Modeling, Analysis, and Simulation of Paste Freezing in Freeze-Form Extrusion Fabrication of Thin-Wall Parts

Abstract

During the freeze-form extrusion fabrication (FEF) process for aqueous-based pastes, the subzero temperature (in Celsius) environment aids the part in maintaining its shape by freezing the water present in the paste. The first few layers of paste freeze very quickly when deposited; however, as the part's height increases, the freezing time increases as the rate of heat conduction to the substrate decreases rapidly. The freezing time can substantially exceed the time required to deposit one layer of paste due to water's high latent heat, leaving the extruded paste in its semiliquid state, and causing the part to deform or even collapse. Therefore, dwell time may be required between layers. A method is needed to predict paste freezing time in order to fabricate a part successfully while minimize the part build time. In this paper, a simplified one-dimensional (1D) heat transfer model was introduced for fabricating thin-wall parts by the FEF process. The simplified model, which could reduce computation times from days to minutes, was validated by the commercial finite element software Fluent. The paste temperature and paste freezing time for various process parameters were computed via numerical simulation using this model. As the layer number increases, the paste freezing time reaches a steady state. The relationship between the steady-state freezing time and the total time, which is the sum of the deposition time for the current layer and the dwell time between the current and next layers, was studied for various convection coefficients, paste materials, paste solids loadings, initial paste temperatures, ambient temperatures, and layer thicknesses.