This work was motivated by a lack of benchmark aeroelastic models for transonic aircraft analysis and design. TheNASA CRM, which is an excellent aerodynamic model that has been widely used, was leveraged to develop two static aeroelastic models: one with a con- ventional AR, and another with a higherARto be representative of next-generation wings. To accurately capture the appropriate “physics” associated with transonic flexible wing de- sign a coupled high-fidelityMDOapproach is utilized to define both models. Both of these models’ geometries feature the jig or undeflected wing shape, making them appropriate for the use in aerostructural and aeroelastic analysis, as well as wing aerostructural design optimization studies.
The first model, the uCRM-9, is a design with an aspect ratio 9 wing that deforms into the CRM geometry under its nominal cruise flight condition of M = 0.85, CL = 0.5. Since this model is defined to be the jig or undeflected shape of theCRMwing it is appro- priate for use in aeroelastic studies. This design was obtained by first defining a realistic wingbox topology for the CRMand sizing it through a structural optimization subject to aerodynamic loads. An inverse design procedure was then performed where the deflection of theCRMwing was iteratively removed from the geometry usingFFDshape variables. The procedure was repeated for several iterations until a reasonably converged results was obtained. In order to verify that the design procedure produced a reasonable approximation to the jig shape of the CRM wing, a static aerostructural analysis was performed. From this, the model was found to be within 0.001% agreement with the drag produced by a
CFD analysis of the CRM about its nominal cruise condition. Finally, an aerostructural grid convergence study was performed on the model. From this study it was also possible to conclude that the meshes used to create this model were reasonably well converged.
The second aeroelastic model, the uCRM-13.5, is a higher aspect ratio winged vari- ant of the CRM. The motivation for the development of this model is for studies of new technology concepts with the goal of enabling higher aspect ratio wing designs. Due to the higher degree of flexibility present in the wing design an aerostructural optimization study was performed to obtain a reasonable geometry and structural sizing for this model. Through this study the importance of considering multiple flight conditions in the optimiza- tion to achieve a robust design was shown, with the multi-point optimized design achieving a 20.0% reduction in average fuel burn over its integrated flight envelope relative to the baseline design. In addition, since buffet onset performance was included and constrained the optimized design was also able to increase the size of the flight envelope, again demon- strating the necessity for buffet onset considerations with respect to transonic wing design
optimization. Furthermore, by including the uCRM-9 in the optimization study it was con- firmed that the design, and by extension the CRM, was already relatively well designed, the optimizer only being able to improve it by a modest 3.7%. As one might expect by extending the aspect ratio of theCRMwing from 9 to 13.5 a reduction of roughly 10.6% in fuel burn can be seen, due mostly to a reduction in induced drag on the wing.
As mentioned previously, all models developed in this chapter are publicly available and include files for the geometry, structures, and external mass distributions. These models provide not only a benchmark for the design studies throughout the rest of this thesis, but also for future high-fidelity aerodynamic, structural, and aeroelastic studies—both static and dynamic. Further developments, such as the inclusion of structural dynamic modal analysis, are expected to result in variable-fidelity models and models that better capture dynamic aeroelastic phenomena.
CHAPTER 4
PySteer: A framework for parametric structural
optimization
In the previous chapter, the uCRM models with conventional metallic structural designs were introduced, in this chapter, the parametrization of the structural model will be ex- tended to unconventional tow-steered composite designs. One of the key differences of a AFPmanufactured structure is the continuous spatial nature of the AFPlayup process. Due to this fact, a panel-level structural parametrization, as described in Chapter3, would no longer be appropriate and an alternative approach must be devised. For this reason, pySteer, a python-based tool for the parametrization of tow-steered and variable stiffness structures was developed. pySteer represents a major development in this work and has made parametric tow-steered optimization possible in theMACHframework. In pySteer, the variable stiffness properties—pattern orientation and panel thickness—are parametrized using interpolations from B-spline control points distributed over each parametric surface of the structure. The B-spline interpolation engine used in this work is borrowed from the Geometry-centric MDAO of aircraft configurations with high fidelity (GeoMACH) frame- work, developed by Hwang and Martins [102]. Throughout the remainder of this chapter a walk through of the computational work flow relating pySteer to theMACHframework will be given. The approach used to model the constitutive properties of the tow-steered elements in theFEMmodel will also be explained.