有限时段源一维水质模型的求解及其简化条件

Solution and simplified conditions of one-dimensional water quality model in the limited period source

有限时段源一维水质模型的求解及其简化为按瞬时源处理的判别条件,对事故性排放污水的应急计算具有十分重要的意义。在等强度有限时段源条件下,采用变量替换和拉普拉斯变换方法,求解了河流污染物浓度分布的解析解。在不同的简化条件下,讨论了该解析解与可对比解析解的一致性。定义了排放数W_t=u^2t_0/D_x,提出了有限时段源可以按瞬时源计算的临界时间t_k(W_t)方程和简化判别条件:当扩散历时t<t_k,按有限时段源的浓度分布公式计算;当扩散历时t≥t_k,按瞬时源的浓度分布公式计算。

The solution of one-dimensional water quality model in limited period source the criteria for simplifying the model as instantaneous source are very important to calculate accidental discharge of sewage in emergency. Analytic solutions of pollutant concentration distribution in rivers are given using variable substitution and Laplace transform method under the condition of equal intensity limited period source. The consistency between the above analytic solution and comparable analytic solutions are discussed under different simplified conditions. The Discharge number,W_t=u^2 t_0/D_x,is defined. The critical time,t_k（W_t）,is given in which limited period source can be calculated by using instantaneous source. The simplified criteria are when diffusion time tt_k,the concentration distribution formula of limited period source is used and when t≥t_k,the formula of instantaneous source is used.