High‐fidelity aerodynamic shape optimization of modern transport wing using efficient hierarchical parameterization

Abstract

SUMMARYAerodynamic shape optimization technology is presented, using an efficient domain element parameterization approach. This provides a method that allows geometries to be parameterized at various levels, ranging from gross three-dimensional planform alterations to detailed local surface changes. Design parameters control the domain element point locations and, through efficient global interpolation functions, deform both the surface geometry and corresponding computational fluid dynamics volume mesh, in a fast, high quality, and robust fashion. This results in total independence from the mesh type (structured or unstructured), and optimization independence from the flow-solver is achieved by obtaining gradient information for an advanced gradient-based optimizer by finite-differences. Hence, the optimization tool can be used in conjunction with any flow-solver and/or mesh generator. Results have been presented recently for two-dimensional aerofoil cases, and shown impressive results; drag reductions of up to 45% were demonstrated using only 22 active design parameters. This paper presents the extension of these methods to three dimensions, with results for highly constrained optimization of a modern aircraft wing in transonic cruise. The optimization uses combined global and local parameters, giving 388 design variables, and produces a shock-free geometry with an 18% reduction in drag, with the added advantage of significantly reduced root moments.

Efficient RBF Mesh Deformation Within An Adjoint-Based Aerodynamic Optimization Framework

“…Some examples are Hicks-Henne bump functions, 20 surface mesh points, 1 B-slines, 21,22 Class function / Shape function Transformation (CST), 23 Radial Basis Functions. 17,18 For detailed surveys of shape parameterization, readers are referred to a paper by Samareh, 24 Mousavi et al, 25 and Castonguay et al 26 B-spline surfaces are used in this work because the parameterization is inherently smooth, wing-body geometries can be represented by a collection of individual B-spline patches, and the optimized design can be easily exported to a CAD file (.iges) for manufacturing purposes. General theory of B-splines can be found in The NURBS Book .…”

“…Therefore, it would be difficult to implement with an adjoint-based optimizer since the mesh sensitivities are not known a priori. Another approach to reduce the cost of RBFs is proposed by Morris et al 17,18 by integrating both the parameterization and the mesh movement scheme with the use of RBFs in a free-form deformation of the geometry. Although this method is fast, robust and efficient, it is restricted to a parameterization via RBFs; thus it is incompatible with other forms of parameterization such as B-splines.…”

Gradient-Limiting Shape Optimisation Applied to AIAA ADODG Test Cases

“…Continuous shape functions are used to describe geometry such that the number of design variables is much less than the number of mesh nodes B-Spline surfaces [5] Bezier surfaces [6] Volume splines: Bezier [7], B-Spline [8], RBF [9] Hicks-Henne [2] CSTs [10] Fictitious loads [11] SVD [12] Multilevel optimisation Successive optimisations are performed where shape control is refined after each stage Subdivision [13,14] B-Spline/Bezier knot insertion [15] RBF [16] Sensitivity filtering Mesh vertices are used for shape control and surface sensitivities are filtered to remove high frequency components…”

“…Among previous studies it is common for the parameterisation to be manually constrained such that only one ordinate is free to move [36], or that certain degrees of freedom (e.g. sweep, taper) are specified by hand [9], or combinations of both [37]. The parameterisation of a single coordinate, thickness, for aerofoils is convenient and commonly adopted since aerofoils are predominantly planar such that most of the surface normals are closely aligned with the vertical coordinate.…”

Three-Dimensional Aeroelastic Solutions via the Nonlinear Frequency-Domain Method

“…Although the original method was computationally expensive, many have contributed to improve its efficiency [35,55,56,67,71,72]. Despite the author's knowledge of these improvements, the method used in this work is the original approach, modified by Walther [88] for parallel computations.…”