Copyright © A. Filippone (1999-2003). All Rights Reserved.

Unsteady Aerodynamics

Dynamic Stall


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.

Dimensionless Parameters

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.

Reduced Frequency

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.

Unbalanced Loads on Rotorcraft

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.

Helicopter Rotor

Figure 1: Azimuth positions of helicopter rotor blades.

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.

Helicopter Rotor

Figure 2: Dynamic stall on helicopter rotor.

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.

Oscillations below CLmax

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.

oscillations below CLmax

Figure 2: Oscillations below Clmax.

Small Perturbations Theory

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.

Oscillations around CLmax

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).

oscillations around CLmax

Figure 3a: Lift oscillations around Clmax.

oscillations around CLmax

Figure 3b: pitching moment oscillation around Clmax.

oscillations 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.

Oscillations above CLmax

oscillations above CLmax

Figure 4: Oscillations above Clmax.

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.

State of the Art

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.).

Related Material

(available on CD-ROM)
  • Dimensionless Groups
  • Airfoil Wake in pitching motion

Selected References

  • Theodorsen T. General Theory of Aeodynamic Instability and the Mechanism of Flutter, NACA TR 496, 1935.

  • McCroskey WJ. Unsteady Airfoils, in Ann. Rev. Fluid Mech., Vol. 14, pages 285-311 (1982).

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Copyright © A. Filippone (1999-2003). All Rights Reserved.