Vortex lattice method

Abstract: A preliminary aerodynamic performance prediction model has been constructed for the Darrieus turbine using a vortex lattice method of analysis. A series of experiments were conducted for the express purpose of validating the analytical model. These experiments were conducted on a series of two dimensional rotor configurations which were towed in a large tank of water. The use of water as a working fluid was intended to facilitate both flow visualization and the ability to measure aerodynamic blade forces while allowing operation at sufficiently high Reynolds numbers. The primary purpose of this research was to allow reasonable predictions of aerodynamic blade forces and moments to be made.

Abstract: The Unsteady Vortex-Lattice Method provides a medium-fidelity tool for the prediction of non-stationary aerodynamic loads in low-speed, but high-Reynolds-number, attached flow conditions. Despite a proven track record in applications where free-wake modelling is critical, other less-computationally-expensive potential-flow models, such as the Doublet-Lattice Method and strip theory, have long been favoured in fixed-wing aircraft aeroelasticity and flight dynamics. This paper presents how the Unsteady Vortex-Lattice Method can be implemented as an enhanced alternative to those techniques for diverse situations that arise in flexible-aircraft dynamics. A historical review of the methodology is included, with latest developments and practical applications. Di erent formulations of the aerodynamic equations are outlined, and they are integrated with a nonlinear beam model for the full description of the dynamics of a free-flying flexible vehicle. Nonlinear time-marching solutions capture large wing excursions and wake roll-up, and the linearisation of the equations lends itself to a seamless, monolithic state-space assembly, particularly convenient for stability analysis and flight control system design. The numerical studies emphasise scenarios where the Unsteady Vortex-Lattice Method can provide an advantage over other state-of-the-art approaches. Examples of this include unsteady aerodynamics in vehicles with coupled aeroelasticity and flight dynamics, and in lifting surfaces undergoing complex kinematics, large deformations, or in-plane motions. Geometric nonlinearities are shown to play an instrumental, and often counter-intuitive, role in the aircraft dynamics. The Unsteady Vortex-Lattice Method is unveiled as a remarkable tool that can successfully incorporate all those e ects in the unsteady aerodynamics modelling.

Abstract: A general technique for constructing reduced order models of unsteady aerodynamic flows about twodimensional isolated airfoils, cascades of airfoils, and three-dimensional wings is developed. The starting point is a time domain computational model of the unsteady small disturbance flow. For illustration purposes, we apply the technique to an unsteady incompressible vortex lattice model. The eigenmodes of the system, which may be thought of as aerodynamic states, are computed and subsequently used to construct computationally efficient, reduced order models of the unsteady flowfield. Only a handful of the most dominant eigenmodes are retained in the reduced order model. The effect of the remaining eigenmodes is included approximately using a static correction technique. An important advantage of the present method is that once the eigenmode information has been computed, reduced order models can be constructed for any number of arbitrary modes of airfoil motion very inexpensively. Numerical examples are presented that demonstrate the accuracy and computational efficiency of the present method. Finally, we show how the reduced order model may be incorporated into an aeroelastic flutter model.

Abstract: A quasi-continuous method is developed for solving thin-wing problems. For the purpose of satisfying the wing boundary conditions, the spanwise vortex distribution is assumed to be stepwise-constant, while the chordwise vortex integral is reduced to a finite sum through a modified trapezoidal rule and the theory of Chebyshev polynomials. Wing-edge and Cauchy singularities are acounted for. The total aerodynamic characteristics are obtained by an appropriate quadrature integration. The two-dimensional results for airfoils without flap deflection reproduce the exact solutions in lift and pitching moment coefficients, the leading edge suction, and the pressure difference at a finite number of points. For a flapped airfoil, the present results are more accurate than those given by the vortex-lattice method. The three-dimensional results also show an improvement over the results of the vortex-lattice method. Extension to nonplanar applications is discussed.

Abstract: An experimental investigation into the properties of the vortex wake behind a wind turbine rotor has been carried out at model scale, using Particle Image Velocimetry (PIV). The two-blade model was operated at tip speed ratios in the range λ=3–8, and chord Reynolds numbers Re=6400–16 000. The blades were untwisted, with flat-plate aerofoil profile. Measurements of wake velocity and vorticity were obtained for a two-dimensional flow field representing an axial cross-section of the wake, extending 2.9 rotor diameters downstream of the rotor. The vorticity maps were compared with calculations made using the Rotor Vortex Lattice Method (ROVLM), an inviscid free-wake code recently developed at the University of Stuttgart. The PIV and ROVLM data show qualitative agreement in terms of the shape of the wake boundary, including downstream wake contraction, and quantitative agreement in terms of the tip vortex pitch. It appears that the fundamental behaviour of the helical vortex wake may be relatively insensitive to blade chord Reynolds number, so long as similarity of tip speed ratio is observed.