Investigation of the fluid flow in an isolated rotor-stator system with a peripheral opening

  • Roger DebuchyEmail author
  • Fadi Abdel Nour
  • Hassane Naji
  • Gérard Bois


This paper deals with an experimental, theoretical and numerical study of a turbulent flow with separated boundary layers between a rotor and a stator. The system is not subjected to any superimposed radial flow. The periphery of the cavity is opened to the atmosphere so that the solid body rotation for infinite discs is not always observed. Emphasis was placed on development of an asymptotic approach and a step-by-step method to compute the radial distribution of the core swirl ratio and the static pressure on the stator side. The theory also includes the radial and axial velocities in the core region. The numerical simulation has been conducted with the commercial CFD code Fluent 6.1. The k-ωSST turbulence model is used, with the assumption of 2D-axisymmetric and steady flow. CFD validations have been performed by comparison of the numerical results with the corresponding theoretical results. Numerical and experimental results are in good agreement with analytical solutions.


rotor-stator cavity analytical solution numerical simulations k-ωSST turbulence model 

dimensionless coefficient of flow rate


peripheral dimensionless coefficient of flow rate, = RoGRe 1/5


dimensionless coefficient of flow rate, = Re 1/5 qr*−13/5/(2πΩR 3)


Ekman number, = 1/ ReG 2


gap ratio, =H/R


axial gap of the cavity


core swirl ratio, = ν θr at z* = 1/2


core swirl ratio in case of solid body rotation


pre-swirl ratio, =K at r*=1


static pressure on the stator


atmospheric pressure


dimensionless static pressure on the stator, \({{ = p - p_{atm} } \mathord{\left/ {\vphantom {{ = p - p_{atm} } {\left( {\frac{1} {2}\rho \Omega ^2 R^2 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\frac{1} {2}\rho \Omega ^2 R^2 } \right)}} \)


volume flow rate


volume flow rate in the core region


volume flow rate in the rotor boundary layer


volume flow rate in the stator boundary layer


radial coordinate


dimensionless radial coordinate, =r/R


radius of the rotor


outer radius of the hub


Reynolds number, = ΩR 2


order of magnitude of the radial velocity


radial mean velocity


tangential mean velocity


axial mean velocity


dimensionless radial velocity, = ν r /U 0


dimensionless tangential velocity, ν θR


dimensionless axial velocity, = ν z /GU 0


dimensionless axial distance from the rotor, = z* − z 0*


axial distance from the wall of the rotor inside the cavity


dimensionless axial distance from the rotor, =z/H


dimensionless axial distance from the rotor


difference between the rotor and stator radii


rotor boundary layer thickness


stator boundary layer thickness


dimensionless rotor boundary layer thickness, = ΔR/νr


dimensionless stator boundary layer thickness, = ΔS/νr


angular speed of the rotor


kinematic viscosity of fluid


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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Roger Debuchy
    • 1
    • 2
    Email author
  • Fadi Abdel Nour
    • 3
  • Hassane Naji
    • 1
    • 2
  • Gérard Bois
    • 4
  1. 1.Laboratoire Génie Civil & géo-Environnement (LGCgE-EA 4515)UArtois/FSA BéthuneBéthuneFrance
  2. 2.Université Lille Nord de FranceLilleFrance
  3. 3.Department of Water EngineeringDamascus UniversityDamascusSyria
  4. 4.LML-PRES Lille Nord de FranceArts et Métiers ParisTechLilleFrance

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