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有限体积控制体圈划方案对掘进巷道围岩散热的影响研究

Research on the influence of the finite volume control volume division scheme on the heat dissipation of the surrounding rock of the excavation roadway

  • 摘要: 掘进巷道围岩散热是导致该区域热害的主要因素之一,其轴对称围岩温度场的准确解算是散热量计算和风温预测的前提。为了优选出轴对称散热问题下有限体积法控制体积的最佳圈划方案,基于Visual Studio平台编制相应的掘进巷道无因次围岩温度场解算软件,分析不同圈划方式下围岩温度场和不稳定换热准数的演化规律,以及网格形状对计算结果的影响,最终优选出合理的圈划方式。结果表明:迎头区域的围岩冷却范围小,远离迎头区域的围岩冷却范围大。相同条件和位置下,1/3圈划方式对应的冷却圈半径最大,1/2圈划方式次之,2/3圈划和重心法圈划方式最小,且二者冷却圈半径相差不大,围岩温度场分布规律也大致相同。周边巷道中靠近迎头的不稳定换热准数最大,随着与迎头的距离增加,不稳定换热准数逐渐减小。2/3和重心法圈划方式计算的不稳定换热准数最大,且二者计算结果相差不大,1/2圈划方式次之,1/3圈划方式最小。在重心法圈划方式下,粗化网格与细化网格的迎头不稳定换热准数计算结果相差最小为0.1269,表明重心法圈划方式的优越性。此外,重心法圈划方式能够充分划分几何模型,不存在缺失、重复和超出计算区域的现象,进一步表明重心法圈划方式的合理性。模拟结果和实测数据的变化规律相同,即随着孔深增加,围岩温度逐渐升高,并最终趋于平稳。2个钻孔模拟和实测温度的最大相对误差分别为12.71%、13.09%,平均相对误差分别为3.84%、3.94%,能够满足工程应用的需求,验证了温度场数学模型和重心法圈划方式离散数学模型的准确性。

     

    Abstract: Heat dissipation from the surrounding rock is one of the major sources of thermal hazards in excavation roadways. Accurate determination of the axisymmetric temperature field of the surrounding rock is therefore essential for quantifying rock heat dissipation and predicting airflow temperature. To optimize the control volume division scheme in the finite volume method for this axisymmetric heat dissipation problem, software was developed on the Visual Studio platform to compute the dimensionless temperature field in excavation roadways. Based on this software, the evolution of the temperature field, the unsteady heat transfer number under different division schemes, and the influence of grid shape on the numerical results were systematically investigated, and an appropriate division scheme was identified. The results show that the cooling zone is relatively limited near the heading face, but becomes much larger in regions farther away. Under the same conditions and at the same location, the cooling radius predicted by the 1/3 division scheme is the largest, followed by the 1/2 division scheme, while the 2/3 and center of gravity division schemes give slightly smaller values with little difference between them. A similar trend is observed for the temperature field distribution. The unsteady heat transfer number reaches its maximum near the heading face in the peripheral roadway and decreases gradually with increasing distance from the heading face. The values obtained using the 2/3 and center of gravity division schemes are the largest and remain close to each other, whereas the 1/2 division scheme yields the smallest values. For the center of gravity division scheme, the difference in the unsteady heat transfer number between the coarse and refined grids at the heading face is only 0.1269, which is the smallest among all schemes, indicating better grid adaptability. In addition, the center of gravity division scheme fully covers the geometric domain without omission, overlap, or extension beyond the computational region, further confirming its rationality. The simulated results agree well with the measurements in terms of variation trend, showing that the surrounding rock temperature increases with borehole depth and eventually approaches a stable value. For the two boreholes, the maximum relative errors between simulated and measured temperatures are 12.71% and 13.09%, respectively, while the corresponding average relative errors are 3.84% and 3.94%. These results satisfy engineering requirements and demonstrate the validity of both the thermal field mathematical model and the discrete model based on the center of gravity division scheme.

     

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