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• 1.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
Models of porous, elastic and rigid materials in moving fluids2016Doctoral thesis, comprehensive summary (Other academic)

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.

• 2.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
Nature-inspired passive flow control using various coatings and appendages2015Licentiate thesis, comprehensive summary (Other academic)

There is a wide variety of tails, fins, scales, riblets and surface coatings, which are used by motile animals in nature. Since organisms currently living on earth have gone through millions of years of evolution, one can expect that their design is optimal for their tasks, including locomotion. However, the exterior of living animals has range of different functions, from camouflage to heat insulation; therefore it is a very challenging task to isolate mechanisms, which are beneficial to reduce the motion resistance of the body.

There are two general categories of mechanisms existing in locomotion and flow control. The first is active flow control, when an organism is actively moving some parts or the whole body (exerts energy) in order to modify the surrounding flow field (for example, flapping bird wings). The second is passive flow control, in which an organism has an appendage or a coating, which is not actively controlled (no energy is spent), but is interacting with surrounding flow in a beneficial way. Our aim is to find novel mechanisms for passive flow control.

We start by looking at a simple model of an appendage (splitter plate) behind a bluff body (circular cylinder). If a recirculation region forms behind the body, already in this simple system there is a symmetry breaking effect for sufficiently short plates, which passively generates turn and drift of the body. We have found that this effect is caused by the pressure forces in the recirculation region, which pushes the plate away from the vertical in a manner similar to how a straight inverted pendulum falls under the influence of gravity. In order to investigate this symmetry breaking, we developed an extension of the immersed boundary projection method, in which the rigid body dynamics and fluid dynamics are coupled implicitly. The method is capable of solving for particle motion in a fluid for very small density ratios. We also explain our findings by a simple yet quantitative reduced-order model and soap-film experiments.

To extend our work, we investigate flow around bodies, which are coated by a porous and elastic material. We have analysed various theoretical approaches to modeling a coating in a continuous manner. We aim to solve the governing equations numerically. We have selected multi-scale expansion approach, of which we present some initial results.

• 3.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
A continuous description of porous and elastic media for the simulation of the flow around coated objects2014Report (Other academic)

Poroelastic materials are commonly found in nature; birds are covered with all sorts of feathers, land animals are covered with different kinds of fur and fishes are covered with various fins and scales. The problem of fluid flow through such materials is very challenging both experimentally and numerically. It is impossible to experimentally measure fluid flow within the material, if the media is densely packed and have fine micro-structure. In such case, direct numerical simulations of the coupled problem with flow in the media and deformation of micro-structure are extremely costly. In order to overcome this limitation, continuum theories have been developed, where average behaviour of the poroelastic material and the fluid within is described. There have already been a significant progress towards describing poroelastic materials similar to examples found in nature; however further work to resolve issues in boundary conditions, modelling and connection between different theories is required. In the current paper, we present a summary of existing theories. Then, we select a multi-scale expansion approach, which we believe is feasible to use for description of the flow in a poroelastic material. Finally, we present preliminary results of a decoupled micro-scale problem with an expansion for two scales. We observe that the two-scale approach is problematic for poroelastic coatings of micro-structure, which is disconnected in a given plane.

• 4.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
A framework for computing effective boundary conditions at the interface between free fluid and a porous medium2017In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 812, p. 866-889Article in journal (Refereed)

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 a multiscale expansion (homogenization) approach, we derive a tensorial generalized version of the empirical condition suggested by Beavers & Joseph (J. Fluid Mech., vol. 30 (01), 1967, pp. 197-207). 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 computes the velocity boundary condition without free parameters over any porous bed.

• 5.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
A framework for computing effective boundary conditions at the interface between free fluid and a porous mediumManuscript (preprint) (Other academic)

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.

• 6.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Passive appendages generate drift through symmetry breaking2014In: Nature Communications, ISSN 2041-1723, E-ISSN 2041-1723, Vol. 5, p. 5310-Article in journal (Refereed)

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.

• 7.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
Passive control of a falling sphere by elliptic-shaped appendages2017In: Physical Review Fluids, E-ISSN 2469-990X, Vol. 2, article id 033901Article in journal (Refereed)

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.

• 8.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
A stable fluid-structure-interaction solver for low-density rigid bodies using the immersed boundary projection method2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 305, p. 300-318Article in journal (Refereed)

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.

• 9.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
A stable fluid-structure-interaction solver for low-density rigid particles using the immersed boundary projection methodManuscript (preprint) (Other academic)

Dispersion of particles with complex geometries and very low or close to unity density ratios are 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 motion of cylindrical and spherical particles with low density ratios, for more complex particles they become unstable. For example, the critical density ratio, for which numerical method becomes unstable, is significantly increased for an explicit coupling, compared to implicit coupling, in simulations of the flow around cylinder with a splitter plate. We present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method. In addition to the Navier-Stokes equations, we solve Newton's equations of motion for a rigid body. In a similar manner to previous work on the immersed boundary projection 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 ensure that our method preserve the efficiency and second-order accuracy in space and third-order accuracy in time of the original method, only with small additional computational cost. We find that implicit coupling yields stable solution for density ratios as low as $10^{-4}$.

• 10.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
A computational continuum model of poroelastic beds2017In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, article id 20160932Article in journal (Refereed)

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.

• 11.
Univ Genoa, Scuola Politecn, DICCA, Via Montallegro 1, I-16145 Genoa, Italy..
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Univ Genoa, Scuola Politecn, DICCA, Via Montallegro 1, I-16145 Genoa, Italy..
Modeling waves in fluids flowing over and through poroelastic media2019In: International Journal of Multiphase Flow, ISSN 0301-9322, E-ISSN 1879-3533, Vol. 110, p. 148-164Article in journal (Refereed)

Multiscale homogenization represents a powerful tool to treat certain fluid-structure interaction problems involving porous, elastic, fibrous media. This is shown here for the case of the interaction between a Newtonian fluid and a poroelastic, microstructured material. Microscopic problems are set up to determine effective tensorial properties (elasticity, permeability, porosity, bulk compliance of the solid skeleton) of the homogenized medium, both in the interior and at its boundary with the fluid domain, and an extensive description is provided of such properties for varying porosity. The macroscopic equations which are derived by homogenization theory employ such effective properties thus permitting the computation of velocities and displacements within the poroelastic mixture for two representative configurations of standing and travelling waves.

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