Experimental and numerical investigation of flapping airfoils interacting in various arrangements

Abstract

In the last decades, flapping wing aerodynamics has gained a great deal of interest. Inspired by insect flight, the utilization of multiple wings has become very popular in Micro Air Vehicle (MAV) and Micromechanical Flying Insect (MFI) design. Therefore, studies aiming to disclose the characteristics of flow around interacting flapping airfoils has received a particular attention. However, the majority of these studies were done using real, complex, three dimensional parameters and geometries without making any assessment on basic two dimensional vortex dynamics. The aim of this study is to identify the baseline flow field characteristics in order to better understand the flapping wing aerodynamics in nature and thus to provide a viewpoint for MAV and MFI design. The thesis contains numerical and experimental investigation of tandem (in line) and biplane (side by side) arrangements of NACA0012 airfoils undergoing harmonic pure plunging motion by means of vortex dynamics, thrust and propulsive efficiency. Additionally, the "deflected wake phenomenon" which is an interesting and a challenging benchmark problem for the validation of the numerical algorithms for moving boundary problems is investigated for a single airfoil due to its flow characteristics which accommodates strong transient effects at low Reynolds numbers. Throughout the study, effects of reduced frequency, non-dimensional plunge amplitude, Reynolds number and phase angle between airfoils are considered. The vorticity patterns are obtained both numerically and experimentally whereas force statistics and propulsive efficiencies are evaluated only in numerical simulations. In the experimental phase of the study, Particle Image Velocimetry (PIV), which is a non-intrusive optical measurement technique, is utilized. Experiments are conducted in the large scale water channel in the Trisonic Laboratory of Istanbul Technical University. The motion of the wings is provided by two servo motors and their gear systems. To obtain a two dimensional flow around the wings, they are placed in between two large endplates one of which is having a slot to permit the connection between the wings and the servo motors. The flow is seeded with silver coated hollow glass spheres of 10µ diameter and illuminated with a dual cavity Nd-Yag laser. To visualize a larger flow area, two 16-bit CCD cameras are used together either inline or side by side depending on the positions of the wings. Dantec Dynamics's Dynamic Studio software is used for synchronization, image acquisition, image stitching and cross correlation purposes. Synchronization between servo motors and data acquisition system is done via LabView software. In post process, an in-house Matlab code is used for masking of the airfoils. CleanVec and NFILVB software are utilized for vector range validation and for filtering. In order to gather mean velocity fields, NWENSAV software is used. From the experimental velocity vector fields, two dimensional vorticity fields are obtained in order to understand the flow field characteristics. The experimental results are also used as a benchmark for the numerical studies. In the numerical phase of the study, an arbitrary Lagrangian-Eulerian (ALE) formulation based on an unstructured side-centered finite volume method is utilized in order to solve the incompressible Navier-Stokes equations. The velocities are defined at the midpoint of each edge where the pressure is defined at element centroid. The present arrangement of the primitive variables leads to a stable numerical scheme and it does not require any ad-hoc modifications in order to enhance pressure-velocity coupling. The most appealing feature of this primitive variable arrangement is the availability of very efficient multigrid solvers. The mesh motion algorithm is based on an algebraic method using the minimum distance function from the airfoil surface due to its numerical efficiency, although in some cases where large mesh deformation occurs Radial Basis Function (RBF) algorithm is used. To satisfy Discrete Geometric Conservation Law (DGCL), the convective term in the momentum equation is modified in order to take account the grid velocity. The numerical grid is created via Gambit and Cubit softwares with quadrilateral elements. Grid and time independencies are achieved by means of force statistics and vorticity fields. To make direct comparison Finite Time Lyapunov Exponent (FTLE) fields are calculated for some cases. FTLE fields characterize fluid flow by measuring the amount of stretching between neighbouring particles and the Lagrangian Coherent Structures (LCS) are computed as the locally maximum regions of the FTLE field. On the other hand, using a second-order Runge-Kutta method particle tracking algorithm is developed based on the integration of the massless particle trajectories on moving unstructured quadrilateral elements. Validation of results is performed by comparing the numerical results with the experimental results and also comparing with the corresponding cases in the literature. Accordingly, the results were substantially compatible within itself and also compatible with the literature. Highly accurate numerical results are obtained in order to investigate the flow pattern around a NACA0012 airfoil, undergoing pure harmonic plunging motion corresponding to the deflected wake phenomenon which are confirmed by means of spatial and temporal convergence. Present study successfully reproduces the details of the flow field which is not produced in literature such as fine vortical structures in opposite direction of the deflected wake and the vorticity structures close to airfoil surface which is dominated by complex interactions of LE with the plunging airfoil. Moreover, highly persistent transient effects and the calculations require two orders of magnitude larger duration than the heave period to reach the time-periodic state which is prohibitively expensive for the numerical simulations. This persistent transient effect is not reported before in the literature. The three-dimensional simulation also confirms highly persistent transient effects. In addition, the three-dimensional simulation indicates that the flow field is highly three-dimensional close to the airfoil leading edge. The three-dimensional structure of the flow field is not noted in the literature for the parameters used herein. In case of tandem arrangement of airfoils, the experimental results agree well with the numerical solutions. Major flow structures are substantially compatible in both numerical and experimental results at Reynolds number of 2,000. For the considered parameters, during upstroke and downstroke co-rotating leading and trailing end vortices merge at the trailing end of the forewing and interact with the downstream airfoil in either constructive or destructive way in trust production. Thrust production of forewing is maximum when airfoil moves from topmost position to mid position for the considered reduced frequencies at all configurations. It is hard to specify thrust-drag generation characteristics of the hindwing since it depends on not only plunge motion parameters, but also on interactions with vortices from the forewing. For the considered phase angles of 0°, 90°, 180° and 270°, in addition to stationary hind wing case, the force statistics are strongly altered due to the airfoil-wake interactions. In case of biplane arrangement of airfoils at phase angle of 180°, experimental and numerical vorticity results are also quite comparable. Regarding the parameters investigated, as the reduced frequency increases, vorticity structures get larger at constant plunge amplitude. However, vorticity structures do not change much after a certain reduced frequency value. As the plunge amplitude increases, the magnitude of vortices increases without depending on reduced frequency. Increasing plunge amplitude results in increased amount of fluid moving in the direction of motion in a constant period of time, commensurate with strong suction between airfoils as they move apart from each other. As a consequence of this suction force, energetic vortex pairs are formed which helps in thrust augmentation. For thrust production, among the phase angles considered, i.e. 0°, 90°, 180° and 270°, in addition to stationary lower wing case, the most efficient is φ=180°. Effect of three dimensionality is not observed at this phase angle for the considered parameters. Additionally, no remarkable difference is observed in general flow structure when Reynolds number is increased from 2,000 to 10,000.