AIAA Fluid Dynamics 2010 Chai W.S., Srigrarom S. and Lim D.

June 2010

On pitching motion of two opposite double flappers in water tunnel at

Re = 25,000 as basis of human crawl-stroke swimming

Chai W.S.1, Srigrarom S.

2 and Lim D.

3

1. PhD candidate, School of Mechanical and Aerospace Engineering,

Nanyang Technological University, Singapore

2. Senior Lecturer, School of Science and Technology

SIM University, Singapore

3. Sport biomechanist, Singapore Sport Council, Singapore

Corresponding e-mail: spot@unisim.edu.sg

Keyword: double flappers, pure pitching flapping, crawl stroke swimming, and dragonfly beating.

Abstract

A pair of two flat plates undergoing pure pitching flapping but in opposite directions was studied. This

double-flapper set was used to simulate the human’s leg undergoing crawl-stroke swimming motion

(stretched straight legs without bending at the knees). Likewise, this work can be extended to the

understanding of the dragonfly’s flight, when the forewings and hindwings beat at opposite direction in

certain flight. The two flat plates rotate about the same axis in similar manner to the human legs

(rotating about the hip). By varying the pitching amplitude (angles) and pitching frequencies

corresponding to its travelling speed and pure thrust produced, the optimum sets of flapping motion,

either for maximum thrust or maximum propulsive efficiency for range and endurance can be sought.

Hence, this is to give light for understanding best swimming condition for crawl-stroke motion and/or

dragonfly’s beating flight.

Introduction

In competitive swimming, kicking is an essential element in providing lift and propulsive thrust forces to

achieve higher swimming speeds. During inefficient kicking, there is a likely increase in cross sectional

area in the direction perpendicular to the travelling direction. A possible cause for the phenomena is a

miss-matching of kick magnitude and frequency. Swimmers and coaches do not have an objective

measurement of the maximal kick thrust generated by kicks with varying kicking magnitude and

frequency and it can only make decision by using time to estimate the highest speed generated by

different kicking techniques. This study aims to make direct measurement of the effects of freestyle and

butterfly kicking by employing an instrumented rig. The rig would be put under varying input

conditions to determine an optimal combination for speed and efficiency.

Methodology

In the double flapper studies, (1) we examined the footage of freestyle and butterfly swimming of highly

trained competitive human swimmers to determine their swimming kinematics like swimming speed and

kick displacement angle. Then, (2) we conducted force measurement on the scaled down double-flapper

model in the water tunnel at various freestream and pitching conditions. The measured force pattern is

then used for comparison with the real measurement as found in literature. Especially, we aimed to

confirm the existence of the peak force, occurs after the kick stroke. We could also identify the best

cases for maximum thrust and maximum efficiency. Then, (3) we selected the maximum thrust case, and

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AIAA Fluid Dynamics 2010 Chai W.S., Srigrarom S. and Lim D.

June 2010

did (a) dye flow visualization as well as (b) Particle Image Velocimetry (PIV). These two flow

visualization techniques enable us to understand the flow physics behind.

The swimmers were separated to sprinters (50m and 100m) and middle distance (200m to 400m)

swimmers. The average swimming speed were calculated when swimming between the 15m and 35m

mark of a swimming pool where the swim is “clean” without the effects of kicking off a wall or a

starting block. The angular displacement of the kick was recorded with an underwater camera and the

angle was estimated from the highest and lowest point of the kick. The free swim speed is estimated at

1.9m/s for sprinters and 1.6m/s for middle distance swimmers respectively. The angular displacement

of the sprinters’ kick is approximately 25 degrees and the middle distance swimmers are around 40

degrees.

For the direct force measurement from the jig, a simple mechanism was developed to mimic a double

flapper. The kicking motion is to be assumed to move at the hip joint and the effects of the knee

extension during the down kick is negated for this experiment. The two flat plates were put inside the

closed loop water channel at Nanyang Technological University, where the free stream flow was

introduced. This was similar to Lagrangian condition. The flappers are made from acrylic (flat plate)

with chord and span of 0.15m × 0.15m. The freestream velocity ranging 0 m/s to 0.17m/s was used,

corresponding to Rechord of 0 to 25,000.

Figure 1: Double flapper model and its supporting movement apparatus in the water channel

The two flat plates were attached to two shafts at the same axial location. The set of gears allow the

apparatus to be driven by just one high resolution stepper motor (Cool muscle motor CM1, selected to

12,000 pulses per revolution). The apparatus was also designed such that the two flappers can be move

in either synchronize or opposite to each other. However, in this paper, the opposite mode was selected.

Figure 1 illustrates the setup, direction of the freestream and the motion of the flapper.

In our experiments, we input the various set of pitching motions parameters through stepper motor. Our

measured outputs were the force and torque generated by the two pitching flappers. These force and

torque generated were recorded by six-axis load cell (ATI gamma SI-32-2.5), collected and post-

processed via the National Instrument DAQ cards, Matlab and LabView

Software. The angular

acceleration was set to 240 deg/s2 which allows the flapper to be flapped as close as the middle distance

swimmer. The maximum angles were set to be 5°, 10°, 15° and 20° (measured from centerline, hence,

AIAA Fluid Dynamics 2010 Chai W.S., Srigrarom S. and Lim D.

June 2010

the angular sweeping ranges are ±5°, ±10°, ±15° and ±20°, corresponding to Strouhal numbers 0.912,

0.366, 0.616 and 0.614 respectively). The input parameters and the results are shown in table 1 below:

Table 1: Input parameters and force measurement results of Double Flappers

Flapping

angle

Pitching

rate, Ω

(°/sec)

Net thrust

force

(at zero

freestream)

Fx (N)

Corresponding

travelling

velocity , U

(m/s)

Dimensionless

pitching rate,

c

U

+ ΩΩ ≡

Strouhal

number,

fASt

U≡

Thrust

coefficient,

2

00.5

xt

FC

S Uρ=

Efficiency

p

FU

Pη =

±5° 45 0.071 0.048 2.45 0.912 1.370 0.089

±10° 90 0.182 0.162 1.46 0.366 0.308 0.251

±15° 136 0.373 0.133 2.68 0.616 0.940 0.325

±20° 181 0.419 0.129 3.65 0.643 1.109 0.265

Force and moment results of double flappers

Figures 2 and 3 show the plots of the net thrust force (Fx) and corresponding travelling velocity (U) for

different flapping angles. It is clear that for higher thrust force, the double flapper should be flapped at

larger angles (amplitude). However, higher flapping angle does not always result in the higher travelling

velocity. It appears that U reaches maximum at ±10° (out of the four angles tested).

Figure 2 Figure 3

Figure 4 Figure 5

Figures 4 and 5 present the similar results but in dimensionless terms. The thrust coefficient (Ct) shows

the same trend as that of figure 2. The efficiency plot in figure 5 indicates that, out of the four angles

tested, the ±15° case provides the maximum efficiency of 32%.

AIAA Fluid Dynamics 2010 Chai W.S., Srigrarom S. and Lim D.

June 2010

Figures 6-9 show the axial forces applied on both flappers in each flapping cycle for all the 4 test cases

(±5°, ±10°, ±15° and ±20°) respectively. Different lines refer to different flapping cycle when the data

was taken. Instead of two thrust force peaks of equal height for two symmetric left and right strokes in

each cycle, there is one dominant peak of thrust force produced and with a few smaller peaks in each

cycle. These happen for all test cases and repeatable. This shows the thrust force is mostly generated by

the initial kick, i.e. peak at the start and later decrease with time. This is in agreement with field

measurement from actual swimmer studies (Craig et al, 2006) as shown in figure 10 (left peak in the

force plot). Further investigation reveals that there is time (phase) lag between the angular position and

the force response, which varies from case to case from 45° to 90° phase lag. Dye flow visualizations

shows two horseshoe vortices created from two upper and lower flappers are interacting with each other,

especially during crossing at 0° (centerline). Hence, it is believed that this non-linear interaction between

two vortices causes the asymmetry of this thrust force within the cycle. The PIV results in the next

section could explain the phenomena further.

Figure 6 Figure 7

Figure 8 Figure 9

Connection of force reading results to the real human kick stroke

With reference from the various thrust versus cyclic time graph for ±5° case (figure 6 above), the

presence of multiple crest during each cycle may correspond to velocity profile during swimming

measured by a linear encoder device. (See figure 10 below)

AIAA Fluid Dynamics 2010 Chai W.S., Srigrarom S. and Lim D.

June 2010

Fig. 10: Thrust force generated by competitive swimmer (Craig et al, 2006)

The current investigation looks at the kinetic contribution of the kicking movement, it is likely to affect

the instantaneous swimming speed of a swimmer. For each drop in thrust, a deceleration in the

swimmer is likely to occur and it is likely that the athlete would be required to produce more effort to

generate sufficient thrust to accelerate. The acceleration and deceleration cycle of the movement is

likely to fatigue the athlete. To possibly reduce the fatigue, the athlete may have to know the required

kinematics to produce a thrust versus cycle time profile which is able to maintain the required thrust.

Comparison of force and moment results of double flappers with single flapper

The second set of experiments is on the investigation of the pitching motion with fixed pitching

frequency and varying pitching angle/amplitude on the double flappers and single flapper with the same

interface area. As the pitching frequency is fixed, the angular velocity and angular acceleration will need

to increase with larger pitching amplitude as the total sweeping range is increased.

Critically, this study on double flappers and single flapper is to imitate human legs swimming in scissor

kicking motion. In order to facilitate an unbiased experimentation, the interaction area for both double

flappers and single flapper shall remain equal. For the double flappers, each flapper measures 0.075m by

0.15m whereas, for the single flapper, it measures 0.15m by 0.15m.

Table 2: Pitching Parameters for Pitching of Double Flappers

Pitching

Amplitude

(Degree)

Pitching

Frequency

(Hz)

Total Sweeping

Range (Degree)

Angular Velocity

(deg/s)

Angular Acceleration

(deg/s2)

±5° 1 20 90 180

2 120 300

2.22 150 350

±10° 1 40 150 180

2 300 450

2.22

±15° 1 60 210 450

2 420 600

2.22

±20° 1 80 300 450

2

2.22

AIAA Fluid Dynamics 2010 Chai W.S., Srigrarom S. and Lim D.

June 2010

The double flappers case was conducted at 3 individual pitching frequencies of 1Hz, 2Hz and 2.22Hz, at

different flapping angles. Table 2 shows the pitching parameters for the double flappers at the 3

frequencies and their corresponding angular velocities and angular accelerations. However, due to the

limitation of the driving motor, experimentations with high pitch rate were abandoned as the motor is

not able to withstand the large force induced from the surrounding fluid at higher pitching speed. Hence,

this investigation on the double flappers and single flapper can be only carried out in pitching frequency

of 1Hz.

Fig. 11 (left): Thrust coefficient (Ct) versus Strouhal number (St) for double flappers and single flapper

Fig. 12 (right): Propulsive efficiency (ηp) versus Strouhal number (St) for double flappers and single flapper

Dye flow visualization and Particle Image Velocimetry (PIV) of double flapper

From the force and moment reading, dye flow visualization were conducted to investigate the flow

pattern, especially between the two pitching plates. The two different colour dye was injected on each

plate. The ejecting tubes of the dye flows were secured at very close proximity to each other so as to

retain consistency between the two dye flows.

Fig. 13 Dye flow visualization on double flapper

Figures 13 (a) and (b) show the dye flow visualization for the double flappers configuration that moves

in the opposite directions to one another, give the maximum thrust. In this case, the pitching amplitude

was ±20° (sweeping range of 40°) with the flow condition of U = 0.129 m/s (Rechord = 21,930). The

pitching rate was 181 °/sec which corresponds to a dimensionless pitch rate of Ω+ = 3.65 and Strouhal

a) b)

AIAA Fluid Dynamics 2010 Chai W.S., Srigrarom S. and Lim D.

June 2010

number, St = 0.643 and propulsive efficiency, ηp = 0.265. (26.5%) As shown in the figure, the blue and

red dyes are mixing together at the downstream of the double flapper. The dye image shows structures

resemblance to the reverse Kármán or horseshoe vortices, hence, indicates thrust generating action.

The Particle Image Velocimetry (PIV) is another flow visualization technique beneficial in mapping out

the velocity and the vorticity fields. We conducted PIV around the flappers and the experiments were

carried out using the Dantec® system that includes DynamicStudio version 1.45.54 software.

The pulsating laser sheet will envelop the horizontal plane of the test section of the water tunnel and cut

through the trailing edge of the single flapping plate. This laser sheet in then captured using a CCD

camera located underneath the test section. In order to enhance the PIV analysis and results, we utilized

hydrogen bubbles as particles that were generated through the electrolysis method. In the schematic Fig.

14 below shows that the aluminum foil on the flapper acts as the cathode that produces the initiation of

the hydrogen bubbles formation and an aluminum rod placed at the far end of the free stream acts as the

anode. Detergent was added to the water for enhancing the formation of bubbles. The cathode and anode

were connected to a DC power supply which provides the current to the circuit.

Fig. 11 Setup arrangement for PIV by using hydrogen bubbles (electrolysis method) as particles

Next, Figure 15 shows the images from PIV technique incorporating hydrogen bubbles on double

flappers, but the single laser plane cut was on one of the two flappers. The flow condition was still U =

0.17 cm/s (corresponding Reynolds numbers, Rec = 25,000). The pitching amplitude, θ = ±5°; rotational

motor speed is 45 deg/s and an angular acceleration of 30 deg/s (Ω+ = 2.45). This corresponds to the first

case in Table 1 above, which is at the maximum thrust. The total time taken for a period is 2.25sec

which corresponds to a pitching frequency of 0.44Hz. Each velocity plot and vertical plot is phase-

averaged from 3 repeat experiments at the same angular motion phase. The flapper start pitching

downward to its maximum angle (-5 degree), back to 0 degree and pitching up to +5 degree and finally

back to 0 degree.

Based on the observations from the experiment, the hydrogen bubbles form is fine and dense thus, the

velocity vector can be computed without providing much error vectors. However, as the hydrogen

bubble is very light, therefore, it has a higher tendency and agility in following the path of the water

flow. The main drawback for this hydrogen bubble particle method is that it is not suitable for very low

speed test as the buoyancy effect will dominate. Since the captured flow field is in the horizontal plane,

the vertical rising displacement of the hydrogen bubble due to buoyancy can be ignored. The shedding

of the reverse Kármán vortices at the trailing wake are circled in the figures.

AIAA Fluid Dynamics 2010 Chai W.S., Srigrarom S. and Lim D.

June 2010

a)

b)

c)

d)

e)

f)

AIAA Fluid Dynamics 2010 Chai W.S., Srigrarom S. and Lim D.

June 2010

Fig. 2: Picture of PIV (0.25sec apart from each frame), Phase average velocity vector plot and vortical plot

In the vorticity plots, the blue region indicates clockwise rotating vortex and red region represent

counter-clockwise rotating vortex. In Part (a) of the figure 11 is at t = 0sec, it shows the normal drag

condition for a free stream flow across an object, with clockwise vortices on top and counter-clockwise

vortices at the bottom.

When the plate is start pitching downward, the red vortices are being pushed which shown in part (b).

The red vortices are further shed downstream in part (c). However, as it change the direction and pitch

up, a blue vortex (circled in part d of figure 11) is formed right behind the trailing edge. Subsequently,

the red region vortex is formed due to the fluid vector of the “following” pitch-up plate. As it pitch up

further, the blue vortex (clock-wise vortex) can be clearly seen (part e) and once it reached part (g), the

plate is pitching down, therefore, an counter-clockwise is form right behind the trailing edge as circled

in third column of part (g). In the next frame, where the plate is pitching down further, it pushes against

the red vortices followed by further vortex shedding downstream which circled in part (i).

These series of PIV images show clear jet-like reverse Kármán vortices, which explain the strongest

thrust generation (hence, maximum thrust coefficient compared to other case in table 1).

Conclusion

Through the studies on double flapper pitching, a better understanding on crawl-stroke swimming

motion (stretched straight legs without bending at the knees) can be achieved. The force and moment

experiments present the force pattern after the dolphin kick mimicked by double flappers. The thrust

force is mostly generated by this initial kick, i.e. peak at the start and later decrease with time. Besides

the force measurement, PIV and dye flow visualization were also conducted in order to have a clearer

i)

h)

g)

AIAA Fluid Dynamics 2010 Chai W.S., Srigrarom S. and Lim D.

June 2010

picture for the flow structure and the interaction of the flapper to the fluid. As a conclusion, an optimal

test case was found from the sets of experiment. It gave the light for the swimmer that during each

swimming mode (start up which need higher thrust or while swimming for better efficiency), different

swimming/kicking amplitude and frequency could be employed.

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