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High-fidelity aerostructural optimization with integrated geometry parameterization and mesh movement

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Abstract

This paper extends an integrated geometry parameterization and mesh movement strategy for aerodynamic shape optimization to high-fidelity aerostructural optimization based on steady analysis. This approach provides an analytical geometry representation while enabling efficient mesh movement even for very large shape changes, thus facilitating efficient and robust aerostructural optimization. The geometry parameterization methodology uses B-spline surface patches to describe the undeflected design and flying shapes with a compact yet flexible set of parameters. The geometries represented are therefore independent of the mesh used for the flow analysis, which is an important advantage to this approach. The geometry parameterization is integrated with an efficient and robust grid movement algorithm which operates on a set of B-spline volumes that parameterize and control the flow grid. A simple technique is introduced to translate the shape changes described by the geometry parameterization to the internal structure. A three-field formulation of the discrete aerostructural residual is adopted, coupling the mesh movement equations with the discretized three-dimensional inviscid flow equations, as well as a linear structural analysis. Gradients needed for optimization are computed with a three-field coupled adjoint approach. Capabilities of the framework are demonstrated via a number of applications involving substantial geometric changes.

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Acknowledgments

The authors would like to acknowledge Prof. J. R. R. A. Martins at the University of Michigan, Ann Arbor for sharing his framework for the purpose of constructing our methodology. The authors are also grateful for the funding provided by Zonta International Amelia Earhart Fellowships, the Ontario Graduate Scholarship, and the National Sciences and Engineering Research Council Postgraduate Scholarship. Computations were performed on the GPC supercomputer at the SciNet HPC Consortium. SciNet is funded by the Canada Foundation for Innovation under the auspices of Compute Canada, the Government of Ontario, Ontario Research fund - Research Excellence, and the University of Toronto.

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  1. University of Toronto Institute for Aerospace Studies, Toronto, ON, Canada, M3H 5T6

    Zimi J. Zhang, Shahriar Khosravi & David W. Zingg

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  1. Zimi J. Zhang
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  2. Shahriar Khosravi
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  3. David W. Zingg
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Correspondence to Zimi J. Zhang.

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This work was previously presented under the title “High-Fidelity Aerostructural Optimization with Integrated Geometry Parameterization and Mesh Movement” at the 56 th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Kissimmee, FL, January 2015.

Appendix A

Appendix A

ᅟ

1.1 Validation based on the HIRENASD Wing

Although the individual components of the aerostructural analysis capability have been separately validated with experimental results, it is also important to compare the static aeroelastic analysis results with experiment. However, it is quite difficult to find a suitable experimental study for validation. Most of the test articles used in relevant experimental studies are structurally too stiff to provide a meaningful way of assessing the deflections. Furthermore, it is a challenge to replicate the exact experimental conditions and test setup in many cases. Nonetheless, the HIgh REynolds Number Aero-Structural Dynamics (HIRENASD) Project does provide some useful static aeroelastic data along with the relevant geometries for validating the framework.

The HIRENASD Project was initiated to provide experimental aeroelastic data for a large transport wing-body configuration (Ballmann et al.2006, 2008, 2009). This section compares static aeroelastic computational results obtained using the present framework with the HIRENASD experimental data. In order to model the test conditions accurately, the Reynolds-Averaged-Navier-Stokes (RANS) capability of the flow solver has been used here for the purpose of the aerostructural analysis. The main objective is to demonstrate that the correct physics are captured even in the presence of the fitting errors. Furthermore, the results of this section motivate the future extension of the current framework to aerostructural optimization based on the RANS equations.

The test condition Mach number, angle of attack, and Reynolds number are 0.80, 1.5∘, and 7.0×106, respectively. An aerostructural analysis is performed to obtain the computational results. The one-equation Spalart-Allmaras turbulence model is used to model the turbulent flow in this test case. Osusky and Zingg (2013) provide comprehensive details on implementation, verification, and validation of the RANS flow solver.

The flow grid has 3,548,095 nodes with an average y + value of 0.24. The finite-element model provided by the HIRENASD project contained solid elements. However, the structural solver, TACS, accepts MITC shell elements only. Furthermore, the current structural model does not include the leading and trailing edges. Thus, an effort has been made to ensure that the structural finite-element model used in this analysis represents the original structure of the HIRENASD wing as closely as possible within these constraints. The finite-element model for the structures has approximately 38,000 second-order MITC shell elements.

Figure 15 provides a comparison of the computational static aerostructural results with the experimental data. The rigid-body results (where there are no structural deflections) are also provided for reference. Figure 15 demonstrates that the static aerostructural results obtained from the present framework consistently show much better agreement with the experimental data than the rigid CFD computations, especially towards the wingtip. Moreover, the computed tip deflection of 12.6 mm is in excellent agreement with the experimental value of 12.5 mm (Chwalowski et al. 2011).

Fig. 15
figure 15

Comparison of experimental and computational pressure coefficient results for the HIRENASD wing geometry. The experimental (black), static aeroelastic (blue), and rigid-wing results (red) are shown for each spanwise station

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Zhang, Z.J., Khosravi, S. & Zingg, D.W. High-fidelity aerostructural optimization with integrated geometry parameterization and mesh movement. Struct Multidisc Optim 55, 1217–1235 (2017). https://doi.org/10.1007/s00158-016-1562-7

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