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The aerodynamic performance of propellers strongly depends on their geometry and, consequently, on aeroelastic deformations. Knowledge of the extent of the impact is crucial for overall aircraft performance. An integrated simulation environment for steady aeroelastic propeller simulations is presented. The simulation environment is applied to determine the impact of elastic deformations on the aerodynamic propeller performance. The aerodynamic module includes a blade element momentum approach to calculate aerodynamic loads. The structural module is based on finite beam elements, according to Timoshenko theory, including moderate deflections. Several fixed-pitch propellers with thin-walled cross sections made of both isotropic and non-isotropic materials are investigated. The essential parameters are varied: diameter, disc loading, sweep, material, rotational, and flight velocity. The relative change of thrust between rigid and elastic blades quantifies the impact of propeller elasticity. Swept propellers of large diameters or low disc loadings can decrease the thrust significantly. High flight velocities and low material stiffness amplify this tendency. Performance calculations without consideration of propeller elasticity can lead to decreased efficiency. To avoid cost- and time-intense redesigns, propeller elasticity should be considered for swept planforms and low disc loadings.
High aerodynamic efficiency requires propellers with high aspect ratios, while propeller sweep potentially reduces noise. Propeller sweep and high aspect ratios increase elasticity and coupling of structural mechanics and aerodynamics, affecting the propeller performance and noise. Therefore, this paper analyzes the influence of elasticity on forward-swept, backward-swept, and unswept propellers in hover conditions. A reduced-order blade element momentum approach is coupled with a one-dimensional Timoshenko beam theory and Farassat's formulation 1A. The results of the aeroelastic simulation are used as input for the aeroacoustic calculation. The analysis shows that elasticity influences noise radiation because thickness and loading noise respond differently to deformations. In the case of the backward-swept propeller, the location of the maximum sound pressure level shifts forward by 0.5 °, while in the case of the forward-swept propeller, it shifts backward by 0.5 °. Therefore, aeroacoustic optimization requires the consideration of propeller deformation.
On the Vanishing Displacement Current Limit for Eddy-Current Problems / Quell, P. ; Reißel, M.
(1996)
This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection.