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Shape Representation Wahid Ghaly Mechanical and Industrial Engineering NATO RTO AVT-167 Lecture Series October 26-27, 2009 Montreal, Canada.

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Presentation on theme: "Shape Representation Wahid Ghaly Mechanical and Industrial Engineering NATO RTO AVT-167 Lecture Series October 26-27, 2009 Montreal, Canada."— Presentation transcript:

1 Shape Representation Wahid Ghaly Mechanical and Industrial Engineering NATO RTO AVT-167 Lecture Series October 26-27, 2009 Montreal, Canada

2 NATO RTO AVT Outline Objectives and context Shape representation/parameterization options Compressor and turbine airfoil representation Turbine stage representation in 3D flow Summary

3 NATO RTO AVT Shape Representation Accurate, flexible and robust shape representation Most suitable representation for a given shape Least number of shape parameters that are directly related to the design parameters and are used as optimization variables Preferably a CAD-native parameterization Can the geometric representation make the optimization approach more efficient? Can it reduce the design problem complexity?

4 NATO RTO AVT Intended applications Component level optimization, e.g. turbine or compressor Single and multiple blade rows, disciplines, objectives, single and multipoint Airfoils (2D) and blades (3D) profiles Global - low fidelity - representation Local/Global high fidelity representation

5 NATO RTO AVT Low and high fidelity representations Global - low fidelity – representation –Shape is represented by a few low order polynomials –Change in any point on the curve affects the shape globally Local/Global high fidelity representation –Shape is represented by a continuous curve with e.g. NURBS, B-splines, Bezier curves, …(Note that the 2 nd and 3 rd representations are subsets of NURBS)

6 NATO RTO AVT Global – low fidelity - representation Turbine airfoil is represented by 5 Conic sections

7 NATO RTO AVT Global – low fidelity - model E/TU-4

8 NATO RTO AVT Global/Local high fidelity rep., NURBS –CNURBS curve –P i Control points –w i Weights –N i,p Basis function –p degree of polynomial, (p=2 in this work) –UKnot vector

9 NATO RTO AVT Examples of C 2 Continuity Curves DFVLR VKI ETU-4

10 NATO RTO AVT Shape optimization methodology –Shape representation –Shape representation: Low order - global - representation High order representation, e.g. NURBS, B-Splines, Bezier –Optimization method: Direct: GA, SA Indirect: Gradient/Newton-based, Control Theory-based –Choice and computation of objective function –Choice and computation of objective function: High fidelity simulations (CFD solver of your choice) Low fidelity using a surrogate model (ANN, RBF, wavelets)

11 NATO RTO AVT Compressor airfoils in 2D flow Inviscid transonic caseviscous subsonic cases

12 NATO RTO AVT Geometric description and parameterization The airfoil shape is described by a camber line and a thickness distribution Camber line overall flow turning Thickness structural constraints They are parameterized using a high fidelity NURBS function with 11 control points for camber line, f(x), and 9 for thickness distribution, T(x). Y-coordinates of the control points are used as the design variables (17 points)

13 NATO RTO AVT NACA Transonic compressor redesign Performance map shows ~ 1.7% Original and redesigned compressor airfoils

14 NATO RTO AVT NACA 65 subsonic compressor redesign Performance map shows ~ 7% Range of airfoil profiles explored in the design space Original and redesigned compressor airfoils

15 NATO RTO AVT A turbine airfoil profile in 2D flow Optimization is done successively on two geometric parameterizations: –Starting from a global shape representation of the airfoil using the design parameters, optimization is carried out –The resulting profile is used as input to a high fidelity shape representation so as to refine the profile locally

16 NATO RTO AVT The original turbine airfoil Total pressure loss coeff. = % Adiabatic efficiency = % Pressure ratio (inlet/outlet) =1.518 Inlet flow angle = 57.4 o Exit flow angle = o Corrected mass flow rate = Note that this is a low subsonic turbine airfoil with over 91% adiabatic efficiency

17 NATO RTO AVT Airfoil shape: global representation, MRATD MRATD model: Feature-based representation. By construction, it eliminates infeasible turbine airfoil shapes

18 NATO RTO AVT Global-Shape Aerodynamic Optimization Objectives –Improve efficiency –Maintain or increase pressure ratio Constraints: Keep the same operating point –Same rotor speed, inlet P t, T t, and exit P s (CFD) –Fixed corrected mass flow rate and flow angles (penalty terms added to the objective function) Design variables –All parameters affecting the airfoil SS (6 in all) Original airfoil: ETU turbine profile MRATD (design) parameters 1.Number of blades = 30 2.Radius = m 3.Axial chord C = m 4.Tangential chord = 78.19% 5.Throat = 33.54% 6.Unguided turning = 12 o 7.TE radius = 0.55% 8.Inlet metal angle = 39.4 o 9.Exit metal angle = o 10.SS Inlet wedge angle =15 o 11.PS Inlet wedge angle = 30 o 12.PS Outlet wedge angle =2.5 o 13.Maximum thickness = 26.86% 14.Axial location of maximum thickness = 35% 15.LE ellipse major diameter = 12.61% 16.LE ellipse minor diameter =5.04%

19 NATO RTO AVT Global-Shape Optimal profile (MRATD) 6 design variables = 0.4% Same pressure ratio, reduced mass flow rate and flow angles

20 NATO RTO AVT Original vs. Optimal MRATD parameters MRATD Design parameters OriginalOptimal Tangential chord0.031m m Throat m m Unguided turning12°9.95° SS inlet wedge angle15°14.83° Maximum thickness m0.0122m LE ellipse minor diameter0.002m m

21 NATO RTO AVT Airfoil shape: local refinement, NURBS A close look at the curvature and pressure distributions helps to pinpoint regions where improvements can be made.

22 NATO RTO AVT NURBS optimal vs. MRATD optimal profile Efficiency improved by an additional 0.165%, for the same pressure ratio, reduced mass flow rate and flow angles, using 6 NURBS control points.

23 NATO RTO AVT Turbine blade profiles in 3D flow Geometry representation: 2D Airfoils: MRATD, B-splines and NURBS Hub-to-tip: stacking line going through the 2D airfoils 3D blade shape: obtained by skinning the stacked 2D airfoils, using compatible B-splines

24 NATO RTO AVT CATIA-CFD integration NURBS and B-splines are CAD-native parameterizations can be directly integrated into the CAD system All blade features are extracted and updated into solid model during the optimization process using: –CAD neutral packages, e.g. CARPI from MIT –CATIA Application Program Interface (API) Note: MRATD can be integrated into CAD using e.g. CATIA-API

25 NATO RTO AVT The Stacking Curve (or line)

26 NATO RTO AVT Quadratic Rational Bezier Curve (QRBC)

27 NATO RTO AVT QRBC as Stacking Curve

28 NATO RTO AVT Leaning the Stacking Curve Circumferential Direction

29 NATO RTO AVT Sweeping the Stacking Curve Axial Direction

30 NATO RTO AVT Bowing the Stacking Curve Circumferential Direction

31 NATO RTO AVT Circumferential Plane Meridional Plane Design Variables

32 NATO RTO AVT Design VariableQRBC ParameterSymbol 1. Sweep angleAxial coordinate of P 2 2. Lean angleCircumferential coordinate of P 2 3. Bowing shape in radial direction Radial coordinate of P 1 4. Bowing shape in circumferential direction Circumferential coordinate of P 1 5. Bowing intensityWeight of P 1 w1w1 Design Variables

33 NATO RTO AVT Stator solidity 1.56 Aspect ratio 0.57 Rotor solidity 1.5 Aspect ratio Single Stage Turbine (E/TU3) Low speed subsonic turbine 7800 (rpm) Flow coefficient 0.74 Stage loading 1.93 Stage P.R. = 2 Reaction 31% Re av = 2 Millions

34 NATO RTO AVT Stage Optimization = 1.2% with 5 design variables Stator Rotor s o r o wrwr tt Min Max Original Optimum

35 NATO RTO AVT Summary Geometric representation can improve the efficiency of the optimization approach It can also reduce the design problem complexity by: –reducing the number of design variables –Eliminating infeasible blade profiles It is critical to pick the right representation and the right parameterization for a given shape

36 NATO RTO AVT Thank You


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