# Effects of surface roughness on the propulsive performance of pitching foils

Rodrigo Vilumbrales-Garcia1<EMAIL_ADDRESS>Melike Kurt1
Gabriel D. Weymouth1,2  Bharathram Ganapathisubramani1  1Faculty of
Engineering and Physical Sciences, University of Southampton, UK,2 Faculty of
Mechanical, Maritime and Materials Engineering (3mE), TU Delft, NL

###### Abstract

The hydrodynamic influence of surface texture on static surfaces ranges from
large drag penalties (roughness) to potential performance benefits (shark-like
skin). Although, it is of wide-ranging research interest, the impact of
roughness on flapping systems has received limited attention. In this work, we
explore the effect of roughness on unsteady performance of a harmonically
pitching foil through experiments using foils with different surface
roughness, at a fixed Strouhal number and within the Reynolds number ($Re$)
range of $15k-30k$. The foils’ surface roughness is altered by changing the
distribution of spherical-cap shaped elements over the propulsor area. We find
that the addition of surface roughness does not improve the performance
compared to a smooth surface over the $Re$ range considered. The analysis of
the flow fields shows near identical wakes regardless of the foil’s surface
roughness. The performance reduction mainly occurs due to an increase in
profile drag. However, we find that the drag penalty due to roughness is
reduced from $76\%$ for a static foil to $16\%$ for a flapping foil at the
same mean angle of attack, with the strongest decrease measured at the highest
$Re$. Our findings highlight that the effect of roughness on dynamic systems
is very different than that on static systems, thereby, cannot be accounted
for by only using information obtained from static cases. This also indicates
that the performance of unsteady, flapping systems is more robust to the
changes in surface roughness.

###### keywords:

Flapping foils, surface roughness, propulsive performance

##  1 Introduction

Surface roughness is ever-present in engineering applications leveraging
fluid-structure interactions. Its implications on the flow and the consequent
drag generation have been widely studied in the related literature. From the
influence of roughness in pipe flow (Achenbach, 1971), to its effects on the
trajectory of a golf ball (Chowdhury et al., 2016), roughness plays a vital
role in any application involving fluid-structure interaction considerations.
For example, surface roughness can be detrimental to the performance of wind
turbines. Sagol et al. (2013) found that the accumulation of contamination
agents in the blades leads to a reduction in power extraction, while, Ehrmann
et al. (2017) reported a performance decrease linked to an increase in
roughness density and height. On the other hand, the use of roughness elements
can lead to a drag reduction and certain performance gains for unsteady
propulsion systems. Previous studies inspired from swimmers and flyers show
that, from shark skin or dolphin skin (Dean & Bhushan, 2010; Wainwright et
al., 2019) to feathers on a wing of a gliding bird (Van Bokhorst et al.,
2015), roughness in varying shapes and texture modifies the fluid flow over
propulsor surfaces, leading to a reduction in drag or a decrease in flow
separation. In engineering applications, Gad-el Hak & Bushnell (1991) analysed
the effects of roughness turbulators and found a $C_{L}/C_{D}$ increase when
compared to a smooth foil for $Re\leq 100000$. Also, the use of surface
riblets can lead to a decrease in skin friction when aligned in the flow
direction (Bechert et al., 1997), achieving a drag reduction of up to $8\%$
(Walsh, 1982). When configured properly, surface roughness can be beneficial.
It can reduce drag production and potentially improve the overall performance.
Surface roughness can also have detrimental effects. Tailoring the surface
roughness to have an improved performance requires a better understanding of
the effect of shape, size, and area distribution of roughness elements on both
the force production and the flow.

The drag-reduction potential of surface roughness on aquatic swimmers have
been explored mainly for static surfaces. For example, sharks can reduce their
skin friction when their riblets are aligned with the flow (Dean & Bhushan,
2010). Bixler & Bhushan (2013) pointed out that the riblets lift and pin the
vortices generated in the viscous sublayer, leading to a decrease in drag.
Bechert et al. (2000) observed a drag reduction for interlocking 3D riblets.
Afroz et al. (2016) concluded that ’shark-like’ textures can act like a
passive flow separation control mechanism. Du et al. (2022) found smaller
separated regions and adverse pressure gradients for the flow over a foil
covered with tilted biomimetic shark scales. The effect of the shape and size
of the rough elements were analysed by Domel et al. (2018), highlighting the
importance of the denticle shape, as they found a drag reduction only for the
smaller of the three considered. Although surface roughness has shown
promising potential for static bodies, its role in unsteady systems is still
not clear. Shark-skin surfaces have been shown to increase the self-propelled
swimming speed and reduce the drag of a flapping foil (Oeffner & Lauder, 2012;
Domel et al., 2018), but only when small denticles are used, whereas the
larger elements can lead to an increase in drag. Wen et al. (2014) reported a
reduction in energy consumption due to a formation of stronger leading-edge
vortices. Guo et al. (2021) found that, for static foils towed at a constant
velocity, the roughness elements resulted in a considerably thicker boundary
layer when compared to the smooth foil, while, for static foils in
acceleration, the changes due to roughness in the wake characteristics were
considerably smaller. Mostly, previous work conclude that shark-inspired
surfaces can improve the performance of an unsteady body, but the potential
benefit is strongly dependent on the shape and size of shark denticles, which
often appear in highly complex geometries. Therefore, it is still to be seen
if such performance improvement can be achieved with simple, commercially
available roughness elements, located on the surface of an unsteady foil in
harmonic motions.

In this study, we analyse experimentally the effects of surface roughness on
the propulsive performance of a pitching foil by using simple roughness
elements. In Section 2, we define the methodology and experimental setup used
to actuate three different foils with varying roughness characteristics. We
investigate the effects of Reynolds number in the range of $15,000\leq Re\leq
30,000$ and report the propulsive performance of a pitching aerofoil in terms
of thrust production ($C_{X}$) and efficiency ($\eta$). In Section 3, we
detail the force and flow measurement results obtained for flapping foils, and
draw a comparison between dynamic and static foil cases.

##  2 Experimental setup and methodology

Figure 1: Schematics of the experimental setup in the water flume (A), the
actuation arm (B), foils with three different roughness area coverage ratio
(C), and the forces acting on the foil (D).

Force and flow measurements are conducted in a recirculating water flume at
the University of Southampton, with a test section of 8.1 m length, 1.2m width
and 0.9m depth. A surface plate is installed at the foil tip and the foil is
placed right above the bottom wall to prevent tip vortex formation and enforce
nominally two-dimensional flow over the foil as shown in Figure 1A.

Three foils with a rectangular planform and a NACA0012 cross-section were
3d-printed, with a chord-length of $c=0.16m$ and an aspect ratio of $AR=2.5$.
Spherical-cap shaped roughness element with a width (diameter) of $W=0.05c$
and height of $H=0.01c$ (Dean & Bhushan, 2010) were placed on pressure and
suction sides of the foils. As shown in Figure 1C, in addition to the smooth
foil, two different roughness levels are considered by varying the area
occupied by the spherical-cap elements to $36\%$ and $70\%$ of the foil
planform area.

Each foil was actuated with a stepper motor (Applied Motions STM23S) in
sinusoidal pitching motions, about a point $0.08c$ distance from the leading
edge. The prescribed motion is defined by $\theta(t)=\theta_{0}sin(2\pi
f_{0}t)$, where $\theta_{0}$ is the pitching amplitude and $f_{0}$ is the
flapping frequency. The pitching amplitude $\theta_{0}$, Strouhal number
$St=2Af_{0}/U$, and reduced frequency $k=2\pi f_{0}c/U$ were fixed all
throughout the experiments at $\theta_{0}=7.5^{\circ}$, $St=0.25$ and $k=6$,
respectively, to ensure the foils to perform in the high-efficiency, thrust
producing regime (Zurman-Nasution et al., 2021; Muscutt et al., 2017; Kurt &
Moored, 2018). A Reynolds number sweep ($Re=Uc/\nu$ where $\nu$ is the
kinematic viscosity) was conducted within the range of $15,000\leq Re\leq
30,000$ by varying the flow velocity. In this range, the propulsive
performance was previously reported to be $Re$ independent (Senturk & Smits,
2019). A summary of the parameters used in this study is given in Table 1.

$Re$ | 15,000 | 20,000 | 25,000 | 30,000
---|---|---|---|---
$U$ [m/s] | 0.10 | 0.14 | 0.17 | 0.21
$f_{0}$ [Hz] | 0.62 | 0.83 | 1.03 | 1.24
$St$ | 0.25 | 0.25 | 0.25 | 0.25
Table 1: Experimental parameters used in the current study

The forces and moments acting on the foils were measured with a six-axis force
sensor (ATI Gamma IP65). The motion was tracked using a rotary, incremental
encoder (US Digital E5) attached on the motor shaft (Figure 1 B). Each trial
was conducted for a total of 100 flapping cycles and repeated five times. The
measured forces were filtered using a Butterworth filter with a low-pass
frequency of five times the flapping frequency. The power was calculated as a
multiplication of pitching moment and the angular velocity which was derived
from the measured angular displacement. The instantaneous and time-averaged
performance metrics are the average values from 500 flapping cycles, measured
over five trials. To distinguish instantaneous forces from time-averaged
results, the latter is denoted by $\overline{(.)}$. The reported streamwise
force (thrust) ($C_{X}$) and power ($C_{P}$) coefficients, and efficiency
($\eta$) are defined as,

$C_{X}=\frac{F_{X}}{\frac{1}{2}\rho U^{2}c},\qquad
C_{P}=\frac{P}{\frac{1}{2}\rho U^{3}c},\qquad\eta=\frac{C_{X}}{C_{P}}$ (1)

where $\rho$ is the density of water and $U$ represents the free-stream flow
velocity.

The force measurements were synchronised with planar Particle Image
Velocimetry (PIV) measurements (cameras: LaVision MX 4MP, lasers: Litron Nano
PIV). The field-of-view captures the entire foil and up to one chord-length in
foil’s wake. The software Davis 10 was used to cross-correlate the acquired
particle image pairs (with 24$\times$24 pixels with 50% overlap). The flapping
cycle was divided into twenty-two phases and twenty-five cycles were acquired
per phase. The velocity fields corresponding to each phase was then averaged
over 25 cycles.

##  3 Results

###  3.1 Flow-field and force production analysis of foils with different
roughness area coverage ratios

Figure 2 compares the out-of-plane vorticity and the instantaneous performance
coefficients, $C_{X}$ and $C_{P}$ for all the roughness cases considered at
$Re=25.000$. The first column (A,D), the second column (B,E) and the third
column (C,F) present the evolution of the vorticity field around three
pitching foils with $0\%$, $36\%$ and $70\%$ surface roughness at $t/T=0.15$,
and $t/T=0.50$, respectively. Surprisingly, change in the roughness does not
lead to any significant alteration in the vorticity fields. Regardless of the
roughness coverage, all foils produce a reverse von Karman-street where two
counter-rotating vortices per flapping cycle are shed from the trailing edge
into the wake, as widely observed in the related literature for smooth foils
(Muscutt et al., 2017; Kurt & Moored, 2018; Zurman-Nasution et al., 2021).
Figure 2 G-H presents the evolution of cycle-averaged thrust and power
coefficients over one flapping cycle. Similar to the flow fields, the
performance coefficients show only minor differences between the smooth foil
and the foils with roughness. Although, we have only revealed the analysis
associated with a single $Re$, these results hold across the $Re$ range
considered here. In the supplementary material, we present the evolution of
the flow-field over one flapping cycle at $Re=15,000$ and $Re=25,000$ as
videos for comparison. Overall, these results from force and flow field
measurements show that incorporating surface roughness does not have a strong
influence on the development of the wake. Other parameters, such as Strouhal
number or kinematics (Schnipper et al., 2009) are known to significantly
affect the evolution of the vortex structures, which can minimise the adverse
effects on performance induced by the roughness elements.

Figure 2: PIV results for $Re=25000$. $t/T=0.15$ (A,D,G) and $t/T=0.50$
(B,E,H) for the Smooth (A,D), $36\%$ (B,E) and $70\%$ (C,F). Instantaneous
$C_{X}$ (H) and instantaneous $C_{P}$ (I)

Figure 3 introduces the spectral analysis conducted for $C_{X}$ presented in
Figure 2 G-H. The power spectra of the thrust force at $Re=25,000$ is shown in
(A). The crosses indicate the location of the peak frequency for each foil. In
(B), we introduce the dominant frequency ratio in the form of $f/f_{0}$, where
$f_{0}$ is the prescribed pitching frequency across the $Re$ range considered.
This analysis shows that the dominant frequency in thrust production
corresponds to the pitching frequency $f_{0}$ for all the $Re$ values, and
contains similar energy density for all the foils. This result combined with
the similarities observed in both the wake and the instantaneous forces
indicates that the performance of the foils is highly dominated by $f_{0}$,
hence, by the kinematics. The dominant effects of the frequency and the
kinematics observed in our study are similar to the findings by Zurman-
Nasution et al. (2021), who reported that compared to flapping frequency and
kinematics, shape-related parameters such as sweep angle, have negligible
effects on propulsive performance.

Figure 3: (A) Fast Fourier Transform (FFT) analysis of the instantaneous
$C_{X}$ at $Re=25,000$. The cross indicates the location of the peak for each
case. The vertical dashed bar denotes $f/f_{0}=1$. (B) Peak frequency across
the $Re$ values considered. A value of 1 denotes that the thrust force signal
peak $f$ is equal to the input pitching frequency $f_{0}$.

Figure 4 presents the change in cycle-averaged performance coefficients for
foils with different roughness coverages against $Re$. Starting with
$\overline{C_{X}}$ (Figure 4A), we compare our results with other NACA0012
studies conducted by Mackowski & Williamson (2015) ($Re=16,600$, $0.1\leq
St\leq 0.4$), and Senturk & Smits (2019) ($500\leq Re\leq 36,000$, $0.2\leq
St\leq 0.6$). Thrust, $\overline{C_{X}}$, obtained for the smooth foil
increases slightly with Reynolds number, a trend similar to previous studies.
The thrust values obtained at $St=0.25$ in the current study fall within the
findings by Senturk & Smits (2019) at $St=0.2$ and $St=0.4$. In the inset
enclosed by a blue box, it is shown that $C_{X}$ decreases with the addition
of surface roughness across the $Re$ range. In Figure 4B, our results indicate
higher efficiency values than Mackowski & Williamson (2015) and Senturk &
Smits (2019), which could be due to differences in the pivot point location
(at $0.08c$ distance from the leading edge here, and at $0.25c$ distance in
previous studies). For each roughness case, $\overline{C_{P}}$ slightly
increases against $Re$, but regardless of the $Re$, increase in roughness
causes a decrease in $\overline{C_{P}}$. The efficiency also decreases as the
surface roughness increases, similar to thrust and power. Although the flow
fields show negligible alterations with the change in roughness, the cycle
averaged forces point to a performance reduction as the roughness increases.
The thrust decrease observed for $36\%$ and $70\%$ roughness coverages
compared to smooth foil can be related to an increase in the profile drag. To
further explore this effect, in the next figure, we have compared our flapping
foil results with static foil measurements carried out using the same foils
within the same $Re$ range.

Figure 4: A) $\overline{C_{X}}$ obtained in the current study (blue range) and
compared with previous studies against $Re$: Senturk & Smits (2019) (gray) and
Mackowski & Williamson (2015) (dark-gray). The data enclosed by the blue box
presents an inset of $\overline{C_{X}}$ data for the $Re$ range of $15,000\leq
Re\leq 30,000$. B) $\overline{C_{P}}$ results (hexagon) and $\eta$ (cross) for
current and previous studies, marked by the same colours used in A.

###  3.2 Comparison between static and flapping regimes

Figure 5: A) static $C_{X}$ vs angle of attack $\Theta$ measured using static
foils at $Re=25,000$. Smooth foil presented in light-blue, $36\%$ in medium-
blue, and $70\%$ in dark-blue. The red dashed-line indicates the $\theta$ used
to compare with the unsteady regime, defined as $\theta_{s}=4.75^{\circ}$ B)
Thrust and drag penalty due to roughness for both the flapping (triangles) and
static results (crosses) for the $36\%$ case (medium blue) and the $70\%$ case
(dark blue).}

In this section, we introduce the data collected for static foils and compare
it with the pitching foil results to further explore why there is a change in
thrust production with a change in roughness coverage. The static data was
acquired within the same $Re$ range and roughness coverages as the flapping
cases, for an angle of attack ($\theta$) range of $-4^{\circ}\leq\theta\leq
20^{\circ}$. To compare both scenarios, we have selected an angle of attack
value equal to the average $\theta$ experienced by the foil during half the
pitching cycle (red dashed-line in Figure 5A, denoted as $\theta_{s}$). Next,
we develop a comparison parameter or penalty, that evaluates the change in
streamwise force generated by the smooth and rough foils. Given that static
state will produce drag (for all three foils) and the flapping cases produce
thrust, we present the penalty in its absolute value to help with the
comparison. Since we have found surface roughness to be detrimental for
$\overline{C_{X}}$ for all cases considered, a positive penalty value in the
static state indicates an increase in drag due to roughness elements, while
$Penalty>0$ in the flapping regime means a decrease in thrust caused by the
roughness elements. Here, $Penalty$ is defined as the relative change in
thrust for a rough foil compared to the smooth,
$|(C_{X,rough}-C_{X,smooth})|/C_{X,smooth}$.

The penalty parameter is presented in Figure 5 for static foil (crosses) and
flapping foil measurements (triangles). The addition of surface roughness
increases the drag production in the static state across the $Re$ range
considered. At $Re=30,000$, it reaches a $76\%$ drag penalty for the $36\%$
roughness and $43\%$ penalty for the $70\%$ roughness coverage, compared to
the smooth foil. On the other hand, the flapping foils with roughness generate
less thrust across the $Re$ range compared to the smooth foil. At $Re=30,000$,
the thrust decreases by $35\%$ and $16\%$ for $70\%$ and $36\%$ roughness
coverages, respectively. However, the flapping state appears to be more robust
to $Re$ changes. It reduces the penalty observed for static foils, especially
for the $36\%$ coverage. At $Re=30,000$, foils with $36\%$ coverage
experiences a roughness penalty of $76\%$ in the static state compared to a
$16\%$ penalty in the flapping state, which could be explained by the dominant
effect that $St$ and the kinematics have on force production.

Figure 6: Pitching cycle-averaged vorticity (A,B,C), flapping instantaneous
vorticity at $\theta=6^{\circ}$ degrees (E,F,G) and static PIV results at
$\theta=6^{\circ}$ (I,J,K). Smooth foil (A,E,I), $36\%$ (B,F,J), and $70\%$
(C,G,K). The comparison of the wakes generated by the foils at each of the
conditions is presented at (D,H,L)

To further analyse the data presented in Figure 5, we present the out-of-plane
vorticity ($\omega_{Z}$) in Figure 6. The first row consists of the cycle-
averaged unsteady pitching $\omega_{Z}$, and the positive vorticity regions
are enclosed with isolines. In second and third rows, we present the flow-
field data measured at $\alpha=6^{\circ}$ for a pitching foil and a static
foil, respectively. The first three columns correspond to $0\%$ (smooth),
$36\%$ and $70\%$ roughness coverages, respectively. The fourth column
introduces a comparison between different roughness cases with overlapped
$\omega_{Z}$ isolines. The comparison of all three flapping cases suggests
that the addition of surface roughness does not introduce major changes in
shedding shear layers. In contrast, in the static state, foils with $36\%$ and
$70\%$ roughness have thicker shear layer in time-average compared to the
smooth case, similar to the findings by Guo et al. (2021). The presence of
thicker shear layers for the roughness cases can be the culprit of $76\%$ drag
penalty shown in Figure 5.

##  4 Conclusions

In this study, we have analysed the influence of surface roughness on the
propulsive performance of flapping foils, using force and flow measurements.
Three NACA0012 foils with different roughness coverage ratios have been
constructed, and tested within the Reynolds number range of $15,000\leq Re\leq
30,000$. We have found that the addition of surface roughness is detrimental
to thrust production and efficiency of a pitching foil. The foils with $36\%$
and $70\%$ roughness produce $16\%$ and $35\%$ less thrust, respectively,
compared to the smooth foil. We have determined that $Re$ does not play an
important role on neither the thrust nor efficiency for the $Re$ range and
roughness coverage ratios considered. Although we have seen no significant
change in the wake flow, the foils with roughness experience a decrease in
thrust and efficiency, which can be explained by an increase in profile drag
associated with the roughness elements. We have compared the effects of
roughness on static and flapping states, finding that the former is
considerably more sensitive to it. The roughness penalty for $36\%$ roughness
coverage is reduced from $76\%$ in the static state to $16\%$ for flapping.
The strongest decrease occurs at the highest Re, highlighting that the effect
of roughness on flapping systems is very different than on static systems.
This shows that the performance of flapping systems is more robust to the
changes in surface roughness.
Declaration of Interests: The authors report no conflict of interest.
Acknowledgements
This research was supported financially by the Office of Naval Research Global
Award N62909-18-1-2091, the Engineering and Physical Sciences Research Council
(Grant No: EP/R034370/1) and the doctoral training award.

Data availability statement
All data supporting this study will be made openly available from the
University of Southampton repository upon publication.

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