Fluid-Structure Interaction Simulations of Flows with Symmetry: From Fish Schooling to Rheology of Suspensions
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A numerical framework is developed to model large symmetric fluid-structure interaction (FSI) systems. The computational framework is based on the curvilinear-immersed boundary (CURVIB) method for FSI simulations. The fluid solver is extended by implementing periodic boundary conditions using parallel programming. For the structure solver, the 3-D rotation of rigid objects is added using quaternion-angular velocity, which do not cause drift as the conventional rotation matrix. We also developed a special treatment for immersed bodies passing through the periodic boundaries. After demonstrating the accuracy and validity of the implemented modifications, solvers were applied to simulate two important FSI problems: 1) Schooling for fish-like swimmers; and 2) Suspension of rigid particles. For fish-like swimming, we have discovered, for the first time, the leading edge vortex reattachment as a physical mechanism that enhances the locomotor force on fish tails. Furthermore, to the best of our knowledge, our large-eddy simulations for fish schooling are the first 3-D numerical simulations of a school of fish at realistic Reynolds number. We found up to 20\% higher swimming speed for fish schools relatives to a single swimmer, while using similar energy. For suspension modeling, we have simulated suspensions of arbitrary complex-shaped particles and, for the first time, calculated all the components of particle stress considering inertia. We found that inertia increases the contribution of the other components of the particle stress, e.g., acceleration and Reynolds stresses, which are typically ignored relative to the stresslet. The contribution of these components is small at low Re, but they are in the order of 10% of the total particle stress for Re ~ O (10) for ellipsoids. We also found that complexity of particles, especially when particles are more slender, can remarkably increase relative viscosity of a suspension compared to suspensions of simple particles. Moreover, normal stress differences are found to be significantly higher compared to Stokesian simulations of suspensions of axisymmetric particles.