Abstract
The flow around a flapping wing is characterized by an unsteady evolution of three-dimensional vortices, which are one of the main sources of loads. The difficulty in directly measuring such low forces by means of sensors and the need of the characterization of the evolution of the flow have lead to the evaluation of loads using the integral form of the momentum equation. This paper describes methods for evaluating instantaneous loads and three-dimensional pressure fields using 3D3C velocity fields only. An evaluation of the accuracy of these methods using DNS velocity fields is presented. Loads and pressure fields are then calculated using scanning tomography PIV velocity fields, around a NACA 0012 airfoil for a flapping motion in a water tank at a Reynolds number of 1,000. The results suggest a sufficient accuracy of calculated pressure fields for a global analysis of the topology of the flow and for the evaluation of loads by integrating the calculated pressure field over the surface of the wing.
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Abbreviations
- \(\alpha\) :
-
Incidence of the wing (°)
- \(\mu\) :
-
Dynamic viscosity (Pa s)
- \(\psi\) :
-
Angular position of the wing along its motion (°)
- \(\rho\) :
-
Density \((\text {kg}\,\text {m}^{-3})\)
- \(c\) :
-
Chord of the wing (m)
- \(C_D\) :
-
Drag coefficient
- \(C_L\) :
-
Lift coefficient
- \(C_p\) :
-
Pressure coefficient
- \(D, D_i\) :
-
Domain and sub-domains for the calculation of the pressure field
- \(D(t)\) :
-
Volume of application of the momentum equation
- \(S(t)\) :
-
Surface of the volume of application of the momentum equation
- \(F\) :
-
Aerodynamic loads (N)
- \(\overrightarrow{n}\) :
-
Vector normal to a surface
- \(Re\) :
-
Reynolds number
- \(T\) :
-
Period of a stroke cycle (s)
- \(\overrightarrow{V}\) :
-
Velocity in an absolute reference frame \((\hbox {m}\,\text {s}^{-1})\)
- \(\overrightarrow{V_0}\) :
-
Reference velocity at \(\frac{2}{3}\) of the \(\hbox {wingspan} (\hbox {m}\,\text {s}^{-1})\)
- \(\overrightarrow{V_r}\) :
-
Velocity in the frame linked to the volume of application of the momentum equation \((\hbox {m}\,\text {s}^{-1})\)
- \(\overrightarrow{W}\) :
-
Control volume velocity \((\hbox {m}\,\text {s}^{-1})\)
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Acknowledgments
The work leading to these results has received funding from the European Communitys Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No 605151 (NIOPLEX project).
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Tronchin, T., David, L. & Farcy, A. Loads and pressure evaluation of the flow around a flapping wing from instantaneous 3D velocity measurements. Exp Fluids 56, 7 (2015). https://doi.org/10.1007/s00348-014-1870-x
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DOI: https://doi.org/10.1007/s00348-014-1870-x