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978-3-8439-3123-6, Reihe Thermodynamik
Modelling of the Initial Ice Growth in a Supercooled Liquid Droplet
141 Seiten, Dissertation Universität Stuttgart (2017), Softcover, A5
Ice formation in atmospheric clouds influences significantly the appearance of the clouds themselves and their characteristics, for example regarding precipitation. Ice formation in supercooled droplets, which are frequently found in the atmosphere, is of special interest. Supercooled droplets remain liquid although the ambient temperature drops below the equilibrium freezing temperature of water; the droplets thus exist in a metastable state. The freezing process is then initiated by a homogeneous or heterogeneous nucleation event. The initial growth of the emerged nucleus is spherical, but after exceeding a certain size, dendrites are formed due to instabilities on the ice particle's surface.
The investigation of ice formation via Direct Numerical Simulations (DNS) can provide deep insight into the underlying physical mechanisms and support the deduction of models that describe the processes on small scales. These models are required for a description of the macrophysical system. The multiphase code, which is used for the numerical studies on the microscale, is extended to a third immiscible phase with a sharp interface in order to account for the three different phases ice, water and air during the freezing process.
Since even the processes on the microscale span about four orders of magnitude, a sub-scale model is deduced in order to describe the initial growth of a nucleus inside the supercooled droplet, which can be reduced to a problem with radial symmetry and belongs to the class of Stefan-type problems. It is characterized by a time-dependent phase boundary coupling the heat conduction equations in the ice and water phase; it is thus highly non-linear.
Classical approaches for the solution of Stefan-type problems cannot represent the physics for the present problem accurately, especially if the degree of supercooling is high. Hence, a semi-analytical solution is deduced. It accounts for all important physical effects like the reduction of the melting temperature or the increase of the ice particle's growth velocity due to the discontinuity in densities across the interface. The derivation of simple fits to the analytical solution allows for a fast evaluation of the quantities that are required as initial conditions for Direct Numerical Simulation of the subsequent dendritic ice growth. The use of this sub-scale model allows for a significant reduction of grid resolution and computational time.