Physics Based Washing Machine Simulations.

Abstract

This thesis describes the development of a simulation of the interaction of cloth and water that takes place inside a washing machine. The simulation consists of four basic parts: a large deformation elastic thin plate model for the cloth based on Love (1944), a rectangular-Cartesian-mesh solver for the Navier-Stokes equations based on Brown et al. (2001), the Immersed Boundary method of Peskin (1972) for cloth/fluid interaction, and a domain-mapping technique for representing irregular domain boundaries on Cartesian grids.

Although the lack of an accompanying experimental effort prevented its thorough validation, the final simulation was subjected to a variety of validation tests involving analytical solutions and experimental measurements in simple geometries. The implementation of the thin plate model combined with the Immersed Boundary method was able to match the natural frequencies of a vibrating plate within +/- 1%, and was able to predict large deformation beam shapes with similar accuracy. In addition, this validation effort suggests that the ratio between the Immersed Boundary method’s Lagrangian and Eulerian point-spacings should be approximately unity for better accuracy, when accounting for finite bending stiffness. Furthermore, it was found that the Immersed Boundary method formulation may provide better results with a narrow desingularization of the two-dimensional cloth onto the three-dimensional Cartesian mesh while sacrificing numerical stability. Complicated moving boundaries are handled by a domain-mapping technique that uses a Heaviside function to switch between solving the equations for the cloth/fluid mixture and specifying the velocity field for the washing machine’s solid boundaries. This boundary-condition formulation was benchmarked against well-known steady and unsteady flow fields: circular Couette flow, and a uniform flow past a cylinder.

Using these individually verified basic components together, two and three-dimensional simulations of the washing machine processes are created. A selection of studies involving the effect of different numerical and physical parameters on the kinematics of cloth motion and the statistics of the cloth stresses in a vertical-axis washing machine are reported. In particular, the coarse grid simulations predicted a realistic and qualitatively correct pattern for the motion of the cloth pieces.