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Research Papers

# Statistical and Theoretical Models of Ingestion Through Turbine Rim Seals

[+] Author and Article Information
Kunyuan Zhou

Department of Engineering
Thermophysics,
School of Jet Propulsion,
Beihang University,
Beijing, 100191, PRC

Simon N. Wood

Department of Mathematical Sciences,
University of Bath,
Bath, BA2 7AY,UK

J. Michael Owen

Department of Mechanical Engineering,
University of Bath,
Bath, BA2 7AY,UK

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received October 7, 2011; final manuscript received October 27, 2011; published online November 1, 2012. Editor: David Wisler.

J. Turbomach 135(2), 021014 (Nov 01, 2012) (8 pages) Paper No: TURBO-11-1223; doi: 10.1115/1.4006601 History: Received October 07, 2011; Revised October 27, 2011

## Abstract

In recent papers, orifice models have been developed to calculate the amount of ingestion, or ingress, that occurs through gas-turbine rim seals. These theoretical models can be used for externally induced (EI) ingress, where the pressure differences in the main gas path are dominant, and for rotationally induced (RI) ingress, where the effects of rotation in the wheel space are dominant. Explicit “effectiveness equations,” derived from the orifice models, are used to express the flow rate of sealing air in terms of the sealing effectiveness. These equations contain two unknown terms: $Φmin$, a sealing flow parameter, and $Γc$, the ratio of the discharge coefficients for ingress and egress. The two unknowns can be determined from concentration measurements in experimental rigs. In this paper, maximum likelihood estimation is used to fit the effectiveness equations to experimental data and to determine the optimum values of $Φmin$ and $Γc$. The statistical model is validated numerically using noisy data generated from the effectiveness equations, and the simulated tests show the dangers of drawing conclusions from sparse data points. Using the statistical model, good agreement between the theoretical curves and several sets of previously published effectiveness data is achieved for both EI and RI ingress. The statistical and theoretical models have also been used to analyze previously unpublished experimental data, the results of which are included in separate papers. It is the ultimate aim of this research to apply the effectiveness data obtained at rig conditions to engine-operating conditions.

###### FIGURES IN THIS ARTICLE
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## Figures

Fig. 1

Typical rim seal for high-pressure gas-turbine stage

Fig. 2

Simplified diagram of ingress and egress

Fig. 3

Schematic of orifice model [1]

Fig. 4

Effect of Γc on variation of ɛ with Φo predicted by orifice models [2]. Solid line, EI ingress; dashed line, RI ingress.

Fig. 5

Variation of Φ¯min, Γ¯c and their standard deviations with n for m = 1000. (Error bars show standard deviations between individual estimates and ensemble averages.)

Fig. 6

Variation of ɛ with Φo for test (c) in Table 1. Black circles: simulated data; black solid line: fitted curve; red dashed line: true curve.

Fig. 7

Comparison between theoretical curves and experimental data of Graber et al. [6] for axial-clearance seal: Gc = 0.00476, Reϕ = 5.1 × 106. (Open symbols are ɛ data; closed symbols are Φi,RI/Φmin,RI data; solid lines are theoretical curves; broken line is theoretical curve of Owen [1].)

Fig. 8

Comparison between theoretical curves and experimental data of Graber et al. [6] for radial-clearance seals: Gc = 0.00238 and 0.00476, Reϕ = 2.6 × 106. (Open symbols are ɛ data; closed symbols are Φi,RI/Φmin,RI data; solid lines are theoretical curves; broken line is theoretical curve of Owen [1].)

Fig. 9

Comparison between theoretical curves and experimental data of Graber et al. [6] for radial-clearance seal: Gc = 0.00476, Reϕ = 2.6 × 106 and 5.2 × 106 (Open symbols are ɛ data; closed symbols are Φi,RI/Φmin,RI data; solid lines are theoretical curves; broken line is theoretical curve of Owen [1].)

Fig. 10

Comparison between theoretical curves and CFD data of Owen et al. [3] for axial-clearance seal: Gc = 0.01, Reϕ = 1.03 × 106. (Open symbols are ɛ data; closed symbols are Φi,RI/Φmin,RI data; solid lines are theoretical curves.)

Fig. 11

Comparison between theoretical curves and experimental data of Johnson et al. [9] for single-overlap seal: Gc = 0.01, Reϕ = 0.59 × 106. (Open symbols are ɛ data; closed symbols are Φi,RI/Φmin,RI data; solid lines are theoretical curves.)

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