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Research Papers

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

[+] Author and Article Information
Mingyang Li, Robert G. Landers, Ming C. Leu

Missouri University of Science and Technology,
Rolla, MO 65409

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received March 16, 2014; final manuscript received August 28, 2014; published online October 24, 2014. Assoc. Editor: David L. Bourell.

J. Manuf. Sci. Eng 136(6), 061003 (Oct 24, 2014) (11 pages) Paper No: MANU-14-1120; doi: 10.1115/1.4028577 History: Received March 16, 2014; Revised August 28, 2014

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.

Copyright © 2014 by ASME
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Figures

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Fig. 1

3D simulation schematic with dynamic meshing and boundary conditions

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Fig. 2

Schematic of 1D model simulation with boundary conditions

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Fig. 3

Paste freezing times obtained from simulations using Fluent and the code based on the proposed 1D model with 45% solids loading, 5 °C initial paste temperature, −10 °C ambient temperature, 580 μm layer thickness, 10 s total time between layers, (a) ZrC paste material, and 35 W/m2 °C convection coefficient (forced convection); (b) Al2O3 paste material, and 6.7 W/m2 °C convection coefficient (natural convection); (c) Al2O3 paste material, and 35 W/m2 °C convection coefficient (forced convection)

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Fig. 4

Paste freezing time for different total times between layers with Al2O3 paste, 45% solids loading, 35 W/m2 °C convection coefficient (forced convection), 5 °C initial paste temperature, −10 °C ambient temperature, and 580 μm layer thickness

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Fig. 5

Paste freezing time for natural and forced convections with Al2O3 paste, 45% solids loading, 5 °C initial paste temperature, −10 °C ambient temperature, 580 μm layer thickness, and 10 s total time between layers

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Fig. 6

Steady-state freezing time versus total time between layers for natural and forced convections with Al2O3 paste, 45% solids loading, 5 °C initial paste temperature, −10 °C ambient temperature, and 580 μm layer thickness

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Fig. 7

Simulated critical freezing time as a power law function of convection coefficient

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Fig. 8

Paste freezing time for total times between layers of 17.00 and 17.10 s with Al2O3 paste, 45% solids loading, 6.7 W/m2 °C convection coefficient (natural convection), 5 °C initial paste temperature, −10 °C ambient temperature, and 580 μm layer thickness

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Fig. 9

Paste freezing time for different paste materials with 45% solids loading, 35 W/m2 °C convection coefficient (forced convection), 5 °C initial paste temperature, −10 °C ambient temperature, 580 μm layer thickness, and 10 s total time between layers

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Fig. 10

Steady-state freezing time versus total time between layers for different paste materials with 45% solids loading, 35 W/m2 °C convection coefficient (forced convection), 5 °C initial paste temperature, −10 °C ambient temperature, and 580 μm layer thickness

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Fig. 11

Simulated critical freezing time as a function of average thermal conductivity

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Fig. 12

Paste freezing time for different paste solids loadings with Al2O3 paste, 35 W/m2 °C convection coefficient (forced convection), 5 °C initial paste temperature, −10 °C ambient temperature, 580 μm layer thickness, and 10 s total time between layers

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Fig. 13

Steady-state freezing time versus total time between layers for different paste solids loadings with Al2O3 paste, 35 W/m2 °C convection coefficient (forced convection), 5 °C initial paste temperature, −10 °C ambient temperature, and 580 μm layer thickness

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Fig. 14

Simulated critical freezing time as a function of solids loading

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Fig. 15

Paste freezing time for different initial paste temperatures with Al2O3 paste, 45% solids loading, 35 W/m2 °C convection coefficient (forced convection), −10 °C ambient temperature, 580 μm layer thickness, and 10 s total time between layers

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Fig. 16

Steady-state freezing time versus total time between layers for different initial paste temperatures with Al2O3 paste, 45% solids loading, 35 W/m2 °C convection coefficient (forced convection), −10 °C ambient temperature, and 580 μm layer thickness

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Fig. 17

Simulated critical freezing time as a function of initial paste temperature

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Fig. 18

Paste freezing time for different ambient temperatures with Al2O3 paste, 45% solids loading, 35 W/m2 °C convection coefficient (forced convection), 5 °C initial paste temperature, 580 μm layer thickness, and 10 s total time between layers

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Fig. 19

Steady-state freezing time versus total time between layers for different ambient temperatures with Al2O3 paste, 45% solids loading, 35 W/m2 °C convection coefficient (forced convection), 5 °C initial paste temperature, and 580 μm layer thickness

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Fig. 20

Simulated critical freezing time as a function of ambient temperature

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Fig. 21

Paste freezing time for different layer thicknesses with Al2O3 paste, 45% solids loading, 35 W/m2 °C convection coefficient (forced convection), 5 °C initial paste temperature, −10 °C ambient temperature, and 10 s total time between layers

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Fig. 22

Steady-state freezing time versus total time between layers for different layer thicknesses with Al2O3 paste, 45% solids loading, 35 W/m2 °C convection coefficient (forced convection), 5 °C initial paste temperature, and −10 °C ambient temperature

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Fig. 23

Simulated critical freezing time as a function of layer thickness

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Fig. 24

Single-wall cylinders fabricated using the FEF process with Al2O3 paste, 45% solids loading, 5 °C initial paste temperature, −10 °C ambient temperature, 580 μm layer thickness, (a) 35 W/m2 °C convection coefficient (forced convection) and 10 s total time between layers; (b) 6.7 W/m2 °C convection coefficient (natural convection) and 10 s total time between layers; (c) 35 W/m2 °C convection coefficient (forced convection); and 5 s total time between layers

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