Comparative assessment of Volume-of-Fluid and Level-Set methods by relevance to dendritic ice growth in supercooled water

Abstract

a b s t r a c tTwo relevant computatio nal models, one relying on a Level-Set approach, the other one on a Volume-ofFluid tracking procedure with piecewise linear inter face reconstruction, are comparatively assessed in terms of their capability to simulate crystallizatio n of supercooled water. The models are preliminary validated by computing a one-dimensional freezing front propagation for which an analytic solution exists. Afterwards, the tip velocity of two-dimensional dendrites growing in supercooled water is determined and compared with corresponding experimental results and theoretical predictions in the range of supercooling between 1 K and 30 K. Present modeling results following closely both the underlying theory and experimen tal findings show very good mutual agreemen t.

Monitoring of Freezing Dynamics in Trees: A Simple Phase Shift Causes Complexity

“…Once nucleated, the ice front can propagate after the exothermal heat has dissipated through the bark (Shibkov et al, 2003), whereby propagation rates within the water column are proportional to the degree of supercooling (Langer et al, 1978;Rauschenberger et al, 2013). In excised branches of P. abies, propagation rates similar to those found in this field study were observed (2 and 4 mm s 21 for 1.5 and 2 K of supercooling, Table I.…”

Direct numerical simulations for multiphase flows: An overview of the multiphase code FS3D

“…The heat fluxes in the solidq s and the liquidq l are determined through the Fourier heat conduction lawq = −k∇T, where the gradient of the temperature fields is calculated through second-order one-sided finite differences [29]. Because of the iterative algorithm, the heat fluxes are closely linked to the mass source termṁ and the released enthalpy of fusion at the interface.…”

“…Because the phase change does not only change the mass in every cell but also the cell energy, the temperature in all boundary cells needs to be updated after every inner iteration step [29].…”

Towards modelling of initial and final stages of supercooled water solidification

“…[7,31] has been correspondingly modified towards fulfilment of an appropriate accuracy level with respect to the thermal energy equation discretization and the approximation of the temperature normal derivative close to the interface.…”

“…In the present work, a computational model based on the level set technique [27] used in Refs. [6,7,31] has been appropriately modified, aiming at increasing the accuracy level of the discretization of the equation governing the thermal energy and the normal-to-interface derivative of the temperature field. The model describes the freezing mechanism under supercooled conditions, relying on the physical and mathematical description of the twophase moving-boundary approach (minimal model of solidification) considering kinetic effects.…”