Theoretical models of the electrical discharge machining process. III. The variable mass, cylindrical plasma model
A variable mass, cylindrical plasma model (VMCPM) is developed for sparks created by electrical discharge in a liquid media. The model consist of three differential equations—one each from fluid dynamics, an energy balance, and the radiation equation—combined with a plasma equation of state. A thermophysical property subroutine allows realistic estimation of plasma enthalpy, mass density, and particle fractions by inclusion of the heats of dissociation and ionization for a plasma created from deionized water. Problems with the zero-time boundary conditions are overcome by an electron balance procedure. Numerical solution of the model provides plasma radius, temperature, pressure, and mass as a function of pulse time for fixed current, electrode gap, and power fraction remaining in the plasma. Moderately high temperatures (≳5000 K) and pressures (≳4 bar) persist in the sparks even after long pulse times (to ̃500 μs). Quantitative proof that superheating is the dominant mechanism for electrical discharge machining (EDM) erosion is thus provided for the first time. Some quantitative inconsistencies developed between our (1) cathode, (2) anode, and (3) plasma models (this series) are discussed with indication as to how they will be rectified in a fourth article to follow shortly in this journal. While containing oversimplifications, these three models are believed to contain the respective dominant physics of the EDM process but need be brought into numerical consistency for each time increment of the numerical solution.