Effect of inexact adjoint solutions on the discrete-adjoint approach to gradient-based optimization

Author(s):  
David A. Brown ◽  
Siva Nadarajah
Author(s):  
Vincenzo Russo ◽  
Simone Orsenigo ◽  
Lasse Mueller ◽  
Tom Verstraete ◽  
Sergio Lavagnoli

Abstract This work presents a 2D optimization of a multi-body turbine vane frame (TVF), a particular configuration that can lead to considerable shortening of the aero-engine shaft as well as weight reduction. Traditionally, the turbine vane frame is used to guide the flow from the high pressure (HP) turbine to the low pressure (LP) turbine. Current designs have a mid turbine frame equipped with non lifting bodies that have structural and servicing functions, while multi-body configurations are characterized by the fact that, in order to shorten the duct length, the mid turbine struts are merged with the LP stator vanes, traditionally located downstream. This design architecture consists therefore of a multi-body vane row, where lifting long-chord struts replace some of the low pressure vane airfoils. However, the bulky struts cause significant aerodynamics losses and penalize the aerodynamics of the small vanes. The objective of the present work is to numerically optimize a TVF geometry with multi-body architecture using a gradient based algorithm coupled with the adjoint approach, enabling the use of a rich design space. Steady-state CFD simulations have been used to this end. The aim of this study is to reduce the total pressure losses of the TVF, while imposing several aerodynamic and structural constraints. The parametrization of the TVF geometry represents the airfoil shapes and their relative pitch-wise positions. The outcome of the optimization is to evaluate the potential improvements introduced by the optimized TVF geometry and to quantify the influence of the different design parameters on the total pressure losses.


2019 ◽  
Vol 85 (2) ◽  
Author(s):  
Thomas Antonsen ◽  
Elizabeth J. Paul ◽  
Matt Landreman

The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis and tolerance calculation. An efficient method for computing the shape gradient for toroidal three-dimensional magnetohydrodynamic (MHD) equilibria is presented. The method is based on the self-adjoint property of the equations for driven perturbations of MHD equilibria and is similar to the Onsager symmetry of transport coefficients. Two versions of the shape gradient are considered. One describes the change in a figure of merit due to an arbitrary displacement of the outer flux surface; the other describes the change in the figure of merit due to the displacement of a coil. The method is implemented for several example figures of merit and compared with direct calculation of the shape gradient. In these examples the adjoint method reduces the number of equilibrium computations by factors of$O(N)$, where$N$is the number of parameters used to describe the outer flux surface or coil shapes.


Author(s):  
Andre C. Marta ◽  
Sriram Shankaran ◽  
D. Graham Holmes ◽  
Alexander Stein

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.


2021 ◽  
Vol 22 (1) ◽  
pp. 109-118
Author(s):  
Sishi Cao ◽  
Zhifei Zhang ◽  
Yunwei Huang ◽  
Quanzhou Zhang ◽  
Zhongming Xu

Author(s):  
Beckett Zhou ◽  
Tim A. Albring ◽  
Nicolas R. Gauger ◽  
Carlos Ilario ◽  
Thomas D. Economon ◽  
...  

AIAA Journal ◽  
2010 ◽  
Vol 48 (9) ◽  
pp. 2008-2016 ◽  
Author(s):  
Byung Joon Lee ◽  
Meng-Sing Liou ◽  
Chongam Kim

Author(s):  
Lasse Mueller ◽  
Tom Verstraete ◽  
Marc Schwalbach

Abstract This paper presents a multidisciplinary adjoint-based design optimization of a turbocharger radial turbine for automotive applications. The aim is to improve the total-to-static efficiency of the turbine while keeping mechanical stresses below a predefined limit. The search for the optimal design is accomplished using an efficient Sequential Quadratic Programming algorithm considering additional aerodynamic and manufacturing constraints. The aerodynamic performance of the wheel is evaluated by a Reynolds-Averaged Navier-Stokes solver, whereas the maximum stresses in the material are predicted by a Finite Element Analysis tool. The design gradients required by the optimizer are computed with the adjoint approach which provides sensitivity information largely independent of the number of design variables. The results presented in this paper show the clear need to take into account mechanical stresses during optimization, as they are the most restrictive design limitation. However, the gradient-based optimization algorithm is able to effectively keep the stress levels below the critical value while significantly improving the turbine efficiency in a few design cycles.


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