Abstract

Small-scale turbomachinery operating at high rotational speed is a key technology for increasing the power density of energy and propulsion systems. A notable example is the turbine of an organic Rankine cycle turbogenerator for thermal recuperation from prime engines and industrial processes. Such systems typically operate with organic compounds characterized by complex molecular structures to allow the design of efficient fluid machinery and flexibility in matching the heat source and sink temperature profiles. Gas-lubricated bearings are considered advantageous compared to traditional oil-lubricated rolling element bearings for supporting the turbine rotor, enabling greater machine compactness and reduced complexity, and avoiding contamination of the working fluid. In certain operating conditions, however, the lubricant of the gas bearing is in thermodynamic states near the saturated vapor line or in the vicinity of the fluid critical point, whereby nonideal effects are relevant and may affect bearing performance. This work investigates the physics of thin film flows in gas bearings operating with fluids made by complex molecules. The influence of nonideal thermodynamic effects on gas bearing performance is discussed by analysis of the fluid bulk modulus. Reduced values of the nondimensional bulk modulus near the critical point or saturated vapor line decrease bearing performance. The main parameter characterizing the influence of molecular complexity on bearing performance is shown to be the acentric factor. For complex fluids with large acentric factors, the impact of nonideal thermodynamic effects on nondimensional bearing load capacity and rotor-dynamic characteristics is less pronounced.

References

1.
Colonna
,
P.
,
Casati
,
E.
,
Trapp
,
C.
,
Mathijssen
,
T.
,
Larjola
,
J.
,
Turunen-Saaresti
,
T.
, and
Uusitalo
,
A.
,
2015
, “
Organic Rankine Cycle Power Systems: From the Concept to Current Technology, Applications, and an Outlook to the Future
,”
ASME J. Eng. Gas Turbines Power
,
137
(
10
), p.
100801
.10.1115/1.4029884
2.
Casey
,
M.
,
Krähenbühl
,
D.
, and
Zwyssig
,
C.
,
2014
, “
The Design of Ultra-High-Speed Miniature Centrifugal Compressors
,”
10th European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC10
, Lappeenranta, Finland, Apr. 15–19, pp.
506
519
.https://www.celeroton.com/wp-content/uploads/celeroton-publication-miniature-compressors.pdf
3.
Lee
,
Y.
,
Park
,
D.
,
Kim
,
T.
, and
Sim
,
K.
,
2012
, “
Development and Performance Measurement of Oil-Free Turbocharger Supported on Gas Foil Bearings
,”
ASME J. Eng. Gas Turbines Power
,
134
(
3
), p.
032506
.10.1115/1.4004719
4.
Zagarola
,
M.
, and
McCormick
,
J.
,
2006
, “
High-Capacity Turbo-Brayton Cryocoolers for Space Applications
,”
Cryogenics
,
46
(
2–3
), pp.
169
175
.10.1016/j.cryogenics.2005.11.018
5.
Kadyk
,
T.
,
Schenkendorf
,
R.
,
Hawner
,
S.
,
Yildiz
,
B.
, and
Römer
,
U.
,
2019
, “
Design of Fuel Cell Systems for Aviation: Representative Mission Profiles and Sensitivity Analyses
,”
Front. Energy Res.
,
7
, p.
35
.10.3389/fenrg.2019.00035
6.
Schiffmann
,
J.
, and
Favrat
,
D.
,
2009
, “
Experimental Investigation of a Direct Driven Radial Compressor for Domestic Heat Pumps
,”
Int. J. Refrig.
,
32
(
8
), pp.
1918
1928
.10.1016/j.ijrefrig.2009.07.006
7.
Giuffré
,
A.
,
Colonna
,
P.
, and
Pini
,
M.
,
2022
, “
The Effect of Size and Working Fluid on the Multi-Objective Design of High-Speed Centrifugal Compressors
,”
Int. J. Refrig.
,
143
, pp.
43
56
.10.1016/j.ijrefrig.2022.06.023
8.
Conboy
,
T.
,
Wright
,
S.
,
Pasch
,
J.
,
Fleming
,
D.
,
Rochau
,
G.
, and
Fuller
,
R.
,
2012
, “
Performance Characteristics of an Operating Supercritical CO2 Brayton Cycle
,”
ASME J. Eng. Gas Turbines Power
,
134
(
11
), p.
111703
.10.1115/1.4007199
9.
DellaCorte
,
C.
,
Radil
,
K.
,
Bruckner
,
R.
, and
Howard
,
S.
,
2008
, “
Design, Fabrication, and Performance of Open Source Generation I and II Compliant Hydrodynamic Gas Foil Bearings
,”
Tribol. Trans.
,
51
(
3
), pp.
254
264
.10.1080/10402000701772579
10.
Guardone
,
A.
,
Colonna
,
P.
,
Pini
,
M.
, and
Spinelli
,
A.
,
2024
, “
Nonideal Compressible Fluid Dynamics of Dense Vapors and Supercritical Fluids
,”
Annu. Rev. Fluid Mech.
,
56
(
1
), pp.
241
269
.10.1146/annurev-fluid-120720-033342
11.
Giuffré
,
A.
,
Colonna
,
P.
, and
Pini
,
M.
,
2023
, “
Design Optimization of a High-Speed Twin-Stage Compressor for Next-Gen Aircraft Environmental Control System
,”
ASME J. Eng. Gas Turbines Power
,
145
(
3
), p.
031017
.10.1115/1.4056022
12.
Giuffré
,
A.
, and
Pini
,
M.
,
2021
, “
Design Guidelines for Axial Turbines Operating With Non-Ideal Compressible Flows
,”
ASME J. Eng. Gas Turbines Power
,
143
(
1
), p.
011004
.10.1115/1.4049137
13.
Tosto
,
F.
,
Lettieri
,
C.
,
Pini
,
M.
, and
Colonna
,
P.
,
2021
, “
Dense-Vapor Effects in Compressible Internal Flows
,”
Phys. Fluids
,
33
(
8
), p.
086110
.10.1063/5.0058075
14.
DellaCorte
,
C.
, and
Valco
,
M.
,
2000
, “
Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications
,”
Tribol. Trans.
,
43
(
4
), pp.
795
801
.10.1080/10402000008982410
15.
DellaCorte
,
C.
,
2011
, “
Stiffness and Damping Coefficient Estimation of Compliant Surface Gas Bearings for Oil-Free Turbomachinery
,”
Tribol. Trans.
,
54
(
4
), pp.
674
684
.10.1080/10402004.2011.589966
16.
Heshmat
,
H.
,
Walowit
,
J. A.
, and
Pinkus
,
O.
,
1983
, “
Analysis of Gas-Lubricated Foil Journal Bearings
,”
ASME J. Tribol.
,
105
(
4
), pp.
647
655
.10.1115/1.3254697
17.
Bruckner
,
R.
,
2009
, “
Windage Power Loss in Gas Foil Bearings and the Rotor-Stator Clearance of High Speed Generators Operating in High Pressure Environments
,”
ASME
Paper No. GT2009-60118.10.1115/GT2009-60118
18.
Conboy
,
T. M.
,
2013
, “
Real-Gas Effects in Foil Thrust Bearings Operating in the Turbulent Regime
,”
ASME J. Tribol.
,
135
(
3
), p.
031703
.10.1115/1.4024048
19.
Lemmon
,
E. W.
,
Bell
,
I. H.
,
Huber
,
M. L.
, and
McLinden
,
M. O.
,
2018
, “
NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10.0
,” National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, MD.
20.
Kim
,
D.
,
2016
, “
Design Space of Foil Bearings for Closed-Loop Supercritical CO2 Power Cycles Based on Three-Dimensional Thermohydrodynamic Analyses
,”
ASME J. Eng. Gas Turbines Power
,
138
(
3
), p.
032504
.10.1115/1.4031433
21.
Guenat
,
E.
, and
Schiffmann
,
J.
,
2018
, “
Real-Gas Effects on Aerodynamic Bearings
,”
Tribol. Int.
,
120
, pp.
358
368
.10.1016/j.triboint.2018.01.008
22.
Reynolds
,
O.
,
1886
, “
IV. On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil
,”
Philos. Trans. R. Soc. A
,
177
, pp.
157
234
.10.1098/rstl.1886.0005
23.
Chien
,
S. Y.
,
Cramer
,
M. S.
, and
Untaroiu
,
A.
,
2017
, “
Compressible Reynolds Equation for High-Pressure Gases
,”
Phys. Fluids
,
29
(
11
), p.
116101
.10.1063/1.5000827
24.
Constantinescu
,
V. N.
,
1959
, “
On Turbulent Lubrication
,”
Proc. Inst. Mech. Eng.
,
173
(
1
), pp.
881
900
.10.1243/PIME_PROC_1959_173_068_02
25.
Ng
,
C.
, and
Pan
,
C. H. T.
,
1965
, “
A Linearized Turbulent Lubrication Theory
,”
ASME J. Basic Eng.
,
87
(
3
), pp.
675
682
.10.1115/1.3650640
26.
Hirs
,
G. G.
,
1973
, “
A Bulk-Flow Theory for Turbulence in Lubricant Films
,”
ASME J. Lubr. Technol.
,
95
(
2
), pp.
137
145
.10.1115/1.3451752
27.
Giuffré
,
A.
, and
Pini
,
M.
,
2022
, “
NiceProp: An Interactive Python-Based Educational Tool for Non-Ideal Compressible Fluid Dynamics
,”
SoftwareX
,
17
, p.
100897
.10.1016/j.softx.2021.100897
28.
Bell
,
I. H.
,
Wronski
,
J.
,
Quoilin
,
S.
, and
Lemort
,
V.
,
2014
, “
Pure and Pseudo-Pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp
,”
Ind. Eng. Chem. Res.
,
53
(
6
), pp.
2498
2508
.10.1021/ie4033999
29.
Kim
,
T. H.
, and
San Andrés
,
L.
,
2008
, “
Heavily Loaded Gas Foil Bearings: A Model Anchored to Test Data
,”
ASME J. Eng. Gas Turbines Power
,
130
(
1
), p.
012504
.10.1115/1.2770494
30.
San Andrés
,
L.
, and
Kim
,
T.
,
2009
, “
Analysis of Gas Foil Bearings Integrating FE Top Foil Models
,”
Tribol. Int.
,
42
(
1
), pp.
111
120
.10.1016/j.triboint.2008.05.003
31.
Invernizzi
,
C.
,
2013
,
Closed Power Cycles: Thermodynamic Fundamentals and Applications
(Lecture Notes in Energy),
Springer
,
London, UK
.
32.
Guardone
,
A.
, and
Argrow
,
B. M.
,
2005
, “
Nonclassical Gasdynamic Region of Selected Fluorocarbons
,”
Phys. Fluids
,
17
(
11
), p.
116102
.10.1063/1.2131922
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