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Chapter 11[pdf]: 11.1 Introduction 11.2 Model of Wing Section in Torsion 11.3 Aeroelastic Configuration Model 11.4 Modular Framework for Aeroelastic Loop 11.5 Case Studies: Elastic-Static Wing Effects
Tutorial: Under Construction
Exercises and Projects – software here pyTornado and Framat.
Review questions to consider before doing calculations
- Explain the terms static and dynamic aero-elasticity
- What does “divergence” mean in this context? Why is a forward-swept wing more prone to divergence than an aft-swept wing?
- How can the divergence speed be estimated? What data is necessary?
- Explain the transfer operators from CFD to structures and vice versa. Why and how might a structural model with shell elements on the skin be easier than the classical “elastic axis” beam model?
Computations for static aero-elasticity
- The example in Ch 11 on a straight wing in a wind-tunnel is modeled by the script WTexample which runs the aero-elastic loop between VLM and an “elastic axis” beam model. Look into the script and make it plot the deformed wing at each iteration.
- HALE configurations are very flexible and have very long wing span to reduce the induced drag. The HALE model from Ch 10 has a straight, rectangular wing which can be modeled easily by a beam with constant cross section from root to tip. The beam bending equation says
EId4w/dy4 = Q with w(0) = w'(0) = 0, w''(b/2) = w'''(b/2) = 0 (*)
where Q(y) [N/m] is the lift force distribution, so the deflection/EI can be computed easily. If Q were constant across the span even by a simple degree 4 polynomial. Since the total lift equals the weight you can do that and plot the deformed wing. Choose EI to make the tip move up 10% of the half-span.
Then investigate the “results” returned from VLM (see ../Ch3Docs for information about the octave Tornado), figure out how to extract Q(y). Then use a simple difference scheme to solve (*) with the correct distribution. The “elastic loop” can now be put in motion by editing the geo file and running VLM on the deformed geometry. Do that manually once.