Clothes washing simulations

Abstract

Better washing machine designs and operation could reduce energy and water usage and extend cloth life. Washing machine studies have been traditionally empirical, since laundering typically involves complex motion of many cloth pieces in an inhomogeneous (fluid, cloth, detergent, agitator) setting. This paper presents a physics-based model of fully-submerged clothes washing in two- and three-dimensions. Multiple cloth pieces are modeled as thin elastic plates with tensile, shear, bending, and torsional stiffness, while the wash fluid is modeled with the incompressible Navier–Stokes equations. The fluid–cloth interaction is modeled via an immersed boundary method, and complex two- and three-dimensional agitator geometries are simulated with a Cartesian domain-mapping technique. The simulations have relatively coarse resolution that does not resolve all length scales for typical washing machine operating conditions. Hence, the converged results shown here are for moderate Reynolds numbers (Re). The simulation results include cloth stresses, torque on the wash basket, and the motion and deformation of the submerged cloth pieces. Specifically, the 3-D results show that the cloth stresses increase and the torque exerted on the outer wash basket decreases with increasing Re. The simulations examine how cloth motions differ with Reynolds number and cloth loading. The results reveal that for an agitator-driven 3-D wash geometry at higher Re, cloth pieces near the agitator at the bottom of the wash basket are first pushed by centrifugal force towards the outer stationary walls of the wash basket, then rise towards the top surface where they return to the axis of rotation and then sink towards the agitator. The variation of the center of mass positions of the cloth pieces are shown to increase for higher Re operating conditions.