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Research Papers

# Prediction of Ingress Through Turbine Rim Seals—Part II: Combined Ingress

[+] Author and Article Information
J. Michael Owen

Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, U.K.ensjmo@bath.ac.uk

Oliver Pountney, Gary Lock

Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, U.K.

J. Turbomach 134(3), 031013 (Jul 15, 2011) (7 pages) doi:10.1115/1.4003071 History: Received July 14, 2010; Revised July 22, 2010; Published July 15, 2011; Online July 15, 2011

## Abstract

In Part I of this two-part paper, the orifice equations were solved for the case of externally induced (EI) ingress, where the effects of rotational speed are negligible. In Part II, the equations are solved, analytically and numerically, for combined ingress (CI), where the effects of both rotational speed and external flow are significant. For the CI case, the orifice model requires the calculation of three empirical constants, including $Cd,e,RI$ and $Cd,e,EI$, the discharge coefficients for rotationally induced (RI) and EI ingress. For the analytical solutions, the external distribution of pressure is approximated by a linear saw-tooth model; for the numerical solutions, a fit to the measured pressures is used. It is shown that although the values of the empirical constants depend on the shape of the pressure distribution used in the model, the theoretical variation of $Cw,min$ (the minimum nondimensional sealing flow rate needed to prevent ingress) depends principally on the magnitude of the peak-to-trough pressure difference in the external annulus. The solutions of the orifice model for $Cw,min$ are compared with published measurements, which were made over a wide range of rotational speeds and external flow rates. As predicted by the model, the experimental values of $Cw,min$ could be collapsed onto a single curve, which connects the asymptotes for RI and EI ingress at the respective smaller and larger external flow rates. At the smaller flow rates, the experimental data exhibit a minimum value of $Cw,min$, which undershoots the RI asymptote. Using an empirical correlation for $Cd,e$, the model is able to predict this undershoot, albeit smaller in magnitude than the one exhibited by the experimental data. The limit of the EI asymptote is quantified, and it is suggested how the orifice model could be used to extrapolate the effectiveness data obtained from an experimental rig to engine-operating conditions.

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## Figures

Figure 1

Effect of Reϕ on variation of Cw,min versus Rew for Gc=0.01 (from Ref. 4)

Figure 2

Theoretical variation of Cw,min,com/Cw,min,RI with ΓΔp1/2 (Ref. 2)

Figure 3

Distribution of f with θ based on data of Phadke and Owen (4)

Figure 4

Variation of Cw,min,RI with Reϕ for Rew=0 (line is least-squares fit and symbols are data from Ref. 4)

Figure 5

Variation of (Cw,min,CI/Cw,min,RI) with (Rew/Reϕ) according to Eq. 35. Symbols correspond to experimental data of Phadke and Owen (4).

Figure 6

Variation of Cd,e/Cd,e,0 for axial-clearance seal with Gc=0.01, Reϕ=0 data (12), – – – polynomial fit (12), —— Eq. 42

Figure 7

Effect of A on variation of Cd,e,CI/Cd,e,RI with Rew/Reϕ according to Eq. 44

Figure 8

Effect of A on variation of Cw,min,CI/Cw,min,RI with Rew/Reϕ according to Eq. 47 for saw-tooth model with variable Cd,e. Symbols correspond to data of Phadke and Owen (4): (a) full range of experimental data and (b) close-up of transition region.

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