Methods for computation of flow-driven string dynamics in a pump and residence time

<jats:p> We present methods for computation of flow-driven string dynamics in a pump and related residence time. The string dynamics computations help us understand how the strings carried by a fluid interact with the pump surfaces, including the blades, and get stuck on or around those surfaces. The residence time computations help us to have a simplified but quick understanding of the string behavior. The core computational method is the Space–Time Variational Multiscale (ST-VMS) method, and the other key methods are the ST Isogeometric Analysis (ST-IGA), ST Slip Interface (ST-SI) method, ST/NURBS Mesh Update Method (STNMUM), a general-purpose NURBS mesh generation method for complex geometries, and a one-way-dependence model for the string dynamics. The ST-IGA with NURBS basis functions in space is used in both fluid mechanics and string structural dynamics. The ST framework provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the turbulent nature of the unsteady flow, and the moving-mesh feature of the ST framework enables high-resolution computation near the rotor surface. The ST-SI enables moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-IGA enables more accurate representation of the pump geometry and increased accuracy in the flow solution. The IGA discretization also enables increased accuracy in the structural dynamics solution, as well as smoothness in the string shape and fluid dynamics forces computed on the string. The STNMUM enables exact representation of the mesh rotation. The general-purpose NURBS mesh generation method makes it easier to deal with the complex geometry we have here. With the one-way-dependence model, we compute the influence of the flow on the string dynamics, while avoiding the formidable task of computing the influence of the string on the flow, which we expect to be small. </jats:p>