Article

Acceleration techniques for an aeroelastic Euler method for a hovering rotor

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Abstract

Computational fluid dynamics (CFD) methodologies for rotors usually do not permit the rotor to deflect during analysis. However, these deflections do occur in the physical domain and can affect the performance of the rotor. By coupling a Euler code and a structural beam model, these deflections have been incorporated into a CFD simulation. The implementation of the structural beam model is straightforward and can be applied to existing CFD methodologies without extensive effort However, the cost of the tightly coupled simulation is prohibitive. Techniques to accelerate the convergence of these methods for the quasisteady hover condition are explored. The methods include application of a loosely coupled aeroelastic methodology (vs a tightly coupled methodology), implementation of the full structural deflections using larger update intervals for methodology stability, application of relaxation factors to the full structural deflections, and application of blade deflections predicted by lower-order aerodynamic methods for initial deflections. All of these methods showed some merit, as discussed fully in this article, Aeroelastic analyses with surface deflection updates every 20 iterations provide results that are within 90% of the more expensive tightly coupled analysis results, These methods, while applied to rotors, are also pertinent for fixed-wing applications.

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... To improve the time efficiency of FSI computations, multi-grid is often employed in CFD codes to speed up convergence [34,35,10,23]. For coupled computations, Marilyn J. Smith [28] proposed two acceleration techniques to reduce the impact of the aeroelastic coupling on the aerodynamic solver. The first technique updates the positions of aerodynamic nodes with entire computed structural deflection, but it increases the number of aerodynamic solver iterations between aeroelastic deflection updates. ...
... Then static elastic equations for the structures were coupled with Navier-Stokes equations, and this technique worked well for small deformations but it did not fit where large deformations occur. The second acceleration technique [28] was also employed in computations carried out by J. Cai et al. [7] and Richard D. Snyder et al. [30], and it had little negative effect on convergence rate but divergence of computations was avoided. This paper introduces a golden section technique to accelerate the convergence of loosely-coupled computations. ...
... The second acceleration technique introduced by Marilyn J. Smith [28] is expressed by a relaxation equation ...
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... 1(d), are also an interesting field of study and the last few decades saw numerous development in the field of flapping wing MAVs, starting with Weis-Fogh [201] and Lighthill [117]. Later, Delaurier [50], Smith [171], and Dickenson et al. [54], addressed the aerodynamic modelling of flapping wings. For a recent review of the development of flapping wing technology, see Shyy et al. [168]. ...
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... 1(d), are also an interesting field of study and the last few decades saw numerous development in the field of flapping wing MAVs, starting with Weis-Fogh [201] and Lighthill [117]. Later, Delaurier [50], Smith [171], and Dickenson et al. [54], addressed the aerodynamic modelling of flapping wings. For a recent review of the development of flapping wing technology, see Shyy et al. [168]. ...
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Thesis (Ph. D.)--Georgia Institute of Technology, 1993. Directed by David A. Peters. Vita. Includes bibliographical references (leaves 172-178).
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A numerical method is presented for calculating the unsteady transonic rotor flow with aeroelasticity effects. The blade structural dynamic equations based on beam theory were formulated by FEM and were solved in the time domain, instead of the frequency domain. For different combinations of precone, droop, and pitch, the correlations are very good in the first three flapping modes and the first twisting mode. However, the predicted frequencies are too high for the first lagging mode at high rotational speeds. This new structure code has been coupled into a transonic rotor flow code, TFAR2, to demonstrate the capability of treating elastic blades in transonic rotor flow calculations. The flow fields for a model-scale rotor in both hover and forward flight are calculated. Results show that the blade elasticity significantly affects the flow characteristics in forward flight.