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The onset of dynamic stall revisited

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Abstract

Dynamic stall on a helicopter rotor blade comprises a series of complex aerodynamic phenomena in response to the unsteady change of the blade’s angle of attack. It is accompanied by a lift overshoot and delayed massive flow separation with respect to static stall. The classical hallmark of the dynamic stall phenomenon is the dynamic stall vortex. The flow over an oscillating OA209 airfoil under dynamic stall conditions was investigated by means of unsteady surface pressure measurements and time-resolved particle image velocimetry. The characteristic features of the unsteady flow field were identified and analysed utilising different coherent structure identification methods. An Eulerian and a Lagrangian procedure were adopted to locate the axes of vortices and the edges of Lagrangian coherent structures, respectively; a proper orthogonal decomposition of the velocity field revealed the energetically dominant coherent flow patterns and their temporal evolution. Based on the complementary information obtained by these methods the dynamics and interaction of vortical structures were analysed within a single dynamic stall life cycle leading to a classification of the unsteady flow development into five successive stages: the attached flow stage; the stall development stage; stall onset; the stalled stage; and flow reattachment. The onset of dynamic stall was specified here based on a characteristic mode of the proper orthogonal decomposition of the velocity field. Variations in the flow field topology that accompany the stall onset were verified by the Lagrangian coherent structure analysis. The instantaneous effective unsteadiness was defined as a single representative parameter to describe the influence of the motion parameters. Dynamic stall onset was found to be promoted by increasing unsteadiness. The mechanism that results in the detachment of the dynamic stall vortex from the airfoil was identified as vortex-induced separation caused by strong viscous interactions. Finally, a revised criterion to discern between light and deep dynamic stall was formulated.

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Abbreviations

a i :

ith Temporal eigenmode of the POD

c :

Chord length

C l :

Lift coefficient

C m :

Pitching moment coefficient

C p :

Pressure coefficient

f osc :

Oscillation frequency

k :

Reduced frequency

Ma :

Mach number

M :

Number of grid points

n :

Probability density

N :

Number of PIV velocity fields

n :

Unit normal vector

r eq :

Reduced pitch rate

Re :

Reynolds number

S :

Two-dimensional area

t n :

Discrete time stamp

t ss :

Time at which static stall angle is exceeded

T :

Period of oscillation

u = (u, v, w):

Local velocity

\(U_{\infty}\) :

Free steam velocity

x = (x, y, z):

Spatial coordinates

α:

Angle of attack

α0 :

Mean incidence

α1 :

Oscillation amplitude

αds :

Dynamic stall angle of attack

αmax :

Maximum angle of attack

αss :

Static stall angle of attack

\(\dot{\alpha}_{\rm ss}\) :

Instantaneous effective unsteadiness

\(\Upgamma\) :

Scalar function

\({\Updelta t}_{\rm ds}\) :

Dynamic stall delay

λ i :

ith Eigenvalue of the POD

θ:

Velocity orientation angle

ω:

Vorticity

ψ i :

ith Spatial eigenmode of the POD

\({\nearrow}\) :

During upstroke

\({\searrow}\) :

During downstroke

O :

Order of magnitude

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Acknowledgments

The authors thank H. Mai, T. Büte, J. Nuhn, and A. Henning for their contribution to the wind tunnel measurements and K. Kindler for comments.

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  1. German Aerospace Center (DLR), Bunsenstr. 10, 37073, Göttingen, Germany

    Karen Mulleners & Markus Raffel

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  1. Karen Mulleners
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  2. Markus Raffel
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Correspondence to Karen Mulleners.

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Mulleners, K., Raffel, M. The onset of dynamic stall revisited. Exp Fluids 52, 779–793 (2012). https://doi.org/10.1007/s00348-011-1118-y

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