Verification of a One-Dimensional Two-Phase Flow Model of the Frontal Gap in Electrochemical Machining

1976 ◽  
Vol 98 (2) ◽  
pp. 431-437 ◽  
Author(s):  
F. Fluerenbrock ◽  
R. D. Zerkle ◽  
J. F. Thorpe
Keyword(s):  
Flow Model ◽  
Radial Flow ◽  
Electrochemical Machining ◽  
Equilibrium Conditions ◽  
Two Phase ◽  
One Dimensional ◽  
Supply Pressure ◽  
Theoretical Predictions ◽  
The One ◽  
Experimental Pressure

A set of six equations, which are based on the ECM model developed by Thorpe and Zerkle, can be solved numerically to yield the one-dimensional distributions of pressure, temperature, gas density, gap thickness, void fraction, and electrolyte velocity in the rectilinear ECM frontal gap under equilibrium conditions. The validity of the model, which also applies to radial flow geometries, is confirmed by comparing experimental pressure and gap profiles with theoretical predictions. It is shown that for a given set of operating parameters there is a minimum supply pressure below which no machining is possible. When machining steel with an aqueous NaCl electrolyte the deposition of a black smut (Fe(OH)2) occurs beyond a certain smut-free entrance length, which was experimentally found to be proportional to the inlet gap thickness.

Modeling of Wall Friction for Multispecies Solid-Gas Flows

1986 ◽  
Vol 108 (4) ◽  
pp. 486-488 ◽  
Author(s):  
E. D. Doss ◽  
M. G. Srinivasan
Keyword(s):  
Shear Stress ◽  
Flow Model ◽  
Flow Characteristics ◽  
Wall Friction ◽  
Gas Flows ◽  
Two Phase ◽  
One Dimensional ◽  
Friction Models ◽  
Wall Interaction ◽  
The One

The empirical expressions for the equivalent friction factor to simulate the effect of particle-wall interaction with a single solid species have been extended to model the wall shear stress for multispecies solid-gas flows. Expressions representing the equivalent shear stress for solid-gas flows obtained from these wall friction models are included in the one-dimensional two-phase flow model and it can be used to study the effect of particle-wall interaction on the flow characteristics.

Prediction of the One-Dimensional Equilibrium Cutting Gap in Electrochemical Machining

1969 ◽  
Vol 91 (3) ◽  
pp. 755-763 ◽  
Author(s):  
J. Hopenfeld ◽  
R. R. Cole
Keyword(s):  
Experimental Data ◽  
Nonlinear Differential Equations ◽  
Electrochemical Machining ◽  
Local Variation ◽  
Two Phase ◽  
One Dimensional ◽  
Proper Design ◽  
Electrolyte Mixture ◽  
The One ◽  
State Case

In electrochemical machining the evolution of gas and heat in the electrolyte results in local variation of the gap between the electrodes. The ability to predict these variations for any given operating condition is a prerequisite of proper design of the cathode tool. This paper provides analytical predictions of the change in gap geometry for the one-dimensional steady-state case. Employing the basic conservation laws, a system of coupled nonlinear differential equations is derived for the gas-electrolyte mixture which flows between the electrodes. The assumption of homogeneity of the two-phase mixture is employed throughout the analysis. Numerical results from the solution of the equations are presented graphically and compared with experimental data. The local variation in gap and the relation between current, gap, and applied voltage compare favorably with the experimental data within the ranges of parameters investigated: current density 45–400 amps per sq in., electrolyte flow rate 0.22–0.98 gpm, entrance gap size 0.015–0.020 in., potassium chloride electrolyte normality 0.67–1.14.

A ONE-DIMENSIONAL TWO-PHASE FLOW MODEL AND EXPERIMENTAL VALIDATION FOR A FLASHING VISCOUS LIQUID IN A SPLASH PLATE NOZZLE

2015 ◽  
Vol 25 (9) ◽  
pp. 795-817 ◽  
Author(s):  
Mika P. Jarvinen ◽  
A. E. P. Kankkunen ◽  
R. Virtanen ◽  
P. H. Miikkulainen ◽  
V. P. Heikkila
Keyword(s):  
Viscous Liquid ◽  
Experimental Validation ◽  
Flow Model ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional

scholarly journals Modelling sedimentation–consolidation in the framework of a one-dimensional two-phase flow model

2013 ◽  
Vol 51 (3) ◽  
pp. 293-305 ◽  
Author(s):  
Julien Chauchat ◽  
Sylvain Guillou ◽  
Damien Pham Van Bang ◽  
Kim Dan Nguyen
Keyword(s):  
Flow Model ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional

Theoretical and computational investigation of the electrochemical machining process for characteristic cases of a stepped moving tool eroding a plane surface

1997 ◽  
Vol 211 (3) ◽  
pp. 197-210 ◽  
Author(s):  
H Hardisty ◽  
A R Mileham ◽  
H Shirvani
Keyword(s):  
Plane Surface ◽  
Electrochemical Machining ◽  
Machining Process ◽  
Surface Erosion ◽  
Computational Investigation ◽  
Step Size ◽  
One Dimensional ◽  
Erosion Rates ◽  
Spatial Differences ◽  
The One

A theoretical and computational investigation into the electrochemical machining (ECM) process for the case of a moving stepped tool eroding an initially flat surface is presented. Five parametric variations of the basic geometry of the stepped tool machining process are possible, depending on the relative distance between the moving tool and eroded work. For each of the five cases, and based on one-dimensional theory, formulae have been developed to predict the minimum depth of working material that must initially be provided to enable a particular step size to be machined to a specified tolerance. The computer simulation of the ECM process which has been developed is based on the finite element method (FEM). The geometry of tool, electrolyte and work is simulated by means of a two-dimensional mesh of square elements. A system of macros has been developed which interact internally with an FE package to move component boundaries systematically to simulate both tool movement and surface erosion. Such boundary movements are accomplished automatically and continuously without user intervention during a simulation run. The algorithms employed to achieve characteristically different erosion rates are described. Results both from one-dimensional ECM theory and from the computer simulations of the characteristic cases are presented. Comparisons show that there is good agreement between computer predictions and theory. The differential erosion process is fundamental to all ECM processes. Complex shapes evolve because of spatial differences in erosion rates. Thus the one-dimensional results presented here for the formation of a step should provide a basis for comparisons between spatially separated regions of one-dimensional differential erosion on bodies of arbitrary shape.

scholarly journals Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

2015 ◽  
Vol 62 (3-4) ◽  
pp. 101-119 ◽  
Author(s):  
Wojciech Artichowicz ◽  
Dzmitry Prybytak
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Integration ◽  
Cross Sections ◽  
Flow Model ◽  
One Dimensional ◽  
Averaging Methods ◽  
Integration Formulas ◽  
Different Types ◽  
The One

AbstractIn this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.

scholarly journals Validation of the generalized model of two-phase thermosyphon loop based on experimental measurements of volumetric flow rate

2016 ◽  
Vol 37 (3) ◽  
pp. 109-138 ◽  
Author(s):  
Henryk Bieliński
Keyword(s):  
Steady State ◽  
Flow Rate ◽  
Vertical Section ◽  
Volumetric Flow Rate ◽  
Working Fluid ◽  
Two Phase ◽  
Generalized Model ◽  
Flow Models ◽  
Theoretical Predictions ◽  
The One

AbstractThe current paper presents the experimental validation of the generalized model of the two-phase thermosyphon loop. The generalized model is based on mass, momentum, and energy balances in the evaporators, rising tube, condensers and the falling tube. The theoretical analysis and the experimental data have been obtained for a new designed variant. The variant refers to a thermosyphon loop with both minichannels and conventional tubes. The thermosyphon loop consists of an evaporator on the lower vertical section and a condenser on the upper vertical section. The one-dimensional homogeneous and separated two-phase flow models were used in calculations. The latest minichannel heat transfer correlations available in literature were applied. A numerical analysis of the volumetric flow rate in the steady-state has been done. The experiment was conducted on a specially designed test apparatus. Ultrapure water was used as a working fluid. The results show that the theoretical predictions are in good agreement with the measured volumetric flow rate at steady-state.

A Linear Stability Analysis for an Improved One-Dimensional Two-Fluid Model

2003 ◽  
Vol 125 (2) ◽  
pp. 387-389 ◽  
Author(s):  
Jin Ho Song
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Fluid Model ◽  
Two Phase ◽  
One Dimensional ◽  
Proposed Model ◽  
Two Fluid Model ◽  
The One ◽  
Two Fluid

A linear stability analysis is performed for a two-phase flow in a channel to demonstrate the feasibility of using momentum flux parameters to improve the one-dimensional two-fluid model. It is shown that the proposed model is stable within a practical range of pressure and void fraction for a bubbly and a slug flow.

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