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Research Papers: Gas Turbines: Structures and Dynamics

# Thermohydrodynamic Analysis of Bump Type Gas Foil Bearings: A Model Anchored to Test Data

[+] Author and Article Information
Luis San Andrés

Turbomachinery Laboratory, Texas A&M University, College Station, TX 77843-3123lsanandres@tamu.edu

Tae Ho Kim

Energy Mechanics Research Center, Korea Institute of Science and Technology, 39-1 Hawolgok-dong, Songbuk-gu, Seoul, Korea 136-791thk@kist.re.kr

Note that a top foil underspring structure or bumps strip layer works only under compression, i.e., when the pressure on its top side is larger than that underneath. Otherwise, the bumps would either work under extension or would detach, both implausible physical conditions. Hence, the necessary condition of foil detachment to avoid a physically unrealistic subambient pressure to evolve.

Reynolds equation for the pressure field is of elliptic type, requiring of boundary conditions on the entire closure of the flow domain. On the other hand, the temperature transport equation is of parabolic type with specified boundary conditions at the inlet plane(s) where the gas flow is supplied.

Note to reader: thermal radiation conditions are not discussed for simplicity. They are accounted for, however.

This deficiency is not unusual since foil bearing technology is guarded closely by its manufacturers. Most unusual is the ability of prior analyses to predict closely the measurements without knowledge of the bearing geometry and operating conditions. See Refs. 11-12,14, for example.

The test values do not strictly represent film temperatures. In the experiments, the temperatures reproduced in Figs.  678 are recorded at the outer surface of a bump strip layer and at its junction with the top foil (6). However, the recorded temperatures are representative of the gas film, as shown later in Fig. 1.

The thermal mixing parameter $λ$ is common in oil lubricated bearings. However, the use of this parameter in gas foil bearings is novel. Since each foil bearing is essentially a custom piece of hardware, with resulting variability even in identical units, the thermal mixing parameter is largely unknown and its estimation yet to be reported.

J. Eng. Gas Turbines Power 132(4), 042504 (Jan 26, 2010) (10 pages) doi:10.1115/1.3159386 History: Received March 24, 2009; Revised March 30, 2009; Published January 26, 2010; Online January 26, 2010

## Abstract

The paper introduces a thermohydrodynamic (THD) model for prediction of gas foil bearing (GFB) performance. The model includes thermal energy transport in the gas film region and with cooling gas streams, inner or outer, as in typical rotor-GFBs systems. The analysis also accounts for material property changes and the bearing components’ expansion due to temperature increases and shaft centrifugal growth due to rotational speed. Gas inlet feed characteristics are thoroughly discussed in bearings whose top foil must detach, i.e., not allowing for subambient pressure. Thermal growths determine the actual bearing clearance needed for accurate prediction of GFB forced performance, static and dynamic. Model predictions are benchmarked against published measurements of (metal) temperatures in a GFB operating without a forced cooling gas flow. The tested foil bearing is proprietary; hence, its geometry and material properties are largely unknown. Predictions are obtained for an assumed bearing configuration, with bump-foil geometry and materials taken from prior art and best known practices. The predicted film peak temperature occurs just downstream of the maximum gas pressure. The film temperature is higher at the bearing middle plane than at the foil edges, as the test results also show. The journal speed, rather than the applied static load, influences more the increase in film temperature and with a larger thermal gradient toward the bearing sides. In addition, as in the tests conducted at a constant rotor speed and even for the lowest static load, the gas film temperature increases rapidly due to the absence of a forced cooling air that could carry away the recirculation gas flow and thermal energy drawn by the spinning rotor; predictions are in good agreement with the test data. A comparison of predicted static load parameters to those obtained from an isothermal condition shows the THD model producing a smaller journal eccentricity (larger minimum film thickness) and larger drag torque. An increase in gas temperature is tantamount to an increase in gas viscosity, hence, the noted effect in the foil bearing forced performance.

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Copyright © 2010 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic view of gas foil bearing, components, and coordinate system

Figure 2

Side view of bearing with inner cooling stream (TCi,PCi) flowing through hollow shaft and outer cooling stream (TCo,PCo) flowing through thin film region and underneath top foil. Outer cooling flow exits to ambient pressure (Pa).

Figure 3

Schematic view of thermal mixing conditions at gap between trailing edge and leading edge of top foil

Figure 4

Nomenclature for temperatures in GFB with cooling gas streams and schematic representation of heat flows

Figure 5

Shaft centrifugal growth versus rotor speed. Solid shaft and hollow shafts (thin and thick wall thicknesses). Material Inconel 718. Shaft outer diameter of 50 mm and wall thickness ts=RSo−RSi.

Figure 6

Predicted film temperature at bearing midplane and Θ∼190 deg versus static load Ws and increasing rotor speeds. Air supply and ambient temperature (To=T∞) at 274.3 K (21°C). Comparison to test data (6).

Figure 7

Predicted film temperatures at bearing midplane and side edge versus static load Ws at Θ∼190 deg and for two rotor speeds, 20 krpm and 40 krpm. Air supply and ambient temperature (To=T∞) at 274.3 K (21°C). Comparison to test data (6).

Figure 8

Predicted axial film temperature profile for three rotor speeds and a static load Ws=133 N at Θ∼190 deg. Air supply and ambient temperature (To=T∞) at 274.3 K (21°C). Comparison to test data (6).

Figure 9

Predicted film (a) pressure and (b) temperature fields in a GFB operating at a rotor speed of 20 krpm. Static load Ws=89 N. Air supply and ambient temperature (To=T∞) at 274.3 K (21°C). Thermal mixing coefficient λ=0.65.

Figure 10

Predicted film (a) pressure and (b) temperature at the bearing midplane versus angle Θ. GFB operating at 20 krpm and increasing static loads. Air supply and ambient temperature (To=T∞) at 274.3 K (21°C). Thermal mixing coefficient λ=0.65.

Figure 11

Predicted radial temperature profile in GFB with rotor speed of 20 krpm and static load Ws=89 N. Peak film temperature=71°C. Air supply and ambient temperature (TCi=To=T∞) at 274.3 K (21°C).

Figure 12

Predicted journal eccentricity and minimum film thickness versus static load from isothermal and thermohydrodynamic flow models. Rotor speed=40 krpm. Air supply and ambient temperature (To=T∞) at 274.3 K (21°C).

Figure 13

Predicted journal attitude angle and drag torque versus static load for isothermal and thermohydrodynamic flow models. Rotor speed=40 krpm. Air supply and ambient temperature (To=T∞) at 274.3 K (21°C)

## Errata

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