Rheometric assessment and numerical simulation of steady-state and periodic flows of fabric-water mixtures in household top-load washing machines

The washing process in household top load washing machines relies on the mass and momentum transport from an agitator to the fluid stream. In such cases, such a periodic flow follows a pattern that recalls the so-called Taylor-Couette flow, whose main characteristic is the confinement between two rotating cylinders. The present paper is aimed at steady-state and periodic-unsteady-state flows of non-Newtonian fluids formed by fabric and water mixtures. A simplified coaxial double cylinder geometry is used as the physical domain for the numerical analyses, whereas an agitation profile (angular swept and speed) was imposed to the inner cylinder. The rheological properties of the working fluid made of aqueous fabric suspensions were obtained in-house by solving the Couette inverse problem using a wide-gap rheometry approach. Four different NNF models have been evaluated - namely, Bingham, Casson, Robertson-Stiff, and Herschel-Bulkley - for data reduction and correlation, when it was observed that the last one provided the best results for different fabric-water suspensions. Numerical simulations were performed using a 3D homemade finite-volume model, and experimental tests (234 runs at steady-state and 80 runs at periodic flow conditions) were carried out by means of a purpose-built testing facility. The simulation model was validated against experimental data indicating an agreement between numerical and experimental torques and velocities within the 20% thresholds.