Presentation on theme: "Wahid Ghaly Mechanical and Industrial Engineering"— Presentation transcript:
1Wahid Ghaly Mechanical and Industrial Engineering Shape RepresentationWahid GhalyMechanical and Industrial EngineeringNATO RTO AVT-167 Lecture SeriesOctober 26-27, 2009Montreal, Canada
2Outline Objectives and context Shape representation/parameterization optionsCompressor and turbine airfoil representationTurbine stage representation in 3D flowSummary
3Shape RepresentationAccurate, flexible and robust shape representationMost suitable representation for a given shapeLeast number of shape parameters that are directly related to the design parameters and are used as optimization variablesPreferably a CAD-native parameterizationCan the geometric representation make the optimization approach more efficient?Can it reduce the design problem complexity?
4Intended applications Component level optimization, e.g. turbine or compressorSingle and multiple blade rows, disciplines, objectives, single and multipointAirfoils (2D) and blades (3D) profilesGlobal - low fidelity - representationLocal/Global high fidelity representation
5Low and high fidelity representations Global - low fidelity – representationShape is represented by a few low order polynomialsChange in any point on the curve affects the shape globallyLocal/Global high fidelity representationShape is represented by a continuous curve with e.g. NURBS, B-splines, Bezier curves, …(Note that the 2nd and 3rd representations are subsets of NURBS)
6Global – low fidelity - representation Turbine airfoil is represented by 5 Conic sections
10Shape optimization methodology Shape representation:Low order - global - representationHigh order representation, e.g. NURBS, B-Splines, BezierOptimization method:Direct: GA, SAIndirect: Gradient/Newton-based, Control Theory-basedChoice and computation of objective function:High fidelity simulations (CFD solver of your choice)Low fidelity using a surrogate model (ANN, RBF, wavelets)
11Compressor airfoils in 2D flow Inviscid transonic case viscous subsonic cases
12Geometric description and parameterization The airfoil shape is described by a camber line and a thickness distributionCamber line overall flow turningThickness structural constraintsThey 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)
14NACA 65 subsonic compressor redesign Range of airfoil profilesexplored in the design spacePerformance map shows Dh ~ 7%Original and redesignedcompressor airfoils
15A 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 outThe resulting profile is used as input to a high fidelity shape representation so as to refine the profile locally
16The original turbine airfoil Total pressure loss coeff. = %Adiabatic efficiency = %Pressure ratio (inlet/outlet) =1.518Inlet flow angle = 57.4oExit flow angle = oCorrected mass flow rate = 0.191Note that this is a low subsonic turbine airfoil with over 91% adiabatic efficiency
17Airfoil shape: global representation, MRATD MRATD model: Feature-based representation.By construction, it eliminates infeasible turbine airfoil shapes
18Global-Shape Aerodynamic Optimization ObjectivesImprove efficiencyMaintain or increase pressure ratioConstraints: Keep the same operating pointSame rotor speed, inlet Pt, Tt, and exit Ps (CFD)Fixed corrected mass flow rate and flow angles (penalty terms added to the objective function)Design variablesAll parameters affecting the airfoil SS (6 in all)Original airfoil: ETU turbine profileMRATD (design) parametersNumber of blades = 30Radius = mAxial chord C = mTangential chord = 78.19%Throat = 33.54%Unguided turning = 12oTE radius = 0.55%Inlet metal angle = 39.4oExit metal angle = -66.0oSS Inlet wedge angle =15oPS Inlet wedge angle = 30oPS Outlet wedge angle =2.5oMaximum thickness = 26.86%Axial location of maximum thickness = 35%LE ellipse major diameter = 12.61%LE ellipse minor diameter =5.04%
19Global-Shape Optimal profile (MRATD) 6 design variablesDh = 0.4%Same pressure ratio, reduced mass flow rate and flow angles
20Original vs. Optimal MRATD parameters MRATD Design parametersOriginalOptimalTangential chord0.031mmThroatmmUnguided turning12°9.95°SS inlet wedge angle15°14.83°Maximum thicknessm0.0122mLE ellipse minor diameter0.002mm
21Airfoil shape: local refinement, NURBS A close look at the curvature and pressure distributions helps to pinpoint regions where improvements can be made.
22NURBS 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.
23Turbine blade profiles in 3D flow Geometry representation:2D Airfoils: MRATD, B-splines and NURBSHub-to-tip: stacking line going through the 2D airfoils3D blade shape: obtained by skinning the stacked 2D airfoils, using compatible B-splines
24CATIA-CFD integration NURBS and B-splines are CAD-native parameterizations can be directly integrated into the CAD systemAll blade features are extracted and updated into solid model during the optimization process using:CAD neutral packages, e.g. CARPI from MITCATIA Application Program Interface (API)Note: MRATD can be integrated into CAD using e.g. CATIA-API
32Design Variables Design Variable QRBC Parameter Symbol 1. Sweep angle Axial coordinate of P2b2. Lean angleCircumferential coordinate of P2a3. Bowing shape in radial directionRadial coordinate of P1g4. Bowing shape in circumferential directionCircumferential coordinate of P1q5. Bowing intensityWeight of P1w132
34Dh = 1.2% with 5 design variables Stage Optimizationasobsoa robrowrhttMin.-30-15-5-10-Max.10520153Original87.50Optimum-29.5-9.42.2-9.70.0588.56Dh = 1.2% with 5 design variablesStatorRotor34
35SummaryGeometric representation can improve the efficiency of the optimization approachIt can also reduce the design problem complexity by:reducing the number of design variablesEliminating infeasible blade profilesIt is critical to pick the ‘right’ representation and the ‘right’ parameterization for a given shape