State space realisation and model reduction of potential-flow aerodynamics for HAWT applications

This paper presents a general state-space realisation of the unsteady vortex-lattice method and combines it with a novel model-order reduction strategy. The aim is to provide a computationally efficient aerodynamic description suitable for integration in horizontal axis wind turbine aeroelasticity. The consistent linearisation is in the 3D components of the vortex lattice geometry. The resulting linear-time invariant system can, therefore, resolve all the component of forces, hence being suitable for linearisation around arbitrary wake shapes and blade geometries/deformations. The wake modelling captures unsteady aerodynamic effects but it results in large state-space models. Projection on low-dimensional degrees-of-freedom and balanced residualisation are, therefore, employed to reduce the model dimensionality. An iterative balancing algorithm based on Smith's method is also developed so as to contain the computational cost of the process. The paper also presents an initial numerical investigation on aerofoils linearised around non-zero reference conditions, showing that this approach can reduce the size of the problem by several orders of magnitude and at a lower computational cost than standard direct methods for system balancing.