Arabian Journal for Science and Engineering

, Volume 44, Issue 2, pp 1583–1600 | Cite as

Effect of the Converging Pipe on the Performance of a Lucid Spherical Rotor

  • Mabrouk MosbahiEmail author
  • Ahmed Ayadi
  • Ibrahim Mabrouki
  • Zied Driss
  • Tullio Tucciarelli
  • Mohamed Salah Abid
Research Article - Mechanical Engineering


Lucid spherical rotor is a cross-flow rotor developed to be installed within a pipeline. The purpose of installing this type of rotor is to collect excess energy available in gravity-fed water pipelines. In order to enhance the efficiency of the rotor which is installed in a channel, this paper aims to study the performance of Lucid spherical rotor with converging pipe. Numerical investigations were carried out to analyze the effect of the converging pipe on the performance of the rotor. Numerical simulations have been carried out using the unsteady Reynolds-averaged Navier–Stokes equations in conjunction with the realizable \(k-{\varepsilon }\) turbulence model. The validation of the numerical method with anterior published studies has been carried out. The hydrodynamic characteristics of the flow around the rotor with and without converging pipe have been analyzed and discussed. Numerical results indicated that the converging pipe increases the performance of the Lucid spherical rotor.


Hydropower Lucid spherical rotor Channel Converging pipe Performance Validation 

List of symbols


Torque coefficient, dimensionless


Power coefficient, dimensionless

\({C}_{1{\varepsilon }}\)

Constant of the \(k-{\varepsilon }\) turbulence model


Blade chord, m


Rotating zone diameter, m


Rotor diameter, m


Converging section diameter, m


Pipe section diameter, m


Blade overlap


Force components, N


Production term of turbulence, \(\hbox {kg\;m}^{-1}\;\hbox {s}^{-3}\)


Fixed domain height, m


Rotor height, m


Turbulent kinetic energy, \(\hbox {m}^{2}\;\hbox {s}^{-2}\)


Fixed domain length, m


Converging section length, m


Pipe section length, m


Rotor torque, N


Pressure, Pa


Rotor power, W


Rotor swept area, \(\hbox {m}^{2}\)


Time, s


Velocity components, \(\hbox {m\;s}^{-1}\)

\({u}_{{i}}^{{\prime }}\)

Fluctuating velocity components, \(\hbox {m\;s}^{-1}\)

\({V}_{\infty }\)

Water velocity, \(\hbox {m\;s}^{-1}\)


Fixed domain width, m


Cartesian coordinate, m


Cartesian coordinate, m


Non-dimensional parameter


Cartesian coordinate, m


Cartesian coordinate, m

\({\varepsilon }\)

Dissipation rate of the turbulent kinetic energy, \(\hbox {W\;kg}^{-1}\)

\({\mu }\)

Dynamic viscosity, Pa s

\({\mu }_\mathrm{t}\)

Turbulent viscosity, Pa s

\({\rho }\)

Density, \(\hbox {kg\;m}^{-3}\)

\({\omega }\)

Rotor revolution speed, \(\hbox {rad\;s}^{-1}\)

\({\lambda }\)

Tip speed ratio

\({\sigma }_{k}\)

Constant of the \(k-{\varepsilon }\) turbulence model

\({\sigma }_{{\varepsilon } }\)

Constant of the \(k-{\varepsilon }\) turbulence model

\({{\delta } }_{{ij}} \)

Kronecker indices


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The authors would like to thank the Laboratory of Electro-Mechanic Systems (LASEM) members for the financial assistance.


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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Laboratory of Electro-Mechanic Systems (LASEM), National School of Engineers of Sfax (ENIS)University of SfaxSfaxTunisia
  2. 2.Higher National Engineering School of Tunis (ENSIT)University of TunisTunisTunisia
  3. 3.Department of Civil, Environmental, Aerospace and Materials Engineering (DICAM)University of PalermoPalermoItaly

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