Borularda Gelişen Türbülanslı Akış ve Giriş Bölgesi Analizi

Abstract

Türbülanslı akışlar tabiatı gereği karmaşık bir yapıya sahiptirler ve gerek sayısal olarak gerekse deneysel olarak incelenmeleri zordur. Türbülanslı akışın hidrodinamik gelişmesi de oldukça karmaşıktır. Bu çalışmada eksenel ve radyal konumlara bağlı olarak boruların hidrodinamik giriş mesafesinde hız dağılımları incelenmiştir. Reynolds sayısına, eksenel ve radyal konumlara göre doğrudan hız profilini verecek bir deneysel bağlantı için literatür taranmıştır. Ayrıca radyal ve eksenel doğrultuda türbülans büyüklükleri değerlendirilerek boruların hidrodinamik giriş mesafesinde hesaplamalı akışkanlar dinamiğinin gerekliliğini vurgulanmıştır. Söz konusu bölgenin ve özelliklerinin ısı transferi açısından değerlendirilmesi yapılmıştır. Ticari HAD yazılımı ile eksenel simetrik boru giriş bölgesi boyutsuz parametrelerle incelenmiştir. Hesaplamalarda 4 farklı Reynolds sayısı kullanılmış olup bunlar 1x104, 1x105, 5x103 ve 5x104 dür. Türbülans modellemesi için standart k-ϵ türbülans modeli ve standart duvar fonksiyonları kullanılmıştır. Eksenel ve radyal profiller yardımıyla hidrodinamik giriş mesafesi, hız profilleri ve türbülans gösterge parametreleri sonuçları sunulmuştur. Elde edilen sonuçlara göre hidrodinamik giriş mesafesinde radyal doğrultuda ısıl taşınıma yol açacak radyal hız bileşeni değerleri bulunmaktadır. Hız profilleri ile türbülans büyüklüklerinin eş zamanlı gelişiminin karakteristik hız profillerine yol açtığı bulunmuştur. Ayrıca hidrodinamik giriş mesafesinde iyi bir çözünürlüğün kolayca hesaplamalı akışkanlar dinamiği ile elde edilebildiği görülmüştür.

Keywords

• Eksenel simetrik akış
• HAD
• Hidrodinamik giriş mesafesi
• k-ϵ türbülans modeli

Developing Turbulent Flow in Pipes and Analysis of Entrance Region

Abstract

Turbulent flows have complex structures due to its nature and its’ analyses are hard either by numerical or experimental means. Hydrodynamic development of turbulent flow is also complex. In this study, velocity distribution in hydrodynamic entrance length of pipes is investigated depending on axial and radial locations. Literature was surveyed for a single empirical expression that provides velocity profile directly according to Reynolds number, radial and axial locations. Requisite for computational fluid dynamics in hydrodynamic entry length of pipes is stressed by assessing turbulence magnitudes in radial and axial directions. Evaluation of the region and its properties are conducted from heat transfer perspective. An axisymmetric pipe entrance region was analyzed by means of a commercial CFD code with nondimensional parameters. Four different Reynolds numbers that are 5x103, 1x104, 5x104, 1x105 were used in calculations. k-ϵ turbulence model and standard wall functions were used for turbulence modeling. Hydrodynamic entry length, velocity profiles and turbulence indicator parameters results are presented by means of axial and radial profiles. According to the obtained results, radial velocity component values exist that would lead to radial thermal convection in hydrodynamic entrance length. It is found that simultaneous development of velocity profiles and turbulence quantities leads to characteristic velocity profiles. Also, it is seen that a good resolution in hydrodynamic entrance length can be easily achieved by computational fluid dynamics.

Keywords

• Axisymmetric flow
• CFD
• Hydrodynamic entrance length
• k-ϵ turbulence model

References

1. 1. E. Canli, 2020, Numerical solution of transient conjugated heat transfer in thick walled pipes with turbulent flow, Ph.D Thesis, The Graduate School of Natural and Applied Science of Selçuk University, Konya, Turkey.
2. 2. E. Canli, Ali Ates, S. Bilir, Comparison of turbulence models and CFD solution options for a plain pipe, EPJ Web of Conferences 180, 02013 (2018)
3. 3. E. Canli, Ali Ates, S. Bilir, Conjugate heat transfer for turbulent flow in a thick walled plain pipe, EPJ Web of Conferences 180, 02014 (2018)
4. 4. E.M. Sparrow, R. Siegel., Unsteady turbulent heat transfer in tubes, Journal of Heat Transfer Transactions of the ASME, 170-178, (1960)
5. 5. R.E. Johnk, T.J. Hanratty, Temperature profiles for turbulent flow of air in a pipe-II The thermal entrance region, Chemical Engineering Science, 17, 881-892, (1962)
6. 6. Y.K. Lin, L.C. Chow, Effects of Wall Conduction on Heat Transfer for Turbulent Flow in a Circular Tube, Journal of Heat Transfer Transactions of the ASME, 106, 597-604, (1984)
7. 7. O.E. Dwyer, H.C. Berry, Heat transfer to liquid metals flowing turbulently and longitudinally through closely spaced rod bundles Part I, Nuclear Engineering and Design, 23, 273-294, (1972)
8. 8. T. Cebeci, K.C. Chang, A general method for calculating momentum and heat transfer in laminar and turbulent duct flows, Numerical Heat Transfer, 1, 39-68, (1978)

9. 9. B.F. Ruth, H.H. Yang, An Empirical Correlation for Velocity Distribution of Turbulent Fluid Flow, A.I.Ch.E. Journal, 3(1), 117-120, (1957)
10. 10. Ateş, A., Darıcı, S., & Bilir, Ş. (2010). Unsteady conjugated heat transfer in thick walled pipes involving two-dimensional wall and axial fluid conduction with uniform heat flux boundary condition. International Journal of Heat and Mass Transfer, 53(23-24), 5058-5064.
11. 11. Darıcı, S., Bilir, Ş., & Ateş, A. (2015). Transient conjugated heat transfer for simultaneously developing laminar flow in thick walled pipes and minipipes. International Journal of Heat and Mass Transfer, 84, 1040-1048.
12. 12. Bilir, Ş., & Ateş, A. (2003). Transient conjugated heat transfer in thick walled pipes with convective boundary conditions. International journal of heat and mass transfer, 46(14), 2701-2709.
13. 13. T. Cebeci, P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer, (Springer-Verlag, 1984)
14. 14. B. Weigand, Analytical Methods for Heat Transfer and Fluid Flow Problems, (Springer, 2015)
15. 15. L.A. Salami, An investigation of turbulent developing flow at the entrance to a smooth pipe, Int. J. Heat & Fluid Flow, 7(4), 247-257, (1986)
16. 16. W.A.S. Kumara, B.M. Halvorsen, M.C. Melaaen, Computational study on non-asymptotic behavior of developing turbulent pipe flow, WIT Transactions on Engineering Sciences, 69, 39-53, (2010)
17. 17. Maddahian, R., Farhanieh, B., & Firoozabadi, B. (2011). Turbulent flow in converging nozzles, part one: boundary layer solution. Applied Mathematics and Mechanics, 32(5), 645.
18. 18. A.E. Vardy, J.M.B. Brown, Transient turbulent friction in smooth pipe flows, Journal of Sound and Vibration, 259(5), 1011–1036, (2003)
19. 19. P.W. Stoltenkamp, Dynamics of turbine flow meters, (Technische Universiteit Eindhoven, 2007)
20. 20. R.P. Singh, K.K. Nigam, P. Mishra, Developing and fully developed turbulent flow through annuli, Journal of Chemical Engineering of Japan, 13(5), 349-353, (1980)
21. 21. K.T. Trinh, Logarithmic Correlations For Turbulent Pipe Flow Of Power Law Fluids, arXiv preprint arXiv:1007.0789, (2010)
22. 22. D.M. McEligot, S.B. Smith, C.A. Bankston, Quasi-Developed Turbulent Pipe Flow with heat Transfer, Journal of Heat Transfer Transactions of the ASME, 641-650, (1970)
23. 23. M. Sakakibara, K. Endoh, Effect of conduction in wall on heat transfer with turbulent flow between parallel plates, Int. J. Heat Mass Transfer, 20, 507-516, (1977)
24. 24. Q.J. Slaiman, M.M. Abu-Khader, B.O. Hasan, Prediction of heat transfer coefficient based on eddy diffusivity concept, Chemical Engineering Research and Design Trans IChemE Part A, 85(A4), 455–464, (2007)
25. 25. H. Biglarian, H. Beyrami, Q. Dorosti A. Sattari, Analytical solution of turbulent pipe flow according to second-gradient theory, Asia-Pac. J. Chem. Eng., 10, 318–324, (2015)
26. 26. R. Martinuzzi, A. Pollard, Comparative Study of Turbulence Models in Predicting Turbulent Pipe Flow Part I: Algebraic Stress and k-ϵ Models, AIAA Journal, 27(1), (1989)
27. 27. A.R. Barbin, J.B. Jones, Turbulent Flow in the Inlet Region of a Smooth Pipe, Journal of Basic Engineering Transactions of the ASME, 29-33, (1963) 28. A. Klein, Review: Turbulent Developing Pipe Flow, Journal of Fluids Engineering Transactions of the ASME, 103, 243-249, (1981)
28. 29. J. Doherty, P.Ngan, J. Monty, M. Chong, The development of turbulent pipe flow, 16th Australasian Fluid Mechanics Conference, 2-7 December 2007, Australia
29. 30. H. Duz, Numerical Flow Analysis of The Variation of Central Axial Velocity Along The Pipe Inlet, EPSTEM, 2, 323-333, 2018
30. 31. J.W. Richman, R.S. Azad, Developing turbulent flow in smooth pipes, Appl. Sci. Res., 28, 419-441, (1973)
31. 32. S. Patankar, Numerical Heat Transfer and Fluid Flow, (CRC Press, 1980)
32. 33. B. Launder, D. Spalding, Computer Methods in Applied Mechanics and Engineering, 3(2), 269-289, (1974)
33. 34. P.J. Roache, Perspective: a method for uniform reporting of grid refinement studies, Journal of Fluids Engineering, 116(3), 405-413, 1994