Quasi-Steady Simulation of Glaze Ice Accretion and Heat Transfer in the Supercooled Large Droplet Regime in Atmospheric Turbulent Air Flow

To avoid the use of a computationally intensive full unsteady simulation while providing an accurate solution, a quasi-steady simulation has been performed to study glaze and mixed ice accretion in the supercooled large droplet (SLD) regime in turbulent flow of atmospheric air. We have attempted to find the minimum time-step necessary to adequately simulate the icing process on an airfoil surface. Based on node displacement, a mesh morphing scheme has been adopted in the computations to account for the moving boundaries that are caused by the continuous ice buildup. We have modeled ice accretion on an airfoil surface for a time period of 232 s using several time steps. At each time-step we solved the steady-state conservation equations for the air and droplet phases and then used the results as initial conditions for the next time position. The magnitude of the time-step ranged from a least accurate two-shot simulation (where the time-step is 116 s) to a most accurate 2320-shot simulation (where the time-step is 0.1 s). In-between these two extreme time steps, we have performed a three-shot simulation (where the time-step is 77.33 s), a four-shot simulation (where the time-step is 58 s), a six-shot simulation (where the time-step is 38.67 s), a 46-shot simulation (where the time-step is 5 s), and a 232-shot simulation (where the time-step is 1 s). We have done so to find out the degree of accuracy (or inaccuracy) of the multishot simulation approach and to find out the appropriate time-step needed for a successful and valid quasi-steady simulation. A valid quasi-steady simulation needs to use a time-step that is small enough to reproduce the full time-dependent solution within a very small error band. We have found that both the 1 s and the 0.1 s time steps produce virtually identical results. This is the primary litmus test that proves the validity of the quasi-steady-state assumption. The results adopted in this paper are thus all based on the more conservative 0.1 s time-step. In the process of performing the simulations, remeshing was required in order to maintain the grid density in zones of high curvature to be able to capture the full physics in those zones. After successfully modeling glaze ice accretion over the airfoil surface using the 0.1 s quasi-steady simulation approach, the effects of supercooled large droplets (SLDs) impacting the surface have been examined and presented in terms of the variation of the local collection efficiency, the water film thickness, and the heat transfer rate. Examination of the variation of the angle that the ice horn makes with the airfoil chord line demonstrated a 20% improvement in angle prediction when the time-step is reduced from 116 s to 0.1 s. The analysis also reveals a 12% or 8.5% increase in the maximum collection efficiency, β_max, depending on whether the value of the liquid water content (LWC) has been doubled from $0.5 g/m3$ to $1 g/m3$⁠, or the value of the freestream velocity has been doubled from $75 m/s$ to $150 m/s$⁠, respectively. Because of the need to monitor the local collection efficiency and convective heat fluxes at each shot (regardless of the number of shots employed), the approach adopted here was found to be effective in successively and successfully reproducing the curvature of the glaze ice horn.