A strongly-coupled model for flexible rotors

Abstract

A fluid-structure model describing the equilibrium state of a flexible blade rotor with its own wake is derived for various external axial flow conditions. The model is based on three building blocks. The twodimensional lifting-line theory is first used to compute the local aerodynamic loads and the blade circulation profile. The blade deformation is then obtained by solving the nonlinear equations for bending and twisting angles deduced from a one-dimensional beam model. Finally, the wake is obtained using a Joukowsky model. In this wake model, the wake of each blade is modelled by two small-core-size counter-rotating vortices emitted from the rotor axis and blade tip. The velocity field induced by these vortices is computed using the Biot-Savart law. We show that, in the rotor frame, we can obtain a stationary vortex structure for almost any vertical flight regimes. This wake solution can then be used to compute the induced velocity in the rotor plane and apply the two-dimensional lifting-line theory again. By iterating a few times this loop, we converge toward a nonlinear solution of the problem for which the aerodynamics loads, blade deformation and wake structure are compatible. As illustration, this newly-developed model is applied to two rotors. We analyse the effects of the external wind conditions, geometry and material properties of the blades on the blade deformation and wake characteristics. We show that we can describe slow descending regimes for which the classical momentum theory does not apply.

Structure and stability of Joukowski's rotor wake model

“…Its circulation is equal to if there is a tip vortex of circulation associated with each of the blades. The procedure used to construct a Joukowski wake model for any circulation profile has been described in Durán Venegas, Le Dizès & Eloy (2019). Note, however, that if the rotor has a single blade, the root vortex cannot be positioned on the rotor axis and is expected to become helically deformed.…”

“…But, in that case, the local lift force can be computed differently, using the exact circulation profile on the blade and the azimuthal average of the induced velocity field, as in Durán Venegas et al. (2019) for instance.…”

Structural dynamics of flexible rotor blades to study aeroelastic phenomena

“…Besides, they investigated the effects of different parameters on flutter boundaries. E.Durán Venegas [4] described a fluid-structure model for flexible rotor blades. The blade deformation is obtained by solving the nonlinear equations for bending and twisting angles from a one-dimensional beam model.…”

Fluid–structure interaction of a flexible rotor in water

“…The development of more efficient rotors for these vehicles, taking into account the flexibility of the blades and potentially using it in a beneficial way, is an active field of research. A recent modelling study aimed at the optimisation of flexible rotors, including also the structure of its wake, was carried out by Durán Venegas et al (2019).…”