Research Papers: Gas Turbines: Structures and Dynamics

Development of a Computational Tool to Simulate Foil Bearings for Supercritical CO2 Cycles

[+] Author and Article Information
Kan Qin

Queensland Geothermal Centre of Excellence,
School of Mechanical and Mining Engineering,
The University of Queensland,
Brisbane, Queensland 4072, Australia
e-mail: k.qin1@uq.edu.au

Ingo Jahn

Centre for Hypersonics,
School of Mechanical and Mining Engineering,
The University of Queensland,
Brisbane, Queensland 4072, Australia
e-mail: i.jahn@uq.edu.au

Rowan Gollan

Centre for Hypersonics,
School of Mechanical and Mining Engineering,
The University of Queensland,
Brisbane, Queensland 4072, Australia
e-mail: r.gollan@uq.edu.au

Peter Jacobs

Queensland Geothermal Centre of Excellence,
School of Mechanical and Mining Engineering,
The University of Queensland,
Brisbane, Queensland 4072, Australia
e-mail: p.jacobs@uq.edu.au

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received December 29, 2015; final manuscript received February 3, 2016; published online March 22, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(9), 092503 (Mar 22, 2016) (19 pages) Paper No: GTP-15-1583; doi: 10.1115/1.4032740 History: Received December 29, 2015; Revised February 03, 2016

The foil bearing is an enabling technology for turbomachinery systems, which has the potential to enable cost efficient supercritical CO2 cycles. The direct use of the cycle's working fluid within the bearings results in an oil-free and compact turbomachinery system; however, these bearings will significantly influence the performance of the whole cycle and must be carefully studied. Moreover, using CO2 as the operating fluid for a foil bearing creates new modeling challenges. These include highly turbulent flow within the film, non-negligible inertia forces, high windage losses, and nonideal gas behavior. Since the flow phenomena within foil bearings is complex, involving coupled fluid flow and structural deformation, use of the conventional Reynolds equation to predict the performance of foil bearings might not be adequate. To address these modeling issues, a three-dimensional flow and structure simulation tool has been developed to better predict the performance of foil bearings for the supercritical CO2 cycle. In this study, the gas dynamics code, eilmer, has been extended for multiphysics simulation by implementing a moving grid framework, in order to study the elastohydrodynamic performance of foil bearings. The code was then validated for representative laminar and turbulent flow cases, and good agreement was found between the new code and analytical solutions or experiment results. A separate finite difference code based on the Kirchoff plate equation for the circular thin plate was developed in Python to solve the structural deformation within foil thrust bearings, and verified with the finite element analysis from ansys. The fluid-structure coupling algorithm was then proposed and validated against experimental results of a foil thrust bearing that used air as operating fluid. Finally, the new computational tool set is applied to the modeling of foil thrust bearings with CO2 as the operating fluid.

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Fig. 1

Schematic diagram of foil thrust bearings in two dimensions

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Fig. 2

Computational domain of turbulent plane Couette flow

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Fig. 3

(a) Velocity distribution of turbulent plane Couette flow and (b) comparison with the law of wall

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Fig. 4

Schematic diagram for the moving interface. An, Bn, Cn, and Dn are the vertices at time level n, An+1, Bn+1, Cn+1, Dn+1 is the vertices at time level n + 1. Aif, Bif, Cif, and Dif are the effective vertices at time level n + 1 and used to calculate the swept volume Vif. WA, WB, WC, and WD grid-velocities associated with the vertices.

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Fig. 5

Ghost cell configuration for a slip wall condition

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Fig. 6

Grid convergence study: (a) local deflection from the developed structural deformation code, (b) local deflection from the Finite element solver in ansys, (c) maximum deflection over the fine mesh from the developed structural deformation code, and (d) maximum deflection over the fine mesh from the finite element solver in ansys

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Fig. 7

(a) Schematic diagram of top foil of foil bearings, (b) deformation comparison between ansys and the developed structural deformation code at different radii

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Fig. 8

Computational domain for NACA0012 airfoil

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Fig. 9

Grid convergence study for the pitching NACA0012

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Fig. 10

Instantaneous pressure coefficient: (a) 0.52 deg, ↓, downward stroke, (b) −0.54 deg, ↑, upward stroke, (c) −2.00 deg, ↑, upward stroke, (d) 2.01 deg, ↓, downward stroke, (e) 2.34 deg, ↓, downward stroke, and (f) −2.41 deg, ↓, downward stroke

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Fig. 11

Comparison between eilmer and experiment: (a) normal force coefficient and (b) moment coefficient

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Fig. 12

Computational domain for the oscillating plate

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Fig. 13

Grid convergence study of oscillating plate: (a) velocity distribution at 1 ms and (b) friction coefficient over the fine mesh in terms of representative cell size at 1 ms

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Fig. 14

Comparison results between eilmer and the analytical solution: (a) velocity profile at different phase angles and (b) local skin friction coefficient

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Fig. 15

Grid convergence study for the pitching NACA64A010 airfoil

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Fig. 16

Comparison results between eilmer and experiment [43]: (a) lift force coefficient Cl versus angle of attack α and (b) moment coefficient Cm versus angle of attack α

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Fig. 17

Computational domain for foil thrust bearings, not to scale

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Fig. 18

Grid convergence study for foil thrust bearings: (a) local deflection at the medium radius and (b) pressure at the medium radius

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Fig. 19

Comparison of measurements and numerical simulation at fixed rotational speed of 21,000 rpm

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Fig. 20

Comparison of maximum deformation between eilmer and numerical results from Ref. [10]

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Fig. 21

Pressure-enthalpy diagram for CO2

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Fig. 22

Comparison of thermodynamic properties at the medium radius with the rotational speed of 30,000 rpm: (a) pressure, (b) compressibility factor, (c) density, (d) temperature, (e) dynamic viscosity, and (f) thermal conductivity

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Fig. 23

Pressure increase contour of foil thrust bearings: (a): CO2, rotational speed: 60,000 rpm and (b): air, rotational speed: 60,000 rpm

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Fig. 24

Comparison of nondimensional pressure distribution at the medium radius between eilmer and Reynolds equation: (a): air, rotational speed: 30,000 rpm, (b): CO2, rotational speed: 30,000 rpm, (c): air, rotational speed: 60,000 rpm, and (d): CO2, rotational speed: 60,000 rpm

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Fig. 25

Ramp region: pressure increase, radial and tangential velocities at the different circumferential angle, the rotational speed: 60,000 rpm, ramp end at 15 deg: (a) 3.55 deg, (b) 9.05 deg, and (c) 12.21 deg

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Fig. 26

Flat region: pressure increase, radial and tangential velocities at the different circumferential angle, the rotational speed: 60,000 rpm, flat start at 15 deg: (a) 24.20 deg, (b) 33.66 deg, and (c) 41.02 deg

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Fig. 27

Approximate streamlines at 90% (rotor) and 10% (stator) film thickness: (a) air:rotor, (b) air:stator, (c) CO2: rotor, and (d) CO2:stator

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Fig. 28

Comparison of tangential velocity profile at laminar and turbulent flows at the medium radius with the circumferential angle of 24.20 deg



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