@misc{FigaschewskyHanschkeKuehhorn, author = {Figaschewsky, Felix and Hanschke, Benjamin and K{\"u}hhorn, Arnold}, title = {Efficient Generation of Engine Representative Tip Timing Data Based on a Reduced Order Model for Bladed Rotors}, series = {Journal of Engineering for Gas Turbines and Power}, volume = {141}, journal = {Journal of Engineering for Gas Turbines and Power}, number = {1}, issn = {0742-4795}, doi = {10.1115/1.4040748}, pages = {9}, language = {en} } @misc{FigaschewskyHanschkeKuehhorn, author = {Figaschewsky, Felix and Hanschke, Benjamin and K{\"u}hhorn, Arnold}, title = {Efficient Generation of Engine Representative Tip Timing Data Based on a Reduced Order Model for Bladed Rotors}, series = {ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, Volume 7C: Structures and Dynamics, Oslo, Norway, June 11-15, 2018}, journal = {ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, Volume 7C: Structures and Dynamics, Oslo, Norway, June 11-15, 2018}, publisher = {ASME}, address = {New York, NY}, isbn = {978-0-7918-5115-9}, doi = {10.1115/GT2018-76342}, pages = {12}, abstract = {In modern compressors the assessment of blade vibration levels as well as health monitoring of the components are fundamental tasks. Traditionally, this assessment is done by the application of strain gauges to some blades of the assembly. In contrast to strain gauges, blade tip timing (BTT) offers a contactless monitoring of all blades of a rotor and there is no need of a telemetry system. A major issue in the interpretation of BTT data is the heavily undersampled nature of the signal. Usually, newly developed BTT algorithms are tested with sample data created by simplified structural models neglecting many of the uncertainties and disturbing influences of real applications. This work focuses on the creation of simulated BTT datasets as close as possible to real case measurements. For this purpose a subset of nominal system modes (SNM) representation of a compressor rotor is utilized. This model is able to include a large number of features present in real measurements, such as mistuning, static blade deflections due to centrifugal loads, aerodynamic damping and multiple mode resonances. Additionally, manufacturing deviations of the blade geometry, probe positioning errors in the BTT system and noise in the time of arrivals (TOAs) are captured by the BTT simulation environment. The main advantage of the created data is the possibility to steadily increase the signal complexity. Starting with a "perfect" signal the simulation environment is able to add different uncertainties one after the other. This allows the assessment of the influence of different features occurring in real measurements on the performance and accuracy of the analysis algorithms. Finally, a comparison of simulated BTT data and real data acquired from a rig test is shown to validate the presented approach of BTT data generation. Copyright © 2018 by Rolls-Royce Deutschland Ltd \& Co KG}, language = {en} } @misc{WeberKuehhorn, author = {Weber, Robby and K{\"u}hhorn, Arnold}, title = {Mistuning Identification Approach With Focus on High-Speed Centrifugal Compressors}, series = {Journal of Engineering for Gas Turbines and Power}, volume = {14}, journal = {Journal of Engineering for Gas Turbines and Power}, number = {3}, issn = {1528-8919}, doi = {10.1115/1.4040999}, pages = {7}, language = {en} } @misc{WeberKuehhornBeirow, author = {Weber, Robby and K{\"u}hhorn, Arnold and Beirow, Bernd}, title = {Mistuning und D{\"a}mpfung radialer Turbinen- und Verdichterlaufr{\"a}der}, series = {MTZ - Motortechnische Zeitschrift}, volume = {80}, journal = {MTZ - Motortechnische Zeitschrift}, number = {9}, issn = {0024-8525}, doi = {10.1007/s35146-019-0094-2}, pages = {74 -- 78}, abstract = {Turbolader tragen erheblich zur Steigerung des Motorenwirkungsgrads bei. Rotierende Komponenten sind infolge der Fliehkraft, der zur Aufladung notwendigen Str{\"o}mungsumlenkungen, der instation{\"a}ren Druckschwankungen der Str{\"o}mung sowie von Temperaturgradienten als hochbelastete Laufr{\"a}der einzustufen, die unter erheblicher Schwingungsanf{\"a}lligkeit leiden. Am Lehrstuhl Strukturmechanik und Fahrzeugschwingungen der BTU Cottbus-Senftenberg wurde im Rahmen eines FVV-Forschungsvorhabens der Einfluss der fertigungsbedingten Toleranzen auf eben jenes Schwingungsverhalten untersucht. Es wird nachgewiesen, dass Intentional Mistuning zu signifikant niedrigeren Belastungen f{\"u}hren kann.}, language = {de} } @misc{FranzKuehhornGierschetal., author = {Franz, Falco and K{\"u}hhorn, Arnold and Giersch, Thomas and Schrape, Sven and Figaschewsky, Felix}, title = {Influence of Inlet Distortions on the Forced Vibration of a High Pressure Compressor Rig}, series = {ASME 2020 Turbo Expo - Virtual Conference, September 2020}, journal = {ASME 2020 Turbo Expo - Virtual Conference, September 2020}, abstract = {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.}, language = {en} } @misc{GambittaKuehhornSchrape, author = {Gambitta, Marco and K{\"u}hhorn, Arnold and Schrape, Sven}, title = {Geometrical Variability Modelling of Axial Compressor Blisk Aerofoils and Evaluation of Impact on the Forced Response Problem}, series = {ASME 2020 Turbo Expo - Virtual Conference, September 2020}, journal = {ASME 2020 Turbo Expo - Virtual Conference, September 2020}, abstract = {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.}, language = {en} } @misc{HeinrichKuehhornSteffetal., author = {Heinrich, Christoph Rocky and K{\"u}hhorn, Arnold and Steff, Klaus and Petry, Nico}, title = {Generalized Model for the Approximation of Coupled Acousto-Mechanical Natural Frequencies in High-Pressure Centrifugal Compressors}, series = {ASME 2020 Turbo Expo - Virtual Conference, Spetember 2020}, journal = {ASME 2020 Turbo Expo - Virtual Conference, Spetember 2020}, abstract = {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.}, language = {en} } @misc{ElMasryKuehhornFigaschewsky, author = {ElMasry, Seif and K{\"u}hhorn, Arnold and Figaschewsky, Felix}, title = {Investigation of Working Line Variation Onto Forced Response Vibrations of a Compressor Blisk}, series = {Turbo Expo 2021, Virtual Conference and Exhibition: September 21, 2020}, journal = {Turbo Expo 2021, Virtual Conference and Exhibition: September 21, 2020}, abstract = {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.}, language = {en} } @misc{HardenbergKuehhornFanter, author = {Hardenberg, Alexander and K{\"u}hhorn, Arnold and Fanter, Maren}, title = {Correlating and Updating Finite Element Models of Different Fidelity Using an Energy-Based Approach}, series = {Turbo Expo 2020, Virtual Conference, Virtual Conference and Exhibition, Online, September 21 - 25, 2020}, journal = {Turbo Expo 2020, Virtual Conference, Virtual Conference and Exhibition, Online, September 21 - 25, 2020}, abstract = {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.}, language = {en} } @misc{NoackKuehhornKoberetal., author = {Noack, Martin and K{\"u}hhorn, Arnold and Kober, Markus and Firl, Matthias}, title = {A new stress-based topology optimization approach for finding flexible structures}, series = {Structural and Multidisciplinary Optimization}, volume = {64}, journal = {Structural and Multidisciplinary Optimization}, number = {4}, issn = {1615-147X}, doi = {10.1007/s00158-021-02960-w}, pages = {1997 -- 2007}, abstract = {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.}, language = {en} }