倾斜岸坡角形域顶点排污浓度分布的理论分析

Analytical solution to concentration distribution discharged from the intersection of effluent into corner field of inclined banks

为了获得倾斜岸坡角形域顶点排污浓度的分布,基于镜像法原理和角形域平面镜映射实验,给出了横向和垂向扩散系数不相等的角形域映射图。从无限区域静止水体中瞬时线源的二维扩散和等强度连续点源三维移流扩散简化方程的解析解人手,分析推导出角形域顶点排污瞬时线源扩散的浓度计算公式,进而得到了角形域顶点排污等强度连续点源移流扩散浓度分布的理论公式。对该理论公式的分析与讨论表明,在简化条件下该理论公式与可对比理论解完全一致,角形域内角角度对污染物的浓度分布影响很大,角形域顶点排污浓度分布具有复杂性和多重性。该理论公式可为水库岸边污染混合区浓度估算提供有力的工具。适用条件为顺直倾斜岸坡大宽度深水情况,满足内角θ=180 /n(n 为自然数)的角形域顶点排污的浓度计算。

Based on the image method theory and experiment of plane mirror mapping, a mapping graph of corner field with different coefficient of transverse diffusion and coefficient of vertical diffusion was obtained. Starting from the analytical solution of simplified equation in infinite area of still water with two-dimensional diffusion of instantaneous line source and 3-D advection-diffusion of continuous source, the analysis of the concentration calculating formula for diffusion of instantaneous line source of intersection discharging in corner field and the theoretical formula of advection-diffusion of continuous point source in the constant time of intersection discharging into corner field were deduced. Analysis and discussion of the results show that, the theoretical formula of advection-diffusion of continuous point source in the constant time of intersection discharging in corner field is in accordance with the comparable theoretical solution. The interior angle of corner field has great influence on distribution of pollutant concentration, with complexity and multiplicity in the concentration distribution discharged from the intersection effluent of corner field. The theoretical formula is very useful for estimating the concentration in reservoir near-bank pollution mixing zone. Its applicable condition is large width and deep water with inclined bank in straight river channel and also meeting the situation of field corner θ=180？/n （n is natural number）. The concentration distribution can be calculated from the intersection of effluent into corner field of inclined bank.