能源桩传热数学新模型及其在热响应测试的适用性

A novel mathematical model for heat transfer of energy pile and its applicability in thermal response test

能源桩热响应测试时,确定数学模型和选择参数反演方法是及时、有效确定桩周土热物性参数的关键因素。为此,首先,根据能源桩内循环回路的径向位置,基于能量守恒原理,提出圆柱面热源在复合介质内层传热的数学模型,并通过拉普拉斯变换、逆变换求得解析解;其次,使用COMSOL建立具有螺旋循环回路的能源桩数值模型,分别模拟混凝土能源桩在饱和黏土和干黏土中为期7 d的热响应测试,并记录桩表面温度;第三,比较目前常用的参数反演方法,确定采用模式搜索法作为参数反演方法;最后,分别使用无限长线热源模型、实心圆柱面热源模型、位于复合介质界面处的圆柱面热源模型以及本文模型,根据记录数据反演热物性参数,并与数值模型输入值比较,明确上述数学模型反演结果的准确度。研究结果表明:当桩周土为饱和黏土时,桩-土的热物性差异较小,采用向两侧同时传热的圆柱面热源模型反演结果的相对误差均在10%以内;当桩周土为干黏土时,桩-土的热物性差异较大,仅本文模型反演结果的相对误差在10%以内,导热系数和热扩散系数的相对误差分别为6.66%和0.29%。本模型反演结果的准确性受能源桩桩径和桩-土热物性差异的影响较小。在实际热响应测试过程中,能源桩桩径较大、土体热物性未知,采用本模型更适宜。

In the thermal response test(TRT) of the energy pile, the determination of mathematical model and the selection of parameter inversion method are the critical factors in inverting the soil’s thermal parameters around the pile timely and effectively. Firstly, based on the radial position of the circulation loop inside the pile and the principle of energy conservation, a novel heat transfer model with the cylindrical heat source at the inner layer of the composite medium was proposed, and the explicit analytical solution was obtained by Laplace transform and inverse transformation. Secondly, the numerical model of the energy pile with a spiral loop was established by COMSOL to simulate the TRT of the concrete energy pile in saturated clay and dry clay for 7 d, and the temperature of the pile’s surface was recorded during the test. Thirdly, the commonly used parameter inversion methods were compared, and the pattern search method was selected as the parameter inversion method. Finally,the infinite line source model, solid cylindrical heat source model, cylindrical heat source at the interface of composite media model, and the model in this paper were used to invert the thermal parameters according to the record data, respectively. The input values of the numerical model were compared to clarify the accuracy of the inversion results of the above mathematical models. The results show that when the soil around the pile is saturated clay, whose thermal property difference is small, the relative errors of inversion results from the cylindrical heat source model with heat transfer to both sides simultaneously are all within 10%. When the soil around the pile is dry clay, whose thermal property difference is huge, only the relative errors of the proposed model is less than 10%, and the relative errors of the thermal conductivity and thermal diffusion coefficient are 6.66% and 0.29%, respectively. The accuracy of inversion results of this model is less affected by pile diameter and thermal property difference between the pile and the soil. In the actual TRT process, the diameter of pile is large and the thermal property of soil is unknown, so the model proposed in this paper is more suitable.