Numerical simulation on a limit cycle oscillation of a rectangular sheet in three-dimensional flow: influence of vortex element model on post-critical behavior

Kumakura, Hiroaki; Hayashi, Yutaka; Watanabe, Masahiro

doi:10.1007/s11071-021-06958-3

Cited by 7 publications

(8 citation statements)

References 52 publications

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“…Inviscid simulations of airfoils and flapping plates in two dimensions and three dimensions have shown that the largest computational errors tend to occur in flow quantities near the trailing edge (Katz & Plotkin 2001;Alben 2008aAlben , 2010Hiroaki et al 2021). The Kutta condition makes the flow velocity and pressure jump finite there, but their spatial derivatives across the edge are infinite there in general (Alben 2010), and the numerical solution is sensitive to the mesh near the trailing edge (Alben 2010;Hiroaki et al 2021). For the present simulations, this sensitivity can be seen in the pressure jump distribution near the trailing edge.…”

Section: Comparisons Of 2-d and 3-d Results With Different Mesh Sizesmentioning

confidence: 99%

“…Each vortex ring consists of four vortex filaments, one along each side of the grid cell. This discretization is a type of vortex-lattice method (Katz & Plotkin 2001;Hiroaki et al 2021). To speed up the computations, we approximate the vortex-sheet geometries as flat, a common approach in vortex-lattice methods (Katz & Plotkin 2001;Hiroaki et al 2021).…”

Section: Methodsmentioning

confidence: 99%

“…This discretization is a type of vortex-lattice method (Katz & Plotkin 2001;Hiroaki et al 2021). To speed up the computations, we approximate the vortex-sheet geometries as flat, a common approach in vortex-lattice methods (Katz & Plotkin 2001;Hiroaki et al 2021). This occurs in the kinematic equation (2.19), which we solve for γ on the body assuming the body position and velocity (i.e.…”

Section: Methodsmentioning

confidence: 99%

“…The Kutta condition makes the flow velocity and pressure jump finite there, but their spatial derivatives across the edge are infinite there in general (Alben 2010), and the numerical solution is sensitive to the mesh near the trailing edge (Alben 2010; Hiroaki et al. 2021). For the present simulations, this sensitivity can be seen in the pressure jump distribution near the trailing edge.…”

Section: Validation Of the 3-d Model And Algorithmmentioning

confidence: 99%

“…There are relatively few studies of 3-D coupled interactions of inviscid flows and flexible bodies. Recently, Hiroaki, Hayashi & Watanabe (2021) and Hiroaki & Watanabe (2021 b ) used nonlinear beam theory and the vortex-lattice method to analyse the limit cycle oscillations of a rectangular plate and plate vibration under harmonic forced excitation (Hiroaki & Watanabe 2021 a ). Previously Gibbs, Wang & Dowell (2012, 2015) studied the 3-D linear stability problem for a flexible plate in an inviscid flow with various boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Membrane flutter in three-dimensional inviscid flow

Mavroyiakoumou

Alben

2022

J. Fluid Mech.

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We develop a model and numerical method to study the large-amplitude flutter of rectangular membranes (of zero bending rigidity) that shed a trailing vortex-sheet wake in a three-dimensional (3-D) inviscid fluid flow. We apply small initial perturbations and track their decay or growth to large-amplitude steady-state motions. For 12 combinations of boundary conditions at the membrane edges we compute the stability thresholds and the subsequent large-amplitude dynamics across the three-parameter space of membrane mass density, pretension and stretching rigidity. With free side edges we find good agreement with previous 2-D results that used different discretization methods. We find that the 3-D dynamics in the 12 cases naturally forms four groups based on the conditions at the leading and trailing edges. The deflection amplitudes and oscillation frequencies have scalings similar to those in the 2-D case. The conditions at the side edges, although generally less important, may have small or large qualitative effects on the membrane dynamics – e.g. steady vs unsteady, periodic vs chaotic or the variety of spanwise curvature distributions – depending on the group and the physical parameter values.

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