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TECHNICAL PAPERS

A Unified Correlation for Slip Factor in Centrifugal Impellers

[+] Author and Article Information
Theodor W. von Backström

Department of Mechanical Engineering,  University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa

J. Turbomach 128(1), 1-10 (Aug 10, 2005) (10 pages) doi:10.1115/1.2101853 History: Received April 01, 2004; Revised August 10, 2005

A method that unifies the trusted centrifugal impeller slip factor prediction methods of Busemann, Stodola, Stanitz, Wiesner, Eck, and Csanady in one equation is presented. The simple analytical method derives the slip velocity in terms of a single relative eddy (SRE) centered on the rotor axis instead of the usual multiple (one per blade passage) eddies. It proposes blade solidity (blade length divided by spacing at rotor exit) as the prime variable determining slip. Comparisons with the analytical solution of Busemann and with tried and trusted methods and measured data show that the SRE method is a feasible replacement for the well-known Wiesner prediction method: it is not a mere curve fit, but is based on a fluid dynamic model; it is inherently sensitive to impeller inner-to-outer radius ratio and does not need a separate calculation to find a critical radius ratio; and it contains a constant, F0, that may be adjusted for specifically constructed families of impellers to improve the accuracy of the prediction. Since many of the other factors that contribute to slip are also dependent on solidity, it is recommended that radial turbomachinery investigators and designers investigate the use of solidity to correlate slip factor.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Control volumes and streamlines for nonrotating low and high radius ratio impellers

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Figure 2

Control volumes and relative-eddy-induced streamlines for low and high radius ratio impellers

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Figure 3

The Busemann slip factor for β=30 deg versus radius ratio for various blade numbers

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Figure 4

The SRE slip factor for β=30deg versus the radius ratio for various blade numbers

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Figure 5

The relationship between solidity coefficient, F, and blade angle, β, in the SRE model

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Figure 6

Variation of the SRE slip factor with solidity, c∕se, with blade angle, β, as a parameter

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Figure 7

SRE and Busemann predictions of the slip factor for Wiesner test cases, versus (c∕se)√cosβ

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Figure 8

SRE and Wiesner predictions of the slip factor for Wiesner test cases, versus (c∕se)√cosβ

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Figure 9

A comparison of A-contours by SRE and Csanady (1960)

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Figure 10

A comparison of A contours by Wiesner and Csanady (1960)

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Figure 11

A comparison of SRE (with RR=0.5) and Busemann slip factors for RR=0

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Figure 12

A comparison of Wiesner and Busemann slip factors for RR=0

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Figure 13

SRE (with RR⩾0.5) and Busemann predictions of the slip factor for Wiesner test cases, versus (c∕se)√cosβ

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Figure 14

SRE (with RR⩾0.5) and Wiesner predictions of the slip factor for Wiesner test cases, versus (c∕se)√cosβ

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Figure 15

SRE prediction and Wiesner test cases for slip factors versus (c∕se)√cosβ

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Figure 16

The slip factor comparison between the SRE prediction and Wiesner test cases

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Figure 17

The slip factor comparison between the Wiesner prediction and Wiesner test cases

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