Turbine Blade Aerodynamic Optimization on Unstructured Grids Using a Continuous Adjoint Method

2012 ◽  
Author(s):  
M. Zeinalpour ◽  
K. Mazaheri ◽  
A. Irannejad
Keyword(s):  
Turbine Blade ◽  
Adjoint Method ◽  
Suction Side ◽  
Adjoint Equations ◽  
Inverse Design ◽  
Aerodynamic Optimization ◽  
Design Variables ◽  
Continuous Adjoint Method ◽  
Flow Variables ◽  
Continuous Adjoint

A gradient based optimization using the continuous adjoint method for inverse design of a turbine blade cascade is presented. The advantage of the adjoint method is that the objective function gradients can be evaluated by solving the adjoint equations with coefficients depending on the flow variables. This method is particularly suitable for aerodynamic design optimization for which the number of design variables is large. Bezier polynomials are used to parameterize suction side of the turbine blade. The numerical convective fluxes of both flow and adjoint equations are computed by using a Roe-type approximate Riemann solver. An approximate linearization is applied to simplify the calculation of the numerical flux of adjoint variables on the faces of computational cell. The problem examined is that of the inverse design of NASA C3X blade that reproduces a given pressure distributions over its surfaces. Adjoint results show a good agreement with those obtained by finite-difference method.

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

Inverse Problem in Aerodynamic Shape Design of Turbomachinery Blades

2006 ◽  
Author(s):  
Yingchen Li ◽  
Dianliang Yang ◽  
Zhenping Feng
Keyword(s):  
Optimization Algorithm ◽  
Adjoint Method ◽  
Adjoint Equations ◽  
Shape Design ◽  
Computational Domain ◽  
Aerodynamic Design ◽  
Aerodynamic Shape ◽  
Design Variables ◽  
Turbomachinery Blades ◽  
Continuous Adjoint

There are various methods for aerodynamic shape design in turbomachinery blades, but at the state of the art the shape design has still been a formidable problem. Optimal shape design based on adjoint method has been developed rapidly in the last decades in aeronautic field with the start of Jameson’s work. As a gradient-based optimization, the adjoint method introduces an adjoint system and the sensitivity derivative is computed by solving a linear adjoint equation, which makes the computational cost almost independent of the number of design variables. Because the adjoint method realizes the quick and exact sensitivity analysis and saves large computational resources, it has been the highlight in aerodynamic shape design of CFD field. Combining the continuous adjoint method with quasi-Newton method, we developed an optimization algorithm for turbomachinery aerodynamic design governed by two-dimensional Euler equations in this paper. The blade shape to be optimized is parameterized by non-uniform B-spline and the computational domain is discreted with H-grids. Then the adjoint equations and their boundary conditions are deduced in detail, both in computational and physical spaces, and are solved numerically by using time-marching finite difference method based on Jameson’s diffusion scheme. With the solved adjoint variables, the final expression of the cost function gradient with respect to the design variables is formulated. Finally, several numerical cases of turbomachinery blade aerodynamic design are presented and analyzed to validate the present optimization algorithm.

Turbofan duct geometry optimization for low noise using remote continuous adjoint method

2014 ◽  
Vol 229 (1) ◽  
pp. 69-90 ◽  
Author(s):  
S Qiu ◽  
H Liu ◽  
WP Li
Keyword(s):  
Adjoint Method ◽  
Near Field ◽  
Acoustic Propagation ◽  
Low Noise ◽  
Adjoint Equations ◽  
Nozzle Geometry ◽  
Special Treatment ◽  
Perturbation Equation ◽  
Continuous Adjoint Method ◽  
Continuous Adjoint

In this paper, a remote continuous adjoint-based acoustic propagation (RABAP) method is proposed for low noise turbofan duct design. The goal is to develop a set of adjoint equations and their corresponding boundary conditions in order to quantify the influence of geometry modifications on the amplitude of sound pressure at a near-field location. The governing equations for the 2.5D acoustic perturbation equation solver (APE) formulation for duct acoustic propagation is first introduced. This is followed by the formulation and discretization of the remote continuous adjoint equations based on 2.5D APE. The special treatment of the adjoint boundary condition to obtain sensitivities derivatives is also discussed. The theory is applied to acoustic design of an axisymmetric fan bypass duct for two different tone noise radiations. The 2.5D APE is further validated using comparisons to an experiment data of the TURNEX nozzle geometry. The implementation of the remote continuous adjoint method is validated by comparing the sensitivity derivative with that obtained using finite difference method. The result obtained confirms the effectiveness and efficiency of the proposed RABAP framework.

scholarly journals Aerodynamic Optimization Based on Continuous Adjoint Method for a Flexible Wing

2016 ◽  
Vol 2016 ◽  
pp. 1-16
Author(s):  
Zhaoke Xu ◽  
Jian Xia
Keyword(s):  
Euler Equations ◽  
Optimization Design ◽  
Adjoint Method ◽  
Structural Model ◽  
Lift Coefficient ◽  
Shell Element ◽  
Aerodynamic Optimization ◽  
Flexible Wing ◽  
Continuous Adjoint Method ◽  
Continuous Adjoint

Aerodynamic optimization based on continuous adjoint method for a flexible wing is developed using FORTRAN 90 in the present work. Aerostructural analysis is performed on the basis of high-fidelity models with Euler equations on the aerodynamic side and a linear quadrilateral shell element model on the structure side. This shell element can deal with both thin and thick shell problems with intersections, so this shell element is suitable for the wing structural model which consists of two spars, 20 ribs, and skin. The continuous adjoint formulations based on Euler equations and unstructured mesh are derived and used in the work. Sequential quadratic programming method is adopted to search for the optimal solution using the gradients from continuous adjoint method. The flow charts of rigid and flexible optimization are presented and compared. The objective is to minimize drag coefficient meanwhile maintaining lift coefficient for a rigid and flexible wing. A comparison between the results from aerostructural analysis of rigid optimization and flexible optimization is shown here to demonstrate that it is necessary to include the effect of aeroelasticity in the optimization design of a wing.

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.

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