Session: 36-01 Adjoint-based approaches - Part 1

Submission Number: 175875

Adjoint Shape Optimization of Three-Dimensional Axial Compressor Blades With Implicit Geometric Smoothing 

Adjoint optimization methods have been widely applied to compressor blades to improve their aerodynamic efficiency. Front stages of aero engine compressors often feature complex three-dimensional geometries due to the transonic flow regimes they operate in. To model these highly three-dimensional blades, a large number of geometric design parameters are required. On one hand, the adjoint method, due to the nearly insensitivity of its computational cost to the dimension of the design space, is a perfect tool for performing such aerodynamic optimization tasks; on the other, due to the rich design space, the resulting optimized geometry often lacks sufficient smoothness, thus introducing risk for structural integrity and causing difficulties for manufacturing. In practice, the lack of smoothness is usually manually fixed with aesthetic or structural considerations, potentially setting back the gain aerodynamic efficiency. Alternatively, one can add a layer of smoothing operations after each optimization or at the end of the entire optimization exercise, which would then confuse the gradient-based optimization algorithms, such as the quasi-Newton method, and increases the optimization cost. We denote both smoothing the update or the gradient as the explicit smoothing approach.

In this work, an implicit geometric smoothing method is proposed. Instead of smoothing the gradient of smoothing the design variable update, the design variables were redefined using an implicit smoothing operator. This approach has the advantage of not polluting the gradient or update information, and thus the gradient-based optimizer does not get confused. With the implicit smoothing operator, the low-frequency geometric modes were emphasized in the optimization process, and thus its contribution amplified and corresponding geometric change were chosen first. In a complete gradient-optimization exercise, implicit smoothing operator does not alter the design space, and thus would render the same converged optimized shape. However, in industrial applications, gradient-based opt are rarely fully converged. Instead, optimization runs are terminated once sufficient efficiency gain is obtained. In such cases, the implicit smoothing technique allows the semi-converged optimization to pick out shape design as smooth as possible. It is also possible to truncate the shape modes by manipulating the implicit smoothing operator, which allows the highest-frequency modes to be removed from the design space altogether. By definition, the resulting shape design even in the converged gradient-based optimization, would be smooth, albeit at the cost of a narrower design space.

The proposed implicit geometric smoothing method is demonstrated on a low-aspect ratio wide-chord transonic fan blade to demonstrate its efficacy. Results were compared with explicit smoothing approaches to show the advantage of the proposed method.

Presenting Author: Sicheng Li Northwestern Polytechnical University

Presenting Author Biography: Mr Sicheng Li is a graduate student in the school of power and energy of the Northwestern Polytechnical University. His research area is the adjoint shape optimization method development and applications for turbomachinery aerodynamics.

Authors:

Jiazi Zhao Northwestern Polytechnical University
Sicheng Li Northwestern Polytechnical University
Dingxi Wang Northwestern Polytechnical University
Shenren Xu Northwestern Polytechnical University