Abstract
A hybrid immersed boundary–lattice Boltzmann and finite difference method for fluid–structure interaction and heat transfer in non-Newtonian flow is presented. The present numerical method includes four parts: fluid solver, heat transfer solver, structural solver, and immersed boundary method for fluid–structure interaction and heat transfer. Specifically, the multi-relaxation time lattice Boltzmann method is adopted for the dynamics of non-Newtonian flow, with a geometry-adaptive technique to enhance the computational efficiency and immersed boundary method to achieve no-slip boundary conditions. The heat transfer equation is spatially discretized by a second-order up-wind scheme for the convection term, a central difference scheme for the diffusion term, and a second-order difference scheme for the temporal term. The structural dynamics is numerically solved using a finite difference method. The major contribution of this work is the integration of spatial adaptivity, thermal finite difference method, and fluid flow immersed boundary-lattice Boltzmann method. Several benchmark problems including the developing flow of non-Newtonian fluid in a channel, non-Newtonian fluid flow and heat transfer around a stationary cylinder and flow around a stationary cylinder with a detached filament are used to validate the present method and developed solver. The good agreements achieved by the present method with the published data show that the present extension is an efficient way for fluid–structure interaction and heat transfer involving non-Newtonian fluid. The heat transfer around an oscillating cylinder in non-Newtonian fluid flow at Reynolds number of 100 is also numerically studied using the present solver, considering the effects of the oscillating frequency and amplitude. The results may be used to expand the currently limited database of fluid–structure interaction and heat transfer benchmark studies.
Highlights
Experiments are expensive and challenging with increasing complexity
The fluid dynamics and heat transfer are solved by the lattice Boltzmann method (LBM) and finite difference method, respectively, with multi-relaxation time and a geometry-adaptive mesh technique to achieve good stability and computational efficiency
We present for the first time an integration of spatial adaptivity, thermal finite difference method, and fluid flow IB-LBM
Summary
Experiments are expensive and challenging with increasing complexity. As an alternative research method, numerical simulations have attracted much attention in the past twenty years [1]. The fluid dynamics and heat transfer are solved by the LBM and finite difference method, respectively, with multi-relaxation time and a geometry-adaptive mesh technique to achieve good stability and computational efficiency. The present method can handle problems involving FSI with complex boundaries and heat transfer in non-Newtonian fluid flow. A hybrid immersed boundary–lattice Boltzmann and finite difference method for FSI and heat transfer in non-Newtonian flow is presented, with the geometry-adaptive Cartesian mesh technique to enhance the computational efficiency. In this contribution, we present for the first time an integration of spatial adaptivity, thermal finite difference method, and fluid flow IB-LBM.
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