An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

Abstract

An arbitrary Lagrangian-Eulerian lattice Boltzmann flux solver (ALE-LBFS) coupled with the mode superposition method is proposed in this work and applied to study two- and three-dimensional flutter phenomenon on dynamic unstructured meshes. The ALE-LBFS is applied to predict the flow field by using the vertex-centered finite volume method with an implicit dual time-stepping method. The convective fluxes are evaluated by using lattice Boltzmann solutions of the non-free D1Q4 lattice model and the viscous fluxes are obtained directly. Additional fluxes due to mesh motion are calculated directly by using local conservative variables and mesh velocity. The mode superposition method is used to solve for the dynamic response of solid structures. The exchange of aerodynamic forces and structural motions is achieved through interpolation with the radial basis function. The flow solver and the structural solver are tightly coupled so that the restriction on the physical time step can be removed. In addition, geometric conservation law (GCL) is also applied to guarantee conservation laws. The proposed method is tested through a series of simulations about moving boundaries and fluid–structure interaction problems in 2D and 3D. The present results show good consistency against the experiments and numerical simulations obtained from the literature. It is also shown that the proposed method not only can effectively predict the flutter boundaries in both 2D and 3D cases but can also accurately capture the transonic dip phenomenon. The tight coupling of the ALE-LBFS and the mode superposition method presents an effective and powerful tool for flutter prediction and can be applied to many essential aeronautical problems.

Keywords

• flutter prediction
• ALE-LBFS
• mode superposition method
• limit cycle oscillation
• transonic dip