the wall so as to enable views in either the (x-y) or (x-z) plane (x, y and z are the streamwise, wallnormal and spanwise directions respectively). The flow visualization images are recorded via a
CCD camera onto a video tape and then digitized through a video card (256 grey levels). Additional
details on the experiment facility can be found in [2]. In the following presentation of the results,
the origin x = 0 is chosen to be at the trailing edge of the roughness element located at about 1 m
(30 roughness elements) downstream of the trip while y = 0 is at the base of the roughness element
along the bottom wall (see Figure 1).
PIV Setup:
The PIV measurements are carried out in an open water channel. The test section is 8m long, 60
cm wide and 60 cm deep. The 2m long rough wall, which consists of transverse square bars (k =
4mm, and λ/k = 11), commences at a distance of 5m downstream of the contraction. The Reynolds
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
number Rθ is about 1620 half way through the rough wall where the measurements have been made.
The ratio δ/k is about 48. A 200 mJ pulsed Nd:Yag was used to illuminate the flow. The laser sheet
was shot from the top through a perspex porthole of about 10 cm diameter. The porthole is flush
with the free surface in order not to disturb the flow. A set of cylindrical lenses converted the laser
light into a vertical thin sheet located at the mid-plane (z = 0) of the channel. A digital camera
(Kodak ES 1.0) was used with a charge-coupled device (CCD) (1008 pixel x 1008 pixel resolution
). The PIV images were post-processed using the adaptive-correlation method (FlowManager
4.30.27; Dantec Dynamics) to obtain the instantaneous velocity fields. Each image was subdivided
into 64 pixel x 32 pixel with 50% overlap. The water was seeded with particles (Optimage Ltd)
with an average size of 30 microns and a specific gravity of 1.0 ± 0.02. These particles were
polycrystalline in structure and provided a high light-scattering efficiency (five times greater than
latex spheres which have a similar refractive index).The water level (h = 50 cm) was kept constant.
3. Results
3.1 PLIF Measurements
Figure 1 shows an example of instantaneous pictures of the near-wall flow between
y
λ
(a)
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Dye injection slot
(b
(c
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k
Fig. 1. (x-y) plan view of the near-wall region. The flow is from left to right. The actual ratio
λ/k is not respected in this presentation.
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
consecutive roughness elements. The figure highlights the existence of a shear layer, which
develops at the tip of the roughness element. It should be noted that this shear layer develops within
a turbulent environment. The interaction between this local shear layer and the overlying flow is
still not clearly understood. Associated with the shear layer, there are coherent structures similar to
those observed in a plane mixing layer and with a streamwise length scale of the order of the
roughness height, k and a wavelength of about 2k. There is a small recirculatory zone (Fig. 1c)
immediately upstream of the consecutive element. This recirculatory motion is intermittent due to
the flapping of the shear layer. An attempt has been made (see section 3.1) to determine the
flapping frequency using the PIV measurements.
The flow for λ/k = 11 is quite different from that observed when λ/k = 2 [2], at least in the nearwall region. In this latter case, the recirculatory motion occupies the whole cavity and is only partly
destroyed when fluid escapes from the cavity. This leads to the interesting question of whether the
structural differences observed in the near-wall region between the two rough surfaces are reflected
in the outer region of the boundary layer. Further measurements are required to address this
question.
z
o
w
6k
x
Fig. 2 (x-z) plan view at a vertical distance of y = k. The flow is from top to
bottom
The structures associated with the shear layer show a particularly high degree of coherence. The
overlying turbulent flow transports these structures without, seemingly, disrupting their evolution.
The manner in which these structures interact with the roughness elements is not trivial. The
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
vertical length scale of the structures is of order k, suggesting that they are likely to dominate the
flow in this region. In that respect, they may play an important role in terms of transporting
momentum and scalar quantities. These structures are also an additional source of turbulent energy
generation which is likely to contribute to the enhancement of the turbulence production near the
wall. To our knowledge, no information exists on the interaction between the shear layer and the
overlying turbulent boundary layer. This is worthy of further investigation.
One may infer from Fig. 1 that the flow in the near-wall region is dominated by two-dimensional
structures. However, the (x-z) plane view of Fig. 2 reveals that this is not the case. The dye is
concentrated within unsteady localized regions in the spanwise direction near the injection point
from where it is entrained downstream. There is a clear demarcation along the spanwise direction in
the dye distribution: in the region 0 < x / k ≤ 6 , the dye appears to be concentrated into elongated
a
b
Fig. 3 Velocity vector field (a) and mean velocity iso-contours with streamlines (b).
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Fig. 4 Longitudinal variations of U (a) and profiles of U between two roughness elements near the
wall (b) within the near wall region; the inset in (b) show the profiles across the boundary layer
narrow regions with a spanwise spacing of about 2-3k. In the region x / k ≥ 6 , the dye is patchy,
suggesting a strong three-dimensionality of the flow. The demarcation “line” corresponds to the
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
reattachment line. It is not yet clear whether the elongated streaky structures observed in the region
0 < x / k < 6 are reminiscent of the low-speed streaks observed when λ/k = 2 or of those for a
smooth wall. However, flow visualization sequences in the (x-z) plane did not reveal mushroomlike structures, usually interpreted as cross-sectional views of low-speed streaks. This suggests that
there is no low-speed streaks when λ/k equals to 11 and supports the idea that the mechanism of
turbulence production is different for λ/k = 11 than that when λ/k = 2 and a smooth wall.
3.1 PIV Measurements
As noted above, it is of interest to document the shear layer originating at the trailing edge of a
roughness element and investigate its interaction with the overlying flow. In this section, we
attempt to do this by exploiting the PIV measurements.
Figure 3 shows a section of the average velocity field (Fig. 3a), lines of constant streamwise
velocity and some streamlines (Fig. 3b). There is a well defined recirculation region behind the
roughness, with an extent of about 4-5k in the x direction and about k in the y direction. The centre
of this region is at about 2.5k behind the roughness element and at y = k. The flow reattaches at the
bottom at a distance of about 6k downstream of the roughness element. This corresponds to the
position of the demarcation line observed in the PLIF data. This is in good agreement with the DNS
data of Leonardi et al. [4]. Notice the strong deflection of the flow at the leading edge of the
roughness indicating not only separation on the top of the element but also a relatively high drag.
Leonardi et al. [4] showed that the maximum drag for this type of roughness occurs when the
separation between the roughness elements is about 8k. Also, this deflection results in a strong
momentum transfer to the outer layer, causing an increase in the turbulence intensity.
Despite the clear separation between the steady recirculation region and the overlying flow, the
instantaneous flow exhibits strong unsteadiness where the overlying flow interacts with the ‘cavity’
flow between roughness elements. This is illustrated in Fig. 4 which presents the longitudinal
variation of the streamwise mean velocity at several vertical planes (Fig. 4a) and the profiles of the
streamwise component of mean velocity at several positions between two roughness elements (Fig.
4b). Notice in Fig. 4a the sharp drop in U at the top of the roughness, which suggests the presence
of a small separation “bubble”, which is consistent with the velocity field of Fig 3a (this was also
observed in [4]). The velocity profiles over the region x/k < 6 show similar features to those
observed in a turbulent flow over a backward facing step.
The instantaneous velocity field (Fig. 5) shows a remarkable similarity to the PLIF data. For
example, by comparing figures 1a and 5a, one can discern similar coherent vortical structures. Also
notice in Fig 5b the vortices that are preceded by a large outward motion; this is similar to what is
pictured in Fig. 1b. The shedding of vortices from the trailing edge of the roughness elements, and
the occurrence of outward motions upstream of the roughness, contributing significantly to the form
drag, reflects the interaction between the ‘cavity’ and the overlying flow above the roughness
elements.
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
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interaction of the shear layer with the boundary layer.
velocity fluid passes over the element, generates a small vortex (figure 6b) which, while convected
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
downstream, increases in size (Fig. 6c and 6d). Notice also the large vortex in 6a which is seen to
be convected in the subsequent images. This sequence of events confirms the presence of a non
stationary shear layer originating at the trailing edge of the roughness element (as clearly seen in
Fig. 7).
The shear layer, reflecting the interactions between the overlying flow and the flow within the
cavities, is created at the interface between the flow issuing from top of the elements and the
recirculatory
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fluid behind the backward step formed by the element and the bottom wall as illustrated in the Fig.
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Fig. 8 A schematic of the shear layer generation mechanism at the trailing edge of a roughness
element.
Shear layer vortices are shed and convected downstream of the roughness elements. Examples of
such shear layer vortices are seen in Figs. 1 and 6. The non stationary nature of the shear layer
stems from the fact that it originates within a turbulent environment.
As can be inferred from Fig. 7, the shear layer can flap causing vortex shedding as seen in Figs. 1,
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
5 and 6. It is likely that pressure fluctuations are responsible for the flapping of the shear layer. The
flapping is responsible for the destruction of the vortical motion just behind the roughness. A
Strouhal number (St = f k/Ue, where f is the shedding frequency or flapping frequency of the shear
layer, and Ue is the freestream velocity) of about 0.045 is estimated from the autocorrelation of the
wall-normal velocity fluctuation. This value is not too different from that (0.06) obtained by Le and
Moin [8] in a turbulent flow over a backward-facing step. One may argue that the present shear
layer has similar structural features to that which occurs over a backward-facing step. However, it is
likely that the magnitude of λ/k plays a role in controlling the shear layer. Further studies should be
carried out to document the characteristics of the present shear layer and how it is affected by this
ratio.
4. Conclusions
Particle Image Velocimetry (PIV) measurements and Planar Laser Induced Fluorescence (PLIF)
visualizations have been made in a turbulent boundary layer over a rough wall. The wall roughness
consists of square bars placed transversely to the flow at a pitch to height ratio λ/k of 11. The
visualizations revealed that the flow near the roughness element is dominated by coherent structures
The PIV data confirmed the presence of such structures. Furthermore, they also revealed that these
structures are associated with non steady shear layers originating at the trailing edge of the
roughness elements. The shear layers are created by the interactions between the overlying flow and
the recirculation behind the roughness elements. Contrary to the λ/k =2 and smooth wall cases,
there appear to be no low-speed streaks over the present surface, indicating that the mechanism for
turbulence production is different. It would seem that the shear layers may play an active role in this
production. A possible scenario for the turbulence production mechanism may be as follows: shear
layer vortices are shed at the trailing edge of the roughness element (Strouhal number of about
0.045) and convected downstream before impacting on the following roughness element. This
results in an outward motion, which leads to an intermittent form drag and strong turbulence
production. From a practical point of view, this chain of events may suggest that an effective way
for reducing the drag of the rough surface might be to control the shear layer in order to reduce or
eliminate the shedding of vortices. As an example, a possible control strategy would be to apply a
pulsating synthetic jet at the trailing edge of the roughness elements. Such an approach has been
tried in a shear layer over a backward- facing step [9].
REFERENCES
[1] Jimenez J (2004), Turbulent flows over rough walls. Ann. Rev. Fluid Mech., 36: 173-196
[2]
Djenidi L, Elavarasan, E, Antonia, RA (1999) Turbulent boundary layer over transverse
square cavities. J Fluid Mech 395:271-294
[3] Townes HW, Sabersky RH (1966) Experiments on the flow over a rough surface. Int J Heat
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13th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 26-29 June, 2006
Mass Transfer 9:729-738
[4] Leonardi S, Orlandi P, Smalley RJ, Djenidi L Antonia RA (2003) Direct numerical
simulations of turbulent channel with transverse square bars on one wall. J Fluid Mech 491:229-238
[5]
Krosgstad P-A, Anderson HI, Bakken OM, Ashrafian A (2005) An experimental and
numerical stydu of channel flow with rough walls. J Fluid Mech 530:327-357
[6] Cui J, Pate VC, Lin C-L (2003) Large-eddy simulation of turbulent flow in a channel with rib
roughness, Int J Heat and Fluid Flow 24:372-388
[7] Rehab H, Djenidi L, Antonia RA (1999) LDV and PLIF measurements in a turbulent boundary
layer over a rough wall, Proc. 2nd Australian Conference on Laser Diagnostics in Fluid Mechanics and
Combustion, Melbourne, 132-137
[8] Le H, Moin, P, 1994 Direct numerical simulation of turbulent flow over a backward-facing
step, Standford University Report no TF-58.
[9] Pastor M, Noack BR, King R (2006) Spatiotemporal waveform observes and feedback in
shear layer control, AIAA paper 2006-1402.
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