Channel constriction due to wall-mounted ice growth in high-Reynolds-number flow

The growth of wall-mounted ice within channel flow which leads to a constriction is of significant practical relevance, especially in applications relating to aero-icing, large-scale pipe networks and mechanical systems. Whilst earlier works have treated ice constrictions as independent of the oncoming flow, few models explicitly account for the two-way coupling between the thermal and dynamical properties of the fluid and the evolving ice. To this end, the present work seeks to describe the interaction between high-Reynolds-number channel flow and constricting ice boundaries governed by Stefan conditions. Numerical simulations of the model indeed reveal that ice forming on the channel walls grows inwards towards the centreline and subsequently creates almost total constriction. In other parameter regimes, however, there is no ice formation. Using both a numerical and asymptotic approach, we identify regions of parameter space in which ice formation, and subsequently flow constriction, does or does not occur.