CFD modelling of ocean wave interaction with thin perforated structures represented by their macro-scale effects

Fluid interaction with thin perforated structures is of interest in a range of contexts. Applications in marine engineering include current and wave interaction with aquaculture containers, breakwaters and, as a new application, platforms for floating wind turbines with perforated outer shrouds. Another more general application is for tuned liquid dampers with baffles for motion attenuation. Thus, there is significant interest in the challenge of simulating the effect of these thin porous structures using Computational Fluid Dynamics (CFD). This thesis proposes and assesses the use of a macro-scale approach to CFD modelling of wave interaction with thin perforated structures. The structures are not resolved explicitly but represented by their spatially averaged effects on the flow by means of a homogeneous porous pressure-drop applied to the Navier-Stokes momentum equation. Two options are explored where the pressure-drop is either applied as a volumetric porous zone or as a jump-condition across a porous surface. The wave modelling capabilities and the basis of the macroscopic porosity implementations are readily available in the open-source code OpenFOAM®, which is used in this work. Minor code modifications were necessary to introduce orthotropic porosity for a cylindrically shaped structure. More significant code development was required to implement accurate motion of a floating porous structure as a new capability as part of a custom motion solver. The method is applied to fixed perforated sheets and cylinders as well as a floating tension leg platform (TLP), and the overall fluid flow behaviour and global forces and motions are assessed. The validation against experimental and potential-flow results demonstrates that a macro-scale porosity representation can accurately reproduce large-scale flow, force and motion effects of all conditions investigated. As the most representative case, the CFD results of the horizontal force on the perforated cylinder differ between 2 and 12% from the experimental results. As part of this work, it is shown that, firstly, the Volume-Averaged Reynolds-Averaged Navier-Stokes (VARANS) equations can not only be used for large volumetric granular material, but also for thin perforated structures, and secondly, that the effects of applying a RANS turbulence model on the results are of minor significance and that the full Navier-Stokes equations give good results. The presented macro-scale approach offers greater flexibility in the range of wave conditions that can be modelled compared to approaches based on linear potential-flow theory and requires a smaller computational effort compared to CFD approaches which resolve the micro-structural geometry of the openings and the fluid flow across it explicitly. This approach can therefore be an efficient alternative to assess large-scale effects for engineering problems

Evolutionary optimization of optical antennas

The design of nano-antennas is so far mainly inspired by radio-frequency technology. However, material properties and experimental settings need to be reconsidered at optical frequencies, which entails the need for alternative optimal antenna designs. Here a checkerboard-type, initially random array of gold cubes is subjected to evolutionary optimization. To illustrate the power of the approach we demonstrate that by optimizing the near-field intensity enhancement the evolutionary algorithm finds a new antenna geometry, essentially a split-ring/two-wire antenna hybrid which surpasses by far the performance of a conventional gap antenna by shifting the n=1 split-ring resonance into the optical regime.Comment: Also see Supplementary material, as attached to the main pape

Tropical surface singularities

In this paper, we study tropicalisations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximal-dimensional type, show that they can generically have only finitely many singular points, and describe all possible locations of singular points. More precisely, we show that singular points must be either vertices, or generalized midpoints and baricenters of certain faces of singular tropical surfaces, and, in some cases, there may be additional metric restrictions to faces of singular tropical surfaces.Comment: A gap in the classification was closed. 37 pages, 29 figure

Permutonestohedra

There are several real spherical models associated with a root arrangement, depending on the choice of a building set. The connected components of these models are manifolds with corners which can be glued together to obtain the corresponding real De Concini–Procesi models. In this paper, starting from any root system with finite Coxeter group W and any W -invariant building set, we describe an explicit realization of the real spherical model as a union of polytopes (nestohedra) that lie inside the chambers of the arrangement. The main point of this realization is that the convex hull of these nestohedra is a larger polytope, a permutonestohedron, equipped with an action of W or also, depending on the building set, of Aut ( ). The permutonestohedra are natural generalizations of Kapranov’s permutoassociahedra

Biocompatibility and degradation of the open-pored magnesium scaffolds LAE442 and La2

Porous magnesium implants are of particular interest for application as resorbable bone substitutes, due to their mechanical strength and a Young's modulus similar to bone. The objective of the present study was to compare the biocompatibility, bone and tissue ingrowth, and the degradation behaviour of scaffolds made from the magnesium alloys LAE442 (n= 40) and Mg-La2 (n= 40)in vivo. For this purpose, cylindrical magnesium scaffolds (diameter 4 mm, length 5 mm) with defined, interconnecting pores were produced by investment casting and coated with MgF2. The scaffolds were inserted into the cancellous part of the greater trochanter ossis femoris of rabbits. After implantation periods of 6, 12, 24 and 36 weeks, the bone-scaffold compounds were evaluated usingex vivo µCT80 images, histological examinations and energy dispersive x-ray spectroscopy analysis. The La2 scaffolds showed inhomogeneous and rapid degradation, with inferior osseointegration as compared to LAE442. For the early observation times, no bone and tissue could be observed in the pores of La2. Furthermore, the excessive amount of foreign body cells and fibrous capsule formation indicates insufficient biocompatibility of the La2 scaffolds. In contrast, the LAE442 scaffolds showed slow degradation and better osseointegration. Good vascularization, a moderate cellular response, bone and osteoid-like bone matrix at all implantation periods were observed in the pores of LAE442. In summary, porous LAE442 showed promise as a degradable scaffold for bone defect repair, based on its degradation behaviour and biocompatibility. However, further studies are needed to show it would have the necessary mechanical properties required over time for weight-bearing bone defects

Comparison of Macro-Scale Porosity Implementations for CFD Modelling of Wave Interaction with Thin Porous Structures

This is the final version. Available on open access from MDPI via the DOI in this recordData Availability Statement: The research data supporting this publication are provided within this paper. The code used for data collection is the existing open source code OpenFOAM® (The OpenFOAM Foundation v5) and the open source libraries OlaFlow/IHFoam [48] and waves2Foam [39,49].Computational fluid dynamics (CFD) modelling of wave interaction with thin perforated structures is of interest in a range of engineering applications. When large-scale effects such as forces and the overall flow behaviour are of interest, a microstructural resolution of the perforated geometry can be excessive or prohibitive in terms of computational cost. More efficiently, a thin porous structure can be represented by its macro-scale effects by means of a quadratic momentum source or pressure-drop respectively. In the context of regular wave interaction with thin porous structures and within an incompressible, two-phase Navier–Stokes and volume-of-fluid framework (based on interFoam of OpenFOAM®), this work investigates porosity representation as a porous surface with a pressure-jump condition and as volumetric isotropic and anisotropic porous media. Potential differences between these three types of macro-scale porosity implementations are assessed in terms of qualitative flow visualizations, velocity profiles along the water column, the wave elevation near the structures and the horizontal force on the structures. The comparison shows that all three types of implementation are capable of reproducing large-scale effects of the wave-structure interaction and that the differences between all obtained results are relatively small. It was found that the isotropic porous media implementation is numerically the most stable and requires the shortest computation times. The pressure-jump implementation requires the smallest time steps for stability and thus the longest computation times. This is likely due to the spurious local velocities at the air-water interface as a result of the volume-of-fluid interface capturing method combined with interFoam’s segregated pressure-velocity coupling algorithm. This paper provides useful insights and recommendations for effective macro-scale modelling of thin porous structures.University of ExeterEngineering and Physical Sciences Research Council (EPSRC)Newton Fun

Using a porous-media approach for CFD modelling of wave interaction with thin perforated structures

This is the final version. Available on open access from Springer via the DOI in this recordAvailability of data and material: The research data supporting this publication are provided within this paper.This work presents the use of a porous-media approach for computational fluid dynamics (CFD) modelling of wave interaction with thin perforated sheets and cylinders. The perforated structures are not resolved explicitly but represented by a volumetric porous zone where a volume-averaged pressure gradient in the form of a drag term is applied to the Navier–Stokes momentum equation. The horizontal force on the structures and the free-surface elevation at wave gauges around the cylinder model have been analysed for a range of porosities and regular wave conditions. The CFD results are verified against results from a linear potential-flow model and validated against experimental results. The applied pressure gradient formulation produces good agreement for all porosity values, wave frequencies and wave steepnesses investigated. It is demonstrated that an isotropic macroscopic porosity representation used for large volumetric granular material can also be used for thin perforated structures. This approach offers greater flexibility in the range of wave conditions that can be modelled compared to approaches based on linear potential-flow theory and requires a smaller computational effort compared to CFD approaches which resolve the flow through the openings. The approach can therefore be an efficient alternative for engineering problems where large-scale effects such as global forces and the overall flow-behaviour are of the main interest.University of ExeterEngineering and Physical Sciences Research Council (EPSRC)National Natural Science Foundation of ChinaNewton Fun

Around the tangent cone theorem

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.Comment: 39 pages; to appear in the proceedings of the Configurations Spaces Conference (Cortona 2014), Springer INdAM serie

Comparison of two pore sizes of LAE442 scaffolds and their effect on degradation and osseointegration behavior in the rabbit model

The magnesium alloy LAE442 emerged as a possible bioresorbable bone substitute over a decade ago. In the present study, using the investment casting process, scaffolds of the Magnesium (Mg) alloy LAE442 with two different and defined pore sizes, which had on average a diameter of 400 μm (p400) and 500 μm (p500), were investigated to evaluate degradation and osseointegration in comparison to a ß‐TCP control group. Open‐pored scaffolds were implanted in both greater trochanter of rabbits. Ten scaffolds per time group (6, 12, 24, and 36 weeks) and type were analyzed by clinical, radiographic and μ‐CT examinations (2D and 3D). None of the scaffolds caused adverse reactions. LAE442 p400 and p500 developed moderate gas accumulation due to the Mg associated in vivo corrosion, which decreased from week 20 for both pore sizes. After 36 weeks, p400 and p500 showed volume decreases of 15.9 and 11.1%, respectively, with homogeneous degradation, whereas ß‐TCP lost 74.6% of its initial volume. Compared to p400, osseointegration for p500 was significantly better at week 2 postsurgery due to more frequent bone‐scaffold contacts, higher number of trabeculae and higher bone volume in the surrounding area. No further significant differences between the two pore sizes became apparent. However, p500 was close to the values of ß‐TCP in terms of bone volume and trabecular number in the scaffold environment, suggesting better osseointegration for the larger pore size