Numerical simulation method for measuring the thermal properties of permafrost by dual-probe heat-pulse sensor

Thermal properties of frozen soil can be measured to evaluate the engineering construction and agricultural production. However, it is still challenging to determine the thermal properties of frozen soil using a dual-probe heat pulse sensor (DPHP). The thermal pulse can cause the ice around the heating probe to melt during DPHP measurement. The commonly- used analytical solution can only consider the heat conduction, resulting in the less accurate measurement on of the thermal conductivity (λ) and specific heat (C_v) at −5 ℃ to 0 ℃. The purpose of this study is to test the feasibility of finite element simulation for the frozen soil DPHP. COMSOL simulation was carried out to consider the latent heat and temperature of phase transition in the measurement process of DPHP. The two-dimensional transient fluid module was used for simulation. The three-dimensional of DPHP experiment was simplified to the heat transfer in two-dimensional cylindrical coordinates. The 150 mm × 150 mm square was constructed as the study area, where was approximated the DPHP probe with a 0.6 mm circle (ignoring internal probe padding and needle body material), and spaced the probe by 6 mm. The boundary of the study area was set as the adiabatic boundary, the boundary of the circular heat source was the heat flux boundary, which was set as 48.51 W/m, and the heating time was set as t₀ = 8 s, respectively. The parameter settings were consistent with the experimental process. The nonlinear relationships between thermal conductivity and specific heat capacity with temperature was were calculated using the nonlinear relationship between liquid water content and temperature as studied by He et al. 2015. These relationships were then set as the thermal conductivity and specific heat capacity of the frozen soil model. Four phase change temperatures were at −0.05-0.05, −2- 0, −1.5-−0.5 , and −0.5-0 ℃, corresponding to phase change intervals of 0.1, 2, 1, and 0.5 ℃, respectively. Four geometric shapes were constructed around the key solving region (around the DPHP probe), each of which the center was located at the center of the heating probe and side lengths of 5, 10, 15, and 20 mm. The reason was that the uniformly refined grids over the domain were resulted in the high computational costs and large memory usage during simulation. The grid was refined at the boundaries of these geometric shapes, in order to achieve the higher solving accuracy. An infinite line heat source (ILS) and real permafrost measurements were used to evaluate the COMSOL simulation. Three COMSOL simulation models were compared with the ILS model and measured with/without considering phase transition and temperature. The results show that: 1) The COMSOL simulation was in better agreement with the ILS model without considering the phase transition. When the initial soil temperature was ranged from 0 ℃ to −1 ℃, the ILS model was significantly deviated from the experimental measurement (R² < 0.0013). At the same time, the presence of the solid-liquid moving interface caused it to be invalid in the ILS model using single-phase heat transfer, when the temperature was close to 0 ℃. 2) The deviation of simulation from experimental data was significantly reduced to consider the phase transition occurrence and temperature. When the phase transition temperature was −1.5-−0.5 ℃, the correlation between the simulated and the measured value (R² > 0.7) was significantly higher than that between the ILS model and the measured value (R² < 0.001 3). Therefore, the heat transfer of transient melt phase transition can be effectively performed on COMSOL simulation. The more accurate measurement of frozen soil thermal properties was achieved, compared with the current mainstream traditional single-phase model. 3) COMSOL simulation can be used to predict the measurement of frozen soil by DPHP, where the liquid water content was obtained in the process of freeze-thaw at the interval of phase transition. The finding can provide the a new idea to measure the thermal properties of frozen soil in the field.