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Numerical Modelling of Static Aeroelastic Deformations of Slender Wing in Aerodynamic Design

Pamela Bugała
Pamela Bugała
, 
Janusz Sznajder
Janusz Sznajder
 and 
Adam Sieradzki
Adam Sieradzki
   | Dec 08, 2023
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Article Category: research article
Published Online: Dec 08, 2023
Page range: 52 - 70
Received: Oct 03, 2022
Accepted: Nov 03, 2023
DOI: https://doi.org/10.2478/tar-2023-0023
Keywords
© 2023 Pamela Bugała et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Diagram of two-way fluid-structure interaction implemented in XAVEL.AVL, Athena Vortex Lattice; XAVEL, X-Foil & AVL wing aeroELasticity.
Diagram of two-way fluid-structure interaction implemented in XAVEL.AVL, Athena Vortex Lattice; XAVEL, X-Foil & AVL wing aeroELasticity.

Figure 2.

An example distribution of RBF source points on the wing surface and at a distance from it, where mesh deformation vanishes. RBF, radial basis functions.
An example distribution of RBF source points on the wing surface and at a distance from it, where mesh deformation vanishes. RBF, radial basis functions.

Figure 3.

Distribution of RBF points along the wing chord (view from the side edge of the wing). RBF, radial basis functions.
Distribution of RBF points along the wing chord (view from the side edge of the wing). RBF, radial basis functions.

Figure 4.

Contour of the spatial distribution of mesh deformation coefficient, computed for mesh nodes between radii r0 and r1 of Eq. (8).
Contour of the spatial distribution of mesh deformation coefficient, computed for mesh nodes between radii r0 and r1 of Eq. (8).

Figure 5.

Distribution of mesh node translations (in meters) in two planes perpendicular to wing chordplane.
Distribution of mesh node translations (in meters) in two planes perpendicular to wing chordplane.

Figure 6.

Mesh deformation in the middle-chord plane, following wing deformation.
Mesh deformation in the middle-chord plane, following wing deformation.

Figure 7.

Deformations of wing cross-sections hosting RBF source points as a result of bending of wing axis (left fragment) and twist (right fragment). RBF, radial basis functions.
Deformations of wing cross-sections hosting RBF source points as a result of bending of wing axis (left fragment) and twist (right fragment). RBF, radial basis functions.

Figure 8.

Static aeroelastic solution for a flight condition of 20,000 m altitude, 25 m/s, and an α = 2° and α = 4°. XAVEL, X-Foil & AVL wing aeroELasticity.
Static aeroelastic solution for a flight condition of 20,000 m altitude, 25 m/s, and an α = 2° and α = 4°. XAVEL, X-Foil & AVL wing aeroELasticity.

Figure 9.

Static aeroelastic solution for a flight condition of 20,000 m altitude, 25 m/s, and an α = 2° and α = 4°. XAVEL, X-Foil & AVL wing aeroELasticity.
Static aeroelastic solution for a flight condition of 20,000 m altitude, 25 m/s, and an α = 2° and α = 4°. XAVEL, X-Foil & AVL wing aeroELasticity.

Figure 10.

Lift force for a flight condition of 20,000 m altitude, 25 m/s, and an α= 2°and α= 4°.XAVEL, X-Foil & AVL wing aeroELasticity.
Lift force for a flight condition of 20,000 m altitude, 25 m/s, and an α= 2°and α= 4°.XAVEL, X-Foil & AVL wing aeroELasticity.

Figure 11.

Convergence of the iteration process of aero-structural analysis.
Convergence of the iteration process of aero-structural analysis.

Figure 12.

Deflection of the test wing computed with the URANS +RBF +FEM approach. RBF, radial basis functions; URANS, unsteady Navier-Stokes equations.
Deflection of the test wing computed with the URANS +RBF +FEM approach. RBF, radial basis functions; URANS, unsteady Navier-Stokes equations.

Figure 13.

Comparison of bending deflection of the test wing, normal to wing planform, computed using the present method with results of Ref. [25]. RBF, radial basis functions; URANS, unsteady Navier-Stokes equations.
Comparison of bending deflection of the test wing, normal to wing planform, computed using the present method with results of Ref. [25]. RBF, radial basis functions; URANS, unsteady Navier-Stokes equations.

Figure 14.

Comparison of twist of the test wing, computed using the present method with results of Ref. [25]. RBF, radial basis functions; URANS, unsteady Navier-Stokes equations.
Comparison of twist of the test wing, computed using the present method with results of Ref. [25]. RBF, radial basis functions; URANS, unsteady Navier-Stokes equations.

Figure 15.

Comparison of distributions of non-dimensionalized normal force computed using the present method with results of [25]. RBF, radial basis functions; URANS, unsteady Navier-Stokes equations.
Comparison of distributions of non-dimensionalized normal force computed using the present method with results of [25]. RBF, radial basis functions; URANS, unsteady Navier-Stokes equations.

Figure 16.

Comparison of distributions of wing twisting moment computed with the present method using the linear and nonlinear variant of the structure model. RBF, radial basis functions; URANS, unsteady Navier-Stokes equations.
Comparison of distributions of wing twisting moment computed with the present method using the linear and nonlinear variant of the structure model. RBF, radial basis functions; URANS, unsteady Navier-Stokes equations.

Geometry and structural properties of the validation case wing [25].

Wing properties Study value
Semi-span [m] 16
Chord [m] 1
Center of gravity Mid-chord
Elastic axis Mid-chord
Inertia about mid stiffness [Nm2] 0.1
Torsional stiffness [Nm2] 1 × 104
Bending stiffness [Nm2] 2 × 104
Edgewise stiffness [Nm2] 5 × 106
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