TY - GEN A1 - Hardenberg, Alexander A1 - Kühhorn, Arnold A1 - Fanter, Maren T1 - Bewertung der Auswirkungen von Strukturmodifikationen und Modellvereinfachungen unter Einsatz der FEA-FEA Korrelation auf das Modalverhalten einer Triebwerksgehäusestruktur T2 - 2. VDI-Fachtagung Schwingungen 2019 : Würzburg, 05. und 06. November 2019 Y1 - 2019 SN - 978-3-18-092366-6 N1 - 1 CD-ROM PB - VDI-Verlag CY - Düsseldorf ER - TY - GEN A1 - Beirow, Bernd A1 - Kühhorn, Arnold A1 - Figaschewsky, Felix A1 - Bornholm, Alfons T1 - Vibration analysis of a mistuned axial turbine blisk T2 - ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition, June 17–21, 2019, Phoenix, Arizona, USA N2 - An axial turbine blisk for turbocharger applications is analyzed with respect to the effect of intentional mistuning on the forced response. Originally, the intentional mistuning pattern has been designed by employing a genetic algorithm optimization in order to reduce the forced response caused by low engine order excitation (LEO) of the fundamental flap mode. The solution found has been implemented in a prototype of that blisk. For the purpose of comparison, a second reference blisk has been manufactured without intentional mistuning. The actual mistuning distributions of the blisks have been identified by employing blade-by-blade impact testing. Alternatively, a new inverse approach has been employed, which is based on a least squares formulation and benefits from less experimental effort. Based on the information gained by the aforementioned testing procedures, subset of nominal systems (SNM)-models have been updated, which allow for considering the aeroelastic coupling by means of aerodynamic influence coefficients (AIC). Despite of small but unavoidable deviations from the design intention it could be proved within numerical simulations that the intended 70 per cent reduction of the maximum forced response is nevertheless achieved. In addition, the paper is addressing the effect of the aforementioned intentional mistuning pattern on a higher mode, which is relevant for the durability as well. Hence, new SNM-models have to be updated in order to calculate the forced response due to EO-excitation caused by the nozzle guide vane. Although the original mistuning pattern has been optimized solely for reducing the forced response of the fundamental flap mode, it hardly affects the higher mode forced response in a negative manner. KW - Turbines KW - Vibration analysis KW - Blades KW - Excitation KW - Computer simulation KW - Design Y1 - 2019 UR - https://asmedigitalcollection.asme.org/GT/GT2019/volume/58691 SN - 978-0-7918-5869-1 U6 - https://doi.org/10.1115/GT2019-92047 ER - TY - GEN A1 - Figaschewsky, Felix A1 - Kühhorn, Arnold A1 - Beirow, Bernd A1 - Giersch, Thomas A1 - Schrape, Sven A1 - Nipkau, Jens T1 - An inverse approach to identify tuned aerodynamic damping, system frequencies and mistuning – Part 3: Application to engine data T2 - ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition, June 17–21, 2019, Phoenix, Arizona, USA N2 - A novel approach for the identification of tuned aerodynamic damping, system frequencies, forcing and mistuning has been introduced in the first part of this paper. It is based on the forced response equations of motion for a blade dominated mode family. A least squares formulation allows to identify the system’s parameters directly from measured frequency response functions (FRFs) of all blades recorded during a sweep through a resonance. The second part has dealt with its modification and application to experimental modal analyses of blisks at rest. This 3rd part aims at presenting the application of the approach to blade tip timing (BTT) data acquired in rig tests. Therefore, blisk rotors of two different engines are studied: a single stage fan rig and a 4.5 stage high pressure compressor (HPC) rig. The rig test campaign of the fan blisk included also an intentional mistuning experiment that allows to study the performance of the identification approach for a similar rotor with two different mistuning levels. It is demonstrated that the approach can identify aerodynamic damping curves, system frequencies, mistuning pattern and forced travelling wave modes (TWMs) from state of the art BTT data monitored during rig or engine tests. All derived mistuning patterns could be verified with reference measurements at standstill. The derived aerodynamic damping curves and system frequencies show a reasonable agreement with simulations. For the HPC case a multitude of excited TWMs could be identified which also lines up with previous simulations. KW - Damping KW - Engines KW - Blades KW - Engineering simulation KW - Rotors KW - Compressors KW - Modal analysis Y1 - 2019 UR - https://asmedigitalcollection.asme.org/GT/proceedings-abstract/GT2019/58684/V07AT36A014/1067111 SN - 978-0-7918-5868-4 U6 - https://doi.org/10.1115/GT2019-91337 ER - TY - GEN A1 - Maywald, Thomas A1 - Heinrich, Christoph Rocky A1 - Kühhorn, Arnold A1 - Schrape, Sven A1 - Backhaus, Thomas T1 - Prediction of Geometrically Induced Localization Effects Using a Subset of Nominal System Modes T2 - ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition June 17–21, 2019 Phoenix, Arizona, USA N2 - It is widely known that the vibration characteristics of blade integrated discs can dramatically change in the presence of manufacturing tolerances and wear. In this context, an increasing number of publications discuss the influence of the geometrical variability of blades on phenomena like frequency splitting and mode localization. This contribution is investigating the validity of a stiffness modified reduced order model for predicting the modal parameters of a geometrically mistuned compressor stage. In detail, the natural frequencies and mode shapes, as well as the corresponding mistuning patterns, are experimentally determined for an exemplary rotor. Furthermore, a blue light fringe projector is used to identify the geometrical differences between the actual rotor and the nominal blisk design. With the help of these digitization results, a realistic finite element model of the whole compressor stage is generated. Beyond that, a reduced order model is implemented based on the nominal design intention. Finally, the numerical predictions of the geometrically updated finite element model and the stiffness modified reduced order model are compared to the vibration measurement results. The investigation is completed by pointing out the benefits and limitations of the SNM-approach in the context of geometrically induced mistuning effects. KW - Blades KW - Compressors KW - Design KW - Disks KW - Finite element model KW - Manufacturing KW - Vibration measurement Y1 - 2019 UR - https://asmedigitalcollection.asme.org/GT/proceedings-abstract/GT2019/58691/V07BT35A012/1067131 SN - 978-0-7918-5869-1 U6 - https://doi.org/10.1115/GT2019-90884 ER - TY - GEN A1 - Naveed, Zishan A1 - Kühhorn, Arnold A1 - Kober, Markus T1 - Contact Behaviour of Isogeometric Analysis for Rotating Structures and its Industrial Application by Coupling to the Classical Finite Element Method T2 - VII International Conference on Isogeometric Analysis, München, 18.-20. September 2019 N2 - Especially for rotating structures like bearings non-smooth contact surfaces, as they appear in classical finite element modeling, lead to various problems during the analysis involving mesh interlocking and spurious oscillations in contact forces. In order to eliminate these issues, very fine meshes and additional smoothing strategies are employed in case of the finite element method (FEM). But also Non-Uniform Rational B-splines (NURBS) based isogeometric analysis (IGA) can be very useful for the contact analysis due to the inherent higher order continuity of NURBS basis functions. In this contribution, the contact behavior using classical FEA and IGA approaches is studied by means of an example of a pendulum under gravitational load. In addition, a more practical example of a coupled IGA–FEM problem with a cylindrical roller bearing is also reported in this paper. This research study of contact analysis has been carried out for the above mentioned examples using LS-DYNA and illustrates that contact surfaces of coarsely meshed geometry lock the rotation of the parts in case of classical FEM. On the contrary, when the contact surface is represented by NURBS elements it allows the rotation of the parts and effectively alleviates the contact force oscillation. Y1 - 2019 UR - http://congress.cimne.com/iga2019/frontal/ProgramPrint.asp?t=todo ER - TY - GEN A1 - Franz, Falco A1 - Kühhorn, Arnold A1 - Giersch, Thomas A1 - Schrape, Sven A1 - Figaschewsky, Felix T1 - Influence of Inlet Distortions on the Forced Vibration of a High Pressure Compressor Rig T2 - ASME 2020 Turbo Expo - Virtual Conference, September 2020 N2 - The accurate prediction of blade vibrations is a key factor for the development of reliable turbomachines. This paper focusses on forced vibrations. The excitation frequency is an integer multiple of the rotor revolution frequency, which is commonly called engine order. Aerodynamic excitation of blades is created by stator wakes or the potential fields of downstream obstacles, which usually leads to high engine orders correlating to the number of vanes. Resonance crossings appear at higher frequencies corresponding to higher modes. Besides high engine orders, low engine orders not related to the number of vanes may exist. They can be caused by a disturbance of the perfect cyclic symmetry of the flow pattern due to geometry variations or inlet distortions. Inlet distortions result from installation effects, maneuvers or crosswind. Low engine orders affect fundamental modes at high engine speeds. High static loads due to centrifugal forces combined with dynamic excitation and low damping may lead to unacceptable high stresses. This paper aims at getting a better understanding of the simulative prediction of low engine order excitation with special focus on inlet distortions. Under investigation is a 4.5 stage research compressor rig, for which an extensive amount of test data is available. A three dimensional CFD-model of the compressor is used to compute the forcings generated by different distortion patterns. The first two stages are modeled as a full-annulus, which allows to fully resolve the spatial content of the inlet distortion patterns. The rotor 2 blisk is of special interest in this investigation. The propagation of the distortion after stage 2 with rotor 2 is not of interest, therefore the downstream stages are modeled as single passages in order to save computational time. The distortion patterns are the outcome of traversals of different screens with total pressure probes. During distortion measurements, the screens located in the inlet duct were rotated relative to the fixed instrumentation. The traversals in resonance of the first bending mode of rotor 2 with a low engine order four showed a dependency of the screen angle on the vibration amplitude. Acceleration and deceleration maneuvers through this resonance were conducted with screen angles set to those of smallest and highest response. Vibration amplitudes of the blisk rotor are measured by strain gauges and a blade tip timing system. Simulation results are compared against vibration measurements. Aerodynamic damping is calculated with the influence coefficient method. The effects of mistuning are included in the calculation of vibration amplitudes via a subset of nominal system modes model to give a meaningful comparison against real engine hardware. The mistuning distribution of the blisk was identified at rest for the fundamental bending mode. The presence of a 2nd excitation mechanism of unknown source explains the observed test data. This unknown source is not included in the CFD model. A direct comparison of simulation and measurement is still possible by leveraging the observed superposition effects of both excitation sources. The consequent approach is to identify and substract the forcing due to the unknown source, leaving only the delta forcing due to inlet distortions. Y1 - 2020 UR - https://asme-turboexpo.secure-platform.com/a/solicitations/105/sessiongallery/4675/application/46115 ER - TY - GEN A1 - Gambitta, Marco A1 - Kühhorn, Arnold A1 - Schrape, Sven T1 - Geometrical Variability Modelling of Axial Compressor Blisk Aerofoils and Evaluation of Impact on the Forced Response Problem T2 - ASME 2020 Turbo Expo - Virtual Conference, September 2020 N2 - The manufacturing process always produces onto the components a certain amount of geometrical uncertainty. This results inevitably in the introduction of a certain amount of variability within the manufactured parts. Even if the differences are small, all the resulting geometries will differ from each other. The present work focuses on the effect of the manufacturing geometrical variability on the high pressure compressor of a turbofan engine for civil aviation. The deviations of the geometry over the axial compressor blades are studied and modelled for the representation in the computational models. Such variability is of particular interest for the forced response problem, where small deviations of the geometry from the ideal nominal model can imply significant differences in the vibrational responses. The information regarding the geometrical mistuning is extracted from a set of manufactured components surface scans of a blade integrated disk (blisk) rotor. The measured geometries are analyzed over a large amount of set radial sections, defining a set of opportune parameters to represent the deviations from the nominal design. A spline fit of the parameters over the radial sections allows the creation of a set of variables describing the geometry. The dimension of the variables domain is reduced using the principal component analysis approach, this allows to obtain an optimal subset of geometrical modes as linear combination of the above mentioned parameters. The reconstruction of the modelled geometries is performed for the implementation in complex CFD and FEM solvers. This is done via the application of the modelled delta nominal-to-measure geometrical offset to the hot geometry of the desired test case. The generated model allows a stochastic representation of the variability, providing an optimal set of variables to represent it. Moreover the approach as defined allows to apply the modelled variability to different blades, e.g. different stators or rotors, utilizing the nominal geometry as input. The aeroelastic analyses considering geometry based mistuning is carried on a test-rig case, focusing on how such variability can affect the modal forcing generated on the blades. A validated CFD model is used to extract the force generated by the unsteady pressure field over the selected vibrational mode shapes of the rotor blades. The blade mode shapes are extracted form a FEM model of the whole blisk and the blades displacements are mapped over the CFD model nodes. The uncertainty quantification of the geometrical variability effect on the modal forcing is performed utilizing Monte Carlo methods. A reduced model for the CFD solution is employed, utilizing a single passage multi blade row which assumes a time-space periodicity solving the governing equations in the frequency domain. This allows for conducting an uncertainty quantification considering the large domain of the variables used to describe the geometries compared to the computational resources needed for the single solution. The unsteady modal forcing is studied as amplitude and phase shift for the different engine orders (frequencies arising from the engine working condition as higher harmonics of the shaft speed). In particular the scatter of the main engine orders forcing amplitudes for the manufactured blades can be compared with the nominal responses to predict the possible amplification due to the geometrical variability. Finally the results are compared to a larger computational model to assess the influence of multiple variable blades in the assembly. Y1 - 2020 UR - https://asme-turboexpo.secure-platform.com/a/solicitations/105/sessiongallery/5296/application/46289 ER - TY - GEN A1 - Heinrich, Christoph Rocky A1 - Kühhorn, Arnold A1 - Steff, Klaus A1 - Petry, Nico T1 - Generalized Model for the Approximation of Coupled Acousto-Mechanical Natural Frequencies in High-Pressure Centrifugal Compressors T2 - ASME 2020 Turbo Expo - Virtual Conference, Spetember 2020 N2 - The oil and gas, chemical, and process industries employ centrifugal compressors for a wide range of applications. Due to this, the conditions, under which centrifugal compressors have to operate, vary significantly from case to case. Gas pipeline compressors, for example, may feature discharge pressures well over 100 bar (1450 psi). In other fields of application, like gas injection, which is used to enhance oil recovery, this quantity can reach considerably higher values. Here, discharge pressures over 600 bar (8702 psi) and gas densities over 300 kg/m3 (18.7284 lb/ft3) are not uncommon. During the last decades, comprehensive research was conducted on the impact of high pressure operating conditions on the vibrational behavior of centrifugal compressor wheels. Nowadays, it is well-known that an increase in gas pressure levels leads to a more pronounced interaction between the side cavities and the impeller, which results in a frequency shift of the acoustic and structural modes. For the safe operation of compressors, it is necessary to predict these coupled natural frequencies accurately. The state-of-the-art approach to achieve this objective is the finite element method. While this technique provides high-quality results, the simulation of acousto-mechanical systems is still a time-consuming process that incurs high computational costs. Therefore, finite element models are, in this case, not suitable for probabilistic studies, sensitivity analyses, and comprehensive simulations of the full operating range of the compressor. In 2013, Magara proposed a simplified model based on an annular plate between two cylindrical cavities to solve this problem. While this method reduces the required computational effort significantly, its use is limited to platelike impellers. The authors of the current paper propose a more generalized method to overcome the challenges mentioned above. It uses the uncoupled structural and acoustic modes of the actual impeller and side cavities in a modal superposition to approximate the natural frequencies of the coupled acousto-mechanical system. In this way, the intended design geometries of the impeller and side cavities are considered while maintaining the advantages of Magara's model regarding the computational effort. In a numerical study, Magara's method and the generalized model are applied to different systems of increasing complexity. The investigation starts with a simple annular plate in a cylindrical cavity and ends with two actual compressor impellers. At every complexity level, the results of both approaches are compared to a finite element analysis. Moreover, measurement data of a simplified rotor in a cylindrical cavity is used to validate the numerical models. Finally, the paper concludes with a discussion of the limitations and benefits of all employed numerical methods. Y1 - 2020 UR - https://asme-turboexpo.secure-platform.com/a/solicitations/105/sessiongallery/5323/application/46866 ER - TY - GEN A1 - ElMasry, Seif A1 - Kühhorn, Arnold A1 - Figaschewsky, Felix T1 - Investigation of Working Line Variation Onto Forced Response Vibrations of a Compressor Blisk T2 - Turbo Expo 2021, Virtual Conference and Exhibition: September 21, 2020 N2 - Avoidance of high vibration amplitudes of rotor blades on the conventional working line of the compressor is a design requirement. However, rotors of aircraft engine compressors could temporarily operate near choke and stall conditions, due to transient manoeuvers or deterioration. As a result, the vibration levels might change, which could lead to a premature high cycle fatigue of the blades. This paper aims at studying the effect of different throttle positions at five constant aerodynamic speed lines ranging from 60% to 100% of the maximum speed onto the resulting vibration amplitudes and aerodynamic damping values on an integrally bladed disk (blisk) of a transonic research compressor. Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD) simulations are performed via an automated workflow, which reads aerodynamic data of the operating points of interest and runs all necessary aeromechanic computations along with their corresponding post-processing routines to calculate the resulting system response and amplitude frequency values. Using this workflow, Eigenfrequencies and mode-shapes of the rotor blades are obtained through multiple FEA simulations that are automatically executed at all relevant shaft speeds. The time-averaged flow pressure field on the blades is extracted from steady CFD simulations of the whole compressor and mapped onto the structural mesh of the rotor. Through a Spokes diagram, operating points in close proximity to resonance spots are identified, as well as their corresponding excited vibration modes. To obtain the time-variable flow pressure fields on the blades, unsteady CFD simulations are performed using a single passage model of the rotor with its upstream and downstream stators, as space-time periodicity of the flow data across the annulus is assumed. Additionally, a CFD rotor model with only a quarter section of the full annulus is built, where a unidirectional coupling approach between the structure and the fluid is applied to calculate the aerodynamic damping values. The calculated vibration amplitudes at engine orders of interest are then compared to strain gauge readings of a corresponding rig test. After validation of the simulation data, the sensitivity of the forced response due to working line variations is studied. Looking at the maximum aerodynamic speed line, it is clear that operating points near compressor stall are accompanied by high vibration response relative to the aerodynamic design point. A possible reason for this amplification is the change of flow incidence and the increase of pressure loss at the upstream blade-row. However, this effect becomes less articulated in the lower speed lines, where amplitudes of the forced vibrations change only slightly between different throttling positions. In this paper, the three-dimensional flow inside the passages is also carefully studied, which allows to better understand the relationship between flow characteristics and the resulting vibration response of compressor blades. Y1 - 2020 UR - https://asme-turboexpo.secure-platform.com/a/solicitations/105/sessiongallery/5322/application/45655 ER - TY - GEN A1 - Weber, Robby A1 - Kühhorn, Arnold A1 - Klauke, Thomas A1 - Schrape, Sven T1 - The Effect of Sand Erosion on a Compressor Blade and its Modal Properties T2 - Proceedings of ASME Turbo Expo 2020, Turbomachinery Technical Conference and Exposition, GT2020, September 21-25, 2020, Virtual, Online N2 - The wear and damage of High-Pressure Compressor (HPC) blades due to erosion or Foreign Object Damage (FOD) have a significant influence on HPC aerodynamic performance, vibration resistance against High-Cycle Fatigue (HCF) and thus component lifetime. The changes in airfoil geometry reduce the overall engine efficiency. Furthermore extended off-wing engine maintenances due to blade failures are increasing the cost of ownership. The safe operation of every engine within a reduced number of shop visits requires a reliable prediction of future deterioration. This enables the optimization of services and off-wing time. One contribution to this is a better understanding of the component’s dynamics and based on this providing an improved wear modeling to reliably predict the remaining lifetime and the decreased efficiency. This contribution determines the material removal of HPC blades due to sand erosion. Originally, this stage was built as a blisk (Blade Integrated Disk). After sand erosion test completion, the blisk was cut into segments containing one airfoil only. First, the material removal is determined for ten blades of one exemplary rotor. A blue light fringe projector is employed to identify the geometrical differences between the eroded blades and the nominal design. Second, realistic finite element models are generated to enable comparable modal analyses of eroded blades. This procedure suffers from unavoidable and mostly random imperfections due to the manufacturing process, which significantly affects the blade surface before the erosion test can be conducted. Therefore, an already published approach is implemented in the third step to predict the blade surface after erosion based on nominal blade design. The investigation is completed by comparing measured and predicted surfaces. Finally, the aforementioned tool is employed to predict the locations and intensities of the material losses and the accompanying change in modal properties of this compressor blade concerning operational time. Y1 - 2020 ER - TY - GEN A1 - Heinrich, Christoph Rocky A1 - Kühhorn, Arnold A1 - Steff, Klaus A1 - Petry, Nico T1 - Generalized Model for the Approximation of Coupled Acousto-Mechanical Natural Frequencies in High-Pressure Centrifugal Compressors T2 - Journal of Engineering for Gas Turbines and Power N2 - The oil and gas, chemical, and process industries employ centrifugal compressors for a wide range of applications. Due to this, the conditions under which centrifugal compressors have to operate, vary significantly from case to case. Gas pipeline compressors, for example, may feature discharge pressures well over 100 bar. During the last decades, comprehensive research was conducted on the impact of high pressure operating conditions on the vibrational behavior of centrifugal compressors. Nowadays, it is well-known that an increase in gas pressure levels leads to a more pronounced interaction between the side cavities and the impeller, which results in a frequency shift of the acoustic and structural modes. For the safe operation of compressors, it is necessary to predict these coupled natural frequencies accurately. The state-of-the-art approach to achieve this objective is the finite element method. While this technique provides high-quality results, it incurs high computational costs and is, therefore, time-consuming. The authors of the current paper propose a generalized model to overcome this challenge. It uses the uncoupled modes of the impeller and side cavities in a modal superposition to approximate the coupled system's natural frequencies. In this way, the intended design geometries are considered while reducing the computational effort significantly. In a numerical study, the generalized model is applied to different systems of increasing complexity, and the results are compared to a finite element analysis. Finally, the paper concludes with a discussion of the limitations and benefits of all employed numerical methods. KW - Approximation KW - Compressors KW - High pressure (Physics) KW - Cavities KW - Impellers KW - Acoustics KW - Finite element methods KW - Numerical analysis Y1 - 2020 U6 - https://doi.org/10.1115/1.4049447 SN - 1528-8919 ER - TY - GEN A1 - Beirow, Bernd A1 - Kühhorn, Arnold A1 - Weber, Robby A1 - Popig, Frederik T1 - Vibration Analyses of an Axial Turbine Wheel with Intentional Mistuning T2 - Journal of Engineering for Gas Turbines and Power N2 - The last stage bladed disk of a steam turbine is analyzed with respect to both flutter susceptibility and limitation of forced response. Due to the lack of variable stator vanes unfavorable flow conditions may occur which increases the risk of flutter at part load conditions. For this reason, intentional mistuning is employed with the objective to prevent any self-excited vibrations. A first step in this direction is done by choosing alternate mistuning, which keeps the manufactural efforts in limits. In this sense, two different series of blades have been made. However, small deviations from the design intention are unavoidable due to the manufacturing procedure, which could be proved by bonk tests carried out earlier. The influence of these additional deviations is considered in numerical simulations. Moreover, the strong dependence of blade frequencies on the speed is taken into account since centrifugal stiffening effects significantly attenuate the blade-to-blade frequency difference. Focusing on the first flap mode it could be shown that a mitigation of flutter susceptibility is achieved by prescribing alternate mistuning, which indeed evokes an increase of originally small aerodynamic damping ratios. Nevertheless, the occurrence of negative damping ratios could not be completely precluded at part load conditions. That is why optimization studies are conducted based on genetic algorithms with the objective function of maximizing the lowest aerodynamic damping ratios. Finally, mistuning patterns could be identified featuring a tremendous increase of aerodynamic damping ratios. The robustness of the solutions could be proved by superimposing additional random mistuning. KW - Blades KW - Computer simulation KW - Damping KW - Design KW - Disks KW - Flow (Dynamics) KW - Flutter (Aerodynamics) KW - Vibration analysis Y1 - 2021 U6 - https://doi.org/10.1115/1.4049449 SN - 1528-8919 SN - 0742-4795 VL - 143 IS - 6 ER - TY - GEN A1 - Hardenberg, Alexander A1 - Kühhorn, Arnold A1 - Fanter, Maren T1 - Correlating and Updating Finite Element Models of Different Fidelity Using an Energy-Based Approach T2 - Turbo Expo 2020, Virtual Conference, Virtual Conference and Exhibition, Online, September 21 – 25, 2020 N2 - Building finite element models of complex structures requires the engineer to make various simplifying assumptions. While there exists no unique way of modeling, the resulting model depends to a level on experience and engineering judgement. The inherent model uncertainties can be subdivided into three categories: idealization errors, discretization errors and parameter errors. Understanding the effect of different modeling assumptions and minimizing these uncertainties is key for creating efficient and physical meaningful finite element models. In this paper the effects of different modeling assumptions are analyzed by comparing finite element models of an aero engine turbine casing. Various models of different fidelity are created reaching from simple shell element representations neglecting geometric features like bosses, fixings and holes, to higher fidelity mixed dimensional models using coupled shell and three-dimensional elements. To quantify their impact on the stiffness and mass properties, the different models are correlated with a high-fidelity three-dimensional finite element model using numerical modal data. A novel method is proposed based on the strain and kinetic energy distribution to assess the effect of different modeling assumptions on the model structure. This is done by splitting the discretized model into multiple sections of interest and calculating the perturbation of energies within the related splits. The derived strain and kinetic energy perturbations are then used in addition to other correlation criteria like the modal assurance criteria or the relative difference in eigenfrequencies to analyze the impact of the different modeling assumptions. Having quantified the differences, the difficulties of error localization using modal data are discussed in the context of the correlation results. Finally, the effectiveness of the derived perturbation values are demonstrated by updating a finite element model of an aero engine turbine casing in the presence of structural simplifications using an evolutionary optimization algorithm and comparing the model updating strategy to the standard sensitivity-based updating approach. If the resulting updated model is used to predict structural modifications or untested loading conditions, the updated parameters might lose their physical meaning when altering regions of the model not in error. Therefore, it is important to examine the physical significance of the updated parameters. It is shown how the energy-based approach can help to address this problem. All in all, the proposed energy-based approach can be used to compare various modeling strategies in order to build efficient finite element models as well as assist in the choice of parameters for subsequent model updating to validate the numerical model against test data. Y1 - 2020 UR - https://asme-turboexpo.secure-platform.com/a/solicitations/105/sessiongallery/5346/application/45406 ER - TY - GEN A1 - Beirow, Bernd A1 - Kühhorn, Arnold A1 - Weber, Robby A1 - Popig, Frederik T1 - Vibration Analyses of an Axial Turbine Wheel With Intentional Mistuning T2 - Turbo Expo 2020, Virtual Conference, Virtual Conference and Exhibition, Online, September 21 – 25, 2020 N2 - The last stage bladed disk of a steam turbine is analyzed with respect to both flutter susceptibility and limitation of forced response. Due to the lack of variable stator vanes unfavorable flow conditions may occur which can lead to flow separation in some circumstances. Consequently, there is the risk of flutter in principle, particularly at nominal speed under part load conditions. For this reason, intentional mistuning is employed by the manufacturer with the objective to prevent any self-excited vibrations. A first step in this direction is done by choosing alternate mistuning, which keeps the manufactural efforts in limits since only two different blade designs are allowed. In this sense, two different series of blades have been made. However, it is well known that small deviations from the design intention are unavoidable due to the manufacturing procedure, which could be proved by bonk tests carried out earlier. The influence of these additional but unwanted deviations is considered in numerical simulations. Moreover, the strong dependence of blade frequencies on the speed is taken into account since it significantly attenuates the blade to blade frequency difference in this particular case. Within an academic study the turbine wheel is modelled as blade integrated disk in order to demonstrate fundamental effects of intentional mistuning on flutter susceptibility and forced response. For that purpose, reduced order models are built up by using the subset of nominal system mode approach introduced by Yang and Griffin [1], which conveniently allows for taking into account both differing mistuning patterns and the impact of aeroelastic interaction. Focusing on the first flap mode it could be shown that a mitigation of flutter susceptibility is achieved by prescribing alternate mistuning, which indeed affects an increase of originally small aerodynamic damping ratios. Nevertheless, the occurrence of negative damping ratios could not be completely precluded at part load conditions. That is why optimization studies are conducted based on genetic algorithms with the objective function of maximizing the lowest aerodynamic damping ratios. Again only two different blade designs are admitted. Finally, mistuning patterns could be identified causing a tremendous increase of aerodynamic damping ratios. The robustness of the solutions found could be proved by superimposing additional random mistuning. Another study is focused on the impact of mistuning strength. Further analyses are addressing the forced response at part speed conditions, where different resonance crossings are becoming apparent in the Campbell plot. An increase of the forced response compared to the tuned counterpart is partly unpreventable because of unfavorable aerodynamic damping curves. Independently, the maximum forced response has to be limited also in case of applying large intentional mistuning. [1] Yang, M. T., Griffin, J. H., „A Reduced-Order model of Mistuning Using a Subset of Nominal System Modes“. J Eng Gas Turb Power, 123, pp. 893-900 (2001). Y1 - 2020 UR - https://asme-turboexpo.secure-platform.com/a/solicitations/105/sessiongallery/5325/application/45830 ER - TY - GEN A1 - Hanschke, Benjamin A1 - Kühhorn, Arnold A1 - Schrape, Sven A1 - Giersch, Thomas T1 - Consequences of Borescope Blending Repairs on Modern HPC Blisk Aeroelasticity T2 - Journal of Turbomachinery N2 - Objective of this paper is to analyze the consequences of borescope blending repairs on the aeroelastic behavior of a modern high pressure compressor (HPC) blisk. To investigate the blending consequences in terms of aerodynamic damping and forcing changes, a generic blending of a rotor blade is modeled. Steady-state flow parameters like total pressure ratio, polytropic efficiency, and the loss coefficient are compared. Furthermore, aerodynamic damping is computed utilizing the aerodynamic influence coefficient (AIC) approach for both geometries. Results are confirmed by single passage flutter (SPF) simulations for specific interblade phase angles (IBPA) of interest. Finally, a unidirectional forced response analysis for the nominal and the blended rotor is conducted to determine the aerodynamic force exciting the blade motion. The frequency content as well as the forcing amplitudes is obtained from Fourier transformation of the forcing signal. As a result of the present analysis, the change of the blade vibration amplitude is computed. Y1 - 2019 U6 - https://doi.org/10.1115/1.4041672 SN - 1528-8900 SN - 0889-504X VL - 141 IS - 2 ER - TY - GEN A1 - Gambitta, Marco A1 - Kühhorn, Arnold A1 - Beirow, Bernd A1 - Schrape, Sven T1 - Stator Blades Manufacturing Geometrical Variability in Axial Compressors and Impact on the Aeroelastic Excitation Forces T2 - Proceedings of ASME Turbo Expo 2021, ASME Paper Number: GT2021-59642 N2 - The manufacturing geometrical variability is a source of uncertainty, which cannot be avoided in the realization of a machinery. Deviations of a component geometry from its nominal design are inevitably present due to the manufacturing process. In the case of the aeroelastic forced response problem within axial compressors, these uncertainties may affect the vibration characteristics. For this reason, the impact of geometrical uncertainties due to the manufacturing process onto the modal forcing of axial compressor blades is investigated in this study. The research focuses on the vibrational behavior of an axial compressor rotor blisk (blade-integrated disk) and in particular the amplitude of the forces acting as source of excitation on the vibrating blades (modal forcing). Within this context, the geometry of the upstream stator plays an important role as in general the main harmonics of the rotor excitation forces are produced by its wake. Therefore, small variations of the upstream stators geometries, such as the ones caused by the manufacturing process, may affect the resulting forcing. In particular, the geometrical variability of the upstream stator implies that the hypothesis of a cyclic-symmetrical flow is no longer valid. This may cause the introduction of lower harmonic components in the modal forces, generally referred to as Low Engine Orders (LEO). The geometrical variability is modelled starting from a series of optical surface scans. A set of optical measurements of manufactured stator blades originating from the same nominal design constitutes the baseline dataset on which the geometrical model is built. The measured blades as well as the relative nominal geometry are parametrized to describe the individual blades surfaces. The parameterization is accomplished by slicing the surfaces in radial sections and describing each of these with a set of NACA-like parameters [1]. The measured geometrical deviations from the nominal model can therefore be described as an offset of such parameters. A reduced representation of the variables representing the input uncertainty (noise variables) is obtained via Principal Components Analysis. Afterwards a sampling on the reduced noise variables domain can be done to represent the modelled uncertainty and perform an Uncertainty Quantification (UQ) on the relative quantities of interest, in this case the modal forcing. The computation of the modal forcing is done through a CFD solver, computing the unsteady flow field around the rotor blades. The domain considered in this case is a 1.5 stage of the axial compressor, including the rotor and the up- and down-stream stators. The solutions are initialized from a validated steady state solution of the considered compressor rig. The time-dependent pressure field calculated on the rotor blades is projected onto the relative vibrational mode shapes of interests (from structural modal analyzes). The resulting forces are analyzed by means of their spectrum, evaluating the amplitudes for the present engine orders (higher harmonics of the shaft mechanical speed). The UQ uses Monte Carlo methods to evaluate the impact of the geometrical variability onto the modal forcing. The modelled uncertainty on the geometries is introduced into the CFD solver to compute the deviations on the quantities of interest. A reconstruction of the forces acting on the rotor during one revolution is obtained. This allows to evaluate the uncertainty on the present engine orders as well as the possible rise of LEO for the rotor blades in presence of a mistuned upstream stator. [1]: Lange A., Vogeler K., Gümmer V., Schrapp H. and Clemen C. (2009). “Introduction of a Parameter Based Compressor Blade Model for Considering Measured Geometry Uncertainties in Numerical Simulation.” Proceedings of ASME Turbo Expo. GT2009-59937 Y1 - 2021 UR - https://asme-turboexpo.secure-platform.com/a/solicitations/137/sessiongallery/6794/application/59642 ER - TY - GEN A1 - Naveed, Zishan A1 - Kühhorn, Arnold T1 - An Isogeometric Based Study of Contact Behaviour for Rotating Structures T2 - 14th World Congress on Computational Mechanics (WCCM)-ECCOMAS Congress 2020, Virtual Conference: 11-15 January 2021 Y1 - 2021 UR - https://www.b-tu.de/fg-strukturmechanik/publikationen/veroeffentlichungen-und-vortraege ER - TY - GEN A1 - Noack, Martin A1 - Kühhorn, Arnold A1 - Kober, Markus A1 - Firl, Matthias T1 - A new stress-based topology optimization approach for finding flexible structures T2 - Structural and Multidisciplinary Optimization N2 - This paper presents a new FE-based stress-related topology optimization approach for finding bending governed flexible designs. Thereby, the knowledge about an output displacement or force as well as the detailed mounting position is not necessary for the application. The newly developed objective function makes use of the varying stress distribution in the cross section of flexible structures. Hence, each element of the design space must be evaluated with respect to its stress state. Therefore, the method prefers elements experiencing a bending or shear load over elements which are mainly subjected to membrane stresses. In order to determine the stress state of the elements, we use the principal stresses at the Gauss points. For demonstrating the feasibility of the new topology optimization approach, three academic examples are presented and discussed. As a result, the developed sensitivity-based algorithm is able to find usable flexible design concepts with a nearly discrete 0 − 1 density distribution for these examples. KW - Topology optimization KW - Flexible structure KW - Stress-based KW - SIMP KW - Conceptual design Y1 - 2021 U6 - https://doi.org/10.1007/s00158-021-02960-w SN - 1615-147X SN - 1615-1488 VL - 64 IS - 4 SP - 1997 EP - 2007 ER - TY - GEN A1 - Gambitta, Marco A1 - Kühhorn, Arnold A1 - Beirow, Bernd A1 - Schrape, Sven T1 - Stator Blades Manufacturing Geometrical Variability in Axial Compressors and Impact on the Aeroelastic Excitation Forces T2 - Journal of Turbomachinery N2 - The manufacturing geometrical variability is a source of uncertainty, which cannot be avoided in the realization of machinery components. Deviations of a part geometry from its nominal design are inevitably present due to the manufacturing process. In the case of the aeroelastic forced response problem within axial compressors, these uncertainties may affect the vibration characteristics. For this reason, the impact of geometrical uncertainties due to the manufacturing process onto the modal forcing of axial compressor blades is investigated in this study. The research focuses on the vibrational behavior of an axial compressor rotor blisk. In particular, the amplitude of the forces acting as a source of excitation on the vibrating blades is studied. The geometrical variability of the upstream stator is investigated as input uncertainty. The variability is modeled starting from a series of optical surface scans. A stochastic model is created to represent the measured manufacturing geometrical deviations from the nominal model. A data reduction methodology is proposed in order to represent the uncertainty with a minimal set of variables. The manufacturing geometrical variability model allows to represent the input uncertainty and probabilistically evaluate its impact on the aeroelastic problem. An uncertainty quantification is performed in order to evaluate the resulting variability on the modal forcing acting on the vibrating rotor blades. Of particular interest is the possible rise of low engine orders due to the mistuned flow field along the annulus. A reconstruction algorithm allows the representation of the variability during one rotor revolution. The uncertainty on low harmonics of the modal rotor forcing can be therefore identified and quantified. KW - aeromechanical instabilities KW - computational fluid dynamics (CFD) KW - turbomachinery blading design Y1 - 2022 U6 - https://doi.org/10.1115/1.4052602 SN - 1528-8900 VL - 144 ER -