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Frost 3D Universal Verification
Frost 3D Universal Has Been Verified Against the Exact Analytical Solution The generally accepted criterion used to determine the validity of a numerical solution is its coincidence with the known exact analytical solution, and Frost 3D Universal was verified against the analytical solution for the soil freezing problem [1]. Problem Statement The 30day temperature distribution on a section of frozen ground is calculated for the following conditions: Table 1: Thermophysical Properties of Soils
The dependence of thermophysical properties on temperature (see Table 1) in compliance with the SNiP “Bases and Foundations on Permafrost” is typical for sand, loamy sand and sandy loam with plasticity index I_{p} < 0.02. The comparison (Figure 1–4) of the derived numerical and the exact analytical solution for the soil freezing problem revealed a 0.5% error in the frost depth calculation using Frost 3D Universal, and we observe that mesh refinement makes the error approach zero.
Comparison of the solutions obtained in Frost 3D Universal and the exact analytical solution: Figure 1: Results of 1st numerical experiment Figure 2: Results of 2nd numerical experiment Figure 3: Results of 3rd numerical experiment Figure 4: Results of 4th numerical experiment Frost 3D Universal Verification Against Experimental Data The freezing of a cylindrical sample of peat with a moisture content of w_{tot} = 5 kg/kg and density ρ_{d} =160 kg/m^{3} was analyzed [2]. The following thermophysical properties are applied in compliance with SNIP 2.02.0488 “Bases and Foundations on Permafrost”: volumetric heat capacity of thawed (C_{th}) and frozen (C_{f}) states, heat conductivity of thawed (λ_{th}) and frozen (λ_{f}) states (Table 2).
Table 2: Thermophysical Properties of Soils
The dependence of the unfrozen water content on temperature is given for peat in compliance with SP 25.13330.2012 (SNiP 2.02.0488). From the expression (B.5), the dependence takes the form shown in the Figure 5. Figure 5: Dependence of unfrozen water content on the temperature The initial temperature of the peat sample is 283 K. Using directional freezing apparatus, the temperature at the end of the cylindrical sample is maintained at 268 K. The experimental temperature distribution data resulting from the freezing of the sample is presented in Figure 6 [1]. Note that this laboratory experiment is comparable to the natural processes of ground freezing. Figure 6: Computational (1, 2) and experimental (1’, 2’ ) temperature distribution and moisture content after freezing: W = 5 kg/kg, ρ = 160 kg/m^{3}, T_{0} = 283 К, T_{c} = 268 К, t = 2.0 h [1] The computational experiment was conducted in a Frost 3D Universal simulation of the same problem. The computed temperature distribution was compared with the experimental data (figure 7), and the discrepancy between the two for the depth of frost penetration was 5%: a 0.020 m computational value for frost depth against the 0.019 m experimental measurement of the same. Note that the main contribution to the total error is the inaccurate determination of the thermophysical properties of the soil. Figure7: Comparison of computational and experimental data
REFERENCES
1. Kislitsin A.A., Shabarov A.B. Heat and Mass Transfer. – Tyumen: TGU, 2007. 

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