Pumping liquid into a closed tank using a vortex pump

The paper presents a mathematical model of the operation of a vortex pump in a hydraulic network. By comparing the equations of performance of vortex pumps, it was found that the linear pressure characteristics (supply — pressure drop) of all vortex pumps are similar. There is a criterion for similarity of energy characteristics (supply — power consumption). The equation of the balance of the mass of water in the tank has been compiled. In general, its solution boils down to the task. Cauchy, which has no analytical solution. The dependence of the dimensionless expenditure on the excess pressure in the tank was calculated numerically. The ratio of hydraulic losses in the pipeline at the highest theoretical supply to the value of the largest theoretical pressure drop was adopted as a similarity criterion. As the diameter of the pipeline in the network increases, the pressure increases. This is due to the reduction of hydraulic losses in the pipeline. But starting from a certain diameter, the pressure practically does not change. This means that under such conditions, hydraulic losses in the pipeline can be neglected. The purpose of the article is to develop a mathematical model of the operation of a vortex pump in a hydraulic network.
EDN: WNXQKE, https://elibrary/wnxqke

References

[1] Meshalkin V.P., Guseva T.V., Malyavin A.S. et al. Principles of chemical engineering as a basis for the development of the international concept of best available techniques. Teoreticheskie osnovy khimicheskoy tekhnologii, 2024, vol. 58, no. 1, pp. 8–16, doi: https://doi.org/10.31857/S0040357124010029 (in Russ.). (Eng. version: Theor. Found. Chem. Eng., 2024, vol. 58, no. 4, pp. 943–951, doi: https://doi.org/10.1134/S0040579525600068)

[2] Meshalkin V.P. Osnovy intensifikatsii i resursoenergoeffektivnosti khimiko-tekhnologicheskikh system [Fundamentals of intensification and resource and energy efficiency of chemical-technological systems]. Smolensk, Printekspress Publ., 2021. 442 p. (In Russ.).

[3] Hungerbühler K., Boucher J.M., Pereira C. et al. Chemical products and processes. Springer, 2021. 332 p.

[4] Komissarov Yu.A., Gordeev L.S., Vent D.P. Protsessy i apparaty khimicheskoy tekhnologii [Processes and apparatuses of chemical engineering]. Moscow, Yurayt Publ., 2024. 1242 p. (In Russ.).

[5] Levochkin P.S., Romasenko E.N., Vidishev V.I. et al. Development and investigation of a low-delivery hermetically sealed installation having a peripheral pump. Konversiya v mashinostroenii [Conversion in Machine Building of Russia], 2006, no. 1, pp. 28–32. (In Russ.).

[6] Zhdanov I.L., Khaustov A.I., Sergievskiy E.D. et al. A liquid flow computation in channels of peripheral pumps. Vestnik MAI [Aerospace MAI Journal], 2003, vol. 10, no. 2. URL: https://vestnikmai.ru/publications.php?ID=32592 (in Russ.).

[7] Camargo C., García C., Duarte J. et al. Statistical model for characterizing and optimizing peripheral pumps. Ingenier?a y Desarrollo, 2018, vol. 36, no. 1, pp. 18–39, doi: https://doi.org/10.14482/inde.36.1.10939

[8] Levicheva O.I., Naumov V.A. Features of the working characteristics of peripheral pumps used in the food industry. Vestnik nauki i obrazovaniya Severo-Zapada Rossii [Journal of Science and Education of North-West Russia], 2021, vol. 7, no. 4, pp. 26–32. (In Russ.).

[9] Akhmedova N.R., Levicheva O.I., Naumov V.A. Kriterii podobiya ustanovok dlya perekachivaniya malovyazkikh pishchevykh zhidkostey vikhrevymi nasosami [Similarity criteria of units for pumping low-viscosity food liquids by peripheral pumps]. Izvestiya KGTU [KSTU News], 2022, no. 66, pp. 78–88. (In Russ.).

[10] Boldyrev A.V., Boldyrev S.V., Karelin D.L. The effect of blade profile on the performance of a side channel pump. Vestnik TyumGU. Fiziko-matematicheskoe modelirovanie. Neft, gaz, energetika [Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy], 2020, t. 6, no. 3, pp. 23–37, doi: https://doi.org/10.21684/2411-7978-2020-6-3-23-37 (in Russ.).

[11] Pokusaev M.N., Bukin V.G., Trifonov A.V. Research tests of the outboard water cooling system vortex pump of the vessel type "Yaroslavets" main engine. Morskie intellektualnye tekhnologii [Marine Intellectual Technologies], 2018, no. 4-4, pp. 89–93. (In Russ.).

[12] Shitokhina O.G., Ananyev N.A. A study of the influence of the dimensions of holes on the surface of the vortex pump rotor on a fluid velocity in the outlet. Nauka, tekhnika i obrazovanie, 2019, no. 1. URL: https://nto-journal.ru/catalog/mashinostroenie/668/ (in Russ.).

[13] Isaev N.Yu., Radchenko S.A. Investigation of the effect of the form of the transfer channel of the centrifugal-vortex pump on the energy characteristics by the methods of hydrodynamic modeling. Gidravlika, 2019, no. 8. URL: https://hydrojournal.ru/images/journal/number8/radchenkoisaev.pdf (in Russ.).

[14] Wang Y., Zhang F., Yuan S. et al. Influence of cavitation on unsteady vortical flows in a side channel pump. Chin. J. Mech. Eng., 2023, vol. 36, art. 25, doi: https://doi.org/10.1186/s10033-023-00842-4

[15] Katalog periferiynykh nasosov Calpeda T, TP [Catalog of Calpeda T, TP peripheral pumps]. calpeda.ru: website. URL: https://calpeda.ru/production/calpeda-t-tp/ (accessed: 17.09.2025). (In Russ.).