Turbomachinery Design Optimization Using Automatic Differentiated Adjoint Code

2007 ◽  
Author(s):  
Mihai C. Duta ◽  
Shahrokh Shahpar ◽  
Michael B. Giles
Keyword(s):  
Design Optimization ◽  
Adjoint Method ◽  
Automatic Differentiation ◽  
Nonlinear Flow ◽  
Flow Solver ◽  
Current State ◽  
Discrete Adjoint ◽  
Gradient Based ◽  
Turbomachinery Design ◽  
Objective Functional

The last decade has established the adjoint method as an effective way in Computational Fluid Dynamics of calculating the gradients of an objective functional in a large dimensional design space. This paper addresses the concerns that code developers face when creating a discrete adjoint computer program for design optimization, starting from a nonlinear flow solver and using Automatic Differentiation. Adjoint code development benefits greatly from using Automatic Differentiation but at its current state of maturity, this technology is best applied selectively rather than on entire codes. The paper discusses the practical aspects of using Automatic Differentiation on a large industrial turbomachinery flow solver with the objective of deriving efficient adjoint code. The use of the adjoint gradients is illustrated in an optimization exercise using gradient based methods on the NASA Rotor 37 public testcase.

Development of Adjoint Solvers for Engineering Gradient-Based Turbomachinery Design Applications

2009 ◽  
Author(s):  
Andre C. Marta ◽  
Sriram Shankaran ◽  
D. Graham Holmes ◽  
Alexander Stein
Keyword(s):  
Adjoint Method ◽  
Automatic Differentiation ◽  
High Fidelity ◽  
Optimization Approach ◽  
Discrete Adjoint ◽  
Gradient Based ◽  
Computational Fluid Dynamics Cfd ◽  
And Function ◽  
Turbomachinery Design ◽  
Fine Tune

High-fidelity computational fluid dynamics (CFD) are common practice in turbomachinery design. Typically, several cases are run with manually modified parameters based on designer expertise to fine-tune a machine. Although successful, a more efficient process is desired. Choosing a gradient-based optimization approach, the gradients of the functions of interest need to be estimated. When the number of variables greatly exceeds the number of functions, the adjoint method is the best-suited approach to efficiently estimate gradients. Until recently, the development of CFD adjoint solvers was regarded as complex and difficult, which limited their use mostly to academia. This paper focuses on the problem of developing adjoint solvers for legacy industrial CFD solvers. A discrete adjoint solver is derived with the aid of an automatic differentiation tool that is selectively applied to the CFD code that handles the residual and function evaluations. The adjoint-based gradients are validated against finite-difference and complex-step derivative approximations.

Aerodynamic Shape Design Optimization for Turbomachinery Cascade Based on Discrete Adjoint Method

2011 ◽  
Author(s):  
Chaolei Zhang ◽  
Zhenping Feng
Keyword(s):  
Design Optimization ◽  
Optimization Design ◽  
Adjoint Method ◽  
Automatic Differentiation ◽  
Design System ◽  
Shape Design ◽  
Flow Solver ◽  
Aerodynamic Shape ◽  
Shape Design Optimization ◽  
Discrete Adjoint

Achieving higher aerodynamic performance in terms of efficiency, pressure ratio or stable operation range has been of interest to both researchers and engineers in the field of turbomachinery. The design of optimal shaped aerodynamic configurations based on Computational Fluid Dynamics (CFD) and predefined targets can be obtained by using deterministic search algorithms, which need to calculate the first and second order sensitivities of the objective function with respect to the design variables. With the characteristics of quick and exact sensitivity analysis, as well as less computational resource requirement, the adjoint method has become a research focus in aerodynamic shape design optimization over the past decades. In this paper, a discrete adjoint solver was developed and validated based on an in-house flow solver code. Moreover, a turbomachinery cascade optimization design system was established by coupling the flow solver, the discrete adjoint solver, the parameterization technology, the grid generation technology and the gradient-based optimization algorithms. During the development process of the discrete adjoint solver, the automatic differentiation tool was used in order to ease the construction of the discrete adjoint system based on the flow solver code. However, in order to save the memory requirement and to reduce the computational cost, the automatic differentiation tool was used selectively to build the fundamental subroutines. The top-most module of the discrete adjoint solver was established based on the discrete adjoint theory and the automatic differentiation technology manually. The treatments of the discontinuity in the flow field, such as strong shocks, and the imposition of strong boundary conditions which were implemented in the adjoint solver were discussed in detail. At the same time, several technologies were used to accelerate convergence. Based on the optimization system, a typical 2D transonic turbomachinery cascade was optimized under the viscous flow environment. The optimization results were analyzed in detail. The validity and efficiency of the present optimization design system were proved.

Sensitivity Analysis of Flexible Multibody Systems Based on the Motion Formalism and the Discrete Adjoint Method

2018 ◽  
Author(s):  
Alfonso Callejo ◽  
Valentin Sonneville ◽  
Olivier A. Bauchau
Keyword(s):  
Sensitivity Analysis ◽  
Design Optimization ◽  
Cross Sections ◽  
Adjoint Method ◽  
Optimization Methods ◽  
Sensitivity Analyses ◽  
Discrete Adjoint ◽  
Discrete Adjoint Method ◽  
Flexible Multibody ◽  
Forward Equations

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.

Computational aeroelastic modelling of airframes and turbomachinery: progress and challenges

2007 ◽  
Vol 365 (1859) ◽  
pp. 2469-2499 ◽  
Author(s):  
R.E Bartels ◽  
A.I Sayma
Keyword(s):  
Order Reduction ◽  
Nonlinear Flow ◽  
Aerospace Vehicles ◽  
Flow Models ◽  
Reduction Techniques ◽  
Current State ◽  
Structural Nonlinearity ◽  
Computational Structural Dynamics ◽  
Computational Analyses ◽  
Turbomachinery Design

Computational analyses such as computational fluid dynamics and computational structural dynamics have made major advances towards maturity as engineering tools. Computational aeroelasticity (CAE) is the integration of these disciplines. As CAE matures, it also finds an increasing role in the design and analysis of aerospace vehicles. This paper presents a survey of the current state of CAE with a discussion of recent research, success and continuing challenges in its progressive integration into multidisciplinary aerospace design. It approaches CAE from the perspective of the two main areas of application: airframe and turbomachinery design. An overview will be presented of the different prediction methods used for each field of application. Differing levels of nonlinear modelling will be discussed with insight into accuracy versus complexity and computational requirements. Subjects will include current advanced methods (linear and nonlinear), nonlinear flow models, use of order reduction techniques and future trends in incorporating structural nonlinearity. Examples in which CAE is currently being integrated into the design of airframes and turbomachinery will be presented.

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

2019 ◽  
Vol 192 ◽  
pp. 104259 ◽  
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

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

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.

Radar Cross Section Reduction and Shape Optimization using Adjoint Method and Automatic Differentiation

2021 ◽  
Vol 36 (3) ◽  
pp. 320-335
Author(s):  
Ming Li ◽  
Junqiang Bai ◽  
Feng Qu
Keyword(s):  
Shape Optimization ◽  
Cross Section ◽  
Optimization Design ◽  
Adjoint Method ◽  
Evaluation Method ◽  
Automatic Differentiation ◽  
Design Method ◽  
Radar Cross Section ◽  
Memory Consumption ◽  
Gradient Based

An efficient Radar Cross Section (RCS) gradient evaluation method based on the adjoint method is presented. The Method of Moments is employed to solve the Combined Field Integral Equation (CFIE) and the corresponding derivatives computing routines are generated by the program transformation Automatic Differentiation (AD) technique. The differential code is developed using three kinds of AD mode: tangent mode, multidirectional tangent mode, and adjoint mode. The differential code in adjoint mode is modified and optimized by changing the “two-sweeps” architecture into the “inner-loop two-sweeps” architecture. Their efficiency and memory consumption are tested and the differential code using modified adjoint mode demonstrates the great advantages in both efficiency and memory consumption. A gradient-based shape optimization design method is established using the adjoint method and the mechanism of RCS reduction is studied. The results show that the sharp leading can avoid the specular back-scattering and the undulations of the surface could change the phases which result in a further RCS reduction.

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