A Framework for Robust and Reliability-Based Design Optimization of Airfoils Considering Geometrical Uncertainties

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Abstract

We present our framework for Robust Design Optimization (RDO) and Reliability-Based Design Optimization (RBDO) and apply it to the UMRIDA BC-02 test case. Two different measures of robustness are defined and evaluated considering both operational uncertainties and a large number of geometrical uncertainties. Here the quantity of interest is the drag coefficient (Cd). The RDO robustness measure is the sum of the mean and the standard deviation of Cd and that of RBDO is the maximum value of Cd expressed by the 99 percentile of the cumulative density function of Cd. The Karhunen-Loève expansion is used to cast the correlated uncertain geometry parameters into a small number of independent parameters [1]. The statistics that are needed to evaluate the robustness measures are then efficiently calculated by a combination of the Sobol sequence-based quasi Monte Carlo method [2] as the Design of Experiment (DoE) and gradient-enhanced Kriging (GEK) [3] surrogate models implemented in DLR´s surrogate and reduced-order modelling toolbox SMARTy. A small number of samples is computed with the full-order CFD code TAU and its adjoint version to construct the GEK model. The robustness measures which are treated as the objective function in the developed framework are optimized by the Subplex algorithm. The BC-02 airfoil is parameterized with 10 Bernstein polynomials. We confirmed that different sampling techniques are essential to obtain accurate statistic and that dynamic adaptive sampling techniques are especially required in the context of RBDO. The optimal solutions in terms of the final airfoil shape produced by these two robustness measures are also significantly different from each other. Finally, the developed framework is also applied to a Korn airfoil for the robust design of a natural laminar flow airfoil.

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• A Framework for Robust and Reliability-Based Design Optimization of Airfoils Considering Geometrical Uncertainties. (deposited 17 Dec 2018 09:25) [Currently Displayed]