Aeroelastic behaviour of a parameterised circulation-controlled wing

  • Nora NeuertEmail author
  • Dieter Dinkler
Original Paper


The aeroelastic behaviour of the wing of a short take-off and landing aircraft using the Coandă effect depends on its properties and shape. An existing reduced-order model is parameterised for detailed investigations. On the one hand, varying mass due to tank level and varying overall stiffness is implemented in the reduced-order model. The influence of the mass change on the aeroelastic behaviour is reflected in the stability maps. On the other hand, two-dimensional steady and unsteady aerodynamics of different nose shapes are investigated with detailed computational fluid simulations and included in the reduced-order model. The dependence on the profile shape and the frequency is described. Their influence on the aeroelastic behaviour is reflected by the stability maps as well.


Aeroelasticity Circulation control Parameterisation Reduced-order model 

List of symbols

\(A_{\text {ref}}\)

Reference wing area

\(c_{\text {L}}\)

Lift coefficient

\(c_{\text {M}}\)

Pitching moment coefficient

\(c_{\text {p}}\)

Pressure coefficient


Momentum coefficient of the circulation control




Net weight


Heave displacement


Chord length



\(\dot{m}_{\text {jet}}\)

Mass flow in the Coandă slot


Generalised coordinate


Dynamic pressure


Approach velocity

\(v_{\text {jet}}\)

Jet velocity in the Coandă slot


(Effective) angle of attack

\(\gamma _i\)

i-th participation factor

\(\delta _{\text {fl}}\)

Flap deflection


Dimensionless chord

\(\eta _{\text {k}}\)

Parameterised stiffness

\(\eta _{\text {m}}\)

Parameterised tank level


Natural frequency

\(\omega _i\)

i-th natural frequency

\(\mathbf {A_0}\)

Aerodynamic stiffness matrix

\(\mathbf {A_1}\)

Aerodynamic damping matrix

\(\mathbf {K}\)

Stiffness matrix

\(\mathbf {L}\)

Aerodynamic load vector

\(\mathbf {M}\)

Mass matrix

\(\mathbf {X}\)

Modal matrix

\(\mathbf {q}\)

Vector of generalised coordinates

\(\mathbf {x}\)

Vector of physical degrees of freedom

\(\hat{\mathbf {x}}_i\)

i-th eigenvector


Constant part


Referring to the initial configuration


Referring to the altered configuration


Referring to the discretisation of the aerodynamic model

\(()_\text {,droop}\)

Referring to droop nose

\(()_{\text {S}}\)

Referring to the discretisation of the structural model

\(\varDelta ()\)

Deviation of variable


Derivative with respect to time


Derivative with respect to x



Financial support has been provided by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) in the framework of the Coordinated Research Centre SFB 880.


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Copyright information

© Deutsches Zentrum für Luft- und Raumfahrt e.V. 2019

Authors and Affiliations

  1. 1.TU Braunschweig, Institute of Structural AnalysisBrunswickGermany

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