Finite element analysis of electrochemical machining problems, validity of electroneutrality assumption, and flow in solution crystal growth system

This thesis consists of three independent parts: In first part, the problems of workpiece shape prediction (direct problem) and tool shape design (inverse problem) in electrochemical machining (ECM) are simulated as free-boundary and optimization problems. The inverse problem is difficult to solve due to its mathematically ill-posed nature, but is extremely important to the ECM industry. The optimization method proves to be a viable approach to the inverse problem. In second part, the question of the validity of applying the electroneutrality condition (ENC) to simulations of electrochemical cells of microelectrodes is answered by simulating a steady-state electrochemical reaction in a microelectrode cell. It is demonstrated that as the size of the microelectrode reduces, the deviation away from the ENC increases, and the ENC is not always a valid assumption for submicron microelectrode cells. In third part, fluid flow encountered in a KDP solution single crystal growth (SCG) system is simulated. Fluid flow around a growing single crystal is important because it can significantly affect growth rate and morphology of the crystal. Due to complicated three dimensional crystal shape, and time-dependent forced agitation, realistically simulating flow in solution SCG systems is a big challenge.; The Galerkin finite element method is employed as the basic research tool for all simulations involved, and computer resources used are IBM RISC6000 work-station and Thinking Machine CM-5 massively parallel supercomputer.