Dynamic responses of a two-dimensional flapping foil motion

2006 ◽  
Vol 18 (9) ◽  
pp. 098104 ◽  
Author(s):  
Xi-Yun Lu ◽  
Qin Liao
Keyword(s):  
Dynamic Responses ◽  
Two Dimensional ◽  
Flapping Foil

A New Global Spatial Discretization Method for Calculating Dynamic Responses of Two-Dimensional Continuous Systems With Application to a Rectangular Kirchhoff Plate

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
K. Wu ◽  
W. D. Zhu
Keyword(s):  
Boundary Conditions ◽  
Continuous System ◽  
Dynamic Responses ◽  
Kirchhoff Plate ◽  
Continuous Systems ◽  
Discretization Method ◽  
Two Dimensional ◽  
Spatial Discretization ◽  
Arbitrary Boundary ◽  
Discretization Methods

A new global spatial discretization method (NGSDM) is developed to accurately calculate natural frequencies and dynamic responses of two-dimensional (2D) continuous systems such as membranes and Kirchhoff plates. The transverse displacement of a 2D continuous system is separated into a 2D internal term and a 2D boundary-induced term; the latter is interpolated from one-dimensional (1D) boundary functions that are further divided into 1D internal terms and 1D boundary-induced terms. The 2D and 1D internal terms are chosen to satisfy prescribed boundary conditions, and the 2D and 1D boundary-induced terms use additional degrees-of-freedom (DOFs) at boundaries to ensure satisfaction of all the boundary conditions. A general formulation of the method that can achieve uniform convergence is established for a 2D continuous system with an arbitrary domain shape and arbitrary boundary conditions, and it is elaborated in detail for a general rectangular Kirchhoff plate. An example of a rectangular Kirchhoff plate that has three simply supported boundaries and one free boundary with an attached Euler–Bernoulli beam is investigated using the developed method and results are compared with those from other global and local spatial discretization methods. Advantages of the new method over local spatial discretization methods are much fewer DOFs and much less computational effort, and those over the assumed modes method (AMM) are better numerical property, a faster calculation speed, and much higher accuracy in calculation of bending moments and transverse shearing forces that are related to high-order spatial derivatives of the displacement of the plate with an edge beam.

Thermoelastic Dynamic Behaviors of a FGM Hollow Cylinder Under Non-Axisymmetric Thermo-Mechanical Loads

2012 ◽  
Vol 29 (1) ◽  
pp. 109-120 ◽  
Author(s):  
H. Xie ◽  
H.-L. Dai ◽  
Y.-N. Rao
Keyword(s):  
Hollow Cylinder ◽  
Material Properties ◽  
Radial Direction ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Two Dimensional ◽  
Governing Equations ◽  
Mechanical Loads ◽  
Temperature Boundary

AbstractThis paper is concerned with two-dimensional (r, θ) thermoelastic dynamic responses of a long functionally graded hollow cylinder subjected to asysmmetrical thermal and mechanical loads. The material properties, except the Poisson's ratio, are assumed to be temperature independent and vary exponentially and continuously in the radial direction. By means of finite difference method and Newmark method, the motion governing equations of the long FGM hollow cylinder are solved. Comparisons between this paper's results and the corresponding analytical results validate the proposed solution. In addition, the effects of the volume fraction, temperature boundary conditions on the hollow cylinder's deformations and stresses distributions are examined, and many other valuable thermoelastic dynamic characteristics are revealed.

Vortex-induced rotations of a rigid square cylinder at low Reynolds numbers

2017 ◽  
Vol 813 ◽  
pp. 482-507 ◽  
Author(s):  
Sungmin Ryu ◽  
Gianluca Iaccarino
Keyword(s):  
Cross Flow ◽  
Reynolds Numbers ◽  
Dynamic Responses ◽  
Two Dimensional ◽  
Square Cylinder ◽  
Low Reynolds Numbers ◽  
Pressure Distributions ◽  
Low Reynolds ◽  
Drag And Lift ◽  
Vortex Patterns

A numerical investigation of vortex-induced rotations (VIRs) of a rigid square cylinder, which is free to rotate in the azimuthal direction in a two-dimensional uniform cross-flow, is presented. Two-dimensional simulations are performed in a range of Reynolds numbers between 45 and 150 with a fixed mass and moment of inertia of the cylinder. The parametric investigation reveals six different dynamic responses of the square cylinder (expanding on those reported by Zaki et al. (J. Fluids Struct., vol. 8, 1994, pp. 555–582)) and their coupled vortex patterns at low Reynolds numbers. In each characteristic regime, moment generating mechanisms are elucidated with investigations of instantaneous flow fields and surface pressure distributions at chosen time instants in a period of rotation response. Our simulation results also elucidate that VIRs significantly influence the statistics of drag and lift force coefficients: (i) the onset of a rapid increases of the two coefficients at $Re=80$ and (ii) their step increases in the autorotation regime.

scholarly journals Performance augmentation mechanism of in-line tandem flapping foils

2017 ◽  
Vol 827 ◽  
pp. 484-505 ◽  
Author(s):  
L. E. Muscutt ◽  
G. D. Weymouth ◽  
B. Ganapathisubramani
Keyword(s):  
Reynolds Number ◽  
Parameter Space ◽  
Entire Range ◽  
Physical Significance ◽  
Two Dimensional ◽  
Low Thrust ◽  
Flapping Foil ◽  
Propulsive Performance ◽  
Flapping Foils ◽  
High Thrust

The propulsive performance of a pair of tandem flapping foils is sensitively dependent on the spacing and phasing between them. Large increases in thrust and efficiency of the hind foil are possible, but the mechanisms governing these enhancements remain largely unresolved. Two-dimensional numerical simulations of tandem and single foils oscillating in heave and pitch at a Reynolds number of 7000 are performed over a broad and dense parameter space, allowing the effects of inter-foil spacing ($S$) and phasing ($\unicode[STIX]{x1D711}$) to be investigated over a range of non-dimensional frequencies (or Strouhal number, $St$). Results indicate that the hind foil can produce from no thrust to twice the thrust of a single foil depending on its spacing and phasing with respect to the fore foil, which is consistent with previous studies that were carried out over a limited parameter space. Examination of instantaneous flow fields indicates that high thrust occurs when the hind foil weaves between the vortices that have been shed by the fore foil, and low thrust occurs when the hind foil intercepts these vortices. Contours of high thrust and minimal thrust appear as inclined bands in the $S-\unicode[STIX]{x1D711}$ parameter space and this behaviour is apparent over the entire range of Strouhal numbers considered $(0.2\leqslant St\leqslant 0.5)$. A novel quasi-steady model that utilises kinematics of a virtual hind foil together with data obtained from simulations of a single flapping foil shows that performance augmentation is primarily determined through modification of the instantaneous angle of attack of the hind foil by the vortex street established by the fore foil. This simple model provides estimates of thrust and efficiency for the hind foil, which is consistent with data obtained through full simulations. The limitations of the virtual hind foil method and its physical significance is also discussed.

Dynamic Analysis of Reticulated Shell Subjected to Earthquake Excitation

2011 ◽  
Vol 90-93 ◽  
pp. 1461-1466
Author(s):  
Zhong Yang ◽  
Yun Xu ◽  
Bing Zhao ◽  
Xu Jun Chen
Keyword(s):  
Shell Structure ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Dynamic Responses ◽  
Dynamic Feature ◽  
Two Dimensional ◽  
Earthquake Excitation ◽  
Nodal Displacements ◽  
Material Nonlinear ◽  
Reticulated Shell Structure

An optimum reticulated shell structure is selected and its dynamic properties are analyzed. In this paper analyses the dynamic feature and gains the elementary parameters from the analysis of free vibration. The frequencies and modes are compared by two finite element methods. The paper analyzes the dynamic responses of the reticulated shell structure subjected to two-dimensional and three-dimensional earthquake waves respectively. Simultaneously analyses the linear，geometric nonlinear and both geometric and material nonlinear dynamic responses in two situations. The nodal displacements and stresses of members are compared and analyzed. The characteristics of elastoplastic seismic responses of the structure are revealed and the basic rules are obtained.

Part 4 — Two dimensional dynamic stall

1987 ◽  
Vol 91 (902) ◽  
pp. 72-88 ◽  
Author(s):  
G. J. Hancock ◽  
J. S. Y. Lam
Keyword(s):  
Limit Cycle ◽  
Dynamic Responses ◽  
Dynamic Stall ◽  
Two Dimensional ◽  
Linear Set ◽  
Impulsive Input ◽  
Aerodynamic Model ◽  
Aerodynamic Derivatives ◽  
Experimental Values ◽  
General Motion

Summary An axiomatic aerodynamic model has been developed for the general motion of a two dimensional aerofoil as it passes in and out of stall, which gives realistic unsteady loads as compared to experimental values. A non-linear set of aerodynamic derivatives with time delays have been derived from the axiomatic aerodynamics. ‘Actual’ and ‘predicted’ dynamic responses of an aerofoil, spring restrained in torsion, following an impulsive input show similar trends, including limit cycle oscillations, although there is a slight difference in frequency and a difference in the magnitude of the initial impulse required to trigger the limit cycle.

scholarly journals Universal scaling law for drag-to-thrust wake transition in flapping foils

2019 ◽  
Vol 872 ◽  
Author(s):  
N. S. Lagopoulos ◽  
G. D. Weymouth ◽  
B. Ganapathisubramani
Keyword(s):  
Scaling Law ◽  
Two Dimensional ◽  
Universal Scaling ◽  
Flapping Foil ◽  
Thrust Generation ◽  
Self Similar ◽  
Induced Velocity ◽  
Flapping Foils ◽  
Insight Into ◽  
Wake Transition

Reversed von Kármán streets are responsible for a velocity surplus in the wake of flapping foils, indicating the onset of thrust generation. However, the wake pattern cannot be predicted based solely on the flapping peak-to-peak amplitude $A$ and frequency $f$ because the transition also depends sensitively on other details of the kinematics. In this work we replace $A$ with the cycle-averaged swept trajectory ${\mathcal{T}}$ of the foil chordline. Two-dimensional simulations are performed for pure heave, pure pitch and a variety of heave-to-pitch coupling. In a phase space of dimensionless ${\mathcal{T}}-f$ we show that the drag-to-thrust wake transition of all tested modes occurs for a modified Strouhal $St_{{\mathcal{T}}}\rightarrow 1$. Physically, the product ${\mathcal{T}}f$ expresses the induced velocity of the foil and indicates that propulsive jets occur when this velocity exceeds $U_{\infty }$. The new metric offers a unique insight into the thrust-producing strategies of biological swimmers and flyers alike, as it directly connects the wake development to the chosen kinematics, enabling a self-similar characterisation of flapping foil propulsion.

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