Joule heat calculations for simulations of multielectrode glass melters and in situ vitrification systems

Abstract

A procedure is developed for calculating Joule heating power density in simulating multielectrode, multiphase, generalized waveform electrically heated glass melters and in situ vitrification systems. A superposition principle valid at low frequencies allows calculating the cycle-averaged power density from a set of potential amplitude solutions, each solution having a current source amplitude in one electrode and a current sink amplitude in another electrode of a driven electrode pair. The calculated cycle-averaged power density can be coupled to balance equations for flow and energy in molten glass or soil. The procedure has advantages over the complex harmonic form for analyzing systems having waveforms chopped by silicon controlled rectifiers. A Scott-T transformer configuration with two emfs driving diagonally opposite electrodes in a rectangular array is one configuration having practical significance. Symmetries of this configuration are affected by amplitudes, phase relations, and waveforms of the electrical driving.