Experimental Validation of Forced Response Methods in a Multi-Stage Axial Turbine

Depending on the in service condition of jet engines, turbine blades may have to be replaced, refurbished, or repaired in the course of an engine overhaul. Thus, significant changes of the turbine blade geometry can be introduced due to regeneration and overhaul processes. Such geometric variances can affect the aerodynamic and aeroelastic behavior of turbine blades. One goal in the development of the regeneration process is to estimate the aerodynamic excitation of turbine blades depending on these geometric variances caused during the regeneration. Therefore, this study presents an experimentally validated comparison of two methods for the prediction of forced response in a multistage axial turbine. Two unidirectional fluid structure interaction (FSI) methods, a time-linearized and a time-accurate with a subsequent linear harmonic analysis, are employed and the results validated against experimental data. The results show that the vibration amplitude of the time-linearized method is in good agreement with the experimental data and, also requires lower computational time than the time-accurate FSI. Based on this result, the time-linearized method is used to perform a sensitivity study of the tip clearance size of the last rotor blade row of the five stage axial turbine. The results show that an increasing tip clearances size causes an up to 1.35 higher vibration amplitude compared to the reference case, due to increased forcing and decreased damping work.

A Physically Consistent Reduced Order Model for Plasma Aeroelastic Control on Compressor Blades

Plasma actuators may be successfully employed as virtual control surfaces, located at the trailing edge of blades, both on the pressure and on the suction side, to control the aeroelastic response of a compressor cascade. Actuators generate an induced flow against the direction of the freestream. As a result, actuating on the pressure side yields an increase in lift and nose down pitching moment, whereas the opposite is obtained by operating on the suction side. A properly phased alternate pressure/suction side actuation allows to reduce vibration and to delay the flutter onset. This paper presents the development of a linear frequency domain reduced order model for lift and pitching moment of the plasma-equipped cascade. Specifically, an equivalent thin airfoil model is used as a physically consistent basis for the model. Modifications in the geometry of the thin airfoil are generated to account for the effective chord and camber changes induced by the plasma actuators, as well as for the effects of the neighboring blades. The model reproduces and predicts correctly the mean and the unsteady loads, along with the aerodynamic damping on the plasma equipped cascade. The relationship between the parameters of the reduced order model with the flow physics is highlighted.

Flutter Analysis of a Flexible UHBR Fan at Different Flight Conditions

A flexible UHBR fan is investigated at different flight conditions with a focus on static deflections and aeroelastic stability. Operating points at varying inlet conditions, which are comparable according to the Mach similarity principle, are investigated. However, not all the aerodynamic characteristics remain identical and aerodynamic damping of mode shape vibrations is changed. When steady deformations of the fan blades are taken into account, the deviation between different inlet conditions increases further. This is mainly due to torsional deflections, changing the effective angle of attack and causing a general shift of the compressor map. Even though the subsequent changes in flutter predictions are not severe for most parts of the compressor map, the behavior at the boundaries is sensitive to the real flight condition. As shown, the Mach similarity principle is not suitable for investigating aeroelastic stability throughout the whole flight envelope, especially when the static blade deformation is not neglectable. The reason for this can be found in the complex interaction between dimension-less numbers (Mach, Reynolds), sized values (pressure difference or aerodynamic loading, natural frequency) and their dependency on each other.

Determination of Aerodynamic Damping at High Reduced Frequencies

In turbomachines, forced response of blades is blade vibrations due to external aerodynamic excitations and it can lead to blade failures which can have fatal or severe economic consequences. The estimation of the level of vibration due to forced response is dependent on the determination of aerodynamic damping. The most critical cases for forced response occur at high reduced frequencies. This paper investigates the determination of aerodynamic damping at high reduced frequencies. The aerodynamic damping was calculated by a linearized Navier-Stokes flow solver with exact 3D non-reflecting boundary conditions. The method was validated using Standard Configuration 8, a two-dimensional flat plate. Good agreement with the reference data at reduced frequency 2.0 was achieved and grid converged solutions with reduced frequency up to 16.0 were obtained. It was concluded that at least 20 cells per wavelength is required. A 3D profile was also investigated: an aeroelastic turbine rig (AETR) which is a subsonic turbine case. In the AETR case, the first bending mode with reduced frequency 2.0 was studied. The 3D acoustic modes were calculated at the far-fields and the propagating amplitude was plotted as a function of circumferential mode index and radial order. This plot identified six acoustic resonance points which included two points corresponding to the first radial modes. The aerodynamic damping as a function of nodal diameter was also calculated and plotted. There were six distinct peaks which occurred in the damping curve and these peaks correspond to the six resonance points. This demonstrates for the first time that acoustic resonances due to higher order radial acoustic modes can affect the aerodynamic damping at high reduced frequencies.

An Approach to Approximate the Full Strain Field of Turbofan Blades During Operation

The measurement of the aeromechanical response of the fan blades is important to quantifying their integrity. The accurate knowledge of the response at critical locations of the structure is crucial when assessing the structural condition. A reliable and low cost measuring technique is necessary. Currently, sensors can only provide the measured data at several discrete points. A significant number of sensors may be required to fully characterize the aeromechanical response of the blades. However, the amount of instrumentation that can be placed on the structure is limited due to data acquisition system limitations, instrumentation accessibility, and the effect of the instrumentation on the measured response. From a practical stand point, it is not possible to place sensors at all the critical locations for different excitations. Therefore, development of an approach that derives the full strain field response based on a limited set of measured data is required. In this study, the traditional model reduction method is used to expand the full strain field response of the structure by using a set of discrete measured data. Two computational models are developed and used to verify the expansion approach. The solution of the numerical model is chosen as the reference solution. In addition, the numerical model also provides the mode shapes of the structure. In the expansion approach, this information is used to develop the algorithm. First, a cantilever beam model is created. The influences of the sensor location, number of sensors and the number of modes included are analyzed using this cantilever beam model. The expanded full field response data is compared with the reference solution to evaluate the expansion procedure. The rotor 67 blade model is then used to test the expansion method. The results show that the expanded full field data is in good agreement with the calculated data. The expansion algorithm can be used for the full field strain by using the limited sets of strain data.

Intentional Mistuning With Predominant Aerodynamic Effects

Intentional mistuning is a well known procedure to decrease the uncontrolled vibration amplification effects of the inherent random mistuning and to reduce the sensitivity to it. The idea is to introduce an intentional mistuning pattern that is small but much larger that the existing random mistuning. The frequency of adjacent blades is moved apart by the intentional mistuning, reducing the effect of the blade-to-blade coupling and thus the effect of the random mistuning. The situation considered in this work is more complicated because the main source for the blade damping is the effect of the aerodynamic forces (as it happens in a blisk for a family of blade dominated modes with very similar frequencies). In this case the damping is clearly defined for the tuned traveling waves but not for each blade. The problem is analyzed using the Asymptotic Mistuning Model methodology. A reduced order model is derived that allows us to understand the action mechanism of the intentional mistuning, and gives a simple expression for the estimation of its beneficial effect. The results from the reduced model are compared with those from a finite element model of a more realistic rotor under different forcing conditions.

A Comparison of Two Microslip Contact Models for Studying the Mechanics of Underplatform Dampers

In turbine blade systems, under-platform dampers are widely used to attenuate excessive resonant vibrations. Subjected to vibration excitation, the components with frictionally constrained interfaces can involve very complex contact kinematics induced by tangential and normal relative motions. To effectively calculate the dynamics of a blade-damper system, contact models which can accurately reproduce the interface normal and tangential motions are required. The large majority of works have been developed using macroslip friction models to model the friction damping at the contact interface. However, for those cases with small tangential displacement where high normal loads are applied, macroslip models are not enough to give accurate results. In this paper two recently published microslip models are compared, between them and against the simple macroslip spring-slider model. The aim is to find to which extent these models can accurately predict damper mechanics. One model is the so called GG array, where an array of macroslip elements is used. Each macroslip element of the GG array is assigned its own contact parameters and for each of them four parameters are needed: normal stiffness, tangential stiffness, normal gap and friction coefficient. The other one is a novel continuous microslip friction model. The model is based on a modification of the original classic IWAN model to couple normal and tangential contact loads. Like the GG array the model needs normal and tangential stiffness, and friction coefficient. Unlike the GG array the model is continuous and, instead of the normal gap required by the GG array, the Modified IWAN model needs a preload value. The two models are here applied to the study of the mechanics of a laboratory under-platform damper test rig. The results from the two models are compared and allow their difference, both for damper mechanics and for the complex-spring coefficients, to be assessed.

High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

Investigating Damping Performance of Laser Powder Bed Fused Components With Unique Internal Structures

An additive manufacturing (AM) process has been used to fabricate beam components with unique internal geometries capable of reducing weight and inherently suppressing vibration of the structure. Using the laser powder bed fusion (LPBF) AM process, four unique designs are investigated to quantify and understand the damping effectiveness of this manufacturing concept. Forced-response tests are conducted to validate the damping capability of each internal design configuration. The effects of external geometry, thermal distribution associated with internal friction, strain amplitude, and loading rate dependence on damping performance are studied. The results of the studied beams are compared to the damping performance of a fully-fused, or solid baseline LPBF beam. With only 1–4% internal beam volume alteration, the four unique beams are capable of providing up to ten times damping into their respective systems compared to the baseline, solid beam. From the studies of different parameter effects on damping, the main mechanism for vibration suppression is identified. Validation of the vibration suppression physics allows for internal feature optimization via LPBF that can maximize damping effectiveness.

Criteria for Best Performance of Pre-Optimized Solid Dampers

This paper furthers recent research by these authors. The starting point is the pre-optimization of solid dampers, which ensures that all dampers bound to misbehave are excluded since the early design stage. The authors now enlarge the scope of their investigations to explore those damper configurations selected inside the admissible design area. The purpose of the paper is to present a set of criteria apt to select a damper configuration which not only avoids unwanted situations, but in addition guarantees high performance under different design conditions. The analysis starts with the definition of a set of requirements a high performance damper should meet. In detail the present investigation seeks to answer the following questions: – in the low excitation regime, what is the frequency shift and the stiffening effect each damper can provide? – for increasing excitation levels, which damper will start slipping sooner? – in the high excitation regime, which damper provides the maximum dissipation? Like pre-optimization, it does not involve nonlinear Finite Element calculations, and unlike existing optimization procedures, is not linked to a specific set of blades the damper may be coupled to. The numerical prediction of the blade-damper coupled dynamics is here used only for validation purposes. The approach on which this paper rests is fully numerical, however real contact parameters are taken from extensive experimental investigations made possible by those purposely developed test rigs which are the distinctive mark of the AERMEC Lab of Politecnico di Torino.