Philip T. Eubank

Theoretical models of the electrical discharge machining process. I. A simple cathode erosion model

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 diele...

Theoretical models of the electrical discharge machining process. II. The anode erosion model

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.

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 ma...

Experimental (p, Vm, T) for pure CO2 between 220 and 450 K

Abstract Densities of pure carbon dioxide were measured using Burnett, Burnett-isochoric, and isochoric techniques. The measurements were made at temperatures from 217.01 to 448.15 K and pressures up to 47.7 MPa. Eleven vapor-pressure measurements were also made. Second and third virial coefficients were derived. Three saturated-liquid and five saturated-vapor densities were also derived from the measurements.

Experimental densities and virial coefficients for steam from 348 to 498 K with correction for adsorption effects

Amount-of-substance densities ϱn of pure ordinary steam were measured from 348 to 498 K at pressures from several kPa to the vapor pressure using the Burnett and Burnett-isochoric methods. Second and third virial coefficients were derived from the ϱn measurements after correction for adsorption errors. New adsorption-correction methods are outlined which provide the form and magnitude of the adsorption isotherm—here, B.E.T. Three independent sets of results are presented. Success or failure to correct each set for adsorption is demonstrated to depend upon: the physical strength of adsorption occurring upon the cell and valve-packing surfaces; and the ingenuity of the adsorption-correction scheme. Comparisons with literature measurements and correlations show which previous results were affected by adsorption. The compatibility of the present second and third virial coefficients with the widely accepted saturation properties of the recent NBS/NRC Steam Tables provides a final test of the accuracy of our corrected values.

Thermophysical properties of gaseous carbon dioxide- water mixtures

Abstract A Burnett-Isochoric (B-I) apparatus was used to obtain precise, experimental, vapor-phase P-ϱ-T data for mixtures of 2%, 5%, 10%, 25%, and 50% water in carbon dioxide for temperatures from 323.15 K to 498.15 K at 25 K intervals, and pressures from 27 kPa to 10.34 MPa or the dew point at each temperature. Separate experimental measurements for pure water, along with corrected compressibility data from the literature, were used to characterize physical adsorption within the B-I apparatus using the Brunauer-Emmett-Teller (B-E-T) adsorption model coupled with the sequential Burnett equations. The resulting adsorption constants were used to correct the compressibility data for the present mixtures and precise values were obtained for the second virial coefficients, enthalpies, and other derived thermodynamic properties. Interaction second virial coefficients, B12, and interaction third virial coefficients, C112 and C122, were also determined from the mixture virial coefficients. The densities are considered accurate to 5/10,000, and the mixture second virial coefficients to ±3 cm 3/mol. In addition, dew points (±1 K and ±14 kPa) were also measured for the above mixtures by noting the change in slope of the isochores.

Carbon dioxide-water phase equilibria results from the Wong-Sandler combining rules

Abstract A model based upon the Peng-Robinson equation of state with the Wong-Sandler mixture combining rule (W-S MCR) can correlate phase equilibria in CO 2 + H 2 O. The W-S MCR requires two energy parameters for liquid behavior and one interaction parameter for gas behavior, k ij . In this paper, we present expressions for the energy parameters which cover a wide temperature range, and we use a new procedure to obtain k ij by relating it to experimental cross second virial coefficients, B ij . The three-phase pressures calculated for this system using our proposed model agree with the experimental data within a fraction of 1 bar. The correlated phase behavior of CO 2 + H 2 O appears to be accurate over the ranges 1 – 1000 bar and 298.15–623.15 K. The proposed model also confirms the advantage of using the W-S MCR for phase equilibrium calculations.

An algebraic method that includes Gibbs minimization for performing phase equilibrium calculations for any number of components or phases

The most widely used technique for performing phase equilibria calculations is the K-value method (equality of chemical potentials). This paper proposes a more efficient algorithm to achieve the results that includes Gibbs minimization when we know the number of phases. Using the orthogonal derivatives, the tangent plane equation and mass balances, it is possible to reduce the Gibbs minimization procedure to the task of finding the solution of a system of non-linear equations. Such an operation is easier and faster than finding tangents or areas, and appears to converge as fast as the K-value method. Examples illustrate application of the new technique to two and three phases in equilibrium for binary and ternary mixtures.

The density of gaseous ethane and of fluid methyl chloride, and the vapor pressure of methyl chloride

Abstract The amount-of-substance density ϱn of gaseous ethane was measured in a Burnett-isochoric apparatus from 323 to 473 K in 25 K increments. Thirteen isochores ranging from 15.94 to 1489.0 mol m−3 nominal ϱn provide pressures from 43.0 to 5390kPa. For methyl chloride values of ϱn were observed at the same temperatures covering the vapor, gas, and near-critical regions. Seventeen isochores ranging from 20.42 to 8653.1 mol m−3 nominal ϱn provide pressures from 55.4 to 14908 kPa. Dense-vapor values near saturation are corrected for adsorption by a new technique. Second and third virial coefficients as well as derived thermophysical properties are reported for both ethane and methyl chloride. Optimal Lennard-Jones and Stockmayer force constants are calculated for ethane and methyl chloride respectively. Two sets of vapor pressures for methyl chloride are reported for the temperature range 313 to 408 K (T68c = 416.27 K).

P—V—T data and virial coefficients for gaseous methane—water mixtures with correction for adsorption effects

Abstract Precise experimental P —ϱ— T measurements for 10, 25, and 50 mole per cent water in methane mixtures were obtained using a Burnett—Isochoric (B—I) apparatus. These data are vapor—phase measurements at temperatures from 398.15 K to 498.15 K and pressures of 72 kPa to 12.03 MPa or the dew point pressure at each temperature. In the analysis of these data, we have corrected for the effects of H 2 O adsorption on the measured pressures using a Brunauer—Emmett—Teller (BET) adsorption model and applicable BET adsorption constants. This analysis yielded precise values of compressibility factors, densities, and mixture and interaction virial coefficients. The densities are believed to be accurate to within 8/10,000 and the mixture second virial coefficients to ± 2 cm 3 /mol. Additionally, dew point pressures were determined for each mixture by calculating the point of slope change in the vapor isochores.