The aim of this work has been to study the internal flow in freezing water droplets on a cold surface and to investigate the different heat transfer mechanisms involved. This is an interesting topic with a great number of applications, specifically in areas where the prevention of unwanted icing is important, e.g. in the case of airplane wings and propellers, wind turbine rotor blades, and roads surfaces.

Combining experimental and numerical methods, this study uses Computational Fluid Dynamics (CFD) to build a model of the freezing process and Particle Image Velocimetry (PIV) to aid for a better understanding of the freezing process. For the numerical part of the study, a model of a droplet with a rigid boundary was created where only the interior was of interest and different boundary conditions on the droplet surfaces were used to induce a flow inside the droplet. The heat transfer mechanisms studied was conduction, natural convection and Marangoni convection. For comparison, an experimental method was developed to visualize the movement of the water and to estimate the velocities inside the droplet. In order to compensate for the refraction at the droplet surface a velocity correction method was applied. The internal flow in freezing droplets was also compared to the internal flow in evaporating droplets. 

The results show that the freezing time is not affected considerably between experiments and the numerical model when including different heat transfer mechanisms, instead the size and contact angle to the surface as well as the substrate temperature are the largest contributors. The direction of the flow and the velocity of the water are highly dependent on the heat transfer mechanisms and these are more difficult to mimic in the numerical model. In the experimental work it was found that the flow is controlled by Marangoni convection for a short time period in the beginning of the freezing process. After this, natural convection instead dominates the flow. When including only conduction and natural convection in the numerical model it can be seen that the gravity effects are most pronounced around the density maximum for water (at T = 4°C). When introducing Marangoni convection in the model the highest velocities are seen in the beginning of freezing. It was found that neither only natural convection nor only Marangoni convection could in itself describe the flow seen in the experimental work. In previous research it has been shown that Marangoni convection is reduced approximately 100 times in the real water droplets compared to theory. This condition yields the best correspondence between numerical results to the experimental results, although there are still differences that have to be investigated further. For evaporating droplets, the Marangoni convection seems to have a little or no effect on the flow.

The main conclusion is that it is possible to work with a simplified CFD model and still capture the main flow features and freezing characteristics in freezing water droplets. Furthermore, an experimental method for studying the freezing droplets and for comparison of the numerical work has also been constructed with good results. For the future it would be interesting to further develop the CFD model for even better correspondence with the experimental work and to unravel the differences between theory and real droplets.