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 P i = 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 m ˙ 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 C eff at about 0.5 ω is an indicator to the system stability since an unstable centrifugal compressor rotor can precess at about 0.5 ω . Increasing inlet LVF increases the value of C eff at about 0.5 ω , reducing the possibility of subsynchronous vibrations (SSVs) at about 0.5 ω . 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 m ˙ , K, and the value of C eff at about 0.5 ω .

This paper conducts a comprehensive study on the effects of the presence of air in the oil on the leakage and rotordynamic coefficients of a long-smooth seal (inner diameter D = 89.306 mm, radial clearance C r = 0.140 mm, and length-diameter ratio L/D = 0.65) under laminar-two-phase flow conditions. The mixture consists of air and silicone oil with inlet gas volume fraction (GVF) up to 10%. Tests are performed at inlet temperature T i = 39.4 °C, exit pressure P e = 6.9 bars, pressure drop PD = 31, and 37.9 bars, and rotor speed ω = 5, 7.5, and 10 krpm. The test seal is always concentric with the rotor, and no intentional fluid prerotation is provided at the seal inlet. The complex dynamic stiffness coefficients H ij of the test seal are measured and fitted by the frequency-independent direct stiffness K, cross-coupled stiffness k, direct damping C, cross-coupled damping c, direct virtual-mass M, and cross-coupled virtual-mass m q coefficients. Under laminar flow conditions, increasing inlet GVF has negligible effects on K, k, C, and effective damping C eff , while it decreases c and M. These trends are correctly predicted by San Andrés's bulk-flow model with laminar flow friction formula. As inlet GVF increases, measured leakage flow rate m ˙ increases slightly. In general, the predictions of K, k, C, c, C eff , and m ˙ are reasonably close to measurements.

Tie bolt rotors for centrifugal compressors comprise multiple shaft components that are held together by a single tie bolt. The axial connections of these rotors—including butt joints, Hirth couplings, and Curvic couplings—exhibit a contact stiffness effect, which tends to lower the shaft bending frequencies compared to geometrically identical monolithic shafts. If not accounted for in the design stage, shaft bending critical speed margins can be compromised after a rotor is built. A previous paper had investigated the effect of tie bolt force on the bending stiffness of stacked rotor assemblies with butt joint interfaces, both with and without pilot fits. This previous work derived an empirical contact stiffness model and developed a practical finite element modeling approach for simulating the axial contact surfaces, which was validated by predicting natural frequencies for several test rotor configurations. The present work built on these previous results by implementing the same contact stiffness modeling approach on a real tie bolt rotor system designed for a high pressure centrifugal compressor application. Each joint location included two axial contact faces, with contact pressures up to five times higher than previously modeled, and a locating pilot fit. The free-free natural frequencies for different amounts of tie bolt preload force were measured, and the frequencies exhibited the expected stiffening behavior with increasing preload. However, a discontinuity in the data trend indicated a step-change increase in the contact stiffness. It was shown that this was likely due to one or more of the contact faces becoming fully engaged only after sufficient tie bolt force was applied. Finally, a design calculation was presented that can be used to estimate whether contact stiffness effects may be ignored, which could simplify rotor analyses if adequate contact pressure is used.

In this paper, a novel bulk-flow model for pocket damper seals (PDS) is introduced. The model is based on two control volumes (CVs) for each circumferential pocket of the seal. The continuity, circumferential momentum, and energy equations are considered for each control volume. The circumferential recirculating flow within the pocket is modeled for the first time. The boundary layer theory is used to estimate the recirculating flow area, and the Swamee–Jain friction factor correlation allows for defining the dissipation of the circumferential velocity. The perturbation method is used to solve the partial derivative governing equations in the zeroth- and first-order system of equations. The rotordynamic coefficients are evaluated by integrating the dynamic pressure and rotor shear stresses along the circumferential direction. The predictions are compared to the experimental data, which refer to test conditions representative of high-pressure centrifugal compressors. Numerical predictions are accurate for both high positive–negative inlet preswirl ratios. Leakage predictions are also aligned with measurements. Finally, sealing selection approach is introduced in the paper for comparing the dynamic behavior of two different sealing technologies and identifying stable regions as a function of the rotor natural frequency and preswirl ratio.

A 300 kW integrated and fully sealed turboexpander-generator for natural gas pressure letdown (PLD) was developed by Baker Hughes, a GE company (BHGE), in conjunction with Calnetix Technologies. This paper describes the design and analysis of the generator, magnetic bearings, and touchdown bearings, with a focus on the dynamic performance and key characteristics of the machine. The permanent magnet (PM) synchronous generator is supported by PM-biased, homopolar magnetic bearings and has a maximum continuous operating speed (MCOS) of 31.5 krpm. A touchdown bearing system is implemented using rolling element bearings with soft mount supports. Also described is a thrust load balancing scheme that uses the thrust bearing coil current for reference. A time transient simulation showing the effect of process conditions on the AMB dynamics is shown. Preliminary data from the prototype mechanical run test are shown, including transfer functions measured using the magnetic bearings, Campbell diagram, and touchdown bearing drop test results.

This paper investigates the impact of liquid presence in air on the leakage and rotordynamic coefficients of a long (length-to-diameter ratio L/D = 0.747) teeth-on-stator labyrinth seal. The test fluid is a mixture of air and silicone oil (PSF-5cSt). Tests are carried out at inlet pressure P i = 62.1 bars, three pressure ratios from 0.21 to 0.46, three speeds from 10 to 20 krpm, and six inlet liquid volume fractions (LVFs) from 0% to 15%. Complex dynamic-stiffness coefficients H ij are measured. The real parts of H ij are too frequency dependent to be fitted by frequency-independent stiffness and virtual-mass coefficients. Therefore, this paper presents frequency-dependent direct stiffness K Ω and cross-coupled stiffness k Ω . The imaginary parts of H ij produce frequency-independent direct damping C. Test results show that, under both pure- and mainly air conditions, the leakage mass flowrate m ˙ of the test seal steadily increases as inlet LVF increases. K Ω is negative under all test conditions, and the magnitude of K Ω increases as inlet LVF increases, leading to a larger negative centering force on the associated compressor rotor. Under pure-air conditions, k Ω is a small negative value. Injecting oil into the air increases k Ω slightly and make the magnitude of k Ω closer to zero. Under mainly air conditions, increasing inlet LVF from 2% to 15% has little impact on k Ω . C normally increases as inlet LVF increases. The value of the effective damping C eff = C − k Ω /Ω near 0.5 ω is of significant interest to the system stability since an unstable centrifugal compressor may precess at approximately 0.5 ω . Ω denotes the excitation frequency. The oil presence in the air has little impact on the value of C eff near 0.5 ω . Also, the liquid presence does not change the insensitiveness of m ˙ , K Ω , k Ω , C, and C eff to change in ω ; i.e., under both pure- and mainly air conditions, changes in ω has little impact on m ˙ , K Ω , k Ω , C, and C eff .

This paper presents an efficient methodology to build a modal solution emulator for the probabilistic study of geometrically mistuned bladed rotors by using the newly developed localized-Galerkin multifidelity (LGMF) modeling and eigensolution reanalysis (ER) with the symmetric successive matrix inversion (SSMI) methods. The key idea of the mistuned blade emulator is to establish a reduced functional relationship between the stochastic geometric variations and the disturbed modal responses. The prediction accuracy of an emulator generally depends on how many training samples of modal solutions are available and how well the potential modal switching due to stochastic mistuning is captured. To reduce the computational costs of generating training samples without sacrificing accuracy, this paper introduces the collaborative framework of the new approaches of multifidelity (MF) modeling and ER. The proposed framework is demonstrated for its computational benefits with several numerical examples including the point-cloud scanned mistuned blade problem.

Interest in small-scale turbines is growing mainly for small-scale power generation and energy harvesting. Conventional bladed turbines impose manufacturing limitations and higher cost, which hinder their implementation at small scale. This paper focuses on experimental and numerical performance investigation of Tesla type turbines for micro power generation. A flexible test rig for Tesla turbine fed with air as working fluid has been developed, of about 100 W net mechanical power, with modular design of two convergent-divergent nozzles to get subsonic as well as supersonic flow at the exit. Seals are incorporated at the end disks to minimize leakage flow. Extensive experiments are done by varying design parameters such as disk thickness, gap between disks, radius ratio, and outlet area of exhaust with speeds ranging from 10,000 rpm to 40,000 rpm. A quasi-one-dimensional (1D) model of the whole setup is created and tuned with experimental data to capture the overall performance. Major losses, ventilation losses at end disks, and nozzle and exhaust losses are evaluated experimentally and numerically. Effect of design parameters on the performance of Tesla turbines is discussed.

In modern gas turbines, endwall contouring (EWC) is employed to modify the static pressure field downstream of the vanes and minimize the growth of secondary flow structures developed in the blade passage. Purge flow (or egress) from the upstream rim-seal interferes with the mainstream flow, adding to the loss generated in the rotor. Despite this, EWC is typically designed without consideration of mainstream–egress interactions. The performance gains offered by EWC can be reduced, or in the limit eliminated, when purge air is considered. In addition, EWC can result in a reduction in sealing effectiveness across the rim seal. Consequently, industry is pursuing a combined design approach that encompasses the rim-seal, seal-clearance profile, and EWC on the rotor endwall. This paper presents the design of and preliminary results from a new single-stage axial turbine facility developed to investigate the fundamental fluid dynamics of egress–mainstream flow interactions. To the authors' knowledge, this is the only test facility in the world capable of investigating the interaction effects between cavity flows, rim seals, and EWC. The design of optical measurement capabilities for future studies, employing volumetric velocimetry (VV) and planar laser-induced fluorescence (PLIF), is also presented. The fluid-dynamically scaled rig operates at benign pressures and temperatures suited to these techniques and is modular. The facility enables expedient interchange of EWC (integrated into the rotor bling), blade-fillet and rim-seal geometries. The measurements presented in this paper include: gas concentration effectiveness and swirl measurements on the stator wall and in the wheel-space core; pressure distributions around the nozzle guide vanes (NGV) at three different spanwise locations; pitchwise static pressure distributions downstream of the NGV at four axial locations on the stator platform.

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 three-dimensional (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 (FE) structural model to produce 3D elastic deformation fields in the bearing pads. Solutions of the governing equations delivers the operating film thickness, required flowrate, and 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 subsurface temperature are benchmarked against published test data for a centrally pivoted eight-pad TPTB with 267 mm in outer diameter (OD) 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 flowrate 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.

Flexure Pivot® Journal Bearings (FPJBs) have typically been used in small high-speed applications such as Integrally Geared Compressors (IGCs) and multistage high-speed compressors, where the temperature management and the rotordynamic stability of the machine are the main targets. Nevertheless, the need for high-speed applications may also be applicable to large compressors and for this reason a large 280mm diameter four-pad FPJB with L/D=0.7 has been designed, built and tested by the Authors. The test facility is a novel rig, set up at the University of Pisa, that includes a floating test bearing and a rigid rotor supported by two stiff rolling element bearings. Both static and dynamic loads are applied through hydraulic actuators, capable of 270kN static and 40kN overall dynamic load. The instrumentation can measure all the relevant test boundary conditions as well as the static and dynamic quantities that characterize the bearing performance. This paper presents the results from a test campaign conceived to explore not only the design conditions (7000rpm rotational speed and 0.75MPa unit load) but also the sensitivity to the unit load (from 0.2MPa minimum load up to 2.2MPa maximum load) as well as the oil flow. The results are discussed and compared with predictions from an existing numerical code.

The performance analysis of mixed-exhaust turbofan engine with multi-annular rotating detonation duct burner is conducted for the first time, considering that the flow path of the bypass duct is ideal for a rotating detonation combustor. The configuration of the multi-annular rotating detonation combustor is constructed aiming at the advantages of a wider operation range and uniform outlet parameters over the single-annular one. Then, a parametric analysis model of the mixed-exhaust turbofan engine with a rotating detonation duct burner is developed. Thereafter, the effects of duct burner parameters on the engine performance and operating characteristics are investigated. The mixed-exhaust turbofan engine with a rotating detonation duct burner shows superior overall performance to that of one with an isobaric afterburner over a wide operation range. The separate-exhaust rotating detonation duct burner can hold characteristics that are higher to those of the mixed-exhaust one at lower values of fan pressure ratio, while the mixed-exhaust one corresponds to lower values of turbine inlet temperature. When the rotating detonation duct burner is "on", the low-pressure rotor operating line moves toward the surge line on the low corrected shaft speed side but away from the surge line on the high corrected shaft speed side.

Centrifugal compressors can suffer from rotordynamic instability. While individual components (e.g., seals, shrouds) have been previously investigated, an integrated experimental or analytical study at the compressor system level is scarce. For the first time, non-axisymmetric pressure distributions in a statically eccentric shrouded centrifugal compressor with eye-labyrinth seals have been measured for various eccentricities. From the pressure measurements, direct and cross-coupled stiffness coefficients have been determined. Thus, the contributions of the pressure perturbations in the shroud cavity and labyrinth seals have been simultaneously investigated. The cross-coupled stiffness coefficients in the shroud and labyrinth seals are both positive and one order of magnitude larger than the direct stiffness coefficients. Furthermore, in the tested compressor, contrary to the common assumption, the cross-coupled stiffness in the shroud is 2.5 times larger than that in the labyrinth seals. Thus, not only eye-labyrinth seals but also shrouds need to be considered in rotordynamic analysis.

The paper provides design and performance data for two envisaged year-2050 engines: a geared high bypass turbofan for intercontinental missions and a contra-rotating pusher open rotor targeting short to medium range aircraft. It defines component performance and cycle parameters, general arrangements, sizes and weights. Reduced thrust requirements reflect expected improvements in engine and airframe technologies. Advanced simulation platforms have been developed to model the engines and details of individual components. The engines are optimised and compared with 'baseline' year-2000 turbofans and an anticipated year-2025 open rotor to quantify the relative fuel-burn benefits. A preliminary scaling with year-2050 'reference' engines, highlights trade-offs between reduced specific fuel consumption (SFC) and increased engine weight and diameter. These parameters are converted into mission fuel burn variations using linear and non-linear trade factors. The final turbofan has an optimised design-point bypass ratio of 16.8, and a maximum overall pressure ratio of 75.4, for a 31.5% TOC thrust reduction and a 46% mission fuel burn reduction per passenger kilometre compared to the respective 'baseline' engine-aircraft combination. The open rotor SFC is 9.5% less than the year-2025 open rotor and 39% less than the year-2000 turbofan, while the TOC thrust increases by 8% versus the 2025 open rotor, due to assumed increase in passenger capacity. Combined with airframe improvements, the final open rotor-powered aircraft has a 59% fuel-burn reduction per passenger kilometre relative to its baseline.

This paper deals with the estimation of forcing function, modal damping and mistuned modal stiffnesses in a bladed rotor. Previous research on parameter estimation in a mistuned bladed rotor relies on the knowledge of the forcing function as well as the vibration data. This paper presents two novel approaches. The first approach relies on knowledge of both the forcing and vibration data. The parameters are treated as states of the system and an augmented state space model is created. Unscented Kalman Filter is then used on the steady state data to estimate the parameters. The second approach eliminates the dependence on forcing data. Both the forcing and parameters are now treated as states of the system to construct an augmented state space model. Unscented Kalman Filter is then used on transient vibration data for estimation. Numerical results are presented for a simple model of a mistuned bladed rotor which considers a single mode of vibration per blade.

The ingress of hot annulus gas into stator-rotor cavities is an important topic to engine designers. Rim-seals reduce the pressurised purge required to protect highly-stressed components. This paper describes an experimental and computational study of flow through a turbine chute seal. The computations - which include a 360º domain - were undertaken using DLR TRACE's time-marching solver. The experiments used a low Reynolds number turbine rig operating with an engine-representative flow structure. The simulations provide an excellent prediction of cavity pressure and swirl, and good overall agreement of sealing effectiveness when compared to experiment. Computation of flow within the chute seal showed strong shear gradients which influence the pressure distribution and secondary-flow field near the blade leading edge. High levels of shear across the rim-seal promote the formation of largescale structures at the wheel-space periphery; the number and speed of which were measured experimentally and captured, qualitatively and quantitatively, by computations. A comparison of computational domains ranging from 30º to 360º indicate that steady features of the flow are largely unaffected by sector size. However, differences in large-scale flow structures were pronounced with a 60º sector and suggest that modelling an even number of blades in small sector simulations should be avoided.

This paper presents experimental and computational results using a 1.5-stage test rig designed to investigate the effects of ingress through a double radial overlap rim-seal. The effect of the vanes and blades on ingress was investigated by a series of carefully-controlled experiments: firstly, the position of the vane relative to the rim seal was varied; secondly, the effect of the rotor blades was isolated using a disc with and without blades. Measurements of steady pressure in the annulus show a strong influence of the vane position. The relationship between sealing effectiveness and purge flow-rate exhibited a pronounced inflexion for intermediate levels of purge; the inflexion did not occur for experiments with a bladeless rotor. Shifting the vane closer to the rim-seal, and therefore the blade, caused a local increase in ingress in the inflexion region; again this effect was not observed for the bladeless experiments. Unsteady pressure measurements at the periphery of the wheel-space revealed the existence of large-scale pressure structures (or instabilities) which depended weakly on the vane position and sealing flow rate. These were measured with and without the blades on the rotor disc. In all cases these structures rotated close to the disc speed.

Labyrinth seals on both rotor casing and blade tip as an effective method to control the leakage flow rate of the shroud and improve aerodynamic performances in a transonic turbine stage are investigated in the present study. Compared to the case without the labyrinth seal structure, the cases with three different types of sealing teeth have been shown to reduce significantly the tip leakage flow by computational simulations. When the gap is 1.4mm, the application of the double-side sealing teeth obtains the maximum turbine efficiency improvement of 1.4%, and the relative leakage flow rate "m" _"leakage" "/" "m" _"passage" is reduced from 3.4% to 1.3%. Although the sealing structures increase the flow loss inside the shroud, they reduce the momentum mixing of the shroud leakage flow with the mainstream at the exit section of the cavity. Therefore, the circumferential distribution of leakage velocity in the cavity is changed, and then the distribution of high-loss zones at the turbine outlet is also altered. Furthermore, the double-side seal improves the leakage-vortex loss more effectively than the passage-vortex loss at the rotor outlet section, which is associated with the blockage effect of tip leakage flow caused by the sealing structure. In addition, it has also been found that with a larger gap at tip, the double-side seal has better effects of reducing the leakage flow and improving the aerodynamic performance in the transonic turbine stage.

1/2X forward whirl repeatedly occurred after a test rotor spinning at 5,800 rpm was dropped onto ball bearing type auxiliary bearings AB, utilized as a backup for magnetic bearings. The measured contact forces that occurred between the rotor and the auxiliary bearing during the ½X subsynchronous vibration were about thirteen times larger than the static reaction force. The vibration frequency coincided with the rotor-support system natural frequency with the rotor at rest on the auxiliary bearing AB, an occurred at ½ of the rotor spin speed when dropped. The test rig provided measurements of rotor-bearing contact force, rotor orbit (vibrations), and rotational speed during rotor drop events. A simulation model was also developed and demonstrated that parametric excitation in the form of a Mathieu Hill model replicated the measured 1/2X forward whirl vibrations. The simulation model included a nonlinear, elastic-thermal coupled, ball bearing type auxiliary bearing model. The transient model successfully predicted the 1/2X vibration when the rotor was passing 5800RPM as well, and the simulation results quantitatively agreed well with the test results in the frequency domain. Several approaches for mitigating the 1/2X forward whirl were presented such as adding an elastomer O-ring or waviness spring in the AB support system. Measurements confirmed that adding AB dampers effectively mitigated the ½ subsynchronous forward whirl and significantly reduced the contact forces.

Blade mounted strain gages are vital during rig and engine development to ensure safe engine operation. However, they also enable a change in dynamics of integrally bladed rotors (IBR). State-of-the-art IBR dynamic response predictions are accomplished using as-manufactured models (AMM) generated via optical measurements and mesh morphing. Two AMM finite element models (FEMs) are created of a 20 bladed IBR. One FEM has no strain gages, where the second FEM includes strain gages on blades. Traditionally, strain gages and lead wires are treated as the same material property as the IBR. It will be shown that the inclusion of strain gages in AMM’s using this method changes the IBR’s mistuning. An alternative AMM approach is developed that changes the material properties of the finite elements attributed to the strain gages. The predicted mistuning for each AMM is accomplished using the Fundamental Mistuning Model (FMMID), where the mistuning will be compared to both Traveling Wave Excitation (TWE) experiments and a rotating compressor rig. Findings show mistuning predictions of the non-strain gaged AMM compare far better to the experiments compared to the inclusion of the strain gages in the AMM. Additionally, altering material properties of the strain gages in the AMM improves mistuning prediction compared to treating the strain gages as the parent IBR material. Therefore, AMM should be acquired using clean, non-strain gaged rotors or the material properties of strain gaged elements need to be altered to more accurately model the component.