Direct Numerical Simulation of shear turbulence interacting with a melting-freezing ice layer

When a turbulent flow of water interacts with an ice boundary at near-freezing temperature, the fluid can undergo freezing or melting, depending on the local temperature. The turbulence structures that develop in proximity to the ice layer can affect the convective heat transport patterns, leading to the formation of complex phase-boundary morphologies. The ice layer evolves as part of the solution and modifies the near-boundary fluid structures, resulting in heat transfer perturbations. We investigate these ice-water interactions at small scales by performing Direct Numerical Simulations of an open channel flow at shear Reynolds number in the range between 10^2 and 10^3. The upper section of the channel is occupied by ice, while free shear conditions are applied at the bottom. Temperature is imposed on both walls. The ice melting/freezing is simulated using a phase field method [1] combined with a volume penalization immersed boundary method. A pseudo-spectral scheme [2] is used to solve the equations for momentum and energy transport and for phase evolution. We investigated how the behavior of the system changes with the flow conditions (i.e. Reynolds number), with a specific focus on characterizing the features of the ice morphology. In particular, we observed a remarkable influence of turbulence intensity on the ice morphology: at low shear Reynolds, the typical streamwise-oriented canyons already reported in similar studies [3] are present. However, at higher shear Reynolds, spanwise instabilities are triggered, making the final ice morphology more complex.

FIgure1: Render view from below of the open channel flow at a low Reynolds number. On the top section of the channel, the corrugated ice layer is shown. On the ice boundary, the normalized heat flux passing through it is displayed (high heat flux is shown in red, low heat flux in blue). The local temperature field is reported on the side domain boundaries. The typical streamwise-oriented canyons at the ice interface are visible and the heat flux correlates well with those patterns (the heat flux is higher inside the canyons).

[1]R. Yang et al., Morphology evolution of a melting solid layer above its melt heated from below, Journal of Fluid Mechanics, 956, A23, 2023.

[2]F Zonta et al., Nusselt number and friction factor in thermally stratified turbulent channel flow under non-Oberbeck–Boussinesq conditions, International journal of heat and fluid flow, 44:489–494, 2013.

[3]L. A. Couston et al., Topography generation by melting and freezing in a turbulent shear flow, Journal of Fluid Mechanics, 911, A44, 2021.