Reduced Order Models for Nonlinear Dynamic Analysis With Application to a Fan Blade

In the present work reduced order models (ROM) that are independent from the full order finite element models (FOM) considering geometrical non linearities are developed and applied to the dynamic study of a fan. The structure is considered to present nonlinear vibrations around the pre-stressed equilibrium induced by rotation enhancing the classical linearised approach. The reduced nonlinear forces are represented by a polynomial expansion obtained by the Stiffness Evaluation Procedure (STEP) and then corrected by means of a Proper Orthogonal Decomposition (POD) that filters the full order nonlinear forces (StepC ROM). The Linear Normal Modes (LNM) and Craig-Bampton (C-B) type reduced basis are considered here. The latter are parametrised with respect to the rotating velocity. The periodic solutions obtained with the StepC ROM are in good agreement with the solutions of the FOM and are more accurate than the linearised ROM solutions and the STEP ROM. The proposed StepC ROM provides the best compromise between accuracy and time consumption of the ROM.

Mistuning Analysis of a Detuned Bladed-Disk With Geometrical Nonlinearities

This work concerns the nonlinear numerical analysis of mistuned blades for a rotating detuned bladed-disk structure with geometrical nonlinearities. The detuning phenomenon is taken into account through a deterministic approach by modifying material properties of some blades. A nonlinear reduced-order model is obtained by setting up a basis using a double projection method. The mistuning uncertainties are implemented through a nonparametric probabilistic approach for which the level of uncertainties is controlled by a hyperparameter. A numerical application is carried out on a bladed-disk structure made up of 24 blades whose finite element model has about 800,000 dofs exhibiting complex dynamic behaviors.

Influence of Lubrication Oil on the Performance of Carbon Fibre Brush Seals for Aero-Engines Bearing Chambers

Carbon fibre brush seals are an alternative to labyrinth seals in aero-engines lubrication systems due to better sealing ability with low power loss. However, the use of brush seals still raises concerns about coking issues. In addition, the influence of oil on the brush seal behaviour needs to be fully assessed. This paper provides an experimental investigation of the effect of lubrication oil on the performance of carbon fibre brush seals under static and dynamic conditions. Eight brush seal samples of various geometrical designs were submitted to an environment recreating the working conditions of a modern aero-engine bearing chamber in terms of rotational speed, air pressure, and oil type of injection and temperature. The test results indicated that the performance of carbon fibre brush seals was deeply influenced by the presence of oil within fibres. Oil deeply influences leakage performance, depending on geometrical parameters (density, fibre length and interference) and operating conditions (oil temperature, rotational speed). Brush seal fibre pack is mainly prone to hydrodynamic lift and oil soaking, which is defined by the ability of lubrication oil to fill in properly the interstices between fibres. Viscosity and surface tension may be the key properties influencing oil soaking. Seal torque data corroborates the presence of a hydrodynamic lift. In addition, in absence of differential pressure, seal torque decrease with when oil temperature increases indicates the existence of a critical viscosity. Finally, oil lubrication within the bristles allows reduction of the inter-bristle friction, thus limiting hysteresis.

The Influence of Ambient Pressure on the Measured Load Capacity of Bump-Foil and Spiral-Groove Gas Thrust Bearings at Ambient Pressures up to 69 Bar on a Novel High-Pressure Gas Bearing Test Rig

This paper will show the influence of ambient pressure on the thrust capacity of bump-foil and spiral-groove gas thrust bearings. The bearings were operating in nitrogen at various pressures up to 69 bar, and were tested to failure. Failure was detected at various pressures by incrementally increasing the thrust load applied to the thrust bearing until the bearing was no longer thermally stable, or until contact was observed by a temperature spike measured by thermocouples within the bearing. These tests were performed on a novel thrust bearing test rig that was developed to allow thrust testing at pressures up to 207 bar cavity pressure at 260°C while rotating at speeds up to 120,000 rpm. The test rig floats on hydrostatic air bearings to allow for the direct measurement of applied thrust load through linkages that connect the stationary thrust loader to the rotor housing. Test results on a 65 mm (2.56 in) bump-foil thrust bearing at 100 krpm show a marked increase in load capacity with gas density, which has not previously been shown experimentally. Results also show that the load capacity of a similarly sized spiral-groove thrust bearing are relatively insensitive to pressure, and supported an order-of-magnitude less load than that observed for the bump-foil thrust bearing. These results are compared with analytical predictions, which agree reasonably with the experimental results. Predicted power loss is also presented for the bump-foil bearing; however, measured power loss was substantially higher.

On the Integration of Hot Foil Bearings Into Gas Turbine Engines: Theoretical Treatment

To achieve high power density Gas Turbine Engines (GTEs), R&D efforts have strived to develop machines that spin faster and run hotter. One method to achieve that goal is to use high temperature capable foil bearings. In order to successfully integrate these advanced foil bearings into GTE systems, a theoretical understanding of both bearing and rotor system integration is essential. Without a fundamental understanding and sound theoretical modeling of the foil bearing coupled with the rotating system such an approach would prove application efforts fruitless. It is hoped that the information provided in this paper will open up opportunistic doors to designs presently thought to be impossible. In this paper an attempt is made to describe how an advanced foil bearing is modeled for extreme high temperature operation in high performance turbomachinery including GTEs, Supercritical CO2 turbine generators and others. The authors present the advances in foil bearing capabilities that were crucial to achieving high temperature operation. Achieving high performance in a compliant foil bearing under the wide extremes of operating temperatures, pressures and speeds, requires a bearing system design approach that accounts for the highly interrelated compliant surface foil bearing elements such as: the structural stiffness and frictional characteristics of the underlying compliant support structure across the operating temperature and pressure spectrum; and the coupled interaction of the structural elements with the hydrodynamic pressure generation. This coupled elasto-hydrodynamic-Finite Element highly non-linear iterative methodology will be used by the authors to present a series of foil bearing design evaluations analyzing and modeling the foil bearing under extreme conditions. The complexity of the problem of achieving foil bearing system operation beyond 870°C (1600°F) requires as a prerequisite the attention to the tribological details of the foil bearing. For example, it is necessary to establish how both the frictional and viscous damping coefficient elements as well as the structural and hydrodynamic stiffness are to be combined. By combining these characteristics the influence of frictional coefficients of the elastic and an-elastic materials on bearing structural stiffness and hence the bearing effective coupled elasto-hydrodynamic stiffness coefficients will be shown. Given that the bearing dynamic parameters — stiffness and damping coefficients — play a major role in the control of system dynamics, the design approach to successfully integrate compliant foil bearings into complex rotating machinery systems operating in extreme environments is explored by investigating the effects of these types of conditions on rotor-bearing system dynamics. The proposed rotor/bearing model is presented to describe how system dynamics and bearing structural properties and operating characteristics are inextricably linked together in a manner that results in a series separate but intertwined iterative solutions. Finally, the advanced foil bearing modeling and formulation in connection with resulting rotor dynamics of the system will be carried out for an experimental GTE simulator test rig. The analytical results will be compared with the experiments as presented previously to demonstrate the effectiveness of the developed method in a real world application [1].

Leakage and Dynamic Force Coefficients of a Pocket Damper Seal Operating Under a Wet Gas Condition: Tests vs. Predictions

High performance centrifugal compressors presently favor pocket damper seals (PDSs) as a choice of secondary flow control element offering a large effective damping coefficient to mitigate rotor sub synchronous whirl motions. Current and upcoming multiple-phase compression systems in subsea production facilities must demonstrate long term operation and continuous availability, free of harmful rotor instabilities. Plain annular seals and labyrinth seals are notoriously bad choices, whereas a PDS, by stopping the circulation of trapped liquid, operates stably. This paper presents experimental and computational fluid dynamics (CFD) results for the leakage and dynamic force coefficients obtained in a dedicated test facility hosting a fully partitioned PDS, four ribbed and with eight pockets per cavity. The test PDS, operating at a rotor speed 5,250 rpm (surface speed 35 m/s) and under a supply pressure/discharge pressure ratio up to 3.2, is supplied with a mixture of air and ISO VG 10 oil whose maximum liquid volume fraction (LVF) is 2.2%, equivalent to a liquid mass fraction of 84%. When supplied with just air (dry condition), the measured leakage increases nonlinearly with supply pressure. Under a wet gas condition, the recorded mass flow increases on account of the large difference in density between the liquid and the gas. CFD derived mass flow rates for both dry and wet gas conditions agree with the measured ones. The test dry gas PDS produces a direct dynamic stiffness (HR) increasing with frequency whereas the direct damping (C) and cross-coupled dynamic stiffness (hR) coefficients remain relatively constant. The CFD predicted damping agrees best with the test C albeit over predicting HR at low excitation frequencies and hR at all frequencies (< 175 Hz ∼ twice rotor speed). Under a wet gas condition with LVF = 0.4%, the test force coefficients show great variability over the excitation frequency range; in particular HR < 0, though growing with frequency due to the large liquid mass fraction. The CFD predictions, on the other hand, produce a dynamic direct stiffness HR > 0 for all frequencies. Both experimental hR and C for the wet gas PDS are larger than their counterparts for the dry gas seal. The CFD predicted C and hR, wet vs. dry, show a modest growth, yet remaining lower than the test data. The CFD derived flow field for a wet gas condition shows the seal radial partition walls (ridges) reduce the circumferential flow velocity and liquid accumulation within a pocket. Both the test data and CFD prediction show that the magnitude of the flexibility function for the PDS test system reduces when the two component mixture flows through the seal, hence revealing the additional effective damping, more pronounced for the test data rather than that from the predictions. Further work, experimental and CFD based, will continue to advance the technology of wet gas seals while bridging the gap between test data and computational physics model simulations.

A Study for Rotordynamic and Leakage Characteristics of a Long-Honeycomb Seal With Two-Phase, Mainly Air Mixtures

This paper investigates the impact of the oil (silicone oil PSF-5cSt) presence in the air on the leakage and rotordynamic characteristics of a long-honeycomb seal with length-to-diameter ratio L/D = 0.748 and diameter D = 114.656 mm. Tests are carried out with inlet pressure Pi = 70.7 bars, pressure ratio PR = 0.35 and 0.25, inlet liquid volume fraction LVF = 0%, 3.5%, and 7%, and shaft speed ω = 10, 15, and 20 krpm. During the tests, the seal is centered. Test results show that leakage mass flow rate ṁ increases (as expected) as inlet LVF increases. Increasing inlet LVF makes direct stiffness K increase more rapidly with increasing excitation frequency Ω. Increasing inlet LVF has a negligible effect on K at low Ω values, but increases K at high Ω values. The value of effective damping Ceff at about 0.5ω is an indicator to the system stability since an unstable centrifugal compressor rotor can precess at about 0.5ω. Increasing inlet LVF increases the value of Ceff at about 0.5ω, reducing the possibility of sub-synchronous vibrations SSVs at about 0.5ω. San Andrés’s model is used to produce predictions. The model assumes that the test fluid in the seal clearance is an isothermal-homogenous mixture. The model adequately predicts ṁ, K, and the value of Ceff at about 0.5ω.

Nonlinear Vibration Prediction of a Highly Flexible Rotor Supported by an Axial Groove Journal Bearing Considering Journal Angular Whirling Motion

In this study, the difference in dynamic behavior of the rotor-bearing system supported by the bearing model that considers both lateral and angular whirling motions of the journal (model A), and the model that considers only lateral whirling motion (model B) is investigated. The rotor model consists of a slender shaft, a large disk and two small disks supported by a self-aligning ball bearing and an axial groove journal bearing of L/D = 0.6. Three positions of the large disk: 410, 560, and 650 mm measured from the ball bearing, are investigated. Numerical integration of the rotor-bearing system which is modally reduced to the 1st forward mode is performed at above the onset speed of instability until either a steady state journal orbit or contact between the journal and the bearing occurs to identify the bifurcation type. Numerical results using model A indicate subcritical bifurcation with the contact between the journal and the inboard side of the bearing in all three large disk positions, whereas those of model B indicate subcritical bifurcation when the large disk position is at 410 mm, and supercritical bifurcation is observed in the other two cases. Lastly, the experiments at the same three large disk positions are performed. Subcritical bifurcation with the contact between the journal and the inboard side of the bearing is observed in all large disk positions, which conforms with the calculation result of model A. As a result, model A is essential in nonlinear vibration analysis of a highly flexible rotor system.

CFD Simulation of Air Ingestion in a Squeeze Film Damper

Squeeze film damper (SFD) is widely adopted in the high performance rotor-bearing systems to eliminate rotor vibration and improve stability. Experiments show that the air ingestion from the open end would have notable impact on the SFD performance. Multiphase Computational Fluid Dynamics (CFD) calculation on the air ingestion in the SFD is conducted in this work. Results are validated with the experimental data to prove the capability of the multiphase CFD on predicting the air ingestion. Air and oil flow in the SFD are analyzed in details. By comparing the CFD results with and without air ingestion, the effect of air ingestion is revealed. Results show that CFD is capable of predicting the air-oil flow in the SFD. The maximum air region is located in the vicinity of the largest bearing clearance region rather than the low pressure zone. And air ingestion in the largest bearing clearance region counteracts the hydrodynamic pressure effect in the vicinity.

Effect of Pad and Liner Material Properties on the Static Load Performance of a Tilting Pad Thrust Bearing

Tilting Pad Thrust Bearings (TPTBs) control rotor axial placement in rotating machinery and their main advantages include low drag power loss, simple installation, and low-cost maintenance. The paper details a novel thermo-elasto-hydrodynamic (TEHD) analysis predictive tool for TPTBs that considers a 3D thermal energy transport equation in the fluid film, coupled with heat conduction equations in the pads, and a generalized Reynolds equation with cross-film viscosity variation. The predicted pressure field and temperature rise are employed in a finite element structural model to produce 3D elastic deformation fields in the bearing pads. Solutions of the governing equations delivers the operating film thickness, required flow rate, shear drag power loss, and the pad and lubricant temperature rises as a function of an applied load and shaft speed. To verify the model, predictions of pad sub-surface temperature are benchmarked against published test data for a centrally pivoted eight-pad TPTB with 267 mm in outer diameter operating at 4–13 krpm (maximum surface speed = 175 m/s) and under a specific load ranging from 0.69 to 3.44 MPa. The current TEHD temperature predictions match well the test data with a maximum difference of 4°C and 11°C (< 10%) at laminar and turbulent flow conditions, receptively. Next, the TEHD predictive tool is used to study the influence of both pad and liner material properties on the performance of a TPTB. The analysis takes a whole steel pad (without a liner or babbitt), a steel pad with a 2 mm thick babbitt layer (common usage), a steel pad with a 2 mm thick hard-polymer (polyether ether ketone, e.g PEEK®) liner, and a pad entirely made of hard-polymer material, whose elastic modulus is just 12.5 GPa, only 6% that of steel. The bare steel pad reveals the poorest performance among all the pads as it produces the smallest fluid film thickness and consumes the largest drag power loss. For laminar flow operations (Reynolds number Re < 580), the babbitted-steel pad operates with the thickest fluid film and the lowest film temperature rise. For turbulent flow conditions Re > 800, the solid hard-polymer pad, however, shows a 23% thicker film than that in the babbitted pad and produces up to 25% lesser drag power loss. In general, the solid hard-polymer TPTB is found to be a good fit for operation at a turbulent flow condition as it shows a lower drag power loss and a larger film thickness, however, its demand for a too large supply flow rate is significant. Predictions for steel pads with various hard-polymer liner and babbitt thicknesses demonstrate that using a hard-polymer liner, instead of white metal, isolates the pad from the fluid film and results in an up to 30°C (50%) lower temperature rise in the pads than that for a babbitted-steel pad. For operations under a heavy specific load (> 3.0 MPa), however, a thick hard-polymer liner extensively deforms and results in a small film thickness.