Proceedings of GT2006 ASME Turbo Expo 2006: Power for Land, Sea and Air

May 8-11, 2006, Barcelona, Spain

GT2006-90503

BLADING AERODYNAMICS DESIGN OPTIMIZATION WITH MECHANICAL AND AEROMECHANICAL CONSTRAINTS

H-D Li, L. He School of Engineering

Durham University Durham DH1 3LE

U. K.

Y S Li, R. Wells Siemens Industrial Turbomachinery Ltd.

Ruston House PO Box 1 Waterside South

Lincoln LN5 7FD U. K.

ABSTRACT

A blading design optimization system has been developed using an aeromechanical approach and harmonic perturbation method. The developed system has the capability to optimize aero-thermal performance with constraints of mechanical and aeromechanical integrity at the same time. ‘Aerodynamic mode shape’ is introduced to describe geometry deformation which can effectively reduce the number of design parameters while preserving surface smoothness. Compared to the existing design optimization practices, the present system is simpler, more accurate and effective. A redesign practice of the NASA rotor-67 at the peak efficiency point shows that the aero thermal efficiency can be improved by 0.4%, whilst the maximum static stress has been increased by 33%. Aeromechanical analysis of the optimized blade shows that the aerodynamic damping of the least stable first flap mode is still well above the critical value though the natural frequencies of the first 5 modes have been reduced by 1~4%. The present finding highlights the need for more concurrent integrations of mechanics, aerodynamics and aeromechanics design optimization.

NOMENCLATURE F,G,H = axial, tangential and radial flux vector n = normal direction of mesh cell surface NF = index of harmonics u,v,w = axial, tangential and radial flow velocities S = source term T = time U = conservative variable vector V = viscous terms ρ = fluid density τ = viscous stress components ω = angular frequency

Subscripts k = unsteady disturbance index x, θ, r = cylindrical polar co-ordinates Superscripts __ = time–averaged ′ = unsteady perturbation ∼ = complex harmonic amplitude

INTRODUCTION To consider aero thermal performance and mechanical

integrity at the same time in the design process is highly demanded due to the fact that an ‘aerodynamic optimum’ may not satisfy mechanical and aeromechanical criteria. Thus, an aerodynamics only design optimization might lead to considerable time delay and extra costs in the blade redesign cycles. On the other hand, multi-stage effects on both aerodynamics and aeromechanics have been identified as significant in gas-turbines. The current and future designs all follow the trend for higher performance and more compact structures. Increased aero-thermal loading of each blade row would naturally lead to intensified interactions between adjacent rows with ever reducing intra-row gap spacing. The impacts of blade rows interaction would not only influence aero-thermal performance, but also blade mechanical integrity through flow induced vibrations (flutter or forced response). However, so far, most design optimization systems focus on aerodynamics performance for either isolated blade row [1][2][3] or steady flow multi-row environment using the conventional mixing-plane model [4~7]. The difficulty of integration of aero thermal performance design optimization and aeromechanical design optimization in the multistage environment lies on the fact that the performance prediction

1 Copyright © 2006 by ASME

and the aeromechanical analysis are very often on different platforms using different software with different data structure. Further more, aeromechanical analysis could be much more time consuming than the aerodynamics simulation as in a typical flutter analysis, several vibration modes at various flow conditions have to be examined. A fully integrated design optimization system involved with both components in the multistage environment could be practically infeasible.

Though design optimization systems differ in various aspects, geometry parametrization, flow solver and optimizer are the most common elements. The challenge for the geometry parametrization is to provide accurate and flexible representations by using as few parameters as possible so that the effort of optimization could be reduced. 3-D turbomachinery blades can be described by B-spline construction [5], Bezier-patches representation [8] or Tensor-product Bezier surface (Hoschek and Lasser [9], Arnone et al. [10]). In either approach, at least 20 parameters are needed for accurate description of each span wise section. Therefore more than 100 parameters could be involved in the fully 3-D geometry representation. In our current work, geometry perturbations are represented by ‘aero mode shape’, which is evolved from blade vibration mode shape but with zero frequency. By using such kind aerodynamic mode shape, the design parameters could be largely reduced to a few most effective modes. However, there is always a tradeoff between the flexibility of geometry representation and the number of design parameters.

The flow solvers applied to numerical optimization are closely linked to the selection of optimizer. In general, optimization methods can be divided into gradient methods such as Sequential Quadratic Programming (SQP) [5] and non-gradient methods, e.g. Genetic Algorithm [8][10]. Non-gradient methods have the ability of finding the global optimal while gradient methods are relatively cheap. However, the number of sensitivity equations is proportional to the number of design parameters. Thus solving sensitivity equations is very time consuming when the number of design parameters is large. Implementation of the adjoint method [11] in sensitivity analysis could avoid this problem by solving adjoint equations which are independent of the number of design parameters. But the derivation of adjoint equations and its corresponding boundary conditions is never an easy job as it closely linked with specific objective functions. In practice, the Response Surface Method (RSM) and Design of Experiment (DOE) are often coupled with either gradient methods or non-gradient methods to reduce computational efforts.

As a compromise between fully integrated aerodynamics aeromechanics design optimization and aerodynamics only optimization, an aeromechanical approach for aerodynamics design optimization with consideration of aeromechanical constraints using harmonic perturbation analysis is pursued in the current study. The harmonic methods have been developed and successfully applied for flutter and forced response analysis [12][13] and blade rows interaction problems [14]. Therefore the same solver can be used for both aerodynamics performance prediction and aeromechanical analysis. Furthermore, the harmonic method can solve unsteady multi-row interaction problems much faster than conventional time marching methods. It has the potential to be applied to multistage design optimization problems. Compared to

conventional gradient methods, the current method doesn’t need to derive and solve separate gradient equations, but it is more accurate than the finite difference approach for gradient calculation as it separated perturbations from the mean flow. The solution of harmonic perturbations can be utilized as gradients of flow variables though it is not necessary to solve the whole harmonic for steady state optimizations. Meanwhile, ‘aerodynamic mode shape’ is adopted to describe blade geometry deformation, which simplified the parametrization procedure and reduced the number of design parameters. An additional advantage of using aerodynamic modes is that there is no need for meshing individual design candidate in each optimization loop, which could save some efforts in interference with the meshing package. Requirement of mechanical and aeromechanical integrity is considered as constraints of the optimization problem.

AERODYNAMIC MODE For the convenience of using the same methodology for

both aeromechanical analysis and aerodynamic optimization, ‘aerodynamic mode shapes’ are introduced to describe 3D blade geometry deformation. The conventional 3-D design features such as sweep and lean are effectively equivalent to ‘the first bending mode’, and the compound lean is equivalent to ‘the second bending mode’ as shown on Fig. 1. Re-stagger of blade sections in span wise direction could be simulated by ‘the first torsion mode’. These aerodynamic modes can be defined section by section or point by point as the result of FE model analysis. For each mode, the modal amplitude is the design parameter which will scale the geometry deformation of each mesh point. As the mode shape of each individual point is flexible, more complicated geometry deformation, e.g. change of camber line and thickness can also be described point by point and again the corresponding modal amplitude will scale the local deformation.

The difference between the aerodynamic mode shape and typical blade vibration mode shape is that these aerodynamic modes have zero frequency and zero inter blade phase angle, but with finite amplitude which represents the blade geometry deformation. By using aerodynamic mode shape, conventional sensitivity analysis of gradient methods could be replaced by aerodynamic mode analysis, which is the same as the aeromechanical analysis but with different mode shape. Instead of getting unsteady flow field induced by blade vibration in the aeromechanical analysis, aerodynamic mode analysis gives perturbations of flow field due to the geometry deformation, which is equivalent to the gradient of flow variables. This aeromechanical approach not only avoids the complexity of deriving and solving sensitivity equations, but also enables aerodynamics performance design optimizations and aeromechanical analysis to be carried out in a closely coupled manner using the same solver.

FLOW SOLVER The flow solver adopted here is based on the linear

harmonic method [14][15]. In this method, an unsteady flow variable can be decomposed into a time-averaged part and an unsteady perturbation, e.g.,

UUU ′+= (1)

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)eU~eU~()t,r,,x(U tik

N

1k

tik k

Fk ω−

−=

ω∑ +=θ′ (2)

where kU~ and kU~ − are a pair of complex conjugates and NF is the number of harmonics for the disturbance with given frequency ωk. Substituting the above expression for the conservative variables into the integral form of the unsteady Navier-Stokes equation and time-averaging them, the resultant time-averaged equation and harmonic equations are given as

∫∫ ⋅+++∫∫∫ ⋅=

∫∫ ⋅+−+

δθθ

δ

δθ

Arrxx

Vi

Armgx

dA]nVnVnV[dVS

dA]nHn)vUG(nF[

(3)

),,,,2,1(

]~~~[)~(

]~)~~(~[~

F

Akrrxx

Vki

Arkmgkkxk

Vk

Nk

dAnVnVnVdVS

dAnHnvUGnFdVUi

⋅=

⋅+++⋅=

⋅+−++⋅⋅−

∫∫∫∫∫

∫∫∫∫∫

δθθ

δ

δθ

δ

ω

(4)

Fig. 2 shows the diagram of the integrated optimization system. It starts with a baseline design and a few identified aero modes which are sensitive to the objective functions. The aerodynamic perturbations of each mode can be found by harmonic analysis of each individual mode shape. At the same time, a number of design scenarios are constructed by superposition of all the aero modes with a multiplier of the mode amplitude. Based on linear assumption of perturbations of each individual mode (which is the same for any sensitivity analysis), the objective function of each reconstructed design scenario can be evaluated by superimposing perturbations with the same multiplier used for design scenario construction. In order to check mechanical validity, FE analysis is carried out for each design scenario to find out its maximum stress level as well as vibration characteristics. A direct search is performed here to find out the best of the constructed designs within the constrained design space. The direct search is well suitable for cases with a few design parameters. Also the direct search has the capability to jump over local optimums where conventional gradient based optimizers could be trapped in.

These governing equations are discretized in space using the cell-centred finite volume scheme, together with the blended 2nd and 4th order artificial dissipation to damp numerical oscillations. The time-averaged equation as well as the harmonic equations are solved in a domain consisting of one passage in each row by using the 4-stage Runge-Kutta time marching scheme, accelerated by a time-consistent multi-grid technique (He, 2000[16]) or conventional multi-grid with local time stepping.

On solid blade/endwall surfaces, the log-law is applied to determine the surface shear stress and the tangential velocity is left to slip. Both 1-D and quasi-3D non-reflective boundary conditions are available to be applied to the harmonic solution at both the inlet and the exit.

Now the linear and nonlinear harmonic perturbations of both aerodynamic modes and aeromechanical modes can be solved using the same solver with different options.

MECHANICAL AND AEROMECHANICAL INTEGRITY A typical blade design procedure starts with aerodynamics

and performance design with mechanical design constraints. Aeromechanics analysis as well as mechanical analysis must be conducted after aerodynamics design to examine if it is mechanically sound. The main drawback of such a procedure is that a good aerodynamics design may not satisfy mechanical and aeromechanical requirement. Therefore aerodynamics redesign needs to be taken to satisfy requirements for mechanical integrity. To reduce the time and cost in aerodynamics redesign and to minimize the number of design iterations, mechanical and aeromechanical integrity requirement can be considered as constraints in the design optimization procedure. Here, mechanical and aeromechanical constraints are considered in two stages during the optimization process. First of all, the static stress level of each design scenario is evaluated by using FE analysis software ANSYS and the maximum stress level has been constrained according to the Goodman Diagram. By using moving grid technique, there is no need of re-meshing each design scenario for the

static stress analysis. Therefore it is a very fast process. At the mean time, mode analysis is carried out so that all the vibration mode shapes and their corresponding natural frequencies can be found. If only the reduced frequency should be controlled for flutter free design, these frequencies can be constrained. At the second stage, when a temporal optimized design has been found, flutter and/or forced response analysis will be conducted to find out the exact aerodynamic damping value and forced response level. The reason for carrying out detailed damping evaluation is that the reduce frequency is not sufficient to rule out flutter risk. This approach has the advantage that the number of calls to forced response/flutter analysis is minimal as it is relatively more time consuming than the aerodynamics analysis.

OPTIMIZATION SYSTEM

An aeromechanical analysis is then called for flutter and forced response analysis to check if the found optimal design satisfies aeromechanical constraints. If the found optimal design doesn’t meet aeromechanical criteria, the system will step back to the search subroutine to find out the next optimal which also satisfies all the aerodynamics and mechanical constraints. This local loop is continuously performed until the sound aeromechanical design is found. The design loop is finally closed by updating the baseline design with the found optimal which is still not the maximum optimal, otherwise the loop will stop and output the maximum optimal.

DESIGN PRACTISE The optimization case considered here is to redesign

NASA rotor-67, which is a low aspect ratio transonic axial flow fan rotor. The rotor design speed is 16043RPM and it has 22 blades. The predicted design point pressure ratio is 1.72 at a mass flow rate of 34.07 kg/s. The Reynolds number based on the mid-span chord length and the inlet free stream velocity is 1.0E6.

The objective function of this design optimization problem is chosen to be the efficiency at design mass flow rate point. Two 3-D design features, sweep and compound lean, have been explored simultaneously with the following constraints: Geometry constraints:

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The maximal displacement of the geometry in each direction should be constrained. For example, the axial displacement of the blade is limited by the spacing between adjacent rows. Here, we assume the following constraints. ∆x < 50% tip chord; ∆θ < 50% pitch Performance constraints:

To achieve the design target, design mass flow rate and design pressure ratio should be kept as close as possible to the original values. %5.0

|| <teMassFlowRaDesignteMassFlowRaδ

%5.0ressure |Pr| <RatioPDesign

oessureRatiδ

Mechanical integrity: The maximal stress level for mechanical integrity can be

determined by looking at the Goodman diagram with the material property. Here we assume titanium blade and the stress is limited as, Maximum static stress < 800 M Pa. Aeromechanical constraint: Flutter safe aerodynamic damping > 0.5% (Log dec)

Fig. 3 shows the mesh distribution in a meridional plane and a span wise section respectively. 110×35×29 meshes in axial direction, pitch wise direction and radial direction are used in the current study. The Mach contours at 90% span section in comparison with the experimental data are plotted on Fig. 4, which shows satisfactory numerical accuracy of the present prediction.

Geometry change and its corresponding effects The geometry change between NASA rotor 67 and the

optimized design is shown on Fig. 5, where both 3D shape change and 2D section changes are plotted. It can be seen that the optimized design is the combination of forward sweep and backward compound lean (the suction surface leans toward the pressure surface). The effects of compound lean have been argued by many researchers [17][18]. Conventional theory based on subsonic turbine design practice suggests that the forward compound lean reduces loading on both root and tip sections and increases loading on the mid-span section. Therefore, high loss generated near end walls are driven towards the middle passage and mixed with main flow, which will reduce the overall loss generation. However, more recent studies suggest that it could be case dependent [19]. In the present design practice, the effect of compound lean is not significant as it can be seen by the loading distribution shown on Fig. 6. The surface pressure distribution on 25%, 50% and 85% span sections are plotted on Fig. 6. First of all, the overall loading hasn’t been changed between two designs. Secondly, it is observed that at the mid span section and the near hub section where the passage shock was moved forward and the strength has been reduced. This phenomenon is largely due to the forward sweep effect and it can also be identified by looking at the pressure contours distribution on both the pressure surface and the suction surface as shown on Fig. 7. The suction surface signature of the passage shock wave was broken at about 80-85% span (Fig 7b) and the shock has been moved forward to the leading edge, while on the pressure surface it is weakened.

The overall loss generation inside the blade passage is then calculated to show the contribution of different parts. The spanwise distribution of the axial and pitchwise mass averaged

loss and the axial distribution of the spanwise and pitchwise mass averaged loss are plotted on Fig. 8. Compared to the original design, loss generation from the leading edge to the mid chord part is almost the same. But the loss generation from the mid chord afterward is consistently lower than the original design. In span wise direction, loss generation in the mid-span region didn’t change very much which confirms that the compound lean effects is small. This might be due to the fact that though the backward compound lean is applied, the resultant geometry is still nearly straight. However, loss generation above 70% span height is consistently lower in the optimized design. This is due to the weakening of passage shock as well as forward sweep effects on the tip leakage vortex, which can be identified by the iso-surfaces of the loss distribution near the tip region shown on Fig. 9. Compared to NASA 67, the loss core of the optimized design, which is located on the suction side about 70% downstream from the leading edge, is smaller and the overall high loss region is confined in a shorter area.

Performance evaluation& mechanical integrity Table 1 lists the comparison of performance parameters

between NASA rotor 67 and the optimized design produced by the current design optimization system. A 0.4% increase of efficiency has been achieved at the design condition while satisfying all constraints. To verify the off design performance of the optimized design, a performance characteristic calculation has been carried out. Fig. 10 shows the comparison of predicted fan characteristic curve with the experiment data of NASA rotor 67. The predicted performance agrees with the experiment data very well, which confirms the performance prediction capability of the current numerical method. Compared to NASA rotor 67, the optimized design has higher efficiency when reducing back pressure towards the choke condition and the choke mass flow rate has been increased. When the back pressure increased towards stall, the efficiency and pressure ratio are almost the same as the NASA rotor 67 but the stall margin has been improved. This is mainly due to the forward sweep effect which was observed previously by Denton and Xu [18].

The mechanical and aeromechanical integrity have been examined along the design optimization procedure. Comparison of the static stress distribution is plotted on Fig. 11, where the maximum stress has been shifted from the hub leading edge to the mid chord. Also the high stress area is concentrated in the centre of the optimized blade which is corresponding to the compound lean. The maximum static stress level has been increased by ~33% though it is still within the safety threshold. This indicates that further improvement of aerodynamics performance has been prevented by mechanical constraints.

Flutter stability analysis of the NASA rotor 67 shows that the first flap mode at 2 nodal diameters in a forward traveling wave mode is least stable. Thus the aerodynamic damping of the optimized design of this mode has been examined and it is slightly higher than the original design. It is interesting to notice that though the natural frequency of the first five modes of the optimized design are consistently lower than NASA67 by 1%~4%, the aerodynamic damping values are not necessarily lower than the original design. A forced response analysis should be carried out with both damping and forcing calculation at the engine crossing point flow condition. There is no practical data available for this task to be conducted though

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the system is ready for performing such a task. Nevertheless, the current finding still shows the necessity for more concurrent integration of aerodynamics and aeromechanics design optimization.

CONCLUSIONS A 3-D design optimization method for aerodynamics

performance optimization with consideration of mechanical and aeromechanical integrity has been developed. The developed system uses an aeromechanical approach with ‘aerodynamic mode’ describing geometry deformation and the harmonic perturbation method has been adopted as the gradient solver. The redesign practice of NASA rotor-67 shows that the present optimization approach can achieve a 0.4% increase in peak efficiency while all the aerodynamics and aeromechanical constraints are well satisfied. The loss reduction in the current design practice seems caused by the weakening of passage shock and the reducing of loss core near the tip of the suction surface. Flutter analysis shows the minimal damping value of the first flap mode is not decreased though the vibration frequency is reduced. Nevertheless, the maximum blade static stress has been increased by 33%. The present case study and results highlight the need for more concurrent mechanic, aerodynamic and aeromechanic design optimizations.

REFERENCES [1] Oyama, A., Liou, M-S, Obayashi, S., 2003, “Transonic

Axial-Flow Blade Shape Optimization Using Evolutionary Algorithm and Three-Dimensional Navier-Stokes Solver”, AIAA paper 2002-5642

[2] Buche, D., Guidati, G. and Stoll, P., 2003, “Automated Design Optimization of Compressor Blades for Stationary, Large-Scale Turbomachinery”, ASME Paper GT2003-38421.

[3] Nagel, M.G. and Baier R. D., 2003, “Experimentally Verified Numerical Optimization of a 3D-parametrised Turbine Vane with Non-Axisymmetric End Walls”, ASME Paper GT2003-38624.

[4] Burguburu, S., Toussaint, C., Bonhomme., and Leroy, G., 2003, “Numerical Optimization of Turbomachinery Bladings”, ASME Paper GT2003-38310.

[5] Kammerer, S., Mayer, J.F., Paffrath, M., Wever, U. and Jung, A. R., 2003, “Three-Dimensional Optimization of Turbomachinery Bladings Using Sensitivity Analysis”, ASME Paper GT2003-38037.

[6] Gallimore, S. J., Bolger, J. J., Cumpsty, N. A., Taylor, M. J., Wright, P. I. and Place J. M. M., 2002, “The Use of Sweep and Dihedral in Multistage Axial Flow Compressor Blading – Parts 1: University Research and Methods Development”, ASME J. of Turbomachinery, 124, pp521-532.

[7] Sieverding, F., Ribi, B., Casey, M., and Meyer, M., 2003, “Design of Industrial Axial Compressor Blade Sections For Optimal Range and Performance”, ASME Paper GT2003-38036

[8] Casey, M.V., 1983, “A Computational Geometry for the Blades and Internal Flow Channels of Centrifugal Compressors”, ASME Journal of Engineering for Power, Vol.105, pp 288-295

[9] Hoschek, J., and Lasser, D., 1993, “Fundamentals of Computer Aided Geometric Design,” A K Peters, ltd, Wellesley, MA, USA.

[10] Arnone, A., Bonaiuti, D., Focacci, A., Pacciani, R., Greco, A.S.D., and Spano, E., 2004, “Parametric Optimization of a High-lift Turbine Vane,” ASME Paper GT2004-54308.

[11] Jameson, A., and Kim, S., 2003, “Reduction of the Adjoint Gradient Formula for Aerodynamic Shape Optimization Problems,”, AIAA Journal, Vol.41, No.11, pp.2114-2123.

[12] Moffatt, S., Ning, W., Li, Y.S., Wells, R. and He, L., 2003, “Blade Forced Response Prediction for Industrial Gas Turbines”, ASME Paper GT2003-38640, to be appear on J. of Power and Propulsion.

[13] Moffatt, S. and He., L., 2005, “On Decoupled and Fully-Coupled Methods for Blade Forced Response Prediction”, J. of Fluids and Structures, Vol 20, No. 2, pp217-234, Feb, 2005.

[14] Ning, W., Li, Y.S., Wells, R. 2004, “Predicting Bladerow Interactions Using a Multi-stage Time-Linearized Navier-Stokes Solver”, ASME J. of Turbomachinery, 125, pp.25-32.

[15] He, L., Chen, T., Wells, R.G., Li, Y.S., and Ning, W., 2002, “Analysis of rotor-rotor and stator-stator interferences in multi-stage turbomachines,” ASME J. of Turbomach., 124, pp. 564-571.

[16] He, L., 2000, "3D Navier-Stokes Analysis of Rotor-Stator Interactions in Axial-flow Turbines", Proc. IMech.E, Part-A, Journal of Power and Energy, Vol.214, pp13-22, Jan. 2000.

[17] Han, W.J., Wang Z.Q., Tan, C.Q., Shi, H. and Zhou M.C., 1994, “Effects of leaning and curving of blades with high turning angles on the aerodynamic characteristics of turbine rectangular cascades”, ASME J. of Turbomach., 116, pp.417-424

[18] Denton, J. D. and Xu, L., 2002, “The effects of lean and sweep on transonic fan performance”, ASME Paper GT-2002-30327

[19] Bagshaw, D.A., Ingram, G.L. and Gregory-Smith, D.G., 2005, “An experimental study of reverse compound lean in a linear turbine cascade”, ImechE Journal of Power and Energy, Part A, Vol. 219, pp.443-449

5 Copyright © 2006 by ASME

Table 1 Comparison between NASA rotor 67 and the optimized design Mass Flow Pressure Ratio Efficiency Static Stress

NASA 67 34.07 kg/s 1.7246 92.01% 493 MPa Optimized Design 34.05kg/s 1.7244 92.41% 654 MPa

Change 0.06% 0.01% 0.40% 32.6%

Table 2 Flutter analysis Mode No. Frequency (Hz) Aero-damping, ND=2

(Log_dec) NASA67 Optimized

design NASA67 Optimized

design 1 599.181 592.170 1.21% 1.41% 2 1303.717 1299.516 3 1910.860 1818.677 4 2705.744 2659.112 5 3093.419 2973.350

Tip

HubAxial direction Circumferential direction

Sweep Lean Compound Lean

Fig. 1 Description of the aerodynamic mode

LOOPStart

Base Flow Cal.

LoopN=1,N_DESP

Gradient Cal.

ScenariosReconstruction

Stress & Freq.Assess

OptimalSearch

Aero-damping Cal.Forced Resp. Cal.

Max Optimal?

Return

AeroMechanicalValid?

N

Y

Y

Update BaselineDesign

N

Nonlinear steady flow

Linear perturbation solutions

Reconstruction from perturbed design parameters

FE mode analysis (ANSYS)

Aeromechanics analysis

Fig. 2 Flow chart of the optimization system

6 Copyright © 2006 by ASME

Fig. 3 Mesh distribution in a span wise section and the meridional plane

1.35

1.35

0.810.93

1.42

Fig. 4 Mach contours comparison at 90% span section (left: Calc; right: Exp)

NASA rotor 67Optimized blade

Fig. 5a 3D blade shape comparison between NASA67 and the optimized design

7 Copyright © 2006 by ASME

NASA67Optimized Design

25% Span

85% Span

50% SpanPS SS

Fig. 5b Blade profiles at different radial sections and an axial view at mid chord

0 0.25 0.5 0.75 1

0.9

1

1.1

1.2

1.3

1.4NASA67Optimized Design

X/C

Cp

0 0.25 0.5 0.75 10.8

0.9

1

1.1

1.2

1.3

1.4NASA67Optimized Design

X/C

Cp

0 0.25 0.5 0.75 1

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

NASA67Optimized Design

X/C

Cp

(a) 25% span (b) 50% span (c) 85% span

Fig. 6 Surface pressure distribution on different span wise sections

a) Pressure surface pressure contours b) Suction surface pressure contours

Fig. 7 Comparison of static pressure on pressure and suction surfaces

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0.025 0.05 0.075 0.10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Optimized designNASA 67

Loss

R/Span

0 1 2

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Optimized designNASA 67

X/C

Loss

T.E.L.E.

(a) Spanwise distribution of axial and pitchwise averaged loss (b) Axial distribution of pitchwise and spanwise averaged loss

Fig. 8 Mass averaged loss generation in the passage

NASA67

OptimizedDesign

Leadingedge

Trailingedge

Loss Core(0.23-0.5)

Trailingedge

Leadingedge

Fig. 9 Iso-surfaces of passage loss distribution

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Flow rate

Effi

cien

cy

29 30 31 32 33 34 35

85

86

87

88

89

90

91

92

93 NASA 67Optimized designExperiment

Flow rate

Effi

cien

cy

29 30 31 32 33 3485

86

87

88

89

90

91

92

93 NASA67Lean+Sweep

Flow rate

Pre

ssur

eR

atio

29 30 31 32 33 34 351.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

1.8

1.85

1.9 NASA67Lean+Sweep

(a) Efficiency-Mass flow curve (b) Pressure-Mass flow curve

Fig. 10 Fan performance characteristic curves

Original Design Optimized design

Max Stress

Fig. 11 Blade static stress contours

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