对普朗特混合长度理论在圆管紊流流动中的应用进行了修正。基于尼古拉兹的圆管紊流速度分布实验结果：在除管中心及其附近位置外的紊流核心区内精确符合对数分布，结合力平衡方程，得出混合长度表达式；考虑圆管紊流实际情况，对混合长度表达式进行合理假设并引入阻尼函数进行改进，形成适用于圆管不同半径位置处的混合长度计算公式，修正后的混合长度表达式在整个圆管半径范围内光滑连续。基于修正后的混合长度表达式，推导出圆管剪切速率分布函数，并得出速度分布沿半径是一条存在二阶导数的光滑曲线；对剪切速率分布函数进行数值积分，计算某一流动状态下的管道速度分布，与实验结果精确吻合，且在圆管中心位置和层流子层区边界不再存在速度突变，更符合流体实际流动情况。%Modification of Prandtle mixing length theory in turbulent pipe flow was made. According to Nikuradse’s classical experimental results, the velocity profile in turbulent core area except the area near pipe center is confirmed to follow logarithmic distribution accurately. A new mixing length theory was proposed by combining force balance equation with the logarithmic velocity distribution. Reasonable hypothesis was put forward and a damping factor was introduced to modify the new mixing length expression. The modified mixing length function is smooth, continuous and applicative in the whole pipe radius range. Based on the modified mixing length, the distribution function of shear rate was worked out and the corresponding velocity profile was proved to be a smooth curve with second-order derivatives. On the basis of shear rate function, velocity distribution in a certain flow condition was computed by numerical integral method and it agrees well with Nikuradse’s classical experimental data. What’s more, there is no abrupt velocity change between the pipe central area and boundary layer any longer, which consists with the actual situation of flow field.
展开▼
