New in the hydraulics of channels with permeable walls: indicator of the relative value of the dissipation

The factors that have led to the creation of the scientific direction “hydraulics of variable mass” to study the fluid movement laws in channels with permeable walls are indicated. The results of applying of the dynamics of a variable mass point for describing the flow in such pipelines are presented. It is noted unjustifiability of the second Newton’s law generalization to the case of motion of a variable mass point for hydrodynamics problems. The functionality of one-dimensional and multidimensional models of fluid motion in permeable channels based on the classical equations of fluid and gas mechanics is characterized. It is substantiated the dominance of one-dimensional models in engineering computational practice, and a number of contradictions in the description of fluid dynamics are shown (with the flow visualization). On the base of the new kinematic image (instead of the generally accepted “solid jet”, when fluid particles are separated or joined), it has been obtained a one-dimensional equation of fluid motion in a permeable channel in which the friction coefficient is an indicator of the relative magnitude of the energy dissipation of the flow. The dependence of the Coriolis coefficient on the flow regime is constructed. The structure of the friction drag coefficient of a permeable channel has been studied using the vector dimension of length. It is shown that the dissipation of the flow energy in a permeable channel is higher both during outflow and inflow of liquid than in channels with solid walls at the same flow rates. The results are in demand in the development of chemical technology devices, nuclear reactors with microfuel elements, filters and heat exchangers containing channels with permeable walls.

1. Makkaveev V. M. Theory of hydrodynamic processes with large energy dissipation. Trudy II vsesoyuznogo gidrologicheskogo s”ezda v Leningrade, 20–27 aprelya 1928 g. [Proceedings of the II All-Union Hydrological Congress in Leningrad, April 20–27, 1928]. Leningrad, State Hydrological Institute, 1930, pp. 49–60 (in Russian).

2. Nenioko J. T. About the fluid motion with variable mass along the way. Trudy Khar’kovskogo gidrometeorologicheskogo instituta [Proceedings of the Kharkiv Hydrometeorological Institute]. Kharkiv, 1938, pp. 3–50 (in Russian).

3. Patrashev A. N. The movement of fluid in channels with variable flow rate along the way. Izvestiya NII gidrotekhniki [News of the Research Institute of Hydraulic Engineering], 1940, vol. 28, pp. 5–30 (in Russian).

4. Petrov G. A. Hydraulics of Variable Mass. Kharkiv, Kharkiv University, 1964. 224 p. (in Russian).

5. Navoian H. A. Examples of Hydraulic Calculations of Culverts. Kyiv, Budivilnic Publ., 1975. 149 p. (in Russian).

6. Newton I. Adventurer in Thought. Chapter 8 – Natural Principles of Mathematics. Cambridge University Press, 2010, pp. 202–224. https://doi.org/10.1017/CBO9780511622403.010

7. Orear J. Physics. New York, Macmillan, 1979. xvi, 752 p.

8. Markeev A. P. The Theoretical Mechanics. Moscow, ChePo Publ., 1999. 572 p. (in Russian).

9. Golubev Yu. F. Fundamentals of Theoretical Mechanics. Moscow, MSU Publ., 2000. 719 p. (in Russian).

10. Batchelor G. K. An Introduction to Fluid Dynamics. Cambridge University Press, 2000. xviii, 615 p. https://doi.org/10.1017/CBO9780511800955

11. Loitsyanskii L. G. Mechanics of Fluid and Gas. Moscow, Nauka Publ., 1978. 736 p. (in Russian).

12. Mescherskii I. V. Equations of the Movement of a Point with Variable Mass in Total Case. Moscow, State Publ. House on Construction and Architecture, 1952. 318 p. (in Russian).

13. Kinney R. B., Sparrow E. M. Turbulent Flow, Heat Transfer, and Mass Transfer in a Tube With Surface Suction. ASME Journal Heat Transfer, 1970, vol. 92, no. 1, pp. 117–124. https://doi.org/10.1115/1.3449600

14. Kochenov I. S., Novosel’skii O. Yu. On the hydraulic resistance of the nuclear reactor cooling system. Atomnaya energiya [Atomic Energy], 1967, vol. 23, no. 2, pp. 113−120 (in Russian).

15. Kagan A. M., Pushnov A. S., Gal’perin I. I. Gas flow distribution in a flat apparatus with an expanded granular layer. Khimicheskaya promyshlennost’ = Industry & Chemistry, 1980, no. 1, pp. 42−44 (in Russian).

16. Gorelik A. G., Melamed L. N., Anitin A. V. Investigation of radial reactors the hydrodynamics for catalytic afterburning of exhaust gases. Teoreticheskie osnovy khimicheskoi tekhnologii = Theoretical Foundations of Chemical Engineering, 1980, vol. 14, no. 3, pp. 378−385 (in Russian).

17. Voitov I. V., Kolos V. P. Reactors with micro fuel particles: hydrodynamics of permeable channels of the bulk assembly. Vestsi Natsyyanal’nai akademii navuk Belarusi. Seryya fizika-tekhnichnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physical-technical series, 2019, vol. 64, no. 2, pp. 182–196 (in Russian). https://doi.org/10.29235/1561-8358-2019-64-1-182-196.

18. Kochenov I. S., Novosel’skii O. Yu. Hydraulic resistance of channels with permeable walls. Journal of Engineering Physics and Thermophysics, 1969, vol. 16, no. 3, pp. 275–281. https://doi.org/10.1007/BF01840621

19. Kuznetskii R. S. Fluid velocity and pressure distributions along a pipe with holes. Journal of Engineering Physics and Thermophysics, 1971, vol. 20, no. 1, pp. 96–99. https://doi.org/10.1007/BF00868595

20. Smyslov V. V., Ezerskii N. J. Analysis of the equation of fluid motion in pipelines with variable distribution along the path. Gidravlika i gidrotekhnika [Hydraulics and Hydraulic Engineering]. Kyiv, 1974, no. 18, pp. 132−130 (in Russian).

21. Grikevich E. A. Distribution of fluid velocity and pressure losses in a well. Vodosnabzhenie i kanalizatsiya [Water Supply and Sewerage], 1974, iss. 4, pp. 77−81 (in Russian).

22. Smyslov V. V., Konstantinov Yu. M. Hydraulic calculation of pipelines with variable distribution along the path. Gidravlika i gidrotekhnika [Hydraulics and Hydraulic Engineering]. Kyiv, 1972, no. 14, pp. 24–31 (in Russian).

23. Anofriev G. I., Bystrov P. I. Hydraulic characteristics of single-row collector systems. Teploenergetika = Thermal Engineering, 1971, no. 9, pp. 32–35 (in Russian).

24. Reizis E. A. Hydraulic calculation of contact radial devices. Teoreticheskie osnovy khimicheskoi tekhnologii = Theoretical Foundations of Chemical Engineering, 1967, vol. 1, no. 3, pp. 380–382 (in Russian).

25. Dilman V. V., Sergeev S. P., Genkin V. S. The description of the stream movement with permeable walls on the basis of the energy equation. Teoreticheskie osnovy khimicheskoi tekhnologii = Theoretical Foundations of Chemical Engineering, 1971, vol. 5, no. 4, pp. 564–572 (in Russian).

26. Shimko K. I., Eliseev K. E. Equation of fluid motion in constant cross section perforated pipelines taking into account the low of consumption distribution along the path. Vodnoe khozyaistvo Belorussii [Water Management of Belarus]. Minsk, 1975, iss. 5, pp. 138–144 (in Russian).

27. Egorov A. I. Investigation of the laws of fluid movement in tubular distributors and collectors of water treatment facilities. Trudy VNII VODGEO [Proceedings of the All-Union Scientific Research Institute of Water Supply, Sewerage, Hydraulic Structures and Engineering Hydrogeology]. Moscow, 1970, no. 27, pp. 22−30 (in Russian).

28. Egorov A. I. Distribution of water by perforated pipes with a constant hole. Trudy VNII VODGEO [Proceedings of the All-Union Scientific Research Institute of Water Supply, Sewerage, Hydraulic Structures and Engineering Hydrogeology]. Moscow, 1972, no. 36, pp. 142–159 (in Russian).

29. Bystrov P. I., Mikhailov V. S. Hydrodynamics of Collector Heatexchange Devices. Moscow, Energoizdat Publ., 1982. 224 p. (in Russian).

30. Meerovich I. G., Muchnik G. F. The Hydrodynamics of Collector Systems. Moscow, Nauka Publ., 1986. 144 p. (in Russian).

31. Idel’chik I. E. Method of calculating flow distribution along contact, filter, and similar apparatus of cylindrical shape. Journal of Engineering Physics and Thermophysics, 1965, vol. 8, no. 5, pp. 433–435. https://doi.org/10.1007/BF00830324

32. Huntley H. E. Dimensional Analysis. London, Macdonald, 1952. 158 p.

33. Trubetskov D. I. Two lectures. Dimensional analysis or paradise life in physics. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, no. 1, pp. 16–32 (in Russian). https://doi.org/10.18500/0869-6632-2012-20-1-16-32

34. Siano D. B. Orientational Analysis − a Supplement to Dimensional Analysis − I. Journal of the Franklin Institute, 1985, vol. 320, iss. 6, pp. 267−283. https://doi.org/10.1016/0016-0032(85)90031-6

35. Siano D. B. Orientational Analysis, Tensor Analysis and Group Prorerties of the SI Supplementary Units − II. Journal of the Franklin Institute, 1985, vol. 320, iss. 6, pp. 285−302. https://doi.org/10.1016/0016-0032(85)90032-8