Geometry Parameterisation and Response Surface-Based Shape Optimisation of Aero-Engine ...

118 Pages·2014·42.23 MB·English

2003:09
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Geometry Parameterisation and Response
Surface-Based Shape Optimisation
of Aero-Engine Compressors
by
JÖRGEN BURMAN
Department of Applied Physics and Mechanical Engineering
Division of Fluid Mechanics
2003:09 • ISSN: 1402 - 1544 • ISRN: LTU - DT - - 03/09 - - SE
Doctoral thesis 2003:09
Geometry Parameterisation and Response
Surface-Based Shape Optimisation
of Aero-Engine Compressors
by
Jörgen Burman
Division of Fluid Mechanics
Department of Applied Physics and Mechanical Engineering
Luleå University of Technology, SE-971 87 Luleå, Sweden
Dissertation
For the degree of Doctor of Philosophy (Ph.D) in the subject area Fluid Mechanics
which with due permission of the Faculty board at Luleå University of Technology
will be defended in public, in room E231 at Luleå University of Technology, on
Monday the 5:th of May, at 09.00 am.
External examiner: Professor Rudolf Schilling, Technische Universität München,
Germany.
Akademisk avhandling
För avläggande av teknologie doktorsexamen inom ämnesområdet strömningslära,
som med vederbörligt tillstånd av tekniska fakultetsnämnden vid Luleå tekniska
universitet kommer att offentligen försvaras, i sal E231 vid Luleå tekniska
universitet, måndagen den 5:e maj kl. 09.00.
Fakultetsopponent är Professor Rudolf Schilling, Technische Universität München,
Tyskland.
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Geometry Parameterisation and Response Surface-
Based Shape Optimisation of Aero-Engine
Compressors
by
Jörgen Burman
Division of Fluid Mechanics
Department of Applied Physics and Mechanical Engineering
Luleå University of Technology
SE-971 87 Luleå
Sweden
Luleå 2003
Preface
This research has been carried out at the Division of Fluid Mechanics, Luleå University of
Technology, Sweden. It was performed during the years 1998-2003 under the supervision of
Associate Professor Rikard Gebart. The research has been performed in close collaboration
with Volvo Aero Corporation in Trollhättan.
The work has been supported by the Swedish Agency for Innovation Systems (VINNOVA)
and The Polhem Laboratory at Luleå University of Technology. A five-month visit at
University of Florida was supported by the The Swedish Foundation for International
Cooperation in Research and Higher Education (STINT).
First of all would like to thank my supervisor Rikard Gebart for his support and valuable
guidance during these years. I would like to thank Hans Mårtensson at Volvo Aero
Corporation for sharing his knowledge on turbomachinery design. I would also like to express
my gratitude to Professor Wei Shyy at University of Florida for inviting me to collaborate
with him and his research group and making my stay in Gainesville memorable and fruitful.
During my time in Florida I also had the opportunity to see a space shuttle launch at Kennedy
Space Center and watch my first live NHL game, which were great experiences.
I would also like to mention my colleagues at the division whom I have been working
together with more or less during the past years: Professor Håkan Gustavsson, Associate
Professor Hans Åkerstedt, Associate Proffesor Staffan Lundström, Associate Professor Marie
Finnström, Research Assistant Allan Holmgren, Ph.D. students Magnus Andersson, Fredrik
Engström, Michel Cervantes, Daniel Marjavaara, Niklas Davidsson, Markus Nordlund, Lars-
Göran Westerberg, John Bergström and Hans Löfgren.
Finally, I would like to thank my parents Ulla and Lars and my sister Anna who always have
supported me in my work.
lörgen Burman
Luleå, April 2003
Abstract
The main goal in jet engine design is to achieve light, compact and highly efficient systems
while reducing the cost and design times. Traditionally, the design has been based on trial-
and-error procedures, which count on the skills and experience of the designer to suggest
design improvements. In step with recent advances in efficient and robust computational
algorithms and the fast development in computer resources, computational fluid dynamics
(CFD) has matured to a stage where it provides substantial insight into the physical processes
involved in engineering flows. The CFD solvers do, however, not indicate which geometry
modifications are required to improve performance. Even if it is possible to investigate a very
large number of design alternatives it is difficult to find the optimum only by trial-and-error
and it can also be very time consuming. The search for an improved design can be aided by
the integration of a numerical optimisation algorithm with the CFD code. Before this can be
done several decisions have to be taken. The first is how to make a parameterisation of the
geometry to describe allowable shape variations in the design. The second decision is to
define problem constraints. Finally, the performance parameters to be used in the definition of
the objective function have to be identified.
The main objective of this work has been to develop and implement methods for shape
optimisation of compressor blades. A large part of the work has been devoted to the
development of a compressor blade design system. The geometry description is based on
Non-Uniform Rational B-Splines (NURBS), which are used by modern computer aided
design tools and have suitable mathematical properties for parameterisation of fluid flow
domains. The problem with the NURBS parameters is that they do not coincide with the
traditional design parameters used by the aerospace engineers. However, keeping the
traditional parameters as design variables will help the designer to chose fewer but more
relevant design parameters for the problem. A separate optimisation algorithm has thus been
integrated in the blade design system to optimise the NURBS parameters to achieve the
desired traditional design parameters, also called implicit design parameters. A second
method to reduce the total number of design parameters is to introduce B-spline mapping
curves that interpolates shape modifications of a starting blade in the spanwise (radial)
direction. This method allows the designer to arbitrary select the number of degrees of
freedom depending on his/her needs.
The blade design system has been used to optimise a compressor blade geometry via
construction of response surface approximations. Optimisation both with and without implicit
design variables has shown that using implicit design variables can substantially reduce the
number of CFD simulations. The response surface method has shown to be efficient in
filtering numerical noise intrinsic to the numerical data produced by the CFD code. The
method is also capable of handling multi-criterion optimisation problems in a straightforward
manner by building a composite response surface from individual response surfaces.
Key words: Geometry parameterisation, Design optimisation, Compressor design, Numerical
noise, Grid size, Response surface methodology
Thesis
This thesis comprises a survey and the following papers:
A Burman, J, Gebart, B.R., and Mårtensson, H., Development of a blade geometry
definition with implicit design variables, AIAA paper 00-0671, 38th AIAA Aerospace
Sciences Meeting and Exhibit, Reno, Nevada (USA), January 10-13, 2000
B Burman, J., and Gebart, B.R., Influence from numerical noise in the objective function
for flow design optimisation, International Journal of Numerical Methods for Heat &
Fluid Flow, Vol. 11, No. 1, pp. 6-19, 2001
C Burman, J., Shape optimisation of two dimensional compressor blades using implicit
design variables, Submitted to International Journal of Numerical Methods for Heat &
Fluid Flow, 2003
D Burman, J., Papila, N., Shyy, W., and Gebart, B.R., Assessment of response surface-
based optimization techniques for unsteady flow around bluff bodies, 9th
AIAA/ISSMO Symposium on Multidisciplinary Optimization, Atlanta, Georgia
(USA), September 4-6, 2002
E Burman, J, Mårtensson, H., and Gebart, B.R., A 3-D parametric blade design system
for axial flow compressors with reduced number of design variables, To be submitted
Contents
INTRODUCTION 1
BACKGROUND 3
FORMULATION OF NUMERICAL OPTIMISATION PROBLEMS 3
CONSTRAINTS 4
DESIGN VARIABLES - GEOMETRY PARAMETERISATION 4
OBJECTIVE FUNCTION 9
OPTIMISATION STRATEGIES 11
GRADIENT-BASED METHODS 11
Sensitivity analysis 12
Adjoint sensitivity analysis 13
RESPONSE SURFACE METHODOLOGY 14
ON THE CHOICE OF OPTIMISATION STRATEGY 17
CONCLUSIONS AND DIRECTION OF FUTURE WORK 18
ACKNOWLEDGEMENTS 19
REFERENCES 19
Introduction
The main goal in jet engine design is to achieve light, compact, highly efficient systems while
reducing the cost and design times. Aero-engines are very complex engineering systems
involving maybe hundreds of thousands of components and many more important design
parameters. Obviously, this is far too many parameters to be handled at the same time. The
solution to this problem is to carry out the design at two different hierarchical levels,
preliminary design and detailed component design. During the preliminary design phase the
engine is considered as an entire system and is modelled very approximately using a large
amount of empiricism from past experience. Only a limited number of fundamental design
parameters are considered and the cost of simulating the entire system is reduced to a few
minutes at most. This makes it possible to investigate a large number of configurations and
compare possible trade-offs.
Different components of the machine, e.g. compressor and turbine, are also designed at a
preliminary and detailed component design level illustrated in Figure 1. The preliminary
design of a multistage compressor involves deciding parameters such as number of stages,
work split, and overall dimensions while trying to maximise the design point efficiency. This
is performed by one-dimensional gas dynamic and thermodynamic considerations employing
loss correlations. The detailed component design is then concerned with the blade shape using
high-fidelity numerical simulations and detailed experiments to satisfy both the aerodynamic
and the mechanical requirements specified in the preliminary design. Based on the outcome
from the detailed design for a given set of engine conditions, a new iteration on the system
level is performed. This design cycle is repeated a number of times but must often be stopped
as soon as an acceptable solution has been found with no guarantee that it is also the
optimum. This is due to the limited time available for the design projects justified by strong
commercial forces to bring the product to market as quickly as possible. The iteration phase
for the detailed design takes normally up to several weeks. Reducing that time is important to
enable another iteration on the system level because decisions made at the preliminary design
phase have a large influence on the final design.
At the detailed design level more and more of the design is based on computer assisted
numerical analysis. This is mainly due to recent advances in efficient and robust
computational algorithms for fluid applications as well as the never-ending increase in
computer speed and memory capacity. The aerodynamic behaviour is typically predicted
using Computational Fluid Dynamics (CFD) codes. The CFD codes have matured to a stage
were they can provide substantial insight into engineering processes involving fluid flows,
and has for that reason become an important tool in the design process. The experimental part
is still important but the trend is to do fewer but more detailed experiments. CFD simulations
do, however, not indicate what geometry modifications are necessary to improve the
performance. This search for improved design has traditionally been based on manual trial-
and-error procedures, which rely on the intuition and experience of the designer. Although
this procedure allows workable designs it can be very time consuming.
As an example the development of the exterior aerodynamics from the Wright Flyer 1, the
worlds first powered aeroplane, to the DC-3 led to substantial performance improvements but
the development time was several decades (see Figure 2).
One way of approaching this problem is to integrate a standard numerical optimisation
procedure with the numerical tools for analysis of the conventional design process, so that the
1
Preliminary Detailed component design
design
Initial geometry
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decisions
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Structural analysis
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Thermal analysis
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Figure 1. Sequential two-level design process.
best design in terms of a predefined criterion can be determined. This approach is attractive
since it replaces workable designs with optimal ones, while reducing the design time.
Optimisation can assist the designer at all stages of the design process. In this thesis the focus
is on the detailed design of compressor blade geometry where a numerical optimisation
algorithm is coupled with a CFD solver. This means that among the different disciplines
involved in the detailed component design, only the aerodynamic performance is optimised,
although some mechanical requirements are handled by constraints.
One of the critical issues of aerodynamic design has always been the high computational costs
involved. For a numerical optimisation problem the number of function evaluations (CFD
analyses) necessary to reach the optimum can be affected by the choice of optimisation
strategy and/or by a reduction of the number of design variables.
(a) (b)
Figure 2. Development in exterior aerodynamics from (a) Wright Flyer 1 (from web page
www.first-to-fly.com) to (b) Douglas DC-3 (Photograph courtesy of Lawrence Feir).
2
For a shape optimisation problem the chosen geometry parameterisation will dictate the
number of design variables. Ideally, the geometry model should allow as much geometry
flexibility as possible with as few design variables as possible. In this work special attention is
given to the geometry description of compressor blades and the employment of different
optimisation techniques for flow design.
Background
Most of the previous work done on design optimisation in fluid mechanics has been related to
aerospace applications, mainly optimum shapes of airfoils. The methods can be divided into
two categories, namely, inverse design methods and numerical optimisation methods (or
direct-design methods). Inverse design methods, first introduced in 1945 by Lighthill for
incompressible flow using a conformal mapping technique (Lighthill, 1945), are an
established approach in which one specifies some aerodynamic quantity, such as surface
pressure distribution, and the method calculates the corresponding airfoil geometry. More
recent inverse design methods are based on the Euler equations using a so-called transpiration
model for wall modifications, see e.g. Giles and Drela (1987) or Van den Braembussche
(1999).
Numerical optimisation methods provide a more general approach for solving design
problems. With this approach a suitable flow analysis tool (flow solver) is coupled with an
optimisation algorithm to modify the geometry in order to minimise some "cost" or objective
function. Early work in this area applied to airfoil design was done by Hicks et al. (1974) and
Iameson(1988).
The disadvantage of numerical optimisation methods compared to inverse design methods is
that this approach is very time consuming computationally. The inverse approach, on the
other hand, requires a priori knowledge of the desired form of the pressure (or velocity)
distribution, which can be difficult to specify, especially for problems with multiple operating
conditions. The designer also has less control of the blade shape, which can result in blades
that are structurally undesirable. Even if the inverse approach can be very efficient for specific
types of well understood problems, e.g. airfoil shape design, the numerical optimisation
methods are more suited for general purpose optimisation and can in most cases be
implemented with any CFD code available. The work presented here will only be based on
numerical optimisation methods. Inverse design methods can be considered as a subset of
numerical optimisation methods by defining the objective function as a deviation between the
actual pressure distribution and a target pressure distribution.
Formulation of numerical optimisation problems
In a design optimisation problem the task is to find the design variables that minimises or
maximises an objective function which measures the performance of the system. In addition,
there may be certain constraints, geometrical or functional (limitations on performance or
behaviour of the design), that must be fulfilled. Mathematically, the optimisation problem can
be expressed as
3