Ismail H. Tuncer

Thrust generation due to airfoil flapping

Thrust generation on a single flapping airfoil and a flapping/stationary airfoil combination in tandem is studied parametrically. A multiblock Navier-Stokes solver is employed to compute unsteady flowfields. The unsteady flowfield around a single flapping airfoil is also computed by an unsteady potential flow code. The numerical solutions predict thrust generation in flapping airfoils and a significant augmentation of thrust in flapping/stationary airfoil combinations in tandem. The propulsive efficiency is found to be a strong function of reduced frequency and the amplitude of the flapping motion. At a flapping amplitude of 0.40 chord lengths and a reduced frequency of 0.10, the propulsive efficiency of a single NACA 0012 airfoil was computed to be more than 70 %. For the airfoil combination in tandem, the propulsive efficiency was augmented more than 40% at a reduced frequency of 0.75 and a flapping amplitude of 0.20 chord lengths when the airfoils are separated by about two chord lengths.

Computational Study of Flapping Airfoil Aerodynamics

Unsteady, viscous, low-speed e ows over a NACA 0012 airfoil oscillated in plungeand/orpitch at various reduced frequency,amplitude, andphaseshift arecomputed. Vortical wakeformations, boundary-layere owsat theleading edge, the formation of leading-edge vortices and their downstream convection are presented in terms of unsteady particletraces.Flowseparationcharacteristicsandthrust-producingwakeproe lesareidentie ed.Computedresults compare well with water tunnel e ow visualization and force data and other computational data. The maximum propulsive efe ciency is obtained for cases where the e ow remains mostly attached over the airfoil oscillated in a combined pitch and plunge.

Optimization of flapping airfoils for maximum thrust and propulsive efficiency

The thrust and/or propulsive efficiency of a single flapping airfoil is maximized by using a numerical optimization method based on the steepest ascent. The flapping motion of the airfoil is described by a combined sinusoidal plunge and pitching motion. Optimization parameters are taken to be the amplitudes of the plunge and pitching motions and the phase shift between them at a fixed flapping frequency. Two-dimensional, unsteady, low-speed, laminar, and turbulent flows are computed by using a Navier‐Stokes solver on moving overset grids. Computations are performed in parallel in a computer cluster. The optimization data show that high thrust values may be obtained at the expense of propulsive efficiency. For a high propulsive efficiency, the effective angle of attack of the airfoil is reduced, and large-scale vortex formations at the leading edge are prevented.

Theoretical and numerical studies of oscillating airfoils

Unsteady flowfields around airfoils oscillating in pitch and associated dynamic stall phenomena are investigated. A viscous flow analysis and a simplified vortical flow analysis, both based on an integro-differential formulation of the Navier Stokes equations are developed and calibrated. The formulation of the viscous flow analysis confines computations only to the viscous flow zone and leads to an efficient zonal solution procedure. In the simplified vortical flow analysis, computational demands are greatly reduced by partial analytic evaluations. Simulated flowfields and computed aerodynamic loads are in good agreement with available experimental data.

Thrust generation caused by flapping airfoils in a biplane configuration

Unsteady, viscous e ows over e apping airfoils in a biplane cone guration are computed on moving overset grids. The overset grid solutions are obtained in parallel in a distributed memory environment. Unsteady e owe elds are described by particle traces. Time-averaged thrust values are obtained from the integration of the unsteady drag coefe cient. It isshown thatairfoilsin abiplanecone guration andoscillatingina combinedpitchand plungemotion with a proper phase shift between them produce 20 ‐40% more thrust than a single e apping airfoil. Turbulence in the e ow further augments the thrust generation. For a maximum thrust at a given e apping frequency, an optimization of the e apping motion parameters is needed.

Nonsinusoidal Path Optimization of a Flapping Airfoil

The path of a flapping airfoil undergoing a combined, nonsinusoidal pitching and plunging motion is optimized for maximum thrust and/or propulsive efficiency. The nonsinusoidal, periodic flapping motion is described using nonuniform rational B splines. A gradient based algorithm is then employed for the optimization of the nonuniform rational B-spline parameters. Unsteady, low speed laminar flows are computed using a Navier-Stokes solver in a parallel computing environment The numerical evaluation of the gradient vector components, which requires unsteady flow solutions, is also performed in parallel. It is shown that the thrust generation may significantly be increased in comparison to the sinusoidal flapping motion. For a maximum thrust generation, the airfoil stays at about a constant angle of attack during the upstroke and the downstroke, and may reach very high effective angle of attack values. The pitching motion mostly occurs at the minimum and maximum plunge positions.

A computational study on the dynamic stall of a flapping airfoil

The dynamic stall boundaries of a NACA 0012 airfoil oscillating in either the pure plunge mode or in the combined pitch and plunge mode is computed using a thin-layer Navier-Stokes solver. Unsteady flowfields are computed at the free-stream Mach number of 0.3, the Reynolds number of 1 • 10, and the Baldwin-Lomax turbulence model is employed. It is found that the pure plunge oscillation leads to dynamic stall as soon as the non-dimensional plunge velocity exceeds the approximate value of 0.35. In addition, the power extraction capability of the airfoil operating in the wingmill mode is studied by computing the dynamic stall boundary for a combined pitch and plunge motion at the reduced frequency values of 0.1, 0.25 and 0.5.

Two-dimensional unsteady Navier-Stokes solution method with moving overset grids

A simple numerical algorithm to localize Intergrid boundary points and to interpolate unsteady solution variables across two-dimensional, structured overset grids is presented. Overset grids are allowed to move in time relative to each other. Intergrid boundary points are localized in a triangular stencil on the donor grid by a directional search algorithm. The final parameters of the search algorithm give the interpolation weights at the intergrid boundary point. Numerical results are presented for steady and unsteady viscous flow solutions over an airfoil undergoing a sinusoidal flapping motion. Computed flowfields demonstrate the accuracy of the method, and excellent agreement is obtained against the single grid solutions. The method is independent of numerical solution algorithms, and it may easily be implemented on any two-dimensional, single-block flow solver to make it a multiblock, zonal solver with arbitrarily overset/overlapping computational grids.

Computational study of subsonic flow over a delta canard-wing-body configuration

Subsonic flowfields over a close-coupled, delta canard-wing-body configuration at angles of attack of 20, 24.2, and 30 deg are computed using the OVERFLOW Navier-Stokes solver. Computed flowfields are presented in terms of particle traces, surface streamlines, and leeward-side surface pressure distributions for the canard-on and -off configurations. The interaction between the canard and the wing vortices, wing vortex breakdown, and the influence of the canard on vortex breakdown are identified. The comparison of the pressure data with the available experimental data at Re = 0.32 x 10 6 and Re = 1.4 x 10 6 shows a significant Reynolds-number dependence

Unsteady aerodynamic characteristics of a dual-element airfoil

Unsteady aerodynamic behavior and load characteristics of a VR-7 slat/airfoil combination oscillating sinusoidally between 5-25 deg have been studied. The unsteady, compressible Navier-Stokes equations are solved on a multiblock grid using an approximate factorization finite difference scheme. In the case of a single airfoil, a massive flow separation and formation of a strong vortex is observed. The vortex-induced suction and the shedding of the vortex into the wake is responsible for high aerodynamic loads and the subsequent stall of the airfoil. In the case of a slat/airfoil combination, the suction peak at the leading edge of the airfoil is reduced significantly in comparison to the single airfoil. Flow separation is confined to the trailing edge of the main airfoil, and the formation of a strong vortical structure is not observed. The slat/airfoil combination does not experience a massive flow separation, and the aerodynamic lift does not undergo the characteristic deep dynamic stall hysteresis loops.