An ALE formulation of embedded boundary methods for tracking boundary layers in turbulent fluid–structure interaction problems

Bio-inspired flapping wings have garnered a large amount of attention in achieving the goal of developing energy efficient highly maneuverable hover-capable Micro Air Vehicles (MAVs). Flapping wings are typically very flexible undergoing large deformations, leading to complex nonlinear interactions between aerodynamics and structure. Computational studies are critical to understanding this highly coupled non-linear Fluid Structure Interaction (FSI) problem and to explore the wide design parameter space for developing efficient and robust flapping wing MAVs. Arbitrary Lagrangian-Eulerian (ALE) methods for Computational Fluid Dynamics (CFD) are unfeasible to handle large structural motions and deformations that are seen in flapping wings. Eulerian Embedded Boundary Methods (EBMs) are particularly attractive in this situation. However, EBMs become expensive in viscous FSI problems, since they do not track the boundary layers around bodies because of their Eulerian nature. Recently, the current authors developed an ALE-embedded framework, in which the underlying non body-fitted mesh tracks structure and therefore providing significant computational savings. The focus of the current work is to apply this framework to study highly flexible flapping wings; the initial step being to carefully validate the methodology with an available experimental data. Three different wings of varying flexibility are simulated for a range of flapping frequencies. The calculations show good qualitative agreement with the experimental measurements in predicting the structural deformations as well as the generated thrust. The quantitative differences are primarily attributed to the uncertainties in the structural model. The results indicate that wing flexibility is beneficial for flapping wing aerodynamics, however excessive flexibility can be counter-productive. Flow visualization show the presence of stable leading edge vortex on moderately flexible wings; whereas no stable vortex is evident on highly flexible wing.

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“…[ 21] in summarized in this section. The main idea behind the formulation is illustrated using a simple example.…”

Section: E Ale Formulation Of Fivermentioning

confidence: 99%

“…The first proposition is computationally inefficient, and the second one is labor intensive. Recently, the authors of the current work developed an ALE formulation of EBM [21], which is simple, and yet computationally reasonable to handle large deformations that are found in flapping wings.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Aeroelastic Analysis of Highly Flexible Flapping Wings Using an ALE Formulation of Embedded Boundary Method

Lakshminarayan

Farhat

2014

52nd Aerospace Sciences Meeting

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“…The detailed modeling of the interaction of a rigid solid with a fluid has been the object of intensive research [1,2,3,4]. However, this is still a challenging subject that entails several difficulties.…”

Section: Introductionmentioning

confidence: 99%

Parallel embedded boundary methods for fluid and rigid-body interaction

Samaniego

Houzeaux

Samaniego

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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The implementations of an updated body-fitted and a non body-fitted method to deal with the interaction of a fluid and a rigid body are described. The physics of the fluid is modeled by the incompressible Navier-Stokes equations. A parallel fluid solver based on the VMS (Variational Multiscale) Finite Element method serves as the basis for the implementation. For the rigid body movement, the Newton-Euler equations are solved numerically. To account for the interaction, the force that the fluid exerts on the rigid body is determined, on the one hand. On the other hand, the velocity of the rigid body is imposed as a Dirichlet boundary condition on the fluid. A fixed Eulerian mesh discretizes the fluid domain, except for nodes in the vicinity of the rigid body boundary for the case of the updated body-fitted approach. The wet boundary of the rigid body is embedded in the fluid mesh and tracked by a moving surface mesh. It is a distinctive characteristic of the updated body-fitted strategy that, in order to impose velocities on the interface, some\ud of the nodes near the body surface are moved by using a local r-adaptivity algorithm to conform with this surface. By contrast, the non body-fitted approach uses kriging interpolation for velocity prescription over the fluid on the interface. Given that fluid nodes can become solid nodes and viceversa due to the rigid body movement, we have adopted the FMALE approach, a variation of the ALE method to keep the fluid mesh fixed. Algorithms to ensure high performance, like skd-trees to determine if a given spatial point is currently inside the solid, are also used. All these ingredients constitute two approaches that are both computationally efficient and accurate. Numerical experiments are presented to assess their performance comparatively.We would like to especially thank Oscar Peredo for his idea and support in introducing a more technical notation and terminology for the data-structures described in this work.Peer ReviewedPostprint (author's final draft

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“…In this fashion AMR methods give a piecewise constant geometric representation of an interface while Chimera grids give a piecewise linear representation. Moreover, unlike AMR methods which need to have the coarse grid lines match up with the fine grid lines along patch boundaries, Chimera grids do not have this requirement and can even move in order to for example follow the motion of moving solids, which is much more efficient for resolving the boundary layers as pointed out by [18]. In this paper, we follow the Chimera grid framework of [14] which uses a multitude of Cartesian grids that can each rotate and translate.…”

Section: Introductionmentioning

confidence: 99%

An adaptive discretization of compressible flow using a multitude of moving Cartesian grids

Qiu

Fedkiw

2016

Journal of Computational Physics

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We present a novel method for simulating compressible flow on a multitude of Cartesian grids that can rotate and translate. Following previous work, we split the time integration into an explicit step for advection followed by an implicit solve for the pressure. A second order accurate flux based scheme is devised to handle advection on each moving Cartesian grid using an effective characteristic velocity that accounts for the grid motion. In order to avoid the stringent time step restriction imposed by very fine grids, we propose strategies that allow for a fluid velocity CFL number larger than 1. The stringent time step restriction related to the sound speed is alleviated by formulating an implicit linear system in order to find a pressure consistent with the equation of state. This implicit linear system crosses overlapping Cartesian grid boundaries by utilizing local Voronoi meshes to connect the various degrees of freedom obtaining a symmetric positive-definite system. Since a straightforward application of this technique contains an inherent central differencing which can result in spurious oscillations, we introduce a new high order diffusion term similar in spirit to ENO-LLF but solved for implicitly in order to avoid any associated time step restrictions. The method is conservative on each grid, as well as globally conservative on the background grid that contains all other grids. Moreover, a conservative interpolation operator is devised for conservatively remapping values in order to keep them consistent across different overlapping grids. Additionally, the method is extended to handle two-way solid fluid coupling in a monolithic fashion including cases (in the appendix) where solids in close proximity do not properly allow for grid based degrees of freedom in between them.

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An ALE formulation of embedded boundary methods for tracking boundary layers in turbulent fluid–structure interaction problems

Cited by 67 publications

References 45 publications

Nonlinear Aeroelastic Analysis of Highly Flexible Flapping Wings Using an ALE Formulation of Embedded Boundary Method

Nonlinear Aeroelastic Analysis of Highly Flexible Flapping Wings Using an ALE Formulation of Embedded Boundary Method

Parallel embedded boundary methods for fluid and rigid-body interaction

An adaptive discretization of compressible flow using a multitude of moving Cartesian grids

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