ASME Conference Presenter Attendance Policy and Archival Proceedings

2017;():V07BT00A001. doi:10.1115/GT2017-NS7B.

This online compilation of papers from the ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition (GT2017) represents the archival version of the Conference Proceedings. According to ASME’s conference presenter attendance policy, if a paper is not presented at the Conference by an author of the paper, the paper will not be published in the official archival Proceedings, which are registered with the Library of Congress and are submitted for abstracting and indexing. The paper also will not be published in The ASME Digital Collection and may not be cited as a published paper.

Commentary by Dr. Valentin Fuster


2017;():V07BT33A001. doi:10.1115/GT2017-63035.

Rotor lifetime and safety primarily depend on the level of rotor vibration. In order to avoid unwanted consequences for the plant due to rotor damage and to meet the highest requirements of design reliability, accurate rotor dynamic predictions are mandatory. Having the correct rotor model is a critical issue in dynamics prediction. Often research activities are focused only on the rotor-bearing system analysis. However, generally, the whole system, which includes the rotor, bearings, casing and structural supports should be considered. Special attention should be paid to the influence of structural supports which reveals when the rotor is supported by ball bearings because of low damping and high bearing stiffness.

The approach presented in this paper allows us to simulate the influence of structural supports on rotor dynamics response and as a result, the full picture of rotor-bearing-support system resonances can be analyzed to avoid potential problems. The methodology is based on support vibrations modal reduction technics. According to the approach, the natural frequencies and their mode shapes should be calculated for the separate support structure applying a three-dimensional finite element model and the relative displacements at bearing location points are measured. Supports’ normalized modal characteristics (modal mass and modal stiffness) for each vibration mode should then be imported in a rotor dynamics algorithm for rotor unbalance response analysis.

The approach allows for simulation of different types of support structures such as bearing pedestals, steel foundations, tabletop-type foundation, frame and pipe supports of arbitrary geometry, and so on. Validation based on the Jeffcott rotor model is presented. The current methodology has been applied to a single-stage compressor’s rotor-bearing-support system which was manufactured and commissioned. The results of the simulations are discussed.

Commentary by Dr. Valentin Fuster
2017;():V07BT33A002. doi:10.1115/GT2017-63142.

In the design phase of developing a rotating machine, it is important to consider the effect that the supporting structure has on the rotordynamic behavior of the system. The American Petroleum Institute’s (API) Standard Paragraphs state that if the support stiffness is greater than 3.5 times the bearing oil film stiffness, the designer may omit the supports from the rotordynamic analysis. As discussed in this paper, there is concern that machines operating near the second critical speed may not be adequately modeled using the rigid support assumption allowed by API. Due to the suspected influence of support dynamics on problem machines in industry, this paper investigates the effectiveness of the support to bearing stiffness ratio threshold of 3.5. A Jeffcott rotor model is used to capture the effect of the support on the separation margin and amplification factors of the first and second critical speeds. The trends are then validated using numerical models of two case studies. Results show that the API support stiffness ratio of 3.5 has limitations as a rigid support threshold and should be used with caution when the second critical speed is near a separation margin boundary. The paper proposes an addendum to the current API specification intended to reduce the risk of separation margin encroachment due to a rigid support assumption. Unlike other papers discussing the influence of flexible supports on rotating machinery, this investigation studies the effects at API’s support stiffness ratio of 3.5 and compares them to a rigid support system.

Topics: Petroleum , Stiffness
Commentary by Dr. Valentin Fuster
2017;():V07BT33A003. doi:10.1115/GT2017-63459.

The long length of sub-sea Electric Submersible Pumps (ESPs) requires a large amount of annular seals. Loading caused by gravity and housing curvature changes the Static Equilibrium Position (SEP) of the rotor in these seals. This analysis predicts the SEP due to gravity and/or well curvature loading. The analysis also interfaces displays the rotordynamics around the SEP.

A static and rotordynamic analysis is presented for a previously studied ESP model. This study differs by first finding the SEP and then performing a rotordynamic analysis about the SEP. Predictions are shown in a horizontal and a vertical orientation. In these two configurations, viscosities and clearances are varied through 4 cases: 1X 1cP, 3X 1cP, 1X 30cP, and 3X 30cP.

In a horizontal, straight-housing position, the model includes gravity and buoyancy on the shaft. At 1cP-1X and 1cP-3X, the horizontal statics show a moderate eccentricity ratio for the shaft with respect to the housing. With 30cP-1X, the predicted static eccentricity ratio is low at 0.08. With 30cP-3X, the predicted eccentricity ratio increases to 0.33.

Predictions for a vertical case of the same model are also presented. The curvature of the housing is varied in the Y-Z plane until rub or close-to-wall rub is expected. The curvature needed for a rub with a 1X 1cP fluid is 7.5 degrees of curvature. Curvature has little impact on stability. With both 1X 30cP and 3X 30cP, the maximum curvature for a static rub are over 25 degrees of curvature. Both 1X 30cP and 3X 30cP remain unstable with increasing curvature.

Commentary by Dr. Valentin Fuster
2017;():V07BT33A004. doi:10.1115/GT2017-63926.

Rotor systems carried in transportation system or under seismic excitations are considered to have a moving base. The objective of this paper is to develop a general model for flexible rotor systems subjected to time-varying base excitations and study the direct effects of angular base motions on the dynamic behaviors of a simple rotor. The model is developed based upon finite element method and Lagrange’s equation. Two groups of Euler angles are introduced to describe the rotation of the rotor and the base, respectively. Six types of base motions are considered in the model. In the numerical simulations, three types of angular base motions (pitching, rolling and yawing) are considered and assumed to be sinusoidal varying with time. The effects of base angular amplitudes, base frequency and rotation speed on the system dynamic behaviors are discussed in detail. It is shown that pitching and yawing have a great influence on the response amplitudes and the shape of the rotor orbits. Especially, resonances occur when the base frequency meets the natural frequencies. The FFT and waterfall plots of the disk horizontal and vertical vibrations are marked with multiplications of the base frequency and sum and difference tones of the rotating frequency and the base frequency.

Commentary by Dr. Valentin Fuster
2017;():V07BT33A005. doi:10.1115/GT2017-64206.

Hybrid bump-metal mesh foil bearings (HB-MFBs) are novel gas foil bearings (GFBs) that comprise foil strips and metal mesh blocks in bearing substructure. HB-MFBs have several advantages over previous GFBs, such as high structural damping, more precise size, dimensional stability, and highly efficient cooling management. This study designed and manufactured HB-MFBs and bump-type foil bearings (BFBs) with identical diameters and bearing clearances to compare their rotordynamic performance in a test rig with a rigid rotor supported by two GFBs and driven by an impulse turbine. The rotordynamic performance of the bearings in terms of mesh density, unbalance mass, and bearing clearance were measured and discussed by comparing the experimental results of the two types of test bearings. Experimental results show that the HB-MFBs can efficiently suppress the motion amplitude of subsynchronous vibrations of a rotor-bearing system at high rotational speed, although the added unbalance mass and bearing clearance vary in a large region.

Commentary by Dr. Valentin Fuster
2017;():V07BT33A006. doi:10.1115/GT2017-64353.

Aiming at the misaligned problems of high-speed flexible multi-supported rotor system, considering the structural characteristics and load characteristics of the rotor, the unbalanced excitation of the rotor with misalignment is presented and quantitatively described. The mechanical model of the high-speed flexible rotor system with multi-support under misaligned excitation is established. Based on the finite element method, the dynamic equation of the rotor system is given and the dynamic response characteristics of rotor systems are studied. The results show that the misalignment for the highspeed multi-support flexible rotor system can not only lead to 2X excitation and support stiffness nonlinearity, but also bring additional unbalanced excitation to the rotor system. The 2X frequency component is one typical feature for the rotor system with bearing misalignment. The vibration response of the rotor showed a trend of “increased slowly first, then reduced quickly as the rotation frequency increased”, and it turns to be more obvious with the increasing of the nonlinear stiffness and unbalance.

Commentary by Dr. Valentin Fuster
2017;():V07BT33A007. doi:10.1115/GT2017-64369.

Structural topology optimization is an innovative approach in turbomachinery to satisfy the increasing demand for higher rotational speeds, light components and optimized natural frequencies, with a remarkable economic impact. Although this approach has never been extensively applied before to rotating machines, it is very promising for the mechanical optimization of rotor and stator components. This approach enables the creation of complex three-dimensional geometries, which are usually difficult or impossible to be built using traditional manufacturing methods. Thanks to innovative technologies and to the use of innovative materials, it is now possible to effectively exploit topology optimization. It allows to change the topology of the structures, significantly improving material distribution within a given design space for a given set of boundary conditions and loads. In this work, the authors have deeply investigated the applicability of topology optimization to the fields of turbomachinery and rotordynamics.

Commentary by Dr. Valentin Fuster
2017;():V07BT33A008. doi:10.1115/GT2017-64816.

It is often desirable to identify the critical components that are active in a particular mode shape or an operational deflected shape (ODS) in a complex rotordynamic system with multiple rotating groups and bearings. The energy distributions can help identify the critical components of a rotor bearing system that may be modified to match the design requirements. Although the energy expressions have been studied by researchers in the past under specific limited conditions, these expressions require computing the displacements and velocities of all degrees of freedom over one full cycle. They do not address the overall time-dependency of the energies and energy distributions, and their effect on the interpretation of a mode shape or an ODS. Moreover, a detailed finite element formulation of these energy expressions including the effects of anisotropy, skew-symmetric stiffness, viscous and structural damping have not been identified by the authors in the open literature. In this article, a detailed account of orbit characteristics and planarity for isotropic and anisotropic systems is presented. The effect of orbit characteristics on the energy expressions is then discussed. An elegant approach to obtaining time-dependent kinetic and strain energies of a mode shape or an ODS directly from the structural matrices and complex eigenvectors/displacement vectors is presented. The expressions for energy contributed per cycle by various types of damping and the destabilizing skew-symmetric stiffness that can be obtained in a similar way are also shown. The conditions under which the energies and energy distributions are time-invariant are discussed. An alternative set of energy expressions for isotropic systems with the degrees of freedom reduced by half is also presented.

Commentary by Dr. Valentin Fuster
2017;():V07BT33A009. doi:10.1115/GT2017-64954.

The exploration of new aero-engine configurations drives unseen and complex dynamic behavior which can only be captured accurately with enhanced modeling techniques. In an earlier publication, it was established that it is possible to analyze large engine models using high-fidelity two-dimensional (2D) axisymmetric harmonic and three-dimensional (3D) shell and solid elements. This finding stands in contrast to the relatively crude one-dimensional (1D) model simplifications that were introduced several decades ago. While motivated by limited computing power and easily obtained gyroscopic terms, these models are still common in the industry today. In spite of staggering advances in computation, however, said enhanced finite element rotor models are still considered to be quite large. When transitioning from the traditional 1D to the fully 3D rotor model, for example, one encounters an increase in model size of three orders of magnitude. This motivates the use of model reduction techniques such as the External Superelement (SE) which is obtained by component mode synthesis (CMS). The External SE represents a structural component by its physical attachment points, strategically selected interior grid points, and a linear combination of its dynamic modes. Its advantages are reduced computational cost, the ability to solve very large problems, the protection of intellectual property, and the enablement of a modular model description that promotes parallel processing as well as the utilization of high performance computing (HPC). In this paper, the analysis of a realistic aircraft engine is presented in which its rotating structures are modeled with high-fidelity 3D solid/shell elements. The dynamics of the engine assembly are solved using modal analysis and External SE technology with the goals to reduce wall time and improve efficiency. A detailed comparison of wall time is presented to quantify the associated performance gain.

Commentary by Dr. Valentin Fuster
2017;():V07BT33A010. doi:10.1115/GT2017-65040.

Many high-speed, rotating machines across a wide range of industrial applications depend on fluid film bearings to provide both static support of the rotor and to introduce stabilizing damping forces into the system through a developed hydrodynamic film wedge. Reduced oil supply flow rate to the bearings can cause cavitation, or a lack of a fully developed film layer, at the leading edge of the bearing pads. Reducing oil flow has the well-documented effects of higher bearing operating temperatures and decreased power losses due to shear forces. While machine efficiency may be improved with reduced lubricant flow, little experimental data on its effects on system stability and performance can be found in the literature. This study looks at overall system performance of a test rig operating under reduced oil supply flow rates by observing steady-state bearing performance indicators and baseline vibrational response of the shaft. The test rig used in this study was designed to be dynamically similar to a high-speed industrial compressor. It consists of a 1.55 m long, flexible rotor supported by two tilting pad bearings with a nominal diameter of 70 mm and a span of 1.2 m. The first bending mode is located at approximately 5,000 rpm. The tiling-pad bearings consist of five pads in a vintage, flooded bearing housing with a length to diameter ratio of 0.75, preload of 0.3, and a load-between-pad configuration. Tests were conducted over a number of operating speeds, ranging from 8,000 to 12,000 rpm, and bearing loads, while systematically reducing the oil supply flow rates provided to the bearings under each condition. For nearly all operating conditions, a low amplitude, broadband subsynchronous vibration pattern was observed in the frequency domain from approximately 0–75 Hz. When the test rig was operated at running speeds above its first bending mode, a distinctive subsynchronous peak emerged from the broadband pattern at approximately half of the running speed and at the first bending mode of the shaft. This vibration signature is often considered a classic sign of rotordynamic instability attributed to oil whip and shaft whirl phenomena. For low and moderate load conditions, the amplitude of this 0.5x subsynchronous peak increased with decreasing oil supply flow rate at all operating speeds. Under the high load condition, the subsynchronous peak was largely attenuated. A discussion on the possible sources of this subsynchronous vibration including self-excited instability and pad flutter forced vibration is provided with supporting evidence from thermoelastohydrodynamic (TEHD) bearing modeling results. Implications of reduced oil supply flow rate on system stability and operational limits are also discussed.

Commentary by Dr. Valentin Fuster

Structural Mechanics, Vibration and Damping

2017;():V07BT35A001. doi:10.1115/GT2017-63027.

Blades with a friction damper have been used in a steam turbine and a gas turbine to improve the blade reliability. In particular, for a gas turbine blade of the upstream stage, under-platform dampers have been widely used, where the damper pieces with various geometries are inserted into the platforms of the adjacent blades. The damper piece is designed so that its surface contacts the platform surface uniformly. However, the contact conditions of the damper piece (in other words, the equivalent stiffness and the damping caused by the damper piece) may change appreciably blade by blade because of the likes of manufacturing tolerance, blade deformation in operation, and wear of the damper piece. Therefore, it is essential to consider the mistuning effect caused by the variation of the contact condition of the damper piece in evaluating the vibration response of the bladed disk with the under-platform damper. In this study, a mistuned bladed disk with under-platform dampers is represented by the equivalent spring-mass model. Frequency response analysis and random response analysis are carried out using the direct method and Monte Carlo simulation. Carrying out an extensive parametric study, the effect of the variation of the contact condition caused by the damper piece on the vibration response of the bladed disk is clarified.

Topics: Dampers , Vibration , Disks
Commentary by Dr. Valentin Fuster
2017;():V07BT35A002. doi:10.1115/GT2017-63138.

The Blade Tip Timing method (BTT) is a well-known approach permitting individual blade vibration behavior characterization. The technique is becoming increasingly popular among turbomachinery vibration specialists. Its advantages include its non-intrusive nature and its capability of being used for long-term monitoring, both in on-line and offline analysis. However, the main drawback of BTT is frequency aliasing.

Frequency aliasing effects in tip timing can be reduced by means of the application of different methods from digital signal analysis that can exploit the non-uniform nature of the data sampled by BTT. This non-uniformity is due to the fact that an optimization of the circumferential distribution of BTT probes is usually required in order to improve the data quality for targeted modes of blade vibration and/or orders of excitation.

The BTT data analysis methods considered in this study are the non-uniform Fourier transform, the minimum variance spectrum estimator approach, a multi-channel technique using in-between samples interpolation, the Lombe-Scargle periodogram and an iterative variable threshold procedure. These methods will be applied to measured data representing quite a large scope of events occurring during gas-turbine compressor operation, e.g. synchronous engine order resonance crossing, rotating stall, suspected limit-cycle oscillations.

Finally, the frequency estimates obtained from all these methods will be summarized.

Topics: Blades
Commentary by Dr. Valentin Fuster
2017;():V07BT35A003. doi:10.1115/GT2017-63193.

The potential of intentional mistuning to reduce the maximum forced response is analyzed within the development of an axial turbine blisk for ship diesel engine turbocharger applications. The basic idea of the approach is to provide an increased aerodynamic damping level for particular engine order excitations and mode shapes without any significant distortions of the aerodynamic performance. The mistuning pattern intended to yield a mitigation of the forced response is derived from an optimization study applying genetic algorithms. Two blisk prototypes have been manufactured a first one with and another one without employing intentional mistuning. Hence, the differences regarding the real mistuning and other modal properties can be experimentally determined and evaluated as well. In addition, the experimental data basis allows for updating structural models which are well suited to compute the forced response under operational conditions. In this way, the real benefit achieved with the application of intentional mistuning is demonstrated.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A004. doi:10.1115/GT2017-63200.

Although the research in non-intrusive techniques for the measurement of vibration have made major progress since the beginning in the 1960’s, they are still mainly used as additional tool to the common strain gauges. Therefore, there is still a great deal of interest in the improvement of such non-contact vibration measurement techniques, to replace the intrusive ones with alternative techniques. One possibility to monitor all blades at once is blade tip-timing. The probes for a blade tip-timing measurement system are mounted circumferentially in the engine casing to log the passing times of the rotor blades. These logged time data will be compared with theoretically calculated passing times. The deviation between measured and calculated passing times can be transformed to blade displacement values. In recent years, several methods to analyse the acquired vibration data have been developed and improved. They are directed to evaluate synchronous and asynchronous blade vibration events. This paper focuses on the identification of asynchronous vibrations on rotor blades using blade tip-timing. Taking the data from all probes into account gives an opportunity to determine the vibration of each single blade. Due to the usage of a research test rig, all measurement data could be acquired in simulated real case operation scenarios. Analysis data were evaluated with a developed post processing routine based on a Fourier transformation algorithm coupled with a least square fitting procedure. Since compressor surge represents one of the most critical non synchronous events during compressor operation, in this paper a special interest is paid to the analysis of compressor surges. Vibration frequencies revealed during surge investigation will be compared with simultaneously measured strain gauge data to ensure the reliability of blade tip-timing measurement and analysis. To explain the results in more detail, the possibility of a blade damaged triggered shift of the blade characteristic frequency is shown. The most promising result of the analysis is the close correlation between the identified vibration frequencies of compressor surge events and the afterwards determined frequency mistuning and crack distributions. Blade damage becomes visible through increasing deviation between characteristic frequencies of different blades as result of multiple surge events. In addition, with the comparison of mean frequency records over each single surge among each other it is possible to restrict the blade damage time. Subsequently, the possibility to develop a process routine to predict blade damage during compressor test series could arise.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A005. doi:10.1115/GT2017-63287.

This paper describes a combined experimental/analytical effort which will provide measurements specifically designed to verify computational tools developed for turbomachinery applications. The hardware used for these measurements is engine-type hardware that will be operated at design speed. The specific hardware to be used is NASA Rotor 67 and the measurements will be performed in the confines of an underground spin pit facility. The experiments are aimed at identifying damping and mistuning properties of the rotor while it rotates at predetermined speed values within the facility. In addition, experiments using a modified Rotor 67 configuration containing added frictional damping elements are described. Light probe and strain gauge data will be obtained in order to compare their individual effectiveness. The response data storage is based on wide bandwidth, low noise signal conditioners used in conjunction with a high sampling-frequency data acquisition system. The rotor can be excited at specific engine-order crossings using air-jets with the number of specific active air-jets and the corresponding force transmitted by each jet estimated from computations. The experimental effort enables the identification of key parameters used in a series of computational tools that have been developed recently. The computational tools include various mistuning and (nonlinear) damping identification methods that have not yet been verified using data obtained from rotating hardware.

Topics: Damping , Design
Commentary by Dr. Valentin Fuster
2017;():V07BT35A006. doi:10.1115/GT2017-63437.

A very detailed experimental analysis at several different rotational speeds was conducted on a simplified blisk to gain in-depth understanding of how the Coriolis effects and their interaction with mistuning evolve with speed to provide a better understanding for future designs. Two different nodal diameter families, characterised by different levels of mistuning, were investigated in greater detail. The blisk dynamics were found to depend both on mistuning levels and speed. Split Campbell diagrams were observed, together with the appearance of Coriolis-induced forward and backward travelling wave modes in the blisk. Three speed ranges characterised by different behaviours were identified at a high level of detail, with a gradual transition from mistuning-dominated behaviour at low speed to Coriolis-dominated features at higher speeds. The evolution of the mode shapes with speed, and the differences between low- and high-mistuning modes were particularly examined. The evolution of the mode shapes with speed, and the differences between low- and high-mistuning modes were particularly examined. An accurate comparison was conducted between the measurement data and finite element results, and confirmed the reliability of the new approach.

Topics: Coriolis force , Disks
Commentary by Dr. Valentin Fuster
2017;():V07BT35A007. doi:10.1115/GT2017-63488.

The reduction of nominal clearances between a rotating bladed-disk and its surrounding casing yields a very significant increase of the overall engine efficiency. However, the smaller the clearances, the higher the risk of structural contacts between static and rotating components that may lead to hazardous interaction phenomena. In particular, at the fan stage of an aircraft engine, impacts between the rotating bladed-disk and the casing may generate forward or backward whirl motions induced by the precession of the shaft axis of rotation. In such specific configuration, an accurate modeling of interaction phenomena requires to account for both centrifugal and gyroscopic effects on the rotor. This contribution addresses the development of efficient reduced-order models of industrial finite element models embedding both centrifugal and gyroscopic effects. Proposed developments are validated on an academic model and are then applied on the finite element model of an aircraft engine fan stage. Results obtained with the academic model underline that the impact of gyroscopic effects on the rotor’s dynamics is essentially related to the frequency split of 1-nodal diameter free-vibration modes of the first modal family. Results presented on the industrial finite element models are limited to a few case studies as a proof-of-concept.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A008. doi:10.1115/GT2017-63628.

Bladed wheel dynamic characterization is a crucial issue to avoid resonance excitations. The test bench presented in this paper was designed to independently excite the wheel sectors with one electromagnetic shaker each blade. Since a wide frequency range (1–10 kHz) is usually considered for bladed wheels, custom electromagnetic devices were designed, and then a closed-loop control software was also implemented. The global mode shapes of the wheel were then reconstructed through subsequent accelerometer measurements on all sectors to evaluate the harmonic response. The main target of the test rig is the reproduction of any operational condition by experimentally simulating an arbitrary number of stator vanes. In this way the response levels of the differently excited modes are measured and the modal damping is optimally quantified by providing a selective excitation of any number of nodal diameters. Preliminary results showed how the test setup actually allows to excite those modes with a specific number of nodal diameters, however, also exposed some difficulties to avoid small load components with different numbers of nodal diameters.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A009. doi:10.1115/GT2017-63629.

The modeling of centrifugal stiffening effects on bladed components is of primary importance in order to accurately capture their dynamics depending on the rotor angular speed. Centrifugal effects impact both the stiffness of the component and its geometry. In the context of the small perturbation framework, when considering a linear finite element model of the component, an assumption typically made in the scientific literature involves a fourth-order polynomial development of the stiffness matrix in terms of the angular speed. This polynomial development may fail to provide an accurate representation of the geometry evolution of a blade. Indeed, the error on the blade-tip displacement associated to the use of a linear finite element model quickly reaches the same order of magnitude as the blade-tip/casing clearance itself thus yielding a 100 % error on the blade-tip/casing clearance configuration. This article focuses on the presentation of a methodology that allows for creating accurate reduced order models of a 3D finite element model accounting for centrifugal stiffening with a very precise description of the blade-tip/casing clearance configuration throughout a given angular speed range. The quality of the obtained reduced order model is underlined before its numerical behaviour in the context of non-linear dynamic simulations be investigated. It is evidenced that the new reduced order model features specific interactions that could not be predicted with a linear model. In addition, results highlight the limitations of numerical predictions made for high angular speeds with a linear model. Finally, a particular attention is paid to the numerical sensitivity of the proposed model. As a downside of its increased accuracy, it is underlined that its computation must be done carefully in order to avoid numerical instabilities.

Topics: Modeling
Commentary by Dr. Valentin Fuster
2017;():V07BT35A010. doi:10.1115/GT2017-63702.

Vibrational resonances of centrifugal compressor and radial inflow turbine impellers are usually identified using either Kushner’s or Singh’s parametric equations in product design and failure analysis. These equations were developed based on positive work accumulated within a certain time period. However, some resonances observed in simulation and testing cannot be understood with those resonance equations.

This paper presents an alternative method to derive vibrational resonance conditions. A new model of general pressure pulsations is developed by taking into account the disturbances resulting from stationary obstacles and rotating blades. Analytical solutions of the forced vibration responses of a rotating disk subjected to different pressure pulsations are then formulated. From the forced responses, both Kushner’s and Singh’s equations can be derived. They can further prove to be equivalent though they focus on different physics.

A general resonance condition is derived from the analytical solutions. This condition is a necessary condition, i.e. all resonances must meet this condition while a system following the condition may or may not be in resonance, depending upon excitation sources. It is noticed that the excitation sources could be related to harmonics due to stationary obstacles, harmonics with combined harmonic orders, or even harmonics to be understood. This general resonance condition can hence provide more “possible resonance points” and assist identifying resonances from more representative modes and more excitation sources. It has been validated by predicting vibrational resonances observed in three centrifugal compressors. This condition has also been successfully employed in the failure analysis and design modification of a radial inflow turbine impeller.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A011. doi:10.1115/GT2017-63752.

We developed a turbo compressor that has water-lubricated bearings driven at 30,000 rpm in a saturation condition, where the ambient pressure is at the saturation point of the discharged lubricant water. Such a saturated water journal bearing is located at both end of the rotor, each of which has a conical part to produce thrust force without another thrust bearing or a thrust collar. The bearings are supported with nonlinear elastomeric O-rings. At rotational speed over 15,000 rpm, the rotor showed many sub-harmonic vibrations that are nonlinear phenomena unpredictable from a linear equation of motion. Instead, a stability analysis with a bifurcation diagram is an effective method to tackle these problems. In this paper, we investigated these rotor vibrations by bifurcation diagrams of the vibrations measured in experiments of saturated water journal bearings. The angular velocity was used as a bifurcation parameter. The bifurcations among synchronous, sub-harmonic, and chaotic vibrations were shown. Next, the nonlinear dynamics of the rotating rigid shaft were analyzed numerically with the nonlinear stiffness obtained by a commercial code that utilizes the two-dimensional Reynolds equation. The dynamic properties of the supporting structure were modeled with a complex stiffness coefficient. The equation of motion of the rotating shaft was solved numerically in a time domain with these dynamic properties. MATLAB Simulink code was built to integrate the equations. As a result, a Hopf bifurcation was found and a sub-harmonic limit cycle appeared spontaneously. The rotational speed and such other properties as the unbalanced force and the damping of the supporting structures were parameterized to investigate the onset and the amplitude of these vibrations. These numerical results agreed well with the experimental results.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A012. doi:10.1115/GT2017-63835.

Current efforts to model multistage turbomachinery systems rely on calculating independent constraint modes for each degree of freedom on the boundary between stages. While this approach works, it is computationally expensive to calculate all the required constraint modes. This paper presents a new way to calculate a reduced set of constraint modes referred to as Fourier constraint modes (FCMs). These FCMs greatly reduce the number of computations required to construct a multistage reduced order model (ROM). The FCM method can also be integrated readily with the component mode mistuning method to handle small mistuning and the pristine rogue interface modal expansion method to handle large and/or geometric mistuning. These methods all use sector level models and calculations, which makes them very efficient. This paper demonstrates the efficiency of the FCM method on a multistage system that is tuned and, for the first time, creates a multistage ROM with large mistuning using only sector level quantities and calculations. The results of the multistage ROM for the tuned and large mistuning cases are compared with full finite element results and are found in good agreement.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A013. doi:10.1115/GT2017-63867.

This paper is focused on the optimization of mistuned blades assembling rearrangement under the forced response. First, in order to avoid the greatly increase of the calculation greatly by the whole circle bladed-disk finite element model, a reduced-order model is developed based on the component mode synthesis. CPU+GPU heterogeneous architecture parallel computation is used to accelerate modal analysis of the disk and blade sectors substructures. Second, a modified ant colony algorithm is applied to the combinatorial optimization to find the optimal rearrangement pattern of bladed-disk assembly. Different from classical algorithm, the individual mistuned information is used to construct heuristic function based on intentional mistuning pattern, which can avoid slow convergence of ant colony algorithm and increase the search speed efficiently. At last, a high-fidelity 3D FEM model with 43 mistuned blades is used to demonstrate the capabilities of the techniques in reducing the maximum displacement resonance response of the bladed-disk system. The numerical simulation showed that this program based on the reduced-order model proposed in this article gained 4.3 speedup compared with ANSYS full model under the scale of 500k nodes. The displacement response amplitude of the blades decreased by 32% with 60 steps (1200 times FEM calculation) by the new optimization method. The physical mechanism of reducing the bladed-disk response is explained by comparing the optimized and worst arrangement patterns. The results clearly demonstrate that the optimized rearrangement pattern of mistuned blades is able to reduce the response amplitude of the forced vibration significantly, and the algorithm proposed in this article is practical and effective.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A014. doi:10.1115/GT2017-63897.

Centrifugal compressor is a piece of key equipment for factories. Among the components of centrifugal compressor, impeller is a pivotal part as it is used to transform kinetic energy to pressure energy. But it usually leads to blade crack or failure as irregular aerodynamic load effect on the blade. Therefore, early crack feature extraction and pattern recognition is important to prevent it from failure. Although time series analysis for monitored signal can be used on feature extraction, incipient weak feature extraction method should be investigated. In this research, pressure pulsation sensors arranged in close vicinity to crack area are used to monitor the blade crack and feature extraction. As there are different kinds of flow interference, the pressure pulsation signal for centrifugal compressor is full of nonlinear characteristics. Therefore, how to obtain the weak information from monitored signal is investigated. Although FFT and envelope analysis have been widely used for rotating equipment, they are not suitable for the determination of incipient crack of a blade as the signal modulation and noise interference. In this research, stochastic resonance is used for the pressure pulsation signal. The results show that it is an effective tool to blade incipient crack classification on centrifugal compressor.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A015. doi:10.1115/GT2017-63972.

Double nodal diameter spectrum (DNDS) method which is used to analyze nodal diameter (ND) components of the vibration modes of impellers with splitters is proposed and its application in quantification of mode localization has been studied. Firstly, ND characteristics of the typical impeller with splitter blades are analyzed by mode shapes and representative subeigenvectors. Secondly, DNDS method is proposed and DNDSs of the representative modes indicate that the tuned modes of impellers with splitter blades contain two ND components. By applying the simplified engine order (EO) excitation in the form of a travelling wave, harmonic response analysis has been carried out by which double nodal diameter vibration characteristics of the structure and the effectiveness of the DNDS method are both validated. Lastly, in terms of quantifying mode localization, the definition of mode localization factor (MLF) is improved based on DNDS. The numerical example proves that the pairing process of choosing the tuned mode corresponding to the mistuned one by utilizing both DNDS and the vibration pattern of blades when calculating the improved MLF could pick out the closest tuned mode to the mistuned one, which has a more explicit physical meaning.

Topics: Impellers , Vibration , Blades
Commentary by Dr. Valentin Fuster
2017;():V07BT35A016. doi:10.1115/GT2017-63980.

Blade tip clearance (BTC) measurement and active clearance control (ACC) have been and continue to be a fundamental concern in turbomachinery, which are closely bound up with the efficiency and reliability. This paper addresses the BTC measurement and ACC experimental study based on eddy current pulse-trigger method (ECPTM). And the implementation of ACC by axial displacement of the blisk is novel and this paper is the first to present the technique. The purpose of this paper is three fold. The first portion of this paper addresses the BTC measurement in different rotating speeds based on the larger scale rig, where a high-bandwidth (100 kHz) eddy current sensor (HECS) is employed. The results show that the relative errors of BTC values are not much bigger than 20%. The result indicates that ECPTM is more generally applicable in the condition where the eddy current sensor (ECS) is insufficient sampling caused by the limit of narrow bandwidth, especially under the high linear velocity condition. The second portion of this paper describes the ACC system where an electro-hydraulic proportional position control system (EHPPCS) is employed as the actuator. EHPPCS has the advantages of small size, fast response, resistance to load stiffness, large output and simple operation, which is widely applicable to the automatic control system of industrial power. This system optimizes the geometry shapes of casing and the blade tips to create a linear relationship of BTC values related to the axial displacement of the rotor. The BTC values can be transferred into axial displacement of the rotor, and then a voltage/current-BTC values characteristic can be obtained by employing EHPPCS in different rotating speeds. Unfortunately, one of the core components of EHPPCS is an overflow valve with a non-linear and time-variable voltage/current-pressure characteristic. Besides, the pressure-axial displacement characteristic of tilting pad thrust bearing is also non-linear. All those non-linear characteristics make it unsatisfactory to use the conventional PID control algorithm to achieve effective control of the system, which cause many difficulties in controlling of axial displacement of the rotor. So the last portion of this paper is the experimental study on ACC based on the above system by adopting sliding mode adaptive control of nonlinear system (SMACNS). The BTC values have been obtained under different outlet pressures by changing the current in different rotating speeds. The results indicate that this approach has nice robustness and smooth controlled quantity, and can overcome the difficulty caused by nonlinearity, parameter uncertainty and load disturbance. And then, the precision verification and error analysis are made. However, this work is a proof-of-concept demonstration using a laboratory setup providing the basis for BTC active control and blade health monitoring (BHM) based on ECS.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A017. doi:10.1115/GT2017-63986.

Generally, turbine blade vibration can be divided into asynchronous vibration and synchronous vibration. Comparing to parameters identification of asynchronous vibration, that of the synchronous vibration is more difficult and needs more sensors. The applicability of the synchronous identification method is more stringent than that of asynchronous identification method. A new method is presented to identify the blade synchronous vibration parameters based on the blade tip-timing (BTT) method and previous achievements in this region. Here, the parameters, such as the frequency of harmonic resonance center, blade vibration amplitude and the initial phase, are obtained by the nonlinear least square fitting algorithm based on relationships between the rotation speed and the blade tip displacement. We call this way as sweep frequency fitting (SFF) method. As the blade is operated at a constant speed that is near the frequency of resonance center, the blade vibration displacement can be obtained by the sensors at different positions, so the blade synchronous vibration Engine Order (EO) can be obtained by the global autoregressive with instrumental variables (GARIV) method. Furthermore the Campbell diagram of blade synchronous vibration can be plotted by the parameters obtained by GARIV method and SFF method. In the experimental study, the parameter identification of blade synchronous vibration is completed and the Campbell diagram of blade vibration is accurately plotted under the excitation of six magnets. Meanwhile, the experimental study and analysis on the harmonic vibration of blade with different numbers of excitation are carried out. The relative deviation of the dynamic frequency of blade between the experimental result and simulation result is less than 1%.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A018. doi:10.1115/GT2017-63999.

Since industrial large-scale models of friction-damped bladed disks for vibration analysis usually comprise numerous degrees of freedom, reduction techniques are required to facilitate the application of frequency and time domain solution methods. Common approaches utilize modal representations of the vibrational behavior considering either fixed, free, or hybrid interface conditions as well as elastic response to either unitary displacements or unitary forces acting on interface degrees of freedom to ensure static completeness. These modes serve as a basis for reduced description of the equation of motion. Often global damping concepts such as Rayleigh damping or hysteretic damping are applied afterwards. If mode-wise damping ratios are known, these can be introduced using modal damping formulation. Provided that variable rotational speed-dependence of the structure is of interest, an expanded speed-independent multi-model reduction basis is needed.

The aim of this paper is to provide a nodal diameter-dependent modal damping approach to account for such damping information in case of variable rotational speed. Therefore, basis transformations between surrogate and multi-model basis are required. Attention will be paid to dealing with linearly dependent bases. Periodic solutions induced by multi-harmonic excitation are sought using a harmonic balance approach. The influence of multi-harmonic excitation onto the vibrational behavior is analyzed, serving as a starting point for nodal diameter-dependent modal damping investigations. Accuracy and scope of the method are finally discussed.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A019. doi:10.1115/GT2017-64023.

For the analysis of essentially nonlinear vibrations it is very important not only to determine whether the considered vibration regime is stable or unstable but also which design parameters need to be changed to make the desired stability regime and how sensitive is the stability of a chosen design of a gas-turbine structure to variation of the design parameters. In the proposed paper, an efficient method is proposed for a first time for sensitivity analysis of stability for nonlinear periodic forced response vibrations using large-scale models structures with friction, gaps and other types of nonlinear contact interfaces. The method allows using large-scale finite element models for structural components together with detailed description of nonlinear interactions at contact interfaces. The highly accurate reduced models are applied in the assessment of the sensitivity of stability of periodic regimes. The stability sensitivity analysis is performed in frequency domain with the multiharmonic representation of the nonlinear forced response amplitudes. Efficiency of the developed approach is demonstrated on a set of test cases including simple models and large-scale realistic blade model with different types of nonlinearities, including: friction, gaps, and cubic elastic nonlinearity.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A020. doi:10.1115/GT2017-64108.

This paper investigates the results of a frequency analysis performed on the blades of the last three compressor stages of two different gas turbines (Case A and B). The axial compressors in A and B have ten and eleven stages, respectively. The studied stages have identical number of blades in both compressors. However turbine B has higher number of upstream vanes before each rotating stage. Turbine B is actually a modified version of A with higher power output. The manufacturer provides acceptable ranges for several natural frequencies of blades of stage No.8 to 10 in case A. One of the purposes of this study is to figure out the logic behind the abovementioned ranges.

FEM has been used in order to determine the natural frequencies of a single blade (for Campbell diagram) and bladed disk (for SAFE diagram). By surveying the results of the Campbell diagrams for blades of case A’s mentioned stages, it is concluded that the manufacturer has obtained the acceptable ranges by considering a 10% difference (at least) between single blade natural frequencies and excitation frequencies (upstream vane passage frequencies (VPF)).

On the other hand, according to Campbell diagram, there is no resonance for these blades within the operational speed while SAFE diagrams show the existence of one resonance mode within the same range. The reason of this contradiction is found to be ignoring the disk stiffness effect on the blades frequencies. A same procedure was also followed to study the critical frequencies of the blades of the last three stages of turbine B’s compressor by SAFE diagrams.

By checking the critical modes, it is concluded that these modes in case B are transferred to one or two modes higher in comparison to A which results in a much better vibrational behavior. This has been acquired by increasing the number of the upstream vanes.

In addition, in case A’s compressor, the blades of the stage No.10 have been designed with far thicker airfoils (approximately 50%) when compared to stage No.8 and 9, even though their other dimensions are almost identical. But, this fault has been corrected in turbine B and the airfoils of all three stages almost have the same thickness. To sum up, although the design of mentioned blades in turbine B looks better and more logical than A, still a more precise look at its stages bladed disk SAFE diagrams reveals another issue. In some references there are some hints that low number of critical nodal diameter (veering region) might cause high level of blade vibration due to mistuning and this means that even in turbine B the design might not be optimal. A cure could be an increase or decrease in the number of upstream vanes in order to have a higher critical nodal diameter.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A021. doi:10.1115/GT2017-64269.

In the turbo-machinery structures with joints the contact pressures at contact interfaces are usually high enough to ensure that the contacting components stay joined and the gross slip does not occur. Nevertheless, the small relative slip over parts of the contact interface, i.e. the micro-slip, contributes significantly to the vibration damping. In the high-fidelity analysis of practical bladed discs the macro-slip model cannot provide sufficient accuracy for the predictive analysis of the properties of the friction damping in the contact interfaces. In this article, numerical studies of micro-slip damping effects is performed using 2D and 3D models of blade root joints. Analysis of hysteresis loops is performed to assess the influence of modelling parameters: choice of reference points, mesh configurations and other physical parameters. The impact of physical parameters, such as the contact geometry, friction coefficient, contact stiffness and tangential and normal loading, on the friction damping are numerically examined. The numerical results give a new insight in the micro-slip friction damping effects.

Topics: Friction , Disks
Commentary by Dr. Valentin Fuster
2017;():V07BT35A022. doi:10.1115/GT2017-64342.

Increasing the efficiency of turbomachines is a major concern as it directly translates into lower environmental impact and improved operational costs. One solution is to reduce the blade-casing operating clearance in order to mitigate aerodynamic losses at the unavoidable cost of increased structural unilateral contact and friction occurrences. In centrifugal compressors, the dynamic behaviour of the structures interacting through unilateral contact and friction is not yet fully understood. In fact, the heat generated during such events may affect the dynamics through thermal stresses.

This paper presents a complete thermomechanical modelling strategy of impeller rotor and casing, and of blade-tip/casing contact events. A fully coupled thermomechanical modal synthesis technique is introduced and applied to turbomachinery-related models. The blisk is reduced via a hybrid modal synthesis technique combining the Craig-Bampton method and the characteristic constraint mode method. The casing model is reduced using an axisymmetric harmonic modal synthesis. Both strategies involve thermomechanical modes embedding thermal dilatation effects. The contact modelling algorithm is then introduced. It handles unilateral contact and friction occurrences together with heating effects. This algorithm uses the above mentioned reduced-order models as input data to avoid CPU-intensive simulations.

The results show that the thermomechanical behaviour of the structures is well preserved by the reduction strategy proposed. Contact simulations on simple cases show qualitative results in accordance with expectations.

Further work is needed in order to validate the strategy based on experimental results. However, this methodology opens the way to extended multiphysics simulations of contact events in turbomachinery.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A023. doi:10.1115/GT2017-64402.

The paper presents a calculation procedure for the design of turbine blades with underplatform dampers. The procedure involves damper “pre-optimization” before the coupled calculation with the blades.

The pre-optimization procedure excludes, since the early design stage, all those damper configurations leading to low damping performance. Pre-optimization involves plotting a design “damper map” with forbidden areas, corresponding to poorly performing damper geometries and admissible design areas, where effective solutions for the damper shape can be explored. Once the candidate damper configurations have been selected, the damper equilibrium equations are solved by using both the multi-harmonic balance (MHB) method, and the direct time integration method (DTI). Direct time integration of the damper dynamic equations is implemented in order to compute the trend of the contact forces in time and the shape of the hysteresis cycles at the different contact points. Based on these trends, the correct number of Fourier terms to represent the contact forces on the damper is chosen. It is shown that one harmonic term together with the static term, are enough in the MHB calculation of a pre-optimized damper.

The proposed method is applied to a test case of a damper coupled with two blades. Experimental forced response functions of the test case with a nominal damper are available for comparison. The purpose of this paper is to show the effectiveness of the “damper maps” in excluding all those damper configurations, leading to undesirable damper behavior and to highlight the strong influence of the blades mode of vibration on the damper effectiveness. From the comparison of dampers with different geometrical parameters, the pre-optimized damper proved to be not only the most effective, in terms of damping capability, but also the one that leads to a faster and more flexible calculation of the damper, coupled with the blades.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A024. doi:10.1115/GT2017-64583.

The component mode synthesis based on the Craig-Bampton method has two strong limitations that appear when the number of the interface degrees of freedom is large. First, the reduced-order model obtained is overweighed by many unnecessary degrees of freedom. Second, the reduction step may become extremely time consuming. Several interface reduction techniques addressed successfully the former problem, while the latter remains open. In this paper we tackle this latter problem through a simple interface-reduction technique based on an a-priory choice of the interface modes. An efficient representation of the interface displacement field is achieved adopting a set of orthogonal basis functions determined by the interface geometry. The proposed method is compared with other existing interface reduction methods on a case study regarding a rotor blade of an axial compressor.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A025. doi:10.1115/GT2017-64636.

Engine fan blade-off (FBO) is an extreme event that could well place the flight safety at risk. When it happens, the engine will experience high-velocity impact at first, and then enter into a “high-power” stage due to huge unbalance before coming to a steady state called “windmilling”. The analytical process for FBO can be split into two phases, one for impact simulation and the other for obtaining the FBO load to pylon. Typically, explicit method with fine mesh finite elements is used in the first phase, and implicit method with coarse meshes is adopted in the second one. In most cases, the only connection between these two analyses may be the unbalance level caused by FBO. More structural responses other than the unbalance level due to fan blade impact are actually ignored in the succeeding implicit analysis. Attempts have been made by Boeing, GE and MSC to integrate these two processes by adding some features in MD Nastran. Yet the intermediate binary files created and the restricted input entries make the integration process quite inflexible.

This paper introduces an explicit-implicit time integration approach for finite element analysis of engine load following an FBO event. The proposed method attempts to connect the two stages more closely, yet in a more flexible manner. In this approach, the engine structural response under FBO obtained from explicit analysis is transferred to the implicit analysis, together with the unbalance level caused by blade loss. The necessity of the approach is discussed, and sensitivity analysis is conducted to understand the factors that play significant roles in the approach. As the models for explicit and implicit analyses are different in mesh sizes and scales, the authors also develop a tool that can interpolate the load information and further, smooth it to fit calculation. Finally, the approach is tested on a full engine model to show its applicability and advantages over the traditional method for load evaluation of FBO event.

Commentary by Dr. Valentin Fuster
2017;():V07BT35A026. doi:10.1115/GT2017-64653.

In this paper a comparison is made between numerical forced response simulations and experimental measurements for two popular Steam Turbine Last Stage Blade (LSB) architectures: a free standing LSB and a single-connected LSB with a mid-span wing (also known as a ‘snubber’). These variants share the same aerodynamic design in operation, i.e. they have the same ‘operating’ geometry. The focus of this study is the level of vibration response induced on the blades by resonance with a non-synchronous excitation. This can reduce the maximum condenser pressure safely attainable by a Steam Turbine during low volume flow (LVF) operation.

The study develops a common method to effectively represent the LVF excitation in FEM harmonic analysis for both free standing and single-connected LSB’s. This is valuable to LSB designers during the initial phase of a new development (when an assessment of the LVF capability is required before experimental measurements have been taken). In addition, the method can be used to evaluate the suitability of an existing LSB design to a revised environment, as it is often the case in retrofit applications.

Topics: Blades
Commentary by Dr. Valentin Fuster
2017;():V07BT35A027. doi:10.1115/GT2017-64814.

Most aircraft turbojet engines consist of multiple stages coupled by means of bolted flange joints which potentially represent source of nonlinearities due to friction phenomena. Methods aimed at predicting the forced response of multi-stage bladed disks have to take into account such nonlinear behavior and its effect in damping blades vibration. In this paper a novel reduced order model is proposed for studying nonlinear vibration due to contacts in multi-stage bladed disks. The methodology exploits the shape of the single-stage normal modes at the inter-stage boundary being mathematically described by spatial Fourier coefficients. Most of the Fourier coefficients represent the dominant kinematics in terms of the well-known nodal diameters (standard harmonics), while the others, which are detectable at the inter-stage boundary, correspond to new spatial small wavelength phenomena named as extra harmonics. The number of Fourier coefficients describing the displacement field at the inter-stage boundary only depends on the specific engine order excitation acting on the multi-stage system. This reduced set of coefficients allows the reconstruction of the physical relative displacement field at the interface between stages and, under the hypothesis of the Single Harmonic Balance Method, the evaluation of the contact forces by employing the classic Jenkins contact element. The methodology is here applied to a simple multi-stage bladed disk and its performance is tested using as a benchmark the Craig-Bampton reduced order models of each single-stage.

Topics: Friction , Flanges , Modeling , Disks
Commentary by Dr. Valentin Fuster
2017;():V07BT35A028. doi:10.1115/GT2017-64877.

Predicting the energy dissipation associated with contact of underplatform dampers remains a critical challenge in turbomachinery blade and friction damper design. Typical turbomachinery blade forced vibration response analyses rely on reduced order models and simplified nonlinear codes to predict blade vibration characteristics in a computationally tractable manner. Recent research has focused on both the model reduction process and simulation of the contact dynamics. This paper proposes two academic turbine blade geometries with coupled underplatform dampers as vehicles by which these model reduction and forced response simulation techniques may be compared. The blades correspond to two types of freestanding turbine blades and demonstrate the same qualitative behavior as more complex industry geometries. The blade geometries are fully described here and analyzed using the same procedure as used for an industry-specific blade. Standard results are presented in terms of resonance frequency, amplitude, and damping across a range of aerodynamic excitation. In addition, the predicted blade vibration characteristics are examined under variations in the contact interface: friction coefficient, damper / platform surface roughness, and damper mass, with relative sensitivities to each term generated. Finally, the effect of the number of modes retained in the reduced order model is studied to uncover patterns of convergence as well as to provide additional sets of standard data for comparison with other model reduction and forced response simulation methods.

Topics: Blades
Commentary by Dr. Valentin Fuster
2017;():V07BT35A029. doi:10.1115/GT2017-64928.

Several experimental apparatus have been designed in the past to evaluate the effectiveness of under-platform dampers. Most of these experimental setups allow to measure the overall damper efficiency in terms of reduction of vibration amplitude in turbine blades. The experimental data collected with these test rigs do not increase the knowledge about the damper dynamics and therefore the uncertainty on the damper behavior remains a big issue. In this paper a different approach to evaluate the damper-blade interaction has been put forward. A test rig has been purposely designed to accommodate a single blade and two under-platform dampers. One side of each damper is in contact with a ground support specifically designed to measure two independent forces on the damper. In this way both the normal and the tangential force components in the damper-blade contact can be inferred. Damper kinematics is rebuilt by using the relative displacement measured between damper and blade. This paper describes the concept behind the new approach, shows the details of the new test rig and discuss the blade frequency response from a new point of view.

Topics: Dampers , Blades
Commentary by Dr. Valentin Fuster
2017;():V07BT35A030. doi:10.1115/GT2017-64973.

This paper extends the Resonance Frequency Detuning vibration reduction approach by analyzing the performance in cases of turbomachinery blade mistuning. A lumped parameter mistuned blade model with included piezoelectric elements is utilized and an analytical solution for frequency sweep excitation is presented and validated using direct numerical integration. A Monte Carlo statistical analysis is then conducted to provide insight regarding vibration reduction performance over a range of parameters of interest such as the degree of blade mistuning, linear excitation sweep rate, damping ratio, and the difference between the open- and short-circuit stiffness states. Vibration reduction is shown to exist across all degrees of blade mistuning as well as the entire range of sweep rates tested. This vibration reduction performance is also maximized for systems with low inherent damping and large electromechanical coupling values.

Topics: Resonance , Blades
Commentary by Dr. Valentin Fuster

Aerodynamic Excitation and Damping

2017;():V07BT36A001. doi:10.1115/GT2017-63008.

This paper presents the results from a research effort on eigenvalue identification of mistuned bladed rotor systems using the Least-Squares Complex Frequency-Domain (LSCF) modal parameter estimator. The LSCF models the frequency response function (FRF) obtained from a vibration test using a matrix-fraction description and obtains the coefficients of the common denominator polynomial by minimizing the least squares error of the fit between the FRF and the model. System frequency and damping information is obtained from the roots of the denominator; a stabilization diagram is used to separate physical from mathematical poles. The LSCF estimator is known for its good performance when separating closely spaced modes, but few quantitative analyses have focused on the sensitivity of the identification with respect to mode concentration. In this study, the LSCF estimator is applied on both computational and experimental forced responses of an embedded compressor rotor in a three-stage axial research compressor. The LSCF estimator is first applied to computational FRF data obtained from a mistuned first-torsion (1T) forced response prediction using FMM (Fundamental Mistuning Model) and is shown to be able to identify the eigenvalues with high accuracy. Then the first chordwise bending (1CWB) computational FRF data is considered with varied mode concentration by varying the mistuning standard deviation. These cases are analyzed using LSCF and a sensitivity algorithm is developed to evaluate the influence of the mode spacing on eigenvalue identification. Finally, the experimental FRF data from this rotor blisk is analyzed using the LSCF estimator. For the dominant modes, the identified frequency and damping values compare well with the computational values.

Topics: Disks , Eigenvalues
Commentary by Dr. Valentin Fuster
2017;():V07BT36A002. doi:10.1115/GT2017-63018.

The aeroelastic prediction of blade forcing is still a very important topic in turbomachinery design. Usually, the wake from an upstream airfoil and the potential field from a downstream airfoil are considered as the main disturbances. In recent years, it became evident that in addition to those two mechanisms Tyler-Sofrin modes, also called scattered or spinning modes, may have a significant impact on blade forcing.

In Schrape et al. [9] it was found that in multi-row configurations not only the next, but also the next but one blade row is very important as it may create a large circumferential forcing variation which is fixed in the rotating frame of reference.

In the present paper a study of these effects is performed on the basis of a quasi 3D multi-row and multi-passage compressor configuration. For the analysis a harmonic balancing code, which was developed by DLR Cologne, is used for various setups and the results are compared to full-annulus unsteady calculations. It is shown that the effect of the circumferentially different blade excitation is mainly contributed by the Tyler-Sofrin modes and not to blade-to-blade variation in the steady flow field.

The influence of various clocking positions, coupling schemes and number of harmonics onto the forcing is investigated. It is also shown that along a speed-line in the compressor map the blade-to-blade forcing variation may change significantly.

In addition, multi-row flutter calculations are performed, showing the influence of the upstream and downstream blade row onto aerodynamic damping.

The effect of these forcing variations onto random mistuning effects is investigated in the second part of the paper.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A003. doi:10.1115/GT2017-63019.

The prediction of aerodynamic blade forcing is a very important topic in turbomachinery design. Usually, the wake from the upstream blade row and the potential field from the downstream blade row are considered as the main causes for excitation, which in conjunction with relative rotation of neighboring blade rows, give rise to dynamic forcing of the blades. In addition to those two mechanisms so-called Tyler-Sofrin (or scattered or spinning) modes, which refer to the acoustic interaction with blade rows further up- or downstream, may have a significant impact on blade forcing. In particular, they lead to considerable blade-to-blade variations of the aerodynamic loading. In part 1 of the paper a study of these effects is performed on the basis of a quasi 3D multi-row and multi-passage compressor configuration.

Part 2 of the paper proposes a method to analyze the interaction of the aerodynamic forcing asymmetries with the already well-studied effects of random mistuning stemming from blade-to-blade variations of structural properties. Based on a finite element model of a sector, the equations governing the dynamic behavior of the entire bladed disk can be efficiently derived using substructuring techniques. The disk substructure is assumed as cyclically symmetric, while the blades exhibit structural mistuning and linear aeroelastic coupling. In order to avoid the costly multi-stage analysis, the variation of the aerodynamic loading is treated as an epistemic uncertainty, leading to a stochastic description of the annular force pattern. The effects of structural mistuning and stochastic aerodynamic forcing are first studied separately and then in a combined manner for a blisk of a research compressor without and with aeroelastic coupling.

Topics: Compressors
Commentary by Dr. Valentin Fuster
2017;():V07BT36A004. doi:10.1115/GT2017-63162.

In this paper, the aerodynamic and aeroelastic effects of part-span shrouds are both investigated by means of numerical simulations. Based on a well-publicized NASA Rotor 67, a modified transonic fan rotor with the inclusion of a fictitious but typical part-span shroud, is selected to be studied. First, by CFD technique, three-dimensional steady-state calculations are performed for aerodynamic study. Numerical results show that the flow blockage and associated flow losses are caused and would become more severe as the operating condition approaches to the stall margin. It is also found that the presence of part-span shrouds could delay the occurrence of stall and extends the operating range. Further, the pressure distributions at different sections of the unshrouded and shrouded blades are compared and relevant analysis is presented. On the other hand, for aeroelastic study, by directly coupling CFD and CSD computations in the time domain, an effective fluid-structure coupled system is constructed. Considering the speciality of the shrouded blade, some special issues on both aerodynamic and structural modeling are discussed. Particularly, respectively corresponding to situations of in-phase and anti-phase vibrations, a single passage model and a double passage model are used. Comparative study shows that the presence of part-span shrouds greatly improves the convergence rates of all modes, numerically verifying their positive effects on aeroelastic stability. Also it is shown that the blade vibrating in opposite phase has a better aeroelastic stability. Besides, since the aeroelastic effect of part-span shrouds is a combined result of aerodynamic and structural factors, this paper also solely assesses the influence of aerodynamic factor by ignoring the forces on the contact plane. The numerical results show that its effect may be negative but negligibly small.

Topics: Rotors
Commentary by Dr. Valentin Fuster
2017;():V07BT36A005. doi:10.1115/GT2017-63376.

This paper studies a subsonic compressor case with concurrent forced response and flutter by using the Harmonic Balance method, and was inspired by historical experimental data. Forced response was observed when the rotating speed was approaching a crossing on the Campbell diagram, where flutter appeared to be suppressed. CFD simulations are conducted by using a quasi-3D configuration at the mid-span of one stage of a 3.5-stage compressor. Due to the constraint of frequency domain methods, the research is conducted in the vicinity of the 1T-44EO crossing with a small frequency shift between flutter frequency and external excitation frequency. The influence from flutter to forced response is observed: a one-way crosstalk at forced response frequency is observed, presented as the anomaly of unsteady velocity and unsteady pressure near the rear section of rotor blades and in the rotor wake region. The anomaly is speculated as the presence of increasing intensity of shedding vortices induced by the vibration of the blade. To further prove the impact of this viscous effect, a numerical experiment was performed with inviscid rotor blades. In contrast to the crosstalk at forced response frequency, no obvious influence on the unsteady behavior is detected at the flutter frequency, and this observation is confirmed at multiple vibration amplitudes. Considering the relationship between unsteady pressure at flutter frequency and aerodynamic damping, we conclude the influence of forced response on the aerodynamic damping is negligible. In addition, a linearity of unsteady pressure at the flutter frequency vs. vibration amplitude is uncovered. The discoveries provide a proof to linearity assumption and single-frequency simplification widely adopted by industry in flutter simulations.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A006. doi:10.1115/GT2017-63391.

The dynamic characteristics of a structure are modified considerably when it is immersed in a dense fluid. Dynamic interaction between fluid and structure includes the phenomenon of Fluid Structure Interaction (FSI). In the present study, transmission of vibration between two parallel plates partially immersed in a fluid is investigated considering FSI. It is assumed that the plates are clamped along their edges and the fluid is bounded between the two parallel plates to form a rigid rectangular container. Excitation of one plate by an impact load results in the response of the opposite plate. An experiment was conducted and the results were compared with the three-dimensional Finite Element Method (FEM) analysis using CAST3M. Wet dynamic displacement, the frequency of vibration of the two parallel plates with variation in the fluid level are the parameters considered in the present study. Effect of liquid free surface and viscous damping are considered. A benchmark validation from literature has been presented for the free vibration of immersed cantilever plate using CAST3M. It is observed that the damping ratio decreases with an increase in the fluid level and the displacement of the response plate increases. This study especially has been carried out towards the investigation of vibration transmission between structures partially immersed in the liquid sodium in Fast reactors. The objective of the present work is the numerical verification and experimental validation of the FEM model which would make it convenient while analyzing the vibration of immersed structures with FSI.

Topics: Fluids , Vibration
Commentary by Dr. Valentin Fuster
2017;():V07BT36A007. doi:10.1115/GT2017-63556.

Impacts of foreign objects can cause cracks and dents in airfoils, especially in the leading edge. The regeneration of high-pressure compressors blisks with current repair methods is often restricted to a local blending of these edges. This can cause significant changes in the airfoils’ geometrical properties, which in turn influence their aerodynamic and aeroelastic characteristics. Changes at the leading edge have a particularly strong influence on the airfoils’ aerodynamic properties. In order to be able to make an informed decision about if and how a repair should be performed, consequences have to be predicted in advance.

To investigate their influence on the aerodynamic and aeroelastic behavior, typical blend repairs are applied to the geometry of a blisk in a 1.5-stage research axial compressor [1], which are representative in shape and size. Blisks (Blade-Integrated-diSK) are function integrated components, which are expected to have a high life span due to significant costs in design and production. Similar modifications are implemented at different radial heights of the blades, in order to investigate the influence of location and penetration depth of blend repairs. It is assured that only the blend repair region is modified while the rest of the blade stays in the original shape. Thus, a realistic change of the geometry is given.

The numerical study presented here deals with the influence of geometric imperfections, blend repairs in particular, on the aerodynamic and aeroelastic behavior of the high pressure compressors blisks. Results show that blend repairs have an influence on the local pressure distribution as well as on the local flow turning. Even though the leading edge is reshaped during repair, performance degradation can be observed. Furthermore, the working range of the compressor stage is influenced by the blend-repairs, which is of great importance for safe operation. Finally, the local changes in aerodynamics and blade deformation influence the aeroelastic behavior. This influence depends on the investigated mode shape and the location of the modification. The closer the modification is located towards the tip, the more pronounced are the shifts in aerodynamic damping and aerodynamic stiffness. Low torsional mode shapes display the highest sensitivity to the modifications.

Topics: Compressors
Commentary by Dr. Valentin Fuster
2017;():V07BT36A008. doi:10.1115/GT2017-63633.

It is well-known that the natural frequencies of structures immersed in heavy liquids will decrease due to the fluid “added-mass” effect. This reduction has not been precisely determined, though, with indications that it is in the 20–40% range for water. In contrast, the mode shapes of these structures have always been assumed to be invariant in liquids. Recent modal testing at NASA/Marshall Space Flight Center of turbomachinery inducer blades in liquid oxygen, which has a density slightly greater than water, indicates that the mode shapes change appreciably, though. This paper presents a study that examines and quantifies the change in mode shapes as well as more accurately defines the natural frequency reduction. A literature survey was initially conducted and test-verified analytical solutions for the natural frequency reductions were found for simple geometries, including a rectangular plate and an annular disk. The ANSYS© fluid/structure coupling methodology was then applied to obtain numerical solutions, which compared favorably with the published results. This initial study indicated that mode shape changes only occur for non-symmetric boundary conditions. Techniques learned from this analysis were then applied to the more complex inducer model. ANSYS numerical results for both natural frequency and mode shape compared well with modal test in air and water. A number of parametric studies were also performed to examine the effect of fluid density on the structural modes, reflecting the differing propellants used in rocket engine turbomachinery. Some important findings were that the numerical order of mode shapes changes with density initially, and then with higher densities the mode shapes themselves warp as well. Valuable results from this study include observations on the causes and types of mode shape alteration and an improved prediction for natural frequency reduction in the range of 30–41% for preliminary design. Increased understanding and accurate prediction of these modal characteristics is critical for assessing resonant response, correlating finite element models to modal test, and performing forced response in turbomachinery.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A009. doi:10.1115/GT2017-63660.

Rotor blade vibrations observed in the Darmstadt transonic compressor rig are investigated in this paper. The vibrations are non-synchronous and occur in the near stall operating region. Rotor tip flow fluctuations traveling near the leading edge against the direction of rotation (in the rotor relative frame of reference) with about 50% blade tip speed are found to be the reason for the occurrence of the vibrations. The investigations show, that the blockage at the rotor tip is an important factor for the aeroelastic stability of the compressor in the near stall region. It is found, that by application of a recirculating tip injection casing treatment, the aeroelastic stability increases as a result of reduced blockage in the rotor tip region.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A010. doi:10.1115/GT2017-63877.

This paper presents an investigation on the aerodynamic damping of bladed disk (also called ‘blisk’) with mistuning. The study focuses mainly on the mechanism of the effect of random and intentional mistuning on the aero-elastic stability of blisk. For the purpose, aero-elastic stability equations of tuned and mistuned blisk in the frequency domain are established. NASA-Rotor37 is taken as the analysis model. In order to obtain the aerodynamic damping, the unsteady aero-elastic forces are calculated by the double channel harmonic method based on phase correction with aid of the general software CFX. Considering the stochastic characteristics of random mistuning, statistical analysis on the aerodynamic damping of mistuned blisk is performed. The effects of mistuning with different levels are compared. The mechanism of the effects of mistuning on the aero-elastic stability of blisk is found that mistuning couples the modes of different travelling waves and it concentrates the aerodynamic damping in a travelling wave-mode-family by increasing the aerodynamic damping ratios in forward travelling wave modes and decreasing the aerodynamic damping ratios in backward travelling wave modes. And the higher the mistuning level, the more obvious the trend. Furthermore, the following result is obtained: Whatever the mistuning level, in a traveling wave-mode-family, the aerodynamic damping of mistuned blisk is greater than the minimum aerodynamic damping of corresponding tuned blisk and less than the maximum value of it. Besides, the harmonic order of intentional mistuning that can be used to raise the aero-elastic stability of blisk is proposed.

Topics: Damping , Disks
Commentary by Dr. Valentin Fuster
2017;():V07BT36A011. doi:10.1115/GT2017-64027.

Deflections at off-design conditions can change the aeroelastic behavior of turbomachinery blades significantly. Therefore, steady-state deformations at each operating point cannot be neglected and need to be captured by CFD-CSM coupling.

The implementation of an automated toolchain for the generation of a compressor map is presented. It includes steady FSC and is preceded by aflutter analysis. The CFD mesh is adapted to steady surface deflections via a mesh deformation using radial basis functions interpolation. Mode shape vibrations are computed at each operating point. Aerodynamic damping for each mode and IBPA is than assessed by unsteady RANS computations with time-linearization around the steady flow field.

A detailed compressor map of a highly flexible CFRP fan, that was optimized within a multidisciplinary toolchain, is generated based on the geometry for design conditions. Elastic deformations affect a shift of the speedlines especially in near-choked conditions. At the surge line, some cases did not reach a steady-state deformation, oscillating between two deflections and indicating possible stall flutter.

The impact of the steady deformation on predicting flutter boundaries for very elastic blades is pointed out by the comparison to a rigid setup. Significant differences are identified in the region of near-surged and stalled conditions and are due to large deformations, especially torsional deflections. The results of the underlying work of this paper will assist in identifying critical designs during optimization runs more quickly.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A012. doi:10.1115/GT2017-64167.

This paper examines the factors which can result in discrepancies between rig tests and numerical predictions of the flutter boundary for fan blades. Differences are usually attributed to the deficiency of CFD models for resolving the flow at off-design conditions. This work was initiated as a result of inconsistencies between the flutter prediction of two rig fan blades, called here Fan F1 and Fan F2. The numerical results agreed well with the test data in terms of flutter speed and nodal diameter for both fans. However, they predicted a significantly higher flutter margin for F2 than for Fan F1, while rig tests showed that the two blades had similar flutter margins. A new set of flutter computations for both blades using the whole LP domain (intake, fan, OGV and ESS) was therefore performed. The new set of computations considered the effects of the acoustic liner and mistuning for both blades. The results of this work indicate that the previous discrepancies between CFD and tests were due to:

1. Differences in the effectiveness of the acoustic liner in attenuating the pressure wave created by the blade vibration as a result of differences in flutter frequencies between the two fan blades.

2. Differences in the level of unintentional mistuning of the two fan blades due to manufacturing tolerances.

In the second part of this research, the effects of blade misstaggering and inlet temperature on aerodynamic damping were investigated.

The data presented in this paper clearly show that manufacturing and environmental uncertainties can play an important role in the flutter stability of a fan blade. They demonstrate that aeroelastic similarity is not necessarily achieved if only aerodynamic properties and the traditional aeroelastic parameters, reduced frequency and mass ratio, are maintained. This emphasises the importance of engine-representative models, in addition to an accurate and validated CFD code, for the reliable prediction of the flutter boundary.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A013. doi:10.1115/GT2017-64211.

A fast-response pressure-sensitive paint (PSP) technique was applied to the measurement of unsteady surface pressure of an oscillating cascade blade in a transonic flow. A linear cascade was used, and its central blade was oscillated in a translational manner. The unsteady pressure distributions of the oscillating blade and two stationary neighbors were measured using the fast-response PSP technique, and the unsteady aerodynamic force on the blade was obtained by integrating the data obtained on the pressures. The measurements made with the PSP technique were compared with those obtained by conventional methods for the purpose of validation. From the results, the PSP technique was revealed to be capable of measuring the unsteady surface pressure, which is used for flutter analysis in transonic conditions.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A014. doi:10.1115/GT2017-64260.

This paper deals with fluid-structure interactions (FSI), involving a blade profile, submitted to different sources of excitations, as if it were included in a real engine. Two forces of excitation will be considered on the NACA 64A010 airfoil, described in : an external force, due to a forced rotation motion of the blade, and an aerodynamic force, induced by fluid flow around the structure.

By using the Harmonic Balance Method, the airfoil’s motion equation becomes an algebraic problem. Then, this system is solved for each frequency of a chosen range. Therefore, the fluid effect on the translation motion of the profile is studied.

To compute the time periodic aerodynamic field, the Time Spectral Method, implemented in the Onera’s elsA solver, is used for a fast and efficient resolution. This method relies on a time-integration scheme that turns the resolution of the turbulent Navier-Stokes problem into the resolution of several coupled steady state problems computed at different instants of the time period of the movement. The Theodorsen approach with several hypothesis exposed in allows an analytic estimation of the unsteady lift effort. The two approaches are compared for an imposed motion.

In order to predict the dynamic behavior of the system, a fully coupled numerical methodology is developed. For each frequency and at each iteration, TSM supplies the flow field which is used by HBM as a nonlinear excitation on the structure to computate a periodic response and conversely, HBM supplies the new deformed mesh used by TSM to compute the flow field. This strategy has the advantage that all computations take place in the spectral domain, allowing thus to find the steady-state behavior of the fluid and the structure without computing any transient state. The analysis provides the Frequency Forced Response. Some frequencies in the range corresponding to a contribution change between structure and fluid damping are precisely highlighted.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A015. doi:10.1115/GT2017-64468.

Turbocharger turbine blades are subjected to resonant excitation that can lead to High Cycle Fatigue (HCF). In vaneless turbines the excitation primarily stems from asymmetries in the turbine housing such as the volute and the tongue. Given the nature of such asymmetries, the excitation is of a Low Engine Order (LEO) type.

The present study deals with the effect of radial turbine housing design on LEO resonant excitation of turbine blades. The study focuses on two geometrical key design parameters of a twin-scroll turbine housing for a radial turbine which is the rotor-tongue distance and the circumferential angle between both tongues. The generalized force approach is used to identify the critical blade surface regions in order to understand the excitation mechanism of each specific design and to assess the differences of design variants with respect to the baseline design. The presented approach is highly practicable, because it is less expensive than full FSI-simulations.

This approach is validated on tip timing test data from full-scale experiments. Correlation to test data shows that the presented approach is capable of capturing the relative trends reliably and hence can efficiently be employed in an industrial design process such as to minimize blade vibration amplitudes. It is shown that a reduction of blade vibration amplitudes by a factor of 10 could be achieved.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A016. doi:10.1115/GT2017-64502.

The effects of detailing on the prediction of forced-response in a transonic axial turbine stage, featuring a parted stator design, asymmetric inlet and outlet casings as well as rotor cavities, is investigated. Ensuring the mechanical integrity of components is of paramount importance for the safe and reliable operation of turbomachines. Among others, flow induced resonance excitation can lead to high-cycle fatigue (HCF) and potentially to damage of components unless properly damped. This numerical study is assessing the necessary degree of detailing in terms of spatial and temporal discretization, boundary conditions of the pre-stressed rotor geometry as well as geometrical detailing for the reliable prediction of the aerodynamic excitation of the structure. In this context, the sensitivity of the aerodynamic forcing is analyzed by means of the generalized force criterion, showing a significant influence for some of the investigated variations of the numerical model.

Moreover, the origin and further progression of several low-engine-orders (LEO) within the flow field, as well as their interaction with different geometric details has been analyzed based on the numerical results obtained from a full 360° CFD-calculation of the investigated turbine stage. The predicted flow induced vibration of the structure has been validated by means of a full forced-response analysis, where a good agreement with tip-timing data has been found.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A017. doi:10.1115/GT2017-64564.

The designs of centrifugal compressors are pushed towards higher pressure ratios, higher mass flow rates, and wider operating conditions. As the change of the actual condition, compressors often operate at low flow rates. There are some important unstable flow conditions at low flow rates such as rotating stall. The exciting forces may cause blade resonance and high dynamic stress level. High cycle fatigue failure is one of the main damage form of compressor impellers. Therefore, the dynamic stress prediction of impeller is an important part of compressor design and failure analysis. This paper is concerned with the prediction of dynamic stress of an actual damaged semi-open centrifugal impellers under unsteady aerodynamic load using a full nonlinear damping model which includes material and aerodynamic damping. Material damping is predicted based on an empirical equation and expressed as a function of stress amplitude. Aerodynamic damping is predicted through unidirectional fluid-structure interaction analysis. In this paper, the aerodynamic damping of the semi-open centrifugal impeller with various vibration amplitudes, modes and operation conditions is estimated. The numerical result indicates that, the material damping increases with the increasing stress amplitude while the aerodynamic damping is independent of the blade vibratory amplitude for a given blade mode. A nonlinear total damping model is then proposed, including both material and aerodynamic damping. The contribution of material damping plays an important part in total damping estimation as well as the aerodynamic damping. With this model, a procedure for dynamic stress estimation is proposed. Aerodynamic load on the surface of the impeller obtained by transient CFD calculation and the load in frequency domain obtained by Fast Fourier Transformation (FFT). Comparing normal condition with low flow condition, the main frequencies of the aerodynamic load are basically coincident and the load amplitude increases significantly under low flow rate. The main frequencies at the leading edge of blades are 4 times, 5 times and 6 times rotation frequency. They may be caused by rotating stall and excite the impeller. As the load of 5 times rotation frequency is maximum, harmonic analysis is performed to estimate the dynamic stress of the semi-open centrifugal compressor blades under the load. The result shows that the resonance stress at the leading edge of the blade under low flow condition is 22 times up on the stress under normal condition. The result of fatigue strength assessment shows that fatigue damage may occur at the leading edge of blades and it is consistent with the actual damaged position of the impeller. Therefore, fatigue damage is likely to happen under low flow rate condition. It is necessary to consider the situation carefully during the design of compressors.

Topics: Stress , Impellers , Failure
Commentary by Dr. Valentin Fuster
2017;():V07BT36A018. doi:10.1115/GT2017-64576.

The phenomena prior to rotating stall were investigated in a high-speed compressor test rig using optical and pneumatic measurement techniques. A number of throttling procedures was performed at transonic and subsonic speedlines with the aim to detect the unsteady effects initiating rotating stall or large amplitude blade vibrations. At transonic speed radial vortices traveling around the circumference were detected in the upstream part of the rotor using phase-locked PIV measurements above 92% span and unsteady wall pressure measurements. When these radial vortices impinge on a blade leading edge, they cause a forward spill of fluid around the leading edge. The effects are accompanied by a large-scale vortex breakdown in the blade passage leading to immense blockage in the endwall region. At subsonic speeds, the observed flow phenomena are similar but differ in intensity and structure.

During the throttling procedure, blade vibration amplitudes were monitored using strain gauges and blade tip timing instrumentation. Non-synchronous blade vibrations in the first torsional eigenmode were measured as the rotor approached stall. Using the different types of instrumentation, it was possible to align the aerodynamic flow features with blade vibration levels. The results show a clear correlation between the occurrence of radial vortices and blade vibrations.

Topics: Compressors , Vortices
Commentary by Dr. Valentin Fuster
2017;():V07BT36A019. doi:10.1115/GT2017-64586.

In this paper the effects of mistuning on the flutter stability of a turbine blade are analysed. Two types of mistuning are considered, frequency mistuning and aerodynamic mistuning. The study concentrates on the the first family of modes (1F, first flap) as the blade fluttered in this mode during test. For the frequency mistuning analysis, the 1F frequency is varied around the annulus but the 1F mode shapes remain the same for all the blades. The mistuning analyses are performed by using a reduced order model (ROM) based on an eigenvalue analysis of the linearized modal aeroelastic system with the aerodynamic matrix calculated from the aerodynamic influence coefficients. The influence coefficients required for this algorithm are obtained from a three-dimensional, non-linear aeroelastic solver (AU3D) by shaking one blade in the datum (tuned) frequency and mode and recording aerodynamic forces on the other blades in the assembly. After the ROM is validated against the non-linear method for the tuned case, it is used for the mistuning and mis-staggering study as time-domain computations of such cases are very time consuming.

The results of this paper indicate that, frequency mistuning is always stabilizing but aerodynamic mistuning can be destabilizing under certain conditions. Moreover, it is shown that the effect of frequency mistuning is much higher than the one of aerodynamic asymmetries and that structural coupling limits the effects of mistuning.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A020. doi:10.1115/GT2017-64621.

Recent demands for a reduction of specific fuel consumption of jet engines have been opposed by increasing propulsive efficiency with higher bypass ratios and increased engine sizes. At the same time the challenge for the engine development is to design safe and efficient fan blades of high aspect ratios. Since the fan is the very first rotor stage, it experiences significant distortions in the incoming flow depending on the operating conditions. Flow distortions do not only lead to a performance and stall margin loss but also to remarkable low engine order (LEO) excitation responsible for forced vibrations of fundamental modes. Additionally, fans of jet engines typically suffer from stall flutter, which can be additionally amplified by reflections of acoustic pressure waves at the intake. Stall flutter appears before approaching the stall line on the fan’s characteristic and limits its stable operating range. Despite the fact that this “flutter bite” usually affects only a very narrow speed range, it reduces the overall margin of safe operation significantly. With increasing aspect ratios of ultra-high bypass ratio jet engines the flutter susceptibility will probably increase further and emphasizes the importance of considering aeromechanical analyses early in the design phase of future fans. This paper aims at proving that intentional mistuning is able to remove the flutter bite of modern jet engine fans without raising issues due to heavily increased forced vibrations induced by LEO excitation. Whereas intentional mistuning is an established technology in mitigating flutter, it is also known to amplify the forced response. However, recent investigations considering aeroelastic coupling revealed that under specific circumstances mistuning can also reduce the forced response due to engine order excitation. In order to allow a direct comparison and to limit costs as well as effort at the same time, the intentional mistuning is introduced in a non-destructive way by applying heavy paint to the blades. Its impact on the blade’s natural frequencies is estimated via finite element models with an additional paint layer. In parallel, this procedure is experimentally verified with painted fan blades in the laboratory. A validated SNM (subset of nominal system modes) representation of the fan is used as a computational model to characterize its mistuned vibration behavior. Its validation is done by comparing mistuned mode shape envelopes and frequencies of an experimental modal analysis at rest with those obtained by the updated computational model. In order to find a mistuning pattern minimizing the forced response of mode 1 and 2 at the same time and satisfying stability and imbalance constraints, a multi-objective optimization has been carried out. Finally, the beneficial properties of the optimized mistuning pattern are verified in a rig test of the painted rotor.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A021. doi:10.1115/GT2017-64633.

This paper is the first part of a two-part paper that presents a comprehensive study of the higher-order mode mistuned forced response of an embedded rotor blisk in a multistage axial research compressor. The resonant response of the second-stage rotor (R2) in its first chordwise bending (1CWB) mode due to the second harmonic of the periodic forcing of its neighboring stators (S1 and S2) is investigated computationally and experimentally at three steady loading conditions in the Purdue Three-Stage Compressor Research Facility. State-of-the-art numerical methods applicable in an industrial design environment are used to construct a 1.5-stage stator/rotor/stator configuration for the prediction of the aerodynamic forcing function of the rotor. The time-averaged component of these simulations provides a good prediction of the compressor performance, rotor tip leakage flow (TLF), and characteristics of the stator aerodynamic disturbances. The contribution of the rotor TLF on the rotor forcing function is small, responsible for less than 5% of the total modal force in amplitude. Moreover, the individual contributions of the upstream and downstream stators to the rotor modal force are separated via a linear forcing decomposition approach. It is shown that the upstream stator provides the dominant forcing function with an amplitude almost 6 times that of the downstream stator, and is mostly due to the impulse-like appearance of the upstream stator wakes which have significant higher-harmonic (including the second-harmonic) contents. An excellent prediction of the tuned 1CWB resonant response amplitudes is achieved with only 35%, 4%, and 7% difference to the measured values at three loading conditions.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A022. doi:10.1115/GT2017-64643.

The prediction of aerodynamic damping is a key step towards high fidelity forced response calculations. Without the knowledge of absolute damping values, the resulting stresses from forced response calculations are often afflicted with large uncertainties. In addition, with the knowledge of the aerodynamic damping the aeroelastic contribution to mistuning can be considered. The first section of this paper compares two methods of one-way-coupled aerodynamic damping computations on an axial turbine. Those methods are: the aerodynamic influence coefficient, and the travelling wave mode method. Excellent agreement between the two methods is found with significant differences in required computational time. The average deviation between all methods for the transonic turbine is 4%. Additionally, the use of transient blade row methods with phase lagged periodic boundaries are investigated and the influence of periodic boundaries on the aerodynamic influence coefficients are assessed. A total of 23 out of 33 passages are needed to remove all influence from the periodic boundaries for the present configuration. The second part of the paper presents the aerodynamic damping calculations for a centrifugal compressor. Simulations are predominantly performed using the aerodynamic influence coefficient approach. The influence of the periodic boundaries and the recirculation channel is investigated. All simulations are performed on a modern turbocharger turbine and centrifugal compressor using ANSYS CFX V17.0 with an inhouse pre- and post-processing procedure at ABB Turbocharging. The comparison to experimental results concludes the paper.

Commentary by Dr. Valentin Fuster
2017;():V07BT36A023. doi:10.1115/GT2017-64647.

This paper is the second part of a two-part paper that presents a comprehensive study of the higher-order mode mistuned forced response of an embedded rotor blisk in a multi-stage axial research compressor. The resonant response of the second-stage rotor (R2) in its first chordwise bending (1CWB) mode due to the second harmonic of the periodic passing of its neighboring stators (S1 and S2) is investigated computationally and experimentally at three steady loading conditions in the Purdue Three-Stage Compressor Research Facility. A Non-Intrusive Stress Measurement System (NSMS, or blade tip-timing) is used to measure the blade vibration. Two reduced-order mistuning models of different levels of fidelity are used, namely the Fundamental Mistuning Model (FMM) and the Component Mode Mistuning (CMM), to predict the response. Although several modes in the 1CWB modal family appear in frequency veering and high modal density regions, they do not heavily participate in the response such that very similar results are produced by the FMM and the CMM models of different sizes. A significant response amplification factor of 1.5∼2.0 is both measured and predicted, which is on the same order of magnitude of what was commonly reported for low-frequency modes. This amplification is also a strong, non-monotonic function of the steady loading. Moreover, on average, the mistuned blades respond at an amplitude only approximately 40% that of the tuned, much lower than what was commonly reported (75∼80%). This is due to the very low level of structural coupling associated with the 1CWB family of the rotor blisk. In this study, a very good agreement between predictions and measurements is achieved for the deterministic analysis. This is complemented by a sensitivity analysis which shows that the mistuned system is highly sensitive to the discrepancies in the experimentally determined blade frequency mistuning.

Topics: Compressors , Rotors
Commentary by Dr. Valentin Fuster
2017;():V07BT36A024. doi:10.1115/GT2017-64657.

This paper investigates superposition and decomposition methods when determining the forcing function on an embedded rotor in a multistage axial compressor. Under investigation is a 3-row stator/rotor/stator configuration where two stators, having the same vane count, can be circumferentially clocked to change the rotor excitation. The combined forcing function on the rotor in any arbitrary clocking arrangement is assumed to be a linear combination of two known clocking positions. In this study, the forcing function from these known positions are first approximated by two 2-row CFD solutions, namely stator/rotor and rotor/stator. It is found that theses approximations are poor, since they do not include the significant effect of stator-stator interaction. Next, these two forcing components are obtained via a linear decomposition using two 3-row CFD solutions at two clocking positions. A linear superposition is performed based on these decomposed results to estimate the combined rotor forcing for any arbitrary clocking position. It is found that although the trend of rotor forcing with respect to clocking is qualitatively captured, considerable quantitative discrepancies exist that refute the proposed linearity assumption. This assumption oversimplifies the multi-row aerodynamic interactions: a change in the stator-stator clocking position does not only alter the relative phase between two stator-induced forcing functions to the rotor, but also these two components themselves.

Topics: Compressors , Rotors
Commentary by Dr. Valentin Fuster
2017;():V07BT36A025. doi:10.1115/GT2017-65244.

This paper examines the lock-in hypothesis of non-synchronous vibration (NSV) in a high speed multistage axial compressor. The unsteady Reynolds-averaged Navier-Stokes (URANS) equations and modal approach based structural dynamic equations are solved. A low diffusion E-CUSP approximate Riemann solver with a 3rd order WENO scheme for the inviscid fluxes and a 2nd order central differencing for the viscous terms are employed. The structural vibration of the blades are solved by a set of modal equations that are fully coupled with the flow equation. The rigid blade simulations are conducted to examine the main driver of NSV. A 1/7th annulus sector of IGV-rotor-stator is used with a time shifted phase lag BC at circumferential boundaries. A dominant excitation frequency caused by the traveling tip vortices are captured. The excitation frequency is not on the engine order. The simulation is then switched to fluid structure interaction that allows the blades to vibrate freely under the flow excitations. The matching of aerodynamic forcing frequency with the structure response frequency seems indicating that the NSV of this compressor is a limit cycle oscillation (LCO) excited by aerodynamic forcing, not caused by flow frequency/phase locked to structural frequency. The rotating speed is varied within a RPM range, in which the rig test detected the NSV. The unsteady flows with rigid blades are simulated first at several RPMs. The simulation indicates that the structure response follows the frequency of the flow excitations existing in the rigid blades. At least under the simulated conditions, the NSV does not appear to be a lock-in phenomenon, which has the flow frequency lock-in to the structure natural frequency.

Commentary by Dr. Valentin Fuster

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