Optimum aerodynamic design for dynamic stall risk mitigation

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Raul, Vishal Vinod
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Leifsson, Leifur
Ward, Thomas
Sharma, Anupam
Wei, Peng
Hu, Chao
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Aerospace Engineering
Mitigating the adverse effects of dynamic stall is critical for many aerodynamic systems as they can be the primary reason for limiting the system performance, fatal structural loads, and reduced fatigue life. Aerodynamic shape optimization (ASO) is a practical approach for mitigating the adverse dynamic stall characteristics without adding any auxiliary systems. The key challenges in ASO for dynamic stall mitigation are (1) computationally intensive and time-consuming computational fluid dynamics (CFD) simulations, (2) multiple and repetitive design evaluations required by conventional optimization algorithms, and (3) high-dimensional parameter space associated with the shape of the aerodynamic surface. The objective of this research is to create efficient ASO algorithms and gain a fundamental understanding of aerodynamic design for dynamic stall risk mitigation. In this work, an optimization problem formulation is created to mitigate the adverse effects of dynamic stall through ASO. Two global optimal design algorithms are created and implemented using high-fidelity Kriging Regression (HF-KR) and multifidelity Cokriging regression (CKR) surrogate modeling methods. These surrogate models are constructed efficiently using error-based and expected improvement infill criteria. The developed models are utilized for optimization and global sensitivity analysis (GSA). GSA quantifies the sensitivities and the importance of the shape parameters to dynamic stall mitigation. Further, manifold mapping (MM), a multifidelity modeling method, is proposed to determine the local optimal design. Initially, the multifidelity modeling similarity condition is investigated to guide the selection of a low-fidelity (LF) model and a trust-region radius, which are vital for the successful implementation of MM. Later, the MM method is efficiently implemented for ASO-based dynamic stall mitigation using KR to create a fast LF model (LF-KR). The proposed methods are demonstrated on an airfoil in sinusoidal oscillating motion in uniform flow undergoing deep dynamic stall. The HF-KR and CKR implementation provide optimal designs that delay and mitigate adverse dynamic stall characteristics. Both the acquired optimal designs show similar shape features. However, the CKR model produces a better optimal design than the HF-KR implementation while saving computational cost by almost $41\%$. The GSA investigation with HF-KR and CKR revealed that the upper airfoil surface thickness, location of thickness, leading-edge radius, and the curvature of the upper surface have a significant effect on the dynamic stall characteristics, whereas the trailing-edge angles has a minimal effect. Further, multifidelity modeling similarity condition investigation with the MM model provided a general approach for LF model selection. The results indicated that the LF model developed from coarser spatial and time discretization can be efficiently used within a small trust-region radius. Lastly, the MM model is implemented with a trust-region-based optimization algorithm and showed significant cost savings in locating an optimal design compared to HF-KR and CKR. Specifically, the MM model demonstrated the capability to determine optimal designs using a LF-KR model with computational cost savings of approximately $84\%$ and $74\%$ compared to the aforementioned HF-KR and CKR implementations.
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