The use of a new aeroelastic computer framework called Flexit is described and the framework is used to analyse the dynamic aeroelastic behaviour of a four-bladed helicopter main rotor. Flexit implements a loose coupling between unsteady vortex lattice method (UVLM) and numerical solution of the inhomogeneous Euler-Bernoulli partial differential equation (PDE). The framework is fast because most of the intensive computational functionality is performed on GPU using NVIDIA CUDA technology, and this makes it suitable for use in the early design stages. The UVLM algorithm uses a free wake model, and solution of the Euler-Bernoulli PDE is approximated using a finite difference algorithm that includes a term to take account of centrifugal forces. The results of simulations are compared with analysis performed with CFD and FSI tools.
We present an example of an entire function with a Baker domain such that the complement of the set of singular values of the function contains annuli of arbitrarily large width. This is the first known example of a function with this property.
This paper focuses on the development of an explicit finite difference numerical method for approximating the solution of the inhomogeneous fourth-order Euler–Bernoulli beam bending equation with velocity-dependent damping and second moment of area, mass and elastic modulus distribution varying with distance along the beam. We verify the method by comparing its predictions with an exact analytical solution of the homogeneous equation, we use the generalised Richardson extrapolation to show that the method is grid convergent and we extend the application of the Lax–Richtmyer stability criteria to higher-order schemes to ensure that it is numerically stable. Finally, we present three sets of computational experiments. The first set simulates the behaviour of the un-loaded beam and is validated against the analytic solution. The second set simulates the time-dependent dynamic behaviour of a damped beam of varying stiffness and mass distributions under arbitrary externally applied loading in an aeroelastic analysis setting by approximating the inhomogeneous equation using the finite difference method derived here. We compare the third set of simulations of the steady-state deflection with the results of static beam bending experiments conducted at Cranfield University. Overall, we developed an accurate, stable and convergent numerical framework for solving the inhomogeneous Euler–Bernoulli equation over a wide range of boundary conditions. Aircraft manufacturers are starting to consider configurations with increased wing aspect ratios and reduced structural weight which lead to more slender and flexible designs. Aeroelastic analysis now plays a central role in the design process. Efficient computational tools for the prediction of the deformation of wings under external loads are in demand and this has motivated the work carried out in this paper.
The computer simulation framework Flexit is used to analyse the fuel economy benefit of aircraft wake surfing. Wake surfing involves multiple aircraft flying in close formation during cruise conditions to reduce overall induced drag and improve overall fuel efficiency. The aircraft fly in echelon such that the kinetic energy lost in vortices generated by the lead aircraft can be partially recovered by the following aircraft flying in regions of the wake where induced velocities have an upwardly directed vertical component. We build on recent theoretical and flight test work by developing a medium fidelity methodology using Flexit for predicting potential performance benefits of wake surfing. We present results from a specific systematic parametric study that corresponds to a series of recent flight tests with two C-17 transport aircraft to demonstrate the methodology and predict the fuel savings that can be obtained by different arrangements of aircraft in a wake surfing formation. The predictions are compared with the flight test data and the trends observed in our simulations agree with the trends of the full scale tests.
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