Flapping wing energy harvesting: aerodynamic aspects

  • W. GeisslerEmail author
Original Paper


Aerodynamic forces on flapping wings create forward thrust. Natural flyers like birds and insects apply these forces effectively. Extensive studies have shown that the efficiency of flapping wings can be improved by various means. Of importance is the development and control of leading edge vortices (LEV’s). Thrust production means that energy is transferred from the flapping system into the fluid. In a similar way it can be achieved that energy flows from the fluid into the flapping system, i.e. fluid energy may be harvested. Responsible for the direction of energy flow is the ratio of pitching amplitude versus amplitude of the induced incidence of the plunging motion. If this ratio is smaller than unity thrust energy is produced; if it is larger than unity energy is transferred into the flapping system. In the present paper, emphasis is placed on the detailed study of the aerodynamic effects and on some ideas of optimization of energy harvesting of a flapping system. It will be shown that similar to the thrust production mode also in the energy harvesting mode, the influence of LEV’s is of major concern. The control of these vortices by airfoil deformation is shown to be beneficial for optimizing the efficiency of energy harvesting.


Flapping wing aerodynamic Energy harvesting mode Effect of LEV’s Optimization procedures 

List of symbols


Speed of sound, m/s


Airfoil chord, m


Power coefficient (time-dependant)


Mean power coefficient


Moment coefficient (time-dependant)


Mean pitching moment coefficient


Normal force coeff. (time-dependant)


Mean normal force coefficient


Difference between the highest and lowest point reached by the airfoil, referred to chord


Frequency of oscillation, Hz


Reduced frequency, fc/U


Non-dimensional plunging amplitude referred to chord, h = z/c


Mach number, Ma  =  U/a


Mean value of section power per unit span, (Nm/s)/m


Pitching moment about pitch axis per unit span, Nm/m


Reynolds number: Re = Uc/ν


Time, s


Non-dimensional time, T = tU/c


Non-dimensional time of an oscillation period Tp = 2π/ω*


Normalized time, T = T/Tp


Free-stream velocity, m/s

x, z

Horizontal and vertical coordinate, m

xD, zD

Location of rotation axis, referred to chord

xp, zp

Location of flex-center, referred to chord

X, Z

Horizontal and vertical section force per unit span, N/m


Mean value of horizontal section force per unit span


Mean value of normal section force per unit span


Effective incidence, θ = θh + θp


Incidence induced by plunging motion, θh = tan−1(vh/U), deg


Incidence of pitching motion, deg


Non-dimensional plunging velocity, Vh = * sin (ω*T)


Non-dimensional pitching velocity, Vθ = θp0ω* sin (ω*T +Φ)


Efficiency: η = P/(1/2ρU 3 d)


Kinematic viscosity, m2/s


Density, kg/m3


Phase shift between pitch and plunge


Nose droop angle


Amplitude of nose-droop angle


Rotational frequency of airfoil oscillation, ω = 2 π f, rad/s


Rotational frequency of airfoil oscillation, ω* = ωc/U = 2πf



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Copyright information

© Deutsches Zentrum für Luft- und Raumfahrt e.V. 2019

Authors and Affiliations

  1. 1.Institute of Aerodynamics and Flow TechnologyGerman Aerospace Center (DLR)GöttingenGermany

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