Numerical simulations of flapping foil and wing aerodynamics

236 Pages·2010·10.59 MB·English

Numerical simulations of flapping foil
and wing aerodynamics
Mesh deformation using radial basis functions
Copyright c 2009 by F.M. Bos
(cid:13)
All rights reserved. No part of this material protected by this copyright notice
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ISBN: 978-90-9025173-8
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Numerical simulations of flapping foil
and wing aerodynamics
Mesh deformation using radial basis functions
Proefschrift
ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus Prof. ir. K.C.A.M. Luyben,
voorzitter van het College voor Promoties,
in het openbaar te verdedigen op woensdag 24 februari 2010 om 10:00 uur
door
Frank Martijn BOS
ingenieur luchtvaart en ruimtevaart
geboren te Naaldwijk.
Dit proefschrift is goedgekeurd door de promotor:
Prof. dr. ir. drs. H. Bijl
Copromotor:
Dr. ir. B.W. van Oudheusden
Samenstelling promotiecommissie:
Rector Magnificus, voorzitter
Prof. dr. ir. drs. H. Bijl Technische Universiteit Delft, promotor
Dr. ir. B.W. van Oudheusden Technische Universiteit Delft, copromotor
Prof. dr. ir. P.G. Bakker Technische Universiteit Delft
Prof. dr. ir. B. Koren Universiteit Leiden
Centrum Wiskunde & Informatica
Prof. dr. H. Jasak Zagreb University
Prof. dr. F-O. Lehmann University of Ulm
Prof. dr. W. Shyy The University of Michigan
This research was supported by The Netherlands
Organisation for Scientific Research (NWO),
NWO-ALW grant 814.02.019.
Voor mijn ouders

Summary
Both biological and engineering scientists have always been intrigued by the flight
of insects and birds. For a long time, the aerodynamic mechanism behind flap-
ping insect flight was a complete mystery, until several decades ago. Experiments
showed the presence of a vortex on top of the flapping wings, generates forces
largerthanobtainedbyusingconventionalaircraftaerodynamics. Flappingwings
producebothliftingandpropulsiveforcessuchthatitbecomespossibleforinsects
and smaller bird species, e.g. hummingbirds, to stay aloft and hover, but also to
performextrememanoeuvres. Becauseofthisversatility,insectsandsmallerbirds
are an inspiration for the development of flapping wing Micro Air Vehicles, small
man-made flyer’s to use in exploration and surveillance.
Several flow visualisation experiments and numerical simulations have been
performed to improve the understanding of flapping wing aerodynamics in order
to design and optimise Micro Air Vehicles. However, the effects of wing kinemat-
ics on the flow and forces is still not fully understood. We performed two- and
three-dimensional numerical simulations in order to systematically vary relevant
parameters, related to the wing motion and flow physics. In order to capture the
boundarylayerandthenearwake,itisimportanttomaintainahighmeshquality
near the moving wing, especially at large rotations. Therefore, an accurate mesh
motiontechniqueisnecessary,whichisabletocopewithlargemeshdeformations.
Inordertoincorporateaflappingwinginournumericalmodel,differentmeshmo-
tion techniques are compared and improved. The overall goal of this part of the
research is to develop a reliable mesh deformation technique, in terms of accuracy
and efficiency, to solve the flow around flapping wings.
The flow around flapping wings, at the scale relevant to insect flight, is highly
unsteady and vortical, described by the unsteady incompressible Navier-Stokes
equations. Different dimensionless numbers are discussed, characterising the flow,
i.e. Strouhal and Reynolds numbers. Since the flow at the considered Reynolds
number, Re = (100), is laminar, there is no need for additional turbulence
O
modelling, such that our simulations, assuming laminar flow, may be treated as a
iv Summary
Direct Numerical Simulation (DNS).
InordertosolvetheunsteadyincompressibleNavier-Stokesequations,thecom-
mercial software Fluentr andtheopen-sourcecodeOpenFOAMr havebeenused
extensively. Different mesh motion solvers are compared. Two existing methods
are assessed, solving the Laplace and a modified stress equation. Both methods
areveryefficientbyusingiterativesolvertechniques. However,thesemeshmotion
solvers are not able to maintain high mesh quality at large rotation angles, which
occur in insect flight. Therefore, a new mesh motion solver is implemented, which
is based on the interpolation of radial basis functions.
This mesh motion solver is a point based method, which means that the dis-
placement of all individual internal mesh points are evaluated, based on a given
boundary displacement, and updated accordingly. No mesh connectivity informa-
tion is necessary, so that it can be applied to unstructured polyhedral meshes.
To increase its efficiency, a coarsening is applied to the set of moving boundary
points, such that only selected control points are used. This decreases the size of
the system of equations and associated computational effort considerably.
After the discussion of the governing equations, finite volume discretisation in
OpenFOAMr and the assessment of the mesh motion solvers, the physical and
numerical modelling are described. The incompressible Navier-Stokes equations
are rewritten in the rotating reference frame in order to identify dimensionless
numbers related to the wing motion. The most important number is the Rossby
number, which represents the wing stroke path curvature.
First a two-dimensional study is performed to investigate the effects of differ-
ent wing kinematic models, with increasing complexity, on hovering flight perfor-
mance. The results show that the ‘sawtooth’ amplitude has a small effect on the
meanliftbutthemeandragisaffectedsignificantly. Thesecondmodelsimplifica-
tion, the ‘trapezoidal’ angle of attack, caused the leading-edge vortex to separate
during the translational phase. This led to an increase in mean drag during each
half-stroke. The extra ‘bump’ in angle of attack as used by the fruit fly model is
not affecting the mean lift to a large extent. The other realistic kinematic feature
isthedeviation,whichisfoundtohaveonlyamarginaleffectonthemeanliftand
mean drag in this two-dimensional study. However, the effective angle of attack is
altered such that the deviation leads to levelling of the force distribution.
Additionally, a numerical model for two-dimensional flow was used to investi-
gate the effect of foil kinematics on the vortex dynamics around an ellipsoid foil
subject to prescribed flapping motion over a range of dimensionless wavelengths,
dimensionless amplitudes, angle of attack amplitudes, and stroke plane angles.
Both plunging and rotating motions are prescribed by simple harmonic functions
which are useful for exploring the parametric space despite the model simplicity.
Optimal propulsion using flapping foil exists for each variable which implies that
aerodynamics might select a range of preferable operating condition. The condi-
tions that give optimal propulsion lie in the synchronisation region in which the
flow is periodic.
Furthermore,differentresultsrelevanttothree-dimensionalflappingwingaero-
v
dynamics, are described. First, the flow around a dynamically scaled model wing
is solved for different angles of attack in order to study the force development
and vortex dynamics at small and large mid-stroke angle of attack. Secondly, the
RossbynumberisvariedatdifferentReynoldsnumbers. AvaryingRossbynumber
representsavariationinstrokepathcurvatureandthusangularacceleration. Itis
shown that a low Rossby number is beneficial for the stability of the leading-edge
vortex, leading to an increase in lift and efficiency. Thirdly, the three-dimensional
wingkinematicsisvariedbychangingtheshapeinangleofattackandbyapplying
a deviation, which may cause a ‘figure-of-eight’ pattern. As in two-dimensional
studies, the deviation may influence the force distribution to a large extent, by
changing the effective angle of attack. Additionally, the three-dimensional flow is
compared with the two-dimensional studies performed on flapping forward flight.
Finally, a preliminary investigation is performed to show the effect of wing
flexing. Therefore,apre-definedflexingdeformationisappliedtoaplungingairfoil
in two-dimensional forward flight and to a three-dimensional flapping wing in
hoveringflight. Concerningtheflexibleairfoilinforwardflight,asimilarbehaviour
was observed as for a rigid plunging airfoil, subjected to additional rotation.
The present simulations have led to important insight to understand the influ-
enceofwingkinematicsanddeformationontheaerodynamicperformance. These
results may be important to design and optimise Micro Air Vehicles.