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Time averaged calculations in pulse electrochemical machining, using a strongly non-linear model

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Abstract

Simulation of the Pulse Electrochemical Machining (PECM) process can provide information on system design and guidelines for practical use. The pulses that are applied to the PECM system have to be described on a time scale that can be orders of magnitude smaller than the physical time scales in the system. If the full detail of the applied pulses has to be taken into account, the time accurate calculation of the variable distribution evolutions in PECM can become a computationally very expensive procedure. In previous work of the authors, approximate techniques were introduced: the hybrid calculation and the Quasi Steady State Shortcut (QSSSC). In other previous work of the authors a model for PECM of steel in NaNO3 was introduced. This model contains a changing polarization behaviour of the double layer as a function of the metal ion surface concentration, which brings a strong non-linearity in the system. In this paper a technique is introduced to integrate the non-linear model into the approximate methods. To achieve this, the strategy of the approximate methods is extended. For the QSSSC, the non-linearity is handled using an extra convergence level. For the hybrid calculation, live averaging is used to take care of the non-linear effects. Performing this, the timesteps used during the high level calculations are no longer dictated by the pulse characteristics. Using this approach, computationally very cheap, yet satisfying results can be obtained. The technique is very general and very powerful and can be used in any multi-timescale system.

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Abbreviations

a :

Polarization parameter 1 (S m−2);

A :

Electrode surface (m2);

b :

Polarization parameter 2 (A m−2);

c :

Concentration (mol m−3);

C p :

Heat capacity (J kg−1 K−1)

D :

Diffusion coefficient (m2s−1)

E 0 :

Equilibrium potential (V)

F :

Faraday constant (= 96485 C mol−1)

h :

Heat transfer coefficient (W m−2 K−1)

I :

Electrical current (A)

J :

Current density distribution (A m−2)

k :

Thermal conductivity (W m−1 K−1)

P dl :

Heat produced, in the double layer (W m−2)

P bulk :

Heat produced in the bulk (W m−3)

Pr t :

Turbulent Prandtl number (–)

\(\overline{r}\) :

General location vector (m)

Re :

Reynolds number (–)

t :

Time (s)

T :

Pulse period (s)

U :

Potential distribution (V)

v :

Velocity (m s−1)

w :

Water depletion factor (–)

x :

Distance (m)

z :

Valence (–)

α:

Duty cycle (–)

η:

Overpotential (V)

\(\Uptheta\) :

Temperature (K)

μ:

Dynamic viscosity (kg m−1 s−1)

ρ:

Density (kg m−3)

σ:

Electrical conductivity (S m−1)

τ:

Time constant (s)

\(\Upphi_c\) :

Mass flux (mol s−1m−2)

ψ:

Pulse delay (s)

ψ*:

Optimal pulse delay (s)

2D:

two dimensional

DC:

Direct current

DNS:

Direct numerical simulation

ECM:

Electrochemical machining

FEM:

Finite elements method

PAP:

Prior averaging pulse

PECM:

Pulse electrochemical machining

QSS:

Quasi steady state

QSSSC:

Quasi steady state shortcut

RANS:

Reynolds averaged Navier-stokes

SS:

Steady state

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Authors and Affiliations

  1. IR / ETEC Department, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium

    N. Smets, S. Van Damme, D. De Wilde, G. Weyns & J. Deconinck

Authors
  1. N. Smets
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  2. S. Van Damme
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  3. D. De Wilde
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  4. G. Weyns
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  5. J. Deconinck
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Correspondence to N. Smets.

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Smets, N., Van Damme, S., De Wilde, D. et al. Time averaged calculations in pulse electrochemical machining, using a strongly non-linear model. J Appl Electrochem 40, 1395–1405 (2010). https://doi.org/10.1007/s10800-010-0116-8

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  • DOI: https://doi.org/10.1007/s10800-010-0116-8

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