Transient hydrodynamic stresses on reciprocating hollow fibers using Hydro-Rattle algorithm: A constraint dissipative hydrodynamics simulation

Hollow fiber membranes are widely used for unit processes in wastewater treatment, including (submerged) membrane bioreactors. Interfacial fouling on the fiber surfaces, often caused by small fiber diameters, is controlled, using energy-intensive bubble blowers. A new cost-effective paradigm is to reciprocate submerged cassettes that carry hollow fibers undergoing hydrodynamic shear stresses. Oscillation dynamics of flexible fibers seems to be a challenging investigation because fluid–fiber hydrodynamic interactions need to be rigorously formulated while applying the wave equation is precluded. As the order-of-magnitude estimation of mechanical stresses on moving fibers is of great interest, we assumed that a hollow fiber can be mathematically modeled as a chain of many connected spheres of an order of O103, having the chain length and sphere diameter set equal to those of identical fibers. Holonomic and non-holonomic constraints are implemented to keep spheres from dispersing and the dissipative hydrodynamics, and to satisfy the position–velocity orthogonality. Hydrodynamic interactions were calculated using the grand-mobility matrix of poly-dispersed spheres, and the constraint forces are implemented using an updated algorithm of Hydro-Rattle [Kim (2012)]. Dynamic locations of the highest mechanical stresses are identified, and practical suggestions for the optimal, long-term operations of the cassette-reciprocating process are included.