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

  • 摘要: 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.

     

    Abstract: The Buckingham equation expresses the relationship between laminarflow velocity and resistance of the Bingham fluid. The Soviet scholarproposed an approximate formula for calculating flow resistance, based onwhich the maximum deviation relative to the exact solution was 6.7%. Inthis paper, with the mathematical analysis and three-dimensionsoptimization, and the change of the parameter of the approximate formula, the deviation isdecreased to a great extent. The deviation is the function of theparameter and thecore-flow relative radius r0. By means of the limiting value, the continuous points and interrupted points in the \bar r0 closedregion are determined, which provides a basis for reducing the deviationin the wholeregion. In the three-dimensional figure of the deviations, the problem toseek the max-value on multi-peak curved surface can be resolved by the useof the cutting plane. Finally, with the optimized parameter, the maximumdeviation of the approximate equation becomes 2.6%, a reduction of 4.1%comparing to 6.7%.

     

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