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Response surface based robust design optimization on the example of a high pressure turbine blade
(2015)
Nowadays in a product design process the manufacturing tolerances have to be considered. Therefore a deterministic optimization needs to be converted into a robust design optimization. Usually the reference geometry is represented by a parametric model and an appropriate set of default parameters. In the robust design approach this set is replaced by a set of distributed parameters. These distributions are known from a previous design or needs to be estimated.
This work is about a robust design and multi objective optimization of a high pressure turbine blade (first row) from an actual aero engine. The multidisciplinary objectives are the combined life of the aero-foil (LCF and creep) for the outer and inner geometry, the efficiency and the mass of the blade. For the input set different kinds of parameter will be examined. Apart from the major geometry parameters, which represent the external surface of the blade, parameters for material and boundary conditions will be investigated as well. The used workflow contains the Rolls-Royce tool parablading for the creation of the external aero-foil, Siemens NX for general geometry manipulation, Hydra as Navier-Stokes solver and SC03 for the structural problem and is set up in the automation software ISight.
Focus of this work is the creation of response surfaces and physical integrity of the delivered results. Therefore, different validation criteria will be consulted. These are implemented in a Matlab toolbox and tested on typical optimization test problems. Based on the validated response surfaces a huge number of evaluations is possible, which is necessary for a robust design optimization. As the major result a set of Pareto optimal designs will be delivered.
The design and development process of an aero engine is a complex and time-consuming task that involves many disciplines and company departments with different objectives and requirements. Along the preliminary design phase, multiple concepts are assessed in order to select a competitive technology. The engine design process, which was traditionally subdivided into modular component tasks, is nowadays considered as a multi-disciplinary workflow. Having recognized the need for developing advanced turbine preliminary design tools, this work focuses on enhancing the integration of turbine design disciplines, improving the accuracy of models and speeding the time to generate models.
The proposed process facilitates an automated turbine Secondary Air System (SAS) and turbine discs concept definition. Furthermore, the process of CAD models and flow network models generation is accelerated via automation of the engineering workflow. This is accomplished through a novel Java based data model, where the design of turbine discs and SAS features is captured in a programmable framework.
In the application section, the preliminary design definition of a reference HP turbine subsystem is replicated using the newly developed common design environment. The automated workflow is then used to generate the corresponding CAD models, recognize the subsystem flow network, and generate the 1D flow network model. The results are then compared to the experimentally validated model of a reference engine. As conclusion, the automated workflow offers a quick and parametric model generation process, while providing a good level of fidelity for the preliminary design phase.
Copyright © 2015 by Rolls-Royce Deutschland Ltd & Co KG
This paper describes preparation, execution and evaluation of a comprehensive bladed disk spin test series. At the example of an turbine impeller the effects of rotation and temperature are analyzed with special focus on mistuning and damping. The forced response is measured synchronously via 13 identical positioned strain gauges on each blade as well as via blade tip-timing. Subsequently it is possible to compare the results of both systems. During the test series rotational speed varies in the range from 10.000 up to 19.000 RPM. Simultaneously, the wheel is heated up to 820 K by an oven. A number of pre-selected natural frequencies, damping ratios and operating deflection shapes are evaluated and compared with respect to different rotational speeds and impeller temperatures.
Copyright © 2015 by ASME
With increasing demands for reliability of modern turbomachinery blades the quantification of uncertainty and its impact on the designed product has become an important part of the development process. This paper aims to contribute to an improved approximation of expected vibration amplitudes of a mistuned rotor assembly under certain assumptions on the probability distribution of the blade’s natural frequencies. A previously widely used lumped mass model is employed to represent the vibrational behavior of a cyclic symmetric structure. Aerodynamic coupling of the blades is considered based on the concept of influence coefficients leading to individual damping of the traveling wave modes. The natural frequencies of individual rotor blades are assumed to be normal distributed and the required variance could be estimated due to experiences with the applied manufacturing process. Under these conditions it is possible to derive the probability distribution of the off-diagonal terms in the mistuned equations of motions, that are responsible for the coupling of different circumferential modes. Knowing these distributions recent limits on the maximum attainable mistuned vibration amplitude are improved. The improvement is achieved due to the fact, that the maximum amplification depends on the mistuning strength. This improved limit can be used in the development process, as it could partly replace probabilistic studies with surrogate models of reduced order. The obtained results are verified with numerical simulations of the underlying structural model with random mistuning patterns based on a normal distribution of individual blade frequencies.
Copyright © 2015 by ASME
To achieve reverse objectives in engine design, advanced modelling and analysis methods are among the key research technologies. In the presented work, a robust design optimization of a first stage high pressure turbine blade has been carried out. This blade derives from a current production of a Rolls-Royce aero engine.
The motivation of this work is to show that the methodology of robust design optimization can be applied to high pressure turbine blades. A fully automated workflow, which encapsulated the integral blade design and analysis process, has been used. The main workflow objective is a representative life value of the external surface of the blade. In addition, the workflow enables the engineering uses to consider sub objectives like mass, efficiency and life at critical locations of the blade. These can also be taken into account in the multi-objective robust design optimization. This research also focuses on the use of surrogate models, with attention to the delivery of a physically correct result. For this purpose, the validation of the applied methods has a huge significance and a toolbox was created to generate and evaluate the quality of the surrogate models.
In the present case sixteen geometry parameters were considered. In order to show that this methodology is not limited to geometry variation, parameters for material specification and for boundary conditions were varied in addition. The surrogate model was trained by the workflow generated DoE-data and could be used for different kinds of optimization.
As a conclusion, it has been demonstrated that the methodology can be used for the engineering design process of turbine blades, while delivering physically correct results. The different techniques for surrogate modelling were examined and compared. With the help of these surrogate models, an optimization of life, mass and efficiency with 22.5 million evaluations was possible. Finally, an overview of the methodology for the case of a real world turbine blade could be given, and an improved blade in the sense of multi-objective robust design was found.
Copyright © 2015 by Rolls-Royce Deutschland Ltd & Co KG
The forced response of an E3E-type high pressure compressor blisk front rotor is analyzed with regard to intentional mistuning and its robustness towards additional random mistuning. Both a chosen alternating mistuning pattern and artificial mistuning patterns optimized concerning the forced response are considered. Focusing on three different blade modes, subset of nominal system mode-based reduced order models are employed to compute the forced response. The disk remains unchanged while the Young’s modulus of each blade is used to define the particular mistuning pattern. The well established aerodynamic influence coefficient technique is employed to model aeroelastic coupling and hence to consider the strongly mode- and inter blade phase angle-dependent aerodynamic damping contribution.
It has been found that a reduction of the maximum forced response beyond that of the tuned reference can be achieved for particular mistuning patterns and all modes considered. This implies an exciting engine order which would cause a low nodal diameter mode in case of a tuned blisk. At best a nearly 50% reduction of maximum response magnitudes is computed for the fundamental bending mode and large mistuning. The solution proved to be robust towards additional random mistuning of reasonable magnitude, which is of particular interest with regard to a potential technical realization. In case of small mistuning as assumed for the first torsion and the longitudinal bending mode the advantage of achieving response magnitudes beyond the tuned reference gets lost indeed, if random mistuning is superimposed. However, mostly a lower response level is calculated compared to responses obtained from models adjusted to mistuning determined by experiment.
Copyright © 2015 by ASME
The impact performance of structural components made of fibre-reinforced plastic is often one of the limiting properties during the design process. To improve the damage resistance regarding transverse low-velocity impact loading, a rubber layer (KRAIBON®) is integrated into the composite laminate of tubular carbon/epoxy specimens. Numerous impact tests, using two different rubber compounds and three different layups, are carried out. The specimens are impacted using a modified Charpy pendulum. Force–time histories have been used to determine the damage threshold load. To visualise damage such as delaminations and inter-fibre failures, the impacted samples have been examined using microsectioning.
It is shown that a significant improvement in impact damage resistance can be achieved by integrating a rubber layer into a carbon/epoxy laminate.
Moderne Verbrennungskraftmaschinen müssen ein stetig wachsendes Anforderungsprofil in Bezug auf Wirtschaftlichkeit, Leistung und Umweltfreundlichkeit erfüllen. In diesem Zusammenhang hat die Turboaufladung von Verbrennungsmotoren an Bedeutung gewonnen. Bei Turboladern kleiner und mittlerer Baugröße, deren Turbinen einen Durchmesser zwischen 30 und 250 mm aufweisen, kommen vornehmlich gegossene Laufräder zum Einsatz. Am Institut für Verkehrstechnik der Brandenburgischen Technischen Universität Cottbus-Senftenberg wurde im Rahmen eines FVV-Forschungsvorhabens der Einfluss charakteristischer Betriebsgrößen eines Turboladers auf das strukturdynamische Verhalten solcher Radialturbinenräder untersucht.
In this paper a successful topology optimization of a centrifugally loaded aero-engine part is presented. For the topology optimization, which is a nonlinear problem due to several contact regions, a self-developed topology optimization algorithm in combination with a commercial FE-solver is used. The goal of the optimization was the reduction of stresses in the structure.
©2014 Rolls-Royce Deutschland Ltd & Co. KG. Published by Elsevier Masson SAS. All rights reserved.
Considerations About the Necessary Mesh Density of Bearings in Detailed Finite Element Models
(2014)
In order to predict properly the behavior of very complex mechanical models, much focus needs to be done on the level of model details as well as the techniques used to predict component movements based on mechanical and thermal loads. In particular bearings and joints play a significant role in big model assemblies such as aero-engines where most of the structures are modeled by solid elements rather than using traditional shell or beam elements. This approach is very complex and expensive in terms of computational effort however can lead to increased simulation accuracy when done properly.
This publication will answer questions related to the modeling techniques required for detailed bearings (not only rotor bearings) and joints of an aero-engine application where these components are not idealized or simplified, i.e. the ball in a ball joint is meshed by solid elements. The investigation will discuss the question about the number of elements needed to mesh a ball joint in such a way that a correct rotation is possible. If the mesh is too coarse, a rotation would be impossible due to the faceting of the rotating parts. It will be shown that a proper rotation depends on a correct relation between the radius of the inner ball, the gap size of the bearing and the number of nodes in the circumferential direction. For this relation an analytical formula has been derived and successfully tested at some examples. Furthermore, some finite element codes offer the possibility of smoothed contact surfaces. These options improve the situation but they might cause issues too. For this reason these smoothed contact options are also considered under the aspects mentioned above.
Copyright © 2014 by Rolls-Royce Deutschland Ltd & Co KG
Aero engine disc forgings are subjected to heat treatment operations, i.e., solution treatment followed by quenching and artificial aging, with the aim of achieving improved mechanical material properties. During heat treatment high inhomogeneous temperature gradients and long loading times at elevated temperatures occur and lead to the development and partial relaxation of bulk residual stresses. The intention of this paper is to describe the residual stress modelling of a nickel-based ATI 718Plus® superalloy disc forging. For this purpose, an uncoupled thermomechanical finite element problem is solved consisting of a thermal model based on transient, spatially varying heat transfer coefficients (HTCs) and a stress model incorporating the nonlinear material behaviour to account for thermal induced inelastic deformations. A graphical user interface based application has been created for the automatic estimation of the a priori unknown HTCs by using a serial solution procedure for the two dimensional inverse heat conduction problem (IHCP) based on the function specification method. The estimated temperature fields have been compared at the thermocouple positions with the corresponding measurement data and confirm the suitability of the inverse algorithm to this problem. A rate-independent elasto-plastic constitutive model is used to simulate the residual stress formation while quenching the disc forging. Two creep models have been adjusted to uniaxial tensile test data and applied to simulate the stress relaxation during aging. Finally, this paper presents the numerical results of the stress analysis.
Copyright © 2014 by Rolls-Royce Deutschland Ltd & Co KG
The design of both efficient and reliable turbomachinery blades demands a detailed knowledge of static and dynamic forces during operation.
This paper aims to contribute to the proper identification of dynamic excitation mechanisms acting on an axial turbine rotor, particularly with regard to deviations of the NGV’s nominal geometry due to the use of variable vanes or tolerances in manufacturing.
As variations of the NGV’s geometry disturb the perfectly periodic pattern of the downstream flow features, other spectral components than those correlated with the number of stator vanes are possible to appear. These frequency components may lead to low engine order excitation of fundamental blade modes at high engine speeds. Under these operating conditions the rotor is already highly loaded with centrifugal forces and additional dynamic excitation may cause unacceptable stresses.
Thus aerodynamic mistuning might be a limiting criterion for the design of a highly loaded turbine rotor.
Within this paper 2 dimensional CFD-models are used to investigate both, the determination of the wake of a geometric mistuned stator guide vane and the influence of the resulting excitation on the adjacent rotor stage due to aerodynamically mistuned flow. In order to generate a mistuned NGV geometry, variations of pitch and stagger angle are taken into account and a mesh morpher is used to produce computational domains of the mistuned geometry on the basis of a nominal mesh.
Additionally a simplified reconstruction process based on a set of CFD computations will be introduced, being able to reproduce the spectral components of the mistuned wake by specifying a certain geometric mistuning distribution.
The prediction of the resulting modal forces is carried out in time domain and approaches with lower fidelity are investigated with respect to their capability of reproducing the key features of an aerodynamically mistuned excitation mechanism.
The forced response of the first rotor of an E3E-type high pressure compressor blisk is analyzed with regard to varying mistuning, varying engine order excitations and the consideration of aeroelastic effects. For that purpose, SNM-based reduced order models are used in which the disk remains unchanged while the Young’s modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient technique is employed to model aeroelastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades’ Young’s modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aeroelastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.
Copyright © 2014 by Rolls-Royce Deutschland Ltd & Co KG
The following paper presents a numerical analysis of a deep surge cycle of a 4.5 stage research compressor. The resulting unsteady loads are used to determine the response of two particular rotor blade rows that are then compared to strain gauge data from measurements. Within a deep surge cycle the compressor experiences a rapid change of the flow field from forward to reversed flow. This rapid breakdown is linked to a new mean blade load. Hence, the rapid change in blade loads are able to excite fundamental blade modes similar to an impulse load. The resulting vibration magnitudes might reach critical levels. This paper demonstrates two different approaches to evaluate the unsteady flow during a surge cycle.
The first uses a three dimensional, time accurate finite volume solver for viscid compressible flows to calculate the transient surge cycle of the compressor. The compressor itself is represented by a multi-blade-row sector model. The second approach makes use of the same solver and compressor domain to determine steady state characteristics of the HPC in forward, stalled and reversed flow. Based on these characteristics an one dimensional finite volume solver for inviscid compressible flows was developed to determine the transient compressor behavior. The one dimensional solver represents the compressor by source terms that are linked to the previously determined steady state characteristics.
Copyright © 2014 by Rolls-Royce Deutschland Ltd & Co KG
Impact of the Secondary Air System Design Parameters on the Calculation of Turbine Discs Windage
(2014)
The rotating components in gas turbines are very highly stressed as a result of the centrifugal and thermal loads. One of the main functions of the secondary air system (SAS) is to ensure that the rotating components are surrounded by air that optimizes disc lifing and integrity. The SAS is also responsible for the blade cooling flow supply, preventing hot gas ingestion from the main annulus into the rotor-stator cavities, and for balancing the net axial load in the thrust bearings. Thus, the SAS design requires a multidisciplinary compromise to provide the above functions, while minimizing the penalty of the secondary flows on engine performance.
The phenomenon known as rotor-stator drag or windage is defined as the power of the rotor moment acting on its environment. The power loss due to windage has a direct impact on the performance of the turbine and the overall efficiency of the engine. This paper describes a novel preliminary design approach to calculate the windage of the rotor-stator cavities in the front of a typical aero engine HP turbine. The new method is applied to investigate the impact of the SAS design parameters on the windage losses and on the properties of the cooling flows leading to the main annulus.
Initially, a theoretical approach is followed to calculate the power losses of each part of the HPT front air feed system. Then, a 1D-network integral model of the cavities and flow passages of the HPT front is built and enhanced with detailed flow field correlations. The new 1D-flow network model offers higher fidelity regarding local effects. A result comparison between the theoretical calculation and the prediction of the enhanced flow network model puts forward the relevance of the local flow field effects in the design concept of the SAS.
Using the enhanced 1D-flow network models, the SAS design parameters are varied to assess their influence on the windage and pumping power calculation. As a conclusion, the paper shows how the SAS design can have a significant influence on the HPT overall power and the air that is fed back into the turbine blade rows. Controlling these features is essential to bid a competitive technology in the aero engine industry.
Copyright © 2014 by Rolls-Royce Deutschland Ltd & Co KG
A mistuned radial turbine impeller is analyzed with respect to the impact of varying ambient pressures and temperatures as well on frequency response functions and modal damping ratios. Beginning at room conditions, a finite element model of an impeller wheel at rest is updated based on experimentally determined mistuning in terms of blade dominated frequencies. The following numerical forced response analyses yield a maximum blade displacement amplification of 67% compared to the tuned reference. In addition, modal damping ratios are determined in dependence on the ambient pressure ranging from technical vacuum at 1 mbar up to 6000 mbar in a pressure chamber. Shaker excitation and laser Doppler vibrometry response measurement is employed in this context. A linear dependence of modal damping ratios on ambient pressure and a dominating damping contribution of the surrounding air even for higher modes could be proved. Moreover, the experimental determination of frequency response functions (FRF) at technical vacuum yields a better separation of resonance peaks compared to room conditions at 1013 mbar and hence, this data allows for more accurate model-updates in principle. It is proved that numerical models updated regarding mistuning at room conditions are well suited to predict the forced response at arbitrary pressures if measured modal damping ratios at these pressures are considered. Finally, within analyzing the effect of increasing structural temperatures with the surrounding air at 1013 mbar included slightly decreasing resonance frequencies but strongly increasing FRF-amplitudes are determined.
Copyright © 2014 by ASME
Diese Arbeit beschäftigt sich mit einem Prozeßschritt bei der Herstellung von Siliziumwafern, welche als Ausgangsprodukt für Halbleiterbauelemente dienen. Die Wafer durchlaufen bei der Herstellung unterschiedliche Prozesse, unter anderem das Annealing. Während des Anneals werden intrinsische Kristalldefekte, sog. Crystal originated Pits (COPs), bei über 1000°C thermisch aufgelöst. Der Temperaturbereich liegt dabei 200-300 °C unterhalb der Schmelztemperatur von Silizium. Demzufolge ist die Fließgrenze extrem herabgesetzt, so daß es infolge mechanischer und thermischer Belastungen zum Vergleiten (Fließen) im Kristallgitter und damit
zur Qualitätsbeeinträchtigung kommen kann.
Es wird erstmals aus mechanischer Sicht der komplexe Annealprozeß mit allen Einzelaspekten simulatorisch abgebildet und quantitativ erfaßbar gemacht. Dabei wird zum Einen das Ziel verfolgt, ein Lagerungskonzept zu entwickeln, welches den Ansprüchen an Reinheit, Temperaturbeständigkeit und Herstellbarkeit gerecht wird und zum Anderen den gesamten Anneal - Prozeß so zu gestalten, daß die Ausbeute von Wafern pro Zeiteinheit maximiert wird, ohne mit unerwünschten Vergleitungen rechnen zu müssen.
Die vorliegende Arbeit gliedert sich in einen Grundlagenteil und einen praktischen Teil. Wesentlich für die Erfassung des Prozesses im Simulationsmodell sind verschiedene Effekte, welche zunächst theoretisch anhand einfacher analytischer und numerischer Beispiele, sowie versuchstechnisch aufgearbeitet werden sollen. Die in der Arbeit untersuchten Effekte beziehen sich auf:
- die besonderen Materialeigenschaften des Silizium - Einkristalls, insbesondere dessen temperaturabhängige Fließgrenze (Upper Yield Stress)
- das Lagerungskonzept, verbunden mit Kontaktproblemen zwischen Wafer und Lager (Support)
- das Biegeproblem im Wafer
- das Aufheizproblem bedingt durch die Wärmeübertragungsmechanismen Strahlung (zwischen Ofenwand und Wafer/Support), Leitung (innerhalb des Wafers und des Supports) und Konvektion des Gases (innerhalb des Ofens)
Im praktischen Teil soll der Anneal mit Hilfe von Simulationssoftware (Finite Elemente Methode, Computational Fluid Dynamics), durch Optimierung der Lagerung und des Aufheizprozesses verbessert werden. Für die Bearbeitung dieses Kapitels werden die Untersuchungen aus dem theoretischen Teil der Arbeit als Referenz herangezogen.
The forced response of the first rotor of an engine 3E (technology program) (E3E)-type high pressure compressor (HPC) blisk is analyzed with regard to varying mistuning, varying engine order (EO) excitations and the consideration of aero-elastic effects. For that purpose, subset of nominal system modes (SNM)-based reduced order models are used in which the disk remains unchanged while the Young's modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient (AIC) technique is employed to model aero-elastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades' Young's modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aero-elastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the interblade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.
Die vorliegende Arbeit hat zum Ziel, dem Stand der Wissenschaft und Technik entsprechende
uni- und bidirektional gekoppelte Berechnungsmethoden unter Verwendung einer partitionierten
Kopplung kommerzieller FE- und CFD-Programme am Lehrstuhl Strukturmechanik
und Fahrzeugschwingungen der Brandenburgischen Technischen Universität Cottbus zu etablieren.
Dazu erfolgt bezüglich der Kopplungsverfahren eine Überprüfung der Funktionalität
am akademischen Beispiel einer querangeströmten, elastischen Platte. Vor dem Hintergrund
der intensiven Forschung des Lehrstuhls auf dem Gebiet der Strukturdynamik integraler
Verdichterlaufräder (Blisks) schließt sich die Validierung des eingesetzten Strömungslösers
hinsichtlich einer transsonischen, instationären Verdichterströmung innerhalb schwingender
Schaufelgitter an. Letztlich wird das grundlegende aeroelastische Verhalten eines realen
Hochdruckverdichterlaufrades anhand eines unverstimmten, zweidimensionalen Modells
analysiert. Ein Vergleich der Methoden zur Berechnung aeroelastischer Parameter ist Bestandteil
der Untersuchungen. Basierend auf bidirektional gekoppelten Ergebnissen wird
abschließend eine Verifizierung von abgeleiteten äquivalenten aerodynamischen Elementen
innerhalb eines mechanischen, unverstimmten Ersatzmodells vorgestellt.
The forced response of an E3E-type high pressure compressor (HPC) blisk front rotor is analyzed with regard to varying mistuning and the consideration of the fluid-structure interaction (FSI). For that purpose, a reduced order model is used in which the disk remains unchanged and mechanical properties of the blades, namely stiffness and damping, are adjusted to measured as well as intentional blade frequency mistuning distributions. The aerodynamic influence coefficient technique is employed to model the aeroelastics. Depending on the blade mode, the exciting engine order, and aerodynamic influences, it is sought for the worst mistuning distributions with respect to the maximum blade displacement based on optimization analyses. Genetic algorithms using blade-alone frequencies as design variables are applied. The validity of the Whitehead limit is assessed in this context. In particular, the question is addressed if and how far aeroelastic effects, mainly caused by aerodynamic damping, combined with mistuning can even cause a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the interblade phase angle is the main driver for a possible response attenuation considering the fundamental as well as a higher blade mode. Furthermore, the differences to the blisk vibration response without a consideration of the flow and an increase of the disk's stiffness are discussed. Closing, the influence of pure damping mistuning is analyzed again using optimization.
As a result of more balanced blade aspect ratios of modern blade-integrated disks (blisks), interactions between disk-dominated and blade-dominated modes are becoming more and more important, especially if blade mistuning is considered. The specific vibration behavior in these transition regions is characterized by a mix of both fundamental mode types into “coupled” modes. In this paper, numerical and experimental investigations based on a front high-pressure compressor (HPC) blisk stage were carried out in order to determine the effect of blade mistuning on those regions in detail. At this, effects like mode localization and amplitude magnification are found to be weakened in an integer frequency-veering zone. Contrary to this, blisks are very sensitive to mistuning in regions of pure blade-dominated mode families with high modal density.
It is important to steadily refine lightweight designs with regard to saving resources and energy in common with good economic efficiency.
Thin structured sheet metals offer significantly improved component stiffnesses in addition to an upgraded buckling behavior compared to flat, unstructured sheet metals.
By using a distortion energy based homogenization method it is possible to develop a mechanical surrogate model which describes effective mean properties. The accurate selection of symmetric and periodic boundaries enables to determine the required parameters. The conditions are contemplated on elementary cells whose structural mechanical behavior is representative for the elastic behavior of large structures. By doing this, the amount of elements can be reduced and thus the calculating time of large components can considerably be saved.
For an efficient surrogate model it is required to analyze and compare numerical with experimental investigations. Some different versions of optimization will be tested to get better approximation of the data.
In the drive for higher cycle efficiencies in gas turbine engines, turbine blades are seeing an increasingly high heat load. This in turn demands improvements in the internal cooling system and a better understanding of both the level and distribution of the internal heat-transfer. A typical approach to enhance the internal cooling of the turbine blade is by casting angled ‘low blockage’ ribs on the walls of the cooling channels. The objective of the present paper is to determine the detailed Nusselt number distribution in rectangular internal channels with ribs. This knowledge can be used to guide the overall design e.g. to achieve high levels of heat-transfer where required. The effects of rotation as well as the interaction effects of the position and direction of ribs on opposite walls of the cooling channel have been investigated.
Numerical calculations have been carried out using the commercial CFD code Fluent to investigate the local Nusselt number enhancement factor in rectangular ducts of different aspect ratios (0.5, 1 and 2) which have 45° or 90° angled ribs located on two opposite walls. This has been studied for different Rotation number Ro (0–0.45) and with a Reynolds number >30000.
The first series of studies has been carried out with the same experimental setup as by Han [1]. The geometry was slightly changed to avoid the effect of high heat transfer at the entry.
This study identifies important vortical structures, which are dependent on the direction and the position of the ribs. This has a profound effect on the distribution of heat-transfer within the passage. It is shown that the two smooth walls of the duct have different average Nusselt number ratio Nu/NuFD enhancement depending on the rib angle.
In addition, based on numerical investigations, simple correlations have been developed for the rotational influence of the internal Nusselt number distribution. A major finding is that the effect of rotation is dominant for low aspect ratio channels and the local enhancement due to the rib position and angle is more dominant for high aspect ratio channels.
The forced response of an E3E-type HPC-blisk front rotor is analyzed with regard to varying mistuning and the consideration of the fluid-structure interaction (FSI). For that purpose, a reduced order model is used in which the disk remains unchanged and mechanical properties of the blades namely stiffness and damping are adjusted to measured as well as intentional blade frequency mistuning distributions. The aerodynamic influence coefficient technique is employed to model the aeroelastics. Depending on the blade mode, the exciting engine order and aerodynamic influences it is sought for the worst mistuning distributions with respect to the maximum blade displacement based on optimization analyses. Genetic algorithms using blade alone frequencies as design variables are applied. The validity of the Whitehead-limit is assessed in this context. In particular, the question is addressed if and how far aeroelastic effects, mainly caused by aerodynamic damping, combined with mistuning can even cause a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental as well as a higher blade mode. Furthermore, the differences to the blisk vibration response without a consideration of the flow and an increase of the disk’s stiffness are discussed. Closing, the influence of pure damping mistuning is analyzed again using optimization.
Radial turbine wheels designed as blade integrated disks (blisk) are widely used in various industrial applications. However, related to the introduction of exhaust gas turbochargers in the field of small and medium sized engines, a sustainable demand for radial turbine wheels has come along. Despite those blisks being state of the art, a number of fundamental problems, mainly referring to fluid-structure-interaction and, therefore, to the vibration behavior, have been reported. Aiming to achieve an enhanced understanding of fluid-structure-interaction in radial turbine wheels, a numerical method, able to predict forced responses of mistuned blisks due to aerodynamic excitation, is presented. In a first step, the unsteady aerodynamic forcing is determined by modeling the spiral casing, the stator vanes, and the rotor blades of the entire turbine stage. In a second step, the aerodynamic damping induced by blade vibration is computed using a harmonic balance technique. The structure itself is represented by a reduced order model being extended by aerodynamic damping effects and aerodynamic forcings. Mistuning is introduced by adjusting the modal stiffness matrix based on results of blade by blade measurements that have been performed at rest. In order to verify the numerical method, the results are compared with strain-gauge data obtained during rig-tests. As a result, a measured low engine order excitation was found by modeling the spiral casing. Furthermore, a localization phenomenon due to frequency mistuning could be proven. The predicted amplitudes are close to the measured data.
Analysis of oxygen exchange-limited transport and chemical stresses in perovskite-type hollow fibers
(2012)