A modal frequency-domain generalised force matrix for the unsteady Vortex Lattice method

Dimitriadis, Grigorios; Giannelis, Nicholas F.; Vio, Gareth A.

doi:10.1016/j.jfluidstructs.2017.10.010

Cited by 17 publications

(4 citation statements)

References 19 publications

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“…where d is the non-dimensional distance between the mid-chord and the pitch axis, as defined by Theodorsen [1]. After combining Equations (11) and 12,…”

Section: Wagner's Sectional Circulatory Liftmentioning

confidence: 99%

“…The VLM flutter solution is obtained using the modal frequency domain version of the method, as detailed in [11]. Rigid body modes are chosen, one for the plunge and one for the pitch.…”

Section: Aeroelastic Equations Of Motionmentioning

confidence: 99%

“…Several efficient transformation methodologies have been developed, notably the minimum state approach [9], but they remain approximations. The Vortex Lattice Method can also be used to derive a generalized aerodynamic force matrix [10,11], which can then be transformed to the time domain.…”

Section: Introductionmentioning

confidence: 99%

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Unsteady Lifting Line Theory Using the Wagner Function for the Aerodynamic and Aeroelastic Modeling of 3D Wings

Boutet

Dimitriadis

2018

Aerospace

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A method is presented to model the incompressible, attached, unsteady lift and pitching moment acting on a thin three-dimensional wing in the time domain. The model is based on the combination of Wagner theory and lifting line theory through the unsteady Kutta–Joukowski theorem. The results are a set of closed-form linear ordinary differential equations that can be solved analytically or using a Runge–Kutta–Fehlberg algorithm. The method is validated against numerical predictions from an unsteady vortex lattice method for rectangular and tapered wings undergoing step or oscillatory changes in plunge or pitch. Further validation is demonstrated on an aeroelastic test case of a rigid rectangular finite wing with pitch and plunge degrees of freedom.

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“…where d is the non-dimensional distance between the mid-chord and the pitch axis, as defined by Theodorsen [1]. After combining Equations (11) and 12,…”

Section: Wagner's Sectional Circulatory Liftmentioning

confidence: 99%

“…The VLM flutter solution is obtained using the modal frequency domain version of the method, as detailed in [11]. Rigid body modes are chosen, one for the plunge and one for the pitch.…”

Section: Aeroelastic Equations Of Motionmentioning

confidence: 99%

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Unsteady Lifting Line Theory Using the Wagner Function for the Aerodynamic and Aeroelastic Modeling of 3D Wings

Boutet

Dimitriadis

2018

Aerospace

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“…As it will be seen, the z-transform allows a closed-form solution for the wake states, which results in an efficient algorithm for frequency-domain analysis. A similar approach has been recently developed by Dimitriadis et al [32] for flat surfaces, who has also employed it to generate ROMs using rational-function approximations. Here, instead, the frequency-domain formulation will be exploited to construct a tailored low-rank balancing algorithm for the LUVLM.…”

Section: Introductionmentioning

confidence: 99%

Parametric Reduced-Order Modeling of the Unsteady Vortex-Lattice Method

Maraniello

Palacios

2020

AIAA Journal

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A method for frequency-limited balancing of the unsteady vortex-lattice equations is introduced that results in compact models suitable for computational-intensive applications in load analysis, aeroelastic optimisation, and control synthesis. The balancing algorithm relies on a frequency-domain solution of the vortex-lattice equations that effectively eliminates the cost associated to the wake states. It is obtained from a Z-transform of the underlying discrete-time equations, and requires no additional geometrical or kinematic assumptions for the lifting surfaces. Parametric reduced-order modelling is demonstrated through interpolation over (a) projection matrices, (b) state-space realisations and (c) transfer functions, which trade accuracy, robustness and cost. Methods are finally exemplified in the dynamic stability of a T-tail configuration with varying incidence. Numerical studies show that a very small number of balanced realisations is sufficient to accurately capture the unconventional aeroelastic response of this system, which includes in-plane kinematics and steady loads, over a wide range of operation conditions. Nomenclature γ i interpolation weight for design parameter p i Γ vector of circulation strengths κ i integration weight at frequency k i K number of integration points, k i

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Finite Wings

2023

Unsteady Aerodynamics

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A modal frequency-domain generalised force matrix for the unsteady Vortex Lattice method

Cited by 17 publications

References 19 publications

Unsteady Lifting Line Theory Using the Wagner Function for the Aerodynamic and Aeroelastic Modeling of 3D Wings

Unsteady Lifting Line Theory Using the Wagner Function for the Aerodynamic and Aeroelastic Modeling of 3D Wings

Parametric Reduced-Order Modeling of the Unsteady Vortex-Lattice Method

Finite Wings

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