## Dissertations and Theses

2021

Dissertation

#### Department

Mechanical Engineering

Taehun Lee

#### Keywords

Computational fluid dynamics; Lattice Boltzmann method; Fluid-particle interactions; Diffuse boundary

#### Abstract

Fluid-structure interaction is very broadly seen and widely used in many industrial, engineering and environmental processes. The lattice Boltzmann method has been preferred for simulating particulate flows due to its advantages of easy implementation, micro- and mesoscopic physical insights and parallel algorithm. Both sharp and diffuse boundary treatments are studied to recover curved and moving boundaries on structured orthogonal grids for the lattice Boltzmann method. These methods can describe curved boundaries more accurately and more smoothly than the naive staircase approximation. However, to improve the order of velocity accuracy and to reduce the fluctuation of force, either interpolation or additional momenta have been introduced to the collision step of lattice Boltzmann equation.

In this dissertation, a new boundary scheme based on diffuse geometry is proposed for lattice Boltzmann method. The scheme is named Diffuse Bounce Back-Lattice Boltzmann Method (DBB-LBM) and is derived by directly incorporating the bounce back condition into the weak form of the propagation step of discretized Boltzmann equation. The new method does not change the collision operator. Therefore it can be easily combined with other fluid models that modify the collision step, such as multi-phase flow model, turbulence model, non-Newtonian model, etc. Although diffuse boundary is introduced, this scheme recovers exact bounce back condition at sharp boundary limit, regardless of the shapes and motions of the boundaries. Numerical tests show that the velocity accuracy of this method is second order.

Under the Diffuse Bounce Back scheme, the boundary force can be simply recovered by taking the first moment of the boundary term. This treatment to boundary force is natural and does not require the calculation of momentum exchange. The new boundary force model is able to recover the drag coefficient of cylinder flows at different Reynolds numbers correctly. In moving boundary problems, the fluctuation of force can be reduced compared to traditional sharp boundary conditions because it does not require extrapolation to fulfill the unknown information of the newly generated fluid nodes around the boundaries. The validated force model can be applied to fluid-particle interaction problems to study the behavior of particle in various flows, including the inertial migration of particle in the Taylor Couette flow.

In this dissertation, the background and applications of fluid-structure interaction are first introduced. Descriptions of previously published models for fluid-structure interaction are expanded upon afterwards. Detailed inspiration and derivation for the new DBB-LBM scheme are explained, and several benchmark problems are initiated to test and validate its accuracy, performance of mass conservation and the effect of different parameters and factors. The force model proposed within the framework of DBB-LBM is then introduced and applied to the cylinder flow benchmark problem for validation. A complete fluid-particle interaction model is built upon the Diffuse Bounce Back boundary scheme, the moment force model, the Velocity Verlét Integration of Newton’s Equations of Motion, together with the models for internal and external forces like gravity and repulsion. The combination is tested by a series of problems including particle in Couette flow, particle in Poiseuille flow, and the drafting, kissing and tumbling of two falling particles. The trajectories of the particles are consistent with the reported data in previous publications. The proposed boundary scheme is finally applied to the 3D Taylor Couette flow simulations with and without particles, in order to study the flow regimes at different Taylor numbers and the behaviors of inertial particle migration under these flow structures.

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