In order to investigate the impact of airfoil thickness on flapping performance, the unsteady flow fields of a family of airfoils from an NACA0002 airfoil to an NACA0020 airfoil in a pure plunging motion and a series of altered NACA0012 airfoils in a pure plunging motion were simulated using computational fluid dynamics techniques. The “class function/shape function transformation“ parametric method was employed to decide the coordinates of these altered NACA0012 airfoils. Under specified plunging kinematics, it is observed that the increase of an airfoil thickness can reduce the leading edge vortex (LEV) in strength and delay the LEV shedding. The increase of the maximum thickness can enhance the time-averaged thrust coefficient and the propulsive efficiency without lift reduction. As the maximum thickness location moves towards the leading edge, the airfoil obtains a larger time-averaged thrust coefficient and a higher propulsive efficiency without changing the lift coefficient.

Since the Micro Air Vehicle (MAV) was generally defined by the Defense Advanced Research Projects Agency (DARPA) in 1997 [

Nevertheless, the influence of airfoil geometry on its flapping performance has not been explored enough. Most of researchers employed a flat plate [

The shape of wing section and other geometry parameters of birds, bats and insects are decided by the evolution of nature, but the parameters of wing sections (airfoils) of man-made FWMAVs could be selected by the designers. It is therefore useful to explore the effects of wing shape on its flapping performance. The present study mainly focuses on the influence of thickness of 2D NACA series symmetric airfoils with pure plunging motion which is the most popular style of current artificial flapping wing flying vehicles. Not only the influence of the maximum thickness magnitude but also the influence of the maximum thickness location on the flapping performance of the airfoil was discussed.

This paper is organized mainly into five parts. Following this introduction is the definition of the flapping model, several important parameters involved in the flapping model and how to calculate the time-averaged thrust coefficient and the propulsive efficiency are described. In Section

As the evolution of academic research on flapping wings [

Flapping wing MAV proposed by Jones and Platzer [

The real flapping model shown in Figure

Illustration of the flapping model in pure plunging motion.

In addition, there are two other important similarity numbers, Reynolds number (

In classical aerodynamics, the lift coefficient

The commercial CFD solver FLUENT v6.3.26 was employed to simulate the unsteady flow fields around moving airfoils with predefined motions. The two-dimensional time-dependent Navier-Stokes equations were solved using the finite volume method, assuming incompressible laminar flow. The mass and momentum equations were solved in a fixed inertial reference frame incorporating a dynamic mesh. The dimensionless mass and momentum conservation equations are given by [

The hybrid mesh which is shown schematically in Figure

Hybrid mesh topology with boundary conditions.

C-type grid very near the airfoil.

A grid sensitivity study was carried out first to evaluate the independence of the numerical solution on the mesh size. Some specified unsteady flow fields around a rigid NACA0014 airfoil with pure plunging motion were computed under conditions of

Grid sensitivities of drag coefficients.

Grid sensitivities of lift coefficients.

Furthermore, to validate the accuracy of the present hybrid mesh, simulations based on the

Time history of drag coefficients.

Time history of lift coefficients.

The three wiggles of the lift coefficient near the peak value, marked as (1), (2), and (3) in Figure

Pressure contours of the airfoil neighborhood at three wiggles.

This section mainly focuses on the effects of the magnitudes of the maximum thickness. The popular NACA 4-digit series airfoils are employed, and the conventional definition of symmetrical 4-digit NACA airfoils can be described by the following [

Conventional definition of airfoils.

Computations for pure plunging motion of a family of airfoils from a NACA0002 airfoil to a NACA0020 airfoil were performed under the conditions of

Time histories of

Pressure contours of NACA0006.

Pressure contours of NACA0020.

In order to check the effect of the maximum thickness location (Loc) on the flapping performance, the “Class function/Shape function Transformation (CST)” parametric geometry representation method is employed to parameterize the 2D airfoil. The universal CST method is defined as follows [

Values of

No. | Loc ( | |||
---|---|---|---|---|

1 | 30.0% | 0.17211035378267 | 0.13867972442717 | 0.15458446304747 |

2 | 35.0% | 0.17211035378267 | 0.11758914339250 | 0.24333708636138 |

3 | 40.0% | 0.17211035378267 | 0.10417878455362 | 0.28842711913075 |

4 | 45.0% | 0.17211035378267 | 0.09353460035375 | 0.31733390835548 |

5 | 50.0% | 0.17211035378267 | 0.08244808744449 | 0.34181598126744 |

Original and CST NACA0012.

Denote

Airfoil shapes with different Loc.

Computations for the unsteady flow fields with pure plunging motion of a series of altered NACA0012 airfoils with Loc = 30.0% to Loc = 50.0% were performed under the conditions of

Trends of

Lift histories for different Loc.

Pressure contours for Loc = 30%.

Pressure contours for Loc = 50%.

The unsteady flow fields for a pure plunging motion of a family of airfoils from an NACA0002 airfoil to a NACA0020 airfoil, and a series of altered NACA0012 airfoils were analyzed using CFD techniques. Some interesting results can be concluded here. Under specified conditions,

Though the numerical simulations were just performed under specified conditions and a single reduced frequency, we hope these conclusions shed a little light to the explanation of the difference between the speed of flat-plat-like wing flying animals, insects and thick-airfoil-like wing flying animals, birds. It is not sure if a similar phenomenon appears in pure pitching motion, combination of plunging motion and pitching motion, and a complete 3D wing. These are recommendations for future research.

The Grant supported from National Science Foundation of China (no. 10972034) and National Science Foundation for Post-doctoral Scientists of China (20090460216) are greatly acknowledged. The first author would like to express his great appreciation to Dr. Brenda M. Kulfan, from the Boeing Company, for her invaluable suggestions on the CST method.