Aeroelastic Computations of a Fokker-Type Wing in Transonic Flow

  • D. Nellessen
  • G. Britten
  • S. Schlechtriem
  • J. Ballmann
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NONUFM, volume 48)


A computational method for the treatment of solid fluid interaction (SOFIA) has been developed to study the aeroelastic characteristics of wings and rotors by direct numerical simulation. It consists of an aerodynamic part to compute the airloads and a structural part to determine the structural deformation. The unsteady, three-dimensional flow is modeled by the Euler equations and calculated using an implicit solver. The elasticity is modeled by a generalized Timoshenko-Flügge beam, which includes the static and dynamic coupling of bending and torsional modes. A finite-element-method is implemented to predict the deformation. Both solvers are coupled in the time domain. SOFIA has been used to investigate a realistic Fokker-type wing in transonic flow. The steady lift distributions have been calculated for the rigid and the elastic wing. Comparison shows remarkable differences between wings with sweep-back and wings with no sweep.


Symbols, structure

\(_{\sim s}^{u}\)





shear angle

EA, \(\textup{EI}_{\approx B}\)

tension and bending stiffness

\(GA, GI_{D11}\)

shear and torsional stiffness


shear coefficient tensor

\(\rho A,\Theta_{\approx s}\)

mass per unit length, rotatory inertia

\(u_{\sim s}^{o}, v_\sim^o\)

initial conditions (displacement)

\(\varphi_\sim^o, w_\sim^o\)

initial conditions (rotation)

\(u_{\sim S}^a,\varphi_\sim^a\)

clamped boundary conditions

\(M_\sim^A, N_\sim^a, Q_\sim^a\)

free boundary conditions

\(\delta I^e\)

extended variation

LB, lB

Lagrangian function, density



\(\delta A^{aero}\)

virtual aerodynamic work


torsional moment per unit length


transverse load per unit length

\(O({x}'_1, {x}'_2, {x}'_3)\)

cartesian co-ordinate system

\(O(\xi, \eta, \zeta)\)

cross-section fixed, Lagrangian system


spatial derivative in ξ-direction

\(t, \binom{\cdot}{\cdots}\)

time, time derivative

Symbols, flow








total specific energy


surface velocity


normal vector




surface of V


local chord length


flight altitude


angle of attack


angle of sweep-back


cartesian Euler system

\(\delta(\cdots)/\delta t\)

special time derivative


lift coefficient


momentum coefficient


pressure coefficient


Mach number


ratio of specific heats


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Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1996

Authors and Affiliations

  • D. Nellessen
    • 1
  • G. Britten
    • 1
  • S. Schlechtriem
    • 1
  • J. Ballmann
    • 1
  1. 1.Lehr- und Forschungsgebiet für Mechanik RWTH-AachenUniversity of TechnologyAachenGermany

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