Pressure dependence of limiting current density of sparking during electrochemical drilling

The cathodic current density used in electrochemical drilling can be increased only up to a certain value, above which current oscillations, sparking and acoustic phenomena appear, whereby the cathode can be damaged. The limiting current density for sparking, j _s, depends on the rate of flow and properties of the electrolyte and on the hydrostatic pressure. Values of j _s were measured for metal capillaries provided with external insulation in the turbulent flow regime in the range of Reynolds numbers from 2 300 up to 30 000 and at hydrostatic pressures ranging from 0.12 to 1.1 MPa. A simple heat generation model is proposed and the limiting current densities for sparking (868 experiments) are correlated with a criterion equation enabling the calculation of j _s.List of symbols c _pE specific heat of electrolyte (J kg^–1 K^–1) - d ₁ inner diameter of the cathode (m) - d ₂ outer diameter of the cathode (m) - I current (A) - I _s limiting current for sparking (A) - j current density (Am^–2) - j _s limiting current density for sparking (Am^–2) KT constant - K _T constant - L characteristic length (m) - N _u Nusselt number - p pressure (Pa) - p ₀ reference atmospheric pressure (Pa) - P exponent - P _r Prandtl number - q exponent - q heat flux (W m^–2) - R exponent - Re Reynolds number - _E linear electrolyte velocity (m s^–1) Greek symbols - heat transfer coefficient (W m^–2 K^–1) - temperature difference (K) - _E electrolyte conductivity (^–1 m^–1) - _E electrolyte thermal conductivity (Wm^–1 K^–1) - µ_E electrolyte viscosity (kgm^–1 s^–1) - _E electrolyte density (kg m^–3)