2D flapping wing by Michael Alletto

From OpenFOAM Wiki
Revision as of 06:06, 29 November 2019 by Jozsef Nagy (talk | contribs)
Jump to navigation Jump to search

Go back to Collection by authors.

Go back to Meshing.

2D flapping wing

You can download the case file sphereSplashSend.tar.gz !!!!!!!!!!!!!!!! here.

Introduction

In this tutorial an additional application of the overset methodology is illustrated: the flapping motion of a two dimensional wing. A flapping wing motion is used by many insects and also vertebrates to execute hoovering manoeuvres. See [1] for a review. Key feature of the hoovering fly is the larger lift generated because of the unsteady wing motion in comparison to the steady flow around a wing. For a two dimensional wing a leading edge vortex is formed. It is responsible for the greatest amount of lift generated since it remains attached throughout almost the whole stroke. The interested reader is referred the review article of [2]. Furthermore during stroke reversal the rotating wing generates a circulation which also contributes to the generation of additional lift.

Set up

The Simulation setup is inspired by the experiments of [3]. The experiments consisted in a flat plate which rotates about the stroke axis with an angle of 0 <= Φ <= 90° and pitches about the rotational axis with an angle of β = +- 50°. The details of the kinematics are described in [3]. The wing span was R = 107mm and the thickness was s = 3.4mm (see [4] since in [3] the thickness of the plate was not described). The distance from the rotational axis to the wing root was ΔR = 71.5mm (private communications). In order to perform a two--dimensional simulation, the rotatory motion of the point located at mid-span is projected on a horizontal plane. That means that the displacement of the point located at the center of the wing in the experiment is the same as the horizontal displacement of the wing in the simulation. The pitching motion is the same in the experiment and in the simulation.

Mesh generation

Since the interpolation errors in overset grids is proportional to the cell size difference between moving and background mesh (of course also to the cell size itself), the purpose of the mesh generation was to minimize this errors. In order to achieve this goal, the size of the cells of the background mesh and the moving grid have to be similar in the region where the interpolation is performed. For this reason the moving mesh was generated with snappyHexMesh in combination with different refinement regions. Since snappyHexMesh can perform only three--dimensional refinements (a hexahedron is split in eight cells with no option for the user to impose only splitting in two directions) the utility extrudeMesh is used. With this utility the 2D mesh at the symmetry plane can be extruded having a mesh with only one cell in span wise direction. The mesh is shown in Figure !!!!!!!!!!!!.


Simulation set up

As for the other tutorials presented, the different zones (background mesh and the moving meshes) should be differentiated by the scalar field zoneID. This field should have a different number (starting with zero) for each mesh (see Figure !!!!!!!!!!!!!!!). The overset method implemented in OpenFOAM detects itself the different cell types. The cells adjacent to the patch denominated as overset are chosen as interpolated. For this cells the matrix coefficients are not derived from the finite volume discretization but using one of overset interpolation method chosen by the user. The cells which are inside the wing are flagged as hole cells and exclude from the calculation. The other cells are treated as calculated (the matrix coefficients are derived from a finite volume discretization). The cell types are visualized on the right of Figure !!!!!!!!!!!!!!!.

The kinematics of the wing are imposed by choosing the adequat motion solver. Since the wing executes a sinusoidal movement in x-direction and pitches at the and of the half stroke with a linear change of the angle β (see Figure !!!!!!!!!!!!!!!!!!1 where the evolution of the x-position of and the angle β during the first cycle is shown), the tabulated6DoFMotion function is chosen. This function allows to impose the temporal evolution of the displacement in x-,y- and z-direction and also the rotation about the same axis. The displacements and rotation are relative to the initial position. The rotation is described about the point denoted as CofG. Since the rotation in the experiment was about an axis located a forth of the chord length from the leading edge, CofG was set to at this position in the initial state. The dynamic mesh dictionary is shown below. 


dynamicFvMesh       dynamicOversetFvMesh; 
solver          multiSolidBodyMotionSolver;
multiSolidBodyMotionSolverCoeffs
{
   movingZone
   {
       solidBodyMotionFunction tabulated6DoFMotion;
       CofG            (0.00546 0.00651 0);
       timeDataFileName "<constant>/6DoF.dat";
   }
}

References

[1] Diana D Chin and David Lentink. Flapping wing aerodynamics: from insects to vertebrates. Journal of Experimental Biology, 219(7):920-932, 2016.

[2] Je D Eldredge and Anya R Jones. Leading-edge vortices: mechanics and modeling. Annual Review of Fluid Mechanics, 51:75-104, 2019.

[3] Swathi Krishna, Melissa A Green, and Karen Mulleners. Flowfield and force evolution for a symmetric hovering at-plate wing. AIAA Journal, 56(4):1360{1371, 2018.

[4] Swathi Krishna, Melissa A Green, and Karen Mulleners. Effect of pitch on the flow behavior around a hovering wing. Experiments in Fluids, 60(5):86, 2019.

[5] YJ Lee, KB Lua, and TT Lim. Aspect ratio effects on revolving wings with rossby number consideration. Bioinspiration & biomimetics, 11(5):056013, 2016.

Retrieved from "https://wiki.openfoam.com/index.php?title=2D_flapping_wing_by_Michael_Alletto&oldid=2874"