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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.