# Method of experimental investigation of the friction facility pneumatic wires

2020;
: 26-36
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
Lviv Polytechnic National University

Aim. Development of a method for experimental study of the coefficient of friction for pneumotransport systems of gaseous media using the method of similarity and dimensionality theory, which allows expanding the number of factors and they intervals by grouping them into dimensionless similarity criteria. Method. The planned experiment was chosen for experimental studies of the coefficient of air friction. The main factors were pressure, diameter of the pipeline, air flow. The response criterion is the calculated coefficient of air friction. A complete factorial experiment was applied at three levels with three factors in the vicinity of the selected point x01 = 0,0028 m, ,  х02 = 1,5 kPa and х03 = 0,003504 m3/ s. As an alternative to the full factorial experiment, the transport of air in the pipeline was subordinated to the method of proportionality and the combination of similarity numbers through the bond equations. In the equation, the first component is the size inverse of the Reynolds number (1/Re), the second component is the size inverse of the Galileo criterion (1/Ga), the third component is the Euler number (Eu), and the ratio η2/d2 has a clear physical meaning - velocity mixture. Applied a complete factorial experiment at three levels with two factors in the vicinity of the selected point Re(x01) = 8532,5 and Eu(х02) = 8424. Results. The coefficient of air friction increases with increasing diameter of the conditional passage of the vacuum line and decreases the volume air flow in a low vacuum medium, due to a decrease in the average air velocity and a decrease in Mach number. With a decrease in the Reynolds number and an increase in the Euler number, the coefficient of air friction according to the design and technological parameters of the vacuum system of the technological installation: volume air flow = 0,0015-0,0060 m3/s; loss of vacuum pressure Δр = 0,6-2,2 kPa; inner diameter of the vacuum line = 0,022-0,038 m - increases nonlinearly. Scientific novelty. For the first time, the correlation dependences of the friction coefficient as a function on the criterion dependences were obtained and correlated with the correlation dependences according to the classical method of a complete factorial experiment. Installed, at the set structural and technological parameters of functioning of vacuum system of technological installation (diameter of the conditional passage of the vacuum line = 0,022 - 0,038 m, vacuum pressure р = 30-60  kPa) Mach number is in the range М ≈ 0,200 - 0,003, the coefficient of air friction λ = 2-17 and the loss of vacuum pressure Δр = 0,6 - 2,3 kPa. Practical value. The use of criterion dependences as factors in the planned experiment expands the limits of the parameters of correlation dependences that describe the functioning of technological pneumotransport systems.

1. He S., Ariyaratne C. Wall shear stress in the early stage of unsteady turbulent pipe flow, Journal of Hydraulic Engineering. – 2011. - Vol. 137, Iss. 5. - P. 606–610 ;

2. Sundstrom, L.R.J., Cervantes, M.J.  On the Similarity of Pulsating and Accelerating Turbulent Pipe Flows,  Flow, Turbulence and Combustion. – 2018. - Vol. 100, Iss. 2. - P. 417-436, doi.org/10.1007/s10494-017-9855-5;

3. Kong R., Kim S. Characterization of Horizontal Air-water Two-Phase Flow, The 16th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-16), August 30-September 4. - 2015. P. 5559-5572, Chicago / USA ;

4. Offor U. H., Alabi S. B. An Accurate and Computationally Efficient Explicit Friction Factor Model, Advances in Chemical Engineering and Science. 2016. - Vol. 6. - P. 237-245,  http://dx.doi.org/10.4236/aces.2016.63024  ;

5. Tarek A. Ganat  and Meftah Hrairi. Gas–Liquid Two-Phase Upward Flow through a Vertical Pipe: Influence of Pressure Drop on the Measurement of Fluid Flow Rate, Energies, MDPI, Open Access Journal. – 2018. -  Vol. 11, Iss. 11. - P. 1-23, doi:10.3390/en11112937 ;

6. Brkic D.,  Praks P. Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow, Applied Sciences. – 2018. - Vol. 8, Iss. 11. – P. 2036,  doi:10.3390/app8112036 ;

7. Medina Y. C., Fonticiella O. M. C., Morales O. F.G. Design and modelation of piping systems by means of use friction factor in the transition turbulent zone, Mathematical Modelling of Engineering Problems. – 2017. - Vol. 4, Iss. 4. - P. 162-167, doi: 10.18280/mmep.040404 ;

8. Azizi N., Homayoon R., Hojjati M. R. Predicting the Colebrook-White friction factor in the pipe flow by new explicit correlations, Journal of Fluids Engineering. – 2018. - Vol. 141, No. 5, doi:10.1115/1.4041232 ;

9. Pimenta B. D., Robaina A. D., Peiter M. X., Mezzomo W., Kirchner J. H., Ben L. H. B. Performance of explicit approximations of the coefficient of head loss for pressurized conduits, Brazilian Journal of Agricultural and Environmental Engineering (Revista Brasileira de Engenharia Agrícola e Ambiental). 2018. - Vol. 22, No. 5. - P. 301-307, http://www.agriambi.com.br ;

10. Ortiz-Vidal L. E., Mureithi N., Rodriguez O. M. H. Friction Factor in Two-Phase Gas-Liquid Pipe Flow, 8-th International  Conference on Multiphase Flow ICMF-2013, May 26-31 Jeju / Korea. – 2013. https://www.researchgate.net/publication/237079232 ;

11. Lukman S., Oke I. A. Accurate Solutions of Colebrook- White’s Friction Factor Formulae,  Nigerian Journal of Technology (NIJOTECH). – 2017. - Vol. 36, No. 4. - P. 1039–1048, Nigeria,;

12. Salmasi F., Khatibi R., Ghorbani M. A. A study of friction factor formulation in pipes using artificial intelligence techniques and explicit equations, Turkish Journal of Engineering and Environmental Sciences. – 2012. - Vol. 36, No. 2. - P. 121-138, http://journals.tubitak.gov.tr/engineering/archive.htm;

13. Offor U. H., Alabi S. B. Artificial Neural Network Model for Friction Factor Prediction, Journal of Materials Science and Chemical Engineering. – 2016. - Vol. 4. - P. 77-83. http://www.scirp.org/journal/msce ;

14. Brkic D., Sojbasic C. Intelligent Flow Friction Estimation, Computational Intelligence and Neuroscience. – 2016.  doi.org/10.1155/2016/5242596 ;

15. Stotsko Z.A. Modeliuvannia tekhnolohichnykh system: navch. posib. – Lviv: Vydavnytstvo Lvivskoi politekhniky, 2013. – 188 s.

16. Dmytriv I.V. Avtomobilnyi transport. Teoriia i praktyka naukovykh doslidzhen: navch. posib. – Lviv: SPOLOM, 2019. – 316 s.

17. Sedov L. I. Metodyi podobiya i razmernosti v mehanike. – M. : Nauka, 1977. – 440 s.

18. Levi I. I. Modelirovanie gidravlicheskih yavleniy. – L. : Energiya, 1967. – S. 237.

19. Mihalev M. A. Teoriya podobiya i razmernostey : ucheb. posobie. – SPb. : Izd-vo MPbGTU, 2001. – 68 s.

20. Dmytriv V.T. Mekhaniko-tekhnolohichni osnovy system doilnykh ustanovok. Teoriia ta praktyka: monohrafiia. Lviv: SPOLOM, 2017. – 350 s.

21.  Abramovich G. N. Prikladnaya gazovaya dinamika : ucheb. rukovodstvo dlya vtuzov. – 5-e izd., pererab. i dop. v 2-h ch. – M. : Nauka. Gl. red. fiz.-mat. lit., 1991. – 304 s.