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Technical Briefs

# Prediction of Axial and Circumferential Flow Conditions in a High Temperature Foil Bearing With Axial Cooling Flow

[+] Author and Article Information
Keun Ryu1

Global Commercial Diesel Product Development, BorgWarner Turbo Systems,Arden, NC 28704kryu@borgwarner.com

A static pressure gauge was not installed in the bearing housing enclosure (i.e., upstream bearing region) at the time of the measurements. This omission can be corrected in future experimentation.

The measurements show that temperature differences between the bearing sleeve and the entrance cooling stream into the bearings are nearly invariant while increasing the cooling flow rate, i.e., TbFE and TbDE are a few degrees (less than 10 °C) higher than Tent . That is, presently, the bearing temperature largely relies on the entrance cooling flow temperature. Note that the outer cooling steam temperature ≈ the bearing sleeve surface temperature (see Ref. [5] for details).

Within the range of present operating conditions (i.e., the light-weight rotor at moderate shaft rotational speed and temperature conditions in Ref. [5]), the isothermal bulk-flow model enables a reasonable approximation for the flow characteristics of axial cooling streams flowing through the thin film region and underneath the top foil. However, note that the isothermal considerations should be employed with caution, since the temperature assumption is conservative, and a thermohydrodynamic model can be used for improved results.

The circumferential flow Reynolds number at the entrance plane is similar with the circumferential flow Reynolds number at the exit plane, i.e., for all test cases, $ReCexit/ReCent≈0.96~0.99$, where $ReCent=(ρent/μ)RΩc+$.

As detailed in Ref. [14], within the inner gas film region, a forced cooling flow retards the evolution of the gas film velocity in the circumferential direction, thus delaying the threshold speed of rotordynamic instability (i.e., reducing the likeliness of subsynchronous rotor whirl motions due to hydrodynamic instability).

Ryu [5] presents details on static (push and pull) load versus foil bearing (FB) deflection measurements at room temperature to determine the ad hoc clearance, i.e., the region with very soft or low stiffness where small forces cause large displacements. The ad hoc clearance for both bearings is in remarkable agreement with that derived from measured bearing dimensions.

1

Work conducted as a Graduate Research Assistant at Texas A&M University.

J. Eng. Gas Turbines Power 134(9), 094503 (Jul 25, 2012) (6 pages) doi:10.1115/1.4006841 History: Received January 10, 2012; Revised May 09, 2012; Published July 23, 2012; Online July 25, 2012

## Abstract

A successful implementation of gas foil bearings (GFBs) into high temperature turbomachinery requires adequate thermal management to maintain system reliability and stability. The most common approach for thermal management in a GFB-rotor system is to supply pressurized air at one end of the bearing to remove hot spots in the bearings and control thermal growth of components. This technical brief presents test data for a laboratory rotor-GFB system operating hot to identify the flow characteristics of axial cooling streams flowing through the thin film region and underneath the top foil. A bulk flow model is used for description of the fluid motion and includes the Hirs’ friction factor formulation for smooth surfaces. Laminar flow prevails through the thin film gas region; while for the cooling flow between the top foil and bearing housing, a transition from laminar flow to turbulent flow occurs as the cooling flow rate increases. Large cooling flow rate and the ensuing turbulent flow conditions render limited effectiveness in controlling temperatures in a test rotor-GFB system.

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## Figures

Figure 1

Schematic view (not to scale) of axial flows induced by forced cooling flow in the test foil bearing system (only free end bearing section shown). Inset shows schematic view of GFB, noting the orientation of the top foil trailing edge with respect to the vertical (gravity) plane.

Figure 2

Shear factor of outer gap flow versus cooling flow rate. FE: free end bearing, DE: drive end bearing. Heater surface temperature Th  = 100 °C. Rotor speed of 10, 20, and 30 krpm. Inset shows schematic view of test rig and measured rotor end temperatures.

Figure 3

Dimensionless pressure (entrance pressure Pent over ambient pressure Pa ) versus cooling flow rate. FE: free end bearing, DE: drive end bearing. Heater surface temperature Th  = 100 °C. Rotor speed of 10, 20, and 30 krpm. Inset shows schematic view of test rig and FB cooling flow path.

Figure 4

Axial flow Reynolds numbers of (a) outer and (b) inner cooling streams versus cooling flow rate. FE: free end bearing, DE: drive end bearing. Heater surface temperature Th  = 100 °C. Rotor speed of 10, 20, and 30 krpm. Note different vertical scale.

Figure 5

Circumferential flow Reynolds number for thin film gas region at the bearing exit plane (P = Pa ) versus cooling flow rate. FE: free end bearing, DE: drive end bearing. Heater surface temperature Th  = 100 °C. Rotor speed of 10, 20, and 30 krpm.

Figure 6

Dimensionless circumferential mean flow velocity versus dimensionless bearing axial length within bearing inner thin film region. Free end bearing. Heater surface temperature = 100 °C. Rotor speed of 30 krpm.

Figure 7

Recorded temperature rise on free end rotor OD and free end bearing sleeve OD per unit cooling flow rate (L/min) versus axial flow Reynolds number of outer cooling stream. Heater surface temperature = 100 °C. Rotor speed of 30 krpm.

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