Alain Batailly

Numerical-Experimental Comparison in the Simulation of Rotor/Stator Interaction Through Blade-Tip/Abradable Coating Contact

Higher aircraft energy efficiency may be achieved by minimizing the clearance between the rotating blade tips and respective surrounding casing. A common technical solution consists in the implementation of an abradable liner which improves both the operational safety and the efficiency of modern turbomachines. However, unexpected abradable wear removal mechanisms were recently observed in experimental set-ups as well as duringmaintenance procedures. Based on a numerical strategy previously developed, the present study introduces a numerical-experimental comparison of such occurrence. Attention is first paid to the review and analysis of existing experimental results. Good agreement with numerical predictions is then illustrated in terms of critical stress levels within the blade as well as final wear profiles of the abradable liner. Numerical results suggest an alteration of the abradablemechanical properties in order to explain the outbreak of a divergent interaction. New blade designs are also explored in this respect and it is found that the interaction phenomenon is highly sensitive to (1) the blade geometry, (2) the abradablematerial properties and (3) the distortion of the casing.

Modeling of Abradable Coating Removal in Aircraft Engines Through Delay Differential Equations

In modern turbomachinery, abradable materials are implemented on casings to reduce operating tip clearances and mitigate direct unilateral contact occurrences between rotating and stationary components. However, both experimental and numerical investigations revealed that blade/abradable interactions may lead to blade failures. In order to comprehend the underlying mechanism, an accurate modeling of the abradable removal process is required. Time-marching strategies where the abradable removal is modeled through plasticity are available but another angle of attack is proposed in this work. It is assumed that the removal of abradable liners shares similarities with machine tool chatter encountered in manufacturing. Chatter is a self-excited vibration caused by the interaction between the machine and the workpiece through the cutting forces and the corresponding dynamics are efficiently captured by delay differential equations. These equations differ from ordinary differential equations in the sense that previous states of the system are involved in the formulation. This mathematical framework is employed here for the exploration of the blade stability during abradable removal. The proposed tool advantageously features a reduced computational cost and consistency with existing time-marching solution methods. Potentially dangerous interaction regimes are accurately predicted and instability lobes match both the flexural and torsional modal responses. Essentially, the regenerative nature of chatter in machining processes can also be attributed to abradable coating removal in turbomachinery.

Numerical Investigation of Abradable Coating Removal in Aircraft Engines Through Plastic Constitutive Law

In the field of turbomachines, better engine performances are achieved by reducing possible parasitic leakage flows through the closure of the clearance distance between blade tips and surrounding stationary casings and direct structural contact is now considered as part of the normal life of aircraft engines. In order to avoid catastrophic scenarios due to direct tip incursions into a bare metal housing, implementation of abradable coatings has been widely recognized as a robust solution offering several advantages: reducing potential nonrepairable damage to the incurring blade as well as adjusting operating clearances, in situ, to accept physical contact events. Nevertheless, the knowledge on the process of material removal affecting abradable coatings is very limited and it seems urgent to develop dedicated predicting numerical tools. The present work introduces a macroscopic model of the material removal through a piecewise linear plastic constitutive law which allows for real time access to the current abradable liner profile within a time-stepping approach of the explicit family. In order to reduce computational loads, the original finite element formulation of the blade of interest is projected onto a reduced-order basis embedding centrifugal stiffening. First results prove convergence in time and space and show that the frequency content of the blade response is clearly sensitive to the presence of abradable material. The continuous opening of the clearance between the blade tip and the casing due to the material removal yields larger amplitudes of motion and new scenarios of structural divergence far from the usual linear conditions provided by the well-known Campbell diagrams.

Modeling of abradable coating removal in aircraft engines through delay differential equations

In modern turbomachinery, abradable materials are implemented on casings to reduce operating tip clearances and mitigate direct unilateral contact occurrences between rotating and stationary components. However, both experimental and numerical investigations revealed that blade/abradable interactions may lead to blade failures. In order to comprehend the underlying mechanism, an accurate modeling of the abradable removal process is required. Time-marching strategies where the abradable removal is modeled through plasticity are available but another angle of attack is proposed in this work. It is assumed that the removal of abradable liners shares similarities with machine tool chatter encountered in manufacturing. Chatter is a self-excited vibration caused by the interaction between the machine and the workpiece through the cutting forces and the corresponding dynamics are efficiently captured by delay differential equations. These equations differ from ordinary differential equations in the sense that previous states of the system are involved in the formulation. This mathematical framework is employed here for the exploration of the blade stability during abradable removal. The proposed tool advantageously features a reduced computational cost and consistency with existing time-marching solution methods. Potentially dangerous interaction regimes are accurately predicted and instability lobes match both the flexural and torsional modal responses. Essentially, the regenerative nature of chatter in machining processes can also be attributed to abradable coating removal in turbomachinery.

Two-Dimensional Modeling of Shaft Precessional Motions Induced by Blade/Casing Unilateral Contact in Aircraft Engines

In the present work, the focus is made on the occurrence of precessional motions of the shaft---whirling motions---in bladed-disk assemblies, initiated by direct blade/casing contacts in one stage of an aircraft engine. These contact events are favored by increasingly reduced blade-tip clearances and are expected to occur during standard operating conditions. However, it has been shown that potentially harmful interactions may arise and threaten the engine structural integrity. A 2D in-plane model of an aircraft engine fan stage is built with a set of curved beams for the casing and an assembly straight beams for the bladed-disk. The flexibility of the shaft is reflected by two linear springs attached to the center node of the disk. Contact is initiated through a prescribed casing distortion and the two structures are then left free to interact. Equations of motion are solved via explicit time-marching and contact forces are computed with Lagrange multipliers method allowing to fully satisfy non-penetration conditions. Friction is accounted for through a Coulomb law and permanent sliding is assumed. Three types of regimes are identified, namely: (1) damped, (2) sustained, (3) divergent, and both forward and backward shaft precessional motions are witnessed. It is shown that the vibratory response of the bladed-disk mainly lies on the first nodal diameter of the first family of modes regardless of the rotational velocity or the type of regime detected. The risk of failure arising from these contact events is highlighted, in particular in the presence of forward whirl, and the need for accurate predictive tools in early design phases of the engine is emphasized.

Influence of Abradable Coating Wear Mechanical Properties on Rotor Stator Interaction

In the field of turbomachines, better engine performances are achieved by reducing possible parasitic leakage flows through the closure of the clearance distance between blade tips and surrounding casings. Accordingly, direct contact is now commonly accepted as part of aircraft engines everyday life. In order to avoid possibly catastrophic scenarii due to high contact forces between the rotating and static components, implementation of abradable coatings has been widely recognized as a robust solution offering several advantages: reducing potential damage to the incurring blade as well as adjusting operating clearances, in-situ, to accept physical contact events. In the present work, macroscopic behavior of the abradable coating is numerically approximated through a piecewise linear plastic constitutive law which allows for real time access to the current abradable layer profile. Contact simulations are carried out considering a three-dimensional industrial finite element model of a blade from a compressor stage and its surrounding casing, assumed perfectly rigid. Due to the large number of degrees of freedom, component mode synthesis methods are used. Simulations are repetitively carried-out over a wide rotational velocity range, and a large number of distinct values for two mechanical parameters of the abradable material are considered. Results show that the amplitude of vibration is highly sensitive to the Young modulus and the plastic modulus of the abradable and that a local maximum is detected. Also, a more realistic description of the contact forces allowing for a contribution in the tangential direction is suggested.Copyright

Redesign of a High-Pressure Compressor Blade Accounting for Nonlinear Structural Interactions

Recent numerical developments dedicated to the simulation of rotor/stator interaction involving direct structural contacts have been integrated within the Snecma industrial environment. This paper presents the first attempt to benefit from these developments and account for structural blade/casing contacts at the design stage of a high-pressure compressor blade. The blade of interest underwent structural divergence after blade/abradable coating contact occurrences on a rig test. The design improvements were carried out in several steps with significant modifications of the blade stacking law while maintaining aerodynamic performance of the original blade design. After a brief presentation of the proposed design strategy, basic concepts associated with the design variations are recalled. The iterated profiles are then numerically investigated and compared with respect to key structural criteria such as: (1) their mass, (2) the residual stresses stemming from centrifugal stiffening, (3) the vibratory level under aerodynamic forced response and (4) the vibratory levels when unilateral contact occurs. Significant improvements of the final blade design are found: the need for an early integration of nonlinear structural interactions criteria in the design stage of modern aircraft engines components is highlighted.Copyright

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 Display FormulaΩc* 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.Copyright

Anti-Optimisation Applied to the Analysis of Rotor/Stator Interaction

There is a drive towards minimising operating clearances within turbomachines in order to limit reverse leakage flows and hence improve their efficiency. This increases the likelihood of contact occurring between the blade and the casing, which can give rise to high amplitude vibration. Modelling this in- teraction represents a significant computational challenge. The non-linear contact precludes the use of well-established linear methods, and is also subject to uncertainties: the contact law is imprecisely known and the exact geometry of imperfections that trigger contactmay be unknown. In this paper a novel approach is presented that aims to account for the uncertainties associated with the non-linearity in a non-probabilistic way. The worst case is sought, by fram- ing the systemas a constrained anti-optimisation problem. The target to be maximised represents a metric of the output of in- terest. The degrees of freedom of the anti-optimisation are the non-linear input forces (considered as external loads), and the constraints are designed to capturewhat is thought to be known about the non-linear contact law and geometry. A realistic three-dimensional model of a turbine blade is used to explore the approach, with contact considered at the leading and trailing edge. The blade dynamics are described in terms of a linear transfer function matrix and the target metric of interest is chosen to be the peak displacement of the contact Address all correspondence to this author: tb267@cam.ac.uk points. The non-linearity is taken to result from an offset shaft, giving a sinusoidal clearance variation. The blade is driven at constant frequency and the scope of the study is limited to find- ing bounds on periodic solutions. A variety of constraint condi- tions are explored that describe aspects of the non-linearity. For example, only compressive forces are permitted (no tension from the contact), and the displacement must not exceed the clear- ance. The method yields encouraging initial results: constraints can be identified that give efficient estimates of the upper bound response of the system as a function of drive frequency. The re- sults are compared with a benchmark time-domain simulation and are found to correctly over-predict the response without be- ing overly conservative. Broad trends are also in agreementwith the benchmark solution. The proposed method appears to be a promising approach for efficiently accounting for uncertainties associated with the non-linearity and thus improving blade de- sign. Copyright

Study of component mode synthesis methods in a rotor-stator interaction case

The study of rotor-stator interactions between blade-tips and outer casings through direct contact in modern turbomachines is very time-consuming if the classical finite element method is used. In order to improve the knowledge over these interaction phenomena, faster methods have to be applied. The construction of reduced-order models using component mode synthesis methods generally allows for dramatic increase in computational efficiency. Two of these methods, namely a fixed interface method and a free interface methods are considered in an original manner to reduce the size of a realistic two-dimensional model. They are then compared in a very specific contact case-study. The equations of motion are solved using an explicit time integration scheme with the Lagrange multiplier method where friction is accounted for. The primary goal of the present study is to investigate the general behavior of such approaches in the presence of contact nonlinearities. It will be shown that in our contact case, a good accuracy can be obtained from a reduced models with very limited number of modes.