Dynamic Stall
Summary
Dynamic stall is a phenomenon that affects airfoils, wings and rotors in unsteady flows. It is due to changes, periodic or not, in the inflow conditions and/or angle of attack. In some cases, such helicopter rotors in advancing flight, dynamic stall is intrinsic to their state of operation.
A comprehensive review of CFD methods for dynamic stall has been published by Ekaterinaris and Platzer (1997); for physical insight, see McCroskey (1981).
In wind turbines it is the result of atmospheric turbulence, wind shears, earth boundary layer, etc. The aerodynamic characteristics are affected to an extend that depends on the frequency of the changes, their amplitude and the point of operation.
Other factors affecting dynamic stall are the Reynolds and Mach numbers and the geometrical shape. There other, maybe minor factors, like the vortex effects, blade flapping and bending, etc…
In the following discussion we will consider the airfoil dynamic stall, which is a particular case of rotor and wing stall. The airfoil is subject to two fundamental periodic oscillations: plunging and pitching.
A plunging oscillation is a periodic translation of the airfoil in a direction normal
to the free stream.
A pitching motion
is a periodic variation of the angle of attack.
The most important parameters affecting the dynamic behavior of an airfoil under
periodic variations of inflow conditions are: amplitude of the oscillation, mean
angle of attack, reduced frequency, Reynolds and Mach numbers, airfoil shape
(thickness, leading edge radius, etc.), surface roughness, and free stream turbulence.
Most of the analyses available are wind tunnel data, although in recent years the
physical models and the introduction of computational fluid dynamics have shifted the
attention toward the prediction aspects.
The effects of periodic oscillations are compared in terms of a reduced frequency.
The importance of the reduced frequency is that wind tunnel tests will be
representative of full scale phenomena as long as the frequency is constant,
the Reynolds and Mach numbers are the same, and the non-linear effects are relatively
mild.
The blades of a helicopter rotor in foward flight experience unbalanced inflow
conditions. The basic azimuth positions are shown in the sketch of Fig. 1.
It can be found that for some values of the advancing speed and the amplitude of the
oscillations (e.g. the rotor diameter) some sections experience back flow
conditions, Fig. 2.
The blade sections more affected by dynamic inflow conditions are at the hub.
The problem is governed by the ratio of the flight speed to the tip speed (tip
speed ratio).
Too large tip speed ratios affect more radically the characteristics of the
rotor, and represent a concrete limit to the flight speed of a helicopter.
At small angles of attack and relatively small reduced frequencies the airfoil
behavior can be treated with a potential flow approach. Accordingly, the viscous
effects can be neglected, Fig. 2.
Theodorsen in the 1930s was the first to give a linearized theory of the aerodynamic
flutter and the consequent instability. In fact, dynamic stall has major consequences
with respect to the structural behavior. The boundary layer remains attached. The
airfoil generates a sinusoidal wake.
The effect of the oscillating wake is to
produce a time lag between the actual conditions and the state of the boundary
layer. As a result the lift (and the other forces) will be in delay, and the
characteristic is a closed loop that is described clockwise.
If the oscillation occurs around a mean angle of attack close to CLmax (static stall)
the viscous effect become predominant. The description of the physical events taking
place is far more difficult. Fig. 3 shows an example of lift hysteresis for an
airfoil oscillating around CLmax (these effects change with the reduced frequency).
Figure 3b: pitching moment oscillation around Clmax.
Figure 3c: drag oscillation around Clmax.
Starting from the point of minimum incidence, the dynamic lift follows the static
lift, until the static lift curve deflects, due to increasing trailing edge
separation. The dynamic lift, instead, keeps growing almost linearly until a
breakdown occurs.
At the breakdown point there is massive flow separation and the lift drops to levels
far below those typical of the static curve. It will take some time to recover more
regular behavior, but the lift will remain below the static lift for most of the
remaining loop.
The increase of the lift above the static CLmax is attributed to the development of a
leading edge vortex on the upper surface that grows and travels downstream. The
breakdown is associated with the point when the leading edge vortex has traveled past
the airfoil trailing edge. The loop is described clockwise.
The loops described above are also called hysteresis loops. They are characteristic
of a loss of energy (due to viscous dissipation) that is proportional to the area
enclosed by the loop. Analogous considerations can be made in regard to drag and
pitching moment coefficient, although the hysteresis loops are somewhat different.
Understanding the initial stages of unsteady separation is extremely important.
It is known now that large scale separation is largely an inviscid problem. The
problem is more complicated in three-dimensions, because it requires the analysis
of different time and length scales.
CFD has made its entry in dynamic stall simulation in a wide range of speeds (up to
transonic) and various frequency ranges. Presently the available computational
methods are limited to two-dimensional stall. Among the main problems encountered
there is the turbulence modeling (all available models have been tried), … The
field is however in a fast expansion.
Since the CFD methods have appeared only a few years ago and are expensive, practical
engineering methods are continuously being developed (indicial methods, methods based
on time lag, etc.).
Dimensionless Parameters
Reduced Frequency
Unbalanced Loads on Rotorcraft
Oscillations below CLmax
Figure 2: Oscillations below Clmax.
Small Perturbations Theory
Oscillations around CLmax
Oscillations above CLmax
State of the Art
Related Material
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Selected References
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