Numerical study on two dimensional distribution of streamwise velocity in open channel turbulent flows with secondary current effect

• Autorzy: Mohan S. , Kundu S. , Ghoshal K. , Kumar J.

Identyfikatory

DOI

10.24423/aom.3610

• Języki publikacji: EN

Abstrakty

EN

For studying mechanism of sediment transport in river flows, open channel flow is a prototype. Flow has always three components of velocity for all types of channel geometry and for a time independent uniform flow along streamwise or main flow direction, all the components of velocity are functions of lateral and vertical coordinates. The present study investigates the two dimensional distribution of streamwise (or longitudinal) velocity starting from the Reynolds averaged Navier–Stokes equation for a turbulent open channel flow which is steady and uniform along the main flow direction. Secondary flows both along the vertically upward direction and along the lateral direction are considered which are also taken as functions of lateral and vertical coordinates. Inclusion of the secondary current brings the effect of dip phenomenon in the model. The resulting second order partial differential equation is solved numerically. The model is validated for all the cross-sectional, transverse and centreline velocity distribution by comparing with existing relevant set of experimental data and also with an existing model. Comparison results show good agreement with data as well as with the previous model proving the efficiency of the model. It is found that the transverse velocity distribution depends on the formation of circular vortex in the cross-sectional plane and becomes periodic as the number of circular vortex increases for increasing aspect ratios.

Słowa kluczowe

EN

velocity distribution; open channel flow; turbulent flow; RANS equations; secondary current; finite difference method

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2021
• Tom: Vol. 73, nr 2
• Strony: 175--200
• Opis fizyczny: Bibliogr. 45 poz., rys. kolor.

Twórcy

autor

Mohan S.

• Department of Mathematics, IIT Kharagpur, Kharagpur-721302, India

autor

Kundu S.

• Department of Mathematics, NIT Jamshedpur, Jharkhand-831014, India

autor

Ghoshal K.

• Department of Mathematics, IIT Kharagpur, Kharagpur-721302, India

autor

Kumar J.

• Department of Mathematics, IIT Kharagpur, Kharagpur-721302, India

Bibliografia

• 1. T. von Karman, Mechanische A¨hnlichkeit und Turbulenz, Nachrichten von der Gesellschaft der Wissenschaften zu Go¨ttingen: Mathematisch-physische Klasse, 58–76, 1930.
• 2. L. Prandtl, Recent results of turbulence research, Technical Memorandum 720, National Advisory Committee for Aeronautics, 1932.198 S. Mohan et al.
• 3. D.E. Coles, The law of the wake in the turbulent boundary layer , Journal of Fluid Mechanics, 1, 191–226, 1956.
• 4. K.V.N. Sarma, P. Lakshminarayana, N.S.L. Rao, Velocity distribution in smooth rectangular open channels, Journal of Hydraulic Engineering, 109, 270–289, 1983.
• 5. N.L. Coleman, Velocity profiles with suspended sediment, Journal of Hydraulic Research, 19, 3, 211–229, 1981.
• 6. N.L. Coleman, Effects of suspended sediment on the open-channel velocity distribution, Water Resources Research, 22, 10, 1377–1384, 1986.
• 7. J. Guo, Turbulent velocity profile in clear water and sediment-laden flows, PhD Thesis, Colorado State University, Fort Collins, CO., 1998.
• 8. K.V.N. Sarma, B.V.R. Prasad, A.K. Sarma, Detailed study of binary law for open channels, Journal of Hydraulic Engineering, 126, 3, 210–214, 2000.
• 9. S.Q. Yang, S.K. Tan, S.Y. Lim, Velocity distribution and dip-phenomenon in smooth uniform open channel flows, Journal of Hydraulic Engineering, 130, 12, 1179–1186, 2004.
• 10. J. Guo, P.Y. Julien, Application of the modified log-wake law in open-channels, Journal of Applied Fluid Mechanics, 1, 2, 17–23, 2008.
• 11. R. Absi, An ordinary differential equation for velocity distribution and dip-phenomenon in open channel flows, Journal of Hydraulic Research, 49, 1, 82–89, 2011.
• 12. S. Kundu, K. Ghoshal, An analytical model for velocity distribution and dipphenomenon in uniform open channel flows, International Journal of Fluid Mechanics Research, 39, 5, 381–395, 2012.
• 13. S.Q. Yang, Influence of sediment and secondary currents on velocity, Water Management, 162, WM5, 299–307, 2009.
• 14. Z.Q. Wang, N.S. Cheng, Time-mean structure of secondary flows in open channel with longitudinal bedforms, Advances in Water Resources, 29, 11, 1634–1649, 2006.
• 15. M. Colombini, Turbulence-driven secondary flows and formation of sand ridges , Journal of Fluid Mechanics, 254, 701–719, 1993.
• 16. S.Q. Yang, S.K. Tan, X.K. Wang, Mechanism of secondary currents in open channel flows, Journal of Geophysical Research, 117, F04014, 2012.
• 17. D. Daniel Duda, J. Bem, V. Yanovych, P. Pavlicek, V. Uruba, Secondary flow of second kind in a short channel observed by piv , European Journal of Mechanics B Fluids, 79, 444–453, 2020.
• 18. I. Nezu, A. Tominaga, H. Nakagawa, Field measurements of secondary currents in straight rivers, Journal of Hydraulic Engineering, 119, 5, 598–614, 1993.
• 19. J.B. Francis, On the cause of the maximum velocity of water flowing in open channels being below the surface, Transactions of the American Society of Civil Engineers, 7, 1, 109–113, 1878.
• 20. F.P. Stearns, On the current-meter: together with a reason why the maximum velocity of water flowing in open channel is below the surface, Transactions of the American Society of Civil Engineers, 12, 1, 301–338, 1883.
• 21. C. Murphy, Accuracy of stream measurements, Water Supply and Irrigation Paper, 95, 111–112, 1904.
• 22. C.H. Keulegan, Laws of turbulence flow in open channels, Journal of Research of the National Bureau of Standards, 21, 707–741, 1938.
• 23. I. Nezu, H. Nakagawa, Cellular secondary currents in straight conduit, Journal of Hydraulic Engineering, 110, 173–193, 1984.
• 24. J. Guo, P.Y. Julien, Turbulent velocity profiles in sediment-laden flows, Journal of Hydraulic Research, 39, 1, 11–23, 2001.
• 25. J. Guo, Modified log-wake-law for smooth rectangular open channel flow, Journal of Hydraulic Research, 52, 1, 121–128, 2013.
• 26. J. Guo, P.Y. Julien, Modified log-wake law in smooth rectangular open-channels, [in:] Advances in Hydraulics and Water engineering, I & II, World Scientific, 2002, 87–99.
• 27. J.Y. Lu, Study on flow velocity distribution of in the yangtze yangtze river riverflow, Journal of Yangtze River Scientific Research Institute, 1, 40–49, 1990.
• 28. H. Bonakdari, F. Larrarte, L. Lassabatere, C. Joannis, Turbulent velocity profile in fully-developed open channel flows, Environmental Fluid Mechanics, 8, 1–17, 2008.
• 29. D.A. Lyn, A similarity approach to open-channel sediment laden flows, Journal of Fluid Mechanics, 193, 1, 1–26, 1988.
• 30. M. Muste, V.C. Patel, Velocity profiles for particles and liquid in open-channel flow with suspended sediment, Journal of Hydraulic Engineering, 123, 9, 742–751, 1997.
• 31. A. Tominaga, I. Nezu, K. Ezaki, H. Nakagawa, Three-dimensional turbulent structure in straight open channel flows, Journal of Hydraulic Research, 27, 1, 149–173, 1989.
• 32. J. Lu, Y. Zhou, Y. Zhu, J. Xia, L. Wei, Improved formulae of velocity distributions along the vertical and transverse directions in natural rivers with the sidewall effect, Environmental Fluid Mechanics, 18, 11, 2018.
• 33. L. Prandtl, Essentials of Fluid Mechanics, London and Glasgow, Blackie & Son Ltd, 1952.
• 34. I. Nezu, H. Nakagawa, Turbulence in Open-Channel Flows, IAHR Monograph, Balkema, Rotterdam, The Netherlands, 1993.
• 35. L. Prandtl, U¨ber die ausgebildete turbulenz , [in:] 2e Internationaler Kongress der Technischen Mechanik, Verhandlung, Fu¨essli, Zu¨rich, 1926.
• 36. Z.Q. Wang, N.S. Cheng, Secondary flows over artificial bed strip, Advances in Water Resources, 28, 5, 441–450, 2005.
• 37. W.H. Graf, Hydraulics of Sediment Transport, McGraw-Hill, New York, USA, 1971.
• 38. S.Q. Yang, Turbulent transfer mechanism in sediment-laden flow, Journal of Geophysical Research, 112, F01005, 2007.
• 39. S. Ikeda, Self forced straight channels in sandy beds, Journal of the Hydraulic Division, 107, 4, 389–406, 1981.
• 40. S. Kundu, Prediction of velocity-dip-position at the central section of open channels using entropy theory, Journal of Applied Fluid Mechanics, 10, 1, 221–229, 2017.
• 41. S. Kundu, K. Ghoshal, Effects of secondary current and stratification on suspension concentration in an open channel flow, Environmental Fluid Mechanics, 14, 2014.200 S. Mohan et al.
• 42. V.A. Vanoni, Experiments on the transportation of suspended sediment by water, PhD Thesis, California Institute of Technology, Pasadina, California, 1940.
• 43. X. Wang, N. Qian, Turbulence characteristics of sediment-laden flows, Journal of Hydraulic Engineering, 115, 6, 781–799, 1989.
• 44. I. Nezu, W. Rodi, Experimental study on secondary currents in open channel flow, [in:] 21th IAHR Congress, 115–119, IAHR, Melbourne, 1985.
• 45. S. Kundu, Theoretical study on velocity and suspension concentration in turbulent flow, PhD Thesis, Indian Institute of Technology Kharagpur, West Bengal, India, 2015.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).