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.

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

2012 ◽  
Vol 135 (2) ◽  
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 nonreflective 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.

Study on Global Aerodynamic Shape Optimization of Transonic Compressor Blade

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Yanhui Duan ◽  
Zhaolin Fan ◽  
Wenhua Wu ◽  
Ti Chen
Keyword(s):  
Shape Optimization ◽  
Optimization Design ◽  
Fluid Dynamic ◽  
Thickness Distribution ◽  
Pressure Ratio ◽  
Compressor Blade ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Transonic Compressor ◽  
Total Pressure Ratio

AbstractIn this paper, global optimization design of a transonic compressor 3D blade (Rotor 37) has been carried out by a self-developed aerodynamic shape optimization (ASO) platform based on improved parallel synchronous particle swarm optimization (PSPSO). To improve the performance of PSPSO, coefficient of variation (COV) based attenuation method with new parameters is proposed and then validated by optimization tests. Flow field of blade is calculated by an in-house computational fluid dynamic (CFD) code called PMB3D-Turbo, which is validated by Rotor 37. Choosing Rotor 37 as the case, optimization object is to maximize the peak adiabatic efficiency, meanwhile constraining mass flow and total pressure ratio. The solutions show that, the ASO platform is effective to transonic compressor blade and variations of thickness distribution near the trailing edge can help improve the adiabatic efficiency of a transonic compressor blade.

An Adjoint-Based Optimization Method for Constrained Aerodynamic Shape Design of Three-Dimensional Blades in Multi-Row Turbomachinery Configurations

2014 ◽  
Author(s):  
Benjamin Walther ◽  
Siva Nadarajah
Keyword(s):  
Pressure Ratio ◽  
Three Dimensional ◽  
Optimization Method ◽  
Adjoint Equations ◽  
Programming Algorithm ◽  
Flow Solver ◽  
Aerodynamic Shape ◽  
Transonic Compressor ◽  
Discrete Adjoint ◽  
Gradient Based

This paper develops the discrete adjoint equations for a turbomachinery RANS solver and proposes a framework for fully-automatic gradient-based constrained aerodynamic shape optimization in a multistage turbomachinery environment. The systematic approach for the development of the discrete adjoint solver is discussed. Special emphasis is put on the development of the turbomachinery specific features of the adjoint solver, i.e. on the derivation of flow-consistent adjoint inlet/outlet boundary conditions and, to allow for a concurrent rotor/stator optimization and stage coupling, on the development of an exact adjoint counterpart to the non-reflective, conservative mixing-plane formulation used in the flow solver. The adjoint solver is validated by comparing its sensitivities with finite difference gradients obtained from the flow solver. A sequential quadratic programming algorithm is utilized to determine an improved blade 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 single-stage transonic compressor. The objective is to maximize the isentropic efficiency while constraining the mass flow rate and the total pressure ratio.

An Introduction of Aerodynamic Shape Optimization Platform for Compressor Blade

2016 ◽  
Author(s):  
Duan Yanhui ◽  
Wu Wenhua ◽  
Fan Zhaolin ◽  
Chen Ti
Keyword(s):  
Flow Field ◽  
Shape Optimization ◽  
High Efficiency ◽  
Optimization Method ◽  
Compressor Blade ◽  
Field Calculation ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Grid Deformation ◽  
First Case

In this paper, an aerodynamic shape optimization platform for compressor blade is introduced. The platform divided into modules on flow field calculation, optimization method, parameterization and grid deformation. Flow field calculation of compressor blade is based on computational fluid dynamics (CFD), which is used for multi-block structure grid. Particle swarm optimization (PSO) is built as optimization method module, in which cost functions are calculated parallel. In parametric module, 3D blade is decomposed in a series of characteristic sections and the section is parameterized by Hicks-Henne function. Algebraic interpolation method is used for grid deformation, which is a high efficiency and robust method. Two cases of rotor 37 are presented. The result of the first case shows that, the CFD code of the optimal platform is reliable and robust. For the second case, the optimal platform is verified by designing rotor 37. The result shows that, the optimal platform is effective for design of compressor blade.

scholarly journals On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization—Part II: Viscous Flows

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 106
Author(s):  
Farzad Mohebbi ◽  
Ben Evans ◽  
Mathieu Sellier
Keyword(s):  
Shape Optimization ◽  
Viscous Flows ◽  
Optimization Method ◽  
Step Length ◽  
Aerodynamic Shape Optimization ◽  
Ansys Fluent ◽  
Transonic Flows ◽  
Aerodynamic Shape ◽  
Design Variables ◽  
Gradient Based

This study presents an extension of a previous study (On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization) to viscous transonic flows. In this work, we showed that the same procedure to derive an explicit expression for an exact step length βexact in a gradient-based optimization method for inviscid transonic flows can be employed for viscous transonic flows. The extended numerical method was evaluated for the viscous flows over the transonic RAE 2822 airfoil at two common flow conditions in the transonic regime. To do so, the RAE 2822 airfoil was reconstructed by a Bezier curve of degree 16. The numerical solution of the transonic turbulent flow over the airfoil was performed using the solver ANSYS Fluent (using the Spalart–Allmaras turbulence model). Using the proposed step length, a gradient-based optimization method was employed to minimize the drag-to-lift ratio of the airfoil. The gradient of the objective function with respect to design variables was calculated by the finite-difference method. Efficiency and accuracy of the proposed method were investigated through two test cases.

A Time-Spectral Adjoint Approach for Aerodynamic Shape Optimization Under Periodic Wakes

2020 ◽  
Author(s):  
Ping He ◽  
Alton Luder ◽  
Charles Mader ◽  
Joaquim R. R. A. Martins ◽  
Kevin Maki
Keyword(s):  
Shape Optimization ◽  
Aerodynamic Shape Optimization ◽  
Aerodynamic Shape ◽  
Adjoint Approach
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