沙粒当量粗糙度的分形表达

Fractal expression of sand grain equivalent roughness

沙粒当量粗糙度ks的准确确定是计算沙粒阻力的关键。针对沙粒轮廓剖面具有自相似精细结构的特点,提出采用分形维数对其复杂性及不规则性进行定量描述;通过粘沙平整床面、初始静平整床面和清水冲刷粗化床面的沙粒阻力试验研究ks的分形表达方法,建立了静平整床面时ks的分形表达式,并对公式进行了验证、比较和讨论;结果表明,公式引入的中值粒径d50、分形维数D和弗劳德数Fr 3个参数,可定量地综合反映床沙颗粒大小、级配组成、随机排列以及水流条件对ks的影响。

Accurate determination of sand grain equivalent roughness is the key to calculate sand grain resistance. In this paper, fractal dimensions were used to describe self-similar complexity and irregularity of sand bed profile. The fractal expression of sand grain equivalent roughness was obtained based on a large number of sand grain resistance experiments, which include sediment-glued flat bed, initially flat stationary bed and armoring bed. The median size d50, fractal dimension D and Froude number Fr are introduced in the proposed expression along with corresponding valida- tion, comparison and discussion of results. The results showed that the expression can comprehensively reflect how equivalent roughness of sand grain is influenced by external factors such as grain size, gradation composition, random arrangement and flow condition.