Numerical method for identifying the flow model in the line pipe



Published May 31, 2020
Vladimir V. Zholobov


With high availability of measuring tools and wide opportunities of modern computer technology, the existing methods of predictive estimations of hydraulic parameters for the fluids’ pipeline transport seem to be too approximate. Due to this, it is relevant to adapt the most accurate relationships available in the scientific and technical literature to real conditions. Based on the review of analytical solutions for calculating friction losses in the pressure lines, the structure of relationships most accurately reflecting the experimental data of I. Nikuradze is determined, where the hydraulic drag coefficient λ is described by the piecewise-continuous relations, given by O. M. Ayvazyan. The hydraulic drag coefficient structural relationship shall be selected with the highest capability to summarize the experimental data available in the scientific and technical literature. Using the pressure measurement data, free parameters included in the selected relationship for the hydraulic drag coefficient shall be identified. The numerical computation algorithm is proposed that enables to recover the values of parameters in the structural relationship of hydraulic drag coefficient λ through multiple application of the well-known method of sensitivity functions and pressure measurement data in the line pipe. The procedure is described for generating the computing system of ordinary differential equations that enables for every fixed set of experimental data (pressure and flow rate) to determine (or correct, if necessary) the corresponding parameters in the unified structural relationship for hydraulic drag coefficient λ. The feature of the proposed algorithm is the absence of embedded cycles. Dynamic control of variable parameters in the hydraulic drag coefficient λ based upon the proposed approach enables to improve the predictive estimations accuracy of flow parameters while pumping fluids and to acquire additional data on the state of the fluids filling the inner pipeline space.

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Zholobov VV. Numerical method for identifying the flow model in the line pipe. PST [Internet]. 2020May31 [cited 2020Aug.8];4(2(4):138-4. Available from:


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Hydraulic drag coefficient, sensitivity function, root-mean-square deviation, minimizing the functional.

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Original Work