Robert J. Bruckner

Glenn Research Center, Cleveland, Ohio

Windage Power Loss in Gas Foil Bearings and the 

Rotor-Stator Clearance of High Speed Generators 

Operating in High Pressure Environments

NASA/TM—2009-215826

November 2009

GT2009–60118
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Robert J. Bruckner

Glenn Research Center, Cleveland, Ohio

Windage Power Loss in Gas Foil Bearings and the 

Rotor-Stator Clearance of High Speed Generators 

Operating in High Pressure Environments

NASA/TM—2009-215826

November 2009

GT2009–60118

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

ASME Turbo Expo 2009

sponsored by ASME

Orlando, Florida, June 8–12, 2009
Acknowledgments

The work presented in this paper was funded under the NASA Fundamental Aeronautics Program, Subsonic Rotary Wing 

Propulsion Project, Fission Surface Power Program, and the former Jupiter Icy Moons Orbiter Program.

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Available electronically at http://gltrs.grc.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2009-215826 1 

Windage Power Loss in Gas Foil Bearings and the Rotor-Stator Clearance 

of High Speed Generators Operating in High Pressure Environments 

Robert J. Bruckner 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

Closed Brayton Cycle (CBC) and Closed Supercritical 

Cycle (CSC) engines are prime candidates to convert heat 

from a reactor into electric power for robotic space exploration 

and habitation. These engine concepts incorporate a 

permanent magnet starter/generator mounted on the engine 

shaft along with the requisite turbomachinery. Successful 

completion of the long-duration missions currently anticipated 

for these engines will require designs that adequately address 

all losses within the machine. The preliminary thermal 

management concept for these engine types is to use the cycle 

working fluid to provide the required cooling. In addition to 

providing cooling, the working fluid will also serve as the 

bearing lubricant. Additional requirements, due to the unique 

application of these microturbines, are zero contamination of 

the working fluid and entirely maintenance-free operation for 

many years. Losses in the gas foil bearings and within the 

rotor-stator gap of the generator become increasingly 

important as both rotational speed and mean operating 

pressure are increased. This paper presents the results of an 

experimental study, which obtained direct torque 

measurements on gas foil bearings and generator rotor-stator 

gaps. Test conditions for these measurements included 

rotational speeds up to 42,000 revolutions per minute, 

pressures up to 45 atmospheres, and test gases of nitrogen, 

helium, and carbon dioxide. These conditions provided a 

maximum test Taylor number of nearly one million. The 

results show an exponential rise in power loss as mean 

operating density is increased for both the gas foil bearing and 

generator windage. These typical “secondary” losses can 

become larger than the total system output power if 

conventional design paradigms are followed. A 

nondimensional analysis is presented to extend the 

experimental results into the CSC range for the generator 

windage. 

Introduction 

High Pressure Power Cycles 

Power generation at remote locations such as the Moon, 

Mars, or onboard deep space satellites is paramount for 

robotic space exploration, in situ scientific investigation, and 

potential human habitation. In order to accommodate future 

missions, power requirements have risen into the 100’s of 

kilowatts range. Closed Brayton Cycles (CBC) and Closed 

Supercritical Cycles (CSC) begin to look attractive to mission 

planners at these power levels (Ref. 1). In addition to these 

elevated power levels, the machinery that drives these power 

cycles will be required to operate without maintenance for 

several years. Thermo-nuclear heat sources will be required at 

such remote locations. Figure 1 shows a thermodynamic 

diagram of a high pressure gas cooled CBC. The figure also 

includes common cycles such as an Open Brayton Cycle and 

high pressure ratio turbofan engine. Figure 1 clearly 

demonstrates the unique feature that these high pressure cycles 

operate entirely above the pressure level of any current power 

cycle. Figure 2 shows a schematic of the components of such 

power cycles as well as an artistic conception of NASA’s 

previously envisioned Jupiter Icy Moon Orbiter. Past studies 

of thermo-nuclear power cycles used multiple working fluids 

that were optimized for a specific purpose. Liquid metals are 

used for their high heat capacities as heat transfer fluids in the 

reactor, gases are used in the turbines to drive the generator 

shaft, and liquid coolants are used to reject heat through the 

radiators. Although each working fluid is optimized for a 

specific purpose, the system as a whole is prone to reliability 

and maintenance limitations. A single fluid cycle is potentially 

simpler and more reliable. To maintain high efficiencies gases 

must be used in the turbines. However, high pressure must be 

utilized in a single fluid cycle to enhance heat capacity and 

reduce in fluid machinery size. Supercritical cycles offer the 

additional advantages of enabling the use of a pump instead of 

a compressor, increasing the total power output of a given 

system volume, and increasing cycle efficiency at lower peak 

cycle temperatures. The challenge involved in the design of a 

single fluid system is that the working fluid must also serve as 

the coolant in the rotor-stator gap of the generator and as the 

lubricant in the bearings that support the turbomachinery 

(Ref. 2). A sample of potential architectures of the machinery 

that would be required to make the thermodynamic cycles a 

reality are shown in Figure 3. These designs indicate that all 4 

state points are potential bearing locations. As such the 

performance of the high pressure gas bearings must be 

understood across the full range of cycle pressures and 

temperatures. There are no validated analytic methods 

available for gas bearings, which can span this property range. 

There are also no verified Taylor-Couette correlations for the 

high speeds and densities at which these machines will 

operate. Therefore an experimental approach is taken in this 

work. The working fluid, which flows through the rotor-stator 
NASA/TM—2009-215826 2 

Figure 1.—Thermodynamic diagram of CBC and CSC cycle. 

Figure 2.—(a) Schematic representation of CBC and 

CSC cycle. (b) Artists concept of the JIMO. 

Figure 3.—Proposed CBC and CSC architectures and 

potential bearing and rotor-stator gap conditions. 

gap is limited to state point 1 or 2 due to the temperature 

limitations of electric machines. However, the kinematic 

viscosity, which is the key property governing the power loss 

in this part of the machine, can vary by 3 orders of magnitude. 

Again, no validated analytic method or correlations are 

available in this region, which is the motivation for the 

experimental approach taken in herein. 

Nomenclature 

Cm Moment coefficient, nondimensional 

D Diameter of journal, mm (in.) 

D Load capacity coefficient, mN/(mm3 krpm) (lbf/(in.3

krpm)) 

d Rotor-Stator gap, m (in.) 

L Length of bearing, mm (in.) 

Mi Moment due to windage on rotor, N m (lbf ft) 

N Rotational speed, kilo-revolutions per minute (krpm) 

P Ambient pressure of bearing cavity, atm 

Ri Radius of rotor, m (in.) 

T Ambient temperature of bearing cavity, C 

Ta Taylor Number, nondimensional 

Ui Surface velocity of rotor, m/s (ft/s) 

W Load supported by foil bearing, N (lbf) 

 Kinematic viscosity m2

/s (ft2/s) 

 Absolute viscosity Pa s (psi s) 

 Density kg/m3 (lbm/ft3

) 

Subscripts 

pl Preload 

t Total 

dw Deadweight 

Gas Foil Bearings 

Blok and VanRussom (Ref. 3) initially discovered the gas 

foil bearing in 1953. Since this discovery gas foil bearing 

supported turbomachines have been developed for a variety of 

applications over the past four decades (Ref. 4). Early 

applications were characterized by ambient pressure, low 

temperature, and lightly loaded conditions in centrifuges, 

cryogenic pumps, and aircraft air cycle machines. Recent 

advances in foil bearing load capacity and high temperature 

solid lubricant coatings have broadened the scope of potential 

applications. Microturbines for distributed power generation 

are commercially available products as are industrial oil-free 

compressors and blowers. Expendable oil-free turbojet engines 

and turbochargers have been demonstrated, while 

development programs are underway to convert larger aircraft 

engines to foil bearing supported systems (Refs. 5 to 7). 

Future applications that are under consideration which are in 

the systems analysis and preliminary design phase include 

microturbines for closed Brayton cycle power generation 

systems. 
NASA/TM—2009-215826 3 

Figure 4.—Early foil bearing designs. (a) Leaf-type foil bearing. 

(b) Bump-type foil bearing. 

Foil gas bearings are compliant surface, self-acting 

hydrodynamic bearings that use ambient gas as the working 

fluid or lubricant. They do not require external pressurization 

and are typically constructed from several layers of sheet 

metal foils from which they derive their name. Figure 4 shows 

examples of early style journal bearings. The top bearing 

(Fig. 4(a)) is commonly referred to as an overlapping leaf 

design while the lower bearing (Fig. 4(b)) is a bump foil 

design. These names stem from the design of the compliant 

layer beneath the top foil. This innermost foil, top foil, serves 

as the hydrodynamic surface that traps the high pressure gas 

film between it and the rotating shaft. Foil gas bearings 

provide a means to eliminate the oil system, which can lead to 

lower system weight, and enhanced temperature capability. 

Additionally, the elimination of the oil system can lead to a 

maintenance-free machine. Under static conditions the top foil 

is preloaded against the shaft, Wpl, such that there is no static 

clearance or eccentricity between the stationary and rotating 

parts. This is a fundamental difference between the foil 

bearing and rigid hydrodynamic bearings and gives rise to 

additional parameters required to characterize these bearings. 

The static preload and dry sliding friction coefficient become 

important parameters in foil bearing characterization. 

Additionally, the design generation or load capacity 

coefficient is a third parameter that characterizes a foil journal 

bearing. Dellacorte (Ref. 8) identifies a design classification 

scheme that correlates compliant foundation complexity with 

bearing load capacity. A generation I design consists of a 

uniform stiffness foundation and is typical of early foil 

bearings. Generation II bearings vary the compliant 

foundation in one direction, for example in the axial or 

circumferential direction. Generation III bearings vary the 

Figure 5.—General operating space of a gas foil bearing. 

compliant foundation in at least two directions. DellaCorte 

goes on to quantify the load capacity of foil journal bearings 

according to Equation (1). In the steady state performance 

testing of foil bearings great care is taken to minimize all 

applied loads other than the preload and deadweight load such 

that the total load is known very accurately. The performance 

coefficient is typically 0.08, 0.19, and 0.27 mN/(mm3

 krpm) 

(0.3, 0.7, and 1.0 lbf/(in.3 krpm)) for generation I, II, and III 

bearings, respectively. 

Wt = D (L  D) (D  N) (1) 

Where, 

Wt = Wpl + Wdw + Wdynamic + Wthermal + 

For the foil bearings used in this test program, typical 

values for friction coefficient, preload and load capacity 

coefficient measured at room temperature and ambient 

pressure are 0.28, 3.7 kPa (0.54 psi), and 

0.27 mN/(mm3 krpm) (1.0 lbf/(in.3 krpm)). The friction 

coefficient is quite high, especially considering that low 

friction is desirable for this application. This high value is 

caused because only materials suitable for high temperature 

applications are used. The foil bearings use uncoated Inconel 

top foils and the shaft is coated with PS304, a high 

temperature solid lubricant (Refs. 9 to 11). Lower friction 

coefficients may be obtained for low temperature applications 

by using highly polished shaft surfaces with thin dense chrome 

plating and organic polymer coated topfoils. 

Gas foil bearings exhibit a unique operating space based on 

their characteristics. Figure 5 presents the general operating 

space of a gas foil bearing in terms of rotational speed (DN) 

and specific load. This plane is initially subdivided by the load 

capacity coefficient, which is a ray originating from the origin 

of the graph. The region above and to the left of this ray 

represents operation of a bearing beyond its load capacity in a 

mode of dry sliding and rubbing. Hydrodynamic operation of 

a gas foil bearing in this region is not possible. The first region 

encountered below the load capacity ray is a region of mixed 

lubrication. In this region the specific power loss is quite high 

and catastrophic failures occur quickly and without warning. 

For these reasons it is not recommended that foil bearings 
NASA/TM—2009-215826 4 

operate in a steady-state mode while in this region. The 

remaining two regions are the minimum power loss region and 

the lightly loaded region. Gas foil bearing operation in these 

two regions is characterized by low specific power loss and 

the ability to recover from overload and special event 

conditions. Operation below and to the right of the power loss 

minimum region is the recommended design range for gas foil 

bearings. 

One impediment to more widespread use of foil bearings in 

high speed turbomachines is the general lack of understanding 

of foil bearing performance at off-design speeds and at 

relevant bearing cavity conditions. Conversely, there exists a 

plethora of information on gas foil bearing performance and 

generator losses operating in air at 1 atmosphere of system 

pressure (Refs. 8, 12, and 13). There exist in the literature 

several experimental and computational studies that quantify 

the effects of geometry on both gas foil bearing performance 

(Refs. 14 and 15) and generator windage. However, the 

extensibility of the proposed nondimensionalization schemes 

to include widely varying fluid properties remains to be 

verified. The data contained herein provides experimental 

evidence to this end. Correlations at high pressures are 

necessary to provide preliminary guidance for the next 

generation oil-free turbomachines. Future closed Brayton 

cycle turbomachines may operate at very high pressures to 

capitalize on several benefits such as increased working fluid 

heat capacity, reduced turbomachinery size, reduced system 

weight, and enhanced reliability. However a major drawback, 

or unknown, in these high-pressure systems is the power loss 

due to windage both in the gas foil bearings and in the rotorstator gap within the generator. 

Generator Windage 

Windage losses occur between any two surfaces moving in 

relation to each other. The significance of these losses depends 

on the rotor surface speed, rotor-stator clearance, surface 

roughness, and fluid properties, in particular the pressure. In 

high-speed turbomachinery, these losses can become 

increasingly significant, especially in the narrow rotor-stator 

gaps or locations where the flow is typically turbulent. There 

has been technical interest in windage losses in high speed 

generators since the days of the Apollo program at the 

National Aeronautics and Space Administration (Refs. 16 to 

19). Windage loss at high speeds continues to be an interest in 

turbomachinery design (Refs. 20 and 21). As is the case with 

gas foil bearings, a typical experimental approach has been to 

conduct experiments while parametrically varying geometric 

parameters and nondimensionalizing results with respect to 

parameters such as Taylor number. However, very little data is 

available which addresses the fluid property effects directly. 

Laminar Taylor-Couette flow is characterized by the 

independence of torque with respect to fluid pressure or 

density. However current experiments show a direct 

relationship between pressure and torque, which is indicative 

Figure 6.—The Taylor-Couette flow regions for concentric 

cylinders. 

of turbulent flow. Most motors and generators rely on a small 

gap between the rotor and the stator to increase efficiency by 

decreasing the divergence of the magnetic field. However, 

decreasing the gap size increases the contribution of power 

loss due to windage. Understanding and being able to quantify 

how speed, pressure, gap size, and surface profile affect the 

windage losses for different working fluids enables the 

prediction of the efficiencies of motors and generators in highpressure systems. Experiments were conducted to directly 

measure the windage losses in a simulated rotor-stator gap 

operating in a high-pressure environment. Only the effects of 

circumferential flow were examined in these experiments. If a 

high axial throughflow is also present the results of this study 

may not be directly applicable. 

The general system that is studied in the current experiment 

is the reaction torque between concentric cylinders, where the 

inner one is rotating, and the outer one is stationary. The 

Taylor-Couette flow theory (Ref. 22) is followed in this 

analysis. The general results of this theory are shown in 

Figure 6. The theory predicts three regions of operation, one 

with completely laminar flow between the cylinders, one with 

Taylor vortices present, and one with turbulent flow between 

the cylinders. These regions can be described by relating the 

conditions of the experiment to two nondimensional values, 

moment coefficient (CM) and Taylor Number (Ta). 

Ri

U d d T i a   (2) 

U R h

M C

i i

i m 2 2

2

1   (3) 

The laminar region corresponds to a Taylor Number less 

than 41.3. In this region, the torque coefficient is related to the 

Taylor Number by the linear theory. 

1  a

i

M T

R

d C A (4) 
NASA/TM—2009-215826 5 

An important feature of the laminar region is that the 

reaction torque independent of fluid pressure or density. The 

effect of increased torque (power loss) with increasing 

pressure is due to the onset of turbulence and therefore is 

primarily a fluid inertia effect. 

Once the Taylor Number exceeds 41.3, the flow becomes 

unstable, which leads to the development of Taylor vortices. 

These vortices rotate around an axis that follows a circular 

path around the rotor, and rotate in alternating opposite 

directions. The development of the vortices causes an initial 

jump in the torque coefficient, which then settles down and 

shows a relationship between the Taylor Number and torque 

coefficient similar to the linear theory, although at a high 

torque level. 

Around a Taylor Number of 400, the flow becomes 

turbulent. The turbulent flow can be approximated by the 

formula: 

0.2 ~  CM Ta (5) 

This proportionality can further be manipulated to show 

that turbulent torque does depend upon fluid density (or 

pressure). 

U Ri d L 0.2 0.8 2.1 1.8 0.3 dimensional_torque ~    (6) 

The experiments that developed these theories used liquids 

and a single fixed radial gap to rotor diameter ratio. The 

current experiments are aimed at validating this theory for a 

variety of gasses at pressures up to 45 atmospheres. A number 

of gap to radius ratios has also been tested as well as 

representative rough stator configurations. 

The Test Rig 

The rig used in this study is the High-Pressure Rig. The rig 

is shown in Figure 7. The rig consists of a motor driven 

spindle and journal capable of speeds up to 42,000 revolutions 

per minute. Two test articles are used on this rig. The first 

article is used to test gas foil bearing performance. The second 

test article can directly measure windage torque. The drive 

motor and test article are completely encased in a pressure 

vessel that can be pressurized to 48 atmospheres with inert 

gas. Testing is limited to 38 C (100 F). 

For the gas foil bearing test article radial loading is 

accomplished by placing balanced annular weights over the 

journal; as such the maximum load that can be tested in this 

rig is approximately 55 N, 61 kPa (12 lbf, 8.6 psi). This limit 

arises from both the available starting torque of the drive 

motor and the space constraints imposed by the pressure 

vessel. There is no ability to vary the applied radial load on 

this rig, which limits the steady state test data to lightly loaded 

conditions. A precision load cell is mounted close to the 

bearing center due to space limitations. This close coupling of 

the load cell also limits the range of reaction torque and power 

Figure 7.—The high pressure test rig. 

loss that can be measured using this rig. The entire test rig is 

enclosed in a pressure vessel. This pressure vessel can be 

evacuated to 0.1 atmospheres and pressurized to 

48 atmospheres. For the current test program helium, nitrogen, 

and carbon dioxide have been used as a foil bearing lubricant. 

Generation III foil journal bearings with uncoated Inconel top 

foils running against conditioned PS304 high temperature 

solid lubricant coated shafts were used in this study. The test 

procedure used on this rig includes a preliminary conditioning 

of the PS304 coated shaft, which includes running a series of 

start-stop cycles under radial load. High temperature start-stop 

cycles cannot be run on this rig, which therefore limits the 

load capacity coefficient to approximately 0.19 mN/(mm3

krpm) (0.7 lbf/(in.3

 krpm)). The test procedure for this rig 

includes using one fixed, “deadweight” load, setting the 

chamber test gas and pressure, and accelerating to maximum 

speed as quickly as possible. Steady state data is then collected 

by reducing speed in set increments and recording reaction 

torque until the minimum power loss level is found. Figure 8 

shows the relationship between bearing performance during a 

controlled acceleration from 0 to 42,000 rpm and data 

obtained during a 5 min dwell time at a given speed to 

measure steady state data. This relationship allows for the 

determination of the power loss minimum point. Steady state 

testing is not continued into the mixed lubrication region due 

to the risk of thermal bearing failure in this region. 

The test article, which was used to measure rotor-stator 

windage, is shown in Figure 9. The main modifications 

included a rotor attached to the motor spindle and a stator

assembly. These are both mounted to the same plate. The rotor 

consists of a 35.3 mm (1.390 in.) diameter aluminum cylinder 

and is balanced with internal mass addition to be able 
NASA/TM—2009-215826 6 

Figure 8.—Comparison of steady state gas foil bearing 

performance with controlled acceleration, transient 

performance. 

Figure 9.—Modifications made to the high 

pressure rig for rotor-stator gap windage 

experiments. (a) rotor mounted to motor 

shaft. (b) Stator assembly mounted to 

precision rail. (c) Various stator inserts. 

to rotate at speeds of up to 42,000 revolutions per minute 

without excessive vibrations or distortion. The stator assembly 

consists of a movable assembly, the stator is held in place by 

two high precision ball bearings, and a load cell. A 

lightweight, high strength monofilament is attached to the load 

cell and wraps around the shaft of the stator, constraining its 

rotational motion. In this arrangement, the stator is free in 

rotation allowing the load cell to measure the torque acting on 

the stator as a result of windage. The load cell is preloaded 

with a known torque to maintain a tension on the load cell. 

The stator assembly is mounted on a sled, which can slide 

along a track mounted to the plate. This allows the stator to be 

easily moved back and forth, to adjust the overlap with the 

rotor, and to work on either the stator or the rotor without 

compromising the precision alignment. 

The stator can be run with only the housing or various 

inserts can be added to change the gap size between the stator 

and the rotor. In the current experimental test program radial 

clearances of 0.0185, 0.0795, and 0.180 in. were tested. In 

addition, the inserts can be modified with strips of copper tape 

to model the surface profile that would be found on the inside 

of a typical motor or generator. 

Results 

Lightly loaded bearing performance data is presented in 

Figure 10. The data show power loss versus rotational speed for 

ambient pressures up to 48 atmospheres, 25 C. Results for 

helium, nitrogen, and carbon dioxide are presented for a 

constant load of 14 N (3.1 lbf). The data for carbon dioxide 

bearing performance is only shown for speeds below 

21,000 revolutions per minute. At speeds greater than 

21,000 revolutions per minute the rig vibrations rose 

dramatically, which caused unknown dynamic loads on the foil 

bearing. The vibrations were due to a rotordynamic problem 

with the journal mounting and were not caused by the test gas. 

For helium the power loss trends at different pressures are 

nearly indistinguishable and follow the typical, mildly 

parabolic trend that is expected in hydrodynamic lubrication. 

For nitrogen and carbon dioxide the effect of pressure 

becomes quite pronounced. Although the trends converge at 

the minimum power loss point, there is a strong effect due to 

pressure as speed increases. The overall trend shows an 

increase in bearing power loss with increasing pressure. 

Data has been obtained and analyzed for all clearances in 

air at 1 atmosphere, clearance of 4.5 mm (0.180 in.) in helium, 

nitrogen, and carbon dioxide up to 48 atmospheres, and for a 

“rough” clearance consisting of a nominal 2.0 mm (0.0795 in.) 

clearance with 75 micrometer (0.003 in.) simulated stator 

features. Figure 11 shows all experimental results plotted 

nondimensionally in terms of Taylor number and moment 

coefficient. Following the Taylor flow theory outlined in 

Equations (2) to (6), it appears as if all of the smooth wall data 

can be reduced to a single trend line provided the moment 

coefficient is modified by the square root of the 
NASA/TM—2009-215826 7 

Figure 10.—Lightly loaded gas foil bearing power loss 

for helium, nitrogen, and carbon dioxide. 

Figure 11.—Experimental rotor-stator windage results. 

clearance to radius ratio. A second trend line appears to 

capture the configuration with simulated roughness. The 

roughness data is currently limited in scope and no 

generalization can be made with regard to the thickness or 

pitch of the roughness. However, it would appear as though 

the general trend and data reduction method as found on the 

Moody charts for pipe flow would be applicable. The data 

presented in Figure 11 combined with Equations (2) to (6) can 

be used directly to estimate windage losses of future high 

pressure power cycles. 

Conclusions 

The experimental results presented herein provide 

quantitative characterization of the windage losses that can be 

expected in high pressure CBC and CSC power cycles for 

lightly loaded gas foil bearings and the rotor-stator clearance 

of the generator. The results for the gas foil bearing exhibit a 

strong influence of system pressure on the power loss when 

nitrogen or carbon dioxide are the lubricants. The gas foil 

bearing is not influenced by system pressure when helium is 

used as the lubricants. This indicates that there may be a fluid 

inertia effect, which is causing the higher power loss when 

using higher molecular weight lubricants. The generator 

windage can be nondimensionalized in terms of moment 

coefficient and Taylor number. Stator surface profiles that 

represent a rough profile have higher torque than the smooth 

walled stator. Future work is required to investigate the 

potential fluid inertia effect in gas foil bearings and to add 

fidelity to the Taylor-Couette correlation as applied to 

generator windage. 

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4. Agrawal, G., “Foil Air/Gas Bearing Technology—An 

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NASA/TM—2009-215826 8 

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Approach to the Solid Lubrication of Foil Air Bearings 

for Oil-Free Turbomachinery,” NASA/TM—2002-

211482. 

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“A Preliminary Foil Gas Bearing Performance Map,” 

NASA/TM—2006-214343, 2006. 

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Foil Journal Bearings for High Load Capacity and High 

Speed Whirl Stability,” Transactions of the ASME 

Journal of Lubrication Technology, vol. 104, no. 2, pp. 

149–156, April 1982. 

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Radial Clearance on the Performance of Foil Air 

Bearings,” NASA/TM—2002-211705. 

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for Turbomachine Shafts Supported on Foil Air 

Bearings,” Tribology Transactions, vol. 47, no. 4, pp. 

508–516, 2004. 

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“Experimental Windage Losses for Close Clearance 

Rotating Cylinders in the Turbulent Flow Regime,” 

NASA Technical Memorandum TM X–52852, 1970. 

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Losses for a Lundell Generator Operating in Air in the 

Turbulent-Flow Region,” NASA Technical Memorandum 

TM X–52905, 1970. 

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116–122, March 1996. 

21. Saint Raymond, M., Kasarda, M.E.F., Allaire, P.E., 

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Supported by Homoplar Active Magnetic Bearings”, 

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New York, 1987. 
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4. TITLE AND SUBTITLE

Windage Power Loss in Gas Foil Bearings and the Rotor-Stator Clearance of High Speed 

Generators Operating in High Pressure Environments 

5a. CONTRACT NUMBER

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6. AUTHOR(S)

Bruckner, Robert, J. 

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WBS 877868.02.07.03.01.01.14 

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National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

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Available electronically at http://gltrs.grc.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

Closed Brayton Cycle (CBC) and Closed Supercritical Cycle (CSC) engines are prime candidates to convert heat from a reactor into electric 

power for robotic space exploration and habitation. These engine concepts incorporate a permanent magnet starter/generator mounted on the 

engine shaft along with the requisite turbomachinery. Successful completion of the long-duration missions currently anticipated for these 

engines will require designs that adequately address all losses within the machine. The preliminary thermal management concept for these 

engine types is to use the cycle working fluid to provide the required cooling. In addition to providing cooling, the working fluid will also 

serve as the bearing lubricant. Additional requirements, due to the unique application of these microturbines, are zero contamination of the 

working fluid and entirely maintenance-free operation for many years. Losses in the gas foil bearings and within the rotor-stator gap of the 

generator become increasingly important as both rotational speed and mean operating pressure are increased. This paper presents the results 

of an experimental study, which obtained direct torque measurements on gas foil bearings and generator rotor-stator gaps. Test conditions 

for these measurements included rotational speeds up to 42,000 revolutions per minute, pressures up to 45 atmospheres, and test gases of 

nitrogen, helium, and carbon dioxide. These conditions provided a maximum test Taylor number of nearly one million. The results show an 

exponential rise in power loss as mean operating density is increased for both the gas foil bearing and generator windage. These typical 

“secondary” losses can become larger than the total system output power if conventional design paradigms are followed. A nondimensional 

analysis is presented to extend the experimental results into the CSC range for the generator windage.

15. SUBJECT TERMS

Foil bearings; Closed cycles; Brayton cycles; High pressure; Turbomachinery 

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