# Aeroelastic behaviour of a parameterised circulation-controlled wing

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## Abstract

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.

## Keywords

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

- \(c_\mu\)
Momentum coefficient of the circulation control

*f*Frequency

*g*Net weight

*h*Heave displacement

*l*Chord length

*m*Mass

- \(\dot{m}_{\text {jet}}\)
Mass flow in the Coandă slot

*q*Generalised coordinate

- \(q_\infty\)
Dynamic pressure

- \(v_\infty\)
Approach velocity

- \(v_{\text {jet}}\)
Jet velocity in the Coandă slot

- \(\alpha\)
(Effective) angle of attack

- \(\gamma _i\)
*i*-th participation factor- \(\delta _{\text {fl}}\)
Flap deflection

- \(\eta\)
Dimensionless chord

- \(\eta _{\text {k}}\)
Parameterised stiffness

- \(\eta _{\text {m}}\)
Parameterised tank level

- \(\omega\)
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- \(()_0\)
Constant part

- \(()_1\)
Referring to the initial configuration

- \(()_2\)
Referring to the altered configuration

- \(()_A\)
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

- \(\dot{()}\)
Derivative with respect to time

- \(()_{,x}\)
Derivative with respect to

*x*

## Notes

### Acknowledgements

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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