双针热脉冲测定冻土热特性的数值模拟方法

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

    • 摘要: 使用双针热脉冲(dual probe heat pulse, DPHP)测定冻土热特性时施加热脉冲后会导致加热探针周围的冰融化,使用目前常用的仅考虑热传导(忽略融化相变、冰水两相分界面)的解析解处理DPHP温度数据,会导致在−5 ℃至0 ℃温度范围内无法准确测量热导率 (λ) 和比热 (Cv)。为了能够准确测定冻土的 λCv,有必要考虑DPHP加热过程中引起的冰融化的相变潜热。该研究基于COMSOL仿真软件模拟了考虑相变潜热、相变区间以及移动冰水界面的DPHP测量过程,采用随温度非线性变化的真实冻土热特性进行模拟,并与真实冻土的DPHP测量数据对比。结果表明:1)COMSOL仿真在不考虑相变条件下与无限线性热源模型结果完全吻合(R2 = 0.9989);2)当土壤初始温度低于−5 ℃时,考虑相变发生的COMSOL仿真能够准确模拟试验结果,表现出较高的相关性(R2 > 0.93),在−1~ 0 ℃的土壤初始温度范围内,无限线性热源模型的结果与试验测量显著偏离(R2 < 0.0013);3)在不同土壤初始温度下,相变温度为−1.5 ~ −0.5 ℃的仿真结果与试验数据具有较高的相关性(R2 > 0.7)。该研究结果检验了有限元仿真用于真实冻土DPHP研究的可行性,可为准确预测冻土热特性的研究提供方法。

       

      Abstract: 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 (Cv) 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.

       

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