Prediction of ingress through turbine rim seals-part II

Combined ingress

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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.
Original languageEnglish
Article number031013
Pages (from-to)1-7
Number of pages7
JournalJournal of Turbomachinery: Transactions of the ASME
Volume134
Issue number3
Early online date15 Jul 2011
DOIs
Publication statusPublished - 1 May 2012

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Seals
Turbines
Orifices
Flow rate
Pressure distribution
Engines

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@article{06199aeea8f743219f390fba983ce65d,
title = "Prediction of ingress through turbine rim seals-part II: Combined ingress",
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.",
author = "Owen, {J Michael} and Oliver Pountney and Gary Lock",
year = "2012",
month = "5",
day = "1",
doi = "10.1115/1.4003071",
language = "English",
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TY - JOUR

T1 - Prediction of ingress through turbine rim seals-part II

T2 - Combined ingress

AU - Owen, J Michael

AU - Pountney, Oliver

AU - Lock, Gary

PY - 2012/5/1

Y1 - 2012/5/1

N2 - 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.

AB - 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.

U2 - 10.1115/1.4003071

DO - 10.1115/1.4003071

M3 - Article

VL - 134

SP - 1

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JO - Journal of Turbomachinery: Transactions of the ASME

JF - Journal of Turbomachinery: Transactions of the ASME

SN - 0889-504X

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M1 - 031013

ER -