A simple cathode erosion model for the electrical discharge machining (EDM) process is presented. This point heat-source model differs from previous conduction models in that it accepts power rather than temperature as the boundary condition at the plasma/cathode interface. Optimum pulse times are predicted to within an average of 16% over a two-decade range after the model is tuned to a single experimental point. A constant fraction of the total power supplied to the gap is transferred to the cathode over a wide range of currents. A universal, dimensionless model is then presented which identifies the key parameters of optimum pulse time factor (g) and erodibility (j) in terms of the thermophysical properties of the cathode material. Compton’s original energy balance for gas discharges is amended for EDM conditions. Here it is believed that the high density of the liquid dielectric causes plasmas of higher energy intensity and pressure than those for gas discharges. These differences of macroscopic dielectric properties affect the microscopic mechanisms for energy transfer at the cathode. In the very short time frames of EDM, our amended model uses the photoelectric effect rather than positive-ion bombardment as the dominant source of energy supplied to the cathode surface.

As a second in a series of theoretical models for the electrical discharge machining (EDM) process, an erosion model for the anode material is presented. As with our point heat-source model in the previous article, the present model also accepts power rather than temperature as the boundary condition at the plasma/anode interface. A constant fraction of the total power supplied to the gap is transferred to the anode. The power supplied is assumed to produce a Gaussian-distributed heat flux on the surface of the anode material. Furthermore, the area upon which the flux is incident is assumed to grow with time. The model is capable of showing, via the determined migrating melt fronts, the rapid melting of the anodic material as well as the subsequent resolidification of the material foation from plasma dynamics modeling could improve substantially our results.

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.

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Thermal membrane distillation (TMD) is an emerging technology which is gaining an increasing level of interest in the area of high-purity separation especially in water treatment. It is driven primarily by heat which creates a vapor-pressure difference across a porous hydrophobic membrane. The integration of TMD with industrial processes offers several advantages. Excess low-level heat from the process can be used to drive TMD. This transfer of heat also reduces the cooling utility load for the process. Therefore, dual heat-reduction benefits accrue as a result of this heat integration. Additionally, process wastewater and utility water may be treated using TMD then recycle or reused in the process or sold to external users. This paper introduces a process integration framework from the thermal coupling of TMD networks and industrial processes. First, a three-parameter model is developed to quantify the water flux through the membranes as a function of heat and temperature. The model is validated using experimental data for direct-contact membrane distillation (DCMD). Next, the trans-shipment model for heat integration is extended to account for the coupling of the process and the TMD network and the need to optimize the extent of heating for the TMD feed. A discretization approach is used to linearize the thermal-coupling constraints. The mathematical-programming formulation is solved to identify the optimal heat integration strategies within the process and with the TMD network. The program also determines the optimal temperature to which the TMD feed should be heated and the system design and specification. A case study is solved to show the integration between a gas-to-methanol process and an adjacent desalination process. Three scenarios are considered: a standalone TMD network, TMD with thermal and water coupling with a process in an eco-industrial park setting, and TMD as part of the processing facility.