Static Aeroelasticity: Typical Section Flashcards
Describe the wing structure and aerodynamics of a typical section.
Wing Structure
* Rigid with a constant section
* Span perpendicular to wind speed
* Deformability concentrates in a torsional spring at root
Aerodynamics
* 2D strip theory
* Linear behavior since only low amplitude pitch oscillations are considered
What is the shear center, the elastic axis, the flexural center and the aerodynamic center?
1. Shear center: It is a point of a 2D section where if you apply a transverse shear load it produces zero change (or rate) of twist of the section. It is a property of the cross-section (also material if it’s multimaterial).
2. Elastic axis: It is the locus of shear centers along the span of the wing. Typically between 35-45% of the chord for semi-monocoque structures.
3. Flexural center: The point where the shear load P applied to a cantilever beam does not cause rotation of the section ACB, but not necessarily elsewhere in the wing. It depends on the load distribution along the wing.
4. Aerodynamic center: The point of the section around which the steady aerodynamics moment coefficient is constant with respect to changes of angle of attack (dCmac/da = 0).
What does CL and it’s derivative with respect to the AoA typically depend on?
CL depends on the AoA, Ma, Re..while CL_alpha depends on Ma, Re.
What does the equilibrium position of the elastic twist depend on?
The numerator is larger than zero, while the denominator is equal to Ks - qKa, where Ks is the structural stiffness and Ka is the aerodynamic stiffness. When Ks-qKa = 0, then the elastic twist goes to infinite, causing a divergence instability.
Explain the typical section divergence with a feedback structure.
- There is an initial aerodynamic moment applied to the structure
- This aerodynamic moment produces an elastic angle θ, equal to the moment divided by the structural stiffness Ks.
- The change of elastic angle produces a change in aerodynamics, which in turn produces a new aerodynamic moment equal to qKa.
- The new aerodynamic moment is added to the initial aerodynamic moment, creating a feedback. The cycle repeatds until the system reaches the twist angle of equilibrium.
What happends at divergence dynamic pressure?
The two stiffnesses, structural and aerodynamic are equal and opposite, which is equivalent to no stiffness.
What happends when the AC is behind the EA (e<0)?
Then qD < 0, divergence is not feasible.
What is the aeroelastic performance index?
The aeroelastic performance index is equal to theta/theta_0, where theta is the value obtained by taking into account the change of aerodynamic moments with the elastic twist, while theta_0 is equal to M0/Ks. It is equal to 1/(1-q/qD) and it shows that the closer q is to qD, the higher will be the incidence of aeroelastic effects.
How else can the torsional divergence problem be solved?
- As a static stability problem.
- As an eigenvalue problem.
How does the aeroelastic and rigid lift compare?
(L-Lr)/L depends on 1/(1-q/qD), which demonstrates that the elastic lift is larger than the rigid lift.
What are the effects of Mach number?
- The AC tends to move forward initially, while the Mach number increases
*When shock waves appear, the AC starts moving backwards. Eventually e can become negative in the supersoning region and flutter does not occur. x_ac is equal to c/4 in the subsonic regime, while it is equal to c/2 in the supersonic regime. - The lift curve slop tends to grow with Mach number, at least for thin airfoils, before reaching the critical Mach number. The thicker the airfoil is, the more the behaviour diverges.
*The equation Ks - qKa can be solved by using the Mach number, which is a function of altitude. Eventually, for every altititude it is possible to identify several divergence Mach numbers, but only one is physically meaningful.
