Voronezh, Voronezh, Russian Federation
UDK 532.542 Движение жидкостей в трубопроводах, в закрытых системах
The engineering calculation and construction of the extrusion tool in the form of cylindrical forming channels with sudden narrowing is associated with the determination of the coefficient of resistance of sudden narrowing and local pressure losses. The available theoretical and experimental data on the values of the resistance coefficient of sudden narrowing are contradictory, approximate in nature and, in some cases, do not take into account the rheological properties of the liquid. Their use to calculate local pressure losses under laminar flow conditions leads to significant errors. To eliminate the indicated problems, a mathematical statement of the problem of isothermal stationary laminar flow of non-Newtonian non-compressible fluid in an axisymmetric channel with sudden narrowing was formulated. The mathematical model of flow in spatial formulation is formalized in the form of equations for preserving momentum and mass. As a rheological model, the Carreau model is taken, taking into account the presence of finite viscosity values at marginal shear rates. The numerical solution of the problem was performed by the finite element method using the Comsol MultiphysicsTM CFD modeling package. As a result of the solution, the picture of the current of the non-Newtonian medium was restored in the form of the distribution of current lines, kinematic and dynamic flow parameters. The impact of Reynolds number on change of geometric characteristics of flow structure, kinematic and dynamic flow parameters was evaluated. Values of local resistance coefficient and pressure losses for overcoming sudden narrowing for selected flow modes are calculated. The results of computational experiments are summarized in the form of a criterion ratio for calculating the coefficient of local resistances depending on the Reynolds number.
Sudden narrowing, non-Newtonian fluid, Carreau model, Ostwald-de Ville equation, local resistance coefficient, Reynolds number, regularization, pressure loss.
1. Pelevina, L.F. Processy i apparaty / L.F. Pelevina, N.I. Pilipenko. - SPb. : Lan', 2020. - 332 s.
2. Berezovskiy, Yu.M. Formirovanie struktur pischevyh mass i formovanie gotovyh izdeliy / Yu.M. Berezovskiy, V.N. Andreev. - M. : OOO «NIPKC Voshod-A», 2017. - 162 s.
3. Termoplasticheskaya ekstruziya v processah pischevoy biotehnologii / A.Yu. Sharikov, V.V. Ivanov, M.V. Amelyakina, E.M. Serba. - M. : Pervoe ekonomicheskoe izdatel'stvo, 2022. - 116 s.
4. Volodin, V.P. Tehnologicheskaya osnastka v proizvodstve profil'nyh izdeliy : prakticheskoe rukovodstvo / V.P. Volodin. - SPb. : Professiya, 2021. - 520 s.
5. Bifurkaciya techeniya psevdoplasticheskih zhidkostey v kanale s rezkim suzheniem i rasshireniem / S.A. Patlazhan, D.E. Roschin, I.V. Kravchenko, A.A. Berlin // Himicheskaya fizika. - 2019. - T. 38, № 9. - S. 71-77.
6. The Origin of Extensional Flow in a Channel with Sudden Contraction and Expansion / I.V. Kravchenko, S.A. Patlazhan, R. Muller, Y.G. Sultanov // Journal of Physics: Conference Series. -2016. - Vol. 774(1). - R. 012026. - DOI:https://doi.org/10.1088/1742-6596/774/1/012026.
7. Inzhenernaya reologiya. Fiziko-mehanicheskie svoystva i metody obrabotki pischevogo syr'ya : ucheb. posobie dlya vuzov / Yu.M. Berezovskiy, S.A. Bredihin, V.N. Andreev, A.N. Marteha ; pod redakciey V.N. Andreeva. - SPb. : Lan'. 2021 - 192 s.
8. Mel'nikova, V.G. Testirovanie vozmozhnostey razlichnyh metodov rascheta dlya modelirovaniya vnutrennih techeniy zhidkosti / V.G. Mel'nikova // Trudy ISP RAN. - 2018. - T. 30, Vyp. 6. - S. 315-328.
9. Minimal'nyy bazis zadach dlya validacii metodov chislennogo modelirovaniya turbulentnyh techeniy vyazkoy neszhimaemoy zhidkosti / A.S. Kozelkov, Yu.N. Deryugin, Yu.A. Cibereva [i dr.] // Trudy NGTU im. R.E. Alekseeva. - 2014. - № 4(104). - S. 21-69.
10. Borzenko E.I. Chislennoe issledovanie harakteristik techeniya nen'yutonovskoy zhidkosti v trube s vnezapnym suzheniem / E.I. Borzenko, K.E. Ryl'ceva, G.R. Shrager // Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika. - 2019. - № 58. - S. 56-70. - DOI:https://doi.org/10.17223/19988621/58/5.
11. Ryl'ceva, K.E. Neizotermicheskie techeniya reologicheski slozhnyh zhidkostey v kanalah peremennogo secheniya : special'nost' 01.02.05 - Mehanika zhidkosti, gaza i plazmy : dis. … kand. fiz.-mat. : zaschischena 25.12.2020 / Kira Evgen'evna Ryl'ceva. - Tomsk, 2020. - 103 s.
12. Raschet koefficienta mestnogo soprotivleniya dlya techeniya vyazkoy neszhimaemoy zhidkosti v trube s vnezapnym suzheniem / E.I. Borzenko, K.E. Ryl'ceva, O.Yu. Frolov, G.R. Shrager // Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika. - 2017. - № 48. - S. 36-48. - DOI:https://doi.org/10.17223/19988621/48/4.
13. Posohin, V.N. O protyazhennosti zon vliyaniya vozmuschayuschih elementov truboprovodnyh sistem / V.N. Posohin, A.M. Ziganshin, D.I. Mudarisov // Izvestiya KGASU. - 2014. - № 2 (28). - S. 121-126.
14. Nosko, S.V. Reologicheskie svoystva i gidrodinamika nestabilizirovanogo potoka nen'yutonovskih sred v rabochih kanalah formovochnogo oborudovaniya / S.V. Nosko // Tehnologicheskiy audi i rezervy proizvodstva. - 2015. - № 3/1(23). - S. 56-60.
15. Dimitrienko, Yu.I. Konechno-elementnoe modelirovanie neizotermicheskogo stacionarnogo techeniya nen'yutonovskoy zhidkosti v slozhnyh oblastyah / Yu.I. Dimitrienko, Li Shuguan // Matematicheskoe modelirovanie i chislennye metody. - 2018. - № 2. - S. 70-93.
16. Numerical investigation of inertia and shear-thinning effects in axisymmetric flows of Carreau fluids by a Galerkin least-squares method / R.R. Martins, F S. Silveira, M L. Martins-Costa, S. Frey // Latin Amer. Appl. Res. -2008. - Vol. 38. - P. 321-328.
17. Friction coefficients for Bingham and power-law fluids in abrupt contractions and expansions / S.L.D. Kfuri, E.J. Soares, R.L. Thompson, R.N. Siqueira // J. of Fluids Engineering. - 2017. - Vol. 139(2). - P. 021203.
18. Borzenko, E.I. Chislennoe issledovanie harakteristik techeniya nen'yutonovskoy zhidkosti v trube s vnezapnym suzheniem / E.I. Borzenko, K.E. Ryl'ceva, G.R. Shrager // Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika. - 2019. - № 58. - S. 56-70. - DOI:https://doi.org/10.17223/19988621/58/5.
19. Dyakova, O.A. Numerical simulation of a non-Newtonian fluid flow in the pipelines with various fittings / O.A. Dyakova, I. Ryltsev, K.E. Ryltseva // AIP Conference Proceedings. − 2019. − Vol. 2103. − P. 020005-1-020005-8.
20. Ryltseva, K.E. Effect of viscous dissipation on the flow structure and pressure losses for a viscoplastic fluid flow through a sudden pipe contraction / K.E. Ryltseva, E.I. Borzenko, G.R. Shrager // IOP Conf. Ser. Mater. Sci. Eng. − 2020. - Vol. 927. − P. 1-7.
21. Marchevskiy, I.K. Ispol'zovanie modificirovannogo metoda LS-STAG dlya rascheta ploskogo techeniya vyazkouprugoy zhidkosti v kanale s vnezapnym suzheniem 4:1 / I.K. Marchevskiy, V.V. Puzikov // Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki. - 2021. − № 3(96). - S. 46 - 63.
22. Optimizaciya tehnologicheskih processov pererabotki termoplastov s ispol'zovaniem metodov matematicheskogo modelirovaniya / A.R. Valeeva, A.G. Girfanova, A.R. Fatkullin [i dr.] // Nauchnyy potencial molodezhi i tehnicheskiy progress : sbornik materialov I mezhdunarodnoy nauchno-prakticheskoy konferencii. - SPb., 2018. − S. 129-130.
23. Matveenko, V.N. Structural Rationale of a Non-Newtonian Flow / V.N. Matveenko, E.A. Kirsanov // Moscow University Chemistry Bulletin. − 2017. − Vol. 72, № 2. - Pp. 69-91.
24. Shapovalov, V.M. On the applicability of the Ostwald-de Waele model in solving applied problems / V.M. Shapovalov // Journal of Engineering Physics and Thermophysics. - 2017. - Vol. 90, № 5. - Pp. 1213-1218.
25. Estimation of the Error in calculating the integral characteristics of the flow structured liquid-like media in a cylindrical channel / A. Khvostov, A. Zhuravlev, E. Shipilova [et al.] // 3nd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency. - 2021. - R. 73-77.
26. Loenko, D.S. Modeli regulyarizacii pri issledovanii svobodnokonvektivnogo teplomassoperenosa psevdoplastichnoy zhidkosti v zamknutoy differencial'no-obogrevaemoy polosti / D.S. Loenko, M.A. Sheremet // Vestnik Permskogo universiteta. - 2021. - № 3. - S. 13-22.
27. Flow of the Bingham-Papanastasiou Regularized Material in a Channel in the Presence of Obstacles: Correlation between Hydrodynamic Forces and Spacing of Obstacles / A. Mehmood [et al.] // Hindawi Modelling and Simulation in Engineering Volume. - 2021. - Vol. 2021. - R. 1-14.
28. Multi-Rheology Design Method of Sheeting Polymer Extrusion Dies Based on Flow Network and the Winter-Fritz Design Equation / A. Razeghiyadaki, D. Wei, A. Perveen, D.A. Zhang / Polymers. - 2021. - № 13. - P. 1924.
29. Parametricheskaya identifikaciya reologicheskoy modeli Karro s ispol'zovaniem regulyarizacii A.N. Tihonova na osnove CFD-modeli / A.A. Hvostov, G.O. Magomedov, V.I. Ryazhskih [i dr.] // Tehnika i tehnologiya pischevyh proizvodstv. - 2021. - T. 51, № 3. - S. 615-627.
30. Rauvendaal, K. Understanding Extrusion / K. Rauvendaal // Carl Hanser Verlag GmbH & Company KG, 2018. - P. 264.
31. Yablonev, A.L. Obosnovanie racional'nyh konstrukciy shnekovyh pressov frezformovochnyh mashin dlya dobychi kuskovogo torfa / A.L. Yablonev, A.M. Guseva, D.M. Scherbakova // Vestnik Tverskogo gosudarstvennogo tehnicheskogo universiteta: seriya Tehnicheskie nauki. - 2019 - № 4. - S. 63-72.
32. Torgan, A.B. Metodika raschetnoy ocenki parametrov techeniya makaronnogo testa v stupenchatyh cilindricheskih kanalah / A.B. Torgan // Vestnik Grodnenskogo gosudarstvennogo universiteta im. Yanki Kupaly. Seriya 6. Tehnika. - 2022. - T. 12, № 1. - S. 90-98.
33. Volodin, V.P. Tehnologiya proizvodstva profil'nyh izdeliy. Nepreryvnoe formovanie iz rasplava : prakticheskoe rukovodstvo / V.P. Volodin. - SPb. : COP «Professiya», 2019. - 272 s.
34. Vasenin, V.I. Issledovanie interferencii mestnyh soprotivleniy litnikovoy sistemy / V.I. Vasenin, A.V. Bogomyagkov, K.V. Sharov // Vestnik Permskogo nacional'nogo issledovatel'skogo politehnicheskogo universiteta. Mashinostroenie, materialovedenie. - 2013. - T. 15, № 1. - S. 82-87.
35. Roshchin, D. Flow bifurcation transitions of inelastic shear thinning fluids in a channel with sudden contraction and expansion / D. Roshchin, I. Kravchenko, S. Patlazhan // Journal of Physics Conference Series. - 2020. - Vol. 1556. - P. 12060.
36. Techenie polimerov v otverstiyah fil'er: teoriya, raschet, praktika /V.I. Yankov, I.O. Glot, N.M. Trufanova, N.V. Shakirov. − Moskva − Izhevsk: NIC «Regulyarnaya i haoticheskaya dinamika», Institut komp'yuternyh issledovaniy, 2010. - 264 s.
37. Pererabotka voloknoobrazuyuschih polimerov. Osnovy reologii polimerov i techenie polimerov v kanalah / V.I. Yankov, V.I. Boyarchenko, V.P. Perevadchuk [i dr.]. − Moskva − Izhevsk: NIC «Regulyarnaya i haoticheskaya dinamika», Institut komp'yuternyh issledovaniy, 2008. - 264 s.
38. Borzenko, E.I. Chislennoe issledovanie harakteristik techeniya nen'yutonovskoy zhidkosti v trube s vnezapnym suzheniem / E.I. Borzenko, K.E. Ryl'ceva, G.R. Shrager // Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika. - 2019. - № 58. - S. 56-70.
39. Grudanov, V.Ya. Vliyanie vnutrennego davleniya testa na prochnost', zhestkost' i progib kruglyh matric dlya proizvodstva makaronnyh izdeliy / V.Ya. Grudanov, A.B. Torgan, P.V. Stankevich // Pischevaya promyshlennost': nauka i tehnologii. - 2019. - T. 12, № 2 (44). - S. 31-42.
