Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-26T00:37:16.535Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of secondary currents on the flow and turbulence in partially filled pipes

Published online by Cambridge University Press:  15 March 2022

Yan Liu ,
T. Stoesser Open the ORCID record for T. Stoesser [Opens in a new window]  and
H. Fang Open the ORCID record for H. Fang [Opens in a new window]
Yan Liu*
Affiliation:
Department of Civil, Environmental and Geomatic Engineering, University College London, London, UK
T. Stoesser
Affiliation:
Department of Civil, Environmental and Geomatic Engineering, University College London, London, UK
H. Fang
Affiliation:
State Key Laboratory of Hydro science and Engineering, Tsinghua University, Beijing, PR China
*
†Email address for correspondence: ucesy10@ucl.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Large-eddy simulations of turbulent flow in partially filled pipes are conducted to investigate the effect of secondary currents on the friction factor, first- and second-order statistics and large-scale turbulent motion. The method is validated first and simulated profiles of the mean streamwise velocity, normal stresses and turbulent kinetic energy (TKE) are shown to be in good agreement with experimental data. The secondary flow is stronger in half- and three-quarters full pipes compared with quarter full or fully filled pipe flows, respectively. The origin of the secondary flow is examined by both the TKE budget and the steamwise vorticity equation, providing evidence that secondary currents originate from the corner between the free surface and the pipe walls, which is where turbulence production is larger than the sum of the remaining terms of the TKE budget. An extra source of streamwise vorticity production is found at the free surface near the centreline bisector, due to the two-component asymmetric turbulence there. The occurrence of dispersive stresses (due to secondary currents) reduces the contribution of the turbulent shear stress to the friction factor, which results in a reduction of the total friction factor of flows in half and three-quarters full pipes in comparison to a fully filled pipe flow. Furthermore, the presence of significant secondary currents inhibits very-large-scale motion (VLSM), which in turn reduces the strength and scales of near-wall streaks. Subsequently, near-wall coherent structures generated by streak instability and transient growth are significantly suppressed. The absence of VLSM and less coherent near-wall turbulence structures is supposedly responsible for the drag reduction in partially filled pipe flows relative to a fully filled pipe flow at an equivalent Reynolds number.

JFM classification

Turbulent Flows: Pipe flow Boundary Layers: Pipe flow boundary layer
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 938 , 10 May 2022 , A16
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Albayrak, I. 2008 An experimental study of coherent structures, secondary currents and surface boils and their interrelation in open-channel flow. Tech. Rep. EPFL.Google Scholar
Banerjee, S., Krahl, R., Durst, F. & Zenger, C. 2007 Presentation of anisotropy properties of turbulence, invariants versus eigenvalue approaches. J. Turbul. 8, N32.CrossRefGoogle Scholar
Berthelsen, P.A. & Ytrehus, T. 2007 Stratified smooth two-phase flow using the immersed interface method. Comput. Fluids 36 (7), 1273–1289.CrossRefGoogle Scholar
Birvalski, M., Tummers, M.J., Delfos, R. & Henkes, R.A.W.M. 2014 PIV measurements of waves and turbulence in stratified horizontal two-phase pipe flow. Intl J. Multiphase flow 62, 161–173.CrossRefGoogle Scholar
Blanckaert, K. & De Vriend, H.J. 2004 Secondary flow in sharp open-channel bends. J. Fluid Mech. 498, 353–380.CrossRefGoogle Scholar
Blanckaert, K., Duarte, A. & Schleiss, A.J. 2010 Influence of shallowness, bank inclination and bank roughness on the variability of flow patterns and boundary shear stress due to secondary currents in straight open-channels. Adv. Water Resour. 33 (9), 1062–1074.CrossRefGoogle Scholar
Bomminayuni, S. & Stoesser, T. 2011 Turbulence statistics in an open-channel flow over a rough bed. J. Hydraul. Engng 137 (11), 1347–1358.CrossRefGoogle Scholar
Bradshaw, P. 1987 Turbulent secondary flows. Annu. Rev. Fluid Mech. 19, 53–74.CrossRefGoogle Scholar
Broglia, R., Pascarelli, A. & Piomelli, U. 2003 Large-eddy simulations of ducts with a free surface. J. Fluid Mech. 484, 223–253.CrossRefGoogle Scholar
Brosda, J. & Manhart, M. 2022 Numerical investigation of semifilled-pipe flow. J. Fluid Mech. 932, A25.CrossRefGoogle Scholar
Cameron, S.M., Nikora, V.I. & Stewart, M.T. 2017 Very-large-scale motions in rough-bed open-channel flow. J. Fluid Mech. 814, 416–429.CrossRefGoogle Scholar
Cevheri, M. & Stoesser, T. 2018 Large-eddy simulation of a jet in crossflow using local mesh refinement. Prog. Comput. Fluid Dyn. 18 (3), 137–149.CrossRefGoogle Scholar
Clark, S.P. & Kehler, N. 2011 Turbulent flow characteristics in circular corrugated culverts at mild slopes. J. Hydraul. Res. 49 (5), 676–684.CrossRefGoogle Scholar
Dai, Y.-J. & Xu, C.-X. 2019 Wall pressure and secondary-flow origination in a square duct. Phys. Fluids 31 (8), 085104.Google Scholar
Duan, J., Gong, J., Yao, H., Deng, T. & Zhou, J. 2014 Numerical modeling for stratified gas–liquid flow and heat transfer in pipeline. Appl. Energy 115, 83–94.CrossRefGoogle Scholar
Ead, S.A., Rajaratnam, N., Katopodis, C. & Ade, F. 2000 Turbulent open-channel flow in circular corrugated culverts. J. Hydraul. Engng 126 (10), 750–757.CrossRefGoogle Scholar
El Khoury, G.K., Schlatter, P., Noorani, A., Fischer, P.F., Brethouwer, G. & Johansson, A.V. 2013 Direct numerical simulation of turbulent pipe flow at moderately high Reynolds numbers. Flow Turbul. Combust. 91 (3), 475–495.CrossRefGoogle Scholar
Emory, M. & Iaccarino, G. 2014 Visualizing turbulence anisotropy in the spatial domain with componentality contours. In Center for Turbulence Research Annual Research Briefs, CTR Stanford University, Stanford, USA, pp. 123–138.Google Scholar
Enfinger, K. & Kimbrough, H. 2004 Scattergraph principles and practice a comparison of various applications of the manning equation. In Pipeline Division Specialty Congress 2004 August 1–4, San Diego, California, United States, pp. 1–13.Google Scholar
Enfinger, K.L. & Schutzbach, J.S. 2005 Scattergraph principles and practice: camp's varying roughness coefficient applied to regressive methods. In Pipelines 2005: Optimizing Pipeline Design, Operations, and Maintenance in Today's Economy, pp. 72–83.Google Scholar
Fedkiw, S.O.R. & Osher, S. 2002 Level set methods and dynamic implicit surfaces. Surfaces 44, 77.Google Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73–L76.CrossRefGoogle Scholar
Fullard, L.A. & Wake, G.C. 2015 An analytical series solution to the steady laminar flow of a newtonian fluid in a partially filled pipe, including the velocity distribution and the dip phenomenon. IMA J. Appl. Maths 80 (6), 1890–1901.Google Scholar
Guala, M., Hommema, S.E. & Adrian, R.J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Guo, J. & Meroney, R.N. 2013 Theoretical solution for laminar flow in partially-filled pipes. J. Hydraul. Res. 51 (4), 408–416.CrossRefGoogle Scholar
Hinze, J.O. 1967 Secondary currents in wall turbulence. Phys. Fluids 10 (9), S122–S125.CrossRefGoogle Scholar
Hsu, T.Y., Grega, L.M., Leighton, R.I. & Wei, T. 2000 Turbulent kinetic energy transport in a corner formed by a solid wall and a free surface. J. Fluid Mech. 410, 343–366.CrossRefGoogle Scholar
Hunt, J.C.R., Wray, A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-S88, pp. 193–208.Google Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Ikeda, S. & McEwan, I.K. 2009 Flow and Sediment Transport in Compound Channels: The Experience of Japanese and UK Research. CRC Press.Google Scholar
Jiménez, J. 2013 Near-wall turbulence. Phys. Fluids 25 (10), 101302.CrossRefGoogle Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.CrossRefGoogle Scholar
Kara, M.C., Stoesser, T. & McSherry, R. 2015 a Calculation of fluid–structure interaction: methods, refinements, applications. Proc. Inst. Civ. Engrs 168 (2), 59–78.Google Scholar
Kara, S., Kara, M.C., Stoesser, T. & Sturm, T.W. 2015 b Free-surface versus rigid-lid LES computations for bridge-abutment flow. J. Hydraul. Engng 141 (9), 04015019.CrossRefGoogle Scholar
Kara, S., Stoesser, T. & Sturm, T.W. 2012 Turbulence statistics in compound channels with deep and shallow overbank flows. J. Hydraul. Res. 50 (5), 482–493.CrossRefGoogle Scholar
Kean, J.W., Kuhnle, R.A., Smith, J.D., Alonso, C.V. & Langendoen, E.J. 2009 Test of a method to calculate near-bank velocity and boundary shear stress. J. Hydraul. Engng 135 (7), 588–601.CrossRefGoogle Scholar
Kim, K.C. & Adrian, R.J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Knight, D.W. & Sterling, M. 2000 Boundary shear in circular pipes running partially full. J. Hydraul. Engng 126 (4), 263–275.CrossRefGoogle Scholar
Lee, J.H., Sung, H.J. & Adrian, R.J. 2019 Space–time formation of very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 881, 1010–1047.CrossRefGoogle Scholar
Liu, Y., Fang, H., Huang, L. & He, G. 2019 Numerical simulation of the production of three-dimensional sediment dunes. Phys. Fluids 31 (9), 096603.Google Scholar
Liu, Y., Stoesser, T., Fang, H., Papanicolaou, A. & Tsakiris, A.G. 2017 Turbulent flow over an array of boulders placed on a rough, permeable bed. Comput. Fluids 158, 120–132.CrossRefGoogle Scholar
McSherry, R., Chua, K., Stoesser, T. & Mulahasan, S. 2018 Free surface flow over square bars at intermediate relative submergence. J. Hydraul. Res. 56 (6), 825–843.CrossRefGoogle Scholar
McSherry, R.J., Chua, K.V. & Stoesser, T. 2017 Large eddy simulation of free-surface flows. J. Hydrodyn. B 29 (1), 1–12.CrossRefGoogle Scholar
Modesti, D., Pirozzoli, S., Orlandi, P. & Grasso, F. 2018 On the role of secondary motions in turbulent square duct flow. J. Fluid Mech. 847, R1.CrossRefGoogle Scholar
Nezu, I. 1985 Experimental study on secondary currents in open channel flows. In Proc. of 21st IAHR Congress, vol. 2, pp. 115–119.Google Scholar
Nezu, I. 2005 Open-channel flow turbulence and its research prospect in the 21st century. J. Hydraul. Engng 131 (4), 229–246.CrossRefGoogle Scholar
Nezu, I. & Nakagawa, H. 1993 Turbulence in Open-Channel Flows, IAHR Monograph Series, pp. 1–281. AA Balkema.Google Scholar
Ng, H.C.-H., Collignon, E., Poole, R.J. & Dennis, D.J.C. 2021 Energetic motions in turbulent partially filled pipe flow. Phys. Fluids 33 (2), 025101.CrossRefGoogle Scholar
Ng, H.C.-H., Cregan, H.L.F., Dodds, J.M., Poole, R.J. & Dennis, D.J.C. 2018 Partially filled pipes: experiments in laminar and turbulent flow. J. Fluid Mech. 848, 467–507.CrossRefGoogle Scholar
Ng, T.S., Lawrence, C.J. & Hewitt, G.F. 2001 Gravity-driven laminar flow in a partially-filled pipe. Chem. Engng Res. Des. 79 (4), 499–511.CrossRefGoogle Scholar
Nicoud, F. & Ducros, F. 1999 Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62 (3), 183–200.CrossRefGoogle Scholar
Nikora, V. 2009 Friction factor for rough-bed flows: interplay of fluid stresses, secondary currents, nonuniformity, and unsteadiness. In Proceedings of the 33rd IAHR Congress: water engineering for a sustainable environment, 9–14 August 2009. Vancouver, British Columbia, Canada.Google Scholar
Nikora, V. & Roy, A.G. 2012 Secondary flows in rivers: theoretical framework, recent advances, and current challenges. In Gravel-Bed Rivers: Processes, Tools, Environments, chap. 1, pp. 1–22. Wiley.CrossRefGoogle Scholar
Nikora, V., Stoesser, T., Cameron, S.M., Stewart, M., Papadopoulos, K., Ouro, P., McSherry, R., Zampiron, A., Marusic, I. & Falconer, R.A. 2019 Friction factor decomposition for rough-wall flows: theoretical background and application to open-channel flows. J. Fluid Mech. 872, 626–664.CrossRefGoogle Scholar
Osher, S. & Sethian, J.A. 1988 Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1), 12–49.CrossRefGoogle Scholar
Ouro, P., Fraga, B., Lopez-Novoa, U. & Thorsten, S. 2019 Scalability of an Eulerian-lagrangian large-eddy simulation solver with hybrid MPI/OpenMP parallelisation. Comput. Fluids 179, 123–136.CrossRefGoogle Scholar
Ouro, P. & Thorsten, S. 2018 Effect of blade cambering on dynamic stall in view of designing vertical axis turbines. J. Fluids Engng 140 (6), 061104.CrossRefGoogle Scholar
Ouro, P. & Thorsten, S. 2019 Impact of environmental turbulence on the performance and loadings of a tidal stream turbine. Flow Turbul. Combust. 102 (3), 613–639.CrossRefGoogle Scholar
Pinelli, A., Uhlmann, M., Sekimoto, A. & Kawahara, G. 2010 Reynolds number dependence of mean flow structure in square duct turbulence. J. Fluid Mech. 644, 107–122.CrossRefGoogle Scholar
Pirozzoli, S., Modesti, D., Orlandi, P. & Grasso, F. 2018 Turbulence and secondary motions in square duct flow. J. Fluid Mech. 840, 631–655.CrossRefGoogle Scholar
Pirozzoli, S., Romero, J., Fatica, M., Verzicco, R. & Orlandi, P. 2021 One-point statistics for turbulent pipe flow up to. J. Fluid Mech. 926, A28.CrossRefGoogle Scholar
Prandtl, L. 1926 Ueber die ausgebildete Turbulenz. In Proceedings 2nd International Congress Applied Mechanics, Zurich, Switzerland 12–17 September 1926, pp 62–75.Google Scholar
Sethian, J.A. & Smereka, P. 2003 Level set methods for fluid interfaces. Annu. Rev. Fluid Mech. 35 (1), 341–372.CrossRefGoogle Scholar
Sterling, M. & Knight, D.W. 2000 Resistance and boundary shear in circular conduits with flat beds running part full. In Proceedings of the Institution of Civil Engineers-Water and Maritime Engineering, vol. 142, pp. 229–240. Thomas Telford.CrossRefGoogle Scholar
Stoesser, T., McSherry, R. & Fraga, B. 2015 Secondary currents and turbulence over a non-uniformly roughened open-channel bed. Water 7 (9), 4896–4913.CrossRefGoogle Scholar
Sussman, M., Smereka, P. & Osher, S. 1994 A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114 (1), 146–159.CrossRefGoogle Scholar
Swaffield, J.A. & Bridge, S. 1983 Applicability of the colebrook-white formula to represent frictional losses in partially filled unsteady pipeflow. J. Res. Natl Bur. Stand. 88 (6) 389–393.CrossRefGoogle ScholarPubMed
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209 (2), 448–476.CrossRefGoogle Scholar
Uhlmann, M., Pinelli, A., Kawahara, G. & Sekimoto, A. 2007 Marginally turbulent flow in a square duct. J. Fluid Mech. 588, 153–162.CrossRefGoogle Scholar
Vollestad, P., Angheluta, L. & Jensen, A. 2020 Experimental study of secondary flows above rough and flat interfaces in horizontal gas-liquid pipe flow. Intl J. Multiphase Flow 125, 103235.CrossRefGoogle Scholar
Vui Chua, K., Fraga, B., Stoesser, T., Ho Hong, S. & Sturm, T. 2019 Effect of bridge abutment length on turbulence structure and flow through the opening. J. Hydraul. Engng 145 (6), 04019024.CrossRefGoogle Scholar
Wang, Z.-Q. & Cheng, N.-S. 2005 Secondary flows over artificial bed strips. Adv. Water Resour. 28 (5), 441–450.CrossRefGoogle Scholar
Wu, X., Baltzer, J.R. & Adrian, R.J. 2012 Direct numerical simulaion of a 30R long turbulent pipe flow at $R^+= 685$: large-and very large-scale motions. J. Fluid Mech. 698, 235–281.CrossRefGoogle Scholar
Yao, J., Chen, X. & Hussain, F. 2018 Drag control in wall-bounded turbulent flows via spanwise opposed wall-jet forcing. J. Fluid Mech. 852, 678–709.CrossRefGoogle Scholar
Zampiron, A., Cameron, S. & Nikora, V. 2020 Secondary currents and very-large-scale motions in open-channel flow over streamwise ridges. J. Fluid Mech. 887, A17.CrossRefGoogle Scholar
Zhao, D.H., Shen, H.W., Lai, J.S. & Tabios, G.Q.III 1996 Approximate Riemann solvers in FVM for 2D hydraulic shock wave modeling. J. Hydraul. Engng 122 (12), 692–702.CrossRefGoogle Scholar