A method combined immersed boundary with multi-relaxation-time lattice Boltzmann flux solver for fluid-structure interaction

Abstract

This paper performs a newly developed method, which combines the immersed boundary method (IBM) with multi-relaxation-time lattice Boltzmann flux solver (MRT-LBFS), for solving fluid-structure interaction problems. Finite volume discretization is used to solve the macroscopic governing equations with the flow variables defined at cell centers. Based on the multi-scale Chapman-Enskog expansion analysis, LBFS builds a relationship between the variables and fluxes in incompressible Navier-Stokes equations and density distribution functions in lattice Boltzmann equation. In order to ensure no-slip boundary condition, boundary condition-enforced immersed boundary method is used to treat the fluid-structure interface. The restoring force can be resolved by making a velocity correction in the flow field. The four-stage RungeKutta scheme is used to solve the motion equation of structure. Using the lattice model and immersed boundary method, fluid-structure coupling calculation can be implemented in a Cartesian grid, without generating the body-fitted mesh and using moving mesh technique. Therefore, the computational process is considerably simplified. In order to verify the validity and feasibility of IB-MRT-LBFS to solve fluid-structure interaction problems, both one-and two-degree of freedom vortex-induced vibrations (VIV) of a circular cylinder and two-degree of freedom VIV of two cylinders in a tandem arrangement are simulated by this proposal method. For a VIV cylinder system, the transverse vibration response is much stronger than the axial response. When the vibration occurs in the range of lock-in regime, the shedding vortex frequency of the wake is close to natural frequency of the cylinder so that resonance appears, consequently causing larger amplitude. For two VIV cylinders in a tandem arrangement, the dynamic behavior of each cylinder is significantly different from that of a single cylinder. The gap spacing between the two cylinder centers is a significant parameter which effects vibration characteristics and the spacing is fixed in the simulations of two tandem cylinders. With the effects of upstream cylinder wake, the axial and transverse amplitudes of downstream cylinder obviously increase with adding the reduced velocity. The downstream cylinder is delayed, coming into lock-in regime, and the range of lock-in regime is expanded under the effects of the wake of the upstream cylinder. As the reduced velocity is relatively large, the vibration response of the upstream cylinder is close to a single cylinder and the vibration response of the downstream cylinder is more intense than the upstream cylinder. Compared with the existing literature results, our result illustrates that IB-MRT-LBFS owns the ability to correctly predict the lock-in regime, dynamic response and the forces of vortex-induced vibrations of cylinders. And this method can accurately capture the wake structures.