With the present drive in turbomachine engine developmenttowards thinner and lighter bladings, closer spaced blade rowsand higher aerodynamic loads per blade row and blade, advanceddesign criteria and accurate prediction methods for vibrationalproblems such as forced response become increasingly importantin order to be able to address and avoid fatigue failures ofthe machine early in the design process. The present worksupports both the search for applicable design criteria and thedevelopment of advanced prediction methods for forced responsein transonic turbine stages. It is aimed at a betterunderstanding of the unsteady aerodynamic mechanisms thatgovern forced response in transonic turbine stages and furtherdevelopment of numerical methods for rotor stator interactionpredictions. The investigation of the unsteady aerodynamic excitationmechanisms is based on numerical predictions of thethree-dimensional unsteady flow field in representative testturbine stages. It is conducted in three successive steps. Thefirst step is a documentation of the pressure perturbations onthe blade surface and the distortion sources in the bladepassage. This is performed in a phenomenological manner so thatthe observed pressure perturbations are related to thedistortion phenomena that are present in the blade passage. Thesecond step is the definition of applicable measures toquantify the pressure perturbation strength on the bladesurface. In the third step, the pressure perturbations areintegrated along the blade arc to obtain the dynamic bladeforce. The study comprises an investigation of operationvariations and addresses radial forcing variations. With thehelp of this bottom-up approach the basic forcing mechanisms oftransonic turbine stages are established and potential routesto control the aerodynamic forcing are presented. For the computation of rotor stator interaction aerodynamicsfor stages with arbitrary pitch ratios a new numerical methodhas been developed, validated and demonstrated on a transonicturbine test stage. The method, which solves the unsteadythree-dimensional Euler equations, is formulated in thefour-dimensional time-space domain and the derivation of themethod is general such that both phase lagged boundaryconditions and moving grids are considered. Time-inclination isutilised to account for unequal pitchwise periodicity bydistributing time co-ordinates at grid nodes such that thephase lagged boundary conditions can be employed. The method isdemonstrated in a comparative study on a transonic turbinestage with a nominal non integer blade count ratio and anadjusted blade count ratio with a scaled rotor geometry. Thepredictions show significant differences in the blade pressureperturbation signal of the second vane passing frequency, whichwould motivate the application of the new method for rotorstator predictions with non-integer blade count ratios.

<p>With the present drive in turbomachine engine developmenttowards thinner and lighter bladings, closer spaced blade rowsand higher aerodynamic loads per blade row and blade, advanceddesign criteria and accurate prediction methods for vibrationalproblems such as forced response become increasingly importantin order to be able to address and avoid fatigue failures ofthe machine early in the design process. The present worksupports both the search for applicable design criteria and thedevelopment of advanced prediction methods for forced responsein transonic turbine stages. It is aimed at a betterunderstanding of the unsteady aerodynamic mechanisms thatgovern forced response in transonic turbine stages and furtherdevelopment of numerical methods for rotor stator interactionpredictions.</p><p>The investigation of the unsteady aerodynamic excitationmechanisms is based on numerical predictions of thethree-dimensional unsteady flow field in representative testturbine stages. It is conducted in three successive steps. Thefirst step is a documentation of the pressure perturbations onthe blade surface and the distortion sources in the bladepassage. This is performed in a phenomenological manner so thatthe observed pressure perturbations are related to thedistortion phenomena that are present in the blade passage. Thesecond step is the definition of applicable measures toquantify the pressure perturbation strength on the bladesurface. In the third step, the pressure perturbations areintegrated along the blade arc to obtain the dynamic bladeforce. The study comprises an investigation of operationvariations and addresses radial forcing variations. With thehelp of this bottom-up approach the basic forcing mechanisms oftransonic turbine stages are established and potential routesto control the aerodynamic forcing are presented.</p><p>For the computation of rotor stator interaction aerodynamicsfor stages with arbitrary pitch ratios a new numerical methodhas been developed, validated and demonstrated on a transonicturbine test stage. The method, which solves the unsteadythree-dimensional Euler equations, is formulated in thefour-dimensional time-space domain and the derivation of themethod is general such that both phase lagged boundaryconditions and moving grids are considered. Time-inclination isutilised to account for unequal pitchwise periodicity bydistributing time co-ordinates at grid nodes such that thephase lagged boundary conditions can be employed. The method isdemonstrated in a comparative study on a transonic turbinestage with a nominal non integer blade count ratio and anadjusted blade count ratio with a scaled rotor geometry. Thepredictions show significant differences in the blade pressureperturbation signal of the second vane passing frequency, whichwould motivate the application of the new method for rotorstator predictions with non-integer blade count ratios.</p>

Due to more and more aggressive designs in turbomachinery, assuring the structural integrity of its components has become challenging. Also influenced by this trend is blade design, where lighter and slimmer blades, in combination with higher loading, lead to an increased risk of failure, e.g. in the form of blade vibration. Methods have been proposed to reduce vibration amplitudes for subsonic engines, but cannot directly be applied to transonic regimes due to the additional physical phenomena involved. Therefore the present work investigates numerically the influence of two methods for reducing blade vibration amplitudes in transonic turbomachines, namely varying the blade count ratio and clocking. As it is known that clocking affects the efficiency, the concurrent effects on vibration amplitudes and efficiency are analyzed and discussed in detail. For the computational investigations, the proprietary Fortran-based non-linear, viscous 3D-CFD solver VolSol is applied on two transonic compressor cases and one transonic turbine case. In order to reduce calculation time and to generate the different blade count ratios a scaling technique is applied. The first and main part of this work focuses on the influence of the reduction techniques on aerodynamic forcing. Both the change in blade count ratio and clocking position are found to have significant potential for reducing aerodynamic force amplitudes. Manipulation of the phasing of excitation sources is found herein to be a major contributor to the amplitude variation. The lowest stimulus results are achieved for de-phased excitation sources and results in multiple blade force peaks per blade passing. In the case of blade count ratio variation it was found that blockage for high blade count ratios and the change in potential field size have significant impacts on the blade forcing. For the clocking investigation, three additional operating points and blade count ratios are analyzed and prove to have an impact on the force reduction achievable by clocking. The second part of the work evaluates the influence of clocking on the efficiency of a transonic compressor. It is found that the efficiency can be increased, but the magnitude of the change and the optimal wake impingement location depend on the operating point. Moreover it is shown that optimal efficiency and aerodynamic forcing settings are not directly related. In order to approximate the range of changes of both parameters, an ellipse approximation is suggested. / <p>QC 20130911</p> / TURBOPOWER

<p>One of the grand challenges faced by industry is the accurate prediction of unsteady aerodynamics events, including frequency lock-in and forced response. These aeromechanical incidents occurring in airplane engines and gas turbines can cause high-amplitude blade vibration and potential failure of the engine or turbine. During the last decades, the development of computational fluid dynamics has allowed the design and optimization of complex components while reducing the need for expensive engine testing. However, the validation of frequency lock-in and forced response numerical results with experimental data is very incomplete. Despite tremendous advances in computational capabilities, industry is still looking to validate design tools and guidelines to avoid these potentially costly aeroelastic events early in the design process. </p><p>The research efforts presented in this dissertation investigate the aeroelastic phenomena of frequency lock-in and forced response in turbomachinery. First, frequency lock-in is predicted for two structures, namely a two-dimensional cylinder and a single three-dimensional airfoil, and the results are compared to experimental data so that the methods can be extended to more complex structures. For these two simpler structures, a frequency domain harmonic balance code is used to estimate the natural shedding frequency and the corresponding lock-in region. Both the shedding frequencies and the lock-in regions obtained by an enforced motion method agree with experimental data from previous literature and wind tunnel tests. Moreover, the aerodynamic model of the vibrating cylinder is coupled with the structural equations of motion to form a fluid-structure interaction model and to compute the limit-cycle oscillation amplitude of the cylinder. The extent of the lock-in region matches the experimental data very well, yet the peak amplitude is underestimated in the numerical model. We demonstrate that the inclusion of the cylinder second degree of freedom has a significant impact on the cylinder first degree of freedom amplitude. Moreover, it is observed that two harmonics need to be kept in the equations of motion for accurate prediction of the unsteady forces on the cylinder. </p><p>The second important topic covered is a comprehensive forced response analysis conducted on a multi-stage axial compressor and compared with the initial data of the largest forced response experimental data set ever obtained in the field. Both a frequency domain and a time domain codes are used. The steady-state and time-averaged aerodynamic performance results compare well with experimental data, although losses are underestimated due to the lack of secondary flow paths and fillets in the model. The use of mixing planes in the steady simulations underpredicts the wakes by neglecting the important interactions between rows. Therefore, for similar cases with significant flow separation, the use of a decoupled method for forced response predictions cannot yield accurate results. A full multi-row transient analysis must be conducted for accurate prediction of the wakes and surface unsteady pressures. Finally, for the first time, predicted mistuned blade amplitudes are compared to mistuned experimental data. The downstream stator is found to be necessary for the accurate prediction of the modal forces and vibration amplitudes. The mistuned rotor is shown to be extremely sensitive to perturbations in blade frequency mistuning, aerodynamic asymmetry, and excitation traveling wave content. Since this dissertation presents the initial results of a five-year research program, more research will be conducted on this compressor to draw guidelines that can be used by aeromechanical engineers to safely avoid forced response events in the design of jet engines and gas turbines.</p> / Dissertation

No description available.

Striving to improve performance and lower weight of aircraft engines, modern compressor blades become thinner and lighter but higher loaded resulting in an increased vulnerability towards flutter. This trend is further aggravated through blisk designs that diminish structural damping and therewith flutter margin. Modern 3D wide-chord blade designs result in complex structural behaviors that add to the difficulty of correctly predicting flutter occurrence. To counteract above tendencies by driving the physical understanding of flutter and thereby helping to improve aero engine design tools, free flutter as well as forced response will be investigated in the 1.5 stage transonic compressor at TU Darmstadt. Aim of the forced response campaign is to determine the system damping in the stable compressor regime. Hence a novel excitation system capable of dynamically exciting specific rotor blade modes is needed. It is aim of the present work to find a promising concept for such a system. In the present work, the requirements for an excitation system to be used in the TUD compressor are defined with respect to achievable frequency, phase controllability, transferred excitation level, mechanical robustness, integrability and cleanliness. Different excitation system concepts, i.e. oscillating VIGVs, rotating airfoils, tangential and axial air injection are investigated numerically. An evaluation of the results obtained through 2D numerical studies proposes axial air injection as the most favorable concept. / Master of Science

The objective of this research work was to develop a design tool to analyze and design undamped beam and rotor systems in two dimensions. Systems modeled in two dimensions, such as beams with different moments of inertia, could produce varying responses in the each direction of motion. A coupling between the vertical and horizontal motions also exists in rotor systems mounted of fluid film bearings. The computer program called 2DBEAM has been developed to model and provide analyses of such systems in two dimensions. The tool has been based on an existing design package, BEAM9, which in its present state provides the response of beams and rotors in one plane of motion. The 2DBEAM program has the capability of performing the static response, free vibration, forced dynamic response, and frequency response analyses of a system. The Transfer Matrix Method has been used in the development of the software and an explanation of the method is included in this thesis. Mathematical problems and solutions encountered while developing 2DBEAM are also documented in this study. The code has been tested against analytical and published solutions for the types of analysis mentioned above and on coupled and uncoupled system models. / Master of Science

<p>Two state of the art finite element reduction techniquespreviously validated against the direct finite element method,one based on classical modal analysis and another based oncomponent mode synthesis, are applied for efficient mistunedfree vibration and forced response analysis of several bladeddisk geometries. The methods are first applied to two testcases in order to demonstrate the differences in computationalefficiency as well as to validate the methods againstexperimental data. As previous studies have indicated, nonoticeable differences in accuracy are detected for the currentapplications, while the method based on classical modalanalysis is significantly more efficient. Experimental data(mistuned frequencies and mode shapes) available for one of thetwo test cases are compared with numerical predictions, and agood match is obtained, which adds to the previous validationof the methods (against the direct finite element method).</p><p>The influence of blade-to-blade coupling and rotation speedon the sensitivity of bladed disks to mistuning is thenstudied. A transonic fan is considered with part span shroudsand without shrouds, respectively, constituting a high and alow blade-to-blade coupling case. For both cases, computationsare performed at rest as well as at various rotation speeds.Mistuning sensitivity is modelled as the dependence ofamplitude magnification on the standard deviation of bladestiffnesses. The finite element reduction technique based onclassical modal analysis is employed for the structuralanalysis. This reduced order model is solved for sets of randomblade stiffnesses with various standard deviations, i.e. MonteCarlo simulations. In order to reduce the sample size, thestatistical data is fitted to a Weibull (type III) parametermodel. Three different parameter estimation techniques areapplied and compared. The key role of blade-to-blade coupling,as well as the ratio of mistuning to coupling, is demonstratedfor the two cases. It is observed that mistuning sensitivityvaries significantly with rotation speed for both fans due toan associated variation in blade-to-blade coupling strength.Focusing on the effect of one specific engine order on themistuned response of the first bending modes, it is observedthat the mistuning sensitivity behaviour of the fan withoutshrouds is unaffected by rotation at its resonant condition,due to insignificant changes in coupling strength at thisspeed. The fan with shrouds, on the other hand, shows asignificantly different behaviour at rest and resonant speed,due to increased coupling under rotation. Comparing the twocases at resonant rotor speeds, the fan without shrouds is lessor equally sensitive to mistuning than the fan with shrouds inthe entire range of mistuning strengths considered.</p><p>This thesis’scientific contribution centres on themistuning sensitivity study, where the effects of shrouds androtation speed are quantified for realistic bladed diskgeometries. However, also the validation of two finite elementreduction techniques against experimental measurementsconstitutes an important contribution.</p>

<p>This research investigates the forced response of mistuned rotor blades that can lead to excessive vibration, noise, and high cycle fatigue failure in a turbomachine. In particular, an embedded rotor in the Purdue Three-Stage Axial Compressor Research Facility is considered. The prediction of the rotor forced response contains three key elements: the prediction of forcing function, damping, and the effect of frequency mistuning. These computational results are compared with experimental aerodynamic and vibratory response measurements to understand the accuracy of each prediction.</p><p>A state-of-the-art time-marching computational fluid dynamic (CFD) code is used to predict the rotor forcing function. A highly-efficient nonlinear frequency-domain Harmonic Balance CFD code is employed for the prediction of aerodynamic damping. These allow the compressor aerodynamics to be depicted and the tuned rotor response amplitude to be predicted. Frequency mistuning is considered by using two reduced-order models of different levels of fidelity, namely the Fundamental Mistuning Model (FMM) and the Component Mode Mistuning (CMM) methods. This allows a cost-effective method to be identified for mistuning analysis, especially for probabilistic mistuning analysis.</p><p>The first topic of this work concerns the prediction of the forcing function of the embedded rotor due to the periodic passing of the neighboring stators that have the same vane counts. Superposition and decomposition methods are introduced under a linearity assumption, which states that the rotor forcing function comprises of two components that are induced by each neighboring stator, and that these components stay unchanged with only a phase shift with respect to a change in the stator-stator clocking position. It is found that this assumption captures the first-order linear relation, but neglects the secondary nonlinear effect which alters each stator-induced forcing functions with respect to a change in the clocking position.</p><p>The second part of this work presents a comprehensive mistuned forced response prediction of the embedded rotor at a high-frequency (higher-order) mode. Three steady loading conditions are considered. The predicted aerodynamics are in good agreement with experimental measurements in terms of the compressor performance, rotor tip leakage flow, and circumferential distributions of the stator wake and potential fields. Mistuning analyses using FMM and CMM models show that the extremely low-cost FMM model produces very similar predictions to those of CMM. The predicted response is in good agreement with the measured response, especially after taking the uncertainty in the experimentally-determined frequency mistuning into consideration. Experimentally, the characteristics of the mistuned response change considerably with respect to loading. This is not very well predicted, and is attributed to un-identified and un-modeled effects. A significant amplification factor over 1.5 is observed both experimentally and computationally for this higher-order mode.</p> / Dissertation

<p>This research presents the detailed investigation of coupled-mode flutter and non-synchronous vibration in turbomachinery. Coupled-mode flutter and non-synchronous vibration are two aeromechanical challenges in designing turbomachinery that, when present, can cause engine blade failure. Regarding flutter, current industry design practices calculate the aerodynamic loads on a blade due to a single mode. In response to these design standards, a quasi three-dimensional, reduced-order modeling tool was developed for identifying the aeroelastic conditions that cause multi-mode flutter. This tool predicts the onset of coupled-mode flutter reasonable well for four different configurations, though certain parameters were tuned to agree with experimentation. Additionally, the results of this research indicate that mass ratio, frequency separation, and solidity have an effect on critical rotor speed for flutter. Higher mass-ratio blades require larger rotational velocities before they experience coupled-mode flutter. Similarly, increasing the frequency separation between modes and raising the solidity increases the critical rotor speed. Finally, and most importantly, design guidelines were generated for defining when a multi-mode flutter analysis is required in practical turbomachinery design. </p><p>Previous work has shown that industry computational fluid dynamics can approximately predict non-synchronous vibration (NSV), but no real understanding of frequency lock-in and blade limit-cycle amplitude exists. Therefore, to understand the causes of NSV, two different reduced-order modeling approaches were used. The first approach uses a van der Pol oscillator to model a non-linear fluid instability. The van der Pol model is then coupled to a structural degree of freedom. This coupled system exhibits the two chief properties seen in experimental and computational non-synchronous vibration. Under various conditions, the fluid instability and the natural structural frequency will lock-in, causing structural limit-cycle oscillations. This research shows that with proper model-coefficient choices, the frequency range of lock-in can be predicted and the conditions for the worst-case, limit-cycle-oscillation amplitude can be determined. This high-amplitude limit-cycle oscillation is found at an off-resonant condition, i.e., the ratio of the fluid-shedding frequency and the natural-structural frequency is not unity. In practice, low amplitude limit-cycle oscillations are acceptable; this research gives insight into when high-amplitude oscillations may occur and suggests that altering a blade's natural frequency to avoid this resonance can potentially make the response worse.</p><p>The second reduced-order model uses proper orthogonal decomposition (POD) methods to first reconstruct, and ultimately predict, computational fluid dynamics (CFD) simulations of non-synchronous vibration. Overall, this method was successfully developed and implemented, requiring between two and six POD modes to accurately predict CFD solutions that are experiencing non-synchronous vibration. This POD method was first developed and demonstrated for a transversely-moving, two-dimensional cylinder in cross-flow. Later, the method was used for the prediction of CFD solutions for a two-dimensional compressor blade, and the reconstruction of solutions for a three-dimensional first-stage compressor blade. </p><p>This research is the first to offer a van der Pol or proper orthogonal decomposition approach to the reduced-order modeling of non-synchronous vibration in turbomachinery. Modeling non-synchronous vibration is especially challenging because NSV is caused by complicated, unsteady flow dynamics; this initial study helps researchers understand the causes of NSV, and aids in the future development of predictive tools for aeromechanical design engineers.</p> / Dissertation