Conjectural Bifurcation Analysis of an Aircraft Engine Blade Undergoing 3D Unilateral Contact Constraints

Prediction of rotor/stator interaction phenomena between a blade-tip and the surrounding abradable coating deposited on the casing has seen recent promising numerical developments that revealed consistency with several experimental set-up. In particular, the location of critical rotational frequencies, damaged blade areas as well as the wear pattern along the casing circumference were accurately predicted for an interaction scenario involving a low-pressure compressor blade and the surrounding abradable coating deposited on a perfectly rigid casing. The structural behaviour of the blade in the vicinity of a critical rotational frequency however remains unclear as brutal amplitude variations observed experimentally could not be numerically captured without assuming contact loss or an improbable drastic and sudden change of the abradable coating mechanical properties during the interaction. In this paper, attention is paid to the structural behaviour of a high-pressure compressor blade at the neighbourhood of a critical rotational frequency. The interaction scenarios for two close rotational frequencies: Ωc and Ωc* are analyzed using empirical mode decomposition based on an adjusted B-spline interpolation of the time responses. The obtained results are compared to the interaction scenario dictated by the abradable coating removal history and the location of contact areas. The unstable nature of the blade vibratory response when the rotational frequency exceeds a critical rotational frequency is underlined and a plausible scenario arises for explaining a sudden and significant decrease of the blade amplitude of vibration without contact separation.

Experimental Identification of Dynamic Force Coefficients for a 110 mm Compliantly Damped Hybrid Gas Bearing

Compliant hybrid gas bearings combine key enabling features from both fixed geometry externally pressurized gas bearings and compliant foil bearings. The compliant hybrid bearing relies on both hydrostatic and hydrodynamic film pressures to generate load capacity and stiffness to the rotor system, while providing damping through integrally mounted metal mesh bearing support dampers. This paper presents experimentally identified force coefficients for a 110 mm compliantly damped gas bearing using a controlled-motion test rig. Test parameters include hydrostatic inlet pressure, excitation frequency, and rotor speed. The experiments were structured to evaluate the feasibility of implementing these bearings in large size turbomachinery. Dynamic test results indicate weak dependency of equivalent direct stiffness coefficients to most test parameters except for frequency and speed, where higher speeds and excitation frequency decreased equivalent bearing stiffness values. The bearing system equivalent direct damping was negatively impacted by increased inlet pressure and excitation frequency, while the cross-coupled force coefficients showed values an order of magnitude lower than the direct coefficients. The experiments also include orbital excitations to simulate unbalance response representative of a target machine while synchronously traversing a critical speed. The results indicate that the gas bearing can accommodate vibration levels larger than the set bore clearance while maintaining satisfactory damping levels.

CFD Assessment of Rotordynamic Coefficients in Labyrinth Seals

Seals used in high speed centrifugal compressors are prone to generate rotordynamic (RD) instabilities. To further understand their influence, a CFD based approach is developed. The objective of the current study is to numerically investigate and characterize the RD coefficients, representative of the dynamic seal forces. Experiments were carried out at high pressure test rig (up to 200 bar seal inlet pressure) which runs at 10000 RPM and has a high pre-swirl (about 0.9) along the same direction of rotor rotation. The rotor shaft in the experiment was instrumented with active magnetic bearings (AMBs) to linearly excite the rotor at three different frequencies: 28 Hz, 70 Hz and 126 Hz. Each frequency is characterized by amplitude of vibration and a phase. CFD simulations were carried out using commercial flow solver, using similar boundary conditions as that of experiments. The paper describes details of CFD model and its comparison against experiments. Numerical results show reasonable agreement of RD coefficients with test results. This job has to be considered as a first approach to CFD methodology applied to annular seals for the authors.

A Study on the Effects of Geometric Non Linearities on the Un-Running Transformation of Compressor Blades

A manufactured, cold, turbomachinery blade will deform elastically under the design centrifugal, aerodynamic and thermal loads, giving the hot blade geometry. The hot-to-cold transformation or blade unrunning process consist in the calculation of the cold blade geometry which, when subject to the design conditions, will deform to match the given hot blade geometry. This paper will use a simple spring-mass model to show how the selection of geometrically linear or large displacement, geometrically non-linear, structural solvers affect the hot-to-cold transformation for compressor blades. The geometrically linear solver gives good results below a certain value of the rotational speed, which depends on the blade geometry and on the ratio of density to elastic modulus of the blade material. Above that speed, the geometrically linear solver predicts unrealistically high deformations. This model is applied to a realistic compressor blade, showing the same behavior.

Parametric Dynamics of Mistuned Bladed Disk

The mistuning of bladed disk comes from manufacturing tolerances and in-service wear and tear. Consequently the cyclic symmetry has been destroyed by mistuning, even small mistuning levels could result in drastic changes in the dynamics of bladed disks. Specifically, mistuning can cause mode localization and an increase of the maximum forced response. It has been known that frequency veering, modal localization and magnification of response are three most classical dynamic properties of bladed disk. However few researches has focused on the relationships between dynamic characters and design parameters, because the proper variation ranges of the design parameters are difficult to be determined. The aim of this paper is to investigate the relationship between designed parameters and dynamic properties of mistuned bladed disk. Based on a lumped parametric model of bladed disk and utilizing parameterized eigenvalue solution, a reasonable range of designed parameter corresponding to specific nodal diameter index was provided. The numerical results showed that the curves of the gap of frequency veering versus coupling strength or blade stiffness have bowel-style. It was also found that there exists a quasi-saddle-surface while the vibration amplification factor varies with coupling strength and mistuning strength. The quasi-saddle-surface reveals that the existence of threshold of vibration amplification factor depends on the value of coupling strength. The result means that a proper choice of combination of coupling strength and mistuning strength could lead to a suppression of mistuned vibration amplification.

Optimization-Aided Forced Response Analysis of a Mistuned Compressor Blisk

The forced response of the first rotor of an E3E-type high pressure compressor blisk is analyzed with regard to varying mistuning, varying engine order excitations and the consideration of aeroelastic effects. For that purpose, SNM-based reduced order models are used in which the disk remains unchanged while the Young’s modulus of each blade is used to define experimentally adjusted as well as intentional mistuning patterns. The aerodynamic influence coefficient technique is employed to model aeroelastic interactions. Furthermore, based on optimization analyses and depending on the exciting EO and aerodynamic influences it is searched for the worst as well as the best mistuning distributions with respect to the maximum blade displacement. Genetic algorithms using blade stiffness variations as vector of design variables and the maximum blade displacement as objective function are applied. An allowed limit of the blades’ Young’s modulus standard deviation is formulated as secondary condition. In particular, the question is addressed if and how far the aeroelastic impact, mainly causing aerodynamic damping, combined with mistuning can even yield a reduction of the forced response compared to the ideally tuned blisk. It is shown that the strong dependence of the aerodynamic damping on the inter-blade phase angle is the main driver for a possible response attenuation considering the fundamental blade mode. The results of the optimization analyses are compared to the forced response due to real, experimentally determined frequency mistuning as well as intentional mistuning.

Time-Linearized Forced Response Analysis of a Counter Rotating Fan: Part I — Theoretical Concept of a Fully Time-Linear Forced Response Analysis

From 2010 to 2013, several institutes of the German Aerospace Center investigated a counter rotating fan arrangement called CRISP2. While having efficiency advantages over rotor-stator arrangements, counter rotating fans might be subject to increased aerodynamic excitation as well. It is well known that rotor-stator interaction (in this case rotor-rotor-interaction) can result in aerodynamic excitation of blades leading to high cycle fatigue. Therefore, forced response calculations and an estimation of the static and dynamic loads during operation are essential prior to production and rig tests. At the Institute of Aeroelasticity, loosely coupled approaches for forced response calculations have been employed for a number of years (Vasanthakumar [1]). Due to a limited time frame for the forced response simulation, it was decided to use this loosely coupled approach for the forced response simulations in CRISP2 as well and to reduce its time consumption even more by using a time-linear approach for the forcing calculations. The theoretical concepts and their implementation into a forced response simulation are highlighted. Special consideration is given to the linearized unsteady simulations with gust boundary conditions that have been implemented into the DLR in-house flow solver TRACE [2]. The advantages and drawbacks of a fully time-linear loosely coupled method compared to more accurate and complicated approaches are discussed.

The Study of Tip Clearance of a Wide-Chord Fan Blade of a High Bypass Ratio Turbo-Fan Engine

The wide-chord swept fan blade (WCSFB) has been extensively used in a advanced high bypass ratio turbofan engines. This paper explores the nature of WCSFB tip clearance. From the static analysis, it is found that the tip radial clearance at leading and trailing edge of WCSFB will be reduced with either bending or torsional deformation of the blade. And the change of the tip radial clearances varies with the twist angle. In this study, dynamic response of the WCSFB with different angular accelerations of the engine has been analyzed. It shows that when the angular acceleration of the fan rotor reaches a certain level, considerable bending and torsional deformation of the blade will occur, accompanied by the reduction of the tip radial clearance, which may lead to abnormal rubbing/impact between the blade tip and the casing. This may cause severe consequence for the blade and casing of the engine. The numerical simulation results show that the rubbing/impact between the WCSFB tip and the casing under angular acceleration loads can lead to local buckling of the tip leading edge of the blade, which will cause severe damage at the blade tip. Moreover, the influence of vibration and mass imbalance of the rotor on the fan blade tip clearance is also analyzed. In this paper, the results of a rig test under irregular acceleration for the WCSFB rotor is also presented, which validates the analytical results. The numerical simulation and test results will assist the blade tip clearance design to reflect the nature of the WCSFB under irregular acceleration to ensure safety.

High-Pressure Compressor Blade Dynamics Under Aerodynamic and Blade-Tip Unilateral Contact Forcings

Recent studies focused on the numerical prediction of structural instabilities that may arise in rotating components of an aircraft engine. These instabilities are commonly classified into two categories: those induced by aerodynamic phenomena (such as the pressure applied on the blade by the incoming air flow) and those related to structural phenomena (such as potential blade/casing contacts). Based on an existing numerical strategy for the analysis of rotor/stator interactions induced by unilateral contacts between rotating and static components, this paper aims at combining both types of instabilities and provides a qualitative analysis of structural interactions that may arise within the high-pressure compressor of an aircraft engine. The aerodynamic pressure on the blade is simplified as a sinusoidal external load whose frequency depends on the number of upstream guide vanes. Results are presented both in time and frequency domains. Detailed bifurcation diagrams and Poincaré maps underline the fundamental differences in the nature of the witnessed interactions with and without aerodynamic loading on the blade.