This paper presents closed form solutions to the classical beam elasticity differential equation in order to effectively model the displacement of standard aerodynamic geometries used throughout a number of industries. The models assume that the components are constructed from in-plane generally anisotropic (though shown to be quasi-isotropic) composite materials. Exact solutions for the displacement and strains for elliptical and FX66-S-196 and NACA 63-621 aerofoil approximations thin wall composite material shell structures, with and without a stiffening rib (shear-web), are presented for the first time. Each of the models developed is rigorously validated via numerical (Runge-Kutta) solutions of an identical differential equation used to derive the analytical models presented. The resulting calculated displacement and material strain fields are shown to be in excellent agreement with simulations using the ANSYS and CATIA commercial finite element (FE) codes as well as experimental data evident in the literature. One major implication of the theoretical treatment is that these solutions can now be used in design codes to limit the required displacement and strains in similar components used in the aerospace and most notably renewable energy sectors.

This paper details a computational fluid dynamic (CFD) study of a constantly loaded actuator disc model featuring different boundary conditions; these boundary conditions were defined to represent a channel and a duct flow. The simulations were carried out using the commercially available CFD software ANSYS-CFX. The data produced were compared to the one-dimensional (1D) momentum equation as well as previous numerical and experimental studies featuring porous discs in a channel flow. The actuator disc was modelled as a momentum loss using a resistance coefficient related to the thrust coefficient (CT). The model showed good agreement with the 1D momentum theory in terms of the velocity and pressure profiles. Less agreement was demonstrated when compared to previous numerical and empirical data in terms of velocity and turbulence characteristics in the far field. These models predicted a far larger velocity deficit and a turbulence peak further downstream. This study therefore demonstrates the usefulness of the duct boundary condition (for computational ease) for representing open channel flow when simulating far field effects as well as the importance of turbulence definition at the inlet.