Graphical Abstract Figure
Graphical Abstract Figure
Close modal

Abstract

This paper describes an aeroelastic experimental campaign on a low-pressure turbine-bladed rotor in a rotating wind tunnel that took place as a part of the Advanced Research Into Aeromechanical Solutions (ARIAS) EU project. The campaign can be considered a continuation of the free-flutter test that was performed as part of the FUTURE EU project, where the saturation of asynchronous vibrations due to dry friction was characterized. This new campaign studied new aspects of the physics behind saturated flutter, including the non-linear interaction between synchronous excitation and asynchronous vibration, the effectiveness of different mistuning patterns to suppress flutter, and the viability of under-platform dampers as a technology to control the amplitude of asynchronous vibrations. Furthermore, the campaign explored various operation conditions for the turbine rotor, including near-stall. In general, there was a good agreement between the theoretical predictions regarding all these different aspects of turbine flutter and the test results.

1 Introduction

Current design trends in turbines involve thin and slender airfoils to reduce weight and increase efficiency. Unfortunately, these trends exacerbate aeroelastic issues. Phenomena like flutter and forced response may affect the high cycle fatigue life of the components and, in practice, impose several restrictive limitations in the design space.

In the last few decades, several EU projects have been focused on aeroelastic phenomena in turbomachinery, such as ADTurB I and II or FUTURE. Beginning in 2018, the last project in this series is the Advanced Research Into Aeromechanical Solutions (ARIAS) project. The second work package inside ARIAS deals with low-pressure turbine (LPT) aeroelasticity. This package is essentially a continuation of the analogous work package from FUTURE [1] and is focused on three particular subjects:

  • Non-linear interaction between amplitude-limited flutter and forced response.

  • Intentional mistuning and its impact on flutter and forced response.

  • Under-platform dampers to contain LPT flutter and reduce its saturation amplitude.

All of these subjects still need to be explored to expand the design space of LPTs. Numerous analytical and numerical works (such as Ref. [2] or Ref. [3]) have considered the potential of intentional mistuning as a method to suppress flutter, but the experimental validation is far more limited (for example, see Ref. [1]). Experimental results considering both the impact on flutter and forced response simultaneously are scarce, but can be found, for example, in Ref. [4].

Under-platform dampers are widely used to reduce forced response amplitude in turbomachinery, with numerous works describing either numerical studies [5], experimental results [6], or both [7,8]. On the other hand, their impact on the saturation of flutter is less documented. Recent works consider flutter simulations in configurations where dry friction is relevant, such as Refs. [911], but experimental data are less common. Works like [12] include both numerical and experimental analyses on flutter saturation, but they involve a simplified configuration, not closely representative of turbomachinery blades, let alone under-platform dampers.

Nevertheless, the subject with the least published material is the interaction between flutter and forced response. Some related works may be found in the literature; for example, Mao and Kielb [13] consider the potential interactions through non-linear aerodynamics in a compressor, and concluded that they are weak. On the other hand, Corral et al. [14] include non-linear dry friction in a turbine case and obtain results where flutter can be locally suppressed by a synchronous excitation. Nevertheless, there was no experimental validation for the claims in Ref. [14].

To explore these subjects, the second work package of the ARIAS project included three main activities:

  • An in-vacuum spin-pit test campaign at Avio, using their STARGATE rig.

  • A second experimental campaign in the high-speed rotating aerodynamic rig at Centro de Tecnologías Aeronáuticas (CTA).

  • A detailed simulation campaign, closely related to the aforementioned experiments.

This article aims to describe the cold-flow experimental campaign at CTA and present its most relevant results.

2 Experimental Setup

In essence, the ARIAS cold-flow test is a continuation of FUTURE's experimental campaign. In FUTURE, an isolated turbine-bladed disk was designed to flutter at rig conditions. Even though it was not the first dedicated free-flutter experiment in turbomachinery (for example, consider Ref. [15] or Ref. [16]), it was one of the few times that such an experiment was successfully conducted in a controlled environment and high-quality measurements were obtained.

For the ARIAS campaign, the test specimen and setup were essentially the same as in the FUTURE project, with some relatively minor modifications. The interested reader is encouraged to consult Ref. [1] for an in-detail explanation of the design of FUTURE's original rotor stage. In the following subsections, only its main features and the modifications that were performed for the new test campaign are described.

All the numerical analyses mentioned in the following subsections were performed using ITP's Design System, mainly the computation fluid dynamics (CFD) code oclMu2s2T [17,18] and the mechanical FEM solver XipeTotec [19]. Aero damping calculations were performed with these codes using a linearized uncoupled methodology described in Ref. [20].

2.1 Rotor Blade Design.

From an aerodynamic point of view, the FUTURE airfoils were designed to represent a LPT rotor stage of an aeronautical gas turbine, particularly in terms of 2D design (exit Mach number and turning). The 3D design of the blades was not really optimized, leading to non-fully representative secondary flow structures; nevertheless, the related impact on flutter was considered negligible.

The ARIAS campaign employed the same blades that were tested during the FUTURE project. However, there was a slight change in the configuration: the rotor blade count was reduced from 146 (used in FUTURE) to 144, leading to a slightly higher pitch/chord ratio. The reasoning behind that decision was the compatibility of the number 144 with many simple mistuning patterns due to its exceptionally versatile prime decomposition (24 × 32). The impact on the 2D aerodynamic loading (see Fig. 1) and the increase in the gap between the tip-shrouds of the blades were considered acceptable.

Fig. 1
Comparison of the Cp in the mid-span section between ARIAS and FUTURE
Fig. 1
Comparison of the Cp in the mid-span section between ARIAS and FUTURE
Close modal

2.2 Aero-mechanic Characteristics.

The blades were designed with the intent of having a strong aeroelastic instability (flutter) in the first mode. They are thin, slender airfoils (aspect ratio, Λ, around 5.3) using the cantilever configuration, which is naturally prone to flutter [20]. The blades are made of aluminum. Furthermore, the blades included several features above the tip shroud, as can be seen in Fig. 2, to enable a number of requirements, namely:

  • Tip timing features were designed so that the BTT (blade tip timing) probes could get a clean pulse when the feature passed in front of them.

  • Balancing mass. Since the assembly was intended for testing at very different conditions (in vacuum in the STARGATE spin-pit at Avio, and different flow conditions at CTA), a removable balancing mass was included in the design to compensate for the momentum of the aerodynamic forces in the blade attachment. The intention was to keep the static loads in the fir-tree realistically balanced in all operation conditions. This also had the side effect of reducing noticeably (around 10%) the frequency of the blades when they were attached.

  • Mistuning mass. As described in Sec. 2.3, several intentional mistuning patterns were induced in some tests. This was achieved by attaching mistuning masses in order to reduce the natural frequencies of specific blades.

  • Magnet attachments. As described in Sec. 2.5, a system based on magnets was included in order to induce a synchronous excitation in the blades.

Fig. 2
Main features of the tip of the blade
Fig. 2
Main features of the tip of the blade
Close modal

All these features increase the mass of the blade near the tip and, for the first vibration modes, lead to a decrease in the natural frequencies below what could be expected from the airfoil's moderate aspect ratio. The reduced frequency k = ωc/Ve for the first mode in nominal conditions is slightly below 0.1.

The disc of the new bladed rotor is also very similar to that of the FUTURE project; it has the same base shape, and is made of the same material (steel), but only 144 fir-tree slots were machined in it. All of this leads to a very stiff disk (compared to the aluminum blades), which affects the modal characteristics of the assembly. As can be seen in Fig. 3, the frequency-nodal diameter (ND) curves are very flat, which is directly related to the high disc stiffness. As a consequence, the first modes have very low disc contribution, even for low ND.

Fig. 3
Frequency versus ND for the first two modes
Fig. 3
Frequency versus ND for the first two modes
Close modal

The aerodynamic damping for a reference operation point computed using a frequency domain linear solver is depicted in Fig. 4. As expected, and consistently with the FUTURE results, the first flap mode (M1) is clearly unstable, particularly for traveling waves with inter blade phase angle around −80 deg (ND around 30). The edge-torsion mode (M2) has a significantly weaker instability.

Fig. 4
Aerodynamic damping versus ND for the first two modes
Fig. 4
Aerodynamic damping versus ND for the first two modes
Close modal

Since the new experimental campaign also involves forced response tests, the Campbell diagram of the assembly is very relevant (Fig. 5). There are four potential resonances of interest inside the speed range that was considered for the experiment: M1 EO6 (Ω = 69%), M1 EO5 (Ω = 87%), M1 EO4 (Ω = 113%), and M2 EO6 (Ω = 140%). As described in Sec. 2.5, it was decided to include an excitation system able to generate EO4 and EO6, which would affect three out of the four potential resonances. However, safety concerns led to limiting the operation speed during the test to 137%, just below the M2 EO6 resonance.

Fig. 5
Campbell diagram considering EO4 and EO6
Fig. 5
Campbell diagram considering EO4 and EO6
Close modal

2.3 Mistuning Patterns.

The small variations in the mechanical properties of the rotor blades in a bladed-disc are often called mistuning, and can have a huge impact on the flutter stability of the assembly [21,22]. During the FUTURE project, the effectiveness of intentional mistuning as a method to suppress flutter was demonstrated [1]. ARIAS further expanded this exploration, including two different mistuning patterns:

  • Alternate mistuning, where only one out of two rotors mount a mistuning mass.

  • 0001 mistuning pattern, where only one out of four blades features a mistuning mass.

Just like in FUTURE, mistuning was induced by attaching mistuning masses to the tip of the blades, as shown in Fig. 2, which led to a reduction in the frequency. The design intention in this experimental campaign was to reduce the flutter instability significantly without entirely suppressing it (contrasting with the predecessor project, FUTURE, which achieved complete stabilization). Therefore, for both patterns, the actual values of the mistuning masses were smaller than in FUTURE (2.67 g leading to a 6.3% frequency decrease in ARIAS, versus 4.3 g leading to an 8.6% decrease in FUTURE). These values were supported by analyses based on the Asymptotic Mistuning Model (AMM) formulation proposed by Martel et al. [23]. It must be taken into account that, to get meaningful and understandable results, the intentional mistuning should be much larger than the random mistuning present in the blades (which was characterized as a scatter in frequency with a standard deviation of around 1% for mode 1).

It must be highlighted that the FUTURE project obtained vibration amplitude results for fluttering cases, but not for synchronous excitation. One of the main motivations for including mistuning patterns in ARIAS was to determine the impact of intentional mistuning on both phenomena.

2.4 Friction Devices.

Mechanical friction may play a prominent role in the dynamics of turbine-bladed discs. Several works consider that the energy dissipated by friction at the fir-tree attachment of the blades can lead to the saturation of aeroelastic instabilities and eventually an asynchronous vibration with a constant amplitude that can be designated as “amplitude-limited flutter” [14,24,25]. The results from the FUTURE project [1] were entirely consistent with this theory, and the saturated vibration amplitude could be estimated with the aerodynamic damping results and the simplified friction model described in Ref. [25]. ARIAS, using exactly the same blades with completely analogous fir-tree slots, was expected to show the same behavior and very similar amplitude levels.

Apart from the friction related to the fir-tree, part of the ARIAS campaign focused on studying under-platform dampers as an additional source of friction. They are commonly used in order to limit vibration amplitude in turbomachinery [26,27]. Since the ARIAS blades are physically the same hardware that was used during the FUTURE project, they do not have a properly designed slot to include an under-platform damper. Instead of designing an optimized damper, which would require reworking the rotor blades, it was decided to use a simple design that fitted the available space under the lower platform (Fig. 6).

Fig. 6
Under-platform damper design
Fig. 6
Under-platform damper design
Close modal

Two sets of dampers were manufactured: one in steel and the other one in aluminum. Both sets were tested during the experimental campaign in the STARGATE at Avio, with the steel ones being slightly more effective at reducing vibration amplitude. During the CTA experiment, only the steel dampers were used.

2.5 Excitation System.

Flutter, as an aeroelastic instability, does not require an external excitation source to manifest. Forced response does, and therefore, it was necessary to include an excitation system. It consisted of magnets mounted both at the tip of the blades and in a holder ring in the casing. Both sets of magnets were oriented to generate a repulsion between the ring and the blades. The ring included multiple slots for different sets of magnets, with four different sizes leading to different values of the magnetic force. They allowed the generation of different excitation patterns, in particular, EO4 and EO6 patterns (either separately or simultaneously).

2.6 Instrumentation.

The instrumentation system was very similar to FUTURE's. As far as possible, non-intrusive measurement techniques were adopted. The main sensors were:

  • General rig controls (rotational speed and feed pressure).

  • Fast response five-hole probes to measure the flow conditions. The configuration was designed for area traverse measurements using moving rakes. It allowed measurement of a 28-deg sector, both in the inlet and outlet sections.

  • BTT optic probes to determine vibration amplitude making use of the features at the tip of the blades. This equipment was provided and operated by Rolls-Royce. The acquired signals were post-processed by Rolls-Royce and Siemens, using different methods to allow for a cross-comparison of the results.

  • A row of unsteady pressure sensors installed in the outer casing, downstream from the rotor row. The main objective was to use them as an indirect measurement of the vibration.

3 Test Campaign

The main test campaign took place between July and September 2021 in CTA in Zamudio (Spain) with previous experience of conducting aeroelasticity projects (such as FUTURE [1] or E-BREAK [28]).

The aero rig at CTA has been designed for aerodynamic measurements and allows detailed characterization of the steady flow at different stations, including area traverse measurements. A scheme of the installation may be seen in Fig. 7.

Fig. 7
CTA's cold-flow rig
Fig. 7
CTA's cold-flow rig
Close modal

Some of the main parameters at the design point of the experiment may be seen in Table 1. In terms of turning, Reynolds and Mach number are quite representative of a subsonic low-pressure turbine.

Table 1

Main parameters of the nominal operation point

MinαinMeαeRe
0.4236.5 deg0.7560 deg1.2 × 105
MinαinMeαeRe
0.4236.5 deg0.7560 deg1.2 × 105

The test campaign involved a complex test matrix totaling more than 600 experimental points. The test matrix included:

  • Several density levels for the rig operation (between 35% and 100% of the nominal density). This mainly acted as a scaling parameter for the aerodynamic forces and the aerodynamic damping.

  • Several pressure ratios which led directly to different exit Mach numbers (from 0.675 to 0.825).

  • Different values for the rotation speed, from 62% to 118% of the nominal value. The flow is in highly off-design conditions for the lowest speed and is mostly detached in that region.

  • Different mistuning patterns (including the nominally tuned configuration).

  • Tests with and without under-platform dampers.

There were two types of maneuvers in this test matrix:

  • Accel–deccel curves, reaching up to a maximum speed value of 137% of the nominal speed for safety reasons. They allowed for the identification of the synchronous resonances and gave a general overview of the dynamics of the row.

  • Stabilized points, where the rotational speed remained constant during the operation. They allowed more accurate determination of the flutter amplitude for given conditions. Some stabilized points were as close as possible to a synchronous resonance, to help characterize the interaction between flutter and forced response.

For all of them, the rotor configuration, the inlet pressure, and the pressure ratio remained constant during the maneuver.

The campaign took place with only one significant incident. While operating in conditions with maximum density and high Mach number, the flutter vibration amplitude surpassed warning levels and the experiment had to be halted. The vibration had been large enough to cause damage to some of the blades due to clashes between the tip-shrouds. Furthermore, a few of the balancing masses detached due to damage to the supporting screws. The experiment could be resumed after replacing the damaged blades with spares; nevertheless, it was decided to adopt some additional precautions when operating the rig from then on:

  • Limiting the density during the operation of the remaining points to 80% of the original intent. This reduced the aerodynamic forcing and led to lower vibration amplitude.

  • Continue the operation without the balancing masses. It must be taken into account that some of their screws were damaged to the point of rupture, and fatigue of the rest was a potential risk. On the other hand, it should be mentioned that the balancing masses were dimensioned to compensate the aerodynamic forces at maximum mass flow; after the newly imposed restriction to the flow density, they were no longer as relevant as initially expected.

4 Main Findings

All in all, the experimental campaign was highly successful. Consistent with the design intention, flutter appeared in most of the tested conditions. The BTT probes obtained high-quality signals, and meaningful vibration levels were determined for all the studied test points. The unsteady pressure sensors recorded clean signals that were qualitatively consistent with the BTT results.

Since this ARIAS campaign is essentially a continuation from FUTURE's, FUTURE's results will be referenced in most of the following subsections. Once again, the interested reader is referred to Ref. [1] for further details.

4.1 Summary of the Blade Tip Timing Results.

The accel–deccel maneuvers gave a quick overview of the dynamics. In a typical case, such as the one depicted in Fig. 8, three sources of vibration can be identified:

  • A synchronous resonance of the mode 1 with EO6.

  • A non-synchronous vibration in the mode 1.

  • A synchronous resonance of mode 1 with the EO4.

Fig. 8
Experimental response, obtained from the BTT signals
Fig. 8
Experimental response, obtained from the BTT signals
Close modal

A weak resonance of the first mode with EO5 can be seen in some points, but it is difficult to separate if from the non-synchronous vibration. In most of the tests, the M2 EO6 resonance was slightly above the maximum speed of the rig and could not be appropriately measured.

This behavior is quite consistent with the design intent and the numerical predictions:

  • The measured frequencies acceptably match the predictions, with differences lower than 2% in most cases. The matching is slightly worse in the cases with dampers.

  • The magnet pattern was designed to generate EO4 and EO6 synchronous excitations; the related responses can be clearly identified.

  • As mentioned in Sec. 2.2, the rig was designed to have an aerodynamically unstable first mode, which is consistent with the recorded non-synchronous signal. Further exploration of this non-synchronous vibration using unsteady pressure transducers (as seen in Figs. 9 and 10) indicates the presence of multiple NDs in the 20–30 range, which is also consistent with the range of unstable nodal diameters that appear in Fig. 4.

Fig. 9
Example of a signal from the pressure sensor
Fig. 9
Example of a signal from the pressure sensor
Close modal

Nevertheless, it must be mentioned that, even without the installed magnets, the M1 EO4 and M1 EO6 resonances can be identified from the readings in most cases, and some faint traces of M1 EO5 can be found in some points. In particular, the amplitude of the M1 EO4 resonance has the same order of magnitude, regardless if the permanent magnets are installed or not. In all likelihood, there is some unintended source of synchronous forcing in the rig, mainly following EO4, whose source is unclear. The most likely theory is that it is related to distortion in the inlet aerodynamic conditions, but, since the area traverse measurements only involve a 28 deg sector, this hypothesis could not be confirmed or denied.

Fig. 10
Detail of the flutter region of the signal from the pressure sensor
Fig. 10
Detail of the flutter region of the signal from the pressure sensor
Close modal

4.2 Interpretation of the Pressure Sensor Signals.

The pressure sensors recorded the unsteady pressure signal in different casing positions; the main objective of installing flushed mounted unsteady pressure transducers was to measure the unsteady pressure field associated with flutter. Since the transducers are mounted on the static frame of reference, and rotor flutter is associated with the rotating frame, it is essential to consider the Döppler shift in the frequencies:
ωStatic=ωRotatingND×Ω
(1)
where ω is the angular frequency in the static or rotating frames, ND is the nodal diameter of the signal (with the proper sign), and Ω is the rotational speed. Since the frequency in the static frame depends on the nodal diameter, this allows us to easily separate the contribution of the different ND of the signal. An example of the pressure signal (in frequency domain) can be seen in Fig. 9. The main features of the signals in a typical test are:
  • The fundamental harmonic associated with the blade passing frequency and its higher harmonics with decaying amplitude (not present in the figure since they are out of range).

  • A number of low-frequency perturbations that are related to installation noise.

  • Several distinct peaks that are consistent with a rotating signal with the M1 frequency and following a number of nodal diameters, mainly in the 20–30 range.

Please note that, due to Eq. (1), synchronous excitations on the rotor have an apparent frequency of zero in the static frame of reference,2 and therefore cannot be extracted from the spectra measured by the unsteady pressure sensors.

In short, the behavior of the pressure signal appears qualitatively consistent with both the flutter predictions and the BTT results.

4.3 Turbine Flutter in Off-Design Conditions.

The base rotor configuration (without mistuning masses or dampers) is unstable in a wide range of operation conditions. The saturation amplitude depends on the operation points; for example, consistent to the results from FUTURE, and for a given pressure ratio, the saturation amplitude is roughly proportional to the mass flow in the facility. But, in any case, the behavior remains qualitatively consistent through most of the operation range (i.e., saturated M1 flutter with varying amplitude).

The main exception of interest appears in the very low-speed region, where the flow is nearly detached. The BTT signal becomes more complex and has non-synchronous contributions both from M1 and M2, as can be seen in Fig. 11. This behavior is consistent with the predictions from the CFD simulations that can be seen in Figs. 12 and 13. In nominal conditions, M1 is much more unstable than M2; however, at lower speeds, the instability for M2 tends to increase. For very low speed (62%), M1 shows a sudden stability increase, and both modes have very similar negative damping. This seems consistent with the BTT interpretation that detected both modes. A detailed analysis of this interaction based on simulations may be found in Ref. [29].

Fig. 11
BTT signal for low-speed conditions (N = 62%)
Fig. 11
BTT signal for low-speed conditions (N = 62%)
Close modal
Fig. 12
Aerodynamic damping versus ND for the flap mode, considering off-design conditions
Fig. 12
Aerodynamic damping versus ND for the flap mode, considering off-design conditions
Close modal
Fig. 13
Aerodynamic damping versus ND for the torsion mode, considering off-design conditions
Fig. 13
Aerodynamic damping versus ND for the torsion mode, considering off-design conditions
Close modal

4.4 Flutter and Forced Response Interaction.

One of the main points of interest in the ARIAS project is the interaction between flutter and forced response. Numerical results from a conceptual model [14] suggested that both phenomena interact non-linearly in situations where non-linear mechanical friction plays a significant role, with forced response being able to suppress flutter (locally and in certain situations). Several of the tests in the campaign intended to shed light on the subject, both by performing short and slow accel–deccel curves in the region around the synchronous resonance and attempting stabilized runs as close as possible to the resonance. The experimental results are consistent with the main conclusions from Ref. [14]. In Fig. 14, an analysis of the BTT results during an acceleration maneuver is depicted. The thick solid line indicates the instantaneous shaft speed. The upper image corresponds to the “raw” signal, while the lower image corresponds to the signal after using a low-pass filter to highlight the M1 EO4 contribution. It can be seen that the pattern of the vibration changes from the flutter-like behavior with several high nodal diameters away from the resonance, to a pattern dominated by the EO of the excitation. Taking into account these measurements, and the results from the model in Ref. [14], it seems that the unstable branch related to flutter is not present, and the vibration follows a pattern dictated by the external forcing, with an amplitude determined by the energy balance between the external forcing, the aerodynamic work due to the vibration, and the dissipation in the fir-tree.

Fig. 14
BTT signal amplitude as a function of time showing a shift in the response behavior around the M1 EO4 resonance. Top: raw signal. Bottom: low-pass filter removing high-frequency flutter signals.
Fig. 14
BTT signal amplitude as a function of time showing a shift in the response behavior around the M1 EO4 resonance. Top: raw signal. Bottom: low-pass filter removing high-frequency flutter signals.
Close modal

4.5 Effect of Intentional Mistuning Patterns.

It is well known that intentional mistuning can alter the dynamics of bladed discs and that relatively small variations in the rotor blade frequencies may have a large impact on the dynamics of the bladed disk. During the FUTURE project, the effectiveness of certain mistuning patterns to suppress flutter was demonstrated [30], but their impact on synchronous response was not measured experimentally.

BTT readings with intentional mistuning patterns (Figs. 15 and 16) showed two distinct peaks for the response of the blades, corresponding both to the baseline and the mistuned rotor blades. Comparing with the tuned results in Fig. 8, the flutter amplitude is reduced (roughly 40% with the alternate pattern) but not entirely suppressed (consistent with the design intent for the ARIAS mistuning patterns). Furthermore, the results for the synchronous response show that there is also a noticeable decrease (around 30% for the alternate pattern). It is important to highlight that we are not comparing a perfectly tuned bladed disk with a mistuned one, but a bladed disk with a relatively small random mistuning with the same mistuned rotor with a superimposed stronger intentional mistuning pattern.

Fig. 15
BTT results for the test with the alternate mistuning pattern
Fig. 15
BTT results for the test with the alternate mistuning pattern
Close modal
Fig. 16
BTT results for the test with the second (0001) mistuning pattern
Fig. 16
BTT results for the test with the second (0001) mistuning pattern
Close modal

Interestingly, the M2 EO6 resonance could be captured by the rotor blades with the mistuning masses (which had a lower frequency), but not by the others (whose resonance was slightly beyond the running range). In the tests with the tuned configuration, this M2 EO6 resonance was fully beyond the running range.

Comparing the results for the alternate pattern (Fig. 15) with the second pattern (Fig. 16), both decrease the vibration amplitude in a similar manner, but the alternate pattern is slightly more effective (around 10%, overall). Interestingly, the dynamics for the second mistuning pattern are more complex; the synchronous resonances split into as many as four peaks (contrasting the two peaks for the alternate pattern). A detailed analysis of the mistuned dynamics, based on conceptual models, may be found in Ref. [31].

4.6 Impact of Under-Platform Dampers.

The campaign also demonstrated the capabilities of under-platform dampers to reduce vibration amplitude in LPT rotors. The post-processing of the BTT signals in Fig. 17 indicates that the dampers actually had a very significant impact on the response, with a reduction larger than 50% in vibration amplitude for the non-synchronous vibration when comparing with the case without dampers in Fig. 8. Nevertheless, the damper was far less effective at reducing the amplitude of the synchronous response (around 25% of amplitude reduction). One of the main reasons for this behavior lies in the ND pattern of the vibration (EO4–6 for the synchronous excitation and ND 20–30 for flutter); under-platform dampers require relative displacement between the adjacent blades to be effective, and this relative displacement increases with the ND.

Fig. 17
BTT results, with steel under-platform dampers
Fig. 17
BTT results, with steel under-platform dampers
Close modal

The markings that could be found after operation suggest that the contact between blades and dampers only involved a fraction of the nominal contact face, mostly involving the edges and with significant differences between individual blades. Nevertheless, the dampers remained reasonably effective, and the total wear, both in the blades and the dampers, was small.

5 Summary and Conclusions

The ARIAS EU Project has successfully managed to characterize limited-amplitude flutter in a rig representative of a low-pressure turbine rotor. The experimental results are consistent with the design intent and different CFD-based prediction methods. The ARIAS project has advanced the understanding of aeroelastic behavior of LPTs beyond that of the predecessor FUTURE project in several key areas:

  • The flutter behavior in strongly off-design conditions has been studied showing that torsion modes can become unstable at low-speed.

  • Detailed BTT measurements and numerical analyses have shown that a synchronous excitation can suppress flutter and that forced response and flutter amplitudes do not superimpose.

  • Dedicated tests to evaluate the effectiveness of under-platform dampers have shown that they can mitigate synchronous and non-synchronous vibration in low-pressure turbine rotors but that they are more effective to reduce flutter-induced vibrations than forced-response-induced vibrations.

  • An in-depth study of the effects of intentional mistuning patterns on all the previous subjects was performed.

Overall, the experimental campaign was highly successful and provided high-quality data regarding turbine aeroelasticity. This information, together with the results from Avio's STARGATE rig, will feed a simulation campaign, also inside the ARIAS project, to validate different types of aeroelastic simulation tools.

Footnote

2

The conditions for resonance impose that ω = ND × Ω in the reference frame of the vibrating row.

Acknowledgment

This work has been carried out within the ARIAS project, funded by the European Union's Horizon 2020 research and innovation program under grant agreement no. 769346.

The authors wish to thank ITP Aero for its support and permission to publish this paper, as well as the ARIAS project members for enabling this study with their rigorous work and dedication.

The authors also wish to thank José Manuel Sánchez Expósito for his help during the setup and calibration of the BTT system.

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Nomenclature

k =

reduced frequency

M =

Mach number

P =

static pressure

Cp =

pressure coefficient

BTT =

blade tip timing

CFD =

computation fluid dynamics

EO =

engine order

HCF =

high cycle fatigue

IBPA =

inter blade phase angle

LPT =

low-pressure turbine

MX =

normal vibration mode X

MX EOY =

resonance of the modal family X with the engine order Y

Re =

Reynolds number

U-RANS =

unsteady Reynolds averaged Navier–Stokes equations

Greek Symbols

α =

relative swirl angle

     Λ =

aspect ratio (span/chord)

ω =

frequency

Ω =

rotational speed

Superscripts and Subscripts

     0 =

total property

e =

exit

in =

inlet

References

1.
Corral
,
R.
,
Beloki
,
J.
,
Calza
,
P.
, and
Elliott
,
R.
,
2019
, “
Flutter Generation and Control Using Mistuning in a Turbine Rotating Rig
,”
AIAA J.
,
57
(
2
), pp.
782
795
.
2.
Sawyer
,
S.
, and
Fleeter
,
S.
,
1995
, “
Flutter Stability of a Detuned Cascade in Subsonic Compressible Flow
,”
J. Propul. Power
,
11
(
5
), pp.
923
930
.
3.
Bleeg
,
J. M.
,
Yang
,
M.-T.
, and
Eley
,
J. A.
,
2008
, “
Aeroelastic Analysis of Rotors With Flexible Disks and Alternate Blade Mistuning
,”
ASME J. Turbomach.
,
131
(
1
), p.
011011
.
4.
Figaschewsky
,
F.
,
Kuhhorn
,
A.
,
Beirow
,
B.
,
Nipkau
,
J.
,
Giersch
,
T.
, and
Power
,
B.
,
2017
, “
Design and Analysis of an Intentional Mistuning Experiment Reducing Flutter Susceptibility and Minimizing Forced Response of a Jet Engine Fan
,”
Volume 7B: Structures and Dynamics of Turbo Expo: Power for Land, Sea, and Air
,
Charlotte, NC
,
June 26–30
.
5.
Sanliturk
,
K. Y.
,
Imregun
,
M.
, and
Ewins
,
D. J.
,
1997
, “
Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers
,”
ASME J. Vib. Acoust.
,
119
(
1
), pp.
96
103
.
6.
Gastaldi
,
C.
,
Berruti
,
T. M.
, and
Gola
,
M. M.
,
2020
, “
A Novel Test Rig for Friction Parameters Measurement on Underplatform Dampers
,”
Int. J. Solids Struct.
,
185–186
, pp.
170
181
.
7.
Petrov
,
E.
,
Di Mare
,
L.
,
Hennings
,
H.
, and
Elliott
,
R.
,
2010
, “
Forced Response of Mistuned Bladed Disks in Gas Flow: A Comparative Study of Predictions and Full-Scale Experimental Results
,”
ASME J. Eng. Gas Turbines Power
,
132
(
5
), p.
052504
.
8.
Szwedowicz
,
J.
,
Gibert
,
C.
,
Sommer
,
T. P.
, and
Kellerer
,
R.
,
2007
, “
Numerical and Experimental Damping Assessment of a Thin-Walled Friction Damper in the Rotating Setup With High Pressure Turbine Blades
,”
ASME J. Eng. Gas Turbines Power
,
130
(
1
), p.
012502
.
9.
Hudson
,
R.
, and
Sinha
,
A.
,
2016
, “
Frictional Damping of Flutter: Microslip Versus Macroslip
,”
ASME J. Vib. Acoust.
,
138
(
6
), p.
061010
.
10.
Gross
,
J.
,
Berthold
,
C.
,
Krack
,
M.
, and
Frey
,
C.
,
2022
, “
Fully Coupled Analysis of Flutter Induced Limit Cycles: Frequency vs. Time Domain Methods
,”
Turbo Expo: Power for Land, Sea, and Air
,
Rotterdam, The Nuetherlands
,
June 13–17
.
11.
Rodríguez-Blanco
,
S.
,
González-Monge
,
J.
, and
Martel
,
C.
,
2023
, “
Asymptotic Evaluation of Nonlinear Friction Effects in Realistic LPT Rotors
,”
Turbo Expo: Power for Land, Sea, and Air
,
Boston, MA
,
June 26–30
.
12.
Schwarz
,
S.
,
Reil
,
J.
,
Gross
,
J.
,
Hartung
,
A.
,
Rittinger
,
D.
, and
Krack
,
M.
,
2023
, “
Friction Saturated Limit Cycle Oscillations—Test Rig Design and Validation of Numerical Prediction Methods
,”
Turbo Expo: Power for Land, Sea, and Air
,
Boston, MA
,
June 26–30
.
13.
Mao
,
Z.
, and
Kielb
,
R. E.
,
2017
, “
Interaction of Concurrent Forced Response and Flutter Phenomena in a Compressor Stage
,”
Volume 7B: Structures and Dynamics of Turbo Expo: Power for Land, Sea, and Air
,
Charlotte, NC
,
June 26–30
.
14.
Corral
,
R.
,
Gallardo
,
J. M.
, and
Ivaturi
,
R.
,
2013
, “
Conceptual Analysis of the Non-linear Forced Response of Aerodynamically Unstable Bladed-Discs
,”
Proceedings of the ASME Turbo Expo 2013
, ASME Paper No. GT2013-94851.
15.
Groth
,
P.
,
Martensson
,
H.
, and
Edin
,
N.
,
2009
, “
Experimental and Computational Fluid Dynamics Based Determination of Flutter Limits in Supersonic Space Turbines
,”
ASME J. Turbomach.
,
132
(
1
), p.
011010
.
16.
Lucio
,
M.
,
Bergmans
,
J.
,
Vogt
,
D.
, and
Fransson
,
T. H.
,
2014
, “
A Remotely Operated Aeroelastically Unstable Low Pressure Turbine Cascade for Turbomachinery Aeromechanics Education and Training Remote Flutter Lab
,”
ASME J. Eng. Gas Turbines Power
,
137
(
3
), p.
032507
.
17.
Corral
,
R.
,
Crespo
,
J.
, and
Gisbert
,
F.
,
2004
, “
Parallel Multigrid Unstructured Method for the Solution of the NavierStokes Equations
,”
Aerospace Sciences Meetings
,
Reno
,
January
.
18.
Gisbert
,
F.
,
Corral
,
R.
, and
Pueblas
,
J.
,
2013
, “
Computation of Turbomachinery Flows With a Parallel Unstructured Mesh Navier-Stokes Equations Solver on GPUs
,”
Fluid Dynamics and Co-Located Conferences
,
San Diego, CA
,
June 24–27
.
19.
Cordoba
,
O.
,
2021
, “
FEM Considerations to Simulate Interlocked Bladed Disks With Lagrange Multipliers
,”
Proceedings of the ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition
, ASME Paper No. GT2020-15140.
20.
Corral
,
R.
,
Manuel Gallardo
,
J.
, and
Vasco
,
C.
,
2007
, “
Aeroelastic Stability of Welded-in-Pair Low Pressure Turbine Rotor Blades: A Comparative Study Using Linear Methods
,”
ASME J. Turbomach.
,
129
(
1
), pp.
72
82
.
21.
Kaza
,
K.-R. V.
, and
Kielb
,
R. E.
,
1982
, “
Flutter and Response of a Mistuned Cascade in Incompressible Flow
,”
AIAA J.
,
20
(
8
), pp.
1120
1127
.
22.
Zhai
,
Y.
, and
Bladh
,
R.
,
2011
, “
Aeroelastic Stability Assessment of an Industrial Compressor Blade Including Mistuning Effects
,” Vol. 6, pp.
1271
1286
, ASME Paper No. GT2011-45800.
23.
Martel
,
C.
,
Corral
,
R.
, and
Llorens
,
J. M.
,
2008
, “
Stability Increase of Aerodynamically Unstable Rotors Using Intentional Mistuning
,”
ASME J. Turbomach.
,
130
(
1
), p.
011006
.
24.
Corral
,
R.
, and
Gallardo
,
J. M.
,
2006
, “
A Methodology for the Vibration Amplitude Prediction of Self-Excited Rotors Based on Dimensional Analysis
,”
Proceedings of the 51st ASME Gas Turbine and Aero Engine Congress, Exposition and Users Symposium
, ASME Paper No. 2005-GT-90668.
25.
Corral
,
R.
, and
Gallardo
,
J. M.
,
2014
, “
Non-Linear Dynamics of Bladed Disks With Multiple Unstable Modes
,”
AIAA J.
,
56
(
6
), pp.
1124
1132
.
26.
Sinha
,
A.
, and
Griffin
,
J. H.
,
1985
, “
Effects of Friction Dampers on Aerodynamically Unstable Rotor Stages
,”
AIAA J.
,
23
(
2
), pp.
262
270
.
27.
Petrov
,
E. P.
, and
Ewins
,
D. J.
,
2007
, “
Advanced Modeling of Underplatform Friction Dampers for Analysis of Bladed Disk Vibration
,”
ASME J. Turbomach.
,
129
(
1
), pp.
143
150
.
28.
Bermejo
,
O.
,
Gallardo
,
J. M.
,
Sotillo
,
A.
,
Altuna
,
A.
,
Alonso
,
R.
, and
Puente
,
A.
,
2024
, “
Numerical and Experimental Study of Flutter in a Realistic Labyrinth Seal
,”
Int. J. Turbomach. Propul. Power
,
9
(
2
), p.
13
.
29.
Rodriguez-Blanco
,
S.
,
Gonzalez-Monge
,
J.
, and
Martel
,
C.
,
2023
, “
Numerical Investigation of Friction Induced Interaction of Flutter Modes in a Realistic Low Pressure Turbine Rotor
,”
ASME J. Eng. Gas Turbines Power
,
145
(
11
), p.
111021
.
30.
Corral
,
R.
,
Khemiri
,
O.
, and
Martel
,
C.
,
2018
, “
Design of Mistuning Patterns to Control the Vibration Amplitude of Unstable Rotor Blades
,”
Aerosp. Sci. Technol.
,
80
, pp.
20
28
.
31.
Rodriguez-Blanco
,
S.
, and
Martel
,
C.
,
2023
, “
Characterization of the Anomalous Vibration Response of an Intentionally Mistuned LPT Rotor
,”
Machines
,
11
(
1
), p.
19
.