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Research Papers: Flows in Complex Systems

# An Analytical Modeling of the Central Core Flow in a Rotor-Stator System With Several Preswirl Conditions

[+] Author and Article Information
Roger Debuchy

IUT de Béthune, Laboratoire de Mécanique de Lille UMR 8107, PRES Université Nord de France, 1230 Rue de l’université BP 819, 62408 Béthune Cedex, Franceroger.debuchy@univ-artois.fr

Arts et Métiers ParisTech, Laboratoire de Mécanique de Lille UMR 8107, PRES Université Nord de France, 8, Boulevard Louis XIV, 59046 Lille Cedex, Francefadi_abdnour@hotmail.com

Gérard Bois

Arts et Métiers ParisTech, Laboratoire de Mécanique de Lille UMR 8107, PRES Université Nord de France, 8, Boulevard Louis XIV, 59046 Lille Cedex, Francegerard.bois@lille.ensam.fr

J. Fluids Eng 132(6), 061102 (Jun 11, 2010) (11 pages) doi:10.1115/1.4001576 History: Received December 10, 2009; Revised April 01, 2010; Published June 11, 2010; Online June 11, 2010

## Abstract

In the most part of an enclosed rotor-stator system with separated boundary layers, the flow structure is characterized by a central core rotating as a solid body with a constant core-swirl ratio. This behavior is not always observed in an isolated rotor-stator cavity, i.e., without any centripetal or centrifugal throughflow, opened to the atmosphere at the periphery: Recent works have brought to evidence an increasing level of the core-swirl ratio from the periphery to the axis, as in the case of a rotor-stator with superposed centripetal flow. The present work is based on an asymptotical approach in order to provide a better understanding of this process. Assuming that the boundary layers behave as on a single rotating disk in a stationary fluid on the rotor side, and on a stationary disk in a rotating fluid on the stator side, new analytical relations are obtained for the core-swirl ratio, the static pressure on the stator, and also the total pressure at midheight of the cavity. An experimental study is performed: Detailed measurements provide data for several values of the significant dimensionless parameters: $1.14≤10−6×Re≤1.96$, $0.05≤G≤0.10$, and $0.07≤104×Ek≤2.65$. The analysis of the results shows a good agreement between the theoretical solution and the experimental results. The analytical model can be used to provide a better understanding of the flow features. In addition, radial distributions of both core-swirl ratio, dimensionless static pressure on the stator, as well as dimensionless total pressure at midheight of the cavity, which are of interest to the designers, can be computed with an acceptable accuracy knowing the levels of the preswirl coefficient $Kp$ and the solid body rotation swirl coefficient $KB$.

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Copyright © 2010 by American Society of Mechanical Engineers
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## Figures

Figure 5

Radial distribution of the core-swirl ratio: influence of Re (or Ek) for a fixed value of G

Figure 4

Dimensionless profiles in case of unshrouded rotor system

Figure 3

Dimensionless profiles in case of unshrouded rotor system

Figure 2

Experimental setup

Figure 1

Comparison between the present analytical law and Abdel Nour solution in Ref. 16

Figure 6

Radial distribution of the core-swirl ratio: (a) influence of G and (b) influence of peripheral boundary conditions

Figure 7

K/KB versus Kp/(Kp+(KB−K)r∗a)

Figure 8

Comparison between measurements and present analytical law in Eq. 10

Figure 9

Comparison between measurements and present analytical law in Eq. 11

Figure 10

Comparison between measurements and present analytical law in Eq. 13

Figure 11

The variation of the power a coupled with (KB–Kp)

Figure 12

Comparison between measurements and present analytical law in Eq. 5

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