宾汉流体阻力近似解公式精度的优化提高

THE OPTIMIZATION OF FLOW RESISTANCE APPROXIMATE FORMULA OF BINGHAM FLUID

针对前苏联学者求解宾汉流体布金汉方程的阻力近似解公式,其与精确解最大偏差为6.7％,首次通过数学分析和三维优化计算,改变公式中的参数,使偏差大幅度降低.偏差是参数和核心流相对半径r0的函数,用极限判定了在r0闭区间内的连续性和间断点,为降低偏差提供了依据.绘制了偏差三维变化图,应用切片平面解决了多峰曲面的极值问题.最终优化出的参数使公式的最大偏差为2.6％,比6.7％降低了4.1％,优化后的公式,在管道输送阻力计算中更有实用价值.

The Buckingham equation expresses the relationship between laminar flow velocity and resistance of the Bingham fluid. The Soviet scholar proposed an approximate formula for calculating flow resistance, based on which the maximum deviation relative to the exact solution was 6.7%. In this paper, with the mathematical analysis and three-dimensions optimization, and the change of the parameter of the approximate formula, the deviation is decreased to a great extent. The deviation is the function of the parameter and the core-flow relative radius fo. By means of the limiting value, the continuous points and interrupted points in the fo closed region are determined, which provides a basis for reducing the devi- ation in the whole region. In the three-dimensional figure of the deviations, the problem to seek the max-value on multi-peak curved surface can be resolved by the use of the cutting plane. Finally, with the optimized parame- ter, the maximum deviation of the approximate equation becomes 2.6%, a reduction of 4.1% comparing to 6.7%.