Modeling and Applications of Electrochemical ...

Proceedings of the ASME 2009 International Mechanical Engineering Congress & Exposition IMECE2009 November 13-19, Lake Buena Vista, Florida, USA Proceedings of the ASME 2009 International Mechanical Engineering Congress & Exposition IMECE2009 November 13-19, Lake Buena Vista, Florida, USA

IMECE2009-12552 IMECE2009-12552 MODELING AND APPLICATIONS OF ELECTROCHEMICAL MACHINING PROCESS Makoto Yamamoto Department of Mechanical Engineering, Tokyo University of Science 1-14-6, Kudankita, Chiyoda-ku, Tokyo, 102-0073, Japan E-mail: [email protected]

Ryo Tsuboi Department of Mechanical Engineering, Tokyo University of Science 1-14-6, Kudankita, Chiyoda-ku, Tokyo, 102-0073, Japan E-mail: [email protected]

ABSTRACT Electrochemical Machining (below ECM) is one of advanced machining technologies and has been developed and applied in highly specialized fields, such as aerospace, aeronautics, defense and medical industries. In recent years, ECM is used in other industries such as automobile and turbo-machinery because of the following advantages. That is, it has no tool wear, and it can machine difficult-to-cut metals and complex geometries with relatively high accuracy. However, ECM still has some problems to be overcome. The efficient tool-design procedure, electrolyte processing, disposal of metal hydroxide sludge are the typical issues. In order to solve these problems, a numerical simulation is considered to be a powerful tool. However, the numerical code that can satisfactorily predict the flow field and the machining process has not been developed because of the complex flow natures such as the three-dimensionality, hydrogen bubble/metal sludge generation (i.e. three-phase effect), temperature increase and flow separation. In present paper, summery of my PhD works is mentioned, about modeling and applications. Modeling for ECM process takes into account metal dissolution, electrolyte flow, void fraction distribution of hydrogen bubbles generated from the tool cathode, thermal, electric potential, and electric conductivity. Especially, two types of method are used for the coupling between gas- and liquid-phase in electrolyte. One is one-way coupling method; only the electrolyte flow affects the void fraction distribution of hydrogen bubbles. The other is two-way coupling method; considering the interaction between the electrolyte flow and the void fraction distribution. In the two-way coupling method, considering bulk density distribution in the electrolyte flow path due to hydrogen bubble, Low-Mach-Number approximation is used for simulations. For applications with our numerical code, simulations for machining 3-D compressor blade are performed. Blade geometry is successfully predicted and we can obtain some guideline of ECM process. INTRODUCTION Electrochemical Machining (ECM) is an advanced machining technology. Gussef proposed and designed an ECM procedure in 1929. Since then, ECM has been developed and applied in highly specialized fields, such as the aerospace, aeronautics, defense, and medical industries. In recent years, ECM has been used in other industries, such

as the automobile and turbo-machinery industries, because of various advantages. For example, ECM has no tool wear, and can machine difficult-to-cut metals and complex geometries with relatively high accuracy. However, ECM still has some problems, including the lack of an efficient tool-design procedure, electrolyte processing, and disposal of metal hydroxide sludge. In order to solve these problems, numerical simulation is considered to be a powerful and promising tool. However, a numerical code that can satisfactorily predict the flow field and the machining process has not yet been developed because of the complex nature of the flows, including three-dimensionality, hydrogen bubble/metal sludge generation (i.e., three-phase effect), temperature increase, and flow separation. In a previous study, Tsuboi et al. [1] numerically investigated an ECM process. They simulated a three-phase flow in an ECM process using an Euler-Lagrange approach for gas and solid phases. Comparing the numerical results with the experimental data reported by Hopenfeld et al. [2], they obtained following findings. The effect of hydrogen bubbles was dominant, on the other hand the effect of metal sludge generation on the final shape of the workpiece was very small. The diameter of hydrogen bubbles of 30 µm was suitable for reproducing the experimental data. However, their simulations were performed while neglecting the interaction between liquid and gas phases (i.e., electrolyte and hydrogen bubbles), although hydrogen bubbles had a certain effect on the flow field. In addition, the density of hydrogen bubbles was very small, so that the number of bubbles was huge. As a result, the simulation with a Lagrangian approach required a large computation cost because a calculation was required for each hydrogen bubble. In an ECM process, hydrogen bubbles might accumulate downstream of the channel, and the void fraction (i.e., the gas volume fraction in the fluid) could exceed 0.5. Therefore, it was better to consider the gas phase as being continuous. Tsuboi et al. [3] presented two ECM process models. One method was based on a one-way coupling method, neglecting the effect from the gas phase to the liquid phase. The second method took into account the interaction between the gas and liquid phases, namely, the second method is a two-way coupling method. In the two-way coupling method, the multi-phase flow was simplified by some assumptions and Low-Mach-Number approximation. Generally, in a gas-liquid flow, the slip-velocity existed between gas and liquid phases. However, each interaction based on the slip-velocity was quite complex, and the simulation cost became very high. Moreover, we attempted to develop a design tool to simulate an

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Copyright © 2009 by ASME

ECM process in a three dimensional configuration, such as a compressor blade, with a reasonable computation cost. Based on these considerations, we assumed that the gas phase had the same velocity as the liquid phase. Neglecting the slip velocity, it was not necessary to consider the interaction force, such as the added mass force, the Basset force, the Magnus force, and the Saffman lift force, which were numerically time-consuming. These assumptions make it easier to treat the two-phase flow. In order to verify the developed model, we simulated the two-phase flow fields in an ECM process for machining a two-dimensional channel configuration. As mentioned above, since the solid phase has very small effects on the electrolyte flow field, we considered only the gas and liquid phases. Comparing the one- and two-way coupling methods, we found that the predicted velocity profiles in the downstream region showed a little difference. Near the cathode side, the electrolyte velocity decreased in the case of the twoway coupling method. Because of the decreased velocity near the cathode region, the void fraction and temperature became high locally. Consequently, the gap height in the two-way simulation is greater than that in the one-way simulation. In addition, the diffusion coefficient of CG = 1.5×10-6 m2/sec showed good agreement, where CG represents the diffusion coefficient for the gas phase. Later, we added a treatment for the hydrogen source. Since we took into account the hydrogen bubble size, the hydrogen source is applied for grids that are closer to the cathode surface than the hydrogen bubble size. After all, the diffusion coefficient of CG = 3.0×10-6 m2/sec showed a good agreement with experimental data. Fujisawa et. al. [4] researched electrochemical machining process for a compressor blade. They use one-way coupling method for the flow field, compared the simulation results with the experimental data. They indicate the difference of the dimension for the Reynolds number. Tsuboi et. al. [5] calculate hydrogen bubble trajectories and investigate the distribution and a behavior of hydrogen bubbles for ECM process in 3D compressor blade. In this paper, summery of my PhD works is mentioned, about modeling and applications. Our previous works are reviewed. First, we proposed modeling of electrochemical machining process. For the validations of the model, we perform the simulations for the flat plate channel configuration and inspected the dependence of the initial gap height on the final shape of the workpiece. And we investigate the difference of one- and two- way coupling method of the interaction of gas and liquid phase for the three-dimensional compressor blade. Finally we summarize the some guideline of simulation in ECM process. GOVERNING EQUATIONS FOR MULTI-PHAE FLOW Equations of Gas-phase Multi-phase flow consists of several phases. But it can be described like a single-phase flow. Continuity and Navier-Stokes equations of gas-phase are given as

∂α G ρ G r + ∇ ⋅ (α G ρ G u G ) = Γ ∂t

(1)

r r r ∂α G ρG uG r + uG ⋅ ∇(α G ρG uG ) = −α G ∇p + α G DG ∇ 2uG ∂t

(2)

path. Sokolichin et al. [6] add the diffusion-like term to the continuity equation of gas-phase, to simulate bubble columns. We follow this simple and easy technique. Thus Equation (1) is rewritten as

r ∂α G ρ G (3) + ∇ ⋅ (α G ρ G uG ) = Γ + CG ∇ 2α G ρ G ∂t where CG is the diffusion coefficient. Note that, in gas-phase, to describe the diffusion of the gas-phase, there are two diffusion coefficients in the governing equations. In addition, DG is the diffusion coefficient for the equation of momentum, and CG is the diffusion coefficient for the equation of mass conservation. However, at present, there is insufficient knowledge to decide the value of CG. Therefore, we need to choose an appropriate value so as to reproduce experimental data. Equations of Liquid-phase Similar to those of the gas-phase, the continuity and N-S equations of liquid-phase are written as,

r ∂α L ρ L + ∇ ⋅ (α L ρ L u L ) = − Γ − CG ∇ 2α G ρ G ∂t

(4)

r r r ∂α L ρ L u L r + u L ⋅ ∇(α L ρ L u L ) = −α L ∇p + α L µ L ∇ 2 u L ∂t

(5)

where αL is liquid volume fraction，and µL is the viscosity coefficient. Γ in Equation (4), like that in Equation (1), is the source term of the mass per unit volume. The 2nd term in Equation (4) is the diffusion effect affected by the gas-phase, expressed in Equation (3). Gas- and liquid- phases occupy most of the domain, while the solid-phase occupies a very small part of the domain in the ECM flow path. The volume fraction of each phase satisfies the following relation:

αG + α L + αS = 1 (α S = 0)

(6)

COUPLING METHOD One-Way Coupling Method In a one-way coupling method, we do not take into account the effects from gas-phase to liquid-phase. Therefore, we can compute each phase individually. First, Equations (4) and (5) for the liquidphase are solved, neglecting 2nd term in Equation (4) and setting αL to unity. In this coupling, the relation between αG and αL expressed as Equation (6) is not considered. The Poisson equation for solving the pressure field is

∇2 p = −

r r ∂D − ∇ ⋅ ∇ ⋅ (ρu L u L ) +ν L ∇ 2 D ∂t

(7)

where νL is the kinematic viscosity coefficient of the fluid. And D is given as r (8) D = ∇ ⋅ ( ρ Lu L ) After a convergence is reached in a simulation, the void fraction distribution is computed using Equation (3), where uG is defined as being equal to uL.

where αG is gas volume fraction and DG is diffusion coefficient. In the present study, DG is assumed to be the same as the viscosity coefficient of liquid phase µL. In Equation (1), Γ is the source of mass per unit volume depending on the phase change that occurs in electrolysis on the cathode in an ECM process. We introduce the diffusion effect of random fluctuations of hydrogen bubble motion in an electrolyte flow

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Two-Way Coupling Method Assuming that gas-phase velocity is equal to liquid-phase velocity, described as r r r (9) uMIX = uG = uL where the MIX subscript denotes variables of multi-phase. Summing Equation (3) and (4), Equation (2) and (5), we obtain Equations (10) and (11).

r ∂ρ MIX + ∇ ⋅ (ρ MIX uMIX ) = 0 ∂t

(10)

r r r ∂ρ MIX uMIX r + uMIX ⋅ ∇(ρ MIX uMIX ) = −∇p + µ MIX ∇ 2uMIX ∂t

(11)

ρ MIX = α G ρ G + α L ρ L

(12)

µ MIX = α G DG + α L µ L

(13)

Equation (10) is the continuity equation and Equation (11) is the N-S equation for simulation of multi-phase flow in the ECM process. Generally, in computing incompressible flow, we neglect the change in density, but in this model, the change in density depends on the void fraction distribution as in Equation (12). Therefore, we must compute pressure field with Low-Mach-Number approximation. From Equation (11), pressure Poisson equation is given as

∇2 p = −

r r µ ∂DMIX − ∇ ⋅ ∇ ⋅ (ρ MIX uMIX uMIX ) + MIX ∇2 DMIX ρ MIX ∂t

(14)

where D is described in Equation (8), and the term of divergence D is solved with Low-Mach-Number approximation, given by ∂D 1  ρ N +1 − ρ N r =  + ∇ ⋅ ρu N ∂t ∆t  ∆t

(

)

(15)



where N denotes a time step for solving the equations. MODELING OF OTHER PHENOMENA Temperature Fields In simulations of incompressible flow, the energy equation to solve the temperature field is given as

∂T r λ i2 + u ⋅ ∇T = ∇ 2T + ∂t ρC p ρC pκ

(16)

where λ is the thermal conductivity, and CP is the specific heat at constant pressure, which are defined as,

λ = α G λG + α L λ L

(17)

C P = α G C PG + α L C PL

(18)

nd

The 2 term on the right-hand side of Equation (16) is the Joule heating effect generated by applying voltage. Electric Potential and Conductivity The electric potential field follows Ohm’s law and is given by

∇ ⋅ (κ ∇E ) = 0

Electrochemical Reaction Model The amount of metal dissolution and hydrogen bubble generation can be analyzed theoretically, using Faraday’s law for electrolysis. This analysis is based on the following assumptions; (1) The processed materials are assumed not to include impurities, and are assumed to be homogeneous. In addition, the material valence is assumed to be known before processing. (2) The dissolution of metal is the only reaction on the anode and hydrogen bubble generation is the only reaction on the cathode. That is, on the electrode, the metal dissolution and hydrogen bubble generation are not accompanied by other subreactions. (3) The metal is removed by only the dissolution and not by the collapse. That is, the processed material is dissolved in an atomic level, and the atoms do not exfoliate and cluster in a group. The electricity required reacting one gram-equivalent of material is F [C], according to Faraday's law. Since the equivalence ratio for one gram of material with a valence of n and an atomic weight of M is n/M, the amount of electricity needed to react one gram of material is nF/M [C]. Therefore, when an electric current of I [A] for t [s] react a mass of w [g] of material, the following equation is obtained: It =

(19)

wnF M

(21)

Electric Current Efficiency Electric current efficiency η indicates the rate of the electrons used for the electrochemical reaction. The current efficiency is expressed as,

η=

wreal wtheoretical

(22)

where subscripts real and theoretical denote the real and theoretical value, respectively. Considering some metal as a reactant material, in case of η > 100%, the metal dissolves with a lower valence than that used in the calculation. That is, the metal collapses on the anode and the cluster of atoms drops out. This is called ‘Chunk effect’ [8]. On the other hand, in case of η < 100%, the metal dissolves with a higher valence than that used in the calculation, and part of the electrons are consumed by some sub-reactions. Metal Processing Speed When the metal volume removed is V and the atomic density is ρ, subscript M denotes variable of metal. wM = ρ M VM

(23)

Substituting this relation into Equation (21), we obtain VM =

MM

ρ M nM F

It

(24)

where, F is Faraday’s constant ( 96485.3 [C/mol] ). If the distance between two points is ∆y, the processing area is S and the electric conductivity of the distance is κ, the resistance R between the two points is expressed as R=

The electric conductivity is represented [4] as

κ = κ 0 (1 − α G ) m {1 + φ (T − T0 )}

temperature. In addition, exponent m is a generalization of heterogeneous conduction mechanism and is taken to be 1.75 [7].

1 ∆y κ S

(25)

If the voltage difference is ∆E, the electric current I through the resistance R is given by

(20)

I = κS

where the zero subscript denotes the condition at the entrance of the flow, φ is the conductance constant and T is the electrolyte

3

∆E ∆y

(26)


Substituting this equation into Equation (24), we obtain VM = κS

∆E

MM

ρ M n M F ∆y

(27)

t

Therefore, the theoretical processing speed vp theoretical is v p theoretical =

(a) Initial stage

VM M M ∆E =κ St ρ M n M F ∆y

(28)

Multiplying this speed by the electric current efficiency, the actual processing speed vp real can be expressed as

v p real = ηv p theoretical

M M ∆E = ηκ ρ M nM F ∆y

(29)

The above equation can be rewritten in a derivative form as follows.

v p real = ηκ

MM

dE

(30)

ρ M nM F dy

We must consider the fact that the direction of processing speed vp real and dE/dy is normal to a dissolved wall.

Hydrogen Bubble Generation To calculate the source of the hydrogen mass, the hydrogen generation model based on Faraday’s law, described below, is used. From Equation (21), the following equation is obtained,

wH 2 =

M H2 nH 2 F

(31)

It

where the H2 subscript denotes variables of the hydrogen bubble. The local current i is expressed as,

i =κ

E y

(32)

Considering the electric current efficiency in ECM process, source of hydrogen mass is modeled as, Γ = ηκ

M H 2 dE nH 2 F dy

(33)

where κ is the electric conductivity, E is the applied voltage, y is the direction normal to the workpiece. and dE/dy is the gradient of the electric potential on the tool surface. Γ is applied for the 1st term in Equation (3) as the mass of the hydrogen bubble generation.

VERIFICATION Configuration and Grid To verify the models we proposed, we simulate the ECM process for the flat plate channel configuration. The configuration is illustrated in Fig. 1. Figures 2(a) and (b) are the computational grid in the initial and the final stage in ECM process, respectively. During ECM process, since tool cathode is fed to the downward direction, the channel width of the final stage becomes smaller than that of initial stage of the ECM process.

Tool (Cathode)

(b) Final stage Fig. 2 Computational Grids

Working Conditions Tables 1 and 2 list the processing conditions of ECM and the physical properties of the electrolytes. These conditions follow the experiment by Hopenfeld et al. [2]. The current efficiency is set to match for the equilibrium gap thickness at the inlet of the channel in the experiment. Since we have no available data about the diffusion of the gas-phase, the diffusion coefficient CG is varied from 3.0 to 4.0×106 [m2/sec]. And we do not account for the solid-phase in these simulations, because we found that the effect of the metal sludge generation is very small for the final shape of workpiece in the previous study [1]. Furthermore, we take into account the hydrogen bubble size. As shown in Fig. 3, the hydrogen source term is applied for the grids that are closer to the cathode surface than the hydrogen bubble size. In the figure, yellow points on the grids are adopted the hydrogen source term. Simulation Results Figure 4 illustrates the comparison of the gap height to the distance from the inlet in the electrolyte flow direction. In Fig. 4, circles show the experimental data by Hopenfeld et al. [2], solid lines are the simulation results neglecting any flow effect, that is, only electric field is solved. With including only thermal effect, the results are shown as dashed lines. As a matter of coerce, their two kinds of line in Fig. 4 are the same results. The color lines in each figure show the simulation results with considering the thermal effect and variations of the H2 diffusion coefficient CG in Equation (3). Red, green, and blue lines show the results with the value of the diffusion coefficient CG = 3.0, 3.5, 4.0×10-6 [m2/sec], respectively. In Fig. 4 and 5, we found same tendency in simulation results with one- and two-way coupling method as follow. Not considering any effects, the gap height is completely flat. Including only thermal effect, the gap height is larger in downstream than that in upstream. Because temperature increasing makes electric conductivity high, big amount of the material dissolves in high temperature region of the downstream. The gap height considering thermal and hydrogen effects, the gap height is smaller than those in the above-mentioned two cases. It is confirmed that the gap height becomes narrower in the case of considering H2 void fraction effect. The increase of H2 void fraction due to generation of hydrogen bubbles decreases the electric Table 1 Working Conditions of ECM Tool feed rate T0 9.27 Applied voltage E 19.5 T0 297.5 Temperature at entrance Q 1750 Electrolyte flow flux n 9.316 Electrochemical equivalent 2698 Metal density ρM 98.9 Current efficiency η

Tool feed

Flow Workpiece (Anode)

[10-6m/s] [V] [K] [10-6m2/s] [10-5g/C] [kg/m3] [%]

Fig. 1 ECM Configuration for flat electrodes

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Table2 Properties of the Electrolyte (NaCl + H2O) 7.0 [1/Ωm] Conductivity κ0 1027 [kg/m3] Density ρL 4180 [J/kgK] Specific heat capacity CP 0.016 [1/K] Thermal constant φ Viscosity coefficient µ L 0.781×10-3 [kg/ms] 0.63 [W/mK] Thermal conductivity λ

Gap Height [mm]

0.5

0.4

0

Fig. 3 Treatment of Hydrogen Source Term

2 Distance [mm]

4

(a) One-way Coupling Simulation

conductivity of the electrolyte, and thus, the amount of dissolved volume of metal decrees. The lager the diffusion coefficient CG is, the smaller the gap height in downstream is. The simulation results show the channel width decrease linearly in the flow direction. Comparisons between one- and two-way coupling simulations depict the following thing. From these results, CG = 4.0×10-6 [m2/sec] with the one-way coupling method, CG = 3.5×10-6 [m2/sec] with the two-way coupling method agree with the experimental data in the view of the gap height, respectively. Figure 5 illustrates the dependence of the initial gap height on the final shape of the workpiece. Circles show the experimental data, dashed line shows the equilibrium gap calculated theoretically. Color lines show the simulation result with the variation of the initial gap (before ECM process). In comparison of the initial gap height of the ECM process, we found the little difference in the final shape of the work piece. That is, in this configuration, there is no dependence of the initial gap height on the final shape of the workpiece.

Gap Height [mm]

0.5

0.4

0

2 Distance [mm]

4

(b) Two-way Coupling Simulation Fig. 4 Comparisons of the Gap Height in 2D Simulation Circle: Exp by Hopenfeld, Line: Neglecting flow effects, Dashed Line: Considering thermal effect, Red: CG = 3.0, Green: CG = 3.5, Blue: CG = 4.0 [×10-6 m2/sec]

APPRICATION FOR COMPRESSOR BLADE Configuration and grid For application of the presented model of ECM process, we choose a process for a compressor blade. The simulation configuration is shown in Fig. 6. Since experimental configuration is so complex, we simplify the configuration for the simulation. Electrolyte flows from the bottom of the blade, and through out of the top of the blade. As the tool gets close to the blade, the flow path between the tool and the blade becomes narrower in time proceeding. The computational grid is illustrated in Fig.7. Figure 7(a1) (a2) show the initial configuration of the ECM process. (a1) is the overview and (a2) is the close up view, respectively. The initial blade is oval shape. Figure 7(b1) (b2) are the grid in the final stage of ECM process. The number of the grid points is about 600,000.

0.6

Gap Height [mm]

Ini.85% Ini.90% Ini.95% Ini.100%

Working Condition Tables 3 and 4 list the processing conditions of ECM and the physical properties of the electrolytes. These conditions follow the experiment. Note the velocity of the tool feed is not constant. Considering the diffusion coefficient CG, the varied value in the verification is applied for the simulations.

Ini.105% Ini.110% Ini.115% Eq. Gap Exp.

0.5

0.4

0

1 2 X Direction [mm]

3

Fig. 5 Dependence of Initial Gap Height

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Simulation Results Figure 8 illustrates the dissolved length distributions on the blade surface, (S1) to (S4) show on the suction side, (P1) to (P4) show on the pressure side. The direction of the dissolved length is normal to the blade surface. In the initial condition in Figs (S1) and (P1), it is confirmed that the dissolved length distribution is uniform and the magnitude is very small. As time proceeding, the distributions are not uniform on the blade surface on the suction and pressure side of the blade. Basically, in the region where the tool electrode and the blade are close, as the gradient of the electric potential on the blade is steep, the dissolved length is large. We can see the region in the downstream on pressure side of the blade and the edge of the blade bottom (see, Figs. (S2) and (P2)). In the later stage of the ECM process, the blade dissolves larger in the all region than in the earlier stage. Comparing between the suction side and the pressure side, larger amount of dissolved length confirmed on the pressure side. Figures 9 show the final geometries in the ECM process for the compressor blade. The geometries are compared in the tip, the two mid spans and the hub region of the blade. Dotted lines are the experimental data, blue and red lines are the simulation results with the one- and two-way coupling method, respectively. We can see the all simulations have good agreements with the experimental data. In detail, the simulation results in the edge of the blade are overestimated in the point of the dissolved length. Furthermore, the blade geometry of the tip region has larger overestimate than that of the hub region. This is because the tip region is the downstream of the flow path. As the thermal and H2 void fraction effects arise in the region, the blade geometries have differences. Comparing the one- and two-way simulations, there is little difference in the view of the blade geometry. Figure 10 illustrates the comparisons of the temperature and the H2 void fraction effects on the dissolved volume. Red and blue lines show

Fig. 6 Configuration in 3D Simulation

the temperature and the void fraction averaged on the blade surface. And green line shows the sum of the dissolved volume in each stage of the ECM process. From this graph, it is confirmed that the H2 void fraction increase from the initial to the mid stage, and decrease from the middle stage to the final stage of the process. Lastly, the averaged values of the H2 void fraction increase. However, the averaged value on the blade surface is very low. On the contrary, the averaged temperature increases in most of the stages. And, the sum of the dissolved volume increases with the temperature increasing. Lastly, table 5 shows comparisons between the one- and two-way coupling simulations totally. Because of using Low-Mach-Number approximation, computing Pressure Poisson equation has un-stability. As the two coupling method have almost the same accuracy for the predicting the blade geometry, we recommend that the numerical simulation for ECM process is solved with the one-way coupling method.

SUMMARY −We reviewed the presented models of ECM processes. −From the validation of the models, we found that CG = 4.0×10-6 [m2/sec] with one-way coupling method, CG = 3.5×10-6 [m2/sec] with two-way coupling method agree with the experimental data in the view of the gap height, respectively. −The initial gap height is independent on the final shape of the workpiece. −Ιn 3D simulations, the blade geometries predicted with one- and two-way coupling method agree with the experimental data. −Due to the computational stability, we recommend using the oneway coupling method for the interaction between the gas and the liquid phase in ECM process.

(a1) Over View in Initial Condition

(a2) Close-up View in Initial Condition

Table 3 Working Conditions of ECM Inlet temperature T0 293.15 [K] Machining time tECM 500 [sec] LFEED 11.0 [mm] Tool feed length Nickel Alloy Metal type Metal density 8000 [kg/m3] ρM Table 4 Properties of the Electrolyte (NaNO3 + H2O) Inlet conductivity 17.02 [1/Ωm] κ0 Density 1109 [kg/m3] ρL 4181 [J/kgK] Specific heat capacity CP 0.016 [1/K] Thermal constant φ Viscosity coefficient µL 0.781×10-3 [kg/ms] 0.583 [W/mK] Thermal conductivity λ

(b1) Over View in 4/4 tECM (b2) Close-up View in 4/4 tECM Fig. 7 Computational Grids for 3D configuration

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(S1) Suction Side in Initial

(S2) Suction Side in 2/4 tECM



(P1) Pressure Side in Initial

(P2) Pressure Side in 2/4 tECM



0.0 [µm]

20.0 [µm] Fig. 8 Dissolved Length Distributions

Exp. Two–way simulation One–way simulation

x–direction

x–direction

(a) 1/4 Height from Bottom

0.06 330

0.04 320

0.02

310

(b) 2/4 Height from Bottom 0



0.5

1

Processing Time t/t ECM

Fig. 10 Comparisons of Effects on Dissolved Volume (Temperature and Void fraction Averaged on Blade Surface), Red: Temperature, Blue: H2 Void fraction, Green: Dissolved Volume

y–direction

y–direction

Temperature [K]

H2Void–Fraction [–] 3 Dissolved Volume [cm ]

340

y–direction

y–direction


Table 5 Comparison between One- and Two-way Simulations

Accuracy x–direction

Computational Time

Stability

x–direction

One-way

(c) 3/4 Height from Bottom (d) 4/4 Height from Bottom Fig. 9 Comparisons of Blade Geometry

Two-way

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REFERENCES [1] R.Tsuboi, K.Toda, M.Yamamoto, R.Nohara and D.Kato, 2005, “Modeling of three phase flow in electrochemical machining”, Proc. ASME FEDSM 2005-77435, pp.1-6 [2] J.Hopenfeld and R.R.Cole, 1969, “Prediction of the OneDimensional Equilibrium Cutting Gap in Electrochemical Machining”, Eng. Industry Aug. 755-765. [3] R.Tsuboi, K.Inaba, M.Yamamoto and D.Kato, 2007, “Modeling of Multi-phase flow in electro-chemical machining”, Proc. ASME FEDSM 2007-37594, pp.1-6 [4] T.Fujisawa, K.Inaba, M.Yamamoto and D.Kato, 2007, “Multiphysics Simulation of Electro-Chemical Machining Process for Three-dimensional Compressor Blade”, Proc. ASME FEDSM 2007-37678, pp.1-6. [5] R.Tsuboi and M.Yamamoto, 2008, “Investigating Behavior of Hydrogen bubbles in Electro-Chemical Machining”, Proc. ASME FEDSM 2008-55296, pp.1-6 [6] D.Landolt, R. Acosta, R.H.Muller, and C.W.Tobias, 1970, “An Optical Study of Cathodic Hydrogen Evolution in High-Rate Electrolysis”, J. Electrochem. Soc. 117, 839-845 [7] A.Sokolichin, G.Eigenberger, A.Lapin and A.Lubbert, 1997, “Dynamic numerical simulation of gas-liquid two-phase flows Euler/Euler versus Euler/Lagrange”, Chem. Engng Sci. 52, 611626 [8] J.F. Thorpe and R.D. Zerkle, 1969,”Analytic determination of the equilibrium electrode gap in electrochemical machining”, Int. J. Math. Tool Des. Res. 9, 131-144. [9] W.J.James, 1974, Advances in Corrosion Science and Technology Vol. 4, Chap. 2, Plenum Press, New York and London, p. 85.

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