2018/3/11 Airfoil Parameterization-(2) 园上声天大学 Universal Shape Parameterization 国上清大学 where y=x/c,=3/c,and 5 =AZre/c. -Shape function B-Splime is the only mathematical term that will produce a round nose (1-)is the term to provide a sharp trailing edge rprovides control over trailing edge thiekness rngthe shape beteenLE shape function =ooo(x)+∑fr Geometry Parameterization 圈上活大坐 Grid generation 国上大坐 Grids can either be structured or unstructured ignt an -Structured hexahedral -Unstructured-tetrahedral Solutions methods Depend upon type of discretization structured Finite volume or finite element:structured or unstructured ·Applications -Thin boundary layers best resolved with highly-stretched structured grids Unstructured grids useful for complex geometries r to read -Unstructured grids permit automatic adaptive refinement based on the malih-Fideity pressure gradient,or regions of interest 》 oernan enn ng Mesh Generation-examples 圈上大坐 Flow field around airfoil 圆上清充大些 Flow around SC(2)0612 airfoil simulated using FLUENT y(F6 Shape Optimization using Orthogonal Parameterization 122018/3/11 12 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Airfoil Parameterization –(2) © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Universal Shape Parameterization is the only mathematical term that will produce a round nose is the term to provide a sharp trailing edge provides control over trailing edge thickness a general function controlling the shape between LE and TE, shape function Shape function © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Geometry Parameterization • Desired features – Well-behaved and produce smooth shapes – Mathematically efficient and numerically stable – Requires relative few variables – Allows specification of physical parameters such as leading edge radius, boat-tail angle – Easy control of design changes – CAD-friendly, easy implementation of automation – Availability of sensitivity information • Various parameterization methods – Use of physical parameters – Interpolation through points – Non-Uniform Rational B-Spline (NURBS) – Linear combination of analytical functions – Linear combination of numerical functions • Papers to read – “Survey of Shape Parameterization Techniques for High-Fidelity Multidisciplinary Shape Optimization”, AIAA Journal, Vol.39, No.5, 2001. – “Universal Parametric Geometry Representation Method”, Journal of Aircraft, Vol.45, No.1, 2008. – “A Rapid Geometry Engine for Preliminary Aircraft Design”, AIAA 2006-929. 69 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Grid generation • Grids can either be structured or unstructured – Structured - hexahedral – Unstructured – tetrahedral • Solutions methods Depend upon type of discretization – Finite differences: structured – Finite volume or finite element: structured or unstructured • Applications – Thin boundary layers best resolved with highly-stretched structured grids – Unstructured grids useful for complex geometries – Unstructured grids permit automatic adaptive refinement based on the pressure gradient, or regions of interest 70 © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Mesh Generation – examples Structured Grid around Airfoil Unstructured Surface Grid for Wing-Body (F6 Geometry) © Shanghai Jiao Tong University – Dr. Wenbin Song School of Aeronautics and Astronautics Flow field around airfoil 72 Flow around SC(2)0612 airfoil simulated using FLUENT Shape Optimization using Orthogonal Parameterization