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Models of porous, elastic and rigid materials in moving fluids
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.ORCID iD: 0000-0003-3094-0848
2016 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Modeller av porösa, elastiska och stela material i strömmande fluider (Swedish)
Abstract [en]

Tails, fins, scales, and surface coatings are used by organisms for various tasks, including locomotion. Since millions of years of evolution have passed, we expect that the design of surface structures is optimal for the tasks of the organism. These structures serve as an inspiration in this thesis to identify new mechanisms for flow control. There are two general categories of fluid-structure-interaction mechanisms. The first is active interaction, where an organism actively moves parts of the body or its entire body in order to modify the surrounding flow field (e.g., birds flapping their wings). The second is passive interaction, where appendages or surface textures are not actively controlled by the organism and hence no energy is spent (e.g., feathers passively moving in the surrounding flow). Our aim is to find new passive mechanisms that interact with surrounding fluids in favourable ways; for example, to increase lift and to decrease drag.

In the first part of this work, we investigate a simple model of an appendage (splitter plate) behind a bluff body (circular cylinder or sphere). If the plate is sufficiently short and there is a recirculation region behind the body, the straight position of the appendage becomes unstable, similar to how a straight vertical position of an inverted pendulum is unstable under gravity. We explain and characterize this instability using computations, experiments and a reduced-order model. The consequences of this instability are reorientation (turn) of the body and passive dispersion (drift with respect to the directionof the gravity). The observed mechanism could serve as a means to enhance locomotion and dispersion for various motile animals and non-motile seeds.

In the second part of this thesis, we look into effective models of porous and poroelastic materials. We use the method of homogenization via multi-scale expansion to model a poroelastic medium with a continuum field. In particular, we derive boundary conditions for the velocity and the pressure at the interface between the free fluid and the porous or poroelastic material. The results obtained using the derived boundary conditions are then validated with respect to direct numerical simulations (DNS) in both two-dimensional and three-dimensional settings. The continuum model – coupled with the necessary boundary conditions – gives accurate predictions for both the flow field and the displacement field when compared to DNS.

Abstract [sv]

Många djur använder sig av fjäll, päls, hår eller fjädrar för att öka sin förmåga att förflytta sig i luft eller vatten. Eftersom djuren har genomgått miljontals år av evolution, kan man förvänta sig att ytstrukturernas form är optimala för organismens uppgifter. Dessa strukturer tjänar som inspiration i denna avhandling för att identifiera nya mekanismer för manipulering av strömning.

Samverkan mellan fluider och strukturer (så kallad fluid-struktur-interaktion) kan delas upp i två kategorier. Den första typen av samverkan är aktiv, vilket innebär att en organism aktivt rör hela eller delar av sin kropp för att manipulera det omgivande strömningsfältet (till exempel fåglar som flaxar sina vingar). Den andra typen är passiv samverkan, där organismer har utväxter (svansar, fjärdar, etc.) eller ytbeläggningar som de inte aktivt har kontroll över och som således inte förbrukar någon energi. Ett exempel är fjädrar som passivt rör sig i det omgivande flödet. Vårt mål är att hitta nya passiva mekanismer som växelverkar med den omgivande fluiden på ett fördelaktigt sätt, exempelvis genom att öka lyftkraften eller minska luftmotståndet.

I den första delen av detta arbete undersöker vi en enkel modell för en utväxt (i form av en platta) bakom en cirkulär cylinder eller sfär. Om plattan är tillräckligt kort och om det finns ett vak bakom kroppen kommer det upprätta läget av plattan att vara instabilt. Denna instabilitet är i princip samma som uppstår då man försöker balansera en penna på fingret. Vi förklarar den bakomliggande mekanismen av denna instabilitet genom numeriska beräkningar, experiment och en enkel modell med tre frihetsgrader. Konsekvenserna av denna instabilitet är en omorientering (rotation) av kroppen och en sidledsförflyttning av kroppen i förhållande till tyngdkraftens riktning. Denna mekanism kan användas djur och frön för att öka deras förmåga att förflytta eller sprida sig i vatten eller luft.

I den andra delen av avhandlingen studerar vi modeller av porösa och elastiska material. Vi använder en mångskalig metod för att modellera det poroelastiska materialet som ett kontinuum. Vi härleder randvillkor för både hastighetsfältet och trycket på gränssnittet mellan den fria fluiden och det poroelastiska materialet. Resultaten som erhållits med de härledda randvillkoren valideras sedan genom direkta numeriska simuleringar (DNS) för både två- och tredimensionella fall. Kontinuumsmodellen av materialet kopplad genom randvillkoren till den fria strömmande fluiden predikterar strömnings- och förskjutningsfält noggrant i jämförelse med DNS.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2016. , 55 p.
Series
TRITA-MEK, ISSN 0348-467X ; 2016:15
Keyword [en]
fluid-structure-interaction, flow control, passive appendages, homogenization, poroelastic coatings, separated flows, surface-fluid interface
Keyword [sv]
fluid-struktur-interaktion, flödeskontroll, passiva utväxter, homogenisering, ytbeläggning, separerade strömning, ytbeläggning-strömning gränssnitt
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-195679ISBN: 978-91-7729-140-4OAI: oai:DiVA.org:kth-195679DiVA: diva2:1044971
Public defence
2016-12-02, Kollegisalen, Brinellvägen 8, Stockholm, 10:15 (English)
Opponent
Supervisors
Funder
Swedish Research Council, VR-2010- 3910,VR-2014-5680Göran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of Technology
Available from: 2016-11-08 Created: 2016-11-07 Last updated: 2016-11-10Bibliographically approved
List of papers
1. Passive appendages generate drift through symmetry breaking
Open this publication in new window or tab >>Passive appendages generate drift through symmetry breaking
Show others...
2014 (English)In: Nature Communications, ISSN 2041-1723, Vol. 5, 5310- p.Article in journal (Refereed) Published
Abstract [en]

Plants and animals use plumes, barbs, tails, feathers, hairs and fins to aid locomotion. Many of these appendages are not actively controlled, instead they have to interact passively with the surrounding fluid to generate motion. Here, we use theory, experiments and numerical simulations to show that an object with a protrusion in a separated flow drifts sideways by exploiting a symmetry-breaking instability similar to the instability of an inverted pendulum. Our model explains why the straight position of an appendage in a fluid flow is unstable and how it stabilizes either to the left or right of the incoming flow direction. It is plausible that organisms with appendages in a separated flow use this newly discovered mechanism for locomotion; examples include the drift of plumed seeds without wind and the passive reorientation of motile animals.

Place, publisher, year, edition, pages
Nature Publishing Group, 2014
Keyword
Reynolds-Number, Soap Film, Flows, Fluid, Cylinder, Forces, Body
National Category
Other Engineering and Technologies
Identifiers
urn:nbn:se:kth:diva-157216 (URN)10.1038/ncomms6310 (DOI)000344061600001 ()2-s2.0-84923335171 (ScopusID)
Funder
Swedish Research Council, VR-2010-3910
Note

QC 20141209

Available from: 2014-12-09 Created: 2014-12-08 Last updated: 2016-11-07Bibliographically approved
2. A stable fluid-structure-interaction solver for low-density rigid bodies using the immersed boundary projection method
Open this publication in new window or tab >>A stable fluid-structure-interaction solver for low-density rigid bodies using the immersed boundary projection method
2016 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 305, 300-318 p.Article in journal (Refereed) Published
Abstract [en]

Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations of motion are often sufficient to solve for the motion of cylindrical particles with low density ratios, for more complex particles - such as a body with a protrusion - they become unstable. We present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method. Similarly to previous work on this method, the resulting matrix equation in the present approach is solved using a block-LU decomposition. Each step of the block-LU decomposition is modified to incorporate the rigid body dynamics. We show that our method achieves second-order accuracy in space and first-order in time (third-order for practical settings), only with a small additional computational cost to the original method. Our implicit coupling yields stable solution for density ratios as low as 10(-4). We also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method.

Place, publisher, year, edition, pages
Academic Press, 2016
Keyword
Immersed boundary method, Fictitious fluid, Newton's equations of motion, Implicit coupling, Low density ratios, Complex particles
National Category
Physical Sciences Computer Science
Identifiers
urn:nbn:se:kth:diva-180478 (URN)10.1016/j.jcp.2015.10.041 (DOI)000366156600016 ()2-s2.0-84946595242 (ScopusID)
Note

QC 20160118

Available from: 2016-01-18 Created: 2016-01-14 Last updated: 2016-11-07Bibliographically approved
3. Passive control of a falling sphere by elliptic-shaped appendages
Open this publication in new window or tab >>Passive control of a falling sphere by elliptic-shaped appendages
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The majority of investigations characterizing the motion of single or multiple particles in fluid flows consider canonical body shapes, such as spheres, cylinders, discs, etc. However, protrusions on bodies – being either as surface imperfections or appendages that serve a function – are ubiquitous in both nature and applications. In this work, we characterize how the dynamics of a sphere with an axis-symmetric wake is modified in the presence of thin three-dimensional elliptic-shaped protrusions. By investigating a wide range of three-dimensional appendages with different aspect ratios and lengths, we clearly show that the sphere with an appendage may robustly undergo an inverted-pendulum-like (IPL) instability. This means that the position of the appendage placed behind the sphere and aligned with the free-stream direction is unstable, in a similar way that an inverted pendulum is unstable under gravity. Due to this instability, non-trivial forces are generated on the body, leading to turn and drift, if the body is free to fall under gravity. Moreover, we identify the aspect ratio and length of the appendage that induces the largest side force on the sphere, and therefore also the largest drift for a freely falling body. Finally, we explain the physical mechanisms behind these observations in the context of the IPL instability, i.e., the balance between surface area of the appendage exposed to reversed flow in the wake and the surface area of the appendage exposed to fast free-stream flow.

National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-195676 (URN)
Funder
Swedish Research Council, VR-2014-5680Göran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of Technology
Note

QC 20161108

Available from: 2016-11-07 Created: 2016-11-07 Last updated: 2016-11-08Bibliographically approved
4. A framework for computing effective boundary conditions at the interface between free fluid and a porous medium
Open this publication in new window or tab >>A framework for computing effective boundary conditions at the interface between free fluid and a porous medium
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Interfacial boundary conditions determined from empirical or ad-hoc models remain the standard approach to model fluid flows over porous media, even in situations where the topology of the porous medium is known. We propose a non-empirical and accurate method to compute the effective boundary conditions at the interface between a porous surface and an overlying flow. Using multiscale expansion (homogenization) approach, we derive a tensorial generalized version of the empirical condition suggested by Beavers & Joseph (1967). The components of the tensors determining the effective slip velocity at the interface are obtained by solving a set of Stokes equations in a small computational domain near the interface containing both free flow and porous medium. Using the lid-driven cavity flow with a porous bed, we demonstrate that the derived boundary condition is accurate and robust by comparing an effective model to direct numerical simulations. Finally, we provide an open source code that solves the microscale problems and computesthe velocity boundary condition without free parameters over any porous bed.

National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-195675 (URN)
Funder
Swedish Research Council, VR-2014-5680
Note

QC 20161108

Available from: 2016-11-07 Created: 2016-11-07 Last updated: 2016-11-08Bibliographically approved
5. A computational continuum model of poroelastic beds
Open this publication in new window or tab >>A computational continuum model of poroelastic beds
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Despite the ubiquity of fluid flows interacting with porous and elastic materials, we lack a validated non-empirical macroscale method for characterizing the flow over and through a poroelastic medium. We propose a computational tool to describe such configurations by deriving and validating a continuum model for the poroelastic bed and its interface with the above free fluid. We show that, using stress continuity condition and slip velocity condition at the interface, the effective model captures the effects of small changes in the microstructure anisotropy correctly and predicts the overall behaviour in a physically consistent and controllable manner. Moreover, we show that the performance of the effective model is accurate by validating with fully microscopic resolved simulations. The proposed computational tool can be used in investigations in a wide range of fields, including mechanical engineering, bio-engineering and geophysics.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-195677 (URN)
Funder
Swedish Research Council, VR- 2014-5680Göran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of Technology
Note

QC 20161108

Available from: 2016-11-07 Created: 2016-11-07 Last updated: 2016-11-08Bibliographically approved

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