Aerodynamic Design Optimization of the Last Stage of a Multi-Stage Compressor by Using an Adjoint Method

2016 ◽  
Author(s):  
Jing Yang ◽  
Jiaqi Luo ◽  
Juntao Xiong ◽  
Feng Liu
Keyword(s):  
Design Optimization ◽  
Adjoint Method ◽  
Guide Vane ◽  
Inlet Guide Vane ◽  
Optimization Approach ◽  
Operation Condition ◽  
Operation Conditions ◽  
Multi Stage ◽  
Last Stage ◽  
Continuous Adjoint

The paper presents the aerodynamic optimization of the last row of a 4.5-stage compressor by means of a gradient-based optimization method that utilizes the continuous adjoint approach. An adjoint mixing-plane formulation is used to allow for the computation of adjoint solutions for multistage turbomachinery problems. Firstly, a conventional one-dimensional design method and empirical correlations are used to produce a base design of a 4.5-stage low-speed, low compression ratio compressor with an inlet guide vane to adjust to different operation conditions. Then the last stage is redesigned by the adjoint method to reduce the flow losses at the operation condition near stall through modifying the aerodynamic shape and stagger angle of the stator blade. The cost function is defined as a weighted sum of the entropy production and a constraint on the mass flow rate. Finally, a multi-point design optimization approach by using the adjoint method is employed to improve the performance of the last stage at two different operation conditions. The results demonstrate that the stator shape modifications improve the aerodynamic performance of the stage and illustrate the functionality of the adjoint-based multi-stage optimization system.

Adjoint Aerodynamic Design Optimization for Blades in Multi-Stage Turbomachines: Part I—Methodology and Verification

2008 ◽  
Author(s):  
D. X. Wang ◽  
L. He
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Design Optimization ◽  
Difference Method ◽  
Adjoint Method ◽  
Adjoint Equations ◽  
Steepest Descent Method ◽  
Compressor Stage ◽  
Multi Stage ◽  
Continuous Adjoint

The adjoint method for blade design optimization will be described in this two-part paper. The main objective is to develop the capability of carrying out aerodynamic blading shape design optimization in a multi-stage turbomachinery environment. To this end, an adjoint mixing-plane treatment has been proposed. In the first part, the numerical elements pertinent to the present approach will be described. The gradients of a single objective function of a weighted sum of objectives and constraints with respect to detailed blade shape perturbations are obtained very efficiently by the continuous adjoint method. The steepest descent method is used to drive the design to an optimum. The adjoint mixing-plane treatment enables the adjoint equations to be solved in a multi-stage environment. The adjoint solver is verified by comparing gradient results with a direct finite difference method and through a 2D inverse design. The adjoint mixing-plane treatment is verified by comparing gradient results against those by the finite difference method for a 2D compressor stage. The redesign of the 2D compressor stage further demonstrates the validity of the adjoint mixing-plane treatment and the benefit of using it in a multi-bladerow environment.

Continuous adjoint aerodynamic optimization design for multi-stage gas turbine with cooling air

2017 ◽  
Vol 89 (3) ◽  
pp. 444-456
Author(s):  
Lei Chen ◽  
Jiang Chen
Keyword(s):  
Gas Turbine ◽  
Optimization Design ◽  
Adjoint Method ◽  
Air Injection ◽  
Aerodynamic Optimization ◽  
Content Type ◽  
Multi Stage ◽  
Surface Code ◽  
Cooling Air ◽  
Continuous Adjoint

Purpose This paper aims to conduct the optimization of the multi-stage gas turbine with the effect of the cooling air injection based on the adjoint method. Design/methodology/approach Continuous adjoint method is combined with the S2 surface code. Findings The optimization of the stagger angles, stacking lines and the passage can improve the attack angles and restrain the development of the boundary, reducing the secondary flow loss caused by the cooling air injection. Practical implications The aerodynamic performance of the gas turbine can be improved via the optimization of blade and passage based on the adjoint method. Originality/value The results of the first study on the adjoint method applied to the S2 surface through flow calculation including the cooling air effect are presented.

S2 Surface Quasi-3D Aerodynamic Design Using the Continuous Adjoint Method for Multi-Stage Turbine

2014 ◽  
Author(s):  
Lei Chen ◽  
Jiang Chen
Keyword(s):  
Objective Function ◽  
Adjoint Method ◽  
Adjoint Equations ◽  
Design System ◽  
Shape Design ◽  
Aerodynamic Design ◽  
Aerodynamic Shape ◽  
Multi Stage ◽  
Gradient Based ◽  
Continuous Adjoint

The adjoint method eliminates the dependence of the gradient of the objective function with respect to design variables on the flow field making the obtainment of the gradient both accurate and fast. For this reason, the adjoint method has become the focus of attention in recent years. This paper develops a continuous adjoint formulation for through-flow aerodynamic shape design in a multi-stage gas turbine environment based on a S2 surface quasi-3D problem governed by the Euler equations with source terms. Given the general expression of the objective function calculated via a boundary integral, the adjoint equations and their boundary conditions are derived in detail by introducing adjoint variable vectors. As a result, the final expression of the objective function gradient only includes the terms pertinent to those physical shape variations that are calculated by metric variations. The adjoint system is solved numerically by a finite-difference method with explicit Euler time-marching scheme and a Jameson spatial scheme which employs first and third order dissipative flux. Integrating the blade stagger angles and passage perturbation parameterization with the simple steepest decent method, a gradient-based aerodynamic shape design system is constructed. Finally, the application of the adjoint method is validated through a 5-stage turbine blade and passage optimization with an objective function of entropy generation. The result demonstrates that the gradient-based system can be used for turbine aerodynamic design.

Aerodynamic Optimization Design of Multi-stage Turbine Using the Continuous Adjoint Method

2015 ◽  
Vol 32 (2) ◽  
Author(s):  
Lei Chen ◽  
Jiang Chen
Keyword(s):  
Optimization Design ◽  
Adjoint Method ◽  
Shape Design ◽  
Aerodynamic Optimization ◽  
Aerodynamic Shape ◽  
Adjoint Formulation ◽  
Multi Stage ◽  
Continuous Adjoint Method ◽  
Continuous Adjoint

AbstractThis paper develops a continuous adjoint formulation for the aerodynamic shape design of a turbine in a multi-stage environment based on S

1008 Investigation on Unsteady Pressure Fluctuation in Multi-stage Centrifugal Blower with Inlet Guide Vane

2014 ◽  
Vol 2014 (0) ◽  
pp. _1008-1_-_1008-4_
Author(s):  
Kiyotaka HIRADATE ◽  
Kiyohide SAKAMOTO ◽  
Yasushi SHINKAWA ◽  
Satoshi JOUKOU ◽  
Takeshi UCHIYAMA
Keyword(s):  
Pressure Fluctuation ◽  
Guide Vane ◽  
Inlet Guide Vane ◽  
Centrifugal Blower ◽  
Unsteady Pressure ◽  
Multi Stage

Design Optimization of Power Plants by Considering Multiple Partial Load Operation Points

2007 ◽  
Author(s):  
Marc Ju¨des ◽  
George Tsatsaronis
Keyword(s):  
Design Optimization ◽  
Power Plants ◽  
Optimization Procedure ◽  
Optimization Methods ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Optimization Task ◽  
Operation Conditions ◽  
Partial Load ◽  
Conventional Optimization

The design optimization of complex energy conversion systems requires the consideration of typical operation conditions. Due to the complex optimization task, conventional optimization methods normally take into account only one operation point that is, in the majority of cases, the full load case. To guarantee good operation at partial loads additional operation conditions have to be taken into account during the optimization procedure. The optimization task described in this article considers altogether four different operation points of a cogeneration plant. Modelling requirements, such as the equations that describe the partial load behavior of single components, are described as well as the problems that occur, when nonlinear and nonconvex equations are used. For the solution of the resulting non-convex mixed-integer nonlinear programming (MINLP) problem, the solver LaGO is used, which requires that the optimization problem is formulated in GAMS. The results of the conventional optimization approach are compared to the results of the new method. It is shown, that without consideration of different operation points, a flexible operation of the plant may be impossible.

Sign in / Sign up

Export Citation Format

Share Document