Aerodynamic Shape Optimization for Natural Laminar Flow Using a Discrete-Adjoint Approach

AIAA Journal ◽  
2016 ◽  
Vol 54 (11) ◽  
pp. 3321-3337 ◽  
Author(s):  
Ramy Rashad ◽  
David W. Zingg
Keyword(s):  
Laminar Flow ◽  
Shape Optimization ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Discrete Adjoint ◽  
Natural Laminar Flow ◽  
Adjoint Approach

Aerodynamic Shape Optimization of Natural-Laminar-Flow Wing Using Surrogate-Based Approach

AIAA Journal ◽  
2018 ◽  
Vol 56 (7) ◽  
pp. 2579-2593 ◽  
Author(s):  
Zhong-Hua Han ◽  
Jing Chen ◽  
Ke-Shi Zhang ◽  
Zhen-Ming Xu ◽  
Zhen Zhu ◽  
...  
Keyword(s):  
Laminar Flow ◽  
Shape Optimization ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Natural Laminar Flow

Constrained Adjoint-Based Aerodynamic Shape Optimization of a Single-Stage Transonic Compressor

2012 ◽  
Author(s):  
Benjamin Walther ◽  
Siva Nadarajah
Keyword(s):  
Shape Optimization ◽  
Pressure Ratio ◽  
Internal Flow ◽  
Optimization Method ◽  
Single Stage ◽  
Programming Algorithm ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Transonic Compressor ◽  
Adjoint Approach

This paper develops a discrete adjoint formulation for the constrained aerodynamic shape optimization in a multistage turbomachinery environment. The adjoint approach for viscous, internal flow problems and the corresponding adjoint boundary conditions are discussed. To allow for a concurrent rotor/stator optimization a non-reflective adjoint mixing-plane formulation is proposed. A sequential-quadratic programming algorithm is utilized to determine an improved airfoil shape based on the objective function gradient provided by the adjoint solution. The functionality of the proposed optimization method is demonstrated by the redesign of a midspan section of a single-stage transonic compressor. The objective is to maximize the isentropic efficiency while constraining the mass flow rate and the total pressure ratio.

scholarly journals Discrete adjoint aerodynamic shape optimization using symbolic analysis with OpenFEMflow

2021 ◽  
Author(s):  
Ali Elham ◽  
Michel J. L. van Tooren
Keyword(s):  
Shape Optimization ◽  
Open Source ◽  
Symbolic Analysis ◽  
State Variables ◽  
Aerodynamic Shape Optimization ◽  
Computationally Efficient ◽  
Exact Integration ◽  
Aerodynamic Shape ◽  
Discrete Adjoint ◽  
Gradient Based

AbstractThe combination of gradient-based optimization with the adjoint method for sensitivity analysis is a very powerful and popular approach for aerodynamic shape optimization. However, differentiating CFD codes is a time consuming and sometimes a challenging task. Although there are a few open-source adjoint CFD codes available, due to the complexity of the code, they might not be very suitable to be used for educational purposes. An adjoint CFD code is developed to support students for learning adjoint aerodynamic shape optimization as well as developing differentiated CFD codes. To achieve this goal, we used symbolic analysis to develop a discrete adjoint CFD code. The least-squares finite element method is used to solve the compressible Euler equations around airfoils in the transonic regime. The symbolic analysis method is used for exact integration to generate the element stiffness and force matrices. The symbolic analysis is also used to compute the exact derivatives of the residuals with respect to both design variables (e.g., the airfoil geometry) and the state variables (e.g., the flow velocity). Besides, the symbolic analysis allows us to compute the exact Jacobian of the governing equations in a computationally efficient way, which is used for Newton iteration. The code includes a build-in gradient-based optimization algorithm and is released as open-source to be available freely for educational purposes.

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