Robust aerodynamic shape optimization—From a circle to an airfoil

He, Xing; Li, Jichao; Mader, Charles A.; Yildirim, Anil; Martins, Joaquim R. R. A.

doi:10.1016/j.ast.2019.01.051

Cited by 126 publications

(35 citation statements)

References 24 publications

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“…Carrier et al [45] apply several different optimization frameworks, eventually obtaining a result of 36.7 drag counts, 1.1 drag counts of which they show correspond to spurious drag. He et al [63] use a volume B-spline obtaining a result of 7.60 drag counts with 50 design variables, the lowest published result for comparable mesh resolution (131K cells).…”

Section: Inviscid Drag Minimizationmentioning

confidence: 98%

Gradient-Limiting Shape Control for Efficient Aerodynamic Optimization

2020

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Local shape control methods, such as B-spline surfaces, are well-conditioned such that they allow high-fidelity design optimization; however, this comes at the cost of degraded optimization convergence rate as control fidelity is refined due to the resulting exponential increase in the size of the design space. Moreover, optimizations in higherfidelity design spaces become ill-posed due to high-frequency shape components being insufficiently bounded; this can lead to nonsmooth and oscillatory geometries that are invalid in both physicality (shape) and discretization (mesh). This issue is addressed here by developing a geometrically meaningful constraint to reduce the effective degrees of freedom and improve the design space, thereby improving optimization convergence rate and final result. A new approach to shape control is presented using coordinate control (x;z) to recover shape-relevant displacements and surface gradient constraints to ensure smooth and valid iterates. The new formulation transforms constraints directly onto design variables, and these bound the out-of-plane variations to ensure smooth shapes as well as the in-plane variations for mesh validity. Shape gradient constraints approximating a C 2 continuity condition are derived and demonstrated on a challenging test case: inviscid transonic drag minimization of a symmetric NACA0012 airfoil. Significantly, the regularized shape problem is shown to have an optimization convergence rate independent of both shape control fidelity and numerical mesh resolution, while still making use of increased control fidelity to achieve improved results. Consequently, a value of 1.6 drag counts is achieved on the test case, the lowest value achieved by any method.

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Section: Inviscid Drag Minimizationmentioning

confidence: 98%

Gradient-Limiting Shape Control for Efficient Aerodynamic Optimization

2020

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“…Zingg et al [8] used knot insertion algorithm to refine B-spline volumes in shape optimisation and proposed to insert a new knot arbitrarily in each knot span of a knot vector. Martins et al [10] also used knot insertion to refine FFD frame and insert a new knot in the middle of each knot span. This may be suitable for simple geometries however for a complex geometry with large number of patches inserting a knot in each knot span without any additional measure may leads to the addition of unnecessary control points on the design surface.…”

Section: Refinementioning

confidence: 99%

“…Note that there exists an infinite number of possibilities, however in this work only three refined control nets are obtained at the end of each optimisation level. To determine which updated control net to choose for the next design level, the adaptation metric proposed by Martins et al [10] is used.…”

Section: Refinementioning

confidence: 99%

Cad-Based Adaptive Shape Parametrisation for Aerodynamic Shape Optimisation

Jesudasan¹,

Müeller²

2021

14th WCCM-ECCOMAS Congress

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Non-Uniform Rational B-Splines (NURBS) have become the industrial standard to represent and exchange a CAD geometry between CAD/CAE systems. CAD-based shape parameterisation uses parameters of a CAD model to modify the shape which allows to integrate a CAD model into the design loop. However, feature-trees of typical commercial CAD systems are not open and obtaining exact derivatives for gradient-based optimisation methods is not possible. Using the CAD-based NSPCC approach a designer can deform multiple NURBS patches in the design loop without violating geometric and/or thickness constraints. The NSPCC approach takes CAD descriptions as input and perturbs the control points of the NURBS boundary representation to modify the shape.

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“…Shape optimization refers to the optimization of domain boundaries and plays an important role in structural design. For instance, shape optimization plays a crucial role in the design of airfoils (He et al 2019;Wang et al 2018;Schmidt et al 2013) and boat hulls (Lombardi et al 2012;Marinić-Kragić et al 2016;Abramowski and Sugalski 2017). Shape optimization is also a useful refinement step to be employed after topology optimization (Bendsoe and Sigmund 2004, Ch.…”

Section: Introductionmentioning

confidence: 99%