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A simple model for deep dynamic stall conditions

DOI:10.1002/we.2463
Authors:
Benedetto Rocchio at Università di Pisa
Benedetto Rocchio
Claudio Chicchiero at Università di Pisa
Claudio Chicchiero
M. V. Salvetti at Università di Pisa
M. V. Salvetti
Stefania Zanforlin at Università di Pisa
Stefania Zanforlin
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The present study is focused on modeling of dynamic stall behavior of a pitching airfoil. The deep stall regime is in particular considered. A model is proposed, which has a low implementation and computational complexity but yet is able to deal with different types of dynamic stall conditions, including those characterized by multiple vortex shedding at the airfoil leading edge. The proposed model is appraised against an extensive data set of experimental (α,CL) curves for NACA0012. The results of an existing widely used model, having comparable complexity, are also shown for comparison. The proposed model is able to well reproduce not only the classic curves of deep dynamic stall but also the curves characterized by lift oscillations at high angles of attack due to the shedding of multiple vortices. Furthermore, the model appears to be robust to variations of its parameters from the optimal values and of the airfoil geometry. Finally, the model is successfully implemented in a commercial CFD software and applied to the simulation of a vertical axis wind turbine within the actuator cylinder approach. The accuracy of the prediction of the turbine power coefficient in the whole rotation cycle is very good for the optimal working condition of the turbine, for which the model parameters were calibrated. Fairly good accuracy is also obtained in significantly different working conditions without any further calibration.
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Received: 31 August 2018 Revised: 3 October 2019 Accepted: 21 November 2019
DOI: 10.1002/we.2463
RESEARCH ARTICLE
A simple model for deep dynamic stall conditions
Benedetto Rocchio1Claudio Chicchiero1Maria Vittoria Salvetti1
Stefania Zanforlin2
1Department of Civil and Industrial
Engineering, University of Pisa, Pisa, Italy
2Dep artment of E nerg y, Systems, Territory
and Constructions Engineering, University of
Pisa, Pisa, Italy
Corres pon dence
Benedetto Rocchio, DICI, Via Girolamo Caruso
8, Pisa 56122, Italy.
Email: benedetto.rocchio@ing.unipi.it
Abstract
The present studyis focused on modeling of dynamic stall behavior of a pitching airfoil. The deep
stall regime is in particular considered. A model is proposed, which has a low implementation
and computational complexity but yet is able to deal with different types of dynamic stall
conditions, including those characterized by multiple vortex shedding at the airfoil leading edge.
The proposed model is appraised against an extensive data set of experimental (𝛼, CL)curves
for NACA0012. The results of an existing widely used model, having comparable complexity,
are also shown for comparison. The proposed model is able to well reproduce not only the
classic curves of deep dynamic stall but also the curves characterized by lift oscillations at high
angles of attack due to the shedding of multiple vortices. Furthermore, the model appears to
be robust to variations of its parameters from the optimal values and of the airfoil geometry.
Finally, the model is successfully implemented in a commercial CFD software and applied to the
simulation of a vertical axis wind turbine within the actuator cylinder approach. The accuracy
of the prediction of the turbine power coefficient in the whole rotation cycle is very good for
the optimal working condition of the turbine, for which the model parameters were calibrated.
Fairly good accuracy is also obtained in significantly different working conditions without any
further calibration.
KEYWORDS
dynamic stall, hydro-kinetic vertical axis wind turbine, vortex shedding
1INTRODUCTION
The term dynamic stall indicates the stall of a lifting surface under unsteady conditions and most commonly when it moves with a pitching,
heaving, or plunging motion. In this work, the attention is focused on the pitching motion because this condition occurs in different engineering
applications, as, eg, for the blades of vertical axis wind turbines, helicopter rotorcrafts, and turbomachines. From a practical viewpoint, the
dynamic stall is characterized by larger loads on the structures then the static one, by larger recirculation areas and by the shedding of multiples
vortices, which can lead to the failure of the structures.1,2 On the other hand, dynamic stall occurs at larger values of the lift coefficient than in
static conditions, and this may be convenient to obtain larger lift values in practical applications.3
When an airfoil undergoes a pitching motion, the aerodynamic angle of attack, 𝛼, changes in time as follows:
𝛼(t)=A0+A1sin(𝜔t).(1)
The (𝛼, CL)curve, where 𝛼is the angle of attack and CLthe corresponding lift coefficient, differs from the static one and its features depend
on the airfoil geometry and on the flow and pitching conditions, ie, the maximum amplitude of the oscillation, A0+A1, and the frequency of the
motion, F=𝜔∕(2𝜋). Usually, dynamic stall is classified in light stall and deep stall. We are, in particular, interested in the latter one, which shows a
large hysteresis in the dynamic (𝛼, CL)curve4-6 during the oscillation cycle. From a physical viewpoint, when the angle of attack is increased, the
deep dynamic stall is in many cases characterized by trailing-edge boundary-layer separation1,7,8 progressively moving towards the leading edge
and by the formation of a leading-edge vortex (LEV). The suctions induced by the LEV lead to the increase of the airfoil lift, even after large flow
separation has occurred (see, eg, previous works6,9,10 ). This vortex grows in strength, detaches, and is convected downstream. A trailing edge
wileyonlinelibrary.com/journal/we © 2020 John Wiley & Sons, Ltd. 915
Wind Energy. 2020;23:915–938.
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... If successful, this can be considered a significant improvement over those in the literature and one that is suitable for predicting the loads on operational wind turbine blades. 16,[22][23][24][25] The wind tunnel measurements used in this paper are selected from a database of two different wind tunnels. Measurements using the NACA 0015 and NACA 0012 airfoils were conducted in the wind tunnel at the University of Glasgow, 19 while the measurements of the S809 and NACA 4415 airfoils are from the NREL database observed in the wind tunnel of Ohio State University. ...
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... Decreasing the angle of attack a hysteresis is observable in the C L − α curve. This behaviour is reproduced in the MATLAB routine through the dynamic stall sub-model developed at the University of Pisa and described in Rocchio et al. (2020). ...
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