Numerical Model of Frost Formation Based on Burton–Cabrera–Frank Theory Considering Complex Transportation of Water Vapor in Frost

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  • HATTORI Akihiro
    Graduate School of Fundamental Science and Engineering, Waseda University
  • SATO Tetsuya
    School of Fundamental Science and Engineering, Waseda University

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<p>A novel frosting model based on Burton–Cabrera–Frank theory is developed. The proposed model contains correction factors for the amount of desublimation (βinn and βsf) and a parameter related to effective diffusivity in frost (F). βinn should be set to approximately 10-3 because of the impact of released latent heat and vapor consumption due to desublimation at nearby interfaces, and the growing ability of ice crystals depending on their crystallographic orientation. In addition, F should be set to approximately 5 to account for the effect of complex transportation of water vapor in frost. Without considering this effect, the frost becomes dense only near the surface. The density distribution becomes inconsistent with experimental findings. This compromises calculation accuracy. Moreover, calculations are performed to validate our model under the following frosting conditions: 243.15 K ≤ Tp ≤ 263.15 K and 8 g/m3 ≤ ρv ≤ 16 g/m3, where Tp is the cold plate temperature, and ρv is the absolute humidity. The results show that the present model can predict the frost mass and average frost thickness with a maximum error of less than 15% at 600 s under a wide range of conditions.</p>

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