Journal articles on the topic 'Multi-Stage Bladed Disks Dynamics'

The effects of disk flexibility and multistage coupling on the dynamics of bladed disks with and without blade mistuning are investigated. Both free and forced responses are examined using finite element representations of example single and two-stage rotor models. The reported work demonstrates the importance of proper treatment of interstage (stage-to-stage) boundaries in order to yield adequate capture of disk-blade modal interaction in eigenfrequency veering regions. The modified disk-blade modal interactions resulting from interstage-coupling-induced changes in disk flexibility are found to have a significant impact on (a) tuned responses due to excitations passing through eigenfrequency veering regions, and (b) a design’s sensitivity to blade mistuning. Hence, the findings in this paper suggest that multistage analyses may be required when excitations are expected to fall in or near eigenfrequency veering regions or when the sensitivity to blade mistuning is to be accounted for. Conversely, the observed sensitivity to disk flexibility also indicates that the severity of unfavorable structural interblade coupling may be reduced significantly by redesigning the disk(s) and stage-to-stage connectivity. The relatively drastic effects of such modifications illustrated in this work indicate that the design modifications required to alleviate veering-related response problems may be less comprehensive than what might have been expected.

Turbine blades having integrally machined tip shrouds, with associated gaps between adjacent shrouds, often exhibit unusual vibratory responses with significant differences between the amplitudes and frequencies of individual blades on the same stage. These differences result from unavoidable variations in the shroud gaps causing, for large enough excitation, nonlinear constraint at the blade tips which varies from blade to blade. This study shows that the blade stresses cannot be adequately represented by the type of single-degree-of-freedom models that are often used for dynamic impact studies, but require the participation of higher frequency beam-type modes. The extension of the resulting beam model to multi-degree-of-freedom systems will allow the study of the “gap mistuning” phenomenon for practical bladed disks.

This paper presents a new and original method for dynamical analysis of multistage cyclic structures such as turbomachinery compressors or turbines. Each stage is modeled cyclically by its elementary sector and the interstage coupling is achieved through a cyclic recombination of the interface degrees of freedom. This method is quite simple to set up; it allows us to handle the finite element models of each stage’s sector directly and, as in classical cyclic symmetry analysis, to study the nodal diameter problems separately. The method is first validated on a simple case study which shows good agreements with a complete 360 deg reference calculation. An industrial example involving two HP compressor stages is then presented. Then the forced response application is presented in which synchronous engine order type excitations are considered.

This paper describes an approach to unidirectional coupled CFD–FEM analysis developed at ABB Turbo Systems Ltd. Results of numerical investigations concerning the vibration behavior of an axial turbocharger turbine are presented. To predict the excitation forces acting on the rotating blades, the time-resolved two-dimensional coupled stator–rotor flow field of the turbine stage was calculated. The unsteady pressure, imposed on the airfoil contour, leads to circumferentially nonuniform and pulsating excitation forces acting on the rotating bladed disk. A harmonic transformation of the excitation forces into the rotating coordinate system of a single blade was elaborated and the complex Fourier amplitudes were determined. The bladed rotor was modeled by a single symmetric segment with complex circumferential boundary conditions. With respect to different nodal diameter numbers, free vibration analyses of the disk assembly were then effectively performed. For calculated resonance conditions, the steady-state responses of the turbocharger bladed disk were computed. By using this coupled CFD–FEM analysis, the dynamic loading of the turbine blades can be determined in the design process.

Abstract The steam turbine blades of low pressure stages are endangerd by the high-cyclic fatigue due to the combined loading of dynamic stresses by the steam time-variant pressure and the pre-stress from centrifugal forces. Therefore, the importance of their experimental dynamic analysis in the design stage is critical. For laboratory tests of the blades, the piezo actuators placed on the blades, unlike electromagnets placed in the stationary space, give a possibility to excite the flexural vibration of the blades within the bladed disk by time continuous forces independently of the rotor revolutions. In addition, the piezo actuators can be also used to control the vibrations of the blade. Therefore, several dynamic experiments of the clamped model blade equipped with PVDF films were performed for the force description of the piezo foils and their behavior as actuators of the blade vibration. The numerical beam models were used for numerical analysis of the vibration suppression effects both by additional parametric excitation and by active damping. The optimal phase shift of piezo actuator voltage supply was ascertained both for amplitude amplification and suppression. The results contribute to the knowledge of the actuation and active damping of blade vibration by the piezo elements

To increase technical level of energy turbomachine in modern turbomachinery, high reliability and durability of structures are required in the design, manufacture and operation of turbomachine. Any change geometry, mass, material properties of the bladed disk of turbomachine in the design is called mistuning parameters. With a small value of mistuning blades can significantly increase amplitude, displacement or stresses of the blades structures. So, analysis influence of the effect mistuning parameters on the dynamic characteristics in the field of turbomachine is an important and urgent task. This article analyzes the effect intentional mistuning of the axial bladed disk turbomachine in order to reduce forced response due to low-order engine excitation. The maximum value forced response of rotor blades turbomachine with mistuning parameters is usually much more than that of the tuned rotors. An increase level mistuning of this critical value actually leads to a decrease magnifications of the forced response. Thus, the actual work has been introducing some degree of intentional mistuning in the design to achieve these purposes. In this paper, we study the effectiveness of intentional mistuning at the design stage bladed disk turbomachine, which is introduced into the rotor design by changing the nominal mass of the blades in harmonic Формаls.

This paper deals with the coupling vibration characteristic of the disk-blade-shaft integration rotor. First, a reduced-order model (ROM) based on an improved hybrid interface component mode synthesis method (IHISCMSM) is carried out, which takes the prestress effect into account. The frequency of the disk-blade-shaft integration rotor at different rotating speeds are calculated and the influence of selecting different mode truncation numbers is investigated. In order to quantitatively evaluate the coupling degree of blade and disk, the coupling factor is defined from the perspective of strain energy, and the influence of prestress on system’s dynamic is discussed. Then, an experimental modal analysis is performed on blades to identify the mistuning parameters, and the mode localization of the disk-blade-shaft integration rotor is analyzed with and without blade mistuning. The results indicate that there are several types of coupling modes among blade, disk and shaft of the integration rotor. After considering the prestress, the frequency increases, and the axial coupling vibration degree and radial coupling vibration degree of the integration rotor change. The mode localization of mistuned rotor is more likely to occur in the modes dominated by mistuning stage blades. There also exists a subtle mode localization phenomenon for tuned integration rotor.

AbstractThe vibration optimum design for a simulated power turbine rotor without blades on the disk by using an optimization method based on the finite element method is described in this paper. The installation position of the two-stage turbine disks is chosen as design variables under the constraints of feasible regions for the critical speeds of the rotor. The objective functions are to minimize the transient response of the acceleration at the bearings and the amplitude of the disks. Predictions of the dynamic characteristics of the rotor are obtained by using ANSYS code. The optimization problem is solved by using commercial optimization code ISIGHT. The optimum installation position of the two-stage turbine disks is determined after optimization design. Experimental tests under the optimized structure show that the amplitude of the two-stage turbine disks which are recognized as the most concerned optimization objectives are reduced by 59 % and 56 % respectively in comparison with the comparative structure. The encouraging results demonstrate the potential of the presented method as an engineering design tool and also lay a foundation for the design of the real power turbine rotor used in turbo-shaft engine.

At Darmstadt University of Technology (Darmstadt, Germany), the Department of Gas Turbines and Flight Propulsion operates a single-stage transonic compressor test stand. Its main purpose is to provide a database for the validation of computational fluid dynamics codes. In addition, it serves as a testbed for new materials and also for the development of new measurement techniques. After setting up the test rig with a baseline rotor (Rotor No. 1), a titanium bladed disk with conventional radially stacked blade sections, a new rotor (Rotor No. 2) was designed, with the addition of considerable amounts of aft sweep and backward lean. The new rotor's flow field and mechanical properties were investigated by using various measurement techniques, including a laser-2-focus setup.

Abstract The paper presents the results of a study in the kinematics and dynamics of a multi-blade disc cutting device. In the advanced hardware scheme, the clipping process is performed as punches. We have a straight blade edge rotated 200 degrees back from the radial direction. As a result, the sliding motion process is reduced and the trunk is easily cut. For this reason, it is advisable to reduce the sliding process when cutting a hard stem, and it is preferable that the blade be made in the form of a hyperbolic spiral, and not an Archimedes spiral, the curvature of which is directed towards the stem, and not in a straight line. Kinematic and dynamic studies performed on a multi-knife disk shearing device accelerate the technological process of the device, increase the pressure of the blade on the trunk, and make it possible to cut it intensively.

The paper reports the procedure of a cutting mode purpose at deep profile grinding on NC multi-axes machines on the basis of the modeling of thermo-dynamic processes in cutting areas with the purpose of ensuring turbine blade fatigue resistance. There are shown simulators allowing the definition and prediction of the dynamics of elastic, thermal and working processes in a technological system, material removal, cutting force, temperatures in the area of cutting and roughness of each elementary area of the surface profile on the basis of cutting modes, disk characteristics.

Abstract A computational fluid dynamics simulation is done for comparative study from the pumping effect on the four surfaces of the stirred tank. The flow field generated by one-stage and bi-stage six-bladed Rushton turbine in the unbaffled square tank was studied. The Reynolds-averaged Navier-Stokes equation with steady-state multi-reference frame approach (MRF) is used to simulate hydrodynamic flow in the tank. The turbulent viscosity, the turbulent kinetic energy and mean velocity distributions obtained in vertical and horizontal plans are analyzed and discussed. We can deduce that the additional Rushton turbine in the upper part of the square tank improves the quality of the mixture.

Interacting between the next rows of the turbine creates a circumferential flow non-uniformity, which leads to origination of resonance dynamic stresses on rotor bladings with frequencies z·fn, where fn - a rotor rotation frequency, z - number of stator vanes. At projection and development of the engine is not always possible detuning from a resonance as the spectrum of eigenfrequencies of rotor blades can be wide enough in relation to a band of working rotor speed. Reduction of exterior exciting forces can be one of ways of a reduction of dynamic stresses in rotor blades. For attenuation of these forces intensity was possibly use of a stator vanes with a different spacing, and also with the blades inclined in a circumferential direction. In the given article numerical research for choice a distribution law of stator vanes spacing and a declivity angle of its blades, allowed to diminish amplitude of the unsteady air forces acting on rotor blades with frequency z·fn are presented. As object for examinations the stage of the air starter turbine, the containing 26 nozzle vanes disposed with different spacings, and 40 rotor blades without a binding has served. Rotor blades and turbine disk of the air starter are made for a single whole of an aluminium alloy. This work was executed stage by stage: in the beginning the angular disposition of vanes blades, giving maximum decrease of exciting forces on rotor blades, by results of unsteady flow calculation in the turbine was chosen; then for the found geometry of a vanes the slope angle of its blades in the circumferential direction, giving the maximum decrease of exciting forces on rotor blades was chosen. The viscous gas unsteady flow was modelled in the computational domain including all blade passages of turbine rows - 26 channels in a nozzle and 40 channels in the rotor wheel. By results of calculation dependence of decrease unsteady force acting on blades and changes of turbine efficiency from a slope angle of vanes is presented. Reduction of dynamic stresses level in rotor blades of the turbine at the expense of decrease of aerodynamic exciting forces amplitude is attained. The numerical result is confirmed experimentally in rig test by decrease of resonance stresses on explored frequencies.

This paper presents a general approach for modeling shrouded blade vibration that takes into consideration the nonlinear friction constraint at the shroud interface. In this approach, linear structures are characterized by receptances and shroud constraints by nonlinear impedances. The proposed methodology is presented in detail for simplified models of the bladed disk and shroud interface. The corresponding governing equations for the dynamic response are derived for both tuned and mistuned stages. As an example the method is applied to an idealized tuned stage. Two cases are considered, a lubricated shroud for which the coefficient of friction is equal to zero, and a frictionally constrained shroud. The effect of varying the shroud-to-shroud preload is studied. In the lubricated case nonlinear behavior is seen when vibrations are strong enough to result in separation of the shroud interfaces. In the case of finite friction there is a profound change in resonant frequencies when the preload is increased sufficiently to prevent gross slip at the shrouds.

In this study, a reduced-order nonlinear dynamic model for shaft-disk-blade unit is developed. The multibody dynamic approach with the small deformation theory for both blade-bending and shaft-torsional deformations is adopted. The equations of motion are developed using Lagrange’s equation in conjunction with the assumed modes method (AMM) for approximating the blade transverse deflection. The model showed strong coupling between the blade bending and shaft torsional vibrations in the form of inertial nonlinearity, modal coupling, stiffening, softening, and parametric excitations. The model is suitable for extensive parametric studies for predesign stage purposes as well as for diagnostics of rotor malfunctions, when blade and shaft torsional vibration interaction is suspected.

Models consisting of chains of particles that are coupled to their neighbours appear in many applications in physics or engineering, such as in the study of dynamics of mono-atomic and multi-atomic lattices, the resonances of crystals with impurities and the response of damaged bladed discs. Analytical properties of the dynamic responses of such disturbed chains of identical springs and masses are presented, including when damping is present. Several remarkable properties in the location of the resonances (poles) and anti-resonances (zeros) of the displacements in the frequency domain are presented and proved. In particular, it is shown that there exists an elliptical region in the frequency–disturbance magnitude plane from which zeros are excluded and the discrete values of the frequency and disturbance at which double poles occur are identified. A particular focus is on a local disturbance, such as when a spring or damper is modified at or between the first and last masses. It is demonstrated how, notably through normalization, the techniques and results of the paper apply to a broad category of more complex systems in physics, chemistry and engineering.

Experimental measurements from a new single stage turbine are presented. The turbine has 26 vanes and 59 rotating blades with a design point stage expansion ratio of 2.5 and vane exit Mach number of 0.96. A variable sealing flow is supplied to the disk cavity upstream of the rotor and then enters the annulus through a simple axial clearance seal situated on the hub between the stator and rotor. Measurements at the annulus hub wall just downstream of the vanes show the degree of circumferential pressure variation. Further pressure measurements in the disk cavity indicate the strength of the swirling flow in the cavity, and show the effects of mainstream gas ingestion at low sealing flows. Ingestion is further quantified through seeding of the sealing air with nitrous oxide or carbon dioxide and measurement of gas concentrations in the cavity. Interpretation of the measurements is aided by steady and unsteady computational fluid dynamics solutions, and comparison with an elementary model of ingestion.

Multi-field coupling problems are taken more and more attention mainly because of the higher requirement of load, efficiency, and reliability in aero-engine operation. This research takes an aero-engine compressor as the research object, 3D flow field and structural models are established. For the method of cyclic symmetric, single-sector model is selected as the calculation domain. Considering the influence of former stator wakes, compressor flow field is simulated. The article analyzes the distribution law of unsteady aerodynamic load on rotor blade. Based on Kriging model, load transfer of aerodynamic pressure and temperature is achieved from flow field to blade structure. Then the effects of centrifugal force, aerodynamic pressure and temperature load are discussed on compressor vibration characteristic and structural strength. The results show dominant fluctuation frequencies of aerodynamic load on rotor blade are manly at frequency doubling of stator–rotor interaction, especially at one time frequency (1 × f0). Magnitude and pulsation amplitude on pressure surface are far greater than that on suction surface. Load transfer with Kriging model has a higher precision, it can meet the requirement of multi-field coupling dynamic calculation. In multi-field coupling interaction, temperature load makes the natural vibration frequencies decrease obviously, centrifugal force is the main source of deformation and stress. Bending stress induced by aerodynamic pressure and temperature load can counteract part of bending stress induced by centrifugal force. However, temperature load causes the maximum displacement of blade-disk system to increase.

With the rapid development of vertical takeoff and landing (VTOL) aircraft, the blade design of a propeller suitable for VTOL aircraft with a wide range of operating conditions has become a challenging and popular task. This paper proposes a multi-objective optimization framework for a VTOL propeller using an inverse design method at the cruising stage, which is developed from the Betz optimum theory and blade element momentum theory (BEMT). Different from passing studies, the maximum thrust-to-weight ratio at hover (MTWRH) is taken as one of the two objectives in this paper, which is closely related to the wind-resistance capability and maneuverability during takeoff and landing. The other objective is the energy consumption of the whole mission profile. A fixed pitch propeller (FPP) and a variable pitch propeller (VPP) are both optimized using the proposed framework for the Vahana A3 tilt-wing aircraft and validated by the computational fluid dynamics (CFD) method. The influences of the level flight energy ratio, hover disk loading and cruising speed toward the optimization result are analyzed, respectively. The results show that the MTWRH has a significant impact on the optimization result both for the FPP and VPP. A comparison between the two propeller forms validates the advantages of the VPP both in energy saving and takeoff maneuverability. The quantitative rules of this advantage with the level flight energy ratio are calculated to provide a reference for choosing the appropriate form. Overall, the methodology and general rules presented in this paper support the propeller optimization and form selection for VTOL aircraft.

Efficiency improvements for gas turbines are strongly coupled with increasing turbine inlet temperatures. This imposes new challenges for designers for efficient and adequate cooling of turbine components. Modern gas turbines inject bleed air from the compressor into the stator/rotor rim seal cavity to prevent hot gas ingestion from the main flow, while cooling the rotor disk. The purge flow interacts with the main flow field and static pressure field imposed by the turbine blades. This complex interaction causes non-uniform and jet-like penetration of the purge flow into the main flow field, hence affecting the endwall heat transfer on the rotor. To improve the understanding of purge flow effects on rotor hub endwall heat transfer, an unshrouded, high-pressure representative turbine design with 3D blading and extended endwall contouring of the rotor into the cavity seal was tested. The measurements were conducted in the 1.5-stage axial turbine facility LISA at ETH Zurich, where a state-of-the-art measurement setup with a high-speed infrared camera and thermally managed rotor insert was used to perform high-resolution heat transfer measurements on the rotor. Three different purge flow rates were investigated with regard to hub endwall heat transfer. Additionally, steady-state computational fluid dynamics simulations were performed to complement the experiments. It was found that the local heat transfer rate changes up to ±20% depending on the purge flow rate. The main part of the purged air is ejected at the endwall trough location and swept towards the rotor suction side, which is caused by the interaction of main flow and the cavity extended endwall design. The presence of low momentum purge flow locally reduces the heat transfer rate. Changes in adiabatic wall temperature and heat transfer (depending on purge rate) are observed from the platform start up to the cross passage migration of the secondary flow structures.

Context. Reconstructing the structure and history of young clusters is pivotal to understanding the mechanisms and timescales of early stellar evolution and planet formation. Recent studies suggest that star clusters often exhibit a hierarchical structure, possibly resulting from several star formation episodes occurring sequentially rather than a monolithic cloud collapse. Aims. We aim to explore the structure of the open cluster and star-forming region NGC 2264 (~3 Myr), which is one of the youngest, richest and most accessible star clusters in the local spiral arm of our Galaxy; we link the spatial distribution of cluster members to other stellar properties such as age and evolutionary stage to probe the star formation history within the region. Methods. We combined spectroscopic data obtained as part of the Gaia-ESO Survey (GES) with multi-wavelength photometric data from the Coordinated Synoptic Investigation of NGC 2264 (CSI 2264) campaign. We examined a sample of 655 cluster members, with masses between 0.2 and 1.8 M⊙ and including both disk-bearing and disk-free young stars. We used Teff estimates from GES and g,r,i photometry from CSI 2264 to derive individual extinction and stellar parameters. Results. We find a significant age spread of 4–5 Myr among cluster members. Disk-bearing objects are statistically associated with younger isochronal ages than disk-free sources. The cluster has a hierarchical structure, with two main blocks along its latitudinal extension. The northern half develops around the O-type binary star S Mon; the southern half, close to the tip of the Cone Nebula, contains the most embedded regions of NGC 2264, populated mainly by objects with disks and ongoing accretion. The median ages of objects at different locations within the cluster, and the spatial distribution of disked and non-disked sources, suggest that star formation began in the north of the cluster, over 5 Myr ago, and was ignited in its southern region a few Myr later. Star formation is likely still ongoing in the most embedded regions of the cluster, while the outer regions host a widespread population of more evolved objects; these may be the result of an earlier star formation episode followed by outward migration on timescales of a few Myr. We find a detectable lag between the typical age of disk-bearing objects and that of accreting objects in the inner regions of NGC 2264: the first tend to be older than the second, but younger than disk-free sources at similar locations within the cluster. This supports earlier findings that the characteristic timescales of disk accretion are shorter than those of disk dispersal, and smaller than the average age of NGC 2264 (i.e., ≲3 Myr). At the same time, we note that disks in the north of the cluster tend to be shorter-lived (~2.5 Myr) than elsewhere; this may reflect the impact of massive stars within the region (notably S Mon), that trigger rapid disk dispersal. Conclusions. Our results, consistent with earlier studies on NGC 2264 and other young clusters, support the idea of a star formation process that takes place sequentially over a prolonged span in a given region. A complete understanding of the dynamics of formation and evolution of star clusters requires accurate astrometric and kinematic characterization of its population; significant advance in this field is foreseen in the upcoming years thanks to the ongoing Gaia mission, coupled with extensive ground-based surveys like GES.

Lystrup ØstergårdA Neolithic workshopIn 2007 a remarkable small site dating from the later part of the Early Neolithic Funnel Beaker culture was discovered at Lystrup, north of Aarhus in Eastern Jutland. Careful total excavation of the site revealed a well-defined cultural deposit with dense concentrations of flint debitage and implements lying in situ in a shallow hollow resulting from a group of windthrows. Via a series of analyses, the distribution of the finds relative to the individual features which were demonstrated, including a central hearth, has made it possible to reconstruct the events which took place, thereby permitting a detailed characterisation of the site. It can be perceived as a workshop which lay isolated in the landscape, at some distance from the actual settlement areas.The finds primarily reflect two activities at the site: The production of blanks for thin-butted flint axes, where the raw material was obtained from the local moraine clay, and an activity which probably involved the working of bone or antler, judging from the remarkable number of burins which were recovered. Flake scrapers, normally the commonest tool type at settlements of this period, were virtually absent. The marked occurrence of burins and the site’s potential with respect to finds-distribution analysis together constitute a situation rarely encountered in a Neolithic context. Through identification of the various sequences of events, the activities acquire the character of brief targeted incidents.Analyses of small Neolithic sites and the identification of specialised workshops can make a significant contribution to our understanding of the period’s patterns of ­settlement and activity – and prompt a critical examination of the settlement models used for the period to date.In a series of regional investigations of Funnel Beaker culture settlement over the last three decades, a model has been applied whereby the sites are divided up into base settlements and hunting stations, respectively. Associated with these were sites related to the ritual sphere: offerings, graves and causewayed enclosures. Collectively, these reveal the general organisation of the population in the landscape. But this model is constructed on the basis of a general consideration that has, in particular, demonstrated changes in the settlement development through time. If we take a closer look at the individual sites in order to obtain a better understanding of the dynamics of Neolithic settlement, the pattern of ‘base settlements and hunting stations’ becomes too rigid to work with – and perhaps even misleading.LandscapeThe site lies within the broad Egå valley, formed at the end of the Ice Age by glacial erosion and melt water. In Atlantic times a 5.5 km long and 1.5 km wide fjord, Egå Fjord, extended inland from the Bay of Aarhus. In the Early Sub-Boreal, when the site was active, the fjord was partially closed at its mouth by beach ridges and constituted a sheltered, shallow brackish water environment. The site lay on a low undulating moraine surface at the foot of the hilly northern side of the valley, 0.8 km from the shore of the fjord (fig. 1).The siteOn the edge of a slight elevation running down towards a narrow, peat-filled depression, the Neolithic finds extended over an area of 47 m2 – 12 m in length and 5.5 m in width – within a shallow hollow (figs. 2-4). The hollow was characterised by two crescent-shaped features (A16, A41), together with a further oval feature to the north (A8) (see figs. 5-6). The crescent-shaped features were able to shed some light on the formation of the hollow. Their form and stratigraphy revealed that they resulted from windthrows. In an archaeological context this phenomenon is often connected with disturbances that have disrupted the stratigraphy of archaeological deposits. But in this case the trees had been blown over prior to formation of the archaeological deposits and the shallow root pits functioned as an actual surface for the activities.The archaeological deposits had an average thickness of 5 cm and comprised dark, charcoal-rich sandy clay within which there was an even spread of dense finds concentrations. These lay directly over the heavy, stony yellow moraine clay. Intervening layers, for example earlier vegetation horizons, were not encountered. In certain areas, the finds, first and foremost flint debitage, a number of flint tools and a small quantity of potsherds, lay densely concentrated in up to three layers, one above the other. In some instances, heaps of homogeneous flint and axe flakes and chips could be readily distinguished, giving the impression of relatively undisturbed episodes of flint working.In spite of a careful search, no traces of post-built dwellings were found associated with the archaeological deposits. A central hearth was, however, revealed as well as possible traces of a fence or a flimsy hut wall (figs. 9-10). The distribution and composition of the finds around the hearth revealed this to be the hub of the site’s structure, where various activities had taken place. Close to the hearth were two large stones which could have served as seats or work surfaces. An elongated flat-bottomed pit of uncertain function located directly north of the hearth should perhaps, together with the discovery of a polygonal axe, be seen as an indication of ritual activities.The orientation of the windthrow pits shows that the trees fell away from each other, resulting in the formation at the site of a small sheltered hollow with exposed moraine clay (figs.7-8). The site stratigraphy suggests that only a short period of time elapsed before the finds were deposited within this hollow. This observation prompts the article’s hypothesis that the windthrow pits gave access to the moraine clay’s rich content of flint, which was then worked in situ.The artefactsThe artefacts are predominantly of flint. In their manufacture, use was made of local moraine-deposited flint which in this area is of particularly good quality and varied type. The flint tools and flint debitage have a total weight of 74.1 kg; the tools number 295 examples, while the debitage is estimated to include c. 10,000 pieces.The distribution of flint and stone artefacts is given in tables 1-2. Almost half the flint debitage can be linked to the production of axes of thin-butted type. In addition to large quantities of various axe flakes/chips, there are seven discarded blanks/rough-outs and 20 hammerstones (fig. 16).In the tool inventory, special attention should be drawn to the 120 burins (40.7%), an unusual feature in a Neolithic context (figs. 11-14), in addition to 38 core and flake drills (12.9%) and 35 knives (11.9%) (fig. 15). Further to these are 52 small tools in the form of blades or flakes with retouch or visible use-wear (17.6%). The burins were produced on simple robust flakes that appear to have been specially produced for the purpose. Transverse burins on retouch are in the majority, followed by edge burins (table 3). One find stands out from the rest, namely half of a finely-worked polygonal axe of basalt (fig. 17). This was not made at the site.A small, poorly-preserved assemblage of pottery (1.8 kg) lay deposited in concentrations around the site. In terms of vessel forms, the presence has been demonstrated of funnel beakers, a lugged beaker and a bowl. The decoration is characterised by simple rim ornamentation, vertical belly stripes and the use of twisted cord (fig. 18). The minimum number of vessels represented in the assemblage is calculated to be seven.DatingThe typological date for the site is based on the pottery, the flint axes, the polygonal axe, denticulates, a single ‘disk knife’ and, to a certain extent, the burins. The vessel form and decoration of the pottery corresponds to the Funnel Beaker culture’s phase TN II. There are close parallels in the pottery recovered from the palisade ditch at Sarup I, which is linked to the Fuchsberg group (note 38). This date is also supported by the flint and stone tools, although these also open up the possibility of a component from the subsequent MNA I.A radiocarbon analysis of a charred seed coat from the archaeological deposits near the hearth shows, with a probability of 95.4% (±2 standard deviations), a double peak with an 8.6% probability of a date of between 3630 and 3580 BC and a 86.8% probability for 3530-3360 BC. The greatest part of the curve corresponds, accordingly, with the radiocarbon dates for Sarup I.With a possible small component from MNA I, the date for the archaeological deposits falls within the Funnel Beaker culture’s TN II phase with links to the Fuchsberg group.SubsistenceThe conditions for preservation of bone at the site were unfortunately very poor. The humus content of the archaeological deposits does, however, bear witness to the presence of a certain amount of degraded organic material. The animal remains comprise two badly-preserved teeth of, respectively, a young domestic cow and a large ruminant. Further to these, 11 small bones were found by fine sieving, of which three are fish bones, probably cod.Soil samples processed by flotation yielded 23 charred cereal grains, of which 11 were of barley and one of wheat, while the others were unidentifiable. Charred hazelnut shells featured in several samples and a single charred apple pip was recorded.A strange component of small water-rolled stones found in the deposits could possibly originate from seaweed, bladder wrack, gathered on the coast. The function of the seaweed is unclear, but there are a number of possibilities, e.g. a soft underlay, fuel, animal fodder or manure; it could also have constituted human food.Activities and activity areasThe natural sources of good raw flint in Eastern Jutland are the coastal cliffs and potentially also the banks of streams and rivers, where the flint is exposed naturally and can be gathered directly. On the forest floor of the interior, flint would have been rarely encountered. It seems therefore very likely that the hollow created by the windfalls gave very welcome access to the flint in the moraine deposits, which could then have been the subject of more systematic searches and collection. Several of the flint nodules found in the archaeological deposits have only one or a few scars resulting from blows, probably resulting from testing of the flint quality. One very large block (42 kg) was found in four pieces scattered around the site, with a few missing pieces that could have been worked further (fig. 19).The debitage from the axe production has been analysed with the aim of discovering the types and number of axes produced at the site. Several definite axe-knapping episodes have been distinguished on the basis of in situ concentrations, identification of debitage from the same flint nodules and with the aid of refitting (figs. 21-23, table 4). The flint flakes have been classified according to the use of hard and soft knapping techniques, i.e. the employment of, respectively, hammerstones and fabricators of antler, in order to discover the number of stages in the production of the four-sided axes present at the site (figs. 20, 24-27). In the course of this analysis the character and extent of the material was compared with related finds and the results of modern experiments (note 60).Large flakes retaining the original cortex of the flint show that some pieces were produced in situ from raw unworked flint nodules (stage I), whereas other examples appear to have been brought to the site as roughly-worked axe blanks (stage II). The aim of the production was the manufacture of axes up to stage III. No clear traces of stage IV, the last trimming of the axe sides and edges, or of the final polishing, stage V, could be demonstrated. A total of about 15 individual axes were worked at the site, of which about half were abandoned and discarded at the site as failures, while the finished examples were taken away to another workshop or a base settlement to be given their final finish. Through comparisons with modern experiments, the total time expenditure for the axe production is estimated as a maximum of 12 hours. If production was continuous, then all that was involved was a single day’s work for two flint knappers. The quality of the work is considered to be fully on a par with the general level in the Funnel Beaker culture.The other activity that characterises the site is apparent from the large number of burins in the assemblage. Burins are associated with the working of hard materials such as antler and bone, and this was confirmed by wear analysis of 13 pieces from the site. The activity could well have involved other elements of the inventory such as drills, knives and diverse tools with retouch. The activities took place in particular in the vicinity of the hearth, but a particularly high concentration of burins and burin spalls was found on the eastern periphery, in the deeper part of the hollow, behind a possible fence (fig. 28). This could represent the deposition of burin waste or the existence of a small isolated work place.Even though burins rarely occur in large numbers at the settlements of the period, they are occasionally present and in a few cases they are seen in large numbers as for example at the site of Grønvang 2, near Kalundborg in Western Zealand.The items which were produced could have been antler axes, chisels, bodkins or harpoons. A close relationship with the production of flint axes is also conceivable in the form of the manufacture of antler fabricators. This is, however, not supported by evidence from other flint axe workshops, where burins have never been recorded in the tool inventory.The settlement around Egå Fjord in TN II (- MNA I)The area around the site and along the northern side of the fjord has, over the course of the past 12 years, been subjected to extensive and comprehensive archaeological investigation in connection with road construction and development of building land. It is therefore now possible to see the site in a wider settlement-related perspective for the period TN II - MNA I (fig. 29). The nearest settlement-like finds have been located 325 m ENE of the workshop site, but these are difficult to evaluate in detail due to disturbance later in prehistory. Possible base settlements with the remains of houses were encountered 2.1 km north and 7 km west of the site, respectively. In addition, possible hunting stations were demonstrated on the nearby shore of the fjord. Four other sites within a 2 km radius bear witness to ritual activities; these comprise two isolated system-ditch complexes and two dolmen sites.The area within a radius of 300 m of the site has been investigated via field-walking and trial excavations, and these did not reveal the existence of any contemporaneous settlement traces here. It can therefore be reasonably securely concluded that the workshop lay at a distance from the settlement sites. It is possible that it was located on the edge of recently-established arable fields. Clearance of the primeval forest would have given the wind easy access to the old forest trees which then, at the woodland edge, became easy victims for storms.Workshop sites of the Funnel Beaker cultureDuring the Funnel Beaker culture, workshops were often associated with flint quarrying and flint-knapping sites and several of these were specifically oriented towards axe production, for example that at Hastrup Vænget in Eastern Zealand.Apart from axe production, specialised workshop activities have rarely been recognised in the Funnel Beaker culture. The above-mentioned Grønvang 2 on Zealand resembles Lystrup Østergård with respect to its size and a large content of burins. Another site with a specialised activity is Studeli Klit in Northern Jutland, characterised by a huge number of flake drills.Neolithic sites that were not actual ordinary settlements but sites for special workshop activities are possibly under-represented in the overall archaeological record, either because they are small and easily overlooked during archaeological investigations or because their uniform and more specific site circumstances are more vulnerable to repeated and possibly also changing use of the localities. Several of the sites we perceive as base settlements could possibly represent the accumulated remains of more specialised activities. An important feature type relative to so-called base settlements is the house! Investigations of Scandinavian house remains from the period have demonstrated a clear tendency for houses, activity areas and refuse deposits not to be located in the same place; there may possibly have been rules with respect to cleanliness around settlement areas. This tendency has subsequently been demonstrated in connection with new archaeological investigations in Scania and in the Sarup area in SW Funen.Consequently, we must see settlement and activities in the early agricultural society as a more widespread and dynamic use of the landscape. In future regional investigations it will be important to look critically at the term ‘settlement’ and distinguish to a greater degree between sites for activities, refuse deposition and habitation. During excavations we should be aware of the minor find complexes and focus on their possible unique features – and remember that houses are to be looked for at some distance from the find-rich areas.Uffe RasmussenMoesgård Museum

An integrated experimental-numerical study of forced response for a mistuned bladed disk has been performed. A full chain for the predictive forced response analysis has been developed including data exchange between the computational fluid dynamics code and a code for the prediction of the nonlinear forced response for a bladed disk. The experimental measurements are performed at a full-scale single stage test rig with excitation by aerodynamic forces from gas flow. The numerical modeling approaches and the test rig setup are discussed. Comparison of experimentally measured and predicted values of blade resonance frequencies and response levels for a mistuned bladed disk without dampers is performed. A good correspondence between frequencies at which individual blades have maximum response levels is achieved. The effects of structural damping and underplatform damper parameters on amplitudes and resonance frequencies of the bladed disk are explored. It is shown that the underplatform damper significantly reduces scatters in values of the individual blade frequencies and maximum forced response levels.

Abstract Measurements revealed the contribution of multiple traveling waves to the flutter vibrations of bladed disks. Saturated flutter vibration, whether in this multi-wave or in its better-understood single-wave form, is a nonlinear phenomenon. However, it is still not understood of what physical origin the relevant nonlinearities are, and under what conditions single-wave or multi-wave flutter vibration occurs. Recent theoretical work suggests that multi-wave flutter vibration can be explained by strongly nonlinear frictional interblade coupling. The verity of this hypothesis is strictly limited by the simplicity of the considered model, namely, a cyclic chain of seven oscillators with frictional coupling and rather unrealistic aeroelastic behavior. In this work, it is demonstrated that nonlinear dynamical contact interactions at tip-shrouds are a likely cause for the observed multi-wave flutter vibration. To this end, a more realistic structural turbine blade row model with a more realistic aeroelastic behavior is considered. Some insight into its intriguing dynamics, dependence of limit states on initial conditions, and eigenvalue placement is provided. For instance, it is shown that there is an intimate relation between internal combination resonance conditions of certain traveling wave modes and the spectral content of single- and multi-wave flutter oscillations.

Abstract As turbomachinery systems continue to push the limits of modern technology, the modeling techniques being developed also continue to push modern computational limits. While modeling the pristine system during the design process is important, it is equally important to model behavior of mistuned systems, due to wear or manufacturing processes. This work carries out a statistical analysis on a two-stage system consisting of integrally bladed rotors. Various forms of large geometric mistuning, such as missing mass, bends, and dents, are considered. These forms of large mistuning are based on previously reported damage seen in actual engines that have ingested volcanic ash. This work also aims to investigate the interaction of these large mistuned systems with various levels of small mistuning to further understand this complex interaction. For every case studied, a reduced-order model (ROM) will be constructed that includes the effects of small and large mistuning. Large mistuning will only be applied to a single sector of a single stage. Random patterns of small mistuning will be applied to each case of large mistuning after which a modal analysis and a forced response analysis are run. By observing the energy distribution of each mode for the mistuned system, a qualitative trend can be created between various types and levels of large mistuning and the impact they have on changing the dynamics of the multistage system. The amplification factors from the forced response analyses help in understanding the impact small mistuning has when coupled with large mistuning and when the effects of small mistuning dominate over the large mistuning effects.

In order to analyze the vibration characteristics of mistuned multistage bladed disks of an aero-engine compressor, a finite element reduction model of mistuned multistage bladed disks is established based on substructure modal synthesis method. The accuracy of the substructure model was verified by comparing calculation accuracy of the substructure model and the integral model. The influence of different modal truncation numbers on the calculation results are discussed. The vibration modes of each stage of the bladed disks are obtained, the forced response is analyzed from the perspective of strain energy. The result shows that modal truncation number, rotation softening effect, and speed have significant effects on the dynamic frequency calculation results of the multistage bladed disks. The typical mode shapes of the first 200 orders of multistage bladed disks are obtained. With the increase of mistuning standard deviation, the strain energy of multistage bladed disk system decreases gradually.

Measurements are presented for a high-pressure transonic turbine stage operating at design-corrected conditions with forward and aft purge flow and blade film cooling in a short-duration blowdown facility. Four different film-cooling configurations are investigated: simple cylindrical-shaped holes, diffusing fan-shaped holes, an advanced-shaped hole, and uncooled blades. A rainbow turbine approach is used so each of the four blade types comprises a wedge of the overall bladed disk and is investigated simultaneously at identical speed and vane exit conditions. Double-sided Kapton heat-flux gauges are installed at midspan on all three film-cooled blade types, and single-sided Pyrex heat-flux gauges are installed on the uncooled blades. Kulite pressure transducers are installed at midspan on cooled blades with round and fan-shaped cooling holes. Experimental results are presented both as time-averaged values and as time-accurate ensemble-averages. In addition, the results of a steady Reynolds-averaged Navier–Stokes computational fluid dynamics (RANS CFD) computation are compared to the time-averaged data. The computational and experimental results show that the cooled blades reduce heat transfer into the blade significantly from the uncooled case, but the overall differences in heat transfer among the three cooling configurations are small. This challenges previous conclusions for simplified geometries that show shaped cooling holes outperforming cylindrical holes by a great margin. It suggests that the more complicated flow physics associated with an airfoil operating in an engine-representative environment reduces the effectiveness of the shaped cooling holes. Time-accurate comparisons provide some insight into the complicated interactions that are driving these flows and make it difficult to characterize cooling benefits.

Abstract This contribution focuses on the combined analysis of mistuning and unilateral blade-tip/casing contacts. A 2D phenomenological finite element model of an aircraft engine fan stage is considered. It is reduced by means of the Craig-Bampton component mode synthesis method and contact treatment relies on a Lagrange multiplier algorithm within an explicit time-integration scheme. Blade-tip/casing contacts are initiated through the deformed shape of a perfectly rigid casing. Mistuning is accounted for on the blades only. Monte Carlo simulations are carried out in both linear and nonlinear configurations, which allows to compare amplifications predicted in both context due to mistuning. Following a thorough convergence analysis of the proposed numerical strategy, the influence of mistuning level as well as the configuration of the external forcing are investigated. Presented results underline the detrimental consequences of mistuning in a nonlinear structural context, yielding even higher vibration amplifications than in a linear context. A cross-analysis between linear and nonlinear computations reveals that no correlation is found between linear and nonlinear amplifications which suggests that the effect of existing strategies to mitigate vibration amplifications within a linear context may not be suitable within a nonlinear context.

The introduction of longer last stage blading in steam turbine power plant offers significant economic and environmental benefits. The modern trend, adopted by most leading steam turbine manufacturers, is to develop long last stage moving blades (LSMBs) that feature a tip shroud. This brings benefits of improved performance due to better leakage control and increased mechanical stiffness. However, the benefits associated with the introduction of a tip shroud are accompanied by an increased risk of blade flutter at high mass flows. The shroud is interlocked during vibration, causing the first axial bending mode to carry an increased, out of phase, torsional component. It is shown that this change in mode shape, compared to an unshrouded LSMB, can lead to destabilizing aerodynamic forces during vibration. At a sufficiently high mass flow, the destabilizing unsteady aerodynamic work will exceed the damping provided by the mechanical bladed-disk system, and blade flutter will occur. Addressing the potential for flutter during design and development is difficult. Simple tests prove inadequate as they fail to reveal the proximity of flutter unless the catastrophic condition is encountered. A comprehensive product validation program is presented, with the purpose of identifying the margin for safe operation with respect to blade flutter. Unsteady computational fluid dynamics predictions are utilized to identify the mechanisms responsible for the unstable aerodynamic condition and the particular modes of vibration that are most at risk. Using this information, a directed experimental technique is applied to measure the combined aerodynamic and mechanical damping under operating conditions. Results that demonstrate the identification of the aeroelastic stability margin for a new LSMB are presented. The stability margin predicted from the measurements demonstrates a significant margin of safety.

Ceramic matrix composites (CMCs) provide several benefits over metal blades including weight and increased temperature capability, and have the potential for increased engine performance by reduction of the cooling flow bled from the compressor and by allowing engines to run at higher turbine inlet temperatures. These CMC blades must be capable of surviving fatigue (high cycle and low cycle), creep, impact, and any tip rub events due to the engine missions or maneuvers that temporarily close blade tip/shroud clearances. As part of a cooperative research program between GE Aviation and the Ohio State University Gas Turbine Laboratory, OSU GTL, the response of a CMC stage 1 low-pressure turbine blade has been compared with the response of an equivalent metal turbine blade using the OSU GTL large spin-pit facility (LSPF) as the test vehicle. Load cells mounted on the casing wall, strain gages mounted on the airfoils, and other instrumentation are used to assess blade tip rub interactions with a 120-deg sector of a representative turbine stationary casing. The intent of this paper is to present the dynamic response of both the CMC and the metal blades with the turbine disk operating at design speed and with representative incursion rates and depths. Casing wear and blade tip wear are both characterized for several types of rub conditions including a light, medium, and heavy rub at room temperature. For each condition, the rub primary dynamic modes have been evaluated, and the corresponding blade tip loads have been calculated. The preliminary results suggest that a CMC blade has similar abilities to a metal blade during a rub event.

An entire family of twisted and tapered low pressure steam turbine fast rotating condensation blading (SK) blades with pinned radial root and loosely assembled conical bolts is designed by scaling the aerodynamic and mechanical properties of the smallest airfoil. For SK blades operating with variable speed, the friction bolts, mounted in the upper airfoil part, provide either damping or coupling capabilities for the blades with respect to resonance conditions. The damping and coupling performance have been proven experimentally in the test rig of the real turbine. The measurements of the smallest SK-disk assembly under different operating conditions have allowed us to understand the dynamic and damping behavior of the bolts that are either friction dampers or coupling devices for the vibrating blades depending on the excitation level. In this paper, nonlinear dynamic analyses of the smallest and large SK-turbine stage are performed and compared with the experimental data. The modal blade dynamics is defined by 30 complex finite element (FE) mode shapes of the freestanding blades coupled by the disk whereby the bolt’s motion is described by six rigid body modes. The sticking contact condition between the blades and bolts is represented by the normal and tangential contact stiffnesses. These values are firstly estimated analytically with Hertz’s formulas for the FE reaction forces and contact areas. More realistic contact stiffness values are obtained from the iterative process, in which the resonance frequencies are calculated with the steady-state simulations and compared to the FE nodal diameter curves for sticking contact conditions that meet the experimental frequencies very well (Szwedowicz, J. et al., 2007, “Scaling Concept for Axial Turbine Stages With Loosely Assembled Friction Bolts: The Linear Dynamic Assessment Part 1,” Proceedings of ASME Turbo Expo 2007, Montreal, Canada, May 14–17, ASME Paper No. GT2007-27502). In nonlinear simulations, in case of exceeding the sticking contact condition, the induced friction forces are linearized by the harmonic balance method. In this manner, the microslipping and sticking contact behavior at all contact points are calculated iteratively for the specified excitation amplitudes, friction coefficient, contact roughness, and aerodamping values that are known from the experiment. The computed results of the tuned smallest SK blades agree with the experimental resonance stresses of 12 measured blades. Differences between the computed and measured stresses are caused by mistuning, which was not quantified in the experiment. The nonlinear dynamic analyses provide evidence of good damping performance for the smallest and large SK blades with respect to a wide range of excitation forces, different friction coefficients, and various aerodynamic damping values. For the analyzed resonances of the eighth engine order, the scalability of damping performance is found for the SK blades of different sizes.

A numerical and experimental study of partial admission in a low reaction two-stage axial air test turbine is performed in this paper. In order to model one part load configuration, corresponding to zero flow in one of the admission arcs, the inlet was blocked at one segmental arc, at the leading edge of the first stage guide vanes. Due to the unsymmetrical geometry, the full annulus of the turbine was modeled numerically. The computational domain contained the shroud and disk cavities. The full admission turbine configuration was also modeled for reference comparisons. Computed unsteady forces of the first stage rotor blades showed cyclic change both in magnitude and direction while moving around the circumference. Unsteady forces of first stage rotor blades were plotted in the frequency domain using Fourier analysis. The largest amplitudes caused by partial admission were at first and second multiples of rotational frequency due to the existence of single blockage and change in the force direction. Unsteady forces of rotating blades in a partial admission turbine could cause unexpected failures in operation; therefore, knowledge about the frequency content of the unsteady force vector and the related amplitudes is vital to the design process of partial admission turbine blades. The pressure plots showed that the nonuniformity in the static pressure field decreases considerably downstream of the second stage’s stator row, while the nonuniformity in the dynamic pressure field is still large. The numerical results between the first stage’s stator and rotor rows showed that the leakage flow leaves the blade path down into the disk cavity in the admitted sector and re-enters downstream of the blocked channel. This process compensates for the sudden pressure drop downstream of the blockage but reduces the momentum of the main flow.

In the early 1980s, Siemens developed a last stage fast rotating condensation blading (SK) blade with strongly twisted and tapered profiles for industrial condensing steam turbines, which operate with variable speed under high steam mass flow and excessive condensing pressures. To suppress alternating stresses of the lowest blade resonances, conical friction bolts are loosely mounted at the upper parts of adjacent airfoils. Also, these bolts couple the rotating blades, since steam excitation is lower than the friction threshold force on the bolt contacts. These coupling and damping capabilities were proven experimentally for the smallest SK blade at the test rig of the real turbine. By considering the similar mechanical and aerodynamic characteristics based on the tested smallest airfoil, the entire SK-blade family has been scaled up for reliable utilization in more than 500 industrial turbines operating for diverse ranges of power and speed. A recent trend to very large compression units, like gas to liquids, acid terephtalic, or methanol plants, imposes a need for further enlargement of the SK-blade family and its friction bolt, whose mechanical properties have been proven experimentally for the smallest airfoil. In this paper, the mechanical capabilities of the smallest and large SK blades coupled by the bolts are verified by using the finite element (FE) method. The static analyses with friction sliding on airfoil interfaces and the linear dynamic behavior of tuned disk assemblies are considered. The FE mesh quality and the proper boundary conditions at the radial fork root are accomplished by getting good agreements between the computed and measured resonance frequencies of the large freestanding blade at standstill. The validated mesh refinement and root boundary conditions are used further in all numerical FE analyses. For the large SK-disk assembly under spin-pit conditions, the obtained FE results are in very good agreement with the experimental Campbell diagrams, which are measured with the three gauges that also identify the stick-slip and stuck bolt’s contact conditions. Concerning the gauge outputs and the FE steady-state blade resonances computed for the analytically determined air jet excitation, the experimental spin-pit results demonstrate that the bolts are mainly in stuck contact conditions. Only in very narrow frequency ranges around resonance peaks, microslips on the bolts occur due to the resonance amplification of blade vibrations. This is proven indirectly by comparison of the overall damping values evaluated from the blade resonances at standstill and in the spin pit. The described linear dynamic concept assesses properly static stresses and free vibrations of the scaled disk assembly with friction bolts. For the steam excitation, which generates dynamic contact reactions bigger than the friction threshold forces, the realistic blade responses need to be obtained from the blade simulation with friction (Szwedowicz, J., Secall-Wimmel, T., and Duenck-Kerst, P., 2007, “Damping Performance of Axial Turbine Stages With Loosely Assembled Friction Bolts; the Non-Linear Dynamic Assessment; Part II,” Proceedings of ASME Turbo Expo 2007, Montreal, Canada, May 14–17, ASME Paper No. GT2007-27506).

In gas turbines, rim seals are fitted at the periphery of stator and rotor discs to minimize the purge flow required to seal the wheel-space between the discs. Ingestion (or ingress) of hot mainstream gases through rim seals is a threat to the operating life and integrity of highly stressed components, particularly in the first-stage turbine. Egress of sealing flow from the first-stage can be re-ingested in downstream stages. This paper presents experimental results using a 1.5-stage test facility designed to investigate ingress into the wheel-spaces upstream and downstream of a rotor disk. Re-ingestion was quantified using measurements of CO2 concentration, with seeding injected into the upstream and downstream sealing flows. Here, a theoretical mixing model has been developed from first principles and validated by the experimental measurements. For the first time, a method to quantify the mass fraction of the fluid carried over from upstream egress into downstream ingress has been presented and measured; it was shown that this fraction increased as the downstream sealing flow rate increased. The upstream purge was shown to not significantly disturb the fluid dynamics but only partially mixes with the annulus flow near the downstream seal, with the ingested fluid emanating from the boundary layer on the blade platform. From the analogy between heat and mass transfer, the measured mass-concentration flux is equivalent to an enthalpy flux, and this re-ingestion could significantly reduce the adverse effect of ingress in the downstream wheel-space. Radial traverses using a concentration probe in and around the rim seal clearances provide insight into the complex interaction between the egress, ingress and mainstream flows.

Abstract A linear quadratic Gaussian controller for active vibratory loads reduction in helicopters is proposed based on a revisited higher harmonic control input by active trailing-edge flaps. Conventional individual blade control input is redefined using N-1/rev inter-blade phase lead, N/rev collective, and N+1/rev inter-blade phase lag signals where 1/rev frequency modulation originate from the multi-blade coordinate transform. A Mach-scaled flap blade is designed and analyzed by the multi-body dynamics analysis DYMORE. A linear time-invariant representation is identified from N/rev envelopes of the input and output responses obtained by DYMORE analysis. A MATLAB/Simulink closed-loop control simulation is designed using the identified state-space realization. The N/rev vibratory loads are reduced up to 52% with flap deflections and the linear control results match well with the nonlinear responses obtained from DYMORE. Furthermore, the multi-variable closed-loop stability estimated by the loop transfer functions using disk margin analysis reveals sufficient gain and phase margins.

A method for inverse design of horizontal axis wind turbines (HAWTs) is presented in this paper. The direct solver for aerodynamic analysis solves the Reynolds-averaged Navier–Stokes (RANS) equations, where the effect of the turbine rotor is modeled as momentum sources using the actuator disk model (ADM); this approach is referred to as RANS/ADM. The inverse problem is posed as follows: for a given selection of airfoils, the objective is to find the blade geometry (described as blade twist and chord distributions) which realizes the desired turbine aerodynamic performance at the design point; the desired performance is prescribed as angle of attack (α) and axial induction factor (a) distributions along the blade. An iterative approach is used. An initial estimate of blade geometry is used with the direct solver (RANS/ADM) to obtain α and a. The differences between the calculated and desired values of α and a are computed and a new estimate for the blade geometry (chord and twist) is obtained via nonlinear least squares regression using the trust-region-reflective (TRF) method. This procedure is continued until the difference between the calculated and the desired values is within acceptable tolerance. The method is demonstrated for conventional, single-rotor HAWTs and then extended to multirotor, specifically dual-rotor wind turbines (DRWT). The TRF method is also compared with the multidimensional Newton iteration method and found to provide better convergence when constraints are imposed in blade design, although faster convergence is obtained with the Newton method for unconstrained optimization.

Abstract Air-cooled gas turbines employ bleed air from the compressor to cool vulnerable components in the turbine. The cooling flow, commonly known as purge air, is introduced at low radius, before exiting through the rim-seal at the periphery of the turbine discs. The purge flow interacts with the mainstream gas path, creating an unsteady and complex flowfield. Of particular interest to the designer is the effect of purge on the secondary-flow structures within the blade passage, the extent of which directly affects the aerodynamic loss in the stage. This paper presents a combined experimental and computational fluid dynamics (CFD) investigation into the effect of purge flow on the secondary flows in the blade passage of an optically accessible one-stage turbine rig. The experimental campaign was conducted using volumetric velocimetry (VV) measurements to assess the three-dimensional inter-blade velocity field; the complementary CFD campaign was carried out using unsteady Reynolds-averaged Navier–Stokes (URANS) computations. The implementation of VV within a rotating environment is a world first and offers an unparalleled level of experimental detail. The baseline flow-field, in the absence of purge flow, demonstrated a classical secondary flow-field: the rollup of a horseshoe vortex, with subsequent downstream convection of a pressure-side and suction-side leg, the former transitioning in to the passage vortex. The introduction of purge, at 1.7% of the mainstream flowrate, was shown to modify the secondary flow-field by enhancing the passage vortex, in both strength and span-wise migration. The computational predictions were in agreement with the enhancement revealed by the experiments.

The amount of cooling air assigned to seal high pressure turbine (HPT) rim cavities is critical for performance as well as component life. Insufficient air leads to excessive hot annulus gas ingestion and its penetration deep into the cavity compromising disk or cover plate life. Excessive purge air, on the other hand, adversely affects performance. Experiments on a rotating turbine stage rig which included a rotor–stator forward disk cavity were performed at Arizona State University (ASU). The turbine rig has 22 vanes and 28 blades, while the cavity is composed of a single-tooth lab seal and a rim platform overlap seal. Time-averaged static pressures were measured in the gas path and the cavity, while mainstream gas ingestion into the cavity was determined by measuring the concentration distribution of tracer gas (carbon dioxide) under a range of purge flows from 0.435% (Cw = 1540) to 1.74% (Cw = 6161). Additionally, particle image velocimetry (PIV) was used to measure fluid velocity inside the cavity between the lab seal and the rim seal. The data from the experiments were compared to time-dependent computational fluid dynamics (CFD) simulations using fluent CFD software. The CFD simulations brought to light the unsteadiness present in the flow during the experiment which the slower response data did not fully capture. An unsteady Reynolds averaged Navier–Stokes (RANS), 360-deg CFD model of the complete turbine stage was employed in order to increase the understanding of the swirl physics which dominate cavity flows and better predict rim seal ingestion. Although the rotor–stator cavity is geometrically axisymmetric, it was found that the interaction between swirling flows in the cavity and swirling flows in the gas path create nonperiodic/time-dependent unstable flow patterns which at the present are not accurately modeled by a 360 deg full stage unsteady analysis. At low purge flow conditions, the vortices that form inside the cavities are greatly influenced by mainstream ingestion. Conversely at high purge flow conditions the vortices are influenced by the purge flow, therefore ingestion is minimized. The paper also discusses details of meshing, convergence of time-dependent CFD simulations, and recommendations for future simulations in a rotor–stator disk cavity such as assessing the observed unsteadiness in the frequency domain in order to identify any critical frequencies driving the system.

The sealing of the stator-rotor gap and rotor-platform cooling are vital to the safe operation of the high-pressure turbine. Contrary to the experience in subsonic turbines, this paper demonstrates the potential to improve the efficiency in transonic turbines at certain rim seal rates. Two types of cooling techniques were investigated: purge gas ejected out of the cavity between the stator rim and the rotor disk, and cooling at the rotor-platform. The tests were carried out in a full annular stage fed by a compression tube at M2is=1.1, Re=1.1×106, and at temperature ratios reproducing engine conditions. The stator outlet was instrumented to allow the aerothermal characterization of the purge flow. The rotor blade was heavily instrumented with fast-response pressure sensors and double-layer thin film gauges. The tests are coupled with numerical calculations performed using the ONERA’s code ELSA. The results indicate that the stator-rotor interaction is significantly affected by the stator-rim seal, both in terms of heat transfer and pressure fluctuations. The flow exchange between the rotor disk cavity and the mainstream passage is mainly governed by the vane trailing edge shock patterns. The purge flow leads to the appearance of a large coherent vortex structure on the suction side of the blade, which enhances the overall heat transfer coefficient due to the blockage effect created. The impact of the platform cooling is observed to be restricted to the platform, with negligible effects on the blade suction side. The platform cooling results in a clear attenuation of pressure pulsations at some specific locations. The experimental and computational fluid dynamics results show an increase in the turbine performance compared with the no rim seal case. A detailed loss breakdown analysis helped to identify the shock loss as the major loss source. The presented results should help designers improve the protection of the rotor platform while minimizing the amount of coolant used.

The effect of rotor purge flow on the unsteady aerodynamics of a high-pressure turbine stage operating at design corrected conditions has been investigated, both experimentally and computationally. The experimental configuration consisted of a single-stage high-pressure turbine with a modern film-cooling configuration on the vane airfoil and the inner and outer end wall surfaces. Purge flow was introduced into the cavity located between the high-pressure vane and the high-pressure disk. The high-pressure blades and the downstream low-pressure turbine nozzle row were not cooled. All of the hardware featured an aerodynamic design typical of a commercial high-pressure ratio turbine and the flow path geometry was representative of the actual engine hardware. In addition to instrumentation in the main flow path, the stationary and rotating seals of the purge flow cavity were instrumented with high frequency response flush-mounted pressure transducers and miniature thermocouples in order to measure the flow field parameters above and below the angel wing. Predictions of the time-dependent flow field in the turbine flow path were obtained using FINE/Turbo, a three-dimensional Reynolds-averaged Navier–Stokes computational fluid dynamics CFD code that had the capability to perform both a steady and unsteady analysis. The steady and unsteady flow fields throughout the turbine were predicted using a three blade-row computational model that incorporated the purge flow cavity between the high-pressure vane and disk. The predictions were performed in an effort to mimic the design process with no adjustment of boundary conditions to better match the experimental data. The time-accurate predictions were generated using the harmonic method. Part I of this paper concentrates on the comparison of the time-averaged and time-accurate predictions with measurements in and around the purge flow cavity. The degree of agreement between the measured and predicted parameters is described in detail, providing confidence in the predictions for the flow field analysis that will be provided in Part II.

Contact interfaces with dry friction are frequently used in turbomachinery. Dry friction damping produced by the sliding surfaces of these interfaces reduces the amplitude of bladed-disk vibration. The relative displacements at these interfaces lead to fretting-wear which reduces the average life expectancy of the structure. Frequency response functions are calculated numerically by using the multi-harmonic balance method (mHBM). The dynamic Lagrangian frequency-time method is used to calculate contact forces in the frequency domain. A new strategy for solving nonlinear systems based on dual time stepping is applied. This method is faster than using Newton solvers. It was used successfully for solving Nonlinear CFD equations in the frequency domain. This new approach allows identifying the steady state of worn systems by integrating wear rate equations a on dual time scale. The dual time equations are integrated by an implicit scheme. Of the different orders tested, the first order scheme provided the best results.

The detailed mechanisms of purge flow interaction with the hot-gas flow path were investigated using both unsteady computationally fluid dynamics (CFD) and measurements for a turbine operating at design corrected conditions. This turbine consisted of a single-stage high-pressure turbine and the downstream, low-pressure turbine nozzle row with an aerodynamic design equivalent to actual engine hardware and typical of a commercial, high-pressure ratio, transonic turbine. The high-pressure vane airfoils and inner and outer end walls incorporated state-of-the-art film cooling, and purge flow was introduced into the cavity located between the high-pressure vane and disk. The flow field above and below the blade angel wing was characterized by both temperature and pressure measurements. Predictions of the time-dependent flow field were obtained using a three-dimensional, Reynolds-averaged Navier–Stokes CFD code and a computational model incorporating the three blade rows and the purge flow cavity. The predictions were performed to evaluate the accuracy obtained by a design style application of the code, and no adjustment of boundary conditions was made to better match the experimental data. Part I of this paper compared the predictions to the measurements in and around the purge flow cavity and demonstrated good correlation. Part II of this paper concentrates on the analytical results, looking at the primary gas path ingestion mechanism into the cavity as well as the effects of the rotor purge on the upstream vane and downstream rotor aerodynamics and thermodynamics. Ingestion into the cavity is driven by high static pressure regions downstream of the vane, high-velocity flow coming off the pressure side of the vane, and the blade bow waves. The introduction of the purge flow is seen to have an effect on the static pressure of the vane trailing edge in the lower 5% of span. In addition, the purge flow is weak enough that upon exiting the cavity, it is swept into the mainstream flow and provides no additional cooling benefits on the platform of the rotating blade.

Abstract The sea is an important renewable energy resource for its extension and the power conveyed by waves, currents, tides, and thermal gradients. Amongst these physical phenomena, sea waves are the source with the highest energy density and may contribute to fulfilling the global increase of power demand. Despite the potential of sea waves, their harnessing is still a technological challenge. Oscillating water column systems operating with Wells turbines represent one of the most straightforward and reliable solutions for the optimal exploitation of this resource. An analytical model and computational fluid dynamics models were developed to evaluate the functioning of monoplane isolated Wells turbines. For the former modeling typology, a blade element momentum code relying on the actuator disk theory was applied, considering the rotor as a set of airfoils. For the latter modeling typology, a three-dimensional multi-block technique was implemented to create the computational domain with a fully mapped mesh composed of hexahedral elements. The employment of circumferential periodic boundary conditions allowed for the reduction of computational power and time. The models use Reynolds-averaged Navier-Stokes (RANS) or u-RANS schemes with a multiple reference frame approach or the u-RANS formulation with a sliding mesh approach. The achieved results were compared with analytical and experimental literature data for validation. All the developed models showed good agreement. The analytical model is suitable for a fast prediction of the turbine operation on a wide set of configurations during the first design stages, while the computational fluid dynamics (CFD) models are indicated for the further investigation of the selected configurations.

This paper summarizes the work of a five year research program into the heat transfer within cavities adjacent to the main annulus of a gas turbine. The work has been a collaboration between several gas turbine manufacturers, also involving a number of universities working together. The principal objective of the study has been to develop and validate computer modeling methods of the cooling flow distribution and heat transfer management, in the environs of multistage turbine disk rims and blade fixings, with a view to maintaining component and subsystem integrity, while achieving optimum engine performance and minimizing emissions. A fully coupled analysis capability has been developed using combinations of commercially available and in-house computational fluid dynamics (CFD) and finite element (FE) thermomechanical modeling codes. The main objective of the methodology is to help decide on optimum cooling configurations for disk temperature, stress, and life considerations. The new capability also gives us an effective means of validating the method by direct use of disk temperature measurements, where otherwise, additional and difficult to obtain parameters, such as reliable heat flux measurements, would be considered necessary for validation of the use of CFD for convective heat transfer. A two-stage turbine test rig has been developed and improved to provide good quality thermal boundary condition data with which to validate the analysis methods. A cooling flow optimization study has also been performed to support a redesign of the turbine stator well cavity to maximize the effectiveness of cooling air supplied to the disk rim region. The benefits of this design change have also been demonstrated on the rig. A brief description of the test rig facility will be provided together with some insights into the successful completion of the test program. Comparisons will be provided of disk rim cooling performance for a range of cooling flows and geometry configurations. The new elements of this work are the presentation of additional test data and validation of the automatically coupled analysis method applied to a partially cooled stator well cavity (i.e., including some local gas ingestion) and also the extension of the cavity cooling design optimization study to other new geometries.

The development of new wake models is currently one of the key approaches envisioned to further improve the levelized cost of energy of wind power. While the wind energy literature abounds with operational wake models capable of predicting in fast-time the behavior of a wind turbine wake based on the measurements available (e.g., SCADA), only few account for dynamic wake effects. The present work capitalizes on the success gathered by the Dynamic Wake Meandering formulation and introduces a new operational dynamic wake modeling framework aimed at capturing the wake dynamic signature at a low computational cost while relying only on information gathered at the wind turbine location. In order to do so, the framework brings together flow sensing and Lagrangian flow modeling into a unified framework. The features of the inflow are first inferred from the turbine loads and operating settings: a Kalman filter coupled to a Blade Element Momentum theory solver is used to determine the rotor-normal flow velocity while a Multi-Layer Perceptron trained on high-fidelity numerical data estimates of the transverse wind velocity component. The information recovered is in turn fed to a Lagrangian flow model as a source condition and is propagated in a physics-informed fashion across the domain. The ensuing framework is presented and then deployed within a numerical wind farm where its performances are assessed. The computational affordability of the proposed model is first confirmed: 7 × 10−4 wall-clock seconds per simulation second are required to simulate a small 12 turbines wind farm. Large Eddy Simulations of wind farm using advanced actuator disks are then used as a baseline and a strong focus is laid on the study of the wake meandering features. Comparison against the Large Eddy Simulation baseline reveals that the proposed model achieves good estimates of the flow state in both low and high Turbulence Intensity configurations. The model distinctly provides additional insight into the wake physics when compared to the traditional steady state approach: the wake recovery is consistently accounted for and the wake meandering signature is captured as far as 12D downstream with a correlation score ranging from 0.50 to 0.85.

Ensuring an adequate life of high pressure turbines requires efficient cooling methods such as rim seal flow ejection from the stator-rotor wheel space cavity interface, which prevents hot gas ingress into the rotor disk. The present paper addresses the potential to improve the efficiency in transonic turbines at certain rim seal ejection rates. To understand this process, a numerical study was carried out, combining computational fluid dynamic (CFD) simulations and experiments on a single stage axial test turbine. The three dimensional steady CFD analysis was performed, modeling the purge cavity flow ejected downstream of the stator blade row at three flow regimes: subsonic M2=0.73, transonic M2=1.12, and supersonic M2=1.33. Experimental static pressure measurements were used to calibrate the computational model. The main flow field-purge flow interaction is found to be governed by the vane shock structures at the stator hub. The interaction between the vane shocks at the hub and the purge flow has been studied and quantitatively characterized as a function of the purge ejection rate. The ejection of 1% of the core flow from the rim seal cavity leads to an increase in the hub static pressure of approximately 7% at the vane trailing edge. This local reduction of the stator exit Mach number decreases the trailing edge losses in the transonic regime. Finally, a numerically predicted loss breakdown is presented, focusing on the relative importance of the trailing edge losses, boundary layer losses, shock losses, and mixing losses, as a function of the purge rate ejected. Contrary to the experience in subsonic turbines, results in a transonic model demonstrate that ejecting purge flow improves the vane efficiency due to the shock structure modification downstream of the stator.