This document describes research on optimizing the design of a natural laminar airfoil using computational fluid dynamics (CFD). The goal was to minimize drag for a symmetric airfoil and maximize endurance by increasing lift for a cambered airfoil. CFD analysis using a k-ω SST transitional model was validated. An optimization framework using gradient-based algorithms and NURBS shape functions was developed to modify 10 control points defining the airfoil. For the symmetric airfoil, optimizing delayed the transition point towards the trailing edge, reducing drag. For the cambered airfoil, optimizing increased the pressure coefficient area to boost lift within the lift constraint. Reasonable designs were achieved but further improvements to the CFD

1. Design Optimization of Natural Laminar Airfoil지도 교수 조창열연구ㆍ발표자 김근우, 김동춘, 김현준2008. 12. 12. (Fri)

2. Table of ContentsObjectiveResearch TechniquesValidation of Flow SolverOptimization FrameworkFormulation of Optimization ProblemDesign Optimization ResultsConclusion

3. 1. ObjectiveResearch Objective○ Design Optimization of 2-D Natural Laminar Airfoil5 Reasons to Optimize ○ Needs Long Endurance Performance ○ Needs High Lift Coefficient ○ Low Reynolds No.-Transitional Flow Flight ○ Test and Validate CFD Code ○ Establish Optimization Framework

4. 2. Research Techniques (1)CFD Analysis of Low Reynolds No. Transitional Flow○ Use k-ω SST TRANSITIONAL MODEL○ Use FLUENT for Flexibility and ReliabilityAerodynamic Design Optimization of Airfoils○ Setup of Design Framework○ Validation of CFD Analysis○ Formulation of Optimization Problem○ Design Optimization

5. 2. Research Techniques (2)Optimization Techniques○ Optimization Algorithms : GBOM, MMFD○ Numerical Optimization Code : DOT○ Mathematical Formulation of Function -> Use Taylor Series ExpansionNetwork-Distributed Computation○ Use Network-Distributed Computation○ TCP/IP Network Environment -> O/S Independent For Optimization

6. 2. Research Techniques (3)Airfoil Shape Design Method○ Use NURBS Shape Function -> Excellent in Local Control of Shape ○ Use CATIA for Shape Export -> IGES, STEP, STL, 3DXML…..NET Framework-Based Programming Model○ Easy and Powerful Rapid Programming Model○ O/S Independent, Can Be Used in Handheld Devices○ Ensure Portability for Various Programming Language

7. 3. Validation of Flow Solver (1)Testing Low Reynolds No. Transitional Flow○ Key Features of Design -> Low Reynolds No. Flow Includes Transition -> Needs High Lift Coefficient -> Used for High Aspect Ratio Wing ○ NACA 653-018 Airfoil ○ Low Reynolds. No Flow Analysis ○ RANS+LRN K-ω Model ○ Boundary Layer Clustered Grid System ○ 65 X 370 CellsGrid System of NACA 653-018

8. 3. Validation of Flow Solver (2)Simulating Separation Bubble○ K-ω SST Transitional Model Simulates Separation Bubble Well

9. 3. Validation of Flow Solver (3)Testing Low Reynolds No. Transitional Flow○ Rec = 3.0 X 106 / Chord Length = 90 in.○ Pressure-Based Solver / K-ω SST Transitional Model ○ Turbulent Intensity / Length Scale -> NASA Langley Low Turbulence Wind Tunnel

10. 4. Optimization Framework(1)Components of Optimization Framework○ Easy, Flexible, Reliable and Robust Design Optimization Framework

11. 4. Optimization Framework(2)Optimization Framework Workflow

12. 5. Formulation of Problem(1)Design Condition○ Angle of Attack : 4.2˚ / REC = 1.56 X 106○ Minimum Lift Coefficient : CL = 1.28 (Cambered Airfoil)Design Problem○ Initial Airfoil Design : NACA0018○ Objective Function -> Minimize Drag Coefficient (Symmetric Airfoil) -> Maximize Endurance Parameter (Cambered Airfoil)○ Constraints -> Subject to CL(X) > 1.28 (Cambered Airfoil) A(X) = A0 (Area of Airfoil)

13. 5. Formulation of Problem(2)NURBS Shape Function○ Excellent in Local Shape Modification, More Smooth Curve○ Reduce Design Variable -> Reduce Computational Cost ○ Use 4th Order Blending Function / Use 10 Control Points43215968710

14. 5. Formulation of Problem(2)Optimization Algorithm○ Gradient Based Optimization Method (GBOM) Gradient-Based Optimization Method can be easily programmed and useful if design space is not distorted. -> Optimizer does not know what kind of problem it is solving. -> Before optimization process starts, it is necessary to check if design space is distorted or not.○ Method of Modified Feasible Direction Search (MMFD) Method of Modified Feasible Direction needs two stage of optimization. -> Finding search direction to find feasible region in design space. -> One-dimensional search determines how design variable can be far from the initial design.

15. 6. Design Optimization Results (1)Symmetric Airfoil Optimization (Drag Minimization)○ Transition position moved towards trailing edge.○ Delaying transition can reduce drag.○ That is, drag could be reduced by maintain more laminar flow region.

16. 6. Design Optimization Results (2)Cambered Airfoil Design (Endurance Param. Maximization)○ Area of pressure coefficient is wider than initial design. Cl is increased.○ Drag coefficient increased too. But optimizer limits increasing of drag coefficient effectively.

17. 6. Design Optimization Results (3)Cambered Airfoil Design (Endurance Param. Maximization)

18. 7. Conclusion ○ In a view point of speed of optimization, approximate concepts for numerical optimization is competitive method than other algorithm like RSM, GA, etc... ○ Reasonable design results we can get with -> Drag Minimized for Symmetric Airfoil -> Endurance Parameter Maximized for Cambered Airfoil ○ By using NURBS for shape design, we could reduce design variables and calculation cost. ○ By using LRN K-ω SST Transitional Model, low reynolds no. flow field and transitional phenomena simulate well. But flow filed includes transition, there may be separation bubble near the wall. But Fluent doesn’t predict this phenomenon sufficiently. Fluctuation of solution delays finishing calculation. ○ Codes that supports automation API(application programming interface) or internal script can be adopted for this framework.

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