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Science China Physics, Mechanics and Astronomy

, Volume 56, Issue 4, pp 745–754

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

Article

## Abstract

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.

## Keywords

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

dimensionless coefficient of flow rate

Cqp

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

Cqr

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

Ek

Ekman number, = 1/ ReG 2

G

gap ratio, =H/R

H

axial gap of the cavity

K

core swirl ratio, = ν θr at z* = 1/2

KB

core swirl ratio in case of solid body rotation

KP

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

p

static pressure on the stator

patm

atmospheric pressure

P*

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

q

volume flow rate

qC

volume flow rate in the core region

qR

volume flow rate in the rotor boundary layer

qS

volume flow rate in the stator boundary layer

r

radial coordinate

r*

dimensionless radial coordinate, =r/R

R

radius of the rotor

RH

outer radius of the hub

Re

Reynolds number, = ΩR 2

U0

order of magnitude of the radial velocity

νr

radial mean velocity

νθ

tangential mean velocity

νz

axial mean velocity

Vr*

dimensionless radial velocity, = ν r /U 0

Vθ*

dimensionless tangential velocity, ν θR

Vz*

dimensionless axial velocity, = ν z /GU 0

y*

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

z

axial distance from the wall of the rotor inside the cavity

z*

dimensionless axial distance from the rotor, =z/H

z0*

dimensionless axial distance from the rotor

ΔR

difference between the rotor and stator radii

ΔR

rotor boundary layer thickness

ΔS

stator boundary layer thickness

ΔR*

dimensionless rotor boundary layer thickness, = ΔR/νr

ΔS*

dimensionless stator boundary layer thickness, = ΔS/νr

Ω

angular speed of the rotor

ν

kinematic viscosity of fluid

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## References

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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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