Abstract
Simulation of the species concentrations during the Pulse Electrochemical Machining (PECM) process can provide information on system design and guidelines for practical use. In detailed numerical calculations the concentrations will be calculated simultaneously with the temperature due to mutual dependencies. 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 variables distributions evolutions in PECM can become a computationally very expensive procedure. In previous work (Smets et al. J Appl Electrochem 37(11):1345, 2007), a time averaging approach was introduced. Performing this, the timesteps used during the calculations are no longer dictated by the pulse characteristics. Using this approach, computationally very cheap, yet satisfying results can be obtained. This work focuses on the behaviour of the concentration evolution. The concentration and the temperature calculation have different requirements for optimal approximated calculations, and a compromise has to be found between them. An analysis is performed on a simplified model, which provides useful guidelines during simulations.
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Abbreviations
- c :
-
Concentration (mol m−3)
- \( \overline c \) :
-
Averaged concentration (mol m−3)
- \( \tilde c \) :
-
Concentration ripple (mol m−3)
- c decay :
-
Concentration decaying component (mol m−3)
- D :
-
Diffusion coefficient (m2 s−1)
- E :
-
Error function (%)
- F :
-
Faraday constant (=96,485 C mol−1)
- J :
-
Current density distribution (A m−2)
- n :
-
Valence (−)
- \( \overline r \) :
-
General location vector (m)
- t :
-
Time (s)
- t′:
-
Time (s)
- T :
-
Pulse period (s)
- T′:
-
Dimensionless pulse period (−)
- \( \overline v \) :
-
Velocity vector (m s−1)
- x :
-
Distance (m)
- α:
-
Duty cycle (−)
- δ:
-
Nernst diffusion layer thickness (m)
- λ:
-
Time (s)
- τ:
-
Time constant (s)
- Φc :
-
Mass flux (mol s−1 m−2)
- ψ:
-
Pulse delay (s)
- ψ*:
-
Optimal pulse delay (s)
- ψlimit :
-
Limit pulse delay (s)
- 1D:
-
One dimensional
- ECM:
-
Electrochemical machining
- PECM:
-
Pulse electrochemical machining
- QSS:
-
Quasi steady state
- QSSSC:
-
Quasi steady state shortcut
- SS:
-
Steady state
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Smets, N., Van Damme, S., De Wilde, D. et al. Time averaged concentration calculations in pulse electrochemical machining. J Appl Electrochem 38, 1577–1582 (2008). https://doi.org/10.1007/s10800-008-9608-1
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DOI: https://doi.org/10.1007/s10800-008-9608-1