Royal Institute of Technology
Bachelors Thesis
Experimental study of a three dimensional cylinder- lament system
Author:
Carl Finmo Supervisors:
Shervin Bagheri Nicolas Brosse Fredrik Lundell
May 20, 2014
Abstract Can plant seeds disperse with- out wind?
This can be said to be the question that sparked this project. Plants and animals use all kinds of appendages to aid their locomotion, e.g. feathers, hairs or ns. Some of these appendages may be used for a type of passive lo- comotion that utilizes the separated
ow around the main body, without the need for additional energy expen- diture.
This report details the investiga- tion of a three dimensional cylinder of diameter D, with a lament of length L attached to the rear. The cylinder is placed in a uniform ow and the mean position of the lament is measured for various lengths.
It is found that long (L/D > 6) and short (L/D < 2) laments tend to align with the ow. Where for interme- diate lament lengths (2 < L/D < 6) the lament lie down on the cylinder and is aligned with the cylinder axis.
Kan frön spridas utan vind?
Detta var frågan som startade detta projekt. Växter och djur använder alla möjliga bihang för att hjälpa deras rörelser, t.ex. fjädrar, hår eller fenor.
En del av dessa bihang kan användas för en slags passiv för yttning som ut- nyttjar den strömning som separerats från kroppen utan att behöva tillföra ytterligare energi.
Den här rapporten handlar om undersökandet av en tredimensionel cylinder, med diameter D, som har ett lament med längd L fastsatt bakom sig. Cylindern är placerad i en homogen strömning och la- mentets medelposition är uppmät för varierande längd på lamentet.
Det observerades att långa (L/D >
6) och korta (L/D < 2) lament rör sig med strömningen. Medans för mel- lanliggande längder på lamentet (2 <
L/D < 6) så lägger sig lamentet ner på cylindern längs med dess axel.
Contents
1 Introduction 3
1.1 Summary of the literature . . . 3 1.2 The project and this report . . . 4
2 Method 5
2.1 Experimental setup . . . 5 2.1.1 Experiment details . . . 6 2.2 Measurement and post processing . . . 7
3 Results 9
3.1 Examples of time evolution of the lament position . . . 9 3.2 Mean position of the lament . . . 10
4 Conclusions 12
4.1 Summary of this work . . . 12 4.2 Perspectives on this work . . . 12
A Secondary results 13
A.1 Free falling disk . . . 14 A.2 Fixed disk . . . 14 A.3 Wake visualization . . . 14
B Flow generator 17
Bibliography 19
Chapter 1
Introduction
Can plant seeds disperse without wind? This could be said to be the question that sparked this project. Plants and animals use all kinds of appendages to aid their locomotion, e.g. feathers, hairs or ns. Some of these appendages may be used for a type of passive locomotion that utilizes the separated ow around the main body.
1.1 Summary of the literature
Figure 1.1: Elastic lament attached to the rear of a circular cylinder, the ow is from left to right. (1) Long lament with a symmetric mean position; (2) and (3) short lament with a non-symmetric mean position. Source: [1]
A recent article by Bagheri et al [1] demonstrates that a single passive
lament hinged on the rear of a blu body placed in a stream can generate a lift force without increasing the mean drag force on the body.
More precisely they have studied - using two dimensional numerical simulations - a cylinder placed in a uniform incom- ing ow with a lament free to ap attached to the rear of the cylinder ( gure 1.1). They have found that the behav- ior of the lament depends on its length. With a lament longer than two cylinder diameters, the mean position of the l- ament align with the incoming ow ( gure 1.1:1). In that con-
guration the mean lift force and torque acting on the cylin- der is zero. Then when the lament length is reduced be- low two cylinder diameters they have observed a symmetry breaking where the mean position of the lament form an an- gle with the direction of the incoming ow ( gure 1.1:2 and 1.1:3).
Even more recently, Ugis et al. have extended this result [2]. In this study, using a two dimensional soap lm experiment, they have con rmed experimentally the symmetry breaking for short exible
laments. They have also studied numerical simulations of a free falling circular cylinder with a splitter plate. Again for short splitter plates the symmetry breaking was observed and they have shown
that this provides a mean drift on the free falling cylinder. They have also pro- posed a theoretical model that provides quantitative predictions for the critical
lament length where the symmetry breaking will occur. This model also re- produces the lift force and torque induced by this symmetry breaking.
Since all the previous work described above have been carried out in two dimen- sions the aim of the present study is to extend this result to three dimensional cases. The present work examines a three dimensional cylinder with a lament attached to the rear is placed in a uniform ow. The ow around a circular cylinder has been extensively studied (see Williamson [3] for a review) and for the Reynolds number - based on the cylinder diameter and the incoming uid velocity - considered in this experimental study the ow will be laminar with vortex shedding.
1.2 The project and this report
The goal of the project was to examine the behavior of a three dimensional free falling object with an appendage. But doing experiments with, for instance, a plant seed falling in air would likely be di cult. So the project concentrated on
nding a simple three dimensional body with an appendage attached to it that could be used to demonstrate that the symmetry breaking, like the one detailed in [2], is also present in three dimensions.
The initial hope for this project was to use a freely falling particle but this proved di cult for various reasons (see appendix A). So the main experiment and results in this report concerns a three dimensional circular cylinder with a
lament attached to its rear, the whole body is xed in an uniform upward ow.
The measurement of the movement of the lament in the wake of the cylinder allows us to determine the position of the lament.
This report is structured as follow. The method chapter describes the experi- ment and tools used. Then the behavior of the exible lament in the wake of the cylinder is described in the results parts. The reports end with conclusions and some perspectives on this work.
Chapter 2
Method
This study concerns a circular cylinder xed in a uniform incoming ow. A
lament that is free to ap is attached to the rear of the cylinder.
This chapter describes the experimental setup, the measurement techniques used in this study and also the post-processing methods used.
2.1 Experimental setup
The experiment was performed in a previously build apparatus shown in gure 2.1 (see also appendix B). The main purpose of this apparatus is to generate a vertical ow of water in the test section. The whole apparatus is about 1.5 m high, 1 m wide and 0.4 m deep. The experiment takes place in the test section (labeled as the test section in gure 2.1). This section is about 20.5 cm wide, 39.7 cm deep, 68 cm high in size. Below the test section is 40 cm long slab of foam that serves to homogenize the ow.
To create the ow a pump was used, with the ow rate speci ed to 53 L/min. Flow rate = 0.76 L/s Fluid velocity U = 1 cm/s
The uid velocity U was determined by measuring the velocity of the rising sur- face when the tank was initially led with the pump, giving U ≈ 1 cm/s. This value and the geometry of the test section would give a ow rate of 43 L/min.
Figure 2.1: Schematic of the ow generator. Source: [4].
2.1.1 Experiment details
Figure 2.2: Photography of the cylinder xed horizontally in the tank. D=20 mm. The silk thread placed at the rear of the cylinder is visible in the center of the image, the part used for adjust the length of the lament is visible on the right of the image.
The experiment consists of a cylinder made from a plastic tube (with di- ameter D = 20 mm and length 20.5 cm, show in gure 2.2) placed in the test section described in the previous part. The axis of symmetry of the cylinder is placed normal to the incoming ow. Two holes were drilled in the cylinder through which a thread made from silk was inserted. This thread lament with
length L, can then be observed to move in the cylinders wake.
The second hole in the cylinder allows for the adjustment of the laments length. The behavior of the lament was measured for dierent lengths, the length ratio Ls= LD was varied between 0.5 and 10.
In this experiments the Reynolds number - based on the cylinder diameter D, the uid velocity U and the cinematic viscosity of water (ν = 1.10−6 m2/s)
- is xed and equal to Re = U Dν = 186. For this Reynolds number the cylinder Re = 186 wake is unsteady with vortex shedding [3].
2.2 Measurement and post processing
(a) Front view, θ1
(b) Side view, θ2
Figure 2.3: Schematic of the angles of de ection of the lament for (a) the front view θ1 and (b) the side view θ2.
The objective of the measurements and post processing is to determine the position of the lament. This position is de ned by the two angles of de ection, one from the front and one from the side - called θ1and θ2 respectively. These two angles are shown schematically in gure 2.3.
To measure the position of the lament, the cylinder was photographed with two cameras, one from the front and one from the side. A number of series (2x17, one for each view point) of gray scale images for lament lengths between 0.5 < DL < 10 were taken. The recording time was 4 minutes and 10 seconds with an acquiring rate of 2 Hz and an exposure time of 10 ms, resulting in 500 images for each lament length measured. The image resolution was 1400x1088 pixels for both the front and side view.
To calculate the average angle of de ection the resulting images were pro- cessed in MATLAB. A brief description of this process follows.
(a) (b)
Figure 2.4: (a) Raw image of the lament given by a camera; (b) the same image after the binarization.
Figure 2.4a presents one raw gray scale image of the lament (vertically), the part of the thread used to adjust the length is visible on the lower left corner of the image. The images were then converted to a binary, black and white, image seen in gure 2.4b.
The angle of de ection was calculated as the angle between the
laments attachment point to the cylinder and the endpoint of the
lament. These are marked with red circles in gure 2.4b. The angle θ is de ned as the angle between the vertical and the line forming by these two points, consequently θ = 0 means that the lament is vertical; positive angles are taken in the clockwise direction.
To obtain the mean angle of de ection, the angles for the entire measurement series (500 images) was averaged. In some cases it was di cult to determine the position of the lament because it fell down and was obscured by the cylinder. In these cases the angle was obtained from a single suitable image.
The calibration was made by recorded images of a ruler for both cameras. Using these images the conversion factor is found to be 4.67 pixels per mm for the front view and 4.95 pixels per mm for the side view, the error in these values is less than 1%. Finally the length of the lament in mm was calculated by averaging the value from the front and the side views.
In order to obtain the lament length in mm this lament length was rst determined in pixels on the images and then converted in mm using these conversions factor.
Chapter 3
Results
In this chapter the main results of this study are presented. Examples of the time evolution of the lament position in the cylinder wake are rst described, then the mean position of the lament as a function of its length is studied.
3.1 Examples of time evolution of the lament position
Figure 3.1 show the time evolution of the angles of de ection, θ1 and θ2, for a
lament length of Ls= 9. The evolution of the angle θ1presents a clear periodic oscillation, the frequency of these oscillations is around 0.11 Hz. The behavior of the angle θ2is more chaotic and no periodic behavior can be found.
Figure 3.2 present the same results but for a shorter lament, Ls= 2, again the angle θ1 presents periodic oscillations while the angle θ2 presents a slow evolution with no clear periodicity.
To obtain the mean angles of de ection used in the next part, the angles θ1
and θ2 were averaged in time.
0 50 100 150 200 250
−8
−6
−4
−2 0 2 4 6 8 10
Time [s]
θ1 [°]
(a) θ1, Ls= 9
0 50 100 150 200 250
−16
−14
−12
−10
−8
−6
−4
−2 0 2 4
Time [s]
θ2 [°]
(b) θ2, Ls= 9
Figure 3.1: Angles of de ection as a function of time for lament length Ls= 9
0 50 100 150 200 250
−20
−15
−10
−5 0 5 10 15
Time [s]
θ1 [°]
(a) θ1, Ls= 1
0 50 100 150 200 250
−55
−50
−45
−40
−35
−30
−25
Time [s]
θ2 [°]
(b) θ2, Ls= 1
Figure 3.2: Angles of de ection as a function of time for lament length Ls= 2
3.2 Mean position of the lament
The average angles of de ection, θ1and θ2, were measured for various lament lengths, 0.5 < Ls < 10. The average angles of de ection as a function of the Ls= L/D
dimensionless lament length Lsare shown in gures 3.3a and 3.3b.
0 1 2 3 4 5 6 7 8 9 10
0 10 20 30 40 50 60 70 80 90
Length [L/D]
<θ1> [°]
Normal Falls down
(a) Front view - θ1
0 1 2 3 4 5 6 7 8 9 10
0 10 20 30 40 50 60 70 80 90
Length [L/D]
<θ2> [°]
Normal Falls down
(b) Side view - θ2
Figure 3.3: Average angles of de ection, hθi, as a function of the lament length
(a) L/D & 6
(b) 2 . L/D . 6
(c) L/D . 2
Figure 3.4: Sketch of front and side view of the cylinder for three characteristic l- ament lengths
For a lament longer than about 6 diameters the angles hθ1iand hθ2iare less than 5◦ and 25◦ respectively (see gure 3.3a and 3.3b).
This indicates that the mean position of the lament is close to ver- tical from the front view, this is schematically shown in gure 3.4a.
Above this length the lament can be observed to make a waving motion from the front, as seen in the front view of this gure. Look- ing at the side view in 3.4a we see that the lament will not always be straight up, re ecting that hθ2iis not zero for these lengths. This angle hθ2i increases when the length Ls is decreased ( gure 3.3b) thus indicating that the lament is starting to fall down.
When the length is reduced below a critical length, LS . 5 − 6, the lament tends to collapse, it means it falls down on the cylinder and aligns with the axis of symmetry of the cylinder ( gure 3.4b).
For these lengths it is observed that the lament does not oscillate.
It should be noted that for these lengths the mean angle is di cult to determine since the lament might be curled up depending on how it falls, so for these length the accuracy of the mean position of the
lament is low. When the lament is near the transition length it seems to stay up for a few periods before falling down.
For lament lengths Ls. 2, the mean angles hθ1iis less than 20◦ ( gure 3.3a) and hθ2i is decreasing from 65◦ for Ls = 2 to 18◦ for Ls = 1 ( gure 3.3b). This indicates that the mean position of the
lament is tilted, this is also shown schematically in gure 3.4c.
Chapter 4
Conclusions
4.1 Summary of this work
This experimental study has focused on the behavior of a lament attached to the rear of a circular cylinder placed in a uniform incoming ow. The length of the lament was varied and for each length the mean position of the lament was determined. For lengths, Ls longer than 5-6 the mean position of the lament is close to be aligned with the incoming ow. For these lengths it is found that the lament oscillates in the plane normal to the cylinder axis. For intermediate lengths, 2 < Ls< 5 − 6, it was found that the lament lie down on the cylinder, it means that the mean position of the lament is aligned with the axis of the cylinder, to our knowledge this behavior of a exible appendages has never been observed before. Finally for Ls less than 2 the mean position is tilted in both directions with respect to the incoming ow.
4.2 Perspectives on this work
As described in appendix A other bodies were initially tested during this project, namely a xed disk and a free falling disk both with a lament attached to the rear. These bodies showed some promise but for issues described in the appendix they were not pursued further. Here is a brief summary of what might still be worth investigating regarding those bodies.
A xed disk with a lament attached to the rear (see appendix A.2) is promising and it should be possible to investigate with the same techniques as used in this project. It would probably require some modi cations of the experiment apparatus used in order to achieved a higher ow rate.
The free falling disk with a lament attached to the rear (see appendix A.1) might be a good candidate body to be used to investigate the symmetry breaking that this work set out to demonstrate. However, as noted in appendix A.1, the lament materials used in this falling disk experiment (a silk ber) was not exible enough to observe any hydrodynamic eect on it. It could be interesting to reproduce this free falling disk experiment with a more exible
lament.
Appendix A
Secondary results
This appendix describes some of the other bodies investigated during this project.
A sphere can have a fairly complicated wake (see e.g. [5]) and was ruled out from the beginning so this study has focused on disks.
(a) A small disk. D=6mm (b) A small disk with a lament attached
(c) Larger, xed disk. D=50mm
Figure A.1: Examples of bodies
A.1 Free falling disk
During this work a free falling disk with an attached lament to the rear was tested. The objective was to observe the eect of a exible appendage on the drift of a three dimensional falling object. The behavior or these falling disks depends on the Reynolds number (see Ern et al 2007 [6]). For su ciently low Reynolds number (Re < 100) they have a rectilinear path with a steady ax- isymmetric wake, for higher Reynolds number they have an oscillatory path with an unsteady wake. The objective was to study a free falling disk with the attached lament in the rectilinear path regime since it would have been di cult to observe the eect of the attached lament when the disk is oscillating.
To obtain such low Reynolds number in practice the density ratio (density of the solid/density of the uid) has to be low so the material chosen to make the disk was Nylon 12 with a speci c density of 1.01 kg/m3and the diameter of the disk was chosen to be 6 mm. Images of the disk are presented in gures A.1a (without the lament) and A.1b (with the lament). The lament is attached to the disk using a 0.8 mm hole drilled in the center of the disk. Then the disk was released in the test section with the water at rest and observed to fall with the eyes.
These preliminary tests have shown that the constraints of having a small enough disk to be stable and a exible enough thread that is sensitive to hy- drodynamic forces was not possible to ful ll. In fact the rigidity of the lament was too high with the types of threads tested here, i.e. silk and cotton, to make an unambiguous observation of the laments movement in the wake of the disk.
A.2 Fixed disk
The second case tested in this study was a xed disk placed in an incoming uniform ow with an attached lament to the rear. In fact a xed disk avoids the problem of oscillations of a free falling disk at Reynolds numbers higher than 100, so with a xed disk Reynolds numbers higher can be tested. A disk with diameter D = 50mm was manufactured and xed on a shaft as shown in
gure A.1c.
For the xed disk it turned out that the ow rate was not high enough to give a wake where the lament would move. In fact using the dye technique to visualize the wake (see section A.3 for description of the technique) it was found that it was not possible to observe a clear wake behind the disk. The exact reason for this was not clear but due to time constraints of the project the xed disk was not investigated further.
A.3 Wake visualization
To get an understanding of the structure of the wake of a body falling in water a chemical called Fluorescein-natrium (C.I. 45350) was used. Approximately 1 part of the powder was solved in 99 parts of water (measured in weight for both water and ourescein) and then applied as a thin coating on the body of interest. The dye is be visible even in normal lighting but for best eect a UV lamp should be used.
A few still images from a video of a falling disk that was coated with oures- cein before being dropped in the water tank is shown in gure A.2.
When viewing a lm of a disk with a lament attached, one can also clearly see the re-circulation in the wake and how the lament is not perturbed by this back ow. This method can be used to verify if a material could be used as a
lament.
(a) t=0 (b)
(c) (d)
(e) (f)
(g) (h) zoomed out
Figure A.2: Fluorescent wake of a falling disk
Appendix B
Flow generator
Figure B.1: Photography of the ow generator
Figure B.1 shows a photography of the ow generator used. Below follows some notes from working with this apparatus that can be useful for someone who wants to perform experiments using a similar setup.
Some caution has to be applied when lling it with water since there are several places where air pockets can form, which will in turn generate bubbles that will disturb the ow where the experiment will take place. Much of the air will get trapped as bubbles in the homogenizer in the mid section of the device and will eventually disappear given enough time. But a good way to ll the device with water is to let the water ow slowly along the walls of the upper container.
It can also be useful to add a few milliliters of dish washing soap which lowers the surface tension and thus bubble formation.
Bibliography
[1] S. Bagheri A. Mazzino and A. Bottaro. Spontaneous symmetry breaking of a hinged apping lament generates lift. Physical Review Letters, 109, 2012.
[2] U. Lacis N. Brosse F. Ingremeau A. Mazzino F. Lundell H. Kellay and S. Bagheri. Passive appendages generate locomotion through symmetry breaking. In preparation, -1, 2014. to appear.
[3] C.H.K Williamson. Vortext dynamics in the cylinder wake. Annual Review of Fluid Mechanics, 28:477-539, 1996.
[4] Cédric Lai Yen Kang. Generation of ber ocs for sedimentation studies.
B.Sc. Thesis at KTH Mechanics and ENSTA ParisTech, 2008.
[5] M.Horowitz and C.H.K Williamson. The eect of reynolds number on the dynamics and wakes of freely rising and falling spheres. Journal of Fluid Mechanics, 651, pp. 251-294., 2010.
[6] P. Ern P. C. Fernandes F. Risso and J. Magnaudet. Oscillatory motion and wake instability of freely rising axisymmetric bodies. Journal of Fluid Mechanics, 573, pp.479-502, 2007.
