Numerical simulation of viscoelastic particulate flows using the immersed boundary method [electronic resource]
Keywords: Mechanical Engineering.

There are no comprehensive simulation-based tools for engineering the flows of viscoelastic fluid-particle suspensions in fully three-dimensional geometries. In many engineering applications, such as in oil and gas industry, 3D Printing etc., the need for such a tool is immense. This work describes the development of a high-performance computational approach that targets the three-dimensional, time-dependent flows of viscoelastic suspensions for a variety of rheological models. The simulation tool is based on an immersed boundary (IB) algorithm, which is a simple, scalable and cost-effective approach to simulate flows around complex, moving and deforming bodies without requiring the generation of a computational grid that conforms to the fluid flow boundaries at every time instant; instead the approach uses a background mesh that covers the domain of interest without the moving bodies and accounts for their effect by modifying the mathematical formulation of the problem, resulting in a two-way coupled simulation, where the flow is resolved at the scale of the particle. Typically in IB methods, the computational grids are chosen to be Cartesian for simplicity. Cartesian grids cannot, however, efficiently represent complex geometries often encountered in engineering applications. With the objective of developing a highly flexible tool, an unstructured mesh framework is combined with an immersed boundary based viscoelastic solver for moving bodies, in a finite volume setting. This strategy has not been presented before and represents the primary highlight of the work. The generality of the resulting computational tools enables us to span a variety of relevant geometrical configurations and a broad range of rheological models; this, in turn, allows us to establish detailed explanations for various phenomena with the long-term potential of designing fluid suspensions for different applications. In this approach, the conservation of mass and momentum equations, which include both Newtonian and non-Newtonian stresses, are solved over the entire domain including the region occupied by the particles. It is assumed that this region is filled with a fluid with the density equal to the particle density. The particle is defined on a separate mesh that is free to move over the underlying grid. The motion of the material inside the particle is constrained to be a rigid body motion by adding a rigidity constraint body force in the momentum equation. We also correct the non-Newtonian stress field, to satisfy isotropic condition inside the particle. Since the grid sizes are such that, the lubrication forces are not resolved, we employ a collision model to treat particle-particle and particle-wall interactions. The development of the numerical algorithm and measures taken to enable efficient parallelization and transfer of information between the underlying fluid grid and the particle mesh are discussed. A number of flows, simulated using this method are presented to assess the accuracy and correctness of the algorithm. The ability of the tool to capture the underlying physics and mechanisms of fluid-particle interaction is highlighted in a few examples. Finally, the solver is applied to carry out two large-scale simulations: particulate flow in an asymmetric T-Junction and sedimentation of suspensions in a Taylor-Couette cell under the action of orthogonal shear.