Fluid dynamics experiments with a passive robot in regular turbulence

Abstract

This paper presents force measurements of a passive fish robot in a regularly turbulent flow. We placed the robot into a controlled hydrodynamic environment, in running water behind a cylinder which created alternately shed vortices (von Kármán vortex street). We monitored the flow field using digital particle image velocimetry and recorded the force measurements using a force plate. The measurements taken at different locations in the turbulent flow show that the lateral force (perpendicular to the flow stream) experienced by the robot increased significantly in the turbulent flow. On the other hand the drag (force along the flow stream) was reduced up to 42% with respect to swimming in the uniform flow. The drag reduction was mainly due to the shadowing effect of the cylinder. However robots didn't gain any advantage through their passive interaction with the vortex street. The drag-position relationship had a single minimum along both longitudinal and lateral axis highlighting a favorable location for energy saving. We interpret the results as an evidence that the turbulent flows can provide rewarding opportunities to derive more energy efficient and stable behavioral strategies for underwater robots.

Full text


Abstract—This paper presents force measurements of a
passive fish robot in a regularly turbulent flow. We placed the
robot into a controlled hydrodynamic environment, in running
water behind a cylinder which created alternately shed vortices
(von Kármán vortex street). We monitored the flow field using
digital particle image velocimetry and recorded the force
measurements using a force plate. The measurements taken at
different locations in the turbulent flow show that the lateral
force (perpendicular to the flow stream) experienced by the
robot increased significantly in the turbulent flow. On the other
hand the drag (force along the flow stream) was reduced up to
42% with respect to swimming in the uniform flow. The drag
reduction was mainly due to the shadowing effect of the
cylinder. However robots didn't gain any advantage through
their passive interaction with the vortex street. The drag-
position relationship had a single minimum along both
longitudinal and lateral axis highlighting a favorable location
for energy saving. We interpret the results as an evidence that
the turbulent flows can provide rewarding opportunities to
derive more energy efficient and stable behavioral strategies for
underwater robots.
I.
INTRODUCTION
TATE-of-the-art underwater robots do not model or
navigate with respect to the flow. Research robots in
laboratory conditions are tested in still water. Field robots
are exposed to the flow but they treat the current or
turbulence as a drift or disturbance to be compensated for.
There is no underwater robot that takes advantage of the
flow for better localization and navigation.
While robot builders consider flow as an annoying
disturbance to be compensated by control algorithms, the
biological evidence suggests that aquatic animals know how
to turn it into an advantage. For example it is suggested that
salmonoids migrating upstream in turbulent rivers spend
time behind an object to recover from fatigue [1]. The
metabolic consumption of oxygen by the rainbow trout is
lower while entraining in the vortex wake [2]. Furthermore
it is shown in many occasions that fish can minimize their
energy consumption by adjusting their locomotion patterns
to the vortex patterns. The best known study is by Liao et al.
demonstrating a dead fish floating upstream behind a vortex
wake of a bluff object [3]. This study suggests that the
vortices encountered by the fish can be beneficial to reduce,
This work is supported by European Union 7
th
Framework program
under FP7-ICT-2007-3 STREP project FILOSE (Robotic FIsh LOcomotion
and SEnsing), www.filose.eu
1
Centre for Biorobotics, Tallinn University of Technology, Estonia
2
Dept. of Computer Science, University of Verona, Italy
neutralize or even overcome the drag experienced by the fish
due to the flow. A similar experiment has been repeated with
a high aspect-ratio passive hydrofoil [1].
Today it is not well defined under which circumstances
such positive fluid-body interactions can take place. When
size of the vortices are too big or too small with respect to
the body size or if the body does not interact with the
vortices in the “right way'', it is expected that vortices can
have negative impacts on the interaction such as increasing
the drag on the body or obstructing its stability [4]. To gain
insight into how to interact with the vortices many studies
have investigated the phenomenon of Kármán gaiting, the
tendency of fish to synchronize with the periodically shed
vortices. Fish adjust their tail beat frequency with the vortex
shedding frequency.
There is no conclusive evidence and established
consensus about whether the flow-exploiting behaviors, such
as entraining and Kármán gaiting are passive or active
(whether fish activate their muscles or they are simply
actuated by the external forces due to the flow.) Also it is not
known if fish need flow sensing to have a control on these
behaviors. Moreover it is not possible to directly measure the
drag of a swimming fish and the indirect measurements are
rather imprecise. It is therefore only possible to indirectly
estimate the energy consumption of fish in different flow
regimes [2].
In this paper we develop a case for the exploitation of the
same energy saving phenomena by an underwater fish robot.
In robot applications we see two ways of taking advantage of
the flow: i) to seek a position in the flow at which the drag is
lower, ii) to interact with the flow “properly'' to capture the
energy which is readily available in the flow.
We describe experiments with passive underwater fish
robots attached to the force plate in a regular turbulence. We
record the force measurements both in downstream and
lateral directions and we visualize the flow using digital
particle image velocimetry. We analyze the relationship
between the drag (proportional to the energy consumption of
the robot) and flow speed at different locations in the vortex
wake. We demonstrate that by choosing a convenient
position inside the vortex wake, the robot can decrease the
perceived drag. We furthermore propose a method to
evaluate if favorable drag conditions arise from choosing the
right spots in the flow or additional energy harvesting as a
result of passive flow-body interaction also takes place.
Fluid Dynamics Experiments with a Passive Robot in Regular
Turbulence
Gert Toming
1
, Taavi Salumäe
1
, Asko Ristolainen
1
, Francesco Visentin
2
, Otar Akanyeti
2
, Maarja
Kruusmaa
1
S
,((( 532
Proceedings of the 2012 IEEE
International Conference on Robotics and Biomimetics
December 11-14, 2012, Guangzhou, China

Overall, the “drag well” inside a regular turbulence has a
well-defined shape with a single minimum. It makes
possible to tracking this minimum using simple gradient
decent and, at least theoretically, by using only the
proprioceptive sensing.
The rest of the paper is organized as follows. Next we
describe the regular turbulence and the method which
enables us to evaluate if the passive robot-vortex interactions
are advantageous or disadvantageous to reduce the perceived
drag. After this we describe the experimental setup and the
methods for analyzing the flow. We then present the
experimental results of the force measurements. Finally we
discuss the results and their possible interpretation from the
point of view of underwater robot design and control.
II. SCOPE OF THE PAPER
A. Regular turbulence
For this investigation we focus on Kármán vortex streets.
Kármán vortex street is a periodic turbulence pattern
observed at moderate Reynolds numbers in a wake of bluff
objects. It is characterized by the vortex shedding frequency.
In nature, regular turbulence often occurs in rivers where
steady flow is obstructed by obstacles (stones, pillars, etc.).
In fish locomotion studies, as well as in experimental fluid
dynamics, Kármán vortex streets offer benchmark problems
in fish behavioral studies, because they are life-like on the
one hand, but stable, relatively easy to characterize and
repeatable on the other hand.
In laboratory conditions, a Kármán vortex street is created
by placing a cylinder or half-cylinder into steady flow. The
frequency of vortices of the Kármán flow can then be
adjusted by calculating f = SV/L where f is the frequency of
the vortices, L is the characteristic length of a shedder bar
(cylinder), V is the velocity of the laminar flow and S is the
Strouhal number for the given shedder bar. The Reynolds
number of the Kármán vortex street nVL/Re , where n is
the kinematic viscosity of the fluid.
B. Drag-Flow Relationship in Kármán Vortex Streets
In a Kármán vortex street we consider two components
that influence the total drag (
KVS
D
F
) experienced by the
object. I.) The shadowing effect of the cylinder: The flow
speed behind the cylinder is reduced due to the cylinder's
shielding effect. We determine the reduced flow drag (
U
D
F
)
using the drag-flow relationship employed in uniform flows
when Re > 1000,
,
2
12
AVCF D
U
D
U
(1)
where V is the velocity of the object relative to the fluid (for
a static object V is equal to the flow speed), ȡ is the mass
density of the fluid, A is the reference area and
D
C is the
drag coefficient [5]. We estimate
U
D
F
using the average flow
speed obtained from flow visualization.
II.) The turbulence in the flow: The interaction between
the body and the turbulence in the flow (mainly periodically
shed vortices if it is a stable vortex street) is complex and till
today not well understood. We will call this component
T
D
F
where T stands for turbulence. We estimate
T
D
F
using the
relation,
,
U
D
KVS
D
T
D
FFF  (2)
where we obtain
KVS
D
F
from the force measurements. In this
work, our goal is not to derive a model for
T
D
F
but to
evaluate if it has a positive or negative value for our passive
robot. Having
T
D
F
< 0 would suggest that the interaction
between the robot and the vortices is beneficial as total drag
is reduced. On the other hand 0!
T
D
F
means additional drag
on the robot. The proposed formulation is also useful to
analyze biological studies. For instance when dead fish
holding station in the vortex street [3], 0
KVS
D
F
, therefore
T
D
U
DFF 
.
III. MATERIALS AND METHODS
A. Robots
Used robots are a fish shaped biomimetic robots
mimicking a rainbow trout. They consist of a rigid heads and
a flexible tails allowing fluid-body interactions. The
prototypes and the fabrication methods are described in
detail in [6]. The anteroposterior length of the T-prototype is
0.43 m and of the X-prototype is 0.5 m. The maximum size
of the T-prototype on the dorsoventral axis is 0.125 m, on
the left-right axis 0.06 m and for the X-prototype 0.145 m
and 0.084 m respectively.
B. The force plate
Prototypes were fixed on the force plate's midpoint with a
rod (see Figure 1). The distance between the prototypes
dorsoventral axis midpoint and force plate was 0.215 m. The
force plate delivers the downstream (F
x
) and lateral force
Fig. 1. Robotic fish T-prototype. 1 – Compliant tail; 2 – Head 3
– Pressure sensors mounted on the tip of the head and on the side
of the head; 4 – Rotational actuation mechanism (not used in the
passive tests); 5 – Force measurement plate with 4 load cells to
measure longitudinal and lateral forces.
533

(F
y
) on the robot. We take F
x
as a measure for the total drag
felt by the robot.
(F
x
, F
y
) were measured using 4 load cells (working range
10 kg). The load cells were assembled in the corner of the
horizontal plate. The signals from the load cells were
amplified (Texas Instruments Instrumentation Amplifier
INA128UA, gain 500) and digitalized (Linear Technology
A/D converter LTC 1867 B). Digitalized data from the load
cells was transferred to the PC through RS-232 port (Atmel
microcontroller ATmega 168).
C. Flow experiments and measurements
The experiments are conducted in a flow pipe with a
working section of 1.5 m x 0.5 m x 0.5 m. The pipe is
embedded into a test tank. Uniform flow in the working
section is created with the help of a U-shaped flow
strengthener and two sequential laminators. An AC motor is
used to create the circulation inside the flow tank and
permits controlling the uniform flow sped with 0.04 m/s
accuracy.
Force measurements were conducted both in uniform
flows and in Kármán vortex street. Figure 2 illustrates the
setup used in Kárman vortex street experiments. We mainly
focused on two flow speeds 0.31 m/s and 0.48 m/s and the
cylinder diameter 0.1 m. We placed the robot at different
positions from the cylinder both in the downstream (D) and
lateral directions (L).
We visualize the flow with digital particle image
velocimetry (DPIV). DPIV provides multipoint velocity
measurements within a planar slice of the flow by tracking
the movement of particle images. A horizontal laser sheet
was positioned at the flow tunnels mid-plane. The UI-
5240HE-M camera from IDS Imaging Development
Systems imaged from top at 50 frames per second. Image
resolution was 1280 x 1024 pixels and the field of view was
48 cm x 38.4 cm giving the resolution of 26.7 pixels per cm.
Images were then processed with MatPIV 1.6.1 toolbox in
Matlab 7.10. Interrogation window size of 32 x 32 pixels
with 50% overlapping was used. The output was a velocity
field of 79 x 63 vectors, giving one vector after every 6 mm.
IV. DPIV FLOW IMAGING
DPIV flow analysis serve for three purposes: i) to validate
the presence of a stable vortex street, ii) to evaluate how the
flow speed varies with the robot's relative distance to the
cylinder (we use these measures to estimate the reduced flow
drag and also to correlate flow with the force measurements)
and iii) to extract hydrodynamically significant features
(such as vortex shedding frequency and vortex shedding
point) which can help us to better interpret the force
measurements.
Having a flow field V
x
(x,y,t) and V
y
(x,y,t) from DPIV
measurements, Figure 3a and b illustrate, respectively, the
time averaged V
x
and the turbulence intensity for the vortex
street generated with 31cm/s flow speed. The turbulence
intensity is computed by V
y
/ı(y), where ı(y) is the standard
deviation, and it indicates how steady the flow is [7]. The V
x
in the middle is significantly lower than the two extremities.
This is due to the shadowing effect of the cylinder. This
middle region corresponds to the Kármán corridor where
vortices are generated and shed. This agrees with high
turbulence in the middle regions. Outside the Kármán
corridor the flow is quasi-uniform therefore we see very low
turbulence.
Fig. 2. Experimental setup. Robot fish placed into the flow
behind the half-cylinder. Red dotted line shows the DPIV
camera field of view.
Fig. 3. Time averaged velocity V
x
(above) and the turbulence
intensity for the Kármán vortex street (below) generated with 31
cm/s flow speed.
0.0
6.0
12.0
18.0
24.0
30.0
36.0
43.0
0.0
6.0
12.0
18.0
24.0
30.0
36.0
−0.1
0
0.1
0.2
0.3
0.4
X (cm)
Y (cm)
V
x
(mean) m/s
−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.0
6.0
12.0
18.0
24.0
30.0
36.0
43.0
0.0
6.0
12.0
18.0
24.0
30.0
36.0
0
0.02
0.04
0.06
0.08
0.1
X (cm)
Y (cm)
τy
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
534

We segment the Kármán corridor into regions in which
the velocity conditions of the flow field is common. These
regions are base suction region where flow recirculates
towards the cylinder (negative V
x
), vortex formation zone
where vortices are generated and the vortex street, the region
in which vortices are detached from the core and travel with
a steady speed. The vortex shedding point is the point that
separates the vortex formation zone and the vortex street.
For stability we track the shed vortices in time; vortex
shedding frequency was around 0.7 Hz and 1.1 Hz,
respectively, for flow speeds 0.31 m/s and 0.48 m/s. We
analyze their spacing ratio between downstream and lateral
directions. The spacing ratio with 0.38±0.1 was within the
error margin of the theoretical value which is necessary for
neutral stability. Table 1 summarizes the complete
characterization of the Kármán vortex streets.
V. FORCE EXPERIMENTS
A. Uniform flows vs. Kármán vortex streets
We first compared force measurements with and without
the cylinder at flow speeds 0.31 m/s and 0.48 m/s. The T-
prototype was placed 0.23 cm behind the cylinder (after the
vortex shedding point). The results (Figure 4) show that the
longitudinal drag force F
x
was lower in the vortex street. The
drag reduction was 42% at 0.31 m/s and 38% at 0.48 m/s.
Two differential factors were i) the reduced flow behind the
cylinder and ii) the passive interaction between the vortices
and the robot. In Section V-D we evaluate how each factor
contributed the total drag.
On the other hand, F
y
increased in the Kármán vortex
street; F
y
/F
x
< 0.2 (in uniform flows) and F
y
/F
x
> 2 (in the
Kármán street). The increase was related to the vortex
effects on the robot and the relative difference between the
average flow speed inside and outside of the vortex street.
Having larger F
y
provides insights to explain why lateral
displacement of a rainbow trout is larger while Kármán
gaiting than while steady swimming [3]. It also raises new
questions on the control side; for instance how to utilize
these forces to increase the swimming efficiency and
stability.
B. Force-downstream position relations in Kármán streets
To study the force-position relation of the robot, we first
placed the T-prototype along the Kármán vortex street
centerline at different positions where D=[0.05, 0.35] m with
a step of 0.03 m from the cylinder. At each position we
recorded the force measurements for 90 s.
Figure 5a presents the F
x
and the time averaged V
x
; note
the high correlation between F
x
and V
x
. Up to the distance of
0.15 m, F
x
was negative; flow was pushing the robot towards
the cylinder. D=0.15 m is relatively in a good agreement
with the suction zone length of 0.11 m. The drag increases
quickly in the vortex formation zone (0.11 m< D <0.19 m).
After the vortex shedding point (D=0.19 m) the rate of
increase slowed down and it stopped at D=0.29 m.
Figure 5b illustrates the F
y
(rms) and V
y
(rms) values. The
evaluation has been done in the rms domain as the readings
oscillated around zero due to alternately shed vortices. Note
that F
y
increased significantly (almost by two times) after the
vortex shedding point (D=0.19 m). Again we see high
correlation between F
y
and V
y.
C. Force-lateral position relations in Kármán streets
Next we check how (F
x
,F
y
) varied as the robot moved
away from the Kármán vortex street center axis (L=[-0.1,0.1]
m with a step of 0.025 m). The downstream distance of the
robot from the cylinder was fixed at 0.2 m. Figure 6a shows
Fig. 4. Fx and Fy in uniform flows (above) and Kármán vortex
streets (below) at flow speeds 0.31 m/s (30 < t < 120 s) and 0.48
m/s (120 < t < 210 s) for the T-prototype. The first 30 s and the
last 60 s of the data set corresponds to still water readings.
0 50 100 150 200 250 300
0
0.2
0.4
0.6
0.8
t(s)
Force (rms) (N)
KVS at 0.31 m/s and 0.48 m/s
Fx
Fy
TABLE I
THE CHARACTERISATION OF THE KÁRMÁN VORTEX STREET
KVS
1
KVS
2
Cylinder diameter (m) 0.10 0.10
Flow speed (m/s) 0.31 0.48
Hydrodynamic features
Base suction length (m) 0.11±0.01 0.11±0.01
Vortex formation length (m) 0.16±0.01 0.13±0.01
Vortex shedding point (m) 0.21±0.01 0.19±0.01
KS width (m) 0.23±0.02 0.24±0.02
Average flow speed (m/s)
inside KS 0.18±0.01 0.18±0.01
outside KS 0.30±0.01 0.47±0.01
Average vortex speed (V
Ȧ
)(m/s) 0.22±0.03 0.30±0.3
Min/Max mean vorticity 0.40±0.10 0.5±0.10
Vortex shedding frequency (f
vs
) (Hz) 0.68±0.05 1.13±0.05
Wake wavelength (Ȝ) (m) 0.32±0.05 0.26±0.05
Spacing ratio 0.32±0.10 0.38±0.10
Strouhal number 0.32±0.20 0.44±0.20
535

that the drag, together with the flow speed, increased
proportionally with the magnitude of L. The robot was
exposed to higher flows.
Both trends of (Fy, Vy) given in Figure 6b were rather M-
shape where they increased towards the two vortex rows
(L=-0.05 m and L=0.05 m). After the vortex rows they
decreased rapidly. When L=-0.1 m and L=0.1 m the robot
was mostly outside of the Kármán corridor which had 0.23
m width.
D. Robot fish size vs. cylinder size
To study the relation between the robot fish size and the
size of the Kármán vortex street we made comparative
experiments also with the X-prototype. Figure 7 shows that
for both prototypes F
x
and F
y
followed the same trend,
however and the drag felt by the X-prototype was about five
times higher than for the T-prototype and lateral forces
affecting the X-prototype were about two times higher than
for T-prototype. This can be explained with the size of the
X-prototype – the robot is more affected by the flow and due
to its greater width it’s interaction with vortices is stronger.
E. The turbulence increased the reduced flow drag
To evaluate the turbulence effect over the experienced
drag, we use the relation in Equation 2. We obtain the total
drag (
KVS
D
F
) from F
x
measurements. To estimate the
reduced flow drag (
U
D
F
), we adapted Equation 1 to our
setup. We measured F
x
in uniform flows at flow speeds 0.1
m/s, 0.2 m/s, 0.3 m/s, 0.4 m/s and 0.48 m/s.
We identified their relationship,
,0093.02766.2
2 VFU
D
(3)
where the mean error of the model was less than 2%. To
estimate
U
D
F
for each position of the robot in a Kármán
vortex street we used the average flow speed measured by
the DPIV at that location. We got the turbulence effect by
subtracting the reduced flow drag from the total drag. Figure
8 illustrates
T
D
F
at different downstream positions (D) in
KVS at flow speeds 0.31 m/s and 0.48 m/s.
The results are consistently positive suggesting that the
turbulence effect on the robot is negative; meaning vortex-
robot interaction adds on the drag experienced by the robot.
The higher the flow speed, the bigger the additional drag.
This opposes to the previous studies reporting energy
harvesting in a Kármán vortex street. During experiments we
observed that the tail of the robot was moving passively with
the vortex shedding frequency but the amplitude of the
oscillation was very small. One possible explanation for the
negative effect would be the ratio between the vortex rows
spacing and the width of the robot (r). When r < 0.1, such as
this one, the major interaction between the robot and vortices
Fig. 5. Fx computed as an average versus downstream distance
from the cylinder. The Vx measured by DPIV was also plotted
(above). Fy computed as a root mean square versus downstream
distance from the cylinder. The rms of Vy was also shown.
11 14 17 20 23 26 29 32 35
−0.06
−0.01
0.05
0.10
0.15
V
x
(mean) cm/s
Distance from cylinder (cm)
11 14 17 20 23 26 29 32 35 −0.38
−0.23
−0.09
0.06
0.21
F
x
(
mean
)
N
F
x
vs V
x
(48 cm/s)
11 14 17 20 23 26 29 32 35
0.13
0.14
0.15
0.16
0.16
V
y
(rms) cm/s
Distance from cylinder (cm)
11 14 17 20 23 26 29 32 35 0.29
0.40
0.52
0.63
0.75
F
y
(rms) N
F
y
vs V
y
(48 cm/s)
Fig. 6. Forces F
x
(above) and F
y
(below) depending on the lateral
distance from the cylinder center axis. Flow velocity components
V
x
and V
y
are also plotted respectively.
−10.0 −7.5 −5.0 −2.5 0.0 2.5 5.0 7.5 10.0
−0.06
0.04
0.13
0.22
0.32
Vx (mean) cm/s
Distance from KS center (cm)
−10.0 −7.5 −5.0 −2.5 0.0 2.5 5.0 7.5 10.0 0.09
0.19
0.29
0.40
0.50
Fx (mean) N
F
x
vs V
x
(48 cm/s)
−10.0 −7.5 −5.0 −2.5 0.0 2.5 5.0 7.5 10.0
0.08
0.10
0.12
0.14
0.16
Vy (rms) cm/s
Distance from KS center (cm)
−10.0 −7.5 −5.0 −2.5 0.0 2.5 5.0 7.5 10.0 0.54
0.63
0.71
0.80
0.88
Fy (rms) N
Fy vs Vy (48 cm/s)
536

Fig. 7. Forces Fx (above) and Fy (below) versus downstream
distance from the cylinder for T-prototype and X-prototype.
11 14 17 20 23 26 29 32 35
−0.19
−0.07
0.05
0.17
0.29
Fx (mean) N
Distance from the cylinder (cm)
F
x
: T prot vs X prot (10cm cyl, 31 cm/s)
T prototype
X prototype
11 14 17 20 23 26 29 32 35
0.12
0.23
0.33
0.44
0.55
F
y
(rms) N
Distance from the cylinder (cm)
F
y
: T prot vs X prot (10cm cyl, 31 cm/s)
T prototype
X prototype
might take place at the head. In this case, the vortices can be
compared to snow balls bombarding the robot and pushing it
away from the cylinder. Probably the vortices were also
dissipated before they reached the anterior part of the robot
(flexible tail). Therefore we observed small tail movements.
That said, unnatural experimental conditions such as
harnessing the robot with a rigid rod and not allowing the
head to rotate should be taken into account while
interpreting the results.
VI. CONCLUSIONS
In this paper we conducted experiments with passive fish-
shaped underwater robots in a uniform flow and regular
turbulence. We measured the force-position relationship in a
Kármán vortex street and compared it with the force
measurements in uniform flows. We furthermore present a
method to analyze the effect of the turbulence by correlating
flow measurements from DPIV with the force
measurements.
The results show that both downstream and lateral forces
to the robot are changing considerably depending on the
position of the robot in the turbulence. In overall the drag is
smaller where the reduction was up to 42% with respect to
uniform flow conditions. Moreover, when the robot was
placed in the suction zone behind the object, the flow pushed
the robot towards the object. The lateral force in a Kármán
vortex street, after vortex shedding point is considerably
higher compared to lateral force in uniform flows.
From the experimental results we draw the following
conclusions and guidelines for future work: The drag well in
the regular turbulence along both longitudinal and lateral
axis has a single local minimum. This point, theoretically,
can be used as a control set point. For instance, the energy
expenditure of the robot can be determined by monitoring
the current consumption and a gradient decent algorithm can
be implemented to trace a drag well. In real life situations,
positioning in a region, where flow activity is low, is
important as it permits hovering and surveillance without
spending energy. Also robots on long missions may stay
there to recharge the solar batteries and thus survive without
human intervention.
There are two ways of turning flow into an advantage: i)
to look for stable regions where forces on the robot are small
and ii) to exploit vortices in the flow in order to capture the
readily available energy. In this work we have demonstrated
that the first way is achievable in a straightforward manner.
The latter, on the other hand, presents significant challenges
as the interplay between flexible bodies and vortices is not
well understood. Even for passive interactions the resultant
effects can have negative impact on the robot as seen in the
presented experiments where the total drag perceived by the
robot was bigger than what it should be in the reduced flows.
REFERENCES
[1] D. N. Beal, F. S. Hover, M. S. Triantafyllou, J. C. Liao, G. V. Lauder,
“Passive propulsion in vortex wakes”, J. Fluid Mech. (2006), vol. 549, pp.
385–402.
[2] C. L. Cook and D. J. Coughlin, “Rainbow trout Oncorhynchus mykiss
consume less energy when swimming near obstructions”, Journal of Fish
Biology (2010) 77, 1716–1723.
[3] C. J. Liao, D. N. Beal, G. V. Laude, M. S. Triantafyllou, “The Kármán
gait: novel body kinematics of rainbow trout swimming in a vortex street”,
Journal of Experimental Biology, vol. 206, 1059 - 1073, 2003.
[4] P. W. Webb, “Entrainment by river chub Nocomis micropogon and
smallmouth bass Micropterus dolomieu on cylinders”, J. Exp. Biol., vol.
201, 2403 – 2412, 1998.
[5] G. K. Batchelor, “An Introduction to Fluid Dynamics”, Cambridge
University Press, ISBN 0521663962, 1967.
[6] T. Salumäe, “Design of a compliant underwater propulsion mechanism
by investigating and mimicking the body of a rainbow trout (Oncorhynchus
mykiss)”, MS Thesis, Tallinn University of Technology, 2010.
[7] R. Michel, D. Arnal, “Laminar-turbulent transition”, In IUTAM
Symposium, Tolouse, France, 1989.
Fig. 8.
T
D
Fat different downstream positions (D).
20 23 26 29 32 35
0.00
0.05
0.09
0.14
0.18
FT
D (N)
D (cm)
V = 31 cm/s
V = 48 cm/s
537