Abstract
The application of active circulation control gives rise to a substantial increase in lift compared to conventional wings. Initial studies of the aeroelastic behaviour of a circulation-controlled wing have shown additional instabilities due to the active circulation control. Besides the heave flutter phenomenon, further investigation also reveals a destabilising effect of the aerodynamic derivatives related to pitch, which is peculiar to circulation-controlled wings. The goal of the present paper is to investigate these phenomena in detail.
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Abbreviations
- \(A_{\mathrm{ref}}\) :
-
Reference wing area
- \(F_\mathrm{L}\) :
-
Lift force
- \(M_y\) :
-
Pitching moment
- S :
-
Centre of mass
- \(a_j\), \(c_j\), \(d_j\) :
-
Exponents of \(\alpha\), \(c_\mu\) and \(\delta _{\mathrm{fl}}\)
- c :
-
Chord length
- \(c_\mathrm{L}\) :
-
Lift coefficient
- \(c_\mathrm{M}\) :
-
Pitching moment coefficient
- \(c_{\mathrm{L}x}\), \(c_{\mathrm{M}x}\) :
-
Dimensionless derivatives referring to the part depending on x
- \(c_p\) :
-
Pressure coefficient
- \(c_\mu\) :
-
Momentum coefficient of the circulation control
- e :
-
Eccentricity
- f :
-
Frequency
- h :
-
Heave displacement
- \(k_h\), \(k_\alpha\) :
-
Spring constants for heave and pitch
- m :
-
Mass
- \(\dot{m}_{\mathrm{jet}}\) :
-
Mass flow in the Coandă slot
- q :
-
Generalised coordinate
- \(q_\infty\) :
-
Dynamic pressure
- t :
-
Time
- \(u_\infty\) :
-
Approach velocity
- \(v_{\mathrm{jet}}\) :
-
Jet velocity in the Coandă slot
- x :
-
Chord coordinate
- \(\varTheta\) :
-
Mass moment of inertia
- \(\alpha\) :
-
(Effective) angle of attack
- \(\alpha _{\mathrm{AC}}\) :
-
Aircraft angle of attack
- \(\alpha _{\mathrm{el}}\) :
-
Elastic deformation angle
- \(\alpha _{\dot{h}}\) :
-
Change in angle of attack due to \(\dot{h}\)
- \(\alpha _{\mathrm{inst}}\) :
-
Local installation angle
- \(\delta _{\mathrm{fl}}\) :
-
Flap deflection
- \(\eta\) :
-
Dimensionless wing span
- \(\omega _i\) :
-
ith natural frequency
- \(\mathbf {A}_{\mathbf {0}}\) :
-
Aerodynamic stiffness matrix
- \(\mathbf {A}_{\mathbf {1}}\) :
-
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
- \(\hat{\mathbf {x}}_i\) :
-
ith eigenvector
- \(()_0\) :
-
Constant part
- \(()_A\) :
-
Referring to the discretisation of the aerodynamic model
- \(()_S\) :
-
Referring to the discretisation of the structural model
- \(\Delta ()\) :
-
Deviation of variable
- \(\delta ()\) :
-
Virtual quantity
- \(\dot{()}\) :
-
Derivative with respect to time
- \(()_{,x}\) :
-
Derivative with respect to x
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Acknowledgments
Financial support has been provided by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) in the framework of the Sonderforschungsbereich 880. Special thanks go to Kay Sommerwerk from the Institute of Aircraft Design and Lightweight Structures for the design of the structural wing model, and to Marco Burnazzi from the Institute of Fluid Mechanics for creating the grids for the flow simulations.
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Dinkler, D., Krukow, I. Flutter of circulation-controlled wings. CEAS Aeronaut J 6, 589–598 (2015). https://doi.org/10.1007/s13272-015-0166-z
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DOI: https://doi.org/10.1007/s13272-015-0166-z