泄洪雨雾输运的数学模型研究

Study on the Numerical Model for the Rain-fog Transportation During Flood Discharge

针对泄洪雨雾在河谷中的对流与沉降问题,提出一种3维有限元计算模型,该模型通过对浓度梯度矢的求解,可保证浓度计算的非负性与单调性。同时,根据气象学中雨滴谱函数与水滴沉降速度等概念,导出雨雾浓度与降雨强度间的定量转换关系,使其与其他雾化近区数学模型实现边界耦合。运用本文模型对瀑布沟电站泄洪洞雾化分布进行模拟,计算结果与真实的物理规律相一致,为今后类似工程问题的研究提供了适用手段。

A three-dimensional finite element model was developed to calculate the rain-fog convection and sedimentation in valley during the flood discharge.By the proper solution of the concentration gradient vector,the nonnegative type and monotonic changes of the concentration is maintained during the transportation.With the concept of raindrop size distribution and settlement velocity,the formulas was derived for the quantitative conversion between the rainfall intensity and water concentration,which is available to couple the boundary with other inner field numerical models.The distribution of rainfall intensity from the cavity discharge was simulated under the different wind fields in Pubugou hydropower station,the calculated results accord with the real physical mechanism well.