嵌入不透水球体复合多孔介质渗流场分析

发布时间：2019-03-30 17:34

【摘要】：嵌入不透水球体的复合多孔介质广泛存在于地下水渗流领域,由于不透水球体的影响,多孔介质中的水在流经不透水球体时发生绕流,且距离球体越近绕流现象越明显。为求解该复合介质的渗流场和等效渗透系数,在球坐标系下采用非线性Brinkman-extended Darcy方程,以无穷远处单向来流均匀和球面不滑移条件作为边界条件,求解出球体周围渗流流速与压强的解析解。分析该解析解表达式可知,此复合介质渗流场流速和压强分布与多孔介质基质的渗透率和地下水动力黏滞系数有关。在此基础上对渗流场流速进行积分,求出了Darcy流平均流速,并将平均流速表达式与Darcy公式表达式进行对比,得出等效渗透系数表达式,并理论证明球体与多孔介质的相对尺寸是影响复合介质等效渗透系数的最主要因素。最后以一定级配的砂作为多孔介质基质,用直径分别为4、6、8 cm的3种有机玻璃球体作为不透水球体,自制试验装置,开展嵌入不透水球体复合多孔介质的常水头渗流试验。试验通过控制多孔介质基质的压实度来保证其渗透系数基本不变,改变填充在多孔介质基质中的不透水球体进行渗流试验,对每一个不透水球体分别进行3组试验,取平均值作为试验结果。试验结果与理论计算的等效渗透系数值误差较小,验证了所推求嵌入不透水球体复合多孔介质渗流场的正确性。
[Abstract]:The composite porous media with impermeable sphere exists widely in the field of groundwater seepage. Due to the influence of impervious sphere, the water in porous media flows through the impervious sphere, and the closer the sphere is, the more obvious the phenomenon is. In order to solve the seepage field and equivalent permeability coefficient of the composite medium, the nonlinear Brinkman-extended Darcy equation is adopted under the spherical coordinate system, and the uniform unidirectional flow and the spherical non-slip condition at infinity are taken as the boundary conditions. The analytical solution of the flow velocity and pressure around the sphere is obtained. The analytical solution shows that the velocity and pressure distribution of the seepage field in the composite medium are related to the permeability of porous media matrix and the dynamic viscosity coefficient of groundwater. On this basis, the mean velocity of Darcy flow is calculated by integrating the velocity of seepage field, and the expression of mean velocity of flow is compared with the expression of Darcy formula, and the expression of equivalent permeability coefficient is obtained. It is proved theoretically that the relative size of sphere and porous medium is the most important factor affecting the effective permeability coefficient of composite media. Finally, three kinds of plexiglass spheres with diameters of 4, 6 and 8 cm were used as impermeable spheres with sand as porous media matrix, and self-made test equipment was used to carry out the constant head seepage test with impermeable sphere composite porous media. By controlling the compactness of porous media matrix to ensure that its permeability coefficient is basically unchanged, the seepage test is carried out by changing the impervious sphere filled in the porous medium matrix, and three groups of tests are carried out on each impervious sphere separately. The average value was taken as the test result. The error between the experimental results and the theoretical value of the equivalent permeability coefficient is small, which verifies the correctness of the proposed seepage field of the composite porous media with impermeable sphere.
【作者单位】：四川大学水力学与山区河流开发保护国家重点实验室水利水电学院;成都理工大学地质灾害防治与地质环境保护国家重点实验室;中国科学院山地灾害与地表过程重点实验室;
【基金】：国家重点基础研究发展计划资助项目(2015CB057903) 中国博士后科学基金资助项目(2016M590890) 四川省科技计划专项资助(2014SS027)
【分类号】：TV139.1

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