Discrete Adjoint Method for Aeroelastic Design Optimization

The combination of analysis and optimization methods in mechanical engineering, also known as design optimization, has great potential in product development. Robust sensitivity analyses that provide reliable and efficient objective function gradients play a key role in design optimization. This paper presents a discrete adjoint method for the sensitivity analysis of flexible mechanical systems. The ultimate goal is to be able to relate the physical properties of beam cross-sections to the dynamic behavior of the system, which is key to design realistic flexible elements. The underlying flexible multibody formulation is one that supports large-amplitude motion, beams with sophisticated composite cross-sections, and kinematic joints. A summary of the kinematic and dynamic foundations of the forward equations is presented first. Then, a discrete adjoint method, along with meaningful examples and validation, is presented. The method has proven to provide extremely accurate and reliable sensitivities.

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Design optimization for self-propulsion of a bulk carrier hull using a discrete adjoint method

Computers & Fluids ◽

10.1016/j.compfluid.2019.104259 ◽

2019 ◽

Vol 192 ◽

pp. 104259 ◽

Cited By ~ 2

Author(s):

Ping He ◽

Grzegorz Filip ◽

Joaquim R.R.A. Martins ◽

Kevin J. Maki

Keyword(s):

Design Optimization ◽

Adjoint Method ◽

Bulk Carrier ◽

Discrete Adjoint ◽

Discrete Adjoint Method

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Aerodynamic Optimization and Inverse Design of 2D and 3D Turbine Cascades Using the Discrete Adjoint Method

Volume 6B: Turbomachinery ◽

10.1115/gt2013-95284 ◽

2013 ◽

Author(s):

Juan Lu ◽

Chaolei Zhang ◽

Zhenping Feng

Keyword(s):

Design Optimization ◽

Optimization Design ◽

Adjoint Method ◽

Inverse Design ◽

Aerodynamic Design ◽

Discrete Adjoint ◽

Design Variables ◽

Discrete Adjoint Method ◽

Turbine Cascades ◽

2D And 3D

The adjoint method has significant advantage in sensitivity analysis because its computation cost is independent of the number of the design variables. In recent years it has been applied greatly in aerodynamic design optimization of turbomachinery. This paper developed the discrete adjoint method based on the authors’ previous work and demonstrated the applications of the method in the aerodynamic design optimization for turbine cascades. The Non-uniform Rational B-Spline (NURBS) technology was introduced in the current design optimization system and a flexible parameterization method for 3D cascade was proposed. Based on the parameterization method, the stack line and the blade profile are parameterized together by using NURBS curves. During the design process, the control points of the profile, the stack point and the stagger angle of the blade on each section can be taken as the design variables. Moreover, the flow solver and the discrete adjoint solver were extended towards the turbulent flow environment by adopting the k – ω turbulence model. Based on the optimization design system, several applications including two optimization design cases and two inverse design cases for 2D and 3D turbine cascades were implemented with the mass flow ratio constraint. The gradient verification and the numerical cases showed the correctness and accuracy of the discrete adjoint solver. The numerical results demonstrated the validity and efficiency of the design optimization system based on discrete adjoint method.

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