# 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.

### 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.

#### Reduced Frequency

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.

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.

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.

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.

### 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).

Figure 3a: Lift oscillations around Clmax.

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.

### Oscillations above CLmax

Figure 4: Oscillations above Clmax.

### 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.

#### 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).