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**A numerical investigation of the effect of curvature and Reynolds number to radial velocity in a curved porous pipe.**
*(English)*
Zbl 1444.76108

Summary: Different irrigation methods are being used in agriculture. However, due to scarcity of water, irrigation methods that use water efficiently are needed. The motivation of this study is the increasing use of porous pipes to meet this requirement. The objective of this study is to investigate the effect of curvature and Reynolds number on radial velocity profile of water across a porous wall of a curved pipe with circular cross-section, constant permeability \(k\) and porosity \(\varphi\). The momentum equations of the two dimensional flow are written in toroidal coordinates. The main flow in the pipe is only characterized by \(\delta\) and \(Re\) as the only non-dimensional groups of numbers. We also considered the flow to be fully developed, unsteady, laminar and irrotational. Darcy law is used to analyse the flow across the porous membrane. The main flow was coupled with the flow through the porous wall of the pipe. The equations were solved using finite difference method. It was observed that effect
of curvature
on the velocity across the pipe wall is negligible while an increase in Reynolds number leads to an increase in the radial velocity. The findings of this study are important in the design of porous pipes and also in their use during irrigation.

### MSC:

76S05 | Flows in porous media; filtration; seepage |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

35Q35 | PDEs in connection with fluid mechanics |

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\textit{M. D. Mathai} et al., Int. J. Adv. Appl. Math. Mech. 5, No. 1, 99--110 (2017; Zbl 1444.76108)

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### References:

[1] | S.A. Berger, L. Talbot, L.S. Yao, Flow in Curved Pipes, Annual Review of Fluid Mechanics 15 (1983) 461-512. · Zbl 0535.76010 |

[2] | A. Kalpakli Experimental study of turbulent flows through pipe bends, Technical reports from Royal Institute of Technology KTH Mechanics, SE-100 44 Stockholm, Sweden, 2012. |

[3] | W.R. Dean, Note on the motion of fluid in a curved pipe, Philosophical magazine 4(20) (1927) 208-222. |

[4] | J. Eustice, Experiments of streamline motion in curved pipes, Proceedings of the Royal Society London, Series A, 85 (1911) 119-131. |

[5] | W.R. Dean, The stream-line motion of fluid in a curved pipe, Philosophical Magazine 3(30) (1928) 673-695. |

[6] | G.I. Taylor, The criterion for turbulence in curved pipes, Proceedings of the Royal Society of London, Series A, containing papers of a mathematical and physical character, 124(794) (1929) 243-249. · JFM 55.0484.19 |

[7] | C.M. White, Streamline flow through curved pipes, Proceedings of the Royal Society of London, Series A, Containing Papers of a Mathematical and Physical Character, 123(792) (1929) 645-663. |

[8] | W.M. Collins, S.C.R. Dennis, The steady motion of a viscous fluid in a curved tube, Q.Jl Mech. Appli. Math. 28(1975). · Zbl 0324.76018 |

[9] | M.A. Masud, R. Islam, R. Sheikh, M. Alam, High curvature effects on fluid flow through curved pipe with circular cross-section, Proceedings of the 4th BSME-ASMEE International Conference on Thermal Engineering, Dhaka, Bangladesh, 2008. |

[10] | M.A. Petrakis, G.T. Karahalios , S. Kaplanis, Steady flow in a curved pipe with circular cross-section, Comparison of numerical and experimental results, The Open Fuels & Energy Science Journal 2(1) (2009) 20-26. |

[11] | M.R.H. Nobari, E. Amani, A numerical investigation of developing flow and heat transfer in a curved pipe, International journal of numerical methods for heat and fluid flow 19(7) (2009) 847-873. |

[12] | M. Hoque, N.S. Anika, M. Alam Numerical analysis of magnetohydrodynamics flow in a curved duct, International Journal of Scientific & Engineering Research 7(4) (2013) 607-617. |

[13] | R. Daneshfaraz, 3-D Investigation of velocity profile and pressure distribution in bends with different diversion angle, Journal of Civil Engineering and Science, 2(4) (2013) 234-240. |

[14] | S.M. Park, Numerical simulation of core-annular flow in a curved pipe, Master of Science thesis, Delft University of Technology, 2014. |

[15] | W. Sobieski, A. Trykozko Darcy’s and Forchheimer’s laws in practice, Part 1, The experiment, Technical Sciences 17(4) (2014) 321-335 |

[16] | O.E. Robey, Porous hose irrigation, Michigan Extension Bulletin 133 (1934) 1-22. |

[17] | A. Fasano, A. Farina, Designing irrigation pipes, Journal of Mathematics in Industry 1(1) (2011) 1-19. · Zbl 1269.76118 |

[18] | M. Labecki, J.M. Piret, B.D. Bowen Two-Dimensional analysis of fluid-flow in hollow fiber modules, Chemical Engineering Science 50(21) (1995) 3369-3384. |

[19] | M.E. Erdo‘gan, C.E. Imrak, On the axial flow of an incompressible viscous fluid in a pipe with a porous boundary, Acta Mechanica 178(314) (2005) 187-197. · Zbl 1078.76070 |

[20] | N.M. Brown, F.C. Lai, Measurement of permeability and slip coefficient of porous tubes, Journal of Fluids Engineering 128(5) (2006) 987-992. |

[21] | A. Nabovati, E.W. Llewellin, A.C.M. Sousa, A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method, Applied science and manufacturing 40(6) (2009) 860-869. |

[22] | A.C. Verkaik, Analysis of velocity profiles in curved tubes, Eindhoven University of Technology 2008. |

[23] | S. Khayamyan, T.S. Lundstrom, Interaction between the flow in two nearby pores within a porous material during transitional and turbulent flow, Journal of Applied Fluid Mechanics 2(8) (2015) 281-290. |

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