Turbulent free convection in large electrochemical cells with a binary electrolyte

A mathematical model proposed by Bark and Alavyoon for modelling laminar natural convection in electrochemical cells, with binary electrolytes, is extended to simulation of two-dimensional turbulent flows. The turbulence was modelled by a standard k-epsilon model. The constants used in the model are the same as those used by Henkes and Hoogendoorn. Steady state calculations were carried out in a square, differentially heated enclosure for Gr = 7 x 10(10) and Pr = 0.71. The turbulence model used could not predict the transition effect on the Nusselt number along the hot wall. Transient calculations performed in an enclosure with an aspect ratio of 35, for Gr = 6.4 x 10(11) and Sc = 2763, revealed large scale fluctuations in the boundary layers near the vertical walls. The model was able to predict qualitatively the velocity field for transitional flow for air induced by buoyancy at Gr(h) = 8100 and Gr(h) = 22 500, The correlation between the Sherwood and Rayleigh numbers was studied by modelling the mass transfer at the electrodes using a Butler-Volmer law. The computed Sherwood number was found to be approximately proportional to the Rayleigh number to the power of 0.2 in the range of Ra-h between 5 x 10(8) and 10(10), and with an order of magnitude of 10(5).