This dissertation provides numerical studies to improve bladed disk assembly design for preventing blade high cycle fatigue failures. The analyses are divided into two major subjects. For the first subject presented in Chapter 2, the mechanisms of transonic fan flutter for tuned systems are studied to improve the shortcoming of traditional method for modern fans using a 3D time-linearized Navier-Stokes solver. Steady and unsteady flow parameters including local work on the blade surfaces are investigated. It was found that global local work monotonically became more unstable on the pressure side due to the flow rollback effect. The local work on the suction side significantly varied due to nodal diameter and flow rollback effect. Thus, the total local work for the least stable mode is dominant by the suction side. Local work on the pressure side appears to be affected by the shock on the suction side. For the second subject presented in Chapter 3, sensitivity studies are conducted on flutter and forced response due to frequency mistuning and aerodynamic asymmetry using the single family of modes approach by assuming manufacturing tolerance. The unsteady aerodynamic forces are computed using CFD methods assuming aerodynamic symmetry. The aerodynamic asymmetry is applied by perturbing the influence coefficient matrix. These aerodynamic perturbations influence both stiffness and damping while traditional frequency mistuning analysis only perturbs the stiffness. Flutter results from random aerodynamic perturbations of all blades showed that manufacturing variations that effect blade unsteady aerodynamics may cause a stable, perfectly symmetric engine to flutter. For forced response, maximum blade amplitudes are significantly influenced by the aerodynamic perturbation of the imaginary part (damping) of unsteady aerodynamic modal forces. This is contrary to blade frequency mistuning where the stiffness perturbation dominates. / Dissertation

This thesis focuses on experimentally measuring the response of varying dilatation ratio bluff body flames under harmonic excitation. Such flames are often encountered in jet engine afterburners and are susceptible to combustion instabilities. Previous work has been done modeling such flames, however, only limited experimental data has been obtained at these conditions and is the motivation for this thesis. The focus of this work is to measure the transfer function of longitudinally forced, varying dilatation ratio bluff body flames. The transfer function is obtained by measuring flame position and flame luminosity fluctuations at the forcing frequency. Specifically, the amplitude and phase of the fluctuations are characterized as a function of flow velocity, axial location, and perturbation amplitude. These measurements are also compared to available theoretical predictions, showing that qualitative measured trends are consistent with theory. In addition, a detailed quantitative comparison is performed at one condition, showing good agreement between predictions and measurements in the near and mid-field of the flame response. However, agreement is not obtained in the far-field, indicating that continued theoretical work is needed to understand the flame response characteristics in this region.

L’enjeu de cette thèse est d’améliorer la compréhension et la prédiction du phénomène de réponse forcée des aubages de turbomachines en situation de résonance. L’étude a été menée au moyen de simulations numériques U-RANS 3D et en s’appuyant sur le compresseur d’essai ERECA, dédié au phénomène de réponse forcée. Pour prédire les amplitudes de vibration des aubages excités aérodynamiquement, la méthode de prédiction la plus répandue consiste à effectuer séparément un calcul d’excitation et un calcul d’amortissement aérodynamique ; on parle alors de calcul découplé. C’est cette méthode qui a été mise en œuvre dans un premier temps. Les calculs d’excitation et d’amortissement aérodynamiques ont été comparés individuellement aux résultats d’essais. Pour cela une méthode de traitement du signal fréquence/amplitude a été développée dans le but d’extraire l’amortissement et l’excitation des résultats d’essais. Les analyses des simulations ont permis de mieux comprendre les mécanismes d’excitation et d’amortissement aérodynamique. On a ainsi pu montrer que le phénomène d’interaction rotor/stator s’apparente par son caractère discontinu à une percussion périodique. Quant au phénomène d’amortissement, il se caractérise par le bilan des contributions de chaque zone d’échange d’énergie sur la paroi de l’aubage. En outre, les amplitudes vibratoires calculées à partir de cette méthode sont très proches des valeurs d’essais. Toutefois, cette procédure de calcul requiert la mise en œuvre de 2 calculs instationnaires différents et ne permet pas à l’heure actuelle d’être utilisée dans un cycle de conception. Dans le but de simplifier et d’améliorer la qualité de prédiction des analyses de réponse forcée, la méthode du couplage dynamique a été mise en œuvre et évaluée. Avec cette méthode, l’aubage répond librement aux sollicitations engendrées par le fluide. Une fois le régime transitoire évacué, l’aubage oscille en régime permanent. Cette méthode permet donc de prédire une amplitude vibratoire à partir d’un seul calcul instationnaire. En revanche, le calcul s’avère bien plus onéreux que la méthode découplée de par l’existence du régime transitoire. Dans le but de rendre accessible cette méthode à un niveau industriel, deux méthodes d’accélération du calcul ont été mises en place. Les résultats obtenus sont très encourageants et devraient permettre de réduire drastiquement les temps de restitution des analyses de réponse forcée. A la connaissance de l’auteur, cette thèse constitue une étude inédite de comparaison entre méthode découplée et couplage dynamique, qui par ailleurs s’appuie sur des résultats d’essais dédiés exclusivement au phénomène de réponse forcée. / The purpose of this PhD thesis is to provide a better understanding of the forced response phenomena of turbomachinery bladings in resonance conditions. The study will use 3D U-RANS calculations relying on experimental results obtained on the ERECA test case, dedicated to the forced response phenomenon. In order to predict the vibrating amplitudes of aerodynamically excited bladings, the most commonly used prediction methodology consists in separated calculations for the prediction of the aerodynamic excitation and damping ; it is the decoupled method. The predictions of these two components have been compared to the experiment individually. For this, a special signal treatment analysis has been developed so as to extract the damping and excitation from the experimental amplitude/frequency signal. The analysis of the results presented hereafter has provided a better understanding of the mechanisms involved in the aerodynamic damping and excitation. The results obtained match very closely the experiment. However, this procedure requires two different unsteady calculations and is therefore hardly usable within the design process of an engine. In order to simplify and improve the quality of the forced response analysis, the time marching method has been developed and analyzed. With this method, the blade responses freely to the aerodynamic solicitations. Once the transient regime is evacuated, the blade oscillates on its permanent regime. In order to enable access to this methodology on an industrial level, several speed-up methodologies have been implemented and the results are very encouraging. To the knowledge of the author, this thesis is the first comparison between the decoupled and the time marching methods that relies on test results from an experiment dedicated to the forced response phenomenon.

The purpose of this master thesis is to provide a reliable methodology to predict the forced response of a monoblock bladed drum from a low pressure compressor. Pre-test forced response calculations have already been made at Techspace Aero in 2013. Now that experimental data are available, the methodology has to be adapted to ensure the best numerical-experimental correlation possible. The final goal is that, at the end of the thesis, engineers at Techspace Aero will be able to launch reliable forced response simulations within a short amount of time. For the sake of confidentiality, some data are not revealed, such as the engine name, some numerical values (forced response, aerodynamic damping, frequency of the mode etc…) and axis scales. In this paper, the study focuses on the forced response of a rotor blade from the first stage under the excitation from the upstream stator. The mode under investigation is the 2S2, the one that responded during the experiment. The TWIN approach is used to compute the forced response of the rotor blade. With this approach, a steady stage computation has first to be carried on as an initialization. Then two unsteady computations are necessary. The first, without blade motion, will provide the excitation aerodynamic forces. The aerodynamic damping will be extracted from the second one, where the motion of the blade is imposed on a given eigenmode. The forced response can then be computed with these two results and some additional structural data.  The results will be compared to the experimental value.

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). 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. 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. / NR 20140805

The goal of this research has been the development of an effective design tool for torsional analysis. In the hopes of achieving this goal the computer program, Torsion 1, has been created. This torsional transfer matrix program provides the user with the ability to easily model multi-rotor systems using a simple user-interface. The program is capable of modeling such components or system characteristics as continuously distributed mass, viscous and structural damping, vibration absorbers, and gear meshes with gear tooth flexibility. The analysis capabilities of the program include forcedresponse and free-vibration analyses. The forced-response analysis module is capable of determining a system’s response to a static or harmonic torsional load. The free-vibration analysis module allows is capable of determining the eigenvalues and eigenvectors for damped and undamped systems. This thesis includes an explanation of the multi-rotor transfer matrix technique employed in Torsion 1. The derivation of transfer matrices for visco-elastic vibration absorbers, pendulum absorbers, flexible gear meshes, and planetary gear trains are included in this work. Finally, the validity of the program results is verified with a set of benchmark examples. / Master of Science

The present thesis discusses the forced response of a rotor’s bladed-disk when excited by the periodic force produced by a wake generator, or Inlet Guide Vane (IGV),with 8 equally-spaced blades. These components are part of an axial transonic compressor rig, moreover the Transonic Compressor Darmstadt 1 (TCD1), located at the Technical University of Darmstadt. The investigation is within the ARIAS (Advanced Research Into Aeromechanical Solutions) project, that aims to improve the predictive capabilities of the design methods used in the aircraft propulsion engine’s industry to study aerodynamically induced blade vibrations. The methodology comprised a set of numerical analyses that were conducted using the software Ansys, addressing both the structural and the aerodynamics sides of the aeroelastic problem, in a co-dependent way. At first, steady-state CFD simulations were conducted to study the mesh convergence and to analyse the operation of the compressor at N80 speed, obtaining its compressor map and its peak efficiency operation point. From these, the aerodynamic static force being applied on theblade was obtained, allowing to determine the pre-stresses of the bladed-disk, orblisk. With a modal analysis, the natural modes of the rotor blisk at N80 speed were obtained and the resonance crossing M2 EO8 was identified, plotting the Campbell and ZZENF diagrams. From the modal displacements of the critical mode, a blade flutter analysis was conducted in order to compute the aerodynamic damping ratio of the rotor blisk. With a transient CFD analysis, the periodic forcing being applied onthe rotor blisk that arises from the IGV wake pattern was determined and exported as Fourier coefficients. Finally, a harmonic simulation was carried out to analyse the forced response of the blisk, introducing both the aerodynamic damping value and the unsteady forcing mapped onto the blade. As a result, the frequency response of both the blade maximum alternating deflections and equivalent stresses was obtained, as well as the respective spatial contour plots at the obtained resonance frequency. Some of the results of the conducted analyses were investigated in order to analyse the aerodynamic phenomena occurring, where it was possible to identify vortex shedding, leading shock, tip-clearance and horse-shoe vortex.  Afterwards, the numerical results were compared to the experimental data optained from rig tests conducted at the TCD1 by partners of the ARIAS projects. The numerical model management to predict well the compressor map, thus the steady-state of the flow, as well as the resonance frequency. The aerodynamic damping value was over- predicted when compared to the entire data set. When it came to the harmonic analysis results, the numerical model under-predicted by one order of magnitude the maximum deflection, and the equivalent stress is, as well, far below the experimental results. These results led to conclude that the model is under-predicting the aerodynamix unsteady forcing that results from the wake pattern generated by the IGV and excites the rotor blades.

The main contributor to the high-cycle fatigue of compressor blades is the response to aerodynamic forcing functions generated by an upstream row of stators or inlet guide vanes. Resonant response to engine order excitation at certain rotor speeds is especially damaging. Studies have shown that flow control by trailing edge blowing (TEB) can reduce stator wake strength and the amplitude of the downstream rotor blade vibrations generated by the unsteady stator-rotor interaction. In the present study, the effectiveness of TEB to reduce forced blade vibrations was evaluated in a modern single-stage transonic compressor rig. A row of wake generator (WG) vanes with TEB capability was installed upstream of the fan blisk, the blades of which were instrumented with strain gages. Data was collected for varied TEB conditions over a range of rotor speed which included one fundamental and multiple harmonic resonance crossings. Sensitivity of resonant response amplitude to full-span TEB flowrate, as well as optimal TEB flowrates, are documented for multiple modes. Resonant response sensitivity was generally characterized by a robust region of substantial attenuation, such that less-than-optimal TEB flowrates could prove to be an appropriate design tradeoff. The fundamental crossing amplitude of the first torsion mode was reduced by as much as 85% with full-span TEB at 1.1% of the total rig inlet flow. Similar reductions were achieved for the various harmonic crossings, including as much as 94% reduction of the second leading edge bending mode resonant response using 0.74% of the rig flow for full-span TEB. At least 32% reduction was achieved for all modal crossings over the broad flow range of 0.5 to 0.9% of the rig flow. Thus the results demonstrate the modal- and flowrate-robustness of full-span TEB for reducing forced response in a modern, closely-spaced transonic compressor. Reduced spanwise TEB coverage was generally found to provide less peak reduction. Widely varying sensitivities of the vibration modes to the spanwise TEB distribution were also noted. While the second chordwise mode experienced roughly the same maximum response reduction of 80% for all of the spanwise TEB configurations, some other modes were amplified from the baseline case under part-span TEB conditions. Part-span TEB was thus found to be less modally-robust than full-span TEB. / Ph. D.

No description available.

Les roues aubagées de turbomachines sont soumises en fonctionnement `a des sollicitations statiqueset dynamiques, qui peuvent conduire `a des situations de fatigue vibratoire pour des excitationsau voisinage des fréquences de résonance. Ce probléme est aggravé par le désaccordage involontaire,auquel sont sujets les ensembles aubagés notamment du fait des dispersions de fabrication.L’objectif de ce travail de recherche est de proposer une stratégie mixte numérique et expérimentalepermettant de caractériser le comportement dynamique d’une roue d’essai au sein des statistiquesdécrivant une flotte simulée de moteurs en service, en vue de la certification vibratoire. Un modèle numérique fidèle basée sur l’acquisition optique d’une roue expérimentale a été développé; une série d’essais en laboratoire a permis de vérifier sa représentativité. L’exploitation de mesures réalisées en configuration moteur a montré une bonne cohérence globale des niveaux d’amplitude prédits à l’aidedu modèle fidèle. Enfin, la simulation du comportement d’une population de roues désaccordées à l’aide d’une approche probabiliste non-Paramétrique a permis de positionner l’amplitude de réponse maximale rencontrée sur la pièce d’essai par rapport à la valeur théorique obtenue par simulation. La stratégie proposée permet une prédiction des niveaux vibratoires maximaux pour une flotte de rouesen service. / Under operating conditions, turbomachinery blisks are subject to static and dynamic loads which mayresult in High-Cycle Fatigue situations when excited at the neighbourhood of resonant frequencies.Random mistuning, which affects blisks due to machining deviations, turns this issue even morecritical. The objective of the current study is to introduce a numerical-Experimental strategy allowingthe dynamic characterization of an experimental bladed disk with regard to the statistics representingthe simulated behaviour for a population of operating blisks. A high-Fidelity numerical model basedon the optical acquisition of an experimental blisk has been set up. Test series performed in labconditions allowed to verify its coherence. The comparison of the response amplitudes measuredunder operating conditions to the model predictions revealed an acceptable matching between testand simulation data. Finally, a non-Parametric probabilistic approach has been used to predict thetheoretical maximal amplification factor. The maximum amplification factor obtained by means ofsimulation was compared to the amplification factor of the test specimen. The strategy proposed inthis study allows maximum amplification factor predictions for a population of blisks