Numerical Evaluation of Turbulent Friction on Walls in the Penstock of the Trois-Gorges Dam by the Swamee-Jain Method
Since the expression of the coefficient of friction by Colebrook-White which turns out to be an implicit equation, equations have been developed to facilitate their applicability. In this work, this equation was applied to the penstock of the Three Gorges dam in order to observe the evolution of the turbulent boundary layer and the friction along the walls. Thus, the study is being carried out using a 3D digital approach in FLUENT in order to take into account the wall effects. It appears that according to the position of the portions, we have a variation in the evolutions of the turbulent friction and of the values of the boundary layer. We also observe that the inclination of the pipe has a significant influence on this turbulent friction; similarly, one could not make a fair evaluation of the latter without specifying the choice and location of the wall.
[1] J. M. Chapallaz, H. P. Mombell, A. Renaud, J. C. Scheder & J. Graf, "Petites centrales hydrauliques : Turbines hydrauliques, Energies Renouvelables". PACER, ISBN 3-905232-54-5, N0 724.247.1f, 134 pages, (1995).
[2] C. F. Colebrook & C. M. White, "Experiments with Fluid Friction in Roughened Pipes". Proc. Roy. Soc., Series A, 161, 367, (1937).
[3] C. F. Colebrook, "Turbulent flow in pipes with particular reference to the transition region between the smooth and rough pipe laws". J Inst Civil Engineers, London, Vol. 11, pp. 133-156, (1939).
[4] P. K. Swamee, & A. K. Jain, "Explicit equations for pipe-flow problems". Journal of the Hydraulics Division. 102 (5): 657–664. (1976).
[5] B. Achour & A. Bedjaoui, "Calcul du coefficient de frottement en conduite circulaire sous pression". Larhyss Edition Capitale, ISSN 1112-3680, n0 05, pp. 197-200, (2006).
[6] C. Wang, T. Meng, H. Hu, L. Zhang, "Accuracy of the ultrasonic flow meter used in the hydroturbine intake penstock of the Three Gorges Power Station". Flow Measurement and Instrumentation, 25: 32–39. (2012), https://doi.org/10.1016/j.flowmeasinst.2011.12.003
[7] N. F. Nkontchou, T. M. Tchawe, N. M. Tientcheu, T. Djiako, B. Djeumako, D. Tcheukam-Toko, Determination of the Dynamic Field in the Penstock of the Trois-Gorges Dam by a Numerical Approach, International Journal of Energy Engineering, Vol. 11 No. 1, pp. 9-16. 2021. https://doi.org/10.5923/j.ijee.20211101.02.
[8] T. Von Karman, "The fundamentals of the statistical theory of turbulence". Journal of Aeronautical Science, 4, 131-138, (1934).
[9] D. Wilson, Turbulence modeling for CFD. DCV industries, 2nd Edition, 1998.
[10] T. M. Tchawe, B. Djeumako, C. Koueni-Toko, D. Tcheukam-Toko & A. Kuitche, "Study of Dynamic Field around a Vertical Circular Cylinder placed in an Open-Chanel Flow". International Journal of Innovative Science, Engineering & Technology, Vol. 2, pp.6. (2015).
[11] T. Tchawe, D. Tcheukam-Toko, B. Kenmeugne, T. Djiako, “Numerical study of flow in the water inlet of the penstock of a hydroelectric dam”, International Journal of Current Research, 10, (7), 71061-71066. https://doi.org/10.24941/ijcr.31203.07.2018
[12] Prandtl, "Ergebnisse Göttingen". 1932, 4, p.
[13] Boussinesq, "Théorie de l’écoulement tourbillonnant et tulmultueux des liquides". Paris, 1897.
[14] Fluent, User manual 6.3.26. (2006).
[15] W. Zhang, J. Yuan, J. Han, C. Huang and M. Li, "Impact of the Three Gorges Dam on sediment deposition and erosion in the middle Yangtze River: a case study of the Shashi Reach". Hydrol. Res. 47 (S1), 175–186. (2016)
[16] S. Haaland, "Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow". Journal Fluids Engineering, 105, 89-90, (1983). DOI: 10.1115/1.3240948
[17] T. K. Serghides, “Estimate friction factor accurately”. Chem. Eng. 91(5), 63–64, 1984.
[18] D. Brkić. “Review of explicit approximations to the Colebrook relation for flow friction”. Journal of Petroleum Science and Engineering, Elsevier, 2011, 77 (1), pp.34-48. 10.1016/j.petrol.2011.02.006.
[19] L. F. Moody, "Friction Factors for Pipe Flow", Transactions of the ASME. 66 (8): 671–684, (1944).
[20] I. Abdalla, Y. Zhiyin & C. Malcolm, “Computational analysis and flow structure of a transitional separated-reattached flow over a surface mounted obstacle and a forward-facing step.” International Journal of Computational Fluid Dynamics, Vol. 23, No. 1, 25–57, January 2009.
[1] J. M. Chapallaz, H. P. Mombell, A. Renaud, J. C. Scheder & J. Graf, "Petites centrales hydrauliques : Turbines hydrauliques, Energies Renouvelables". PACER, ISBN 3-905232-54-5, N0 724.247.1f, 134 pages, (1995).
[2] C. F. Colebrook & C. M. White, "Experiments with Fluid Friction in Roughened Pipes". Proc. Roy. Soc., Series A, 161, 367, (1937).
[3] C. F. Colebrook, "Turbulent flow in pipes with particular reference to the transition region between the smooth and rough pipe laws". J Inst Civil Engineers, London, Vol. 11, pp. 133-156, (1939).
[4] P. K. Swamee, & A. K. Jain, "Explicit equations for pipe-flow problems". Journal of the Hydraulics Division. 102 (5): 657–664. (1976).
[5] B. Achour & A. Bedjaoui, "Calcul du coefficient de frottement en conduite circulaire sous pression". Larhyss Edition Capitale, ISSN 1112-3680, n0 05, pp. 197-200, (2006).
[6] C. Wang, T. Meng, H. Hu, L. Zhang, "Accuracy of the ultrasonic flow meter used in the hydroturbine intake penstock of the Three Gorges Power Station". Flow Measurement and Instrumentation, 25: 32–39. (2012), https://doi.org/10.1016/j.flowmeasinst.2011.12.003
[7] N. F. Nkontchou, T. M. Tchawe, N. M. Tientcheu, T. Djiako, B. Djeumako, D. Tcheukam-Toko, Determination of the Dynamic Field in the Penstock of the Trois-Gorges Dam by a Numerical Approach, International Journal of Energy Engineering, Vol. 11 No. 1, pp. 9-16. 2021. https://doi.org/10.5923/j.ijee.20211101.02.
[8] T. Von Karman, "The fundamentals of the statistical theory of turbulence". Journal of Aeronautical Science, 4, 131-138, (1934).
[9] D. Wilson, Turbulence modeling for CFD. DCV industries, 2nd Edition, 1998.
[10] T. M. Tchawe, B. Djeumako, C. Koueni-Toko, D. Tcheukam-Toko & A. Kuitche, "Study of Dynamic Field around a Vertical Circular Cylinder placed in an Open-Chanel Flow". International Journal of Innovative Science, Engineering & Technology, Vol. 2, pp.6. (2015).
[11] T. Tchawe, D. Tcheukam-Toko, B. Kenmeugne, T. Djiako, “Numerical study of flow in the water inlet of the penstock of a hydroelectric dam”, International Journal of Current Research, 10, (7), 71061-71066. https://doi.org/10.24941/ijcr.31203.07.2018
[12] Prandtl, "Ergebnisse Göttingen". 1932, 4, p.
[13] Boussinesq, "Théorie de l’écoulement tourbillonnant et tulmultueux des liquides". Paris, 1897.
[14] Fluent, User manual 6.3.26. (2006).
[15] W. Zhang, J. Yuan, J. Han, C. Huang and M. Li, "Impact of the Three Gorges Dam on sediment deposition and erosion in the middle Yangtze River: a case study of the Shashi Reach". Hydrol. Res. 47 (S1), 175–186. (2016)
[16] S. Haaland, "Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow". Journal Fluids Engineering, 105, 89-90, (1983). DOI: 10.1115/1.3240948
[17] T. K. Serghides, “Estimate friction factor accurately”. Chem. Eng. 91(5), 63–64, 1984.
[18] D. Brkić. “Review of explicit approximations to the Colebrook relation for flow friction”. Journal of Petroleum Science and Engineering, Elsevier, 2011, 77 (1), pp.34-48. 10.1016/j.petrol.2011.02.006.
[19] L. F. Moody, "Friction Factors for Pipe Flow", Transactions of the ASME. 66 (8): 671–684, (1944).
[20] I. Abdalla, Y. Zhiyin & C. Malcolm, “Computational analysis and flow structure of a transitional separated-reattached flow over a surface mounted obstacle and a forward-facing step.” International Journal of Computational Fluid Dynamics, Vol. 23, No. 1, 25–57, January 2009.
@article{"International Journal of Architectural, Civil and Construction Sciences:80850", author = "T. Tchawe Moukam and N. Ngongang François and D. Thomas and K. Bienvenu and T. -Toko Dénis", title = "Numerical Evaluation of Turbulent Friction on Walls in the Penstock of the Trois-Gorges Dam by the Swamee-Jain Method", abstract = "Since the expression of the coefficient of friction by Colebrook-White which turns out to be an implicit equation, equations have been developed to facilitate their applicability. In this work, this equation was applied to the penstock of the Three Gorges dam in order to observe the evolution of the turbulent boundary layer and the friction along the walls. Thus, the study is being carried out using a 3D digital approach in FLUENT in order to take into account the wall effects. It appears that according to the position of the portions, we have a variation in the evolutions of the turbulent friction and of the values of the boundary layer. We also observe that the inclination of the pipe has a significant influence on this turbulent friction; similarly, one could not make a fair evaluation of the latter without specifying the choice and location of the wall.", keywords = "Hydroelectric dam, penstock, turbulent friction, boundary layer, CFD.", volume = "16", number = "6", pages = "169-7", }
