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Research Papers: Gas Turbines: Structures and Dynamics

Thermal Management and Rotordynamic Performance of a Hot Rotor-Gas Foil Bearings System—Part II: Predictions Versus Test Data

[+] Author and Article Information
Luis San Andrés, Keun Ryu

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843

Tae Ho Kim1

Energy Mechanics Research Center, Korea Institute of Science and Technology, 39-1 Hawolgok-dong, Songbuk-gu, Seoul136-791, Korea

1

Work conducted as a Post-Doctoral Research Associate at Texas A&M University.

J. Eng. Gas Turbines Power 133(6), 062502 (Feb 17, 2011) (8 pages) doi:10.1115/1.4001827 History: Received April 09, 2010; Revised April 15, 2010; Published February 17, 2011; Online February 17, 2011

Implementation of gas foil bearings (GFBs) in microgas turbines relies on physics based computational models anchored to test data. This two-part paper presents test data and analytical results for a test rotor and GFB system operating hot. A companion paper (Part I) describes a test rotor-GFB system operating hot to 157°C rotor OD temperature, presents measurements of rotor dynamic response and temperatures in the bearings and rotor, and includes a cooling gas stream condition to manage the system temperatures. The second part briefs on a thermoelastohydrodynamic (TEHD) model for GFBs performance and presents predictions of the thermal energy transport and forced response, static and dynamic, in the tested gas foil bearing system. The model considers the heat flow from the rotor into the bearing cartridges and also the thermal expansion of the shaft and bearing cartridge and shaft centrifugal growth due to rotation. Predictions show that bearings’ ID temperatures increase linearly with rotor speed and shaft temperature. Large cooling flow rates, in excess of 100 l/min, reduce significantly the temperatures in the bearings and rotor. Predictions, agreeing well with recorded temperatures given in Part I, also reproduce the radial gradient of temperature between the hot shaft and the bearings ID, largest (37°C/mm) for the strongest cooling stream (150 l/min). The shaft thermal growth, more significant as the temperature grows, reduces the bearings operating clearances and also the minimum film thickness, in particular, at the highest rotor speed (30 krpm). A rotor finite element structural model and GFB force coefficients from the TEHD model are used to predict the test system critical speeds and damping ratios for operation at increasing shaft temperatures. In general, predictions of the rotor imbalance show good agreement with shaft motion measurements acquired during rotor speed coastdown tests. As the shaft temperature increases, the rotor peak motion amplitudes decrease and the system rigid-mode critical speed increases. The computational tool, benchmarked by the measurements, furthers the application of GFBs in high temperature oil-free rotating machinery.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

Nomenclature for temperatures in a foil bearing operating with a hot rotor and an outer cooling gas stream. Schematic representation of heat flows shown.

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Figure 3

Measured and predicted temperatures rise (TDE−Tamb) at the OD of drive end bearing versus rotor speed. Operation without and with a cooling stream at ∼50 l/min. Ambient and cooling stream temperatures, Tamb=TCo=21°C. Heater off (cold shaft). Inset shows schematic view of heat flows.

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Figure 4

Predicted temperature rise along radial direction in foil bearing and rotor. Peak and axially averaged (mean) temperatures shown. Operation without and with a cooling stream at 50 l/min. Ambient and cooling stream temperature Tamb=TCo=21°C. Heater off (cold shaft). Rotor speed=30 krpm. Static load ∼6.5 N.

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Figure 5

Drive end GFB: predicted gas film pressure and temperature fields. No forced cooling stream. Ambient temperature Tamb=21°C. Heater off (cold shaft). Rotor speed=30 krpm. Static load ∼6.5 N: journal eccentricity=7 μm and attitude angle=59 deg, minimum film thickness=27 μm.

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Figure 6

Measured and predicted temperature rise at drive end FB and free end FB versus heated shaft temperature rise. No forced cooling flow. Ambient temperature Tamb=21°C. Rotor speed=30 krpm. Test condition 2 (1). Static loads ∼6.5 N and ∼3.6 N for DE and FE GFBs, respectively.

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Figure 7

Drive end GFB: predicted gas film pressure and temperature fields. Heated shaft OD at 100°C and ambient temperature Tamb=21°C. No forced cooling stream. Rotor speed=30 krpm. Static load ∼6.5 N: journal eccentricity=4.5 μm and attitude angle=67°, minimum film thickness=28 μm.

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Figure 8

Measured temperature rise at drive end FB cartridge versus (heated) shaft temperature rise. Effect of cooling flow rate, 0–150 l/min. TCo∼21°C. Cooling stream and ambient temperatures TCo=Tamb=21°C. Rotor speed=30 krpm. Static load ∼6.5 N. Test conditions 2–5 (1).

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Figure 9

Predicted temperature rise along radial direction in foil bearing and rotor. Peak and axially averaged (mean) temperatures shown. Operation with heated rotor and forced cooling flow rates to 150 l/min. Cooling stream and ambient temperatures TCo=Tamb=21°C. Rotor speed=30 krpm. Static load ∼6.5 N. Test conditions 2–5 (1).

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Figure 10

Drive end GFB: predicted gas film pressure and temperature fields. Forced cooling stream at 150 l/min and TCo=21°C cooling Heated shaft OD at 64°C. Ambient temperature Tamb=32°C. Rotor speed=30 krpm. Static load ∼6.5 N: journal eccentricity=5.5 μm and attitude angle=62 deg, minimum film thickness=27 μm.

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Figure 11

Predicted temperature along radial direction in foil bearing and hollow rotor. Peak and circumferentially averaged temperatures shown. Operation without cooling flow and cartridge heater reference temperature Ths=200°C and 360°C. Ambient temperature Tamb=21°C. Rotor speed=30 krpm. Static load ∼6.5 N.

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Figure 12

Drive end GFB: predicted journal eccentricity and attitude angle versus rotor speed. Operation with cold shaft (TSo=Tamb=21°C) and with shaft heated at TSo=67°C and 110°C (cartridge heater reference temperatures Ths=200°C and 360°C). Static load 6.5 N. No forced cooling flow.

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Figure 13

Drive end GFB: predicted minimum film thickness and drag torque versus rotor speed. Operation with cold shaft (TSo=Tamb=21°C) and with shaft heated at TSo=67°C and 110°C (cartridge heater reference temperatures Ths=200°C and 360°C). Static load 6.5 N. No forced cooling flow.

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Figure 14

Drive end GFB: predicted gas film peak temperature rise and shaft thermal growth versus rotor speed. Operation with cold shaft (TSo=Tamb=21°C) and with shaft heated at TSo=67°C and 110°C (cartridge heater reference temperatures Ths=200°C and 360°C). Static load 6.5 N. No forced cooling flow.

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Figure 15

Drive end GFB: predicted force coefficients versus rotor speed. Operation with cold shaft (TSo=Tamb=21°C) and with shaft heated at TSo=67°C and 110°C (cartridge heater reference temperatures Ths=200°C and 360°C). Static load 6.5 N. No forced cooling flow.

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Figure 16

Finite element model of test hollow rotor supported on gas foil bearings. Drive end on left shows connecting rod and flexible coupling.

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Figure 17

Predicted damped natural frequency map for rotor-GFB system. Operation at ambient condition (no heating). Forward mode shapes denoted.

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Figure 18

Predicted damping ratio (ξ) versus speed for rotor-GFB system. Operation at ambient condition (no heating).

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Figure 19

Drive end: predicted and measured amplitude of rotor synchronous response versus speed. Operation wit cold shaft (no heating) and with hot shaft with cartridge heater Ths=200 and 360°C. No forced cooling flow. Measurements from Fig. 6 in Ref. 1.

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Figure 1

Schematic side view of foil bearing with heat source warming hollow rotor and outer cooling stream (TCo,PCo) flowing through thin film region and underneath top foil. Outer cooling flow exits to ambient pressure (Pa).

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