phd_thesis_emanuela.

FLUID MOTION BY
UNDULATING FINS AND FILAMENTS
AS ESSENTIAL ACTUATORS
OF
UNDER WATER LIFE FORMS
Der Technischen Fakultät
der Friedrich–Alexander Universität Erlangen–Nürnberg
zur Erlangung des Doktorgrades
Dr.–Ing.
vorgelegt von
Emanuela Kos
aus Timişoara
STRÖMUNGSERZEUGUNG
DURCH UNDULIERENDE
FLOSSEN UND FILAMENTE
ALS ESSENTIELLE ANTRIEBE FÜR
UNTERWASSERLEBEWESEN
Der Technischen Fakultät
der Friedrich–Alexander Universität Erlangen–Nürnberg
zur Erlangung des Doktorgrades
Dr.–Ing.
vorgelegt von
Emanuela Kos
aus Timişoara
Als Dissertation genehmigt
von der Technischen Fakultät
der Friedrich–Alexander Universität Erlangen–Nürnberg
Tag der mündlichen Prüfung: 17.11.2014
Vorsitzende des Promotionsorgans: Prof. Dr.–Ing. habil. Marion Merklein
Gutachter: Prof. Dr.–Ing. habil. Antonio Delgado
Prof. Dr. Cornelia Denz
Abstract
In various biological systems, filaments (cilia) have different essential functions
like feeding and shifting which allow the persistence of micro–organisms. With
regard to technical applications there are ciliates, namely, Opercularia asymmetrica,
which participate to the formation of Granular Activated Sludge (GAS) as a result
of their cilia beat and induced micro–flow in the near field of the ciliates. This novel
and promising technology can be used for improving the purification of wastewater
due to a higher settling velocity of the GAS in comparison to conventional activated
sludge. Furthermore, the results gained by the investigation of the cilium beat can
be utilised for the development of micro–mixers to enhance mass and heat transfer
processes in flows.
In general, it is proven that the transfer of bio–mechanical expertise to technical
scale applications is an important feature in bionics. Biological flows induced by
under water life forms are developing to an important basic research topic in fluid
mechanics and biology. The present work focuses also on seahorses, Hippocampus
reidi. Due to their anatomy, seahorses have a very low ratio between the area of
the active moving fins and the passive, stiff as well as upright swimming body. In
comparison to other fishes, they swim slow but they possess an exceptional ability to
stabilise and control their locomotion precisely in all directions due to the flow that
is induced by their fins. The knowledge about kinematics of fins and the flow field
in the vicinity of fins can be utilised for the development of under water vehicles as
such required to perform repairs on drilling platforms.
This work delivers some extended basic understanding of complex and efficient
undulating bio–kinetic processes of under water life forms which can be suggested
for novel technical applications or improve the existing ones over a wide scale range
iv
v
from micro scale (Opercularia asymmetrica) to macro scales (Hippocampus reidi) by
means of experimental techniques and numerical approaches (i.e., Computational
Fluid Dynamics).
Important results achieved during the investigations of Opercularia asymmetrica are related to the experimental and analytical description of the cilia motion
pattern and discussions on their beat efficiency. It is shown that the cilia of Opercularia asymmetrica do not execute planar oscillations. During each beat and stroke
execution, the cilium tries to strike out a maximum amplitude, leading to a continuous elliptical motion. Therefore, important parameters like two–dimensional and
three–dimensional cilium velocity, the half diameter (in focal plane displacement of
the cilium) as well as the half depth (out of focal plane displacement of the cilium)
of the ellipse trajectory have been determined experimentally by using a dynamical
scanning in layers method. A direct dependency is found between the two and
three–dimensional cilium velocities and the beat frequency. It is found that the ellipse depth decreases when the cilium velocity increases, leading to flattened ellipse
trajectories at higher velocities. This way the cilium performs a shorter distance
within the same time interval that requires less energy from the micro–organism.
The undulatory motion pattern of the cilia row develops because of a temporal shift
between consecutive cilia. The observed time–shift is decreasing with increasing
velocity of the cilia, leading to a faster propagation of the mechatronal wave. The
performed set of experiments showes that the motion of the cilia is undulatory and
periodical while the induced flow is continuous, steady and consists of two counter
rotating vortex pairs (Zima et al. (2009)). The dominance of the molecular momentum transport in micro scale can explain these findings, where the surrounding
medium is only slowly reacting on the undulatory motion of cilia.
Moreover, in the present study correlations between the fin motion of Hippocampus reidi, the flow induced by the fins and the precise manoeuverability of seahorses
during stagnation are found. From the conducted numerical and experimental investigations of the fin motion and the induced flow, it was observed that the undulating
motion of fins induces a flow which is steady and laminar. In these small scales where
the viscous effects are dominant, the reaction of the surrounding medium on the pe-
vi
riodically undulating fin is slow, which leads to a steady induced flow. Additionally,
the fin oscillations are between 30 and 50 Hz and induce a local flow that is not
propagating into the surrounding medium. The profile of the induced flow consists
of two counter rotating vortex pairs whose rotation direction is predetermined by
the propagation direction of the fin wave. The experimental and numerical investigations show that the frequency of the undulating fin influences directly the flow
velocity, leading to higher flow velocities at higher frequencies of the fin. By controlling the fin motion, seahorses can vary the magnitude and direction of the induced
flow. The flow induced thrust allows them to vary the swimming velocity and makes
maneuvering and stabilization in water possible.
vii
Zusammenfassung
In einer Vielzahl biologischer Systeme haben Filamente (Cilien) unterschiedliche
essentielle Funktionen, wie Nahrungsaufnahme und Fortbewegung, wodurch sie das
Überleben und Fortdauern der Mikroorganismen ermöglichen. Im Hinblick auf technische Anwendungen existieren Ciliaten wie Opercularia asymmetrica, die aufgrund
ihres Cilienschlages und der damit induzierten Mikroströmung im Nahfeld der Ciliaten das Entstehen von granularem Belebtschlamm (GBS) ermöglichen. Diese neue
und vielversprechende Technologie kann aufgrund der schnelleren Sinkgeschwindigkeit
des GBS im Vergleich mit konventionellem Belebtschlamm zu einer verbesserten Abwasseraufbereitung führen. Die Ergebnisse, die aus den Untersuchungen des Cilienschlages erhalten werden, können zur Entwicklung von Mikromischern genutzt werden, die Transportprozesse von Masse und Wärme in Strömungen verbessern.
Allgemein erweist sich die Übertragung biomechanischen Wissens auf technische
Anwendungen in der Bionik als Gewinn, weshalb sich biologische Strömungen, die
durch Unterwasserlebewesen induziert werden, gleichermaßen zu einem wichtigen
Forschungsthema in der Strömungsmechanik und in der Biologie entwickeln. Die
vorliegende Arbeit befasst sich demzufolge auch mit Seepferdchen der Gattung Hippocampus reidi, die aufgrund ihrer Anatomie ein sehr kleines Verhältnis zwischen
den Flächen der aktiven Flossen und des steifen, aufrecht schwimmenden Körpers
aufweist. Obwohl diese Fischgattung sehr langsam schwimmt, verfügen sie über
die Ausnahmefähigkeit, ihren Körper mit Hilfe der flosseninduzierten Strömung zu
stabilisieren und ihre Fortbewegung sehr präzise in allen Raumrichtungen zu kontrollieren. Das Wissen über die Kinematik der Flossen und der induzierten Strömung
kann zur Entwicklung von Unterwasservehikeln genutzt werden, die etwa Reparaturarbeiten an Bohrinseln durchführen.
Diese Arbeit liefert anhand von experimentellen und numerischen Untersuchungen, angefangen von einer Mikroskala (Opercularia asymmetrica) bis zu einer Makroskala (Hippocampus reidi), ein vertieftes Grundwissen auf dessen Grundlage komplexe, effiziente biokinetische Prozesse verstanden werden können, die für neue technische Anwendungen oder zur Verbesserung der existierender Technologien genutzt
viii
werden können.
Die experimentelle und analytische Beschreibung des Bewegungsmusters von
Cilien sowie deren Schlageffizienz zählen zu den zentralen Ergebnissen, die während
der Untersuchungen von Opercularia asymmetrica erzielt wurden. Es wurde gezeigt,
dass die Cilien der Gattung Opercularia asymmetrica keine planare Oszillationen
ausführen. Da jedes Cilium während des Schlages mit einer maximalen Amplitude auszuholen versucht, führt zu einer kontinuierlichen und elliptischen Bewegung. Aus diesem Grund wurden wichtige Parameter wie die zwei- und dreidimensionale Ciliengeschwindigkeit, die radiale Halbachse (Bewegung entlang der fokalen
Ebene) und die vertikale Halbachse (Bewegung senkrecht zur fokalen Ebene) der
Ellipse durch die Anwendung einer dynamischen Abtastmethode in Schichten experimentell ermittelt. Die Ergebnisse zeigen eine direkte Abhängigkeit zwischen
Schlagfrequenz und der zwei- und dreidimensionalen Ciliengeschwindigkeit. Die Ellipsentiefe nimmt mit zunehmender Schlaggeschwindigkeit ab, was zu einer flacheren
Ellipsenbahn bei höheren Geschwindigkeiten führt. Damit legt das Cilium eine
kürzere Strecke im gleichen Zeitintervall zurück, was einen geringeren Energieeintrag benötigt. Die wellenförmige Bewegung mehrerer Cilien ergibt sich aus einer
zeitlichen Verschiebung zwischen aufeinander folgenden Cilien. Diese zeitliche Verschiebung nimmt mit zunehmender Schlaggeschwindigkeit ab, was zu einer Beschleunigung der mechatronen Welle führt. Die erzielten Ergebnisse haben gezeigt, dass
die Bewegung von Cilien wellenförmig und periodisch ist, während die induzierte
Strömung kontinierlich, stationär und aus zwei entgegengesetzt rotierenden Wirbelpaaren besteht (Zima et al. (2009)). Diese kann durch die Dominanz des molekularen Impulstranportes im Mikroskala erklärt werden, wonach das umgebende Medium sehr langsam auf die oszillierende Bewegung der Cilien reagiert.
Darüber hinaus wurden Zusammenhänge zwischen der Flossenbewegung von
Hippocampus reidi, der flosseninduzierten Strömung und der präzisen Manövrierfähigkeit während der Stagnation aufgezeigt. Aus den durchgeführten numerischen
und experimentellen Untersuchungen der Flossenbewegung und der induzierten Strömung geht außerdem hervor, dass die wellenförmige Bewegung der Flossen eine
stationäre und laminare Strömung induziert. Die stationäre Strömung stellt eine
ix
Konsequenz dieser kleinen Skalen dar, in welchen Viskositätseffekte dominieren
und die Reaktion des umgebenden Mediums auf die periodischen Wellenbewegung
der Flosse langsam erfolgt. Zudem wurde beobachtet, dass die Oszillationen der
Flossen, die zwischen 30 und 50 Hz liegen, eine lokale Strömung erzeugen, die sich
nicht in das umgebende Medium ausbreitet. Das Profil der induzierten Strömung
besteht aus zwei entgegengesetzt rotierenden Wirbeln, deren Rotationsrichtung von
der Wellenausbreitungsrichtung der Flosse vorgegeben wird. Die experimentellen
und numerischen Untersuchungen haben ergeben, dass die Frequenz der undulierenden Flosse die Strömungsgeschwindigkeit direkt beeinflußt, wobei höhere Frequnezen
der Flosse ein höhere Strömungsgeschwindigkeit erzeugen. Durch die Kontrolle der
Flossenbewegung können Seepferchen die Stärke und die Richtung der induzierten
Strömung variieren. Der durch die Strömung erzeugte Schub ermöglicht Variationen
in der Schwimmgeschwindigkeit und trägt dadurch zur Stabilisierung und Fortbewegung im Wasser bei.
To my dear family and friends
Acknowledgements
I would like to express my gratitude to my supervisors, Prof. Dr.–Ing. habil. Antonio Delgado and Prof. Dr.–Ing. habil. Cornelia Rauh for giving me the opportunity
to work on this interesting research project. I thank Prof. Dr. Cornelia Denz and
Prof. Dr.–Ing. habil. Aldo Boccaccini for acting as my second examinors. I also
thank Prof. Dr. Andreas Wierschem for being the chairman of the doctoral viva.
Special thanks to Horst Weber, for his great ideas and help during the practical work.
Thanks to all the colleagues of LSTM and the members of the LSTM workshop for
making this work possible in a helpful and loyal way.
xi
Contents
Abstract
iv
Acknowledgements
xi
List of Figures
xv
List of Tables
xix
List of Publications
xx
1 Introduction
1
1.1
Appearance of undulating and oscillating motions in nature . . . . . .
1.2
Motivation and objectives of the present study on Opercularia asymmetrica and Hippocampus reidi . . . . . . . . . . . . . . . . . . . . .
5
1.2.1
Opercularia asymmetrica . . . . . . . . . . . . . . . . . . . . .
5
1.2.2
Hippocampus reidi
7
. . . . . . . . . . . . . . . . . . . . . . . .
2 Some most relevant aspects in literature
2.1
1
10
Optical visualisation techniques in biological systems . . . . . . . . . 10
2.1.1
Optical visualisation methods in micro scale - brief literature
review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2
Optical visualisation methods in macro scale - brief literature
review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3
2.2
Experimental evaluation methods . . . . . . . . . . . . . . . . 15
Numerical approaches for flapping and undulating motions . . . . . . 20
2.2.1
Brief literature review . . . . . . . . . . . . . . . . . . . . . . 20
xii
Contents
2.2.2
xiii
Numerical evaluation methods . . . . . . . . . . . . . . . . . . 22
Governing equations of fluid mechanics . . . . . . . . . . . . . 22
Harmonic wave equation . . . . . . . . . . . . . . . . . . . . . 23
Numerical moving grid method . . . . . . . . . . . . . . . . . 24
3 Materials and methods
3.1
26
Experimental procedures . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1
µ–PTV Experimental evaluation method . . . . . . . . . . . . 26
µ–PTV Setup and calibration . . . . . . . . . . . . . . . . . . 26
µ–PTV Evaluation . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.2
PIV Experimental evaluation method . . . . . . . . . . . . . . 32
PIV Setup and evaluation . . . . . . . . . . . . . . . . . . . . 32
3.1.3
3.2
Experimental drag force measurements . . . . . . . . . . . . . 34
Numerical procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.1
Numerical drag force calculation . . . . . . . . . . . . . . . . . 37
3.2.2
Numerical kinematic investigations of fins . . . . . . . . . . . 40
4 Results and discussion
4.1
45
Motion pattern of filaments . . . . . . . . . . . . . . . . . . . . . . . 45
4.1.1
Two–dimensional investigations of the cilium motion at a stagnant focal plane . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.1.2
Three–dimensional motion pattern of the cilium at moving
focal plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2
4.1.3
Motion pattern of a cilia collective . . . . . . . . . . . . . . . 54
4.1.4
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Motion pattern and flow control of fins . . . . . . . . . . . . . . . . . 57
4.2.1
Swimming capability of seahorses compared to those of other
fishes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.2
Fin kinematics and flow pattern induced by fins . . . . . . . . 62
Fin kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Detailed numerical investigations of the flow pattern induced
by fins . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Contents
xiv
Detailed experimental investigations of the flow pattern induced by fins . . . . . . . . . . . . . . . . . . . . . . 71
4.2.3
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5 Summary and outlook of the present study on Opercularia asymmetrica and Hippocampus reidi
81
5.1
Opercularia asymmetrica . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2
Hippocampus reidi
Bibliography
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
86
List of Tables
2.1
Seeding particles implemented in the PIV measuring technique for
visualisation of air and water flows . . . . . . . . . . . . . . . . . . . 17
4.1
Time shift ∆tshif t between consecutive cilia as a function of the cilia
velocity vs and frequency f . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2
Drag coefficients and Reynolds numbers for different fish species . . . 62
4.3
Averaged maximum velocity over one undulation period (sampled at
2.5 mm away from the fin outlet) and the corresponding frequencies . 70
4.4
Maximum flow velocities, which are induced at the dorsal and pectoral
fin and the corresponding frequencies . . . . . . . . . . . . . . . . . . 79
xv
List of Figures
1.1
Flow pattern induced by the undulatory cilia motion of one cillium
(left image) and a colony of ciliates (right image) at 50 fold objective
magnification (Zima et al., 2009) . . . . . . . . . . . . . . . . . . . .
2.1
Basic PTV/PIV setup consisting of a light source (laser), working
area (light sheet plane with seeding particles) and detection (camera)
2.2
6
16
Schematic desccription of a double pulsed Nd:YAG-Laser system; (1)
pump cavity, (2) back mirror, (3) variable reflectivity output mirror,
(4) Q–switch, (5) λ/4 plate, (6) polarizer, (7) mirror (50% transmission), (8) Brewster polarizer, (9) filter, (10) phase angle adjustment,
(11) delaying–plate (λ/2), (12) beam trap . . . . . . . . . . . . . . . 18
3.1
Time intervals characterising one image exposure of the camera . . . 28
3.2
µ-PTV setup consisting of a microscope Axiotech 100 (Carl Zeiss),
high speed CMOS camera (PCO AG) and piezo actuator (piezosystem
jena) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3
Calibration image for the µ-PTV measurements . . . . . . . . . . . . 30
3.4
Cilium images after contrast enhancement and edge detection at the
beginning (A) and end (B) of an effective stroke . . . . . . . . . . . . 31
3.5
PIV experimental setup consisting of pulsed Nd-YLF laser, high speed
camera (Photron Phantom v12) and aquarium with seahorses . . . . 33
3.6
Alignment of the seahorse in the measurement compartment between
laser light (green line) and the movable plate (blue line). The distance
between investigated fins and laser light sheet plane varied between
0 and 4 mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
xvi
List of Figures
3.7
xvii
Setup consisting of a opened ceiling water channel, centrifugal pump,
a laboratory balance, a mechanism with two lever arms l1 = 0.13 m
and l2 = 0.22 m to transfer the flow force acting on the seahorse
balance point to the laboratory scale and a seahorse casting out of
brass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.8
Dimensions and the components of the water channel used to determine the flow force (F2 ) acting on the balance point of the seahorse
(red point) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.9
Geometry and re–meshed surface for the hydrodynamic investigations
of the seahorse structure in a front position of the seahorse relative
to the inlet flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.10 Monitoring of the drag coefficient at increasing number of inner iterations at 0.1 m/s inlet velocity . . . . . . . . . . . . . . . . . . . . . 39
3.11 Fin undulation during seahorse swimming . . . . . . . . . . . . . . . 40
3.12 Geometry and re–meshed surface used for the fin undulation simulations, with the two boundaries fin inlet and fin outlet . . . . . . . . . 41
3.13 Progression of the maximum flow velocity (averaged for each period)
with increasing number of time steps. The maximum flow velocity
was sampled in a plane section (perpendicular to the fin) 1 mm in
front of the fin tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.14 Deformed fin mesh image at a certain time step . . . . . . . . . . . . 43
4.1
Captured original images of the cilium motion during the active (faster)
stroke at a stagnant focal plane . . . . . . . . . . . . . . . . . . . . . 47
4.2
Elliptical model of the cilium trajectory (Juelicher et al., 1996). The
motion between the points 1 to 4 represents the active stroke (means
for example 6 ms), the motion backwards represents the recurring
stroke (means for example 12 ms). In seldom cases the time duration
of the effective stroke is equal to the one of the recurring stroke . . . 48
4.3
Two–dimensional cilium velocity vs in the focal plane as a function
of the cilium frequency . . . . . . . . . . . . . . . . . . . . . . . . . . 49
List of Figures
4.4
xviii
Ellipse half diameter a (in focal plane displacement) as a function of
the cilium frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.5
Three–dimensional cilium velocity vsz as a function of the cilium frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.6
Ellipse half depth b (out of focal plane displacement) as a function of
the cilium frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.7
Distribution of the total drag coefficient (shear and pressure) with
increasing Reynolds number . . . . . . . . . . . . . . . . . . . . . . . 59
4.8
Velocity field at Re = 2000, in a plane section which is cutting the
seahorse body through the abdomen and which is perpendicular to
the upright swimming position of the seahorse . . . . . . . . . . . . . 60
4.9
Quadratic dependency of the maximum pressure at the stagnation
point from the Reynolds number. The pressure component is the
main source for drag on the seahorse body . . . . . . . . . . . . . . . 60
4.10 Fin deformation during one undulation period of 20 ms at a fin frequency of 50 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.11 Induced velocity vector field at a fin frequency of 50 Hz in a plane
section which is placed perpendicular to the fin and 2.5 mm away from
the undulating fin; (A) velocity field for a positive angular velocity;
(B) velocity field for a negative angular velocity . . . . . . . . . . . . 67
4.12 Plot of the surface averaged velocity evaluated in a plane section
which is placed perpendicular to the undulating fin and 1 respectively
2.5 mm away from the undulating fin . . . . . . . . . . . . . . . . . . 69
4.13 Influence of different fin oscillation frequencies on the Reynolds number of the induced flow . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.14 Characteristic flow pattern induced by the dorsal fin (at a fin frequency of 50 Hz and vertical downwards propagation of the fin wave)
and pectoral fin (at a fin frequency of 30 Hz and vertical upwards
propagation of the fin wave) . . . . . . . . . . . . . . . . . . . . . . . 72
List of Figures
xix
4.15 Development of the flow induced by the dorsal fin within short time
steps of 5 ms, at a fin frequency of 50 Hz. The white curve represents
the contour of the seahorse body and of the dorsal fin . . . . . . . . . 74
4.16 Development of the flow induced by the pectoral fin within short time
steps of 5 ms, at a fin frequency of 30 Hz. The white curve represents
the contour of the seahorse with the pectoral fin . . . . . . . . . . . . 75
4.17 Shear rate distribution of the induced flow at the dorsal (50 Hz ) and
pectoral fin (30 Hz ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
List of Publications
1) Kos, E., Rauh, C., Delgado, A. (2010) Fluid mechanical investigations of
seahorse locomotion, Presented at Euromech conference in Bad Reichenhall 2010.
2) Kos, E., Rauh, C., Delgado, A. (2010) Analysis of the flow induced by the
undulatory fin motion of seahorse, Presented at GALA conference in Cottbus 2010,
pp. 28 1–10.
3) Kos, E., Rauh, C., Delgado, A. (2009) Bio–compatible visualisation of micro
flow and periodic reciprocating cilia beat induced by Opercularia asymmetrica with
micro particle image velocimetry and micro particle tracking velocimetry, Presented
at GALA conference in Erlangen 2009, pp. 57 1–8.
4) Zima–Kulisiewicz, B.E., Kos, E., Delgado, A. (2009) Biocompatible visualization of flow fields generated by micro–organisms, Imaging Measurement Methods
for Flow Analysis – Results of the Priority Programme 1147, Springer Verlag, pp.
269–278.
xx
Chapter 1
Introduction
1.1
Appearance of undulating and oscillating motions in nature
This chapter will give an overview of oscillating and undulating kinematics applied by micro organisms, insects, birds and fishes. Furthermore, the impact of these
kinematics on surrounding medium will be discussed to show their importance in
propulsion and locomotion.
Starting form a very small scale there is the hypothesis that life can only exist
if motion exists. Smallest micro–organisms need the motion of their flagella or cilia
to achieve propulsion. They guarantee in a certain way the movement and agility
of these small creatures in media with various viscosities. These highly complex
filaments which perform a propelling motion consist of three different parts: paddle,
rotor and motor. The direction of rotation or oscillation decides whether they are
advancing or drafting (Alberts et al., 1995). Cilia are also responsible for many
essential biological functions like feeding and progeny. Their study has been of great
interest for more than two centuries. Thus, at the beginning of the 20th century
Gray, already mentioned the diversity of ciliary beat forms (Gray, 1922). Gray also
found that the typical two phase beating cycle (effective and regenerating stroke) as
a common element of different beating forms by stroboscopic observation methods
(Gray, 1930).
1
1.1. Appearance of undulating and oscillating motions in nature
2
In recent years cilia achieved also great medical interest, since fluid movements
induced by cilia play a decisive role in early development of embryos in vertebrates,
particularly for symmetry breaking events. Several researchers focused on the cilia
within the ventral node, which is placed on the surface of the embryo (Nonaka et
al., 1998; Okada et al., 1999; Supp et al., 1999; Takeda et al., 1999). Whereas in
earlier studies these cilia were considered as immobile, Nonaka showed that mammal
cilia perform a whirling motion which was later described and modeled as three–
dimensional conical rotation tilted to the posterior and able to produce the observed
leftward flow (Cartwright et al., 2004; Brokaw, 2005; Smith et al., 2008). How
this flow induces exactly the determination of left/right asymmetry is still issue of
controversial discussions among researchers, who prefer either the model of chemo–
sensing or the model of mechano–sensing (Nonaka et al., 1998; McGrath et al.,
2003).
Another phenomenon that has been deeply discussed is the mechatronal coordination of large cilia and flagella population. Due to experiments performed by
Machemer (1972) and calculations by Blake (1974), for a long time hydrodynamical
coupling between the cilia and the surrounding fluid has been assumed to be the
reason for the wave like beating coordination.
In larger scales highly complex and aerodynamically efficient phenomena are
taking place as well. Insects and birds use the flapping motion of their wings to
achieve propulsion, lift and thrust. When air passes a sharp leading edge of insect
wings, it forms a leading edge vortex (LEV) on the upper side of wings. The
LEV is directed due to this flapping motion in spiraled and stable ways along the
leading edge of wings toward the wings tip. This way a delayed stall is achieved.
Where the vortex flow appears, a lower static pressure is achieved increasing the
lift force on the flying animal (Ellington et al., 1996). Further investigations on
the LEV were performed by Wakeling and Ellington (1996). Their investigations on
Sympetrum sanguineum and Calopteryx splendence showed that these two insects
have the highest lift coefficients of 1.07 and 1.15 respectively. Since Calopteryx
splendence has identical fore wing and hind wing whereas Sympetrum sanguineum
has two different ones, Wakeling and Ellington (1996) concluded that the flight
1.1. Appearance of undulating and oscillating motions in nature
3
aerodynamic is affected by the shape of the wings as well.
The flight of dragonfly is among many insects the most interesting one, since
it produces the highest lift. Dragonflies are able to control and adjust their flight
musculature, stroke frequency (approximately 30 Hz ), amplitude, flapping phase
as well as vary independently the angle of attack for all four wings. According to
Thomas et al. (2004) a fast increase of attack angle is the most important factor for
the formation and shedding of the LEV. The second tandem wing of the dragonfly
can further increase the efficiency and thrust of the insect flight (Tuncer and Platzer,
1996).
Although birds and bats have generally a lower flapping frequency than insects,
the formation of LEV can be observed as well. LEV formation on the top of the hand
wing of an Apus apus wing model and LEV attachment during slow forward flight
of bat were observed by Videler et al. (2004) and Mujires et al. (2008) respectively.
The decryption of the kinematics which is used by insects, birds and fishes to
perform locomotion had initially attracted lots of studies. For instance, the locomotion of fishes was investigated by Sir James Lighthill, who is a famous researcher in
the field of fluid mechanics and aero–acoustics. His theory is known as the elongated
body theory. He found out by using analytical investigations that fishes can induce
an unsteady flow and put much higher volume of surrounding water into motion than
the volume of their own body by means of an oscillating tail (tail fin) at a relatively
stiff front body. Hence, the actuated water reacts back on the fish, transferring
momentum to the swimming fish and enabling this way thrust into the direction
of locomotion (Lighthill, 1971). These highly complex and efficient processes were
mainly transferable on low scale applications like the development of small under
water vehicles. Still fishes with their high variety of fin and body actuation patterns
are worth to be investigated in more detail, to increase the transfer potential on
technical applications.
Sfakiotakis et al. (1998 and 2001) recapitulated different types of fish swimming.
Eels like Anguilla anguilla can perform locomotion by undulating their whole body
which is called anguilliform swimming. Thunniform fishes like sharks and mackerels
have a rather stiff front body and produce strong propulsion by means of the flexible
1.1. Appearance of undulating and oscillating motions in nature
4
tail fin. Although the manoeuvrability is reduced in comparison to the anguilliform
swimming, the tunniform swimming is considered as the most efficient way to achieve
propulsion in the reign of fishes. It produces high speeds over a long distance. High
manoeuvrability and stability can be achieved by the oscillation and undulation of
the pectoral fins (labriform swimming). During labriform swimming amplitude and
frequency of motion can be adjusted depending on the fish species and the performed
manoeuvre by the fish. With an adequate anatomical feature (distance between the
fins; body shape) and a good coordination of the fin oscillations, labriform swimming
fishes can achieve different locomotion velocities and manoeuvres.
In general, fishes can produce sufficient propulsion and lift forces for swimming
due to the induced flow by their undulatory body and fin motion. In addition, they
can adapt well to streamlines of flow due to their anatomy, so that the drag force
against water flow can be reduced.
Drucker and Lauder (2001) investigated intensively the structure of wake flow
during sunfish swimming where the propulsion takes place mainly due to oscillating
motion of tail (tail fin). Two distinct type of wake flows were observed. One of them
is induced by oscillations of tail and the other one is induced by motion of dorsal
fin (median fin). Due to a suitable interaction between the two wake flows, sunfish
is able to achieve lower drag force and more thrust during swimming.
Triantafyllou et al. (2000) found that fishes are able to produce high and efficient
forces for a short time due to a good coordination of the body and tail fin motion.
Therefore, the energy losses from the wake flow are kept at a very low level for a
certain time interval. These observations can be transferred to oscillating air foils in
order to control the wake flow energy, to improve propulsion and lift. Detached eddies of the front oscillating foil can interact destructively with the detached vortices
of the rear foil. This impact decreases the energy of the wake flow and increases
the propulsion energy of the whole system. An optimal combination of flapping
frequency, amplitude and phase shift of the foils as well as position of the foils in
the flow, leads to an enhanced propulsion and lift of the complete system (Tuncer
and Platzer, 1996; Kaya and Tuncer, 2009). In recent years flapping foils became
an interesting research topic especially for aircraft and marine industry.
1.2. Motivation and objectives of the present study on Opercularia
asymmetrica and Hippocampus reidi
1.2
5
Motivation and objectives of the present study
on Opercularia asymmetrica and Hippocampus reidi
Both under water life forms Opercularia asymmetrica (micro scale) and Hippocampus reidi (macro scale) are using the undulating motion of their filaments and
fins at a relatively stiff main body, in order to induce a near flow field and to achieve
efficient mixing during feeding, stabilisation, locomotion and manoeuvre. Both of
these under water life forms are very interesting research topics. Their actuation
pattern can be used for the development of future micro mixing technologies or
under water propulsion systems.
1.2.1
Opercularia asymmetrica
In this section, motivation which initiated the research about the cilia kinematics
of Opercularia asymmetrica is given. Additionally, some established micro mixing
applications are presented and the implemented methods to pursue the objectives
of the present study and to understand the kinematics of cilia.
The undulatory motion of the cilia collective which was observed to be aligned
in two rows at the mouth of the sessile protozoon Opercularia asymmetrica, induce
a vortex flow (see Figure 1.1) which allows transport of the nutrients from the
surrounding medium into their immobile body. At the same time the induced flow
enhances the formation of GAS which offers a habitat for ciliates (Zima et al., 2009).
The cilia motion represents a very efficient method to bring substances and micro
particles from a bulky phase into direct contact with an immobile surface. The
knowledge about the cilia kinematics can be used for development of new micro
mixing technologies.
Some micro mixing processes have been already developed which are using either
an electrical excitation to stir very small volumes of solution (µl), or an external
rotating magnetic field to rotate a micro magnetic stir bar (Oddy et al., 2001; Lu
et al., 2002; Yi et al., 2002; Mensing et al., 2004; Ryu et al., 2004). Micro mixing
1.2. Motivation and objectives of the present study on Opercularia
asymmetrica and Hippocampus reidi
6
Figure 1.1: Flow pattern induced by the undulatory cilia motion of one cillium (left image) and a colony of ciliates (right image) at 50 fold objective magnification
(Zima et al., 2009)
can be also induced by ultrasonic vibration or bubbles which are vibrated by the
external sound field (Liu et al., 2002; Yang et al., 2001). Khatavkar et al. (2007)
proposed an interesting numerical approach, namely, an active micro mixer which
is inspired by motion of cilia. Additionally, artificial cilia or micropillars can be
used for under water flow sensing or turbulent boundary layer sensing (Fan et al.,
2002; Bruecker et al., 2005). Consequently, the application of such cilia in sensor
technologies should also be taken into consideration.
To the best knowledge of the author, no research on cilia kinematics of Opercularia asymmetrica has been reported in literature. Therefore, the present study
provides a description of two–dimensional (in focal plane direction) and three–
dimensional (in and out of focal plane direction) motion pattern applied by one
cilium and a collective of cilia. In addition, phase shift between two consecutive
cilia was determined. The visualisation of the cilium beat and the determination of
the cilium velocity were carried out experimentally by using micro particle tracking
velocimetry (µ-PTV). The effect of the cilia motion on the induced micor flow was
elaborated as well.
1.2. Motivation and objectives of the present study on Opercularia
asymmetrica and Hippocampus reidi
1.2.2
7
Hippocampus reidi
This section regarding Hippocampus reidi is organized as follows. First, the
motivation is presented which led to fin kinematics and flow control research on
Hippocampus reidi. Then, several existing technical implementations to achieve
under water propulsion are presented. Finally, the proposed objectives of the study
as well as the numerical and experimental methods are given.
Seahorses, namely, Hippocampus reidi belong to the species of fishes. In comparison to other fish species, they have different locomotion and body shape. Their
pendulous locomotion is slow (few cm/s) and they possess an upright swimming,
edgy as well as stiff body with no streamlining (Kuiter, 2000). Although seahorses
are very vulnerable species due to their slow swimming, they can still survive over
long periods of time since they are very well adapted to their ecosystem (algae).
The optical and motion camouflage system which makes seahorses not perceivable
to their natural enemies is main reason for this. The color of their skin is similar to
the colour of their habitat (algae) and their pendulous motion is alike the motion of
algae.
Moreover, they are able to manoeuvre and stabilise their levitating body not only
by means of their swim bladder but also with the aid of small and high frequency
(20–60 Hz ) undulating actuators (fins) (Flynn and Ritz, 1999). Their translational
motion in all directions is propelled by synchronous kinematics of the dorsal and
pectoral fins. The high manoeuvrability of seahorses has a high transfer potential to
future technical applications. They use a flow for stabilization which almost cannot
be perceived by surrounding creatures. This shows that the induced flow might
have a very small extent which makes them very interesting for military applications
like under water drones. Furthermore the knowledge about the fin kinematics, the
induced flow and consequently high manoeuvrability of seahorses can be utilised for
the development of under water vehicles to perform repairs on under water drilling
platforms. Also these insights are assumed being possibly transferred to oscillating
discs in combustion engines to enhance turbulence and produce a more homogeneous
chemical and temperature profile.
The average fin oscillation frequency of fishes is approximately 1 Hz. As a re-
1.2. Motivation and objectives of the present study on Opercularia
asymmetrica and Hippocampus reidi
8
sult, the fin frequency of seahorses is rather comparable to the beating frequency
of insects. The advancing ratio of seahorses (Hippocampus reidi; 0.3) and insects
(Manduca sexta; 0.54) are similar and less than unity which indicates that unsteady
flow conditions and unsteady effects need to be taken into consideration for both
species (Delgado et al., 2009).
In fish bionics several investigations have been reported. In 1985, Nachtigall et al.
induced coupled bending and rotating oscillations of a fin model in a water channel.
In 1995, the brothers Triantafyllou built a fish model with an oscillating tail fin.
Kato (1998) achieved, by the feathering and lead/lag motion of artificial pectoral
fins, a slow swimming forwards and backwards as well as turning in one plane of
a fish robot. In 2005, Liu et al. built a fish robot and in 2006 Willy developed a
robotic system mimicking the undulating motion of a fish fin.
The first investigation on seahorse locomotion were performed by Breder and
Edgerton (1942). They implemented stroboscopic light and a motion camera to
analyse fin movement. Then, in 1976, cinematography investigation of Blake enabled
some analysis on translational motion of seahorses. Consi et al. (2001) modeled for
the first time the kinematics of seahorse fin ray, by using a moving membrane. In
2004, first biological classification of seahorses was provided by Lourie et al. However, the flow which is induced by their undulating fins and their spectacular ability
to manoeuvre and stabilise their whole body with small actuators were not completely understood. Therefore, there is a need for further investigations in this area
to understand clearly the mechanisms of actuation which are used by Hippocampus
reidi and apply the knowledge to future technical applications.
The hydrodynamics of the seahorse structure was analysed by using numerical
tools, namely, STAR-CCM+ which is a commercial software, in order to understand
what are the reasons for the slow swimming of seahorses. First drag coefficient was
calculated numerically, then the flow field around seahorse structure was simulated
with STAR-CCM+. The drag coefficient of the seahorse structure was evaluated
experimentally and compared with the numerical findings, as well as with the drag
coefficient of other fish species. The fin (dorsal and pectoral) induced flow which has
a stabilising effect on the seahorse body during locomotion, stagnation or sideways
1.2. Motivation and objectives of the present study on Opercularia
asymmetrica and Hippocampus reidi
9
motion was analysed two–dimensionally by using particle image velocimetry (PIV)
technique. Moreover, the time dependency of the characteristic flow patterns which
are induced by dorsal and pectoral fins during stagnation were investigated in detail
experimentally.
In a joint project where research on seahorse was performed, Krupczynski (2009)
showed that seahorses possess different fin actuation patterns. They are able to vary
undulation frequency, amplitude, wave number and wave traveling direction of the
fins. In this study the fin kinematics was found experimentally with particle tracking
velocimetry (PTV). During the two–dimensional PTV measurements, the fin was
hardly accessible and fully visible in the laser light. Only few cases were found, where
it was possible to track the fin deformation. Hence, the experimental achieved PTV
data were used as input for first numerical simulations. Then the effect of modified
fin parameters (fin frequency and wave traveling direction) on the induced flow were
investigated numerically in detail. In the present study numerical results of the
induced flow were validated successfully against the measurements.
The experimental investigations of the flow which is induced by fins, indicated
the important role of this flow in the locomotion control of seahorses. In the present
study it was found that especially the frequency of the undulating fin and the direction in which the wave of the fin is propagating are influencing the flow in the near
field of the seahorse significantly.
Chapter 2
Some most relevant aspects in
literature
2.1
Optical visualisation techniques in biological
systems
In the present study optical visualisation methods were implemented both in
micro scale and macro scale. The micro scale visualisation helps to investigate the
cilia motion of Opercularia asymmetrica and the flow which is induced by the cilia
motion. In macro scale, the fin motion of Hippocampus reidi and the flow which is
induced by the fin motion was found. Hence, this section contains a brief literature
review of the implemented optical visualisation methods in micro and macro scale
which are relevant for this study. That followed, the experimental evaluation method
which is necessary to conduct the optical investigations is presented in detail as well.
2.1.1
Optical visualisation methods in micro scale - brief
literature review
The investigations on the cilia motion were conducted in the present study with
µ-PTV. Therefore, this section provides a brief literature review of the implemented
µ-PTV techniques for tracking motion of biological and technical systems in micro scale. Micro–flow investigations with µ-PIV which appear in literature will be
10
2.1. Optical visualisation techniques in biological systems
11
exemplified as well.
In early studies of bacteria movement, stroboscopic methods were used by Gray
(1930) who marked a milestone in the two–dimensional study of high frequency
motion. Up till now detailed three–dimensional analysis of motion in micro scale
still remains a challenging task. Berg (1971) traced for the first time the motion
of Escherichia coli bacteria by constantly keeping one bacterium in focus. For this
purpose, he used a complex electronic detection device with integrated fiber optics
to track the position change of a bacterium. The detection device was coupled to
an electromechanical transducer which was moving the box with the bacteria suspension in such a way that the bacterium which was swimming with approximately
50 bacterium diameters per second stayed focused during the whole experiment.
A common method to visualise motion is stereoscopic micro particle tracking/image velocimetry (stereo-µ-PTV/PIV). This method which is implemented in
micro scale as well as in macro scale measurements, uses at least two cameras to
obtain all three velocity components of the tracked object or flow in the focal plane
(micro scale) or in the laser light sheet plane (macro scale). Although Stereo-µPTV/PIV requires a high demand on optical equipment, it was implemented successfully by Maas et al. (1993), Malik (1993) and Bown et al. (2006). Malik et
al. (1993) reconstructed three–dimensional particle trajectories with a three camera
system. Bown et al. (2006) applied a super resolution PTV algorithm to stereoµ-PIV data, for the investigation of flow over a backward facing step in a micro
channel. The authors observed that the accuracy of the out of focal plane velocity
measurement is restricted due to the misalignment of the two focal planes in the
stereo microscope. With this method they were largely able to remove the velocity
deviations and to reduce the experimental uncertainty of the measurements caused
by geometry and location.
Stereo-µ-PTV/PIV using stereo microscopes cannot reach high resolutions due
to numerical aperture of the stereo lens and herewith connected focal plane depth
(Santiago et al., 1998; Lindken et al., 2006). Santiago et al. (1998) reported resolution difficulties in out of focal plane direction after using a microscope with
oil–immersion objective (NA = 1.4, 100 fold optical magnification). Lindken et al.
2.1. Optical visualisation techniques in biological systems
12
(2006) investigated static mixing processes in a T–mixer. The authors developed
a self calibrating three–dimensional stereo-µ-PIV system and evaluation method,
where the refractive indices of the used optics were included. They performed a
three–dimensional scanning (planes separated by 22 µm) of flow in the T–mixer and
found that the error of the velocity component perpendicular to the measuring plane
was below 10 % of the mean flow velocity. Consequently the accuracy of stereo-PIV
technique in macro scale can not be reached.
Due to the above mentioned difficulties, most µ-PTV applications are based
on other methods like digital holographic methods (Hinsch, 2002; Satake et al.,
2006) or techniques which are analyzing diffraction patterns of defocused images
(Willert et al., 1992; Wu, 2005; Wu et al., 2005). Wu et al. (2005) and Wu (2005)
reported about defocused µ-PTV technique with one camera. They observed by
using a conventional microscope with an objective lens that the defocused image of
a fluorescent particle with 1 µm diameter has a bright outer ring due to the spherical
aberration of the lens system. The radius of the ring increases as the particle moves
closer to the lens. This method, which assumes fluorescent particles and an adequate
calibration, was successfully implemented by the authors to track three–dimensional
trajectories of swimming Escherichia coli cells.
Three–dimensional µ-PTV with one camera can be also performed with deconvolution microscopy (Park et al., 2006). Based on a diffraction rings identifying
algorithm the authors performed three–dimensional velocity field measurements of
a creeping flow in a micro channel (100 µm x 100 µm) with a spherical obstacle.
The developed µ-PTV technique uses an epi–fluorescent microscope (NA = 0.75, 40
fold objective magnification) and fluorescent seeding particles (500 nm).
To understand undulatory cilia motion of Opercularia asymmetrica, in the present
work µ-PTV investigations were accomplished two–dimensionally and three–dimensionally.
The two–dimensional investigations (in focal plane direction) of cilium motion were
done with the µ-PTV method. For this method one microscope and one camera
were used. The cilium motion was tracked also three–dimensionally (in and out
of focal plane direction). Therefore, the µ-PTV setup used for two–dimensional
investigations was extended. In addition, a piezo actuator was implemented. The
2.1. Optical visualisation techniques in biological systems
13
piezo actuator moves the objective and consequently the focal plane into out of focal
plane direction. With this method which is comparable to a dynamical scanning in
layers, it was possible to track concomitantly the cilium motion in and out of the
focal plane direction and to determine all three velocity components of the moving
cilium. The complete experimental setup and procedure implemented in the present
study is explained in details in section 3.1.1.
2.1.2
Optical visualisation methods in macro scale - brief
literature review
In the present study PTV and PIV studies were conducted, to understand the
undulatory motion of seahorse fins and their effect on the surrounding medium.
Therefore, this section presents some relevant studies where PIV and PTV techniques were implemented, in order to visualise flapping, undulating motions of fins
and fishes, as well as the flows induced by these motions. Also a brief description of
the achieved insights in these studies are presented.
Anderson et al. (1998) used the digital-PIV technique with one camera to visualize the wake flow induced by a flapping foil and to analyse the effect of different
heaving and pitch amplitudes of a vertically hanging flapping foil at a frequency of
0–0.7 Hz. Performing force measurements in parallel the authors concluded that, under optimal wake conditions, such a system can achieve maximum thrust efficiencies
up to 87 %.
Anderson et al. (2000) conducted boundary layer investigations of two swimming
fish species, Stenotomus chrysops (carangiform swimming) and Mustelus canis (anguilliform swimming), respectively, by using the two–dimensional, two–component
PIV (2D-2C-PIV) technique with one camera. For both swimming species the authors found that the boundary layer thicknesses, friction coefficients and fluid velocities at the border of the boundary layers are oscillating at undulating body motions.
Furthermore, the boundary layer profiles indicated laminar flows at lower velocities
and turbulent flows at higher velocities. In comparison to corresponding rigid fish
bodies, the drag coefficient is reduced due to a delayed separation.
Mueller et al. (1997) visualised the wake flow of a continuously swimming mullet
2.1. Optical visualisation techniques in biological systems
14
with the 2D-2C-PIV technique. Their research leaded to very interesting results.
They were able to couple the modulation of thrust and the shape of the wake flow,
with the ratio between swimming velocity and wave traveling velocity through the
fish body. The authors observed that the wake flow consists of alternating vortices
arranged in double rows, which are separated by an undulating jet. For ratios
smaller than unity the wake flow decays without any changes in shape. For ratios
greater than unity, when the fish decelerates the shape of wake flow changes forming
a single row of oval vortices.
Bluegill sunfish was investigated regarding its mobility by Drucker and Lauder
(2001) with 2D-2C-PIV, by using a 5 W argon laser for illumination and a high
speed video camera with a frame frequency of 250 Hz. The authors observed that
sunfish achieves propulsion at low velocities by means of the paired fins. At higher
velocities (1.1 body lengths per second) the dorsal (median) fin becomes also active.
Furthermore, they visualised the reverse Karman vortex flow induced by the dorsal
fin during steady swimming and side turning. The same authors implemented one
year later the stereoscopic PIV technique (stereo-PIV) with two cameras to visualise
the wake flow induced by the dorsal fin and to perform accurate force calculations
(Lauder et al., 2002).
Naunen et al. (2002) implemented a stereo-PIV technique to visualise wake flow
of swimming rainbow trout at 1.2 body lengths per second. Their measurements
showed that the caudal fin induces little flow forces in vertical direction and strong
flow forces in lateral direction.
Standen and Lauder (2005) used three synchronised high speed cameras with
a frame frequency of 500 Hz to investigate kinematics of median fins (dorsal and
anal) of bluegill sunfish. The role of these fins was found to be very important, since
they keep the body of the fish in balanced swimming position. At steady swimming
velocities, which are above 1.5 body lengths per second, they did not observe any
phase shift between the oscillation of the two fins. At the same swimming velocity a
phase lag between the body oscillation and the oscillation of the fins was observed.
The authors concluded that the anal fin balances the thrust produced by the dorsal
fin and controls additionally the forward thrust of the fish. They also observed that
2.1. Optical visualisation techniques in biological systems
15
a reduced fins area in fast forward swimming mode reduces the drag force against
the flow.
In the present study the flow induced by the action of dorsal and pectoral fins
during seahorse manoeuvring was investigated two–dimensionally with the 2D-2CPIV technique. The fin kinematic was studied two–dimensionally with the 2D-2CPTV method. The 2D-2C-PTV investigations were very restricted due to the poor
optical accessibility of the small fins. Consequently, they were performed in a smaller
extent. With these optical visualisation methods it was possible to investigate the
flow induced by the undulating fins and the kinematics of the fins, to an extent
which has not been yet reported in literature at the time when the experimental
work of this study was conducted. Detailed descriptions of the 2D-2C-PIV/PTV
measuring technique and the used experimental setup are given in section 3.1.2.
2.1.3
Experimental evaluation methods
Investigations on the cilia kinematics of Opercularia asymmetrica were performed
in this study two and three–dimensionally with µ-PTV. The fin kinematics of Hippocampus reidi and the flow induced in the vicinity of the fins were determined with
2D-2C-PTV and 2D-2C-PIV measuring techniques. Therefore, this section provides the necessary theoretical background to describe the 2D-2C-PTV/PIV techniques and presents the most important experimental components involved in this
approach. For further informations about the stereo-PTV/PIV technique, the manual Particle Image Velocimetry – A practical guide written by Raffel, Willert and
Kompenhans (1998) is recommended.
The PTV/PIV measuring technique represents a non–intrusive and fast technique to capture a whole flow field during one measurement. It is an approach
where time intervals are kept constant and changes in space are measured. The
velocity is determined from constant time interval and measured space distance.
Depending on the density of seeding particles in the flow it is possible to distinguish
between PTV and PIV. At low seeding density images, each particle is tracked.
This method determines position and velocity of each particle and is known as PTV
technique. At a medium seeding density images, it is not anymore possible to track
2.1. Optical visualisation techniques in biological systems
16
each particle. Here the whole image is segmented into interrogation areas, where
each area contains enough tracer particles to perform standard statistical evaluation
techniques. For this method, known as PIV measuring technique, displacement of
the whole interrogation area is determined.
Figure 2.1: Basic PTV/PIV setup consisting of a light source (laser), working area (light
sheet plane with seeding particles) and detection (camera)
A basic 2D-2C-PIV setup is sketched in Figure 2.1. Following components are
necessary: light scattering tracer particles (seeding) which follow easily the motion of
flow, intensive pulsed laser light for sharp images, optics (rotating mirror, cylindrical
lens) which expands the laser beam to a laser light sheet plane and one camera which
records two consecutive image pairs within a short and defined time interval.
The experimental procedure can be described as follows. Flow is marked with
tracer particles, the scene is highlighted twice, within short time steps by a pulsed
laser and the two image pairs are recorded with the camera. The chosen time in-
2.1. Optical visualisation techniques in biological systems
17
crement between images is adjusted to the investigated flow velocity range. High
flow velocities require short time increments in the range of nano seconds or micro
seconds. For the PIV technique the recorded image pairs are divided into rectangular interrogation areas. The interrogation area size is chosen small enough to
avoid significant influence on measured velocity gradients. The interrogation area
size determines the number of velocity vectors in the velocity field and the spatial
resolution. Between each corresponding interrogation area of the time consecutive
image pairs, correlation algorithms are used to determine the displacement of each
interrogation area in the laser light sheet plane.
For the 2D-2C-PTV technique a similar measuring setup and experimental procedure is implemented. Depending on the case which is investigated a suitable evaluation method is developed to track the motion of individual particles or objects.
In some cases correlation algorithms are used as well.
fluid–medium
seeding particles
diameter [µm]
air
aluminium–oxide
<8
air
gllycerine
0.1–5
air
silicone oil
1–3
air
water
1–2
water
aluminium powder
< 10
water
bubbles
5–500
water
glass balloons
10–150
water
milk
0.3–3
Table 2.1: Seeding particles implemented in the PIV measuring technique for visualisation of air and water flows
Table 2.1 contains some tracer particles used for PIV applications in air and
water flows. When choosing seeding particles a compromise must be made between
optimal light scattering for good contrast images (bigger particles) and flow tracking
ability for realistic results (smaller particles). The concentration of particles has to
be high and they have to be distributed equally in the flow, to achieve sufficient
2.1. Optical visualisation techniques in biological systems
18
and homogeneous light scattering. Often smoke, fog and seeding generators are
implemented (Raffel et al., 1998). Their density in the flow has to be optimal,
for the following evaluation step where a minimum number of tracer particles per
interrogation area is required. Another way to achieve sufficient tracer particles
per interrogation area is to increase the size of the interrogation area during the
evaluation step.
Figure 2.2: Schematic desccription of a double pulsed Nd:YAG-Laser system; (1) pump
cavity, (2) back mirror, (3) variable reflectivity output mirror, (4) Q–switch,
(5) λ/4 plate, (6) polarizer, (7) mirror (50% transmission), (8) Brewster
polarizer, (9) filter, (10) phase angle adjustment, (11) delaying–plate (λ/2),
(12) beam trap
The demands on illumination are high as well. To achieve good particle contrast
short light pulse durations are necessary. The light sheet plane has to be illuminated
equally and it has to be slender since the measurements are performed in one plane.
To achieve good particle induced light scattering and good signal–to–noise ratios a
high light energy is required. Consequently short light pulses with high energy are
necessary. For PIV/PTV measurements often double pulsed Nd:YAG-laser systems
are implemented with two resonators as sketched in Figure 2.2. This laser can
achieve high energy pulses (25 MW ) with pulse duration in the range of nano
seconds (5-10 ns). Here a Q-switch (Pockels cell) is built into the laser system.
The Q–switch is an electro–optical crystal under voltage, which is able to rotate the
polarity of light allowing the discharge of the laser light with a certain energy load
from the cavity for a very short time interval. With an external electrical modulating
signal the pulse repetition rate can be adjusted. In other applications shutters are
2.1. Optical visualisation techniques in biological systems
19
implemented to induce laser pulses or mode lockers to achieve extremely short pulse
durations of a few femto seconds.
To achieve good quality images for the following evaluation step, laser light
sheet plane is focused by the objective of camera. Afterward consecutive images
are recorded with a light sensitive, low noise CCD camera (Charge Coupled Device
sensor) which is able to read out the acquired images sequentially. The transfer
time to the shift register is approximately 200 ns for CCD cameras. Lately very
fast CMOS cameras (Complementary Metal Oxide Semiconductor sensor) have been
used for PTV/PIV applications as well.
The correlation algorithm allows evaluation of images in a systematic and fast
way (Raffel et al., 1998). For two gray scale time consecutive image segments (interrogation areas) a1 (x, y) and a2 (x, y), where x and y describe the size of the segments
in pixels, the correlation function is defined as follows:
Ra1 a2 (ζ, η) =
M −ζ N −η
XX
1
a1 (x, y) a2 (x + ζ, y + η)
(M − ζ) (N − η) x=1 y=1
(ζ, η ≥ 0) (2.1)
or
M
Ra1 a2 (ζ, η) =
N
XX
1
a1 (x, y) a2 (x + ζ, y + η)
(M + ζ) (N + η) x=1 y=1
(ζ, η ≤ 0) (2.2)
In equations (2.1) and (2.2) ζ and η represent the dislocation of the two image segments till a maximum correlation peak is found where the two image segments are
overlapping. The correlation peak can be determine efficiently by employing FFT–
algorithms. In addition, with a suitable calibration factor, determined image displacements ∆x and ∆y in pixels can be transformed into real object displacements.
From the displacements ∆x and ∆y and the time interval between two image segments the two–dimensional (in the laser light sheet plane), two–component velocity
of the interrogation area is determined. The complete vector field is determined by
applying such a correlation algorithm to all image segments .
To eliminate unrealistic results and too large velocity vectors, some simple methods are developed which limit the velocity data to a prescribed interval around the
average velocity value.
2.2. Numerical approaches for flapping and undulating motions
2.2
20
Numerical approaches for flapping and undulating motions
The hydrodynamics of the Hippocampus reidi structure and the kinematics of
the dorsal and pectoral fins were accomplished in the present study by means of
numerical approaches. Consequently, this section provides a brief literature review
of some previous numerical attempts to compute flows induced by flapping and
undulating motions as well as flows around complex geometries which is relevant for
the present study. Also the theoretical background which is necessary to perform
the numerical investigations is presented.
2.2.1
Brief literature review
Since rigid translatory motions cannot produce enough forces to achieve propulsion in air and water, the unsteady effects of fluid flows induced by flapping wings
and undulating fishes have to be taken into consideration. Consequently, the transfer
of complex bio kinematic processes to computational fluid dynamics is a challenging
task.
Ramamurti and Sandberg (2002) solved with a finite differences method for
incompressible media, the unsteady flow and flow forces induced by the three–
dimensional translatory and rotary wing motion of Drosophila. It was observed
that rotation of the wing before recoil induces a higher acceleration force than a
coincidental or delayed rotary motion.
Tanida (2003) conducted two–dimensional analytical investigations about the
reciprocal influence of two tandem wings of dragonfly. At a wing flapping frequency
of 30 Hz, he found that the optimal acceleration and propulsion efficiency occurs, if
between the oscillation of the front and hind wing a certain phase lag exists.
Wang (2000) implemented a Navier Stokes solver and the harmonic oscillation
equation to simulate the two–dimensional flapping motion of a wing and the unsteady viscous flow. He investigated trailing and shedding of a LEV and characterised time dependent vorticity and induced flow forces. Furthermore, an optimal
flapping frequency and attack angle was found where the occurring thrust coefficient
2.2. Numerical approaches for flapping and undulating motions
21
is maximum.
Tuncer and Platzer (1996) computed the unsteady flow profile over a flapping
foil and over a combination of flapping and stationary foils. For the combined
case a stationary foil was placed behind the flapping foil. Flow was assumed to be
turbulent (Baldwin Lomax turbulence model) and the computational domain was
chosen large enough. It contained foils, boundary layers and wake flow. They proved
that a stationary foil placed in the wake flow of a flapping front foil can interact
with wake energy of the front foil and double the lift coefficient of a single flapping
foil. Kaya and Tuncer (2009) showed that a biplane configuration of two flapping
foils exposed to an external flow can also increase the total propulsive efficiency.
Leroyer et al. (2005) simulated numerically the motion of a self propelled fish
like body. Therefore, a Reynolds Averaged Navier Stokes (RANS) flow solver was
implemented, with a re–griding algorithm to simulate the body deformation and
a method to couple the reciprocal interaction between solid kinematics and flow
motion. To compute new position of the fish according to the force induced by
flow, Newton’s law was applied. Muensch et al. (2008) investigated fluid structure
interactions of a rigid and elastic cylindrical body. To resolve the flow field in
time, the authors implemented Large Eddy Simulation techniques with an explicit
time marching scheme and with small time steps. To investigate the fluid structure
interactions the flow solver was coupled to a finite element code with a new numerical
predictor–corrector method.
Mittal et al. (2008) developed a numerical method, which solves the three–
dimensional unsteady Navier Stokes equation for incompressible viscous media, to
simulate flows around complex and periodically moving structures of fishes. The
immersed body structure consists of a triangular unstructured mesh, while for the
flow non uniform Cartesian grid was implemented. Furthermore, in order to determine the boundary cells and the boundary conditions of the immersed body the
ghost cells method for each time step was applied.
Gilmanov et al. (2005) developed a three–dimensional, unsteady, incompressible
Navier Stokes solver for the simulation of immersed, complex bodies with impressed
kinematics. Therefore, the authors used a staggered/non staggered grid layout and
2.2. Numerical approaches for flapping and undulating motions
22
a second order finite difference scheme. To capture the complex geometry unstructured triangular mesh was employed. With these settings they were able to simulate
the reverse Karman flow induced by a mackerel.
In the present study the hydrodynamic investigations of the complex Hippocampus reidi structure and of the undulating kinematics of the dorsal and pectoral fins
were done with the commercial software STAR-CCM+. This solver is based on a
finite volume method on collocated grids. A coupled and a segregated flow solver
are integrated to compute compressible and incompressible flows. For the investigated cases the segregated flow solver was used. The implemented polyhedral mesh
model in STAR-CCM+, which was used for all simulations turned out to be very
suitable for complex geometries and mesh deformations. A detailed description of
the computational domain along with the boundary conditions and the used models
are presented in the sections 3.2.1 and 3.2.2, respectively.
2.2.2
Numerical evaluation methods
In this section the theoretical background which is necessary to perform the
numerical hydrodynamic investigations of the seahorse structure and the kinematic
investigations of the fin undulation is presented.
Governing equations of fluid mechanics
This section gives a short introduction to the governing equations of fluid mechanics (see for example the manual Grundlagen der Strömungsmechanik written
by Durst (2006)).
The motion of a flow through a control volume can be described with balance
equations for mass, momentum and energy. The first equation which has to be
taken into consideration is the mass conservation equation known as the continuity
equation. Equation (2.3) represents the general form of the continuity equation,
which is valid for both compressible and incompressible flows. In this equation ρ
is the density of the transported medium and Ui the velocity of the medium in all
directions (i = 1, 2, 3) of space xi (Durst, 2006).
2.2. Numerical approaches for flapping and undulating motions
∂ρ ∂ (ρUi )
+
=0
∂t
∂xi
23
(2.3)
The general form of the three–dimensional momentum conservation equation (second law of Newton) for Newtonian fluids is presented in equation (2.4) (Durst, 2006).
This equation in tensor notation, states that a change of momentum of a control
volume is induced by pressure forces (first term on the right side), viscous forces
(second term on the right side) or gravity forces (third term on the right side) which
are acting on the control volume. The molecular momentum transport and the viscous forces are driven by velocity gradients in the moving fluid.
ρ
∂Uj
∂Uj
+ Ui
∂t
∂xi
=−
∂P
∂τij
−
+ ρgj
∂xj
∂xi
(i,j = 1, 2, 3)
(2.4)
From the momentum equation (2.4), the equation for mechanical energy can be
determined very easily by multiplying this equation with the velocity Uj . The mechanical energy equation is presented in equation (2.5), where G is the gravity force
(Durst, 2006).
ρ
∂Uj
∂(τij Uj )
D 1 2
∂Uj
∂(Uj P )
+P
−
+ τij
[ Uj + G] = −
Dt 2
∂xj
∂xj
∂xi
∂xi
(2.5)
Taking into account the mechanical and internal energy e of a control–volume, the
resulting total energy equation has the following expression:
ρ
D
1
[e + Uj2 + G] =
Dt
2
∂ q̇
−
∂x
| {z }i
heat conduction
−
∂(P Uj )
−
∂xj
| {z }
convection
∂(τij Uj )
∂x
| {zi }
(2.6)
molecular transport
Harmonic wave equation
In this section the wave equation is presented due to its relevance for the description of the undulatory fin motion.
The spatial and temporal propagation of harmonic and periodic waves is described with the differential wave equation, where Ψ represents the wave function
and c the wave propagation velocity (see equation (2.7)). Equation (2.8) represents
the solution in time t and space y of the wave function, where k is the wave number
2.2. Numerical approaches for flapping and undulating motions
24
and ω = 2 · π · f requency (Meschede, 2001).
2
∂ 2Ψ
2∂ Ψ
=
c
∂t2
∂y 2
(2.7)
Ψ(x, t) = ei(ky−ωt)
(2.8)
More clearly one of the solutions of the wave function can be also written as:
Ψ(x, t) = z(y, t) = A · sin(ky − ωt)
(where A = motion amplitude)
(2.9)
Numerical moving grid method
The governing equations of fluid mechanics which were presented in the previous
section are solved numerically for discretised elements (Finite Element Method–
FEM) or volumes (Finite Volume Method–FVM) of the computational domain.
Basically there are three different mesh structures available: structured, block structured and unstructured meshes, which can be used for various geometries (Anderson,
1995). The balance equations are solved on these meshes with different numerical
methods. A common numerical method to solve these equations for incompressible flows, is the SIMPLE (Semi-implicit Method for Pressure Linked Equations)
method. The SIMLE algorithm which is implemented in STAR-CCM+, is based
on an initial guess of the pressure field, which is then inserted in the momentum
equation (2.4) to get the corresponding velocity field. The pressure is then corrected
by using the pressure correction equation until the corresponding velocities satisfy
the continuity equation (2.3) (Peric et al., 2002). Consequently, with the SIMPLE
method it is possible to get from the conservation equations for mass and momentum
the correct pressure and veloicty fields.
The numerical methos for solving flow fileds are only presented marginally in
the present work. For further informations, for example the book Computationam
Methods for Fluid Dynamics written by Ferziger and Peric (2002) is recommended.
A special feature of the fin kinematics simulations is the impressed motion of the
mesh in the fin region. The mesh moves after each time step, inducing this way a
change of the surrounding medium and a flow in the vicinity of the fin. For a moving mesh the partial differential equations have to be modified (Peric et al., 2002).
2.2. Numerical approaches for flapping and undulating motions
25
Starting with the general volume integrated one–dimensional continuity equation,
it can be observed, that the integration borders and the grid positions are time
dependent if the mesh is moving (see equation (2.10)).
Z
x2 (t)
x1 (t)
∂ρ
dx +
∂t
Z
x2 (t)
x1 (t)
∂(ρu)
dx = 0
∂x
(2.10)
With some mathematical modifications, like using the Leibniz rule for the first integral and the product rule for the second, equation (2.10) can be transformed to
(Peric et al., 2002):
Z
x2 (t)
x1 (t)
∂(ρu)
dx =
∂x
Z
x2 (t)
x1 (t)
∂ρ
∂u
u+ρ
∂x
∂x
Z
x2 (t)
dx =
x1 (t)
∂ρ
udx +
∂x
Z
x2 (t)
ρ
x1 (t)
∂u
dx (2.11)
∂x
Assuming that u1 = u(x1 (t)), u2 = u(x2 (t)), ρ1 = ρ(x1 (t)), ρ2 = ρ(x2 (t)) and u =
∂x
∂t
equation (2.11) can be written also as:
d
dt
Z
x2 (t)
ρdx + (v2 ρ2 − v1 ρ1 ) + (ρ2
x1 (t)
∂x2
∂x1
− ρ1
)=0
∂t
∂t
This case exemplifies the complexity of such a moving mesh problem compared to
static mesh problems, although the above equation can be simplified for incompressible flows where ρ1 = ρ2 . Consequently the demands on the implemented mesh
structure are very high. The right mesh choice influences parameters like convergence, convergence speed and effectiveness of the numerical simulation. Further
discussions and explanations on this topic will be presented in section 3.2.2.
Chapter 3
Materials and methods
3.1
Experimental procedures
In the present study experimental investigations were conducted to find the motion pattern of cilia (Opercularia asymmetrica) and of fins (Hippocampus reidi ) as
well as the flow induced by fins. This section presents the experimental procedures
and evaluation methods implemented in the present study for both cases. The experimental procedure to determine the drag coefficient of the seahorse structure is
presented as well.
3.1.1
µ–PTV Experimental evaluation method
The investigations concerning the cilia kinematics were determined in the present
study two and three–dimensionally with µ-PTV. This section presents the systematic experimental procedure and evaluation method implemented for the µ-PTV
investigations.
µ–PTV Setup and calibration
For µ–PTV measurements which were performed under the microscope, granule
probes with living ciliates were added with some nutriment (milk emulsion) on a
glass plate. The ciliates were selected out of a sequencing batch reactor maintained
in the laboratory. The prepared samples were covered with a thin glass plate and
26
3.1. Experimental procedures
27
analysed with microscope at room temperature (200 C). The milk emulsion with a
milk to water ratio of 1 : 3 was added to the granule probes, because at this ratio
the activity of Opercularia asymmetrica occurred to be ideal. The mixture density
amounted to 1.0 · 103 kg/m3 and the kinematic viscosity 1.2 · 10−6 m2 /s.
The cilium kinematics in the focal plane was observed by using a transmitted
light microscope Axiotech 100 and an EC-Plan Neofluar oil–immersion objective
from Carl Zeiss. The light path was adjusted according to Kohler, in order to achieve
good illumination and cilium images with high sharpness and contrast. For the
kinematic investigations an objective with 100 fold optical magnification is necessary
because of the small cilia dimensions (cilia length = 10–12 µm). The numerical
aperture NA of the objective is 1.3. The depth d of the focal plane was determined
according to the technical data of the objective (see equation (3.1)) and it amounted
to 325 nm. In the present study the illuminated focal plane undertakes the function
of the laser light sheet plane used in conventional PIV/PTV applications (see section
2.1.3).
d=
550nm
(N A)2
(3.1)
In order to obtain results as under real life conditions, bio compatibility must be
ensured as shown by Petermeier et al. (2007). Here, the 6 Watt lamp built in the
microscope was used as only light source. This light is white and continuous. Raffel
et al. (1998) reported about PIV applications where pulsed white light sources
are used for illumination. Instead of a pulsed light source, in this application a
camera with a high frame rate was used, to generate a constant time difference
between images. For the µ-PTV measurements a high speed CMOS camera (1200–
hs PCO AG) with an exposure time of 2 ms (frame rate = 500 Hz ) and a resolution
of 1280 pixels x 1024 pixels was used. The above mentioned frame rate of the
camera is sufficient to measure frequency and velocity of cilia correctly, since the
cilia frequency varies between 20 and 80 Hz. The camera was operated in an auto
sequence mode at a pixel–clock of 86 MHz. Between two consecutive images a time
parallel image acquisition and read out took place. Figure 3.1 contains the time
intervals characterising one image exposure of the camera at the above mentioned
pixel–clock.
3.1. Experimental procedures
28
To determine concomitantly the velocity components of the moving cilium in
focal plane and out of focal plane direction, additionally a piezo actuator (piezo-
Figure 3.1: Time intervals characterising one image exposure of the camera
system jena) which moves the microscope objective into out of the focal plane direction was used. The piezo actuator was synchronised with the high speed camera
through an external triggering unit (see Figure 3.2). The maximum piezo actuator
range, between 0–250 µm, is adjustable with an external modulation signal between
0–10 Volts. Consequently, for the desired range of 50 µm an external modulation
signal of 2 V is necessary. Since the velocity component of the cilium in the out
of focal plane direction is not known different piezo actuator velocities were tested
during the experiments till the velocity of the cilium and of the piezo actuator overlapped. The displacement frequency of the piezo actuator was set to 5, 10, 20 and
40 Hz within 50 µm, which corresponds to a displacement velocity of 250, 500, 1000
and 2000 µm/s.
The synchronisation between camera and piezo element can be described as
follows. When the piezo actuator just starts to move with one of the four possible
displacement velocities and to perform the 50 µm range, at the acquire enable input
of the camera a voltage level of 5 V is set to trigger the camera. While the voltage
is kept at this constant level, camera records images with an exposure time of 2 ms.
After finishing the 50 µm range, the voltage level at the camera drops to zero, the
3.1. Experimental procedures
29
camera stops recording and the piezo element goes back to the initial position.
During experiments it was possible to trigger the piezo actuator consecutively 1,
4, 6, 8 and 10 times. The camera recorded continuously while the piezo performed
1, 4, 6, 8 and 10 times in the 50 µm range at the selected velocity. In addition, a
good operating point of the piezo actuator was found at 54 V, where no hysteresis
after each piezo cycle was observed. After each cycle, the piezo element had the
same initial position and the acquired cilium images had the same initial sharpness.
Figure 3.2: µ-PTV setup consisting of a microscope Axiotech 100 (Carl Zeiss), high
speed CMOS camera (PCO AG) and piezo actuator (piezosystem jena)
The images were calibrated with a micrometer illustrated in Figure 3.3. Here
510 pixels correspond to 100 µm.
µ–PTV Evaluation
The acquired images (image size: 1280 pixels x 1024 pixels; .bmp–format; 8–bit
image) were evaluated by using image processing tools integrated in Matlab (Math
Works). A routine which is explained in this section, was written to determine the
velocity of the cilium tip in the focal plane.
3.1. Experimental procedures
30
Figure 3.3: Calibration image for the µ-PTV measurements
The acquired images were read in automatically using a programmed loop in
Matlab. Each 8–bit gray scale image in .bmp format acquired by the camera represents now a 1280 x 1024 matrix. Each matrix component has a value between 0
and 254. 0 represents colour black, 254 represents colour white and the values in
between are different shades of gray. For all the images only the relevant region
where the cilium exists was cut out and the contrast was improved consecutively
with the imadjust and histeq functions integrated in Matlab. The imadjust function
maps the intensity values in the initial gray scale image to new values, such that 1
% of the data is saturated at low and high intensities of the initial matrix. histeq
enhances the contrast of initial images by transforming the values in an intensity
image, so that the histogram (plot of grayscale value against grayscale occurrence
or intensity) of the output image matches approximately a specified histogram.
After contrast improvement, an edge detection was performed to find the exact
cilium tip position. The achieved binary images after edge detection are presented
for one stroke (A–B) in Figure 3.4. It is visible that the spatial resolution of the
cilia is maintained after edge detection. During one stroke the displacement of one
3.1. Experimental procedures
31
cilium is too large to perform correlations between the two images. Between the
positions A and B the cilium moves out of the stagnant focal plane, hence in this
region the cilium is not sharply visible and no edge detection is possible (Further
discussions are given in section 4.1). As a consequence the white image points (see
Figure 3.4) with a value of unity were written out and the tip displacement was
determined manually between A and B. This way the two–dimensional dislocation
of the cilium tip was found. Dividing the two–dimensional dislocation of the cilium
tip in the focal plane with the time interval between the positions A and B, the two–
dimensional, two–component velocity of the cilium tip in the focal plane was found.
During one experiment the velocity of the cilium tip for the same effective stroke was
determined several times and a mean velocity value was found. For each performed
experiment the deviation of each measured velocity from the mean velocity value
was less than 2%.
Figure 3.4: Cilium images after contrast enhancement and edge detection at the beginning (A) and end (B) of an effective stroke
3.1. Experimental procedures
32
The same evaluation method was implemented for the µ-PTV measurements at
a moving focal plane where a good synchronisation between the motion of the piezo
actuator and the cilium allowed sharp cilium images between the points A and B as
well.
3.1.2
PIV Experimental evaluation method
The flow caused by the simultaneous undulating motion of the dorsal and pectoral fins during seahorse stagnation was analysed by using 2D-2C-PIV technique.
This section provides an overview of the implemented 2D-2C-PIV experimental
setup and evaluation method.
Furthermore, the kinematics of the dorsal fin were determined with 2D-2C-PTV.
Here exactly the same experimental setup was used as for the 2D-2C-PIV measurements and the same evaluation technique as described in subsection 3.1.1 (µ–PTV
Evaluation).
PIV Setup and evaluation
Seahorses (Hippocampus reidi ) were kept in an aquarium with a size of 120 cm
x 60 cm x 60 cm. All optical measurements were performed in artificial sea water
at a temperature of 230 C, density of 1.0 · 103 kg/m3 and viscosity of 1.1 · 10−3 P as.
The 2D-2C-PIV experimental setup is pictured in Figure 3.5. For illumination
an Nd-YLF laser (Litron LDY 303; output energy 20 mJ ; pulse rate 10 kHz ) was
used with a light wave length of 527 nm. The laser beam was expanded to a light
sheet plane with a cylindrical lens. Hollow glass spheres with a diameter of 10 µm
were used as tracer particles. The images were recorded with a high speed camera
(Photron Phantom v12). The time step between the recorded images was 5 ms
(exposure rate = 200 Hz ) and the image size was set to 1280 pixels x 800 pixels. An
exposure rate of 200 Hz at the camera turned out to be enough for the flow field
investigations, since for seahorses low flow velocities of a few cm/s were expected.
This exposure rate was also sufficient for the fin kinematics investigations since the
fin frequency varied from 20 to 60 Hz.
The images were evaluated with the commercial PIVview2C software (PIVTEC
3.1. Experimental procedures
33
GmbH) in a cross correlation mode (Raffel et al., 1998). The PIV investigations
were carried out by using multiple pass interrogation algorithm which is included
in the PIVview2C software. The interrogation area size was set to 32 pixels x 20
pixels. The evaluated data were post processed in Tecplot (Amtec Engineering).
Figure 3.5: PIV experimental setup consisting of pulsed Nd-YLF laser, high speed camera (Photron Phantom v12) and aquarium with seahorses
The flow fields and fin kinematics were measured in a separate compartment (40
cm x 40 cm x 50 cm) of the aquarium (see in Figure 3.5 the transparent box at
the upper right side of the aquarium). In this compartment the seahorses showed
their natural behavior and made different typical swimming manoeuvres (stagnation,
sideways swimming). During the measurements the compartment was closed from
all sides, the aquarium itself closed from the front side and a movable plate at the
back side. The measurements were performed whilst the seahorse resided between
the movable plate and the light sheet plane with its dorsal or pectoral fin oriented
toward the light sheet plane (see Figure 3.6). The distance between the plate and
the light sheet plane was kept constant at 7 cm during the investigations of the flow
induced by the dorsal fin and at 3.5 cm for the investigations at the pectoral fin. In
3.1. Experimental procedures
34
this way it was possible to keep the distance between the investigated fins and the
light sheet plane for all measurements nearly constant. This distance varied between
0 and 4 mm.
Figure 3.6: Alignment of the seahorse in the measurement compartment between laser
light (green line) and the movable plate (blue line). The distance between
investigated fins and laser light sheet plane varied between 0 and 4 mm
3.1.3
Experimental drag force measurements
In this section the measuring technique built to determine the drag force of the
seahorse structure is presented. The inlet or swimming velocity which was found
numerically to cause the lowest drag was validated experimentally.
Basically, the setup shown in Figure 3.7 consists of an opened ceiling water
channel, a centrifugal pump (Schmitt centrifugal pump; type: U 80, volumetric
rate: 1000 l/h, efficiency: 0.7), a laboratory balance (Kern GS; mmax = 4100 g, d
= 0.01g), a nearly friction free mechanism with two lever arms (l1 = 0.13 m and l2
= 0.22 m) to transfer the flow force acting on the balance point of the seahorse to
the laboratory balance and a seahorse casting out of brass. For these experimental
investigations and for the numerical hydrodynamic investigations identical seahorse
3.1. Experimental procedures
35
structures were used.
The balance point of the seahorse structure was determined by segmenting the
whole structure into triangles. From the barycentre of each triangle, the total balance point of the seahorse was found. It is placed close to the dorsal fin (see red
point in Figure 3.8).
Figure 3.7: Setup consisting of a opened ceiling water channel, centrifugal pump, a laboratory balance, a mechanism with two lever arms l1 = 0.13 m and l2 =
0.22 m to transfer the flow force acting on the seahorse balance point to the
laboratory scale and a seahorse casting out of brass
The dimensions, assembly and the components of the water channel with a cross
section area of 0.06 m x 0.12 m, are sketched in Figure 3.8. The seahorse was placed
in the middle of the cross section of the channel. The projecting area of the seahorse
(∼ 10 cm2 ) covered approximately 14 % (≤ 15%) of the cross section area of the
channel. Thus homogenous flow conditions in the seahorse region can be assumed.
The measuring and evaluation procedure can be described as follows. During
measurements the channel was filled with aquarium water. When the water was
standing still in the channel, the laboratory balance was tared and a mass of 0
3.1. Experimental procedures
36
g was displayed on the balance monitor. While the seahorse position was kept
completely fixed due to the built measuring system, the pump was switched on and
a constant mass value was displayed on the laboratory balance caused by the flow
motion. Multiplying this mass value with acceleration of gravity (9.81 m/s2 ), the
force F1 acting on the balance was determined. The flow force F2 which is acting
on the balance point of the seahorse (see red point in Figure 3.8) was calculated
according to equation (3.2).
Figure 3.8: Dimensions and the components of the water channel used to determine the
flow force (F2 ) acting on the balance point of the seahorse (red point)
l1 · F1 = l2 · F2
(3.2)
The triangle formed by the resulting flow force (F2 ) and the negative drag force
(−FD ) is similar to the triangle formed by the lever arms l1 and l2 , where α = 30.60
(see Figure 3.8). The absolute value of the drag force |FD | was calculated from the
product between F2 and cosine of α.
After the drag force FD is known, drag coefficient was determined according to
equation (3.3). In this equation, the water density ρ amounts to 1 · 103 kg/m3 ,
the seahorse total area Aseahorse = 0.053 m2 (see chapter 3.2.1) and the velocity u
3.2. Numerical procedure
37
representes the inlet flow velocity or the seahorse swimming velocity.
cD =
3.2
2 · FD
Aseahorse · ρ · u2
(3.3)
Numerical procedure
In the present study, the hydrodynamical investigations of the seahorse structure
and the kinematic investigations of the undulating fin were performed numerically.
In this section the implemented geometries, mesh models, flow models and boundary
conditions which are necessary to perform the simulations are presented.
3.2.1
Numerical drag force calculation
Seahorses swim slowly at a few centimeters per second. The hydrodynamical
investigations should clarify, with the help of drag coefficient calculations, the reason
why seahorses do not require to swim faster.
This subsection clarifies how the seahorse structure was reproduced, measured
and imported into STAR–CCM+ (version 5.02) the commercial software, which was
used to perform all simulations. Also the setup of the simulation file (geometry;
space and time discretisation; mesh and flow models; boundary conditions) is presented.
A deceased female seahorse of approximately 10 cm length, 2 cm width (at the
abdomen) and 1 cm thick was frozen, to preserve the exact real life structure. The
frozen seahorse was used to obtain a casting out of white silicone. The casting was
measured with a laser scanning technique, and a triangular surface mesh with a base
size of 250 µm and a total surface size of 0.0525 m2 was created. The generated
file in .stl format was imported into STAR–CCM+. The seahorse structure was
introduced into a channel with the following dimensions: 0.2 m x 0.2 m x 0.48 m.
The geometry of the problem and the re-meshed surface are presented in Figure 3.9.
The space between the wall of the seahorse structure and the channel walls was
set as fluid region or computational domain. The whole geometry was re–meshed
(surface wrapper; polyhedral mesh model) and a new base size of 0.002 m was
defined. To resolve the seahorse structure, a smaller mesh was necessary at the
3.2. Numerical procedure
38
seahorse surface. Related to the 0.002 m, the base size was defined between 25 %
(at the seahorse surface) and 200 % (at the channel outer walls). Consequently, at
the seahorse surface the base size amounted to 0.0005 m and at the walls of the
channel 0.004 m. After re–meshing the total number of cells amounted to 3281244
in the computational domain. Furthrmore, a finer mesh at a smaller base size of
0.00158 m led to the same computational results as the bigger base size of 0.002 m.
Thus all achieved results are grid independent.
Figure 3.9: Geometry and re–meshed surface for the hydrodynamic investigations of the
seahorse structure in a front position of the seahorse relative to the inlet flow
The simulations were run for different inlet velocities (or swimming velocities) of
0.01, 0.05, 0.1, 0.15, 0.2, 0.4, 0.8 and 1.6 m/s till a steady state of the simulations
was reached.
The distance between time instances was set to 0.01 sec. Consequently, with this
time step and the chosen grid size the Courant number (see equation (3.4)) was kept
smaller than 10 for all investigated inlet velocity cases in the whole computational
domain. This shows that for all simulations the convergence criterion was fulfilled.
Courant number = vinlet ·
∆t
∆x
(3.4)
The total number of iterations was adapted for each investigated inlet velocity
case in such way, that the product between the total iteration time (physical time)
and the inlet velocity was equal to or greater than the channel length. For example
at an inlet velocity of 0.1 m/s the total number of time steps amounted to 500,
which corresponds to a physical time of 5 seconds.
3.2. Numerical procedure
39
Drag coefficient monitoring was used to check if the steady state of the simulation was reached. Figure 3.10 shows the monitoring of the drag coefficient at an
inlet velocity of 0.1 m/s. It can be observe that after 50 iterations and 1000 inner
iterations (20 inner iterations per iteration) the drag coefficient stayed constant and
a steady state of the simulation was reached. All presented results in section 4.2.1
are steady state cases.
Figure 3.10: Monitoring of the drag coefficient at increasing number of inner iterations
at 0.1 m/s inlet velocity
For the simulations a second order numerical scheme was used and for the fluid
continuum the following models were chosen: implicit unsteady, segregated flow,
liquid with constant density of 1.0 · 103 kg/m3 and viscosity of 1.1 · 10−3 P as. Although the investigated inlet velocities are low and rather typical for laminar flows,
seahorses have a very edgy structure, which can cause even at small Reynolds numbers a laminar–turbulent transition in the shear layer which can appear behind the
seahorse. The most accurate numerical results are achieved with the Direct Numerical Simulation (DNS) method, but this is a computationally expensive option just
like the Large Eddy Simulation (LES) method, since they require very small time
seps and mesh sizes. Hence, to capute the physics of this problem correctly at lower
computational costs, in this study the Reynolds Averaged Navier Stokes (RANS)
3.2. Numerical procedure
40
method with Realizable κ–turbulence model was used for all investigated cases.
The Realizable κ–turbulence model selected in this study provides a good compromise between robustness, computational cost and accuracy and it is often used
in industrial applications (combustion engines, gas turbines) that contain complex
recirculation.
3.2.2
Numerical kinematic investigations of fins
The complex undulating kinematics of the dorsal fins, which induce a flow in the
vicinity of the seahorse and allows a very precise manoeuvring, is presented in Figure
3.11. By means of velocity, velocity vector and pressure plots in the vicinity of the
fin, a link between the fin deformation and the induced flow is gained. The effect
of slightly modified parameters (oscillation frequency and wave travelling direction)
on the induced flow are investigated as well.
In this section the setup of the simulation (geometry; space and time discretisation; mesh and flow models; boundary conditions) is presented. These investigations
were performed with the STAR–CCM+ (version 5.02) software.
Figure 3.11: Fin undulation during seahorse swimming
3.2. Numerical procedure
41
The geometry of the problem and the re-meshed surface are presented in Figure
3.12. Here a real to scale dorsal fin, with length, width and thickness of 0.02 m x
0.004 m x 0.0001 m was placed in a channel. After the extent of the induced flow
was found experimentally with 2D-2C-PIV, the size of the channel was adapted to
0.14 m x 0.08 m x 0.14 m. For the computational domain the surface remesher,
the polyhedral and prism layer mesher were used. The first chosen base size was
0.0001 m, which corresponds to the fin thickness. Unfortunately this base size led
to negative volume cells at the beginning of the simulation. Gradually the base size
was increased, till it became possible to run the simulation. The final base size was
set at 0.004 m. It was defined in an interval between 40 % (at the fin surfce) and
100 % (at the channel surfce) related to the 0.004 m. Close to the fin surface the
base size amounted to 0.0016 m and at the channel walls 0.004 m. The number of
all cells in the computational domain amounted to 14230.
Figure 3.12: Geometry and re–meshed surface used for the fin undulation simulations,
with the two boundaries fin inlet and fin outlet
The inlet velocity [ux , uy , uz ] was set to [0.01, 0, 0] m/s for all simulation cases.
Smaller inlet velocities led to reverse flows and aborted the running simulation. 0.01
3.2. Numerical procedure
42
m/s was the lowest velocity where it possible to start running stable simulations.
Higher velocities were not investigated, since they would interfere too strongly with
the fin induced flow and also exceed the swimming velocity of seahorses.
The time steps size was set to 0.0001 s. The choice of extremely small time steps
is maybe one of the most important factors while running simulations with mesh
deformations, thus avoiding the formation of negative volume cells at the beginning
of the simulation.
During the simulations the fin is deforming periodically with time inducing a
periodic change of fluid motion as well. Still the average velocity over one complete
undulation period stays constant for the whole simulation time, if the steady state of
the simulation is reached. Let’s have a look at the 50 Hz undulation frequency case,
where the simulation was run for 4500 time–steps (20 inner iterations per time–step;
physical time 0.45 s). Here the maximum flow velocity was sampled for each time
step in a perpendicular plane section at 1 mm in front of the undulating fin tip (see
fin outlet in Figure 3.12) and a mean value for each period was found. Figure 3.13
Figure 3.13: Progression of the maximum flow velocity (averaged for each period) with
increasing number of time steps. The maximum flow velocity was sampled
in a plane section (perpendicular to the fin) 1 mm in front of the fin tip
3.2. Numerical procedure
43
shows that for this case a constant (steady) value of the maximum flow velocity
(averaged for each period) occurs after the fifth undulation period. For each investigated frequency case in this study the number of iterations were adapted, so that
all results which are presented in Chapter 4.2.2 fulfill the steady state criteria.
A second order numerical scheme was used and for the fluid continuum the following models were chosen: implicit unsteady, segregated flow, liquid with constant
density (1.0 · 103 kg/m3 ) and viscosity (1.1 · 10−3 P as), RANS method with Realizable κ–turbulence model. With all these settings it was possible to run the flow
simulations stable.
To achieve the fin deformation as shown in Figure 3.14, two boundaries for the
fin, namely, fin inlet and fin outlet are defined (see Figure 3.12). The fin inlet
boundary is fixed during the whole simulation time and has zero velocity. The fin
outlet boundary is moving periodically in time according to the wave motion equation (2.9). At the fin outlet boundary a grid velocity is required, which is achieved
by deriving wave equation (2.9) in time:
vgrid =
∂z(y, t)
= −A · 2πf · cos(k · y − 2πf · t)
∂t
Figure 3.14: Deformed fin mesh image at a certain time step
(3.5)
3.2. Numerical procedure
44
In STAR-CCM+ there is a syntax convention that scalar functions as the Time
have to be referenced with one dollar sign while vector functions as the Position
with two. Consequently, the motion equation (see equation (3.5)) for the fin outlet boundary was introduced into STAR–CCM+ through the following field function:
vgrid = −A · 2πf · cos(k · $$P osition[1] − 2πf · $T ime)
(3.6)
If fin length (y–coordinate), fin frequency f and amplitude A are known, equation
(3.6) shows that each time step ($Time) a new position ($$Position) of the fin
outlet boundary is computed. The region of the fin between the fin inlet and fin
outlet boundaries is adapting automatically due to the floating boundary condition
set in this region. Informations regarding fin length, frequency and amplitude were
extracted from the experimental PTV data.
The positions of the mesh vertices in the computational domain is computed
during the imposed fin deformation with the adaptive mesh (Morphing) method
implemented in STAR–CCM+.
Chapter 4
Results and discussion
4.1
Motion pattern of filaments
Ciliates are creatures which are able to move the cilia at their mouth in undulatory mode and to induce two counter rotating vortex pairs which are allowing
the tranport of nutriments from surrounding medium into their body (Zima et al.,
2009). Therefore, the knowledge about kinematics of cilia can be utilized for mixing
application in micro scale.
This chapter contains investigations on the two–dimensional and three–dimensional
motion pattern of cilium of Opercularia asymmetrica and dynamic undulatory motion pattern of a cilia collective. The achieved results together with interpretations
and discussions are presented as well. The implemented experimental procedure
was presented in Section 3.1.1. First, the motion of a cilium is investigated two–
dimensionally at a stagnant focal plane in section 4.1.1. This is a much simpler
but a good method which is able to provide detailed and clear informations about
the motion pattern of a cilium, two–dimensional velocity (in focal plane direction)
and frequency range of the cilium beat. Since cilia are performing a strong two–
dimensional oscillation, the two–dimensional velocity is the dominant component.
The three–dimensional measuring method at a moving focal plane is presented in
Section 4.1.2. Having used this method it was possible to exactly reproduce the
three–dimensional motion pattern of the cilium and to quantify not only the two–
dimensional velocity in focal plane direction but also the third velocity component
45
4.1. Motion pattern of filaments
46
which is in out of focal plane direction. This measuring technique is more precise
but time–consuming since it is a challenge to get the motion of the focal plane which
is controlled by a piezo actuator and the motion of the cilium synchronised. The
time phase shift between consecutive cilia was found when implementing the two–
dimensional measuring method, although initially it was assumed that the three–
dimensional measuring technique would be more suitable for the reproduction of the
undulatory motion of the cilia collective. Results and explanations regarding this
topic are presented in Section 4.1.3.
4.1.1
Two–dimensional investigations of the cilium motion
at a stagnant focal plane
With the two–dimensional measuring technique at a stagnant focal plane it is
possible to determine the velocity and the displacement of the cilium in the direction of the focal plane. Correlations between the cilium frequency and the two–
dimensional velocity in the direction of the focal plane as well as the corresponding
displacement of the cilium are presented in this section.
During several experiments of this study it has been observed that each cilium
of Opercularia asymmetrica is performing an oscillatory motion consisting of two
strokes, where usually one stroke is faster then the other one (Satir, 1967). Some
cases were also found where the time duration of these two strokes are same. In
the present work the faster beat is named as active stroke while the slower beat
is named recurring stroke. The first question is, if the oscillatory cilium motion is
planar or not. In Figure 4.1, the captured cilium motion during the active stroke
at a stagnant focal plane is presented. The duration of the active beat, in this
particular case is 6 ms. It can be observed that during the active stroke, the cilium
is clearly visible at the positions 1 and 4 and not clearly visible between them.
At the positions 1 and 4 the cilium is exactly in the focal plane and in the space
between these two positions the cilium is moving out of the focal plane. It can be
concluded that during the cilium beat, the cilium is not performing a planar motion
while moving from position 1 to 4, then stops at the position 4 and moves back
to position 1 during the recurring stroke. Figure 4.2 shows that during the active
4.1. Motion pattern of filaments
47
and recurring stroke, cilium rather follows a continuous motion along an elliptical
trajectory (Juelicher et al., 1996). This continuous elliptical motion between these
two points is more advantageous then a planar oscillation where the cilium has to
periodically accelerate and deaccelerate.
Figure 4.1: Captured original images of the cilium motion during the active (faster)
stroke at a stagnant focal plane
Although the beating pattern of the cilia has been observed to be the same
in all experiments, each micro-organism seemed to beat their cilia with different
frequencies or velocities. In order to evaluate the two–dimensional velocity and the
beat frequency of a cilium in the stagnant focal plane, different experiments were
conducted. First, when some activity of Opercularia asymmetrica was observed
which means that their cilia were beating, images of the beating cilium were aquired.
Only for sharp cilium images an exact detection of the cilium tip is possible at the
positions 1 and 4 (see Figure 4.2). Then the two–dimensional velocity of the active
stroke in the focal plane (in the s–direction) was determined out of the spatial (2a)
and temporal intervals (∆t) between the points 1 and 4. During one experiment it
has been observed that the cilium is moving several times between the points 1 and
4 with nearly the same velocity. In one experiment the velocity in the focal plane
was measured three times (i.e., at the beginning, middle and at the end of the image
acquisition). From these three velocity values a mean value vs was determined. The
deviation of the three measured velocity values from the mean velocity value vs was
4.1. Motion pattern of filaments
48
less than 2% which shows that during one experiment the cilium was indeed moving
with nearly constant beat velocity. The frequency of the cilium beat was determined
out of the total time which takes the cilium to perform one full cycle (i.e., active
and recurring stroke together).
Figure 4.2: Elliptical model of the cilium trajectory (Juelicher et al., 1996). The motion
between the points 1 to 4 represents the active stroke (means for example
6 ms), the motion backwards represents the recurring stroke (means for
example 12 ms). In seldom cases the time duration of the effective stroke is
equal to the one of the recurring stroke
For different experiments the measured two–dimensional velocity vs of the cilium
and the half displacement of the cilium in the focal plane (see ellipse half diametre
a in Figure 4.2) are plotted against the cilium frequency in the Figures 4.3 and
4.4. Each point in these figures represents a different experiment. In Figure 4.3 it
can be observed that with increasing frequency, the velocity of the active stroke is
also increasing. Frequencies between 20 and 100 Hz are the most dominant ones.
The measured velocities exceed several times the cilium length per second (the typical cilium length is 10 µm). At a frequency of 100 Hz the cilium velocity is up
to 360 times the cilium length per second. It can be also seen that for a certain
frequency different velocity values were measured. This can be explained easily,
since in different experiments always different micro organisms were used. There-
4.1. Motion pattern of filaments
49
fore, some ciliates were performing the full cycle (active and recurring stroke) within
the same time but the active stroke slightly faster and the recurring stroke slightly
slower then others. To the best knowledge of the author, during the time when
this experimental work was conducted, no other similar quantitative data regarding
the two–dimensional velocity vs of the cilium beat of Opercularia asymmetrica was
available in literature. In Figure 4.4, it can be seen that for different experiments
the half displacement of the cilium in the direction of the focal plane (ellipse half
diametre a) is not systematically dependent from the cilium frequency. It is distributed randomly around the mean value of 3.9 µm. It can be suspected that the
whole motion amplitude (2a) which corresponds to the displacement of the cilium
in the focal plane is rather determined by the cilium length of each micro organism
and the angle which is spanned between the positions 1 and 4 (Kos et al., 2009).
Further correlations between the displacement of the cilium in the focal plane and
the cilium length or the angle which is spanned between the positions 1 and 4 were
not considered in this study.
Figure 4.3: Two–dimensional cilium velocity vs in the focal plane as a function of the
cilium frequency
In order to characterise the induced flow, Reynolds number was computed for
4.1. Motion pattern of filaments
50
all measured cilium velocities, vs , according to equation (4.1). In this equation, the
typical cilium length, L, of Opercularia asymmetrica is 10 µm and the kinematic
viscosity of the surrounding medium, µ, is 1.2 · 10− 6 m2 /s (see chapter 3.1.1; µ–
PTV Setup and calibration). Therefore, the Reynolds number rages from 0.003
to 0.047. The induced flow can be estimated as a creeping flow for the whole
investigated velocity ranged due to the low order of magnitude of the Reynolds
number (Kos et al., 2009). Similar observations were reported by Zima et al. (2009)
who additionally showed that the chacteristic flow motion is steady and consists
of two counter rotating vortex pairs. Similar counter rotating vortex pairs were
observed for a Dean flow in micro channels at Dean numbers above 150 (Nguyen,
2012).
Re =
vs · L
µ
(4.1)
Figure 4.4: Ellipse half diameter a (in focal plane displacement) as a function of the
cilium frequency
4.1. Motion pattern of filaments
4.1.2
51
Three–dimensional motion pattern of the cilium at
moving focal plane
With the three–dimensional measuring technique at a moving focal plane it was
possible to determine the three–dimensional velocity of the cilium and its displacement in and out of focal plane direction. Correlations between the cilium frequency,
the three–dimensional velocity and the out of focal plane displacement of the cilium
are presented in this section as well.
Due to the piezo actuator displacement in positive z -direction or positive out of
the focal plane direction, it was possible to track the cilium when it was propagating
clockwise on the ellipse at the points 1, 2 and 3 (see Figure 4.2). Possible counter
clockwise motions of the cilium were also observed during this study, but were not
investigated in detail during the three–dimensional measurements (Hilfinger et al.,
2008). At these three points 1, 2 and 3 sharp images of the cilium were acquired.
After the cilium reached position 3, the focal plane was further moving in positive
z -direction while the cilium followed the elliptical trajectory and moved in negative
z -direction towards position 4. Consequently, after position 3 was reached the cilium
was not anymore clearly visible. The reason why the focal plane continued moving
in positive z -direction is because this technique was developed to track the motion
of the whole cilia row and not only one cilium. Investigations regarding the motion
of the whole cilia row, will be presented in more detail in the next section. Since
with this technique it was possible track the cilium at the points 1, 2 and 3, it was
also possible to determine the velocity and the displacement of the cilium in and
out of the focal plane direction.
Since the magnitude of the cilium velocity in z -direction is not known, various
measurements at different piezo actuator velocities of 250, 500, 1000 and 2000 µm/s
were conducted in order to find enough cases where the velocity of the cilium (vz )
and the velocity of the piezo actuator in positive z -direction are synchronised. For
such synchronised cases the cilium was sharply visible at the positions 1, 2 and 3
(see Figure 4.2). As a consequence, the velocity component of the cilium in positive
z -direction vz (out of focal plane direction) is equal to the velocity with which the
4.1. Motion pattern of filaments
52
focal plane is moved by the piezo actuator in the positive z -direction. Furthermore,
the out of focal plane displacement of the cilium (see ellipse half depth, b, in Figure
4.2) is equal to the displacement of the piezo actuator, which is know at each point
in time and for each aquired image. The velocity in the direction of the focal plane
vs was determined in similar manner as presented in section 4.1.1, where it was
computed out of the measured spatial and temporal intervals between the points 1–
2 and 2–3. After measuring concomitantly the velocity components vs (in the focal
plane direction) and vz (out of the focal plane direction) between the positions 1–2
and 2–3, the corresponding three–dimensional velocity vsz between the positions 1–2
and 2–3 was determined. For each experiment, the mean three–dimensional velocity
vsz was determined out of the three–dimensional vsz velocity values between the
positions 1–2 and 2–3. The deviation of the determined vsz velocity values between
the positions 1–2, 2–3 and the mean vsz velocity value are less then 2%.
Since the depth of the focal plane is 325 nm and the displacement b of the
cilium in z -direction is a few micrometers, the cilium was tracked only at these
three separate positions. For very high cilium velocities in z -direction, the cilium
was tracked only at the points 1 and 3.
The Figures 4.5 and 4.6 show the measured three–dimensional mean cilium velocity vsz and the ellipse half depth b as a function of the cilium frequency. Each
point represents a separate experiment. For the investigated frequencies the three–
dimensional mean velocity vsz is in a similar range as the two–dimensional velocity
vs (see Figure 4.3), since the velocity component in the z -direction vz (out of focal
plane direction) is smaller than the velocity component in the s-direction vs (in focal
plane direction). Hence, the three–dimensional cilium velocity vsz is dominated by
the two–dimensional in the focal plane velocity component.
When the frequency increases, the three–dimensional velocity vsz increases as
well, but the elliptical half depth b decreases. Therefore, the ellipse trajectory
becomes flattened with increasing velocity of the cilium. This result makes sense
otherwise the cilium would need to perform a longer distance within the same time
interval, which would require more energy input from the micro–organism. Hence,
the cilium beat seems to be optimized in a natural way to be as efficient as possible.
4.1. Motion pattern of filaments
53
Figure 4.5: Three–dimensional cilium velocity vsz as a function of the cilium frequency
Figure 4.6: Ellipse half depth b (out of focal plane displacement) as a function of the
cilium frequency
4.1. Motion pattern of filaments
4.1.3
54
Motion pattern of a cilia collective
This study showed that one cilium performs an elliptical motion when it is executing the active and recurring strokes. During experiments, it has been also
observed that a row of cilia are performing an undulatory time dependent motion.
This motion pattern of the row, which is comparable with a mechatronal wave, is
caused by the time shift or time delay between consecutive cilia. From the aquired
images it was possible to see that there is always a small spatial distance between
consecutive cilia which is caused by the time delay between them. Satir (1967) also
reported about the lateral cilia of Elliptio complanatus, where the cilia slide against
each other with a phase difference. In this section, the correlation between the time
phase shift and the cilia velocity and frequency are presented.
It can be assume that the three–dimensional measuring technique, where the
focal plane is moved by a piezo actuator, is the more suitable method to reproduce
the undulatory motion of cilia. During experiments it was observed that one cilium
can be partially tracked (till position 3 in Figure 4.2) by the moving focal plane
but the cilia behind it were not anymore sharpy visible, while the focal plane was
moving. Same problem occured for all used focal plane velocities of 250, 500, 1000
and 2000 µm/s. Such a problem was observed, since the cilia row was not aligned
in a prependicular manner with the moving focal plane, consequently the cilia were
not sharply visible when the focal plane was moving. Since there was no method
available to align the cilia row perpendicular to the moving focal plane, the three–
dimensional measuring method was not implemented in this case. It can be also
assume that the cilia at the mouth of Opercularia asymmetrica are not aligned
in a straight line but rather in a curved line, which makes the three–dimensional
measuring method also difficult to implement.
Due to an advantageous position of the cilia during the image acquisition of the
two–dimensional measurements, in certain experiments two consecutive cilia were
sharply visible in the stagnant focal plane. Although both consecutive cilia move
with the same frequency f and two–dimensional velocity vs , a spatial distance was
observed between them which is caused by the time shift of one cilium relative to
the other one. From the measured distance between them and their velocity vs ,
4.1. Motion pattern of filaments
55
the time shift ∆tshif t between consecutive cilia was determined. The velocity in the
focal plane direction vs was determined in similar manner as presented in Section
4.1.1. For different experiments, the temporal shift ∆tshif t is presented in Table 4.1.
vs [µm/s] f [Hz ] ∆tshif t [ms]
526
15
6
776
19
5
808
31
4
1128
38
3
Table 4.1: Time shift ∆tshif t between consecutive cilia as a function of the cilia velocity
vs and frequency f
It can be observed that with increasing velocity and frequency of the cilia the
time shift between consecutive cilia becomes shorter (Kos et al., 2009) and it is in
the expected range of milliseconds (Satir, 1967). Consequently, if ciliates beat their
cilia with a higher velocity, the higher will be also the velocity of the mechatronal
wave, since the time shift between consecutive cilia becomes smaller.
At this point it is interresting to observe that the periodical and the undulating
motion of cilia are inducing two steady counter rotating vortex pairs (Zima et al.,
2009). Due to the fact that in micro scale, diffusion effects are dominant, the reaction
of the surrounding medium is slow compared to the fast motion of the undulating
cilia (Nguyen, 2012). In general the Reynolds number can be understood as a
ratio between convective and diffusive momentum or as a ratio between diffusion
and convection time. Hence, the diffusion time of the surrounding medium can be
estimated according to equation (4.1), where the characteristic size of the vortex
flow D is 100 µm and the kinematic viscosity of the water and milk mixture is
1.2 · 10−6 m2 /s. The diffusion time in this case is 0.012 seconds while the duration
of the cilium beat at the maximum measured frequency of 125 Hz is 0.008 seconds.
This simple estimation shows that the diffusion time can be longer then the duration
of the periodical cilia motion, leading finally to a steady flow in the vicinity of the
cilia which is reacting slowly on the fast oscillation of cilia.
4.1. Motion pattern of filaments
tdif f usion = D2 /viscosity
4.1.4
56
(4.1)
Conclusions
This study showed that the cilia of the investigated ciliates (Opercularia asymmetrica) do not execute planar oscillations. Each cilium rather follows a continuous
elliptical trajectory during the execution of the active and recurring stroke (Juelicher
et al., 1996). This continuous elliptical motion is more advantageous then a planar
oscillation where the cilium has to periodically accelerate and deelerate. Therefore,
important parameters like two–dimensional and three–dimensional cilium velocity
(vs and vsz ), the half diameter a (in focal plane displacement of the cilium) as well
as the half depth b (out of focal plane displacement of the cilium) of the elliptical
trajectory were determined experimentally. Between the two and three–dimensional
cilium velocity and the cilium frequency a direct dependency was found. On the
other hand, it was found that the ellipse depth b decreases when the cilium velocity
increases, leading to flattened ellipse trajectories at higher velocities. This way the
cilium performs a shorter distance within the same time interval which requires less
energy input from the micro–organism.
The undulatory motion pattern of a cilia row develops due to a temporal shift
between consecutive (neighboring) cilia (Satir, 1967). This shift in time was determined experimentally as well and it was observed that with increasing velocity
of the cilia the temporal shift between consecutive cilia is decreasing, leading to a
faster propagation of the mechatronal wave.
With the achieved set of experiments it was also observed that the motion of
the cilia is undulatory and periodical. On the other hand, Zima et al. (2009)
found that the induced flow consists of two steady counter rotating vortices. The
dominance of the molecular momentum transport in micro scale can explain these
findings, where the surrounding medium is only slowly reacting on the undulatory
cilia motion leading to a steady induced flow.
4.2. Motion pattern and flow control of fins
4.2
57
Motion pattern and flow control of fins
Seahorses are another kind of creatures, which due to the undulatory motion
pattern of their fins, are able to induce a flow which allows locomotion and high
maneuvering skills. In comparison to other fishes, seahorses can not perform a fast
locomotion which makes them very vulnerable (Blake, 1974). However, their maneuvering skills are remarkable. From biological point of view a good maneuvering
allows seahorses to reach places where they can find nutrition. Additionally, they can
perform a pendular motion which is comparable to the motion of the surrounding algae. This pendular motion enables camouflage in their natural habitat and protects
them from natural enemies. This section elaborates the disability of seahorses to
swim fast and the tools what they are using in order to overcome this deficit and to
achieve good maneuvering. Hence, in Section 4.2.1, the measured and numerically
determined drag coefficients of the seahorse structure are compared with the drag
coefficient of other fishes. The kinematics applied by the seahorse fins and the flow
profiles induced by the undulating motion of seahorse fins (dorsal and pectoral) are
presented in the Section 4.2.2.
4.2.1
Swimming capability of seahorses compared to those
of other fishes
In comparison to other fishes like salmon or luce, seahorses do not have the
ability to perform fast locomotion. As observed during the experimental work,
seahorses have a relatively rigid body, which is one of the causes of this disability.
Unlike a dolphin or a shark, seahorses are not able to achive thrust by moving
their whole body in undulatory mode during swimming. Their body does not have
a smooth surface, they have many small bumps on their skin which makes their
surface rather rough. In opposite to other fishes, seahorses swim in a vertical position
which leads to a large face area relative to the swimming direction and probably
to a higher drag force. Other fishes swim in a horizontal mode which allows them
to swim faster and at a lower drag. In this section, all these informations are
taken as input and used to investigate the hydrodynamical features of the seahorse
4.2. Motion pattern and flow control of fins
58
body in a vertical position. The numerically and experimentally determined drag
coefficients are presented for different swimming velocities. Then, the drag coefficient
and the corresponding swimming velocity of the seahorse are compared with the drag
coefficient and swimming velocity of other fishes. The implemented numerical and
experimental procedures are presented in the Sections 3.2.1 and 3.1.3, respectively.
Seahorses are able to swim with a few centimetres per second. For the velocity
range between 0.01 and 0.1 m/s where seahorse swimming takes place, the drag
coefficient was determined numerically. The effect of higher swimming velocities up
to 1.6 m/s on the drag coefficient were investigated as well, in order to better understand how much drag force would a seahorse encounter, if the swimming velocity is
ten times more than the usual seahose swimming velocity. Consequently, the total
drag coefficient which includes the shear and pressure drag (see equation (3.3)) was
determined numerically at the following swimming velocities: 0.01, 0.05, 0.1, 0.2,
0.8, 1.6 m/s. These swimming velocities correspond to the inflow velocities which
were applied at the inlet of the numerical domain.
In Figure 4.7, the total drag coefficient is plotted against the Reynolds number
which was determined according to equation (4.2) for different swimming velocities
(uswimming ) of 0.01, 0.05, 0.1, 0.2, 0.8 and 1.6 m/s. In equation (4.2), Labdomen represents the width of the seahorse abdomen which is 2 cm and µ the viscosity of the
surrounding water, which is 1.2 · 10−6 m2 /s. In Figure 4.7, it can be observed that
for the investigated velocity range the total drag coefficient of the seahorse body increases rapidly for the Reynolds numbers above 2000 and swimming velocities above
1 m/s. Hence, with increasing swimming velocity or Reynolds number, the shear
and the pressure drag force acting on the seahorse body are increasing significantly,
leading to a considerable increase of the drag coefficient of nearly 0.2 at a Reynolds
number of 8000 (uswimming = 1.6 m/s). The minimum drag coefficient of 0.014 is
achieved at a Reynolds number of 2000 which corresponds to a swimming velocity
of 0.1 m/s. It turns out, that at the usual seahorse swimming velocity of 0.1 m/s,
they are experiencing the lowest drag coefficient. Therefore, it is not beneficial for
a seahorse to swim above 0.1 m/s, since at higher swimming velocities, the drag
coefficient and the drag force which seahorses have to overcome in order to swim are
4.2. Motion pattern and flow control of fins
59
increasing significantly.
Re =
uswimming · Labdomen
µ
(4.2)
Since the seahorse body is not streamlined, in front of the seahorse body the
flow is decelerated at the stagnation point (see Figure 4.8), where the kinetic energy
of the flow is transformed into pressure energy. The pressure which is developing at
the stagnation point and which is the main cause for drag is directly proportional to
the quadratic swimming velociy magnitude. Figure 4.9, demonstrates the quadratic
increase of the maximum pressure at the stagnation point with the Reynolds number for the investigated velocity ranges. Consequently, this plot showes one more
time that with increasing swimming velocity of the seahorse the pressure which is
generated at the stagnation point and the drag coefficient of the seahorse body are
also increasing.
Figure 4.7: Distribution of the total drag coefficient (shear and pressure) with increasing
Reynolds number
4.2. Motion pattern and flow control of fins
60
Figure 4.8: Velocity field at Re = 2000, in a plane section which is cutting the seahorse body through the abdomen and which is perpendicular to the upright
swimming position of the seahorse
Figure 4.9: Quadratic dependency of the maximum pressure at the stagnation point
from the Reynolds number. The pressure component is the main source for
drag on the seahorse body
4.2. Motion pattern and flow control of fins
61
The numerically determined drag coefficient at a swimming velocity of 0.1 m/s
was validated experimentally. Under this flow condition the numerically determined
drag coefficient was minimal and it was found as 0.014. For the experimental determination of the drag force the procedure described in Section 3.1.3 was applied
where the drag force acting on the seahorse body was transferred by a suitable mechanism to a laboratory scale. At a incoming flow velocity of 0.1 m/s, experiments
were repeated 20 times. The mass displayed on the laboratory balance monitor
which was able to measure two decimal places exactly, varied between 1.05 and 1.15
g. The averaged mass which was determined from all experiments was 1.1 g (4.5%
deviation), led to an averaged drag force of 0.004 N and an averaged drag coefficient
of 0.016. Consequently, the implemented numerical and experimental methods to
determine the drag coefficients were in good agreement. It can be concluded, that
the numerically determined drag coefficient was validated successfully against the
measurements.
Table 4.2 contains some drag coefficients (related to the total surface of the fish)
and Reynolds numbers for different fish species. During experimental work it was
observed that seahorse swimming usually takes place at 0.1 m/s which corresponds
to a Reynolds number of 2000. In Table 4.2 it can be seen that the Reynolds number
of other fishes (salmon, harp seal) is two or three orders of magnitude higher than
the seahorse Reynolds number. Hence, seahorses are slow swimmers and have at this
low swimming velocities and Reynolds numbers, the same drag coefficient as a harp
seal which is able to swim much faster (Reynolds number = 1.79 · 106 ). It can be
concluded that seahorses are swimming relatively slow compared to other fishes and
at a relatively high drag coefficient due to their immobile, non-streamlined, edgy and
vertical swimming body. However, they are still able to manoeuvre their immobile
body precisely to perform stagnation and locomotion in all directions of space. The
reason for this statement is commented in Section 4.2.2 where the investigations of
the fin induced flow are presented.
4.2. Motion pattern and flow control of fins
62
species
cD [-]
Re [-]
source
dolphin
0.0026
1.37 · 106
F.E. Fish (1993)
harp seal
0.016–0.028 0.98 − 1.79 · 106
F.E. Fish (1993)
mackerel
0.01
3 · 104
R.W. Blake (1983)
luce
0.005
1 · 106
R.W. Blake (1983)
salmon
0.015
3.5 · 105
R.W. Blake (1983)
seahorse
0.016
2 · 103
present work
Table 4.2: Drag coefficients and Reynolds numbers for different fish species
4.2.2
Fin kinematics and flow pattern induced by fins
As demonstrated by Delgado et al. (2009), seahorses posses different undulatory
fin actuation patterns which enable a high maneuvering flexibility. Their small fins
which are approximately two centimetre long (dorsal fin) and half centimetre wide
can move very fast in undulatory mode. The wave which is created during the
undulatory action of the fin can travel periodically along the fin length in both
directions and can have different amplitudes, wave numbers, frequencies and decay
constants (Delgado et al., 2009). Additionally, seahorses are able to manoeuvre even
in situations where only one fin (dorsal or pectoral) is active. Exact quantification of
parameters like amplitude, wave number and decay constant as well as correlations
between the fin frequnecy and the induced flow velocity are not yet available in
literature. The fin motion which is triggered by the seahorse, induces a flow in the
surrounding water which is comparable to a local small jet and which can transfer
momentum or thrust to the seahorse body and allow locomotion in water. The
knowledge about the fin kinematics and the flow induced by fins, can lead to the first
developments of well camouflaged and stabilized underwater propulsion systems.
Consequently, this section contains quantitative investigations on fin kinematics and
detailed numerical and experimental investigations of the flow profile induced at the
dorsal and pectoral fins.
4.2. Motion pattern and flow control of fins
63
Fin kinematics
The PIV measuring technique presented in Section 3.1.2 was applied to measure
the induced flow and the kinematics of fins. In some very seldom cases the seahorse
moved slowly with the dorsal fin into the laser light sheet plane (see Figure 3.11),
which made the recording of the fin motion posible. During these fin kinematics
investigations, it was not possible to measure the induced flow due to the shadow
created by the fin of the seahorse.
In Figure 3.11, where the forced kinematic of the fin is presented, it can be
observed that the part of the fin which is attached to the seahorse body is not moving.
The part of the fin which is free is performing a forced kinematic in undulatory mode.
For this case, no decay of the fin wave is observed, the fin displacement in time can
be easily described with a sine wave (see equation (2.9)) which is characterised by
a motion amplitude, wave number and frequency.
During many experiments seahorses were also slightly moving their body. This
motion of the seahorse body during the image acquisition was disturbing the measurements and made the optical accessibility of the fins very hard. At the end only
one case was found where the fin motion was tracked. From the recorded images,
the motion pattern as well as the amplitude, the wave number and the frequency of
the fin motion were exactly determined. Here the same evaluation and calibration
techniques were used as the ones implemented for the ciliates. The fin frequency
was measured from the time which elapsed till the fin wave travelled once through
the fin length and returned to the initial position. After measuring the undulation
frequency f (50 Hz ), amplitude A (0.003 m), wave number k (610 m−1 ) and fin
length L (0.02 m), it was possible to insert all these variables into equation (2.9)
and get a simplified equation which describes the fin deformation for this particular
case:
z(y, t) = 0.003 · sin(610 · y − 2π · 50 · t)
(4.3)
Further investigations of the fin kinematics were not conducted in this study,
but as mentioned before, it is known that seahorses have also other fin actuation
paterns. This first result regarding the fin kinematics is very helpful for all further
numerical investigations of the induced flow, since equation (4.3) can be used as a
4.2. Motion pattern and flow control of fins
64
boundary condition for the dorsal fin motion. Additionally, equation (4.3) can be
used to investigate numerically how various frequencies are influencing the induced
flow. Consequently, following sections contain detailed numerical and experimental
investigations of the fin induced flow. The effect of different fin frequencies on
flow velocity which were found numerically and experimentally are presented in the
following sections.
Detailed numerical investigations of the flow pattern induced by fins
This section contains detailed numerical investigations of the characteristic flow
profile induced by the undulatory fin motion. The fin motion helps seahorses to
perform locomotion in the surrounding medium. Parameters which can be adjusted
during the fin motion are, for example, the fin frequency, wave number and wave
amplitude. Since the fin dimension (0.02 m) and the induced wave amplitudes
(0.003 m) are very small, it can be expected that the induced flow velocity is mainly
influenced by the fin frequency (up to 50 Hz ) which dictates how fast the wave is
travelling along the fin, how fast the flow is actuated and how fast the seahorse
can perfom locomotion. Since a strong connection between fin frequency and flow
velocity is expected, the effect of different fin frequencies on the flow velocity are
presented in this section.
As described in Chapter 3.2.2, an undulatory motion equation (see equation
(3.5)) needs to be applied at the moving fin tip or fin outlet boundary (see Figure
3.12), in order to simulate a real fin motion and the induced flow. From the investigations presented in section Fin kinematics the motion amplitude A of 0.003 m, fin
length L of 0.02 m and the frequency f of 50 Hz are resumed. The wave number k
of 610 m−1 found from the kinematic investigations was not adopted due to numerical instabilities. At a fin frequency of 50 Hz and a wave number of 610 m−1 the
simulation was crashing and it was necessary to lower the wave number up to 225
m−1 , in order to make this cases run stable. It is worth to mention that lowering
the frequency to 30 Hz allowed also investigations at higher wave numbers up to
400 m−1 . Hence the final formula for the fin deformation which was inserted at the
fin outlet boundary and which corresponds to the grid velocity (mesh velocity) at
4.2. Motion pattern and flow control of fins
65
the fin outlet is:
vgrid =
∂z(y, t)
= −0.003 · 2π · 50 · cos(225 · y − 2π · 50 · t)
∂t
(4.4)
In equation (4.4), t represents simulation time and y the length coordinate of
a real fin which takes values from 0 to 0.02 m. The fin inlet which represents the
part of the fin which is attached to the seahorse body is fixed. Consequently, a fixed
fin inlet and a fin outlet which is moving according to equation (4.4), describes one
possible real motion of a fin and can be used for the investigations of the flow which
is induced by the undulating fin.
For the present case, Figure 4.10 shows the forced kinematics of the fin during
one undulation period of 20 ms in four different time steps (t0 , t1 , t2 , t3 ). This
periodic fin motion is perfomed in repetitive mode till the end of the simulation
time and the induced flow is determined. In Figure 4.10, it can be observed that
the fin wave is traveling in positive y-direction, since the sign of the angular velocity
is positive (+2πf ). In Figure 4.11 A, the tangential velocity vector field in a plane
section which is perpendicular to the fin and 2.5 mm away from the moving fin
outlet is presented for a certain time instance during the fin undulation. It can be
observed that the incoming flow is continously directed in positive y-direction since
it follows the motion of fin, which propagates in the same direction. Some lateral
effects of the flow can be also observed, because the fin motion has also a lateral
component. For a negative angular velocity (-2πf ) the fin wave is travelling in the
negative y-direction and the induced flow as well (see Figure 4.11 B).
For these one-way coupled investigations, only the effect of the fin motion on the
induced flow was considered. Still it can be assumed that the upwards motion of
the fin will be strongly enhanced by an upwards directed flow and vice versa.
In Figure 4.11, it can be observed that the flow is actuated only in the vicinity of
the small fin and that it is not propagating into the surrounding medium. Although
the undulation frequencies of seahorse fins are relatively high compared to those of
other fishes, the resulting flow is local due to the fact that the fins are small and
cannot generate motion amplitudes which are high enough to strongly actuate the
surrounding medium.
4.2. Motion pattern and flow control of fins
66
Figure 4.10: Fin deformation during one undulation period of 20 ms at a fin frequency
of 50 Hz
At such small scales viscosity effects are dominant and lead to a local flow which is
not propagating into the surrounding medium. This local character of the flow is in
general beneficial for seahorses since no finger prints are created in water which
4.2. Motion pattern and flow control of fins
67
Figure 4.11: Induced velocity vector field at a fin frequency of 50 Hz in a plane section
which is placed perpendicular to the fin and 2.5 mm away from the undulating fin; (A) velocity field for a positive angular velocity; (B) velocity
field for a negative angular velocity
4.2. Motion pattern and flow control of fins
68
can be perceived by their natural enemies and ensures camouflage.
During these investigations it was also found that the surface averaged velocity
in the plane section which is placed very close to the undulating fin outlet (1 mm)
is changing periodically with a bigger amplitude than the surface averaged velocity
in the plane section which is placed slightly more away (i.e., 2.5 mm). This result
is presented in Figure 4.12. It can be concluded that at a very close distance from
the moving fin, the flow is reacting fast on the fin deformation leading to some periodical changes of the surface averaged flow velocity in the vicinity of the fin. With
increasing distance from the fin, these periodical changes of the surface averaged
velocity decrease and become nearly constant. Since in these small scales the viscosity effects of the surrounding medium are stronger. Here two time scales must be
taken into consideration, namely the actuation time of the fin and the viscous time
scales. More detailed discussions on this topic are shown in the next section where
the experimental results of the flow field are presented as well.
Investigations of the periodically averaged flow velocity showed that this quantity
is not changing with time (see Figure 3.13). In Figure 3.13, where the maximum
flow velocity (averaged for each period) is plotted with respect to time, it can be
observed that the value of the maximum flow velocity is not changeing with time.
These findings indicate again a periodically steady flow.
In the present experimental work frequencies above 50 Hz were not found, although Delgado et al. (2009) showed that fin frequencies of seahorse can amount
up to 60 Hz. The most often frequencies were observed between 30 and 50 Hz ; this
will become clear in the next section where experimental correlations between the
fin frequency and the flow velocity are presented. Since a strong connection between
fin frequency and flow velocity is expected, the influence of different fin frequencies
on the induced flow are also investigated. Consequently, three additional cases were
investigated numerically at 20, 30 and 40 Hz while the amplitude of the fin oscillation, wave number and fin length were kept constant at 0.003 m, 225 m−1 and
0.02 m. For the whole investigated frequency range (20-50 Hz ), the character of the
induced flow was observed to be local and steady as in the previous investigations.
4.2. Motion pattern and flow control of fins
69
Figure 4.12: Plot of the surface averaged velocity evaluated in a plane section which is
placed perpendicular to the undulating fin and 1 respectively 2.5 mm away
from the undulating fin
Since the angular velocity was set to +2πf , the induced flow was continously
directed upwards. In this part of the work, the periodically averaged maximum
velocity (sampled at 2.5 mm away from the fin outlet) which is constant for the
whole simulation time, was evaluated for different fin frequencies. This quantity
was selected for these investigations, since this results will be compared with the
experimental findings where the maximum velocity of the flow was evaluated also.
Since during experiments the flow field was measured at a few millimeters away
from the undulating fin (see Figure 3.6), it is important to apply the same procedure for the numerical approach and sample the maximum velocity at a certain
distance from the moving fin (2.5 mm) and then create a periocally averaged value.
The periodically averaged maximum velocity together with the fin length and the
kinematic viscosity of the fluid were used to determine the Reynolds number of the
induced flow which is ploted against the frequency in Figure 4.13.
It can be observed that for the investigated frequency range, Reynolds number
of the induced flow is increasing linearly with the fin frequency. Consequently, the
4.2. Motion pattern and flow control of fins
70
Figure 4.13: Influence of different fin oscillation frequencies on the Reynolds number of
the induced flow
faster the seahorse fin is moving due to an increasing frequency, the more momentum
is tranferred to the surrounding fluid and the higher is the velocity of the induced
flow. For the whole investigated frequency range, the low range of the Reynolds
number (upper limit 2793 at 50 Hz fin frequency) indicates a laminar flow regime
where the viscous forces are dominant.
The averaged maximum velocity over one undulation period (sampled at 2.5 mm
away from the fin outlet) and the corresponding frequencies are presented in Table
4.3.
max. flow velocity [m/s] frequency [Hz ]
0.14
50
0.12
40
0.09
30
0.06
20
Table 4.3: Averaged maximum velocity over one undulation period (sampled at 2.5 mm
away from the fin outlet) and the corresponding frequencies
4.2. Motion pattern and flow control of fins
71
These velocity values which were sampled at 2.5 mm away from the fin outlet are
compared in the next section with the measured maximum flow velocities which
were measured also at a few millimeters away from the moving fin.
Detailed experimental investigations of the flow pattern induced by fins
This section depicts the experimentally determined flow patterns induced by the
seahorse dorsal and pectoral fins during stagnation. In moments where the seahorse
was standing still and with the active dorsal or pectoral fin a few millimetres (1-4
mm) away from the laser light sheet plane (see Figure 3.6), it was possible to aquire
good images of the induced flow. In this section, the numerically found characteristic
flow pattern is verified experimentally. Stabilizing effects of the induced flow on
the seahorse body are investigated and presented in this section as well. Lastly,
correlations between fin frequency and the velocity of the induced flow are verified
experimentally.
When some fin activity and flow motion in the laser light sheet plane were oserved
simultaneously, the camera of the PIV system was triggered for image acquisition.
Afterwards the images were evaluated in a classic PIV manner described in Section
3.1.2. Since the fin was also visible in the background of the acquired flow images,
it was possible to evaluate frequency of the fin and propagation direction. The fin
frequency was measured from the time which elapsed till the fin wave travelled once
through the fin length and returned to the initial position. Figure 4.14 illustrates
the characteristic flow profile induced at the dorsal and pectoral fin during vertical
stagnation of the seahorse. For these cases, the dorsal fin oscillated at a frequency
of 50 Hz in downwards direction while the pectoral fin oscillated at a frequency of
30 Hz in upwards direction.
Since the flow measurements at the dorsal and pectoral fin were performed separately, the two flow images presented in Figure 4.14 represent two different experiments with no correlations between them. From the flow profile induced at the
dorsal and the pectoral fin, it can be deducted that in the vicinity of the dorsal
fin a downwards directed flow is induced and in the vicinity of the pectoral fin an
upwards directed flow is induced. Simultaneously, the wave of the dorsal fin was
4.2. Motion pattern and flow control of fins
72
traveling downwards and the wave of the pectoral fin was travelling upwards.
Figure 4.14: Characteristic flow pattern induced by the dorsal fin (at a fin frequency of
50 Hz and vertical downwards propagation of the fin wave) and pectoral
fin (at a fin frequency of 30 Hz and vertical upwards propagation of the fin
wave)
This quantitative result is in good agreement with the numerical findings, where
it was found that the direction of fin wave propagation determines the direction of
the induced flow. With the PIV measuring technique, it was possible to capture
not only the direction of the induced flow but also the whole flow profile, which
for both fins consist of two counter rotating vortices, which in this case rotate
downwards at the dorsal fin and upwards at the pectoral fin. In Figure 4.14, it can
be observed that the flow is moving with a strong momentum input in the direction
predetermined by the fin motion. These experimental investigations additionally
showed that the induced vortices have a secondary lateral velocity component which
is transporting the surrounding medium in a sidewise direction. On both sides of
the moving fin a velocity component can be observed which is directed oppositely
to the fin motion and which is closing the whole vortex cycle. Consequently, these
4.2. Motion pattern and flow control of fins
73
experimental investigations showed the complete nature of the induced flow. Not
last, during vertical stagnation of the seahorse, for both fins a local flow in the
vicinity of the fin can be observed which is not propabating into the surrounding
water. Consequently, this result reinforces one more time the numerical findings
of a local induced flow. For all other performed experiments at the dorsal and
pectoral fins identical characteristic flow patterns were observed where the induced
flow consists of two counter rotating vortices which follow the direction of the fin
wave propagation and which exist only in the vicinity of the fins (Kos et al., 2010).
These PIV investigations affirm that due to the undulatory motion of the dorsal
and pectoral fins the surrounding medium is actuated. A momentum transfer from
the fluid to the seahorse body takes place which can preserves an equilibrium of forces
and stabilises the levitating body of the seahorse during stagnation. Consequently,
this function is not only carried out by the swim bladder but also by the fin induced
flow. Since in this section the flow force will be evaluated, beforehand the flow has to
be investigated more closely and it needs to be checked how it develops with time.
The experimental investigations regarding the fin kinematics showed that the fin
undulation itself is periodical with respect to time, on the other hand the numerical
investagations showed that the induced flow is steady. Since the seahorse is in a
stagnant position during the experimental measurements of the induced flow, it can
be presumed that the actuated flow is steady as well. Consequently, the numerical
findings regarding the steady induced flow are verified experimentally and the flow
fields at the dorsal and pectoral fins are observed with respect to time for the two
cases presented in Figure 4.14.
Figure 4.15 shows the characteristic flow profile induced at the dorsal fin during
short consecutive time steps of 5 ms (e.g. t0 and t1 ). Since the fin frequency
amounts to 50 Hz the flow profile presented in Figure 4.15 is valid for one undulation
period of the fin. Although seahorses are living organisms and usually perform small
movements with their body, within the time frame presented in Figure 4.15 it can
be observed that the position of the seahorse is nearly unchanged.
4.2. Motion pattern and flow control of fins
74
Figure 4.15: Development of the flow induced by the dorsal fin within short time steps
of 5 ms, at a fin frequency of 50 Hz. The white curve represents the contour
of the seahorse body and of the dorsal fin
The velocity changes of the induced flow which consists of two downwards directed
counter rotating vortices, are negligibly small and the position of the induced vortex
4.2. Motion pattern and flow control of fins
75
flow is not changing with time relative to the seahorse body (Kos et al., 2010). This
experimental finding during seahorse stagnation verifies the steady character of the
flow which was also found before numerically.
Similar flow investigations as for the dorsal fin were also performed during seahorse stagnation at the pectoral fin at a fin frequency of 30 Hz. The flow induced
at one pectoral fin is depicted within short time steps of 5 ms (e.g. t0 and t1 ) in
Figure 4.16. In the presented time frame, the velocity changes of the induced flow
which consists of two upwards directed counter rotating vortices are negligibly small
and the position of the induced vortex flow is not changing with time relative to the
seahorse body (Kos et al., 2010). Hence, during seahorse stagnation the induced
flow at the pectoral fin is steady as well.
Figure 4.16: Development of the flow induced by the pectoral fin within short time steps
of 5 ms, at a fin frequency of 30 Hz. The white curve represents the contour
of the seahorse with the pectoral fin
4.2. Motion pattern and flow control of fins
76
At this point a strong similarity between the undulatory motion of seahorses fins
and cilia can be observed, since for both cases the induced flow is steady and directly
attached to the body of the animal. Consequently, for both scales, the same effect
of a dominating molecular momentum transport applies, where the oscillations time
scales are much shorter then the viscous time scales. This allows only a slow reaction
of the fluid on the fast actuation of the fin, leading finally to a local induced flow.
In nature similar counter rotating vortices are observed frequently. For example
three dimensional counter rotating votices are formed during the filling process of
a heart ventricle in order to compensate the deceleration of the incoming blood jet
(Oertel, 2001). In the wake flow of a slowly forwards flying sea gull, the vortices induced at the wing tips pass over into counter rotating vortices which are periodically
detaching (Oertel, 2001).
Just as in other natural systems, seahorses are also using the effects induced by
counter rotating vortex pairs. Based on the findings of the present work regarding
the extent of the fin induced vortex flow as well as the velocity range, it is possible to estimate the magnitude of the thrust which acts on the seahorse body and
interacts with the swim bladder buoyancy to stabilize altogether the seahorse body
during swimming. The buoyancy and gravity force induced by the seahorse body
are excluded from these investigations, since the density of the seahorse body and
the density of the surrounding aquarium water are roughly equal (Delgado et al.,
2009).
The thrust is approximated for the dorsal fin at a fin frequency of 50 Hz and at the
pectoral fin for a fin frequency of 30 Hz. The thrust which is induced by the micro
jet in the vicinity of the seahorse body can be determined according to equation
(4.5), where vf low represent the velocity of the induced flow, ρ the measured density
of the aquarium water ( 1.0 · 103 kg/m3 ) and A the cross section surface through
which the induced flow passes with a strong momentum input from the fin. The
cross section area is relatively small and can be approximated as 1 cm2 at the dorsal
and pectoral fins.
F = ρ · vf2low · A
(4.5)
4.2. Motion pattern and flow control of fins
77
Since the frequency of the dorsal fin beat equals in this case to 50 Hz, from the
previous investigations it was found that the maximum velocity of the induced flow
is 0.09 m/s (see Figure 4.15). Consequently, according to equation (4.5) a thrust of
8.1 · 10−4 N can be estimated at the dorsal fin. A pectoral fin frequency of 30 Hz
induces a maximum flow velocity of 0.03 m/s and a trust of 9 · 10−5 N. For both
cases, the thrust on the seahorse body acts in opposite of induced flow direction.
According to Delgado et al. (2009), by using computer tomography it was found
that the three–dimensional shape of the swim–bladder filled with oxygen is elliptical
with 15 mm x 10 mm diameter and 5 mm height. The oxygen density at the
aquarium temperature of 230 C is equal to 1.3 kg/m3 . The buoyancy force induced
by the bladder can be calculated easily from the product of the bladder mass (7.8 ·
10−7 kg) and the acceleration of gravity (9.81m/s2 ). Then, the buoyancy force is
computed as 7.6 · 10−5 N. From these simple calculations it can be concluded that
the thrust which acts on the seahorse body and the bladder induced buoyancy force
are in a similar range. They can be seen as different tools which a seahorse can use
during maneuvering and stabilization in water.
The shear rate distribution of the flow induced by the dorsal (50 Hz ) and pectoral
(30 Hz ) fins during seahorse stagnation might provide an additional insight, on the
stabilizing mechanisms of the flow induced by the dorsal and pectoral fins on the
whole seahorse body. Figure 4.17 shows the shear rate distribution at the dorsal
and pectoral fin. For both fins the region of maximum shear rate is located close
to the seahorse body where the flow is deflected. Since the shear stress is directly
proportional to the shear rate presented in Figure 4.17 and the region of maximum
shear is placed close to the seahorse body, it can be assumed that in this region,
strong flow velocity gradients occur which support the seahorse during maneuvering.
From the present study, it can be also deducted that the fin undulation takes
place at high frequencies of up to 50 Hz. This ensures according to the second Stokes
problem a lower shear layer thickness σ around the moving fin (see equation (4.6)),
which allows a fast actuation of the surrounding medium and a good momentum
transfer from the moving fin to the fluid and vice versa.
4.2. Motion pattern and flow control of fins
78
q
σ ∝ ν/f reqf in
(4.6)
Figure 4.17: Shear rate distribution of the induced flow at the dorsal (50 Hz ) and pectoral fin (30 Hz )
Numerical investigations have showed that the flow velocity is directlly influenced by fin frequency. In Table 4.4 some experimentally determined time averaged
maximum velocities of the induced flow and corresponding fin frequencies are presented for the dorsal and pectoral fins. The maximum velocity was determined for
ten consecutive exposures of the camera (time interval between exposures is 5 ms)
and a mean value was determined. For the presented average values deviations of
up to ± 18% were found. From the experimental results presented in Table 4.4 and
form the numerical results presented before in Table 4.3, it can be observed that an
increasing fin frequency causes a higher flow velocity. Hence, if a seahorse needs to
perform a faster locomotion then it needs to actuate the fin with a higher frequency
which will cause a faster induced flow and a bigger thrust which is acting on the
seahorse body. Since the flow velocities at 40 and 50 Hz are nearly equal (see Table
4.4), it can be assumed that the flow velocity which is induced by the fin undulation is also influenced by further parameters like oscillation amplitude or wave
4.2. Motion pattern and flow control of fins
79
number. The effect of the different wave numbers or oscillation amplitudes on the
flow velocity were not investigated in the present work since with the implemented
PIV measuring technique it was not possible to simulaneously track the flow and fin
motion precisely.
fin
max. flow velocity [m/s] frequency [Hz ]
dorsal
0.09
50
dorsal
0.08
40
dorsal
0.03
30
pectoral
0.07
50
pectoral
0.03
30
Table 4.4: Maximum flow velocities, which are induced at the dorsal and pectoral fin
and the corresponding frequencies
After comparing the numerically and experimentally determined velocities (see
Tables 4.3 and 4.4), it can be concluded that for equal fin frequencies the numerically
and experimentally determined flow velocities are in a similar laminar range. For
both methods an increasing frequency led to a higher flow velocity. Further it can be
deducted that for the same frequency values, the experimentally determined maximum flow velocities are slightly smaller than the numerically determined velocities.
Since the numerical investigations showed that the magnitude of the flow velocity
is decreasing with increasing distance from the moving fin (see Figure 4.12), this
effect occurs because of the fact that the flow measurements conducted with PIV
were performed at a slightly bigger distance of up to 4 mm away from the moving
fin tip (fin outlet) while the numerical velocity values were sampled at exactly 2.5
mm away from the moving fin outlet.
4.2.3
Conclusions
In this section it has been shown that, seahorses are swimming relatively slow
compared to other fishes and their body has at a relatively high drag due to the fact
that it is non-streamlined, edgy and in upright swimming position. Still seahorses
4.2. Motion pattern and flow control of fins
80
can manoeuvre their immobile body very precisely and perform stagnation and
locomotion in all directions of space due to the flow which is induced by their fins.
From the reported numerical and experimental investigations of the fin motion
and the induced flow, it can be concluded that the undulating motion of fins induces
a flow which is steady and laminar. In these small scales where the viscous effects are
dominant, the reaction of the surrounding medium on the periodically undulating fin
is slow, which is leading to a steady induced flow. Additionally, the fin oscillations
which have been observed to be between 30 to 50 Hz, induce a local flow which
is not propagating into the surrounding medium. The profile of the characteristic
induced flow consists of two counter rotating vortex pairs whose rotation direction is
predetermined by the propagation direction of the fin wave. The measured velocities
of the induced flow were between 0.03 m/s at a fin frequency of 30 Hz and 0.09 m/s
at a fin frequency of 50 Hz.
In this study, experimental and numerical investigations showed that the frequency of the undulating fin is directly influencing the flow velocity, leading to
higher velocities of the flow at higher frequencies of the fin. By controlling the fin
motion, seahorses can vary the magnitude and direction of the induced flow which
then allows a variation of swimming velocity and direction.
In the present work it was also found that the flow induced thrust which directly
acts on the seahorse body and the bladder buoyancy force are in a similar range.
It becomes clear that seahorses posses different actuation tools which make maneuvering and stabilization in water possible. This maneuvering skills are essential for
the life–sustain of seahorses since they can use them for foraging and camouflage.
Chapter 5
Summary and outlook of the
present study on Opercularia
asymmetrica and Hippocampus
reidi
After presenting the scientific results of this study, it can be concluded that some
basic understanding for complex, bio kinetic processes of filaments in micro scale
and fins in macro scale were provided. These kinematics, which are applied by the
immobile under water life forms Opercularia asymmetrica and Hippocampus reidi
can be suggested for novel technical applications or to improve the existing ones.
The investigations were conducted by using experimental techniques and numerical
approaches.
5.1
Opercularia asymmetrica
Ciliates as Opercularia asymmetrica are creatures which are able to move the
cilia at their mouth in undulatory mode and to induce two counter rotating vortex
pairs which are allowing the tranport of nutriments from the surrounding medium
into their body (Zima et al., 2009). Additionally, the induced flow is enhancing
the formation of granular activated sludge which forms the living environment of
81
5.1. Opercularia asymmetrica
82
ciliates. The knowledge about the kinematics of cilia is essencial, since it can be
used for the development of novel micro mixing technologies particularly for the
cases where diffusion limitations occur. Moreover, in catalytic applications, the
transport of educts to catalytic active surfaces can be improved with such micro
mixers. In bigger scales, this actuation can be also used to enhance heat and mass
transfer processes, between an immobile surface and the bulky phase.
This study showed that the cilia of the investigated ciliates (Opercularia asymmetrica) do not execute planar oscillations. Each cilium rather follows a continuous
elliptical trajectory during the execution of active and recurring stroke. This continuous elliptical motion is more advantageous then a planar oscillation where the
cilium has to periodically accelerate and deaccelerate. Therefore, important parameters like two–dimensional and three–dimensional cilium velocity (vs and vsz ), the
half diameter a (in focal plane displacement of the cilium) as well as the half depth
b (out of focal plane displacement of the cilium) of the ellipse trajectory were determined experimentally by using a dynamical scanning in layers method. Between the
two and the three–dimensional cilium velocities and the cilium frequency a direct
dependency was found. On the other hand, it was found that the ellipse depth b is
decreasing when the cilium velocity is increasing, leading to flattened ellipse trajectories at higher velocities. This way the cilium performs a shorter distance within
the same time interval which requires less energy input from the micro–organism.
The undulatory motion pattern of the cilia row develops because of a temporal
shift between consecutive cilia. This shift in time was determined experimentally
as well and it was observed that with increasing velocity of the cilia the temporal
shift between consecutive cilia is decreasing, leading to a faster propagation of the
mechatronal wave. With the achieved set of experiments it was observed that the
motion of the cilia is undulatory and periodical. On the other hand, Zima et al.
(2009) found that the induced flow is continuous, steady and consists of two counter
rotating vortex pairs. The dominace of the molecular momentum transport in micro
scale can explain these findings, because in this case the surrounding medium is only
slowly reacting on the undulatory cilia motion leading to a steady induced flow.
For future investigations of the three–dimensional cilium velocity it is recom-
5.2. Hippocampus reidi
83
mended, during a single experiment to perform consecutively the desired piezo actuator displacement of 50 µm at different piezo actuator velocities of 250, 500, 1000
and 2000 µm/s. With this approach, the probability that the motion of the piezo
actuator and cilium overlap is increasing. Therefore experimental effort can be reduced. The experimental data which was acquired during the present study can be
used for the development and investigation of novel technical micro mixers which
have a similar actuation pattern as the cilia of Opercularia asymmetrica.
5.2
Hippocampus reidi
Due to the undulatory motion pattern of fins, seahorses are able to induce a flow
which allows locomotion and high maneuvering skills. In comparison to other fishes,
seahorses can not perform a fast locomotion which makes them very vulnerable.
However, their maneuvering skills are remarkable. To reach places where seahorse
can find food, the good maneuvering is very important. Additionally, they can perform a pendular motion which is comparable to the motion of the surrounding algae.
This pendular motion enables camouflage in their natural habitat and protects them
from natural enemies. Although the relative size of the seahorse fins to their body
is small, they can manoeuvre and stabilize their huge body precisely by controlling
the swim bladder bouancy and the fin induced flow. The motion of the undulating
fin induces a local and small jet which then transfers momentum or thrust to the
seahorse body and allows locomotion in water. The good manoeuvrability, due to
the local fin induced flow, has a high transfer potential for future technical applications. For example, under water vehicles can be used to perform repairs at drilling
platforms and under water drones can be used for military applications.
This study showed that seahorses are swimming relatively slow compared to
other fishes and their body has at a relatively high drag due to the fact that the
body of seahorses is non-streamlined, edgy and in upright swimming position. Still
they can manoeuvre their immobile body very precisely and perform stagnation and
locomotion in all directions of space, due to the flow which is induced by their fins.
From the reported numerical and experimental investigations of the fin motion
5.2. Hippocampus reidi
84
and the induced flow, it can be concluded that the undulating motion of fins induces
a flow which is steady and laminar. In these small scales where the viscous effects are
dominant, the reaction of the surrounding medium on the periodically undulating fin
is slow, which is leading to a steady induced flow. Additionally, the fin oscillations
which have been observed to be between 30 to 50 Hz, induce a local flow which is not
propagating into the surrounding medium. The profile of the induced flow consists
of two counter rotating vortex pairs whose rotation direction is predetermined by
the propagation direction of the fin wave. The measured velocities of the induced
flow were between 0.03 m/s at a fin frequency of 30 Hz and 0.09 m/s at a fin
frequency of 50 Hz. Hence, experimentally and numerically it was shown that the
frequency of the undulating fin is directly influencing the flow velocity, leading to
higher velocities of the flow at higher frequencies of the fin. By controlling the
fin motion, seahorses can vary the magnitude and direction of the induced flow.
The induced flow thrust allows them to vary the swimming velocity and direction.
Additionally it was found that the flow induced thrust which directly acts on the
seahorse body and the bladder bouyancy force are in a similar range. It becomes
clear that seahorses posses different actuation tools which make maneuvering and
stabilization in water possible. This maneuvering skills are essential for seahorses
since they can use them for foraging and camouflage.
For future works, some further two–dimensional, three component PIV (2D-3CPIV) measurements are recommended, to investigate at once the two and three–
dimensional stabilizing effects of the induced flow on the seahorse body.
The present numerical investigations considered only the effect of an impressed
fin motion on the surrounding medium. It is recommended, to investigate the vice
versa influence between fin motion and the induced flow, since it can be speculated
that the undulatory fin motion is not only controlled by the fin muscles, but also
by the induced flow. Still this task is difficult, not only due to the numerical complexity, but also because the material properties of the fin are not well known and
must be approximated. To simulate the fin deformation the chimera grid method
is rather recommended, since the present study showed that the morphing method
has limitations when larger deformations occur. Still the experimental data acquired
5.2. Hippocampus reidi
85
during the present study can be used to better understand the actuation pattern of
seahorse fins and the fin induced flow which can be very helpful when developing
new under water actuation systems.
Bibliography
Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., Watson, J.D. (1995) Molekularbiologie der Zelle, VCH Verlagsgesellschaft Weinheim Germany, pp. 963–969.
Anderson, J.D. (1995) Computational Fluid Dynamics–The basics with applications,
McGraw Hill, pp. 247–248.
Anderson, J.M., Streitlien, K., Barrett, D.S., Triantafyllou, M.S. (1998) Oscillating
foils of high propulsive efficiency, Journal of Fluid Mechanics vol. 360, pp. 41–72.
Anderson, E.J., McGillis, W.R., Grosenbaugh, M.A. (2000) The boundary layer of
swimming fish, Journal of Experimental Biology 204, pp. 81–102.
Berg, H.C. (1971) How to Track Bacteria, The review of scientific instruments, pp.
868–871.
Blake, J. (1974) Hydrodynamic Calculations on the Movements of Cilia and Flagella
- I. Paramecium, Journal of theoretical Biology 45, pp. 183–203.
Blake, J. (1983) Fish Locomotion, Cambridge University press.
Blake, R.W. (1976) On seahorse locomotion, Journal of the Marine Biological Association of the United Kingdom 56, pp. 939–949.
Bown, M.R., MacInnes, J.M., Allen, R.W.K., Zimmerman W.B.J (2006) Threedimensional, three–component velocity measurements using stereoscopic microPIV and PTV, Measurement Science and Technology 17, pp. 2175–2185.
Breder, C.M., Edgerton, H.E. (1942) An analysis of the locomotion of the seahorse,
Hippocampus hudsonius, by means of high speed cinematography, Annals of the
New York Academy Sciences 43, pp. 145–172.
86
BIBLIOGRAPHY
87
Brokaw, C.J. (2005) Computer Simulation of Flagellar Movement IX. Oscillation
and Symmetry Breaking in a Model for Short Flagella and Nodal Cilia, Cell Motility and the Cytoskeleton 60, pp. 35–47.
Bruecker, Ch., Spatz, J., Schroeder, W. (2005) Feasibility study of wall shear stress
imaging using micro structured surfaces with flexible micro pillars, Experiments
in Fluids 39, pp. 464–474.
Cartwright, J.H.E., Piro, O., Tuval, I. (2004) Fluid-dynamical basis of the embryonic
development of left-right asymmetry in vertebrates, Proceedings of the National
Academy of Sciences of the U.S.A. 101, No. 19, pp. 7234–7239.
Consi, T.R., Seifert, P.A., Triantafyllou, M.S., Edelmann, E.R. (2001) The dorsal
fin engine of the seahorse (Hippocampus sp.), Journal of Morphology 248, pp.
80–97.
Delgado, A., Zima–Kulisiewicz, B.E., Lienhart, H., Krupczinsky, P., Schuster, S.
(2009) Evolutionary optimizes locomotion control and acoustic emission induced
by small are propulsion systems in water, Presentation of DFG Priority Program
SPP1207 in Berlin.
Drucker, E.G., Lauder, E.V. (2001) Locomotor function of the dorsal fin in teleost
fishes: experimental analysis of wake forces in sunfish, The Journal of Experimental Biology 204, pp. 2943–2958.
Drucker, E.G., Lauder, E.V. (2001) Wake dynamics and fluid forces of turning manoeuvres in sunfish, The Journal of Experimental Biology 204, pp. 431–442.
Durst, F. (2006) Grundlagen der Strömungsmechanik, Springer–Verlag Berlin Heidelberg, pp. 123ff.
Ellington, C.P., van den Berg, C., Willmott, A.P., Thomas, A.L.R. (1996) Leadingedge vortices in insect flight, Nature 384, pp. 626–630.
Fan, Z., Chen, J., Zou, J., Bullen, D., Liu, C., Delcomyn, F. (2002) Design and
fabrication of artificial lateral line flow sensors, J. Micromech. Microeng. 12, pp.
655–661.
BIBLIOGRAPHY
88
Fish, E.F. (1993) Power output and propulsive efficiency of swimming bottle nose
dolphins, Journal of experimental Biology 185, pp. 179–193.
Flynn, A.J., Ritz, D.A. (1999) Effect of habitat complexity and predatory style on
the capture success of fish feeding on aggregated prey, J. Mar. Biol. Ass. U.K. 79,
pp. 487–494.
Gilmanov, A., Sotiropoulos, F. (2005) A hybrid Cartesian/immersed boundary
method for simulating flows with 3D, geometrically complex, moving bodies, Journal of Computational Physics, pp. 457–492.
Gray, J. (1922) The Mechanism of Ciliary Movement, Proceedings of the Royal
Society of London, Series B, Containing Papers of a Biological Character 93, No.
650, pp. 104–121.
Gray, J. (1930) The Mechanism of Ciliary Movement VI. Photographic and Stroboscopic Analysis of Ciliary Movement, Proceedings of the Royal Society of London.
Series B, Containing Papers of a Biological Character 107, No. 751, pp. 313–332.
Gueron, S., Levit–Gurevich, K. (2001) A three–dimensional model for ciliary motion
based on the internal 9 + 2 structure, Proceedings of the Royal Society of London.
Series B 268, pp. 599–607.
Hilfinger, A., Juelicher, F. (2008) The chirality of ciliary beat, Physical Biology Vol.
5, Abstract 016003.
Hinsch, K.D. (2002) Holographic particle image velocimietry, Measurement Science
and Technology 13, R61–R72.
Juelicher, F., Vilfan, A. (1996) Hydrodynamic flow patterns and synchronisation of
beating cilia, Physical Review Letters 96, pp. 058102 1-4.
Kato, N. (1998) Locomotion by mechanical pectoral fins, Journal of Marine Science
and Technology 3, pp. 113–121.
BIBLIOGRAPHY
89
Kaya, M., Tuncer, I. H. (2009) Optimization of Flapping Motion Parameters for
Two Airfoils in a Biplane Configuration, Journal of Aircraft, Vol. 46, No. 2, pp.
583–592.
Khatavkar, V., Anderson, P.D., den Toonder, J.M.J., Meijer,H.E.H. (2007) Active
micromixer based on artificial cilia, Physics of Fluids 19, pp. 083605 1–12.
Kos, E., Rauh, C., Delgado, A. (2009) Bio–compatible visualisation of micro flow
and periodic reciprocating cilia beat induced by Opercularia asymmetrica with micro particle image velocimetry and micro particle tracking velocimetry, Presented
at GALA conference in Cottbus 2009, pp. 57 1–8.
Kos, E., Rauh, C., Delgado, A. (2010) Analysis of the flow induced by the undulatory
fin motion of seahorse, Presented at GALA conference in Cottbus 2010, pp. 28
1–10.
Kuiter, R.H. (2000) Seahorses, pipe fishes and their relatives: a comprehensive guide
to Syngnathiformes, Chorleywood, UK: TMC Publications.
Lauder, G.V., Naunen, J.C., Drucker, E.G. (2002) Experimental Hydrodynamics
and Evolution: Function of Median Fins in Ray-finned Fishes, Integr. Comp. Biol
42, pp. 1009–1017.
Leroyer, A., Visonneau, M. (2005) Numerical methods for RANS simulations of a
self–propelled fish–like body, Journal of Fluids and Structures, pp. 975–991.
Gray, J. (1930) Large–amplitude elongated–body theory of fish locomotion, Proc. R.
Soc. Lond. B. 179, pp. 125–138.
Lindken, R., Westerweel, J., Wieneke, B. (2006) Stereoscopic Micro Particle Image
Velocimetry, Experiments in Fluids 41, pp. 161–171.
Liu, R.H., Yang, J., Pindere, M.Z., Athavale, M., Grodzinski, P. (2002) Bubbleinduced acoustic micromixing, Lab Chip 2, pp. 151–157.
BIBLIOGRAPHY
90
Liu, J., Dukes, I., Hu, H. (2005) Novel mechatronics design for a robotic fish,
International Conference on Intelligent Robots and Systems (IROS 2005), pp.
807–812.
Lourie, S.A., Foster, S.J., Cooperr E.W.T., Vincent, A.C.J.A. (2004) Guide to
the identification of seahorses, Project seahorse and TRAFFIC North America.
Washington D.C. University of British Columbia and World Wildlife Fund.
Low, K.H., Willy, A. (2006) Biomimetic Motion Planning of an Undulating Robotic
Fish, Journal of Vibration and Control 12(12), pp. 1337–1359.
Lu, L.H., Ryu, K.S., Liu, C. (2002) A magnetic micro stirrer and array for micro
fluidic mixing, J. Microelectromech. Syst. 11, pp. 462–469.
Maas H.G., Gruen, A., Papantoniou, D. (1993) Particle Tracking Velocimetry In
Three-Dimensional Flows, Part 1. Photogrammetric determination of particle coordinates, Experiments in Fluids 15, pp. 133–146.
Machemer, H. (1972) Ciliary Activity and the Origin of Metachrony in Paramecium:
Effects of increased viscosity, The Journal of Experimental Biology 57, pp. 239–
259.
Malik, N.A., Dracos, Th., Papantoniou, D.A. (1993) Particle tracking velocimetry
in three-dimensional flows, Experiments in Fluids 15, pp. 279–294.
McGrath, J., Somlo, S., Makova, S., Tian, X., Brueckner, M. (2003) Two Populations of Node Monocilia Initiate Left–Right Asymmetry in the Mouse, Cell 114,
pp. 61–73.
Mensing, G.A., Pearce, T.M., Graham, M.D., Beebe, D.J. (2004) An externally
driven magnetic micro stirrer, Philos. Trans. R. Soc. London, Ser. A 362, pp.
1059–1068.
Meschede, D. (2001) Gerthsen Physik, Springer Verlag, Auflage 22, pp. 160–163.
Mittal, R., Dong, H., Bozkurttas, M., Najjar, F.M., Vargas A., von Loebbecke A.
(2008) A versatile sharp interface immersed boundary method for incompressible
BIBLIOGRAPHY
91
flows with complex boundaries, Journal of Computational Physics 227, pp. 4825–
4852.
Mueller, U.K., Van der Heuvel, B., Stamhuis E.J., Videler, J.J. (1997) Fish foot
prints: Morphology and energetics of the wake behind of continuously swimming
mullet (Chelon labrosus Risso), Journal of Experimental Biology 200, pp. 2893–
2906.
Muensch, M., Breuer, M. (2008) Fluid–Structure Interaction Using LES – A Partitioned Coupled Predictor–Corrector Scheme, Proc. Appl. Math. Mech. 8, pp.
10515–10516.
Muijres, F.T., Johansson, L.C., Barfield R., Wolf, M., Spedding, G.R., Hendenstroem, A. (2008) Leading–Edge Vortex Improves Lift in Slow–Flying Bat, Science
Vol. 319, pp. 1250–1253.
Nachtigall, W., Mees, H.B., Hofer, H. (1985) Vortriebserzeugung bei der Regenbogenforelle durch phasisch gekoppelte Biege–Dreh–Schwingungen der Schwanzflosse:
Einen messtechnische Bestaetigung der Hertelschen Theorie nach Analyse des
Schwimmers in Freiwasser und Wasserkanal, Zool. Jb. Anat., pp. 513–519.
Naunen, J.C., Lauder, G.V. (2002) Quatification of the wake of rainbow trout (Oncorhynchus mykiss) using three–dimensional stereoscopic digital particle image velocimetry, Journal of Experimental Biology 205, pp. 3271–3279.
Nguyen, N.T. (2012) Micromixers Fundamentals, Design and Fabrication, Second
Edition, pp. 201–203.
Nonaka, S., Tanaka, Y., Okada, Y., Takeda, S., Harada, A., Kanai, Y., Kido, M.,
Hirokawa N. (1998) Randomization of Left-Right Asymmetry due to Loss of NodalCilia Generating Leftward Flow of Extra embryonic Fluid in Mice Lacking KIF3B
Motor Protein, Cell 95, pp. 829–837.
Oddy, M.H., Santiago, J.G., Mikkelsen, J.C. (2001) Electro kinetic instability micro
mixing, Anal. Chem. 73, pp. 5822–5832.
BIBLIOGRAPHY
92
Oertel, H. (2008) Biostroemungsmechanik Grundlagen, Methoden und Phaenomene,
Vieweg + Teubner Verlag, pp. 41 and 186.
Okada, Y., Nonaka, S., Tanaka, Y., Saijoh, Y., Hamada, H., Hirokawa, N. (1999)
Abnormal Nodal Flow Precedes Situs Inversus in iv and inv mice, Molecular Cell
4, pp. 459–468.
Park, J.S,. Kihm, K.D. (2006) Three dimensional micro-PTV using deconvolution
microscopy, Experiments in Fluids 40, pp. 491–499.
Peric, M,. Ferziger, J.H. (2002) Computational Methods for Fluid Dynamics,
Springer–Verlag Berlin Heidelberg, pp. 373–381.
Petermeier, H., Kowalczyk, W., Delgado, A., Denz, C., Holtmann, F. (2007) Detection of micro organismic flows by linear and nonlinear optical methods and
automatic correction of erroneous images artefacts and moving boundaries in image generating methods by a neuro numerical hybrid implementing the Taylor’s
hypothesis as a priori knowledge, Experiments in Fluids 42, pp. 611–623.
Raffel, M., Willert, C., Kompenhans, J. (1998) Particle Image Velocimetry: A Practical Guide, Springer-Verlag, Heidelberg.
Raffel, M., Willert, C., Kompenhans, J. (1998) Particle Image Velocimetry: A Practical Guide, Springer-Verlag, Heidelberg, pp. 34.
Ramamurti, R., Sandberg, W.C. (2002) A three–dimensional computational study
of the aerodynamic mechanisms of insect flight, Journal of Experimental Biology
205, pp. 1507–1518.
Ryu, K.S., Shaikh, K., Glouch, E., Fan, Z., Liu, C. (2004) Micro magnetic stir–bar
mixer integrated with parylene microfluidic channels, Lab Chip 4, pp. 608–613.
Santiago, J.G., Wereley, S.T., Meinhart ,C.D., Beebe, D.J., Adrian, R.J. (1998) A
Particle Image Velocimetry System for Microfluidics, Experiments in Fluids 25,
pp. 316–319.
BIBLIOGRAPHY
93
Satake, S., Kunugi, T., Sato, K., Ito, T., Kanamori, H., Taniguchi J. (2006) Measurements of 3D flow in a micro-pipe via micro digital holographic particle tracking
velocimetry, Measurement Science and Technology 17, pp. 1647–1651.
Satir P. (1967) Morphological Aspects of Ciliary Motility, Journal of General Physiology pp. 249.
Sfakiotakis, M., Davies, J. B. C., Lane, D. M. (1998) Review of Fish Swimming
Modes for Aquatic Locomotion, IEEE Journal of Oceanic Engineering 24, pp.
237–252.
Sfakiotakis, M., Lane, D.M., Davies, B.C. (2001) An experimental undulating fin
device using the parallel bellows actuator, Proceeding of the IEEE International
Conference on Robotics and Automation, Seul, Korea 3, pp. 2356–2362.
Smith, D.J., Blake, J.R., Gaffney, E.A. (2008) Fluid mechanics of nodal flow due to
embryonic primary cilia, Journal of the Royal Society Interface 5, pp. 567–573.
Standen, E.M., Lauder, G.V. (2005) Dorsal and anal fin function in bluegill sunfish Lepomis macrochirus, three–dimensional kinematics during propulsion and
manoeuvring, Journal of Experimental Biology 208, pp. 2753–2763.
Supp, D.M., Brueckner, M., Kuehn, M.R., Witte, D.P., Lowe, L.A., McGrath, J.M.,
Coralles, J., Potter, S.S. (1999) Targeted deletion of the ATP binding domain of
left-right dynein confirms its role in specifying development of left-right asymmetries, Development 126, pp. 5495–5504.
Takeda, S., Yonekawa, Y., Tanaka, Y., Okada, Y., Nonaka, S., Hirokawa N. (1999)
Left-Right Asymmetry and Kinesin Superfamily Protein KIF3A: New Insights in
Determination of Laterality and Mesoderm Induction by kif3A-/- Mice Analysis,
Journal of Cell Biology 145, pp. 825–836.
Tanida, Y. (2003) Locomotion by Tandem and Parallel Wings, JSME International
Journal, Series B, Vol. 46, No. 2, pp. 244–249.
Thomas, A.L.R., Taylor, G.K., Srygley, R.B., Nudds, R.L., Bomphrey, R.J. (1996)
Dragonfly flight: free-flight and tethered flow visualizations reveal a diverse array
BIBLIOGRAPHY
94
of unsteady lift-generating mechanisms, controlled primarily via angle of attack,
Journal of Experimental Biology 207, pp. 4299–4323.
Triantafyllou, M. S., Triantafyllou, G. S., Yue, D.K.P. (2000) Hydrodynamics of
Fishlike Swimming, Annual Revue Fluid Mechanics, 32, pp. 33–53.
Triantafyllou, M. S., Triantafyllou, G. S. (1995) An efficient swimming machine,
Scientific American 272(3), pp. 64–70.
Tuncer, I.H., Platzer,M.F. (1996) Thrust generation due to airfoil flapping, Am.
Instit. Aeronaut. Astronaut. J. 34(2), pp. 324–331.
Videler, J.J., Stamhuis, E.J., Povel, G.D.E. (2004) Leading edge vortex lifts swifts,
Science 306, pp. 1960–1962.
Wakeling, J.M., Ellington, C.P. (1996) Dragonfly flight; Gliding flight and steady
state aerodynamic forces, Journal of Experimental Biology 200, pp. 543–556.
Wang, J. (2000) Vortex shedding and frequency selection in flapping flight, Journal
of Fluid Mechanics 410, pp. 323–341.
Willert, C., Gharib, M. (1992) Three–dimensional particle imaging using a single
camera, Experiments in Fluids 12, pp. 353–358.
Wu, M. (2005) Tracking bacterial dynamics in three dimensions, American Physical
Society, 58th Annual Meeting of the Division of Fluid Dynamics, November 20-22,
abstract FA.006
Wu, M., Roberts, J.W., Buckley, M. (2005) Three-dimensional fluorescent particle
tracking at micron-scale using a single camera, Experiments in Fluids 38, pp.
461–465.
Yang, Z., Goto, H., Matsumoto, M., Maeda, R. (2001) Ultrasonic micromixer for
microfluidic systems, Sensors and Actuators A 93, pp. 266–272.
Yi, M., Qian, S., Bau, H.H. (2002) A magneto hydrodynamic chaotic stirrer, J. Fluid
Mech. 468, pp. 153.
BIBLIOGRAPHY
95
Zima-Kulisiewicz, B.E., Delgado, A. (2009) Synergetic micro–organismic convection
generated by Opercularia asymmetrica ciliates living in colony as effective fluid
transport in micro scale, Journal of Biomechanics 42, pp. 2255-2262.

Download Report

phd_thesis_emanuela.

Paperzz.com

Your Paperzz