Turbomachinery Design and Optimization: A systematic approach for turbomachinery blade design, flow analysis and performance optimization

76 Pages·2012·83.372 MB·English

by  Abdus Samad

Abdus Samad
Turbomachinery Design and
Optimization
A systematic approach for turbomachinery blade
design, flow analysis and performance
optimization
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Impressum/lmprint (nur fur Deutschland/only for Germany)
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marken- oder patentrechtlichem Schutz bzw. sind Warenzeichen oder eingetragene My most sincere acknowledgements go to advisor and chair of my advisor
Warenzeichen der jeweiligen Inhaber. Die Wiedergabe von Marken, Produktnamen,
Gebrauchsnamen, Handelsnamen, Warenbezeichnungen u.s.w. in diesem Werk berechtigt committee, Prof. Kwang-Yong Kim, for his remarkable wisdom and valuable
auch ohne besondere Kennzeichnung nicht zu der Annahme, dass solche Namen irn Sinne
guidance. He has open door policy welcoming every idea and consistent support
der Warenzeichen- und Markenschutzgesetzgebung als frei zu betrachten waren und
daher von jederrnann benutzt werden durften.
in developing my career and motivation. I always believe that he has subtle but
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Heinrich-B6cking-Str. 6-8, 66121 Saarbrucken, Deutschland
Telefon [phone], Telefax [phone] I am grateful to many individuals for their support in this research effort. The
Email: [email protected]
greater part of this work was made possible by the instruction of my teachers
Approved by: Incheon, Inha University, Thesis, 2008
and by the love and support of my family and friends. Sincere thanks to all of
Herstellung in Deutschland:
Schaltungsdienst Lange o.H.G., Berlin them.
Books on Demand GmbH, Norderstedt
I would like to thank my lab colleagues for their tremendous support in all
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Amazon Distribution GrnbH, Leipzig aspect of my research work. I want to convey special thanks to my lab seniors;
ISBN: 978-3-8484-1612-7
Dr. C.M. lang (Korean Institute of Construction Technology) and Dr. l.H. Choi
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AbdusSamad
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August, 2008
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NOMENCLATURE Greek symbols
Roman symbols a Sweep variable
Bult) Bezier blending function fJ Lean variable
c Regression coefficient y Skew variable
Cf.1 Constant J Variable normal to chord line
E Error ( Variable along chord line
F Objective function ,;,K Constants of PBA surrogate model
Fw( =I]ad+ W,P,otal.er;/P,olal.illlel Adi.a bati.c effici.e ncy = (p'v ,,,I.,·,,, /P" ""1,;,,1,, )'-1)" _1
I]ml
k Ratio of specific heats (Equation 2.7) T,o/(d,( ..I ·it / T,(I/lIUlllel - I
Turbulent kinetic energy (Equation 2.5) I:: Turbulent energy dissipation rate
P Pressure f.11 Turbulent or eddy viscosity
Pi Coordinates of control points P Fluid density
p, q, r, S Coefficients of cubic polynomials (Equation 2.13) T Shear stress, turbulence intensity
k'
Rr Turbulent Reynolds number, Rr = L
pc: Subscripts
S(x) Polynomial segments EJJ Efficiency
T Temperature Expt Experimental
Normalized parameter ofa curve h, m and t Hub, mid span and tip, respectively
u, v, w velocity components (Equation 2. l to 2.5) inlet Inlet
w Weight (Equation 3.26) outlet Outlet
WI Weighting factor opt Optimized
x,y Spatial coordinates P Pressure ratio
y + (PYIlI1)/( TIIP) 1/2 Ref Reference
T Temperature ratio
total Total
wf Weighting factor
w Value at the wall
II \11
Table captions
Abbreviations
Table 1.1 Literatures on turbo machinery blade shape optimization
ANN Artificial neural network
Table 2.1 Design specifications of NASA rotor 37
CV Cross validation
Table 4.1 Design ranges of blade sweep, lean, and skew
DOE Design of experiments
Table 4.2(a) Weights for PBA model to construct weighted average model for
GA Genetic algorithm
F£fJ.
GMSE Generalized mean square error
Table 4.2(b) Optimal designs suggested by various surrogates and
KRG Kriging
corresponding predicted RANS results for objective F£ff-
LE Leading edge
Table 4.3(a) Weights for PBA model to construct weighted average model for
LHS Latin hypercube sampling
objective function, Fr.
MOEA Multi-Objective evolutionary algorithm
Table 4.3(b) Optimal designs suggested by various surrogates and
MOGA Multi-Objective genetic algorithm
corresponding predicted RANS results for objective Fr.
NSGA Non-dominated sorting genetic algorithm
Table 4.4(a) Weights for PBA model to construct weighted average model for
PBA PRESS based averaging
objective function, Fp.
PDE Partial differential equation
Table 4.4(b) Optimal designs suggested by various surrogates and
POF Pareto optimal front
corresponding predicted RANS results for objective Fp.
PRESS Predicted error sum of squares
Table 4.5 Root-mean-square averaged errors in predictions of the surrogates at
PS Pressure surface
12 optimal points.
RANS Reynolds average Navier Stokes
Table 4.6 Design variables and ranges
RBNN Radial basis neural network
Table 4.7 Results of optimizations: (a) Design variables and (b) Objective
RMS Root mean square
functions
RSA Response surface approximation
Table 4.8 Design space
RSM Response surface method
Table 4.9 Results of optimizations: (a) Design variables and (b) Objective
SA Simple averaging
functions
SS Suction surface
Table 4.10 Weights assigned to surrogates to construct PBA model: (a) For
SQP Sequential quadratic programming
'1ad,opl blade, (b) For Fp.opl blade and (c) For Fulopi blade
TE Trailing edge
IV
V
Fig. 4.S Results of multiple-objectives optimization: (a) Design variables and
(b) Objective function values
Figure captions Fig. 4.6 Sensitivity analyses for optimum shape by RSM
Fig. 2.1 NASA rotor 37 Fig. 4.7 Limiting streamlines on the blade suction surface: (a) Reference
Fig. 2.2 Meridional view of Rotor 37 blade and (b) Efficiency Optimized blade
Fig. 2.3 Computational grids: (a) Perspective view and (b) Grids at hub of Fig. 4.8 Mach number contours on the planes of 10, 7S and 90% span
LE and TE (interval of contour lines =0.1): (a) 90% span, (b) 7S% span and (c) 10%
Fig. 2.4 Definition of blade sweep: (a) Top view and span
(b) Side view Fig. 4.9 Temperature contours on surfaces of optimum blades: (a) Reference
Fig. 2.S Definition of blade lean (top view) blade, (b) Efficiency optimized blade, (c) Pressure ratio optimized blade
Fig. 2.6 Definition of blade skew (front view) and (d) Temperature ratio optimized blade.
Fig. 2.7 Computational domain Fig. 4.10 Pressure coefficient contours on surfaces of optimum blades: (a)
Fig. 2.8 Convergence plots: (a) Residual history and Reference blade, (b) Efficiency optimized blade, (c) Pressure ratio
(b) Imbalances optimized blade and (d) Temperature ratio optimized blade.
Fig. 2.9 Definitions of thickness variables Fig. 4.11 Axial velocity normalized by sound velocity (interval between
Fig. 3.1 Optimization procedure contours = O.OS): (a) 30 percent chord from blade leading edge and (b)
Fig. 3.2 Design of experiments: (a) Full factorial design and Blade trailing edge
(b) Latin hyper cube sampling Fig. 4.12 Distribution of vorticity on the quasi-orthogonal planes to the
Fig. 3.3 Radial basis network (single neuron) leakage vortex and leakage streamlines (interval between contours= 1.0):
Fig. 3.4 Radial basis function (a) Reference and (b) Optimum by RBNN
Fig. 3.S Multiobjective optimization procedure Fig. 4.13 Optimum blade shape
Fig. 4.1 Spanwise distribution of efficiency Fig. 4.14 Pareto optimal design
Fig. 4.2 Adiabatic efficiency according to normalized mass flow rates Fig. 4.IS Spanwise efficiency distributions
(vertical solid line: design flow rate) Fig. 4.16 Spanwise total temperature ratio distributions
Fig. 4.3 RANS calculations at the optimum points predicted by different Fig. 4.17 Spanwise total pressure ratio distributions
surrogates Fig. 4.18 Spanwise Mach number distributions
Fig. 4.4 Errors in predictions of surrogates at different points in design space: Fig. 4.19 Mach number contours at 80% span: (a) Reference blade, (b)
(a)FE{f, (b) FTand (c) F" Efficiency optimized blade and (c) Total pressure ratio optimized blade
VI VII
Fig. 4.20 Stream lines: (a) Reference blade, (b) Efficiency optimized blade
TABLE OF CONTENTS
and (c) Pressure optimized blade
Fig. 4.21 Result validations with experimental data
ACKNOWLEDGEMENTS
Fig. 4.22 Variables and objective function values with di fferent weighting
NOMENCLATURES ................................................................................... 11
factors
LIST OF TABLES
Fig. 4.23 Reference and optimized blade shapes
LIST OF FIGURES ...... Vl
Fig. 4.24 Mach number contours at different span of blade: (a) 10% span, (b)
CHAPTERS
50% span and (c) 90% span
I. INTRODUCTION
Fig. 4.25 Mach number contours on blade suction surfaces: (a) Ref, I-I Literature survey
(b )I]ad,opl,(c ) F P.Opl and (d) Fwfol'l 1-2 Objective and scope ....................................................................... 21
Fig. 4.26 Stream lines on blade surfaces: (a) Ref; (b) I]ad,opI> (c) Fp.ol'l and (d) 2. NUMERICAL FORMULATION OF TURBOMACHINERY BLADE ... 23
F>~/:opl 2-1 Transonic axial compressor rotor
Fig. 4.27 Pressure contour at blade surface: (a) Ref, (b) 1]0'/.01'1, (c) Fp,upi and 2-2 Reynolds-Averaged Navier-Stokes Analysis ......................... 24
(d) F"f,opl 2-2.1 Zero-equation or algebraic eddy viscosity mode ............ 25
Fig. 4.28 Blade loading: (a) 20% span, (b) 50% span and (c) 80% span.
2-2.2 Two equation model ............................................ 26
2-3 Blade stacking line modification ..................................................... 28
2-3.1 Numerical analysis method ............................................... 28
2-3.2 Objective functions and design variables ......................... 30
2-4 Blade stacking line and thickness modification ............................. ~
2-4.1 Numerical analysis method
2-4.2 Objective functions and design variable ........................... 38
3. OPTIMIZATION PROCEDURE
3-1 Introduction
3-1.1 Design space ................................................................... .41
3-1.2 Design of experiments ..................................................... 43
3-1.3 Full factorial design ....................................................... .43
3-1.4 Latin hypercube sampling ............................................. .43
3-2 Optimization procedure .................................................... :. ........ .44
3-2.1 Surrogate approach ........................................................ .45
VIII
IX
3-2.1.1 Response surface approximation mode ...... .46
3-2.1.2 Radial basis neural network model... ............... .47 CHAPTER I
3-2.1.3 Kriging model... ................................................ 50 INTRODUCTION
3-2.1.4 PBA model... ..................................................... 53
3-2.1.5 Simple average model. ...................................... 55 Design optimization of fluid machinery based on computer simulation has
3-2.2 Multi-objective optimization .......................................... 55 become a reality today because of development of high speed computers.
3-2.2.1 Weighted sum approach .................................... 56 Highly complex flow patterns are being predicted by solving mass, momentum
3-2.2.2 Hybrid MOEA approach ................................... 56 and energy equations and near accurate solutions at an acceptable level are
3-3 Optimization algorithm ................................................................ 60 achieved. On the other hand implementation of optimization techniques to
4. RESULT AND DISCUSSION design the turbo machinery systems has reduced the computational and
4-1 Blade stacking line modification .................................................. 63 experimental expenses. The performance of turbo machinery is directly related
4-1. I Validation of numerical simulation ................................. 63 to reduction of consumption of fuel, mass, vibration, etc. Hence, the thesis
4-1.2 Optimization results ........................................................ 66 describes turbomachinery blade shape optimization targeting to enhance the
4-1.3 Flow characteristics with reference and optimum blade aerodynamic performance and guidance to the fluid machinery designers
Blades ....................................................................................... 77 by a comparative analysis of surrogate based approximation models for
4-1.4 Multi-objective optimization through MOEA ................ 88 optimization.
4-1.5 Flow analysis .................................................................. 91
The turbomachinery designs require enhancement of performance in terms of
4-2 Blade stacking line and thickness modification .......................... 98
thermodynamics parameters; efficiency, pressure ratio and structural
4-2.1 Optimization results ....................................................... 98
parameters; noise, vibration, weight, etc. These parameters are considered to be
4-2.2 Validation of numerical simulation ............................... 98
objectives of designs and the geometric parameters as variables; such as blade
4-2.3 Flow characteristics with reference and optimum blades
dimensions etc are changed. If the blade geometry is deduced from the
III
objectives, the design is called inverse design. I f the geometrical change is used
5. CONCLUDING REMARK 117
to predict the objectives, the design called direct design. The present work
REFERENCES 119
follows the direct design procedure.
AUTHORS PUBLICATIONS 129
BIOGRAPHICAL SKETCH 136 Historically, turbomachinery including pumps, compressors, turbines, etc. is
being developed from centuries. Engineer Heron of Alexandria (I 0-70AD) first
developed steam turbine and that engine was gradually improved to catch the
modern day's requirement of high performance aerospace gas turbine or large
x
II III
power plant. Initial wind tunnel tests and later computational power gave a new design optimization is the modeling fidelity. The surrogate models include
momentum for high efficiency designs. In last decades, owing to the rapid polynomial response surface approximation [9], Kriging [10], and radial basis
developments of high-speed computers and computational fluid dynamics neural network [II] and, in addition, weighted average models based on global
(CFD) theories, the complex three-dimensional flows in turbomachinery could error measures are also implemented in shape optimization and design.
be analyzed more easily. Weighted average modeling is an effective approach to employ multiple
surrogates, based on the same training data, to offer approximations from
Reynolds-averaged Navier-Stokes (RANS) equations have been effectively used
alternative modeling viewpoints [12].
in various fields like heat transfer or turbomachinery applications. These
equations are solved for various flow problems and different turbulence models The basic procedure for optimization followed in this thesis is design of
are used to predict turbulence structures. Different applications of experiments (DOE) [9], numerical simulation, construction of surrogates and
computational codes are being reported considering different grid resolution, model validation. The DOE is the sampling plan and important part is to select
numerical algorithm, and turbulence models etc. Despite the differences which sparsely distributed design variables in design space. The key question in this
still exists between numerical simulations and reality, it is possible to predict step is to find the design points where the numerical simulations can be
many of the flow characteristics and the losses due to the non-isentropic performed. The RANS equations are solved at the simulation stage to find
features of the flow for example shocks, viscous layers, tip clearance effects, objective functions values. These values are then used to construct the
passage vortices etc. The accurate flow prediction inside a transonic axial surrogate based approximation models. Two questions are of interest for
compressor rotor using CFD is difficult due to its extremely complex features: surrogate construction step: model selection and model identification. In present
three-dimensional, unsteady and vortical nature in the blade passage. However, thesis, different surrogates are constructed and tried to find these questions. The
CFD has obvious advantages over the traditional experimental analysis. CFD optimum design is searched via a gradient based search algorithm.
helps us to analyze the effects of individual feature more easily as compared to
1-1 Literature survey
the ex peri mental method [1-7].
Flow analysis for NASA rotor 37, a transonic axial compressor rotor has been
The Mathematical and statistical tools for optimization are being used in
discussed in details by Reid and Moore [13] and in AGARD advisory report
optimization area in single as well as multidisciplinary design and optimization
[14]. As the test data are available in these references, many researchers have
area. These tools combined with numerical analysis methods for flow field have
made efforts to validate their computational codes, and also to optimize the
reduced the experimental expenses to design turbo machinery blades in recent
rotor. The efforts for design optimization include single objective as well as
years. With the development of CFD analysis methods, accuracy of prediction
multi-objective and multi-disciplinary optimizations. The blade shape defining
for the flow becomes acceptable for the purpose of blade design [8].
stacking line, airfoil shapes, etc. are modified to get better efficiency, pressure
The surrogate based approaches are extensively used in the design of structural
ratio, surge margin, etc.
and multi-disciplinary optimizations. A major issue in surrogate model-based
I
2 3
II
I
Recently, the use of sweep, lean (dihedral), and skew (stacking line in rotational fan with skewed blade. With the reduction of a secondary flow and the
direction) in axial flow compressor rotor has become a matter of interest in the thickness of a rotor wake, they could reduce a broadband noise. Fischer, et al.
design of turbo machinery blades [15-21]. The blade shape parameters formed a [21] observed the effect of bowed stators on the performance of a compressor,
three-dimensional stacking line is generally introduced to reduce shock losses, and showed that the separation was reduced in the bowed stator leading to
corner separation in the blade hub, and tip clearance losses in transonic increase in the stagnation pressure ratio and efficiency.
compressor rotor. For example, Gallimore et al. [15] introduced three
A set of papers [22-63] contributed to single and multi-objective optimizations
dimensional blade designs using a sweep and a lean in an axial flow compressor
of turbo machines to enhance their performance as presented in Table 1.1. It has
rotor for engine. They showed that the positive lean reduced a hub corner and
been reported that the efficiency is increased due to movement of separation
tip clearance losses excepting near the mid-span region. The improvement in the
lines towards downstream direction reducing the separation vortex, end-wall
compressor performance as well as the large reduction in the cost and
losses, etc. These papers describe the blade shape optimization considering
timescales associated with a rig test was also obtained together with CFD
stacking line modification in terms of sweeping, leaning or skewing and airfoil
calculation.
shape modification in terms thickness, leading edge, trailing edge modification
One of the significant design trends is the use of aerodynamic sweepto improve etc.
the performance and stability of transonic compressor blades. The pioneer study
The surrogate models being used widely in multi-disciplinary optimizations
on blade sweep in compressors has been done by Bliss [16]. The main objective
should be evaluated in two important aspects; computational economy that
in this study was to reduce the noise level induced by shock waves. Hah, et al.
requires as few data points as possible for constructing a surrogate model, and
[17] studied both forward-and backward-swept compressor blades, and showed
accuracy in 'representing the characteristics of the design space. Response
that a backward-swept blade could suppress the intensity of the shock loss and a
surface approximation (RSA) method [9] which is a global optimization method
forward-swept blade can suppress secondary flow and tip entropy generation.
is recently introduced as a tool of design optimization for turbomachinery, This
Watanabe and Zangeneh [18] reported that the blade sweep in the design of a
is one of the simplest surrogate models to apply to optimize the system because
transonic turbomachinery blade was an effective parameter to control the
this method does not require calculation of the local sensitivity of each design
strength and position of the shock wave at the tip of the transonic rotors. Denton
variable, and is able to perform tasks in parallel easily, The RSA can utilize
and Xu [19] investigated the effects of sweep and lean on the performance of a
information collected from various sources and by different tool. Thus, this
transonic fan, and showed that the stall margin was significantly improved with
method is effective for both of single- and multi-disciplinary optimization
the forward swept blade although a very little change in the peak efficiency was
problems [22-26]. Neural network [II], which is another surrogate
produced by the blade sweep or lean.
approximation model, and RSA based optimization were reported by Papila et
There are a number of studies on the advantages of a skewed rotor. Cai, et al. al. [31].
[20] studied on aerodynamic and aero-acoustic characteristics of an axial flow
4 5