0
Technology Reviews

Freeform Deformation Versus B-Spline Representation in Inverse Airfoil Design

[+] Author and Article Information
Eleftherios I. Amoiralis

Department of Production Engineering and Management,  Technical University of Crete, University Campus, GR-73100 Chania, Greece

Ioannis K. Nikolos

Department of Production Engineering and Management,  Technical University of Crete, University Campus, GR-73100 Chania, Greecejnikolo@dpem.tuc.gr

http://tracfoil.free.fr/airfoils/h.htm.

J. Comput. Inf. Sci. Eng 8(2), 024001 (Apr 30, 2008) (13 pages) doi:10.1115/1.2906694 History: Received April 16, 2007; Revised February 01, 2008; Published April 30, 2008

Freeform deformation (FFD) is a well established technique for 3D animation applications, used to deform two—or three-dimensional geometrical entities. Over the past few years, FFD technique has aroused growing interest in several scientific communities. In this work, an extensive bibliographic survey of the FFD technique is initially introduced, in order to explore its capabilities in shape parametrization. Moreover, FFD technique is compared to the classical parametrization technique using B-spline curves, in the context of the airfoil design optimization problem, by performing inverse airfoil design tests, with a differential evolution algorithm to serve as the optimizer. The criterion of the comparison between the two techniques is the achieved accuracy in the approximation of the reference pressure distribution. Experiments are presented, comparing FFD to B-spline techniques under the same flow conditions, for various numbers of design variables. Sensitivity analysis is applied for providing further insight into the differences in the performance of the two techniques.

Copyright © 2008 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

The initial lattice of control points around the object to be deformed (a symmetrical airfoil)

Grahic Jump Location
Figure 2

The initial and the deformed lattice of control points

Grahic Jump Location
Figure 3

The deformed lattice and the resulting airfoil

Grahic Jump Location
Figure 4

The cost function to be minimized in the optimization procedure is the area formed between the target pressure distribution and the calculated one for each candidate solution

Grahic Jump Location
Figure 5

The initial lattice and the object to be deformed. The red control points in the last column are fixed during the optimization procedure.

Grahic Jump Location
Figure 6

The final (deformed) airfoil and the corresponding deformed lattice

Grahic Jump Location
Figure 7

Airfoil representation using a single B-spline curve; only the y coordinates of the control points are allowed to vary within predefined ranges in this case

Grahic Jump Location
Figure 8

Experimental results of the inverse airfoil design tests for the first test case

Grahic Jump Location
Figure 9

Experimental results of the inverse airfoil design tests for the second test case

Grahic Jump Location
Figure 10

Experimental results of the inverse airfoil design tests for the third test case

Grahic Jump Location
Figure 11

Comparison between the reference and the computed pressure distributions (upper) and the reference and computed airfoils (lower), for Test Case 3, using the FFD technique with a 3×10 lattice and a range of variation equal to 0.1 for the y coordinates of the control points (27 design variables)

Grahic Jump Location
Figure 12

The convergence histories of the DE optimization procedure for the third test case, with a variation of only the y coordinates of the control points, within a range equal to 0.1 (FFD 3×10, B-spline with 27 control points)

Grahic Jump Location
Figure 13

Comparison between the reference and the computed pressure distributions (upper) and the reference and computed airfoils (lower), for Case 3, using the B-spline technique with 27 control points and a range of variation equal to 0.1 for the y coordinates of the control points (25 design variables). The mismatching between the reference and the computed values is located at the leading edge region of the airfoil.

Grahic Jump Location
Figure 14

Experimental results of the airfoil recovery tests for the third case

Grahic Jump Location
Figure 15

Upper: the sensitivity analysis results for the third case, using the FFD technique with a 3×10 lattice and a range of variation equal to 0.1 for the y coordinates of the control points (27 design variables); lower: the positions of the lattice control points for the best computed solution

Grahic Jump Location
Figure 16

The sensitivity analysis results for the third test case, using the B-spline technique with 27 control points and a range of variation equal to 0.1 for the y coordinates of the control points (25 design variables)

Grahic Jump Location
Figure 17

The sensitivity analysis results for the third test case, using the FFD technique with a 3×6 lattice and a range of variation equal to 0.1 for both the x and y coordinates of the control points (27 design variables). The missing numbers of design variables refer to the control points that are not allowed to move in the corresponding direction.

Grahic Jump Location
Figure 18

The sensitivity analysis results for the third test case, using the FFD technique with a 4×5 lattice and a range of variation equal to 0.1 for both the x and y coordinates of the control points (28 design variables). The missing numbers of design variables refer to the control points that are not allowed to move in the corresponding direction.

Grahic Jump Location
Figure 19

The sensitivity analysis results for the third test case, using the B-spline technique with 17 control points and a range of variation equal to 0.1 for both the x and y coordinates of the control points (27 design variables). The missing numbers of design variables refer to the control points that are not allowed to move in the corresponding direction.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In