Parametric Geometry Model for Design Studies of Tailless Supersonic Aircraft

Morris, Craig C.; Allison, Darcy L.; Schetz, Joseph A.; Kapania, Rakesh K.; Sultan, Cornel

doi:10.2514/1.c032340

Cited by 12 publications

(10 citation statements)

References 5 publications

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“…T he Class-Shape Transformation (CST) parametrization method 1, 2, 3 has become an increasingly popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. 4,5,6,7 CST parametrization can be used to represent a wide variety of two-and threedimensional shapes with a modest number of parameters, and it provides built-in design variables for use in shape optimization. The use of analytical functions means that the surface representation is smooth and continuous to as fine a degree as desired, without the need for interpolation between discrete points.…”

Section: Nomenclaturementioning

confidence: 99%

“…In several studies, the planform shape has been specified using simple linear parametrizations for a known class of wing (e.g. a simple subsonic transport wing 9 or a cranked delta wing 6 ). The planform shape has also been specified by defining the chord and leading-edge x and z coordinates using additional analytical functions of η = 2y/b.…”

Section: Nomenclaturementioning

confidence: 99%

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Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

Olson

2015

16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two-and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parametrizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

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Section: Nomenclaturementioning

confidence: 99%

Section: Nomenclaturementioning

confidence: 99%

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

Olson

2015

16th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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“…Morris et al (2014), Nejat et al (2014), and Su et al (2015) have showed the shape of curves for different values of N 1 and N 2 . They also claimed that when describing an airfoil, the values we normally use are N 1 =0.5 and N 2 =1.…”

Section: Parameterization Methodsmentioning

confidence: 99%

A study of airfoil parameterization, modeling, and optimization based on the computational fluid dynamics method

Zhang

Huang

Wang

et al. 2016

J. Zhejiang Univ. Sci. A

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An excellent airfoil with a high lift-to-drag ratio may decrease oil consumption and enhance the voyage. Based on NACA 0012, an improved airfoil is explored in this paper. The class/shape function transformation has been proved to be a good method for airfoil parameterization, and in this paper it is modified to improve imitation accuracy. The computational fluid dynamics method is applied to obtain numerically the aerodynamic parameters of the parameterized airfoil, and the result is proved credible by comparison with available experimental data in the open literature. A polynomial-based response surface model and the uniform Latin hypercube sampling method are employed to decrease computational cost. Finally, the nonlinear programming by quadratic Lagrangian method is utilized to modify the multi-island genetic algorithm, which has an improved optimization effect than the method used on its own. The obtained result shows that the modified class/shape function transformation method produces a better imitation of an airfoil in the nose and tail regions than the original method, and that it will satisfy the tolerance zone of the model in a wind tunnel. The response surface model based on the uniform Latin hypercube sampling method gives an accurate prediction of the lift-to-drag ratio with changes in the design variables. The numerical result of the flow around the airfoil shows reasonable agreement with the experimental data graphically and quantitatively. Ultimately, an airfoil with better capacity than the original one is acquired using the multi-island genetic algorithm based nonlinear programming by quadratic Lagrangian optimization method. The pressure contours and lift-to-drag ratio along with the attack angle have been compared with those of the original airfoil, and the results demonstrate the strength of the optimized airfoil. The process for exploring an improved airfoil through parameterization to optimization is worth referencing in future work.

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“…There are many studies on parametric modeling of HGVs [1], [6], [10], [11] and common methods include the B-spline method [12], [13], non-uniform rational B-spline (NURBS) method [14], class/shape function transformation (CST) method [15], parametric section (PARSEC) method [16], Hicks-Henne method [17], radial basis function (RBF) method [18], and free form deformation (FFD) method [19]. Among these, the FFD method can be used in arbitrary geometrical models and creates arbitrary theoretical deformation results, thereby providing a wide design space.…”

Section: Introductionmentioning

confidence: 99%

Free Form Deformation Method Applied to Modeling and Design of Hypersonic Glide Vehicles

Zhang

Feng

et al. 2019

IEEE Access

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The aerodynamic shape of the hypersonic glide vehicle (HGV) has become a research topic nowadays due to its excellent aerodynamic performances. Some limitations need to be reduced when the free-form deformation (FFD) method is applied to parametric modeling and design of an HGV. In this paper, a typical lifting body is considered as an example, and we propose a border-based FFD modeling method that transforms the boundary of FFD lattice into the border of the windward side. Then, the superiority of the border-based FFD modeling method is demonstrated by comparison with the traditional FFD modeling method, and the mesh quality parameters are used to validate the well-deformed model and good geometric continuity of the proposed method. Finally, the border-based FFD modeling method is applied to deformable modeling and aerodynamic simulation of three typical HGV shapes. The results show that the higher efficiency, wider design space, and better applicability are performed by using the border-based FFD modeling method that outperforms the traditional FFD modeling method, and this method we proposed can allow a designer to achieve the better aerodynamic shape of HGVs. INDEX TERMS Hypersonic gliding vehicle, aerodynamic shape design, parametric modeling, free form deformation, windward side.

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Parametric Geometry Model for Design Studies of Tailless Supersonic Aircraft

Cited by 12 publications

References 5 publications

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

A study of airfoil parameterization, modeling, and optimization based on the computational fluid dynamics method

Free Form Deformation Method Applied to Modeling and Design of Hypersonic Glide Vehicles

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