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2008 | Buch

Optimization and Computational Fluid Dynamics

herausgegeben von: Prof. Dr.-Ing. Dominique Thévenin, Dr.-Ing. Gábor Janiga

Verlag: Springer Berlin Heidelberg

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Inhaltsverzeichnis

Frontmatter

Generalities and methods

Frontmatter

Chapter 1. Introduction

Abstract

A book dedicated to optimization applied to practical engineering configurations must probably start with a warning: “optimization” means much more than “improvement”! It is indeed a pity that so many researchers and engineers still employ the terminology “optimization” in the title or abstract of their publications when they simply mean in practice that starting from a non-satisfactory configuration, they have tried two or three other ones and chosen at the end the best case. This is undoubtedly related to optimization, but in a very minimalistic sense! In the present book optimization means

Dominique Thévenin

Chapter 2. A Few Illustrative Examples of CFD-based Optimization

Heat Exchanger, Laminar Burner and Turbulence Modeling

Abstract

In this chapter, several multi-objective design optimizations are performed in order to illustrate major issues associated with CFD-based optimization. First, a heat exchanger configuration (Case A) is considered using the coupled solution of the flow/heat transfer processes. The aim of the procedure is to find the positions of the tubes most favorable to simultaneously maximize heat exchange while obtaining a minimum pressure loss.

Next, the optimization of the flame shape of a laminar burner is investigated when varying the fuel/air ratio in a primary and a secondary inlet (Case B). The objectives are to reduce the CO emission at a prescribed distance from the injection plane and to obtain the most homogeneous temperature profile at the same position. The flow involving chemical reactions is solved using the in-house Computational Fluid Dynamics (CFD) code UGC ⁺. These two cases are the continuation of our previous studies, introducing new results and new aspects.

The last case presented here is a new proposal to optimize the model parameters of an engineering turbulence model (Case C).

In all the presented cases, an Evolutionary Algorithm (EA) is applied to find the optimal configurations. An in-house computer package, called Opal, performs the optimization process in a fully automatic manner. The EA relies on a relatively large number of simulations which may result in a considerable computational effort, depending on the configuration. The procedure can thus be performed in parallel on a Linux PC-cluster to reduce user waiting time.

Gábor Janiga

Chapter 3. Mathematical Aspects of CFD-based Optimization

Abstract

There exist several computational strategies of different efficiency for the solution of model-based optimization problems — particularly, in the case of models based on challenging CFD problems. Applied mathematics provides means for their analysis and for advice on their proper usage.

In this chapter, methods are mainly analyzed based on the explicit treatment of the underlying CFD-problem as a constraint of a nonlinear optimization problem, thus providing the potential for high computational efficiency. Methods of this form are termed optimization boundary value problem methods, simultaneous optimization methods or one-shot optimization methods. The necessary conditions of optimality play a key structural role in devising those strategies. Special attention is given to the following issues: modular sequential quadratic programming with approximate linear solvers, preconditioning of the Karush-Kuhn-Tucker (KKT) system and multigrid optimization in the case of stationary problems. In the case of unsteady problems, we will concentrate on time-domain decomposition such as by multiple shooting, and on algorithmic developments for real-time optimization. The aim of the presentation is to give a survey on advanced and fast methods for optimization within a CFD framework. For details, the reader is referred to the relevant literature.

Hans Georg Bock, Volker Schulz

Chapter 4. Adjoint Methods for Shape Optimization

Abstract

In aerodynamic shape optimization, gradient-based methods often rely on the adjoint approach, which is capable of computing the objective function sensitivities with respect to the design variables. In the literature adjoint approaches are proved to outperform other relevant methods, such as the direct sensitivity analysis, finite differences or the complex variable approach. They appear in two different formulations, namely the continuous and the discrete one, which are both discussed in this chapter.

In the first part, continuous and discrete approaches for the computation of first derivatives are presented. The mathematical background for both approaches is introduced. Based on it, adjoints for either inverse design problems associated with inviscid or viscous flows or for the minimization of viscous losses in internal aerodynamics are developed. The Navier-Stokes equations are used as state equations. The elimination of field integrals expressed in terms of variations in grid metrics leads to a formulation which is independent of the grid type and can thus be employed with either structured or unstructured grids. From the physical point of view, the minimization of viscous losses in ducts or cascades is handled by minimizing either the difference in total pressure between inlet and outlet (the objective function is, then, a boundary integral) or the field integral of entropy generation. The discrete adjoint approach is, practically, used to compare and cross-check the derivatives computed by means of the continuous approach.

In the second part of this chapter, recent theoretical formulations on the computation and use of the Hessian matrix in optimization problems are presented. It is demonstrated that the combined use of the direct sensitivity analysis for the first derivatives followed by the adjoint approach for second derivatives may support the Newton method at the cost of N+2 equivalent flow solutions per optimization cycle. The computation of the exact Hessian is demonstrated using both discrete and continuous approaches.

Test problems are solved using the proposed methods. They are used to compare the so-computed first and second derivatives with those resulting from the use of finite difference schemes. On the other hand, the efficiency of the proposed methods is demonstrated by presenting and comparing convergence plots for each test problem.

Kyriakos C. Giannakoglou, Dimitrios I. Papadimitriou

Specific Applications of CFD-based Optimization to Engineering Problems

Frontmatter

Chapter 5. Efficient Deterministic Approaches for Aerodynamic Shape Optimization

Abstract

Because detailed aerodynamic shape optimizations still suffer from high computational costs, efficient optimization strategies are required. Regarding the deterministic optimization methods, the adjoint approach is seen as a promising alternative to the classical finite difference approach. With the adjoint approach, the sensitivities needed for the aerodynamic shape optimization can be efficiently obtained using the adjoint flow equations. Here, one is independent of the number of design variables with respect to the numerical costs for determining the sensitivities. Another advantage of the adjoint approach is that one obtains accurate sensitivities and gets rid of the laborious tuning of the denominator step sizes for the finite differences.

Differentiation between continuous and discrete adjoint approaches is noted. In the continuous case, one formulates the optimality condition first, then derives the adjoint problem and finally does the discretization of the so obtained adjoint flow equations. In the discrete case, one takes the discretized flow equations for the derivation of the discrete adjoint problem. This can be automated by so-called algorithmic differentiation (AD) tools.

The different adjoint approaches will be explained for single disciplinary aerodynamic shape optimization first and then their extension to multidisciplinary design optimization (MDO) problems will be discussed for aerostructure cases. Finally, we will discuss the so-called one-shot methods. Here, one breaks open the simulation loop for optimization.

Nicolas R. Gauger

Chapter 6. Numerical Optimization for Advanced Turbomachinery Design

Abstract

The multilevel-multidisciplinary-multipoint optimization system developed at the von Kármán Institute and its applications to turboma-chinery design is presented. To speed up the convergence to the optimum geometry, the method combines an Artificial Neural Network, a Design Of Experiment technique and a Genetic Algorithm. The different components are described, the main requirements are outlined and the basic method is illustrated by the design of an axial turbine blade.

A procedure for multipoint optimization, aiming for optimal performance at more than one operating point, is outlined and applied to the optimization of a low solidity diffuser.

The extension to a multidisciplinary optimization, by combining a Navier-Stokes solver with a Finite Element Analysis, allows an efficient search for a compromise between the sometimes conflicting demands of high efficiency and respect of mechanical constraints. It is shown that a significant reduction of the stresses is possible with only a small penalty on the performance and that this approach may lead to geometries that would normally be excluded when using less sophisticated methods.

René A. Van den Braembussche

Chapter 7. CFD-based Optimization for Automotive Aerodynamics

Abstract

The car drag reduction problem is a major topic in the automotive industry because of its close link with fuel consumption reduction. Until recently, a computational approach of this problem was unattainable because of its complexity and its computational cost. A first attempt in this direction has been presented by the present author as part of a collaborative work with the French car manufacturer Peugeot Citroën PSA [4]. This article described the drag minimization of a simplified 3D car shape with a global optimization method that coupled a Genetic Algorithm (GA) and a second-order Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. The present chapter is intended to give a more detailed version of this work as well as its recent improvements. An overview of the main characteristics of automotive aerodynamics and a detailed presentation of the car drag reduction problem are respectively proposed in Sects. 7.1 and 7.2. Section 7.3 is devoted to the description of various fast and global optimization methods that are then applied to the drag minimization of a simplified car shape discussed in Sect. 7.4. Finally in Sect. 7.5, the chapter ends by proposing the applicability of CFD-based optimization in the field of airplane engines.

Laurent Dumas

Chapter 8. Multi-objective Optimization for Problems Involving Convective Heat Transfer

Abstract

In this chapter, focused on Computational Fluid Dynamics (CFD)-based optimization for problems involving convective heat transfer, we present our approach for the multi-objective shape optimization of periodic wavy channels, representative of the repeating module of many heat exchangers.

The first problem is of fundamental nature and considers the geometric parametrization and shape optimization of two- and three-dimensional periodic wavy channels. The geometry of the channel is parametrized either by means of linear-piecewise profiles or by non-uniform rational B-splines. The second case, of industrial interest, illustrates the development and application of an automatic method for the design of gas turbine recuperators.

After a literature review of shape optimization in heat transfer, we describe in detail both aforementioned problems in terms of physical assumptions and mathematical formulation. In the numerical methods section we indicate the CFD codes used and describe the implementation of periodic boundary conditions. Thereafter in the geometry parametrization section, we illustrate the different types of numerical geometry representation used in the two problems, and the corresponding definition of the design variables whose variation leads to different shapes of the computational domain.

After a comprehensive classification and description of optimization methods and algorithms, we present the results obtained for the two different cases. For both problems the objectives considered are the maximization of heat transfer rate and the minimization of friction factor, with the additional objective of minimization of heat transfer surface for the recuperator module. Since there is no single optimum to be found, we use a multi-objective genetic algorithm and the so-called Pareto dominance concept.

The results obtained are very encouraging, and the procedure described can be applied, in principle, to even more complex convective problems.

Marco Manzan, Enrico Nobile, Stefano Pieri, Francesco Pinto

Chapter 9. CFD-based Optimization for a Complete Industrial Process: Papermaking

Abstract

Development of tailored software tools based on coupling of Computational Fluid Dynamics (CFD) with optimization is presented in this paper. In papermaking, industrial applications deal with fluid dynamics at the wet-end of a paper machine as well as in the entire papermaking process.

First, the CFD tools being developed for optimal shape design and optimal control problems at the wet-end (where the paper web is formed) are presented. Different levels of complexity of CFD modeling and a dimension reduction technique are considered in this paper. The reduced CFD model used is validated with a complete model.

In addition, optimization of the whole papermaking process being modeled with different modeling techniques is considered. Our approach is based on interactive multi-objective optimization because the papermaking process as well as the produced paper require multiple criteria to be optimized simultaneously. Typically, the objectives are conflicting which means that compromises need to be done. This is illustrated with numerical examples.

Finally, a completely new design of decision support tools based on multiobjective optimization and multiphysical modeling of large industrial systems is discussed.

Jari Hämäläinen, Taija Hämäläinen, Elina Madetoja, Henri Ruotsalainen

Backmatter

Titel: Optimization and Computational Fluid Dynamics
herausgegeben von: Prof. Dr.-Ing. Dominique Thévenin
Dr.-Ing. Gábor Janiga
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-540-72153-6
Print ISBN: 978-3-540-72152-9
DOI: https://doi.org/10.1007/978-3-540-72153-6

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