## Trim Angle of Attack of Flexible Wings Using Non-Linear Aerodynamics

##### Abstract

The present algorithm requires the CFD code to be run for each of the generalized coordinates. Therefore, to reduce the number of generalized coordinates considerably, we employ the modal superposition approach to represent the structural displacements. Results available for the Aeroelastic Research Wing (ARW) are used to evaluate the performance of the modal superposition approach. Calculations are made at a fixed angle of attack and the results are compared to both the experimental results obtained at NASA Langley Research Center, and computational results obtained by the researchers at NASA Ames Research Center. Two CFD codes are used to demonstrate the modular nature of this research. Similarly, two separate Finite Element codes are used to generate the structural data, demonstrating that the algorithm is not dependent on using specific codes. The developed algorithm is tested for a wing, used for in-house aeroelasticity research at Boeing (previously McDonnell Douglas) Long Beach. The trim angle of attack is calculated for a range of desired lift values. In addition to the Newton's method algorithm, a non derivative method (NDM) based on fixed point iteration, typical of fixed angle of attack calculations in aeroelasticity, is employed. The NDM, which has been extended to be able to calculate trim angle of attack, is used for one of the cases. The Newton's method calculation converges in fewer iterations, but requires more CPU time than the NDM method. The NDM, however, results in a slightly different value of the trim angle of attack. It should be noted that NDM will converge in a larger number of iterations as the dynamic pressure increases.

For one value of the desired lift, both viscous and inviscid results were generated. The use of the inviscid flow model while not resulting in a markedly different value for the trim angle of attack, does result in a noticeable difference both in the wing deflection and the span loading when compared to the viscous results.

A crude (coarse-grain) parallel methodology was used in some of the calculations in this research. Although the codes were not parallelized, the use of modal superposition made it possible to compute the sensitivity terms on different processors of an IBM SP/2. This resulted in a decrease in wall clock time for these calculations. However, even with the parallel methodology, the CPU times involved may be prohibitive (approximately 5 days per Newton iteration) to any practical application of this method for wing analysis and design. Future work must concentrate on reducing these CPU times. Two possibilities: (i) The use of alternative basis vectors to further reduce the number of basis vectors used to represent the structural displacement, and (ii) The use of more efficient methods for obtaining the flow field sensitivities. The former will reduce the number of CFD analyses required the latter the CPU time per CFD analysis. NOTE: (03/2007) An updated copy of this ETD was added after there were patron reports of problems with the file.

##### Collections

- Doctoral Dissertations [12617]