Experimental Campaign on a Generic Model for Fluid-Structure Interaction Studies

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Report Number: EKV / 725

Experimental Campaign on a Generic Model for Fluid-Structure Interaction Studies

Hakim Ferria

Master of Science Thesis Energy Technology 2007 KTH School of Energy and Environmental Technology

Heat and Power Technology SE-100 44 STOCKHOLM

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Master of Science Thesis EGI 2008: 725

Experimental Campaign on a Generic Model for Fluid-Structure Interaction Studies

Hakim Ferria

Approved

2008-04

Examiner

Prof. Torsten Fransson

Supervisor

Nikos Andrinopoulos

Commissioner Contact person

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ABSTRACT

Fluid-structure interactions appear in many industrial applications in the field of energy technology. As the components are more and more pushed to higher performance, taking fluid-structure interaction phenomena into account has a great impact on the design as well as in the cost and safety. Internal flows related to propulsion systems in aerodynamics area are of our interest; and particularly aeroelasticity and flutter phenomena.

A new 2D flexible generic model, so called bump, based on previous studies at the division of Heat and Power Technology about fluid-structure interactions is here presented. The overall goal is to enhance comprehension of flutter phenomenon. The current study exposes a preliminary experimental campaign regarding mechanical behaviour on two different test objects: an existing one made of polyurethane and a new one of aluminium.

The setup is built in such a way that it allows the bumps to oscillate until 500Hz. The objective is to reach this frequency range by remaining in the first bending mode shape which is indeed considered as fundamental for flutter study. In this manner being as close as possible to the bending flutter configuration in high-subsonic and transonic flows will provide a deeper understanding of the shock wave boundary layer interaction and the force phase angle related to it. The results have pointed out that the bumps can reach a frequency of 250Hz by remaining in the first bending mode shape. The one in polyurethane can even reach frequency up to 350Hz; however, amplitude is higher than the theoretical one fixed to 0.5mm. Then unsteady pressure measurements for one operating point have been performed based on using recessed-mounted pressure transducers with Kulite fast response sensors. Variation amplitudes and phases of the unsteady pressure are thus correlated with the vibrations of the model. The operating point has been defined with respect to previous studies on the same static geometric model in order to use steady state base line; the steady flows appear consistent with each other.

The results have pointed out that the shock wave induces strong amplification of the steady static pressure; however, this rise decreases when the reduced frequency increases. Finally some elements regarding propagating waves are suggested in the analysis for deeper investigations on such complex phenomena.

Keywords: Aeroelasticity, Boundary layer, Flutter, Reduced frequency, Unsteady pressure measurement, Shock wave.

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ACKNOWLEDGEMENTS

I would like to express my gratitude to both Professor Torsten H. Fransson at the Chair of Heat and Power Technology at the Royal Institute of Technology, Stockholm, and Doctor Pascal Ferrand at “Ecole Centrale de Lyon”, Ecully, for having given me the chance to perform experimental works in the Department of Heat Power and Technology at KTH.

Special thanks to Nikos Andrinopoulos who I worked with during my stay. Thanks him for giving me time, for introducing me his PhD field and his facility and for fun time.

“ευχαριστώ, Nikos!”

I want also thank Dr Damian M. Vogt for his efficiency, the time he gave me and especially during the last months, for running the compressor the last day.

“Vielen Dank, Damian!”

I would like to thank the technicians for their precious help, their advices and their useful tools, for having designed in a nice “gold-way” the sensors connector.

“Tack så mycket!”

I would also like to thank all people I met during my stay for having good time especially MSc and PhD students.

The financial support from both “Consortium Industrie Recherche en Turbomachines” and SUSPOWER / KTH are gratefully acknowledged.

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LIST OF FIGURES

Fig. 2-1: Collar’s aeroelastic triangle. ... 17

Fig. 2-2: Operating map of a multistage compressor. ... 19

Fig. 2-3: Classical flutter illustrated by “force phase angle” Φ. ... 20

Fig. 2-4: Graphical interpretation of the reduced frequency. ... 21

Fig. 2-5: The VM100 test section, dimensions in mm, [Bron, 2004]. ... 23

Fig. 2-6: Flow configuration over the 3D bump, [Bron, 2004]. ... 24

Fig. 2-7: 3D bump, [Bron, 2004]. ... 24

Fig. 2-8: 2D bump manufactured in aluminium, [Bron, 2004]. ... 24

Fig. 2-9: Experimental and 2D RANS results comparison in 2D nozzle. (Same operating point,P_s₂ =112kPa), [Bron, 2004]... 25

Fig. 2-10: Experimental, 2D RANS and 3D RANS results comparison in 2D nozzle, [Bron, 2004]. ... 25

Fig. 2-11: Steady state weak shock structure in 2D nozzle, [Bron, 2004]. ... 25

Fig. 2-12: Steady state strong shock structure in 2D nozzle, [Bron, 2004]. ... 26

Fig. 2-13: Comparison between experiments, 2D RANS and 3D RANS (Shock position and Separation region location), [Bron, 2004]. ... 26

Fig. 2-14: Experiments and 3D RANS comparison on the 3D bump, 2D plot at mid channel, P_s₂ =112kPa, [Bron, 2004]. ... 26

Fig. 2-15: Sonic pocket and streamlines within the separated flow region,P_s₂ =112kPa, [Bron, 2004]. ... 27

Fig. 2-16: Experimental phase shift underneath shock location, [Bron, 2004]. ... 28

Fig. 2-17: Section view of the mechanical actuator with prismatic cam. ... 28

Fig. 2-18: Composition of the flexible bump, [Allegret-Bourdon, 2004]. ... 29

Fig. 2-19: View of the overall test facility with optical accesses, [Allegret-Bourdon, 2004]. ... 29

Fig. 2-20: Variation of ensemble averaged shock wave movement towards bump motion, [Allegret-Bourdon, 2004]. ... 30

Fig. 2-21: Experimental shock motion for strong shock configuration (P_s₂ =106kPa) and high perturbation amplitude (amp= ±2.12kPa), [Bron, 2004]. ... 30

Fig. 2-22: Chordwise repartition of unsteady pressure coefficient and phase lead of static pressure towards bump local deformation, [Allegret-Bourdon, 2004]. ... 31

Fig. 3-1: From blades to bump. ... 34

Fig. 4-1: Overall facility at HPT. ... 35

Fig. 4-2: Sketch of the wind tunnel flow control. ... 35

Fig. 4-3: Lateral section of the wind tunnel. ... 36

Fig. 4-4: Test section. ... 36

Fig. 4-5: Flexible generic models (top): polyurethane bump (left) and aluminium bump (right) and its schematic representation (bottom). ... 37

Fig. 4-6: Illustration of the laser triangulation measurement, [Allegret-Boudon, 2004]. ... 39

Fig. 4-7: Pressure measurements locations in the wind-tunnel. ... 39

Fig. 4-8: Static calibration of the Kulite transducers. ... 40

Fig. 4-9: Dynamic calibration unit (top right), the fluctuating pressure generator (top left) and the calibration head (bottom). ... 41

Fig. 4-10: Dynamic transfer properties: magnitude ratio (up) and phase (down). ... 41

Fig. 4-11: Transfer characteristic at 5 different axial positions. ... 42

Fig. 4-12: Influence of the capillarity tube length. ... 43

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Fig. 4-13: Transfer characteristic for the tap4 with 6 sensors. ... 43

Fig. 4-14: Influence of the pressure jet. ... 44

Fig. 4-15: Signal reconstruction (70Hz). ... 44

Fig. 5-1: Sinusoidal shape of the oscillations (50Hz) of the polyurethane bump. ... 47

Fig. 5-2: Instantaneous amplitude (top) and phase (bottom) of the polyurethane bump. .. 48

Fig. 5-3: Sinusoidal shape of the oscillations (50Hz) of the aluminium bump. ... 49

Fig. 5-4: 3D mesh of the aluminium bump. ... 49

Fig. 5-5: First normal mode of the aluminium bump. ... 50

Fig. 5-6: Pin test for the aluminium bump. ... 50

Fig. 5-7: Positions of the laser beam for each side of the aluminium bump. ... 51

Fig. 5-8: Instantaneous amplitude of the aluminium bump for 2 spanwises. ... 51

Fig. 5-9: Checking of the constant velocity of the motor. ... 52

Fig. 5-10: Clockwise and counter clockwise speed of the motor. ... 52

Fig. 5-11: Repeatability for the laser measurement (aluminium bump – 100Hz). ... 53

Fig. 5-12: Repeatability for the laser measurement (aluminium bump – 200Hz). ... 53

Fig. 5-13: Instantaneous amplitude (top) and phase (bottom) of the aluminium bump at 50Hz, 100Hz, 250Hz, 300Hz and 320Hz. ... 54

Fig. 5-14: Amplitude magnification of the aluminium bump. ... 55

Fig. 5-15: Amplitude magnification normalized showing 3 behaviours of the bump. ... 55

Fig. 5-16: Schematic representations of the polyurethane bump (top) and the aluminium bump (bottom). ... 56

Fig. 6-1: Steady state pressure measurement layout on the bump. ... 57

Fig. 6-2: Pressure in terms of Ps (a) and Cp (b) and isentropic Mach number distributions along the bump surface. ... 59

Fig. 6-3: Operating conditions in Bron’s 2D experiments, [Bron, 2004]. ... 60

Fig. 6-4: Steady state shock induced separation, [Bron, 2004]. ... 60

Fig. 6-5: Particular aerodynamic points. ... 60

Fig. 6-6: Shock location (Schlieren and 3D NS simulation) forP_s₂ =104kPa, [Bron, 2004]. 61 Fig. 7-1: Instantaneous amplitude (a), unsteady pressure coefficient (b) and phase of unsteady pressure towards the bump motion (c) at frequencies 10Hz, 25Hz and 50Hz. ... 66

Fig. 7-2: Instantaneous amplitude (a), unsteady pressure coefficient (b) and phase of unsteady pressure towards the bump motion (c) at frequencies 75Hz, 100Hz and 150Hz. ... 67

Fig. 7-3: Instantaneous amplitude (a), unsteady pressure coefficient (b) and phase of unsteady pressure towards the bump motion (c) at frequencies 250Hz and 300Hz. .. 68

Fig. 7-4: Relative variations of the section (left) and relative variations of the velocity (right). ... 69

Fig. 7-5: Pressure and velocity perturbations ratio at the throat. ... 70

Fig. 7-6: Velocity gradient (a) and coefficient G_k(b) versus the reduced frequency. ... 71

Fig. 7-7: Module of K. ... 71

Fig. 7-8: Module of the shock motion amplitude and its phase. ... 72

Fig. 7-9: Mach number gradient ... 73

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LIST OF TABLES

Table 2-1: Operating conditions and reduced frequencies. ... 29

Table 4-1: Mechanical properties of the bumps. ... 38

Table 6-1: The operating conditions. ... 57

Table 6-2: Pressure rise location on the bump surface. ... 58

Table 6-3: Aerodynamic throat and shock localisations. ... 59

Table 7-1: Reduced frequencies of the full frequency range. ... 63

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NOMENCLATURE

Latin letters

a speed of sound

A theoretical amplitude of the bump oscillations Cp steady pressure coefficient

ˆp

C unsteady pressure coefficient

c blade chord

f frequency

k reduced frequency

M Mach number

Pˆ complex pressure

P pressure

Q mass-flow

T temperature

V velocity

Greek letters

γ ratio of specific heats, γ = C_p C_v (1.4 for air) Subscripts

1 inlet value

2 outlet value

ax axial

iso isentropic value

ref reference

s static condition

t total condition

Abbreviations

2D Two Dimensional

3D Three Dimensional

AC Alternative Current

CFD Computational Fluid Dynamics

DFSD Discrete Fourier Series Decomposition ECL Ecole Centrale de Lyon

HPT Heat and Power Technology

KTH Kungliga Tekniska Högskola (Royal Institute of Technology) KT8000 Kaiser Threde 8000 system

OP Operating Point

PSD Position Sensitive Detector

RANS Reynolds Averaged Navier Stokes SBLI Shock Boundary Layer Interaction

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VM100 Wind Tunnel Facility at HPT

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1 INTRODUCTION

Fluid-structure interactions appear in many industrial applications in the field of energy technology. As the components are more and more pushed to higher performance, taking fluid-structure phenomena into account has a great impact on the design as well as in the cost and safety. Internal flows related to propulsion systems in aerodynamics area are of our interest; and particularly aeroelasticity instabilities that have always existed and are usually complex non linear phenomena that could cause structural failure.

High speeds, i.e. high-subsonic and transonic velocities, in such flows ineluctably lead to weak or strong shock waves that act with the boundary layers and thus with the structure.

As a result strong pressure fluctuations can occur and generate unsteadiness. However the understanding of when the unsteady phenomena start is still under investigation so that many research efforts base on a forced unsteadiness created by a perturbation generator. Only a good comprehension of the physics, i.e. a good understanding of the complex interdisciplinary field in which aerodynamical and structural point of views should be considered, will enable to perform studies on aeroelasticity. For this reason it is necessary to lead both experimental and numerical campaigns.

Flutter is one of the phenomena related to aeroelasticity issues; it appears when the structure and the flow around it interact with each other. The instantaneous motion of the structure leads to an energy exchange between the body and the flow. If the fluid gives energy to the structure, this one will absorb energy and hence its displacement will be magnified. As a result, it causes an amplification of the fluid response and therefore a rapid divergence. In order to know if the studied phenomenon is divergent or not one can determine the sign of the aerodynamic damping in different operating points characterized by reduced frequencies and various amplitude of the oscillating structure.

The report exposes an experimental campaign on a generic model for fluid-structure interactions studies. It strongly relates on previous works led by Bron [2004] and Allegret- Bourdon [2004]. It presents firstly a background of physical phenomena related to aeroelasticity issues and on the other hand a non exhaustive overview of experimental campaigns performed at the Chair of Heat and Power Technology on generic models.

Secondly measurements on two different flexible models will be presented. The measurements will focus on the mechanical behaviour of the structure and then pressure measurements for one operating point will be carried out.

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2 BACKGROUND

This chapter aims at introducing the basic knowledge of aeroelasticity and the physical phenomena related to it. On the other hand an overview of the previous investigations on 2D flexible bumps at HPT will justify the followed path in the overall project.

2.1 Aeroelasticity

The word “aeroelasticity” is used for defining an interdisciplinary physical phenomenon.

The multiplicity of forces that interferes with each other yields to complex phenomena.

Actually the terminology “aeroelasticity”, when it refers to interactions between fluid and structure, is not accurate, the appropriate one is “fluido-elasticity”.

Aeroelasticity consists of three forces: aerodynamic, inertia and elastic forces that are caused by the flow around the body, its accelerated mass and its elastic structure respectively, in such a way that the structure and flow around it interact with each other.

This complex combination that leads the structure to vibrate can be illustrated by the Collar’s triangle [1946] (Fig. 2-1).

Fig. 2-1: Collar’s aeroelastic triangle.

These three forces can interact with each other or all together, hence different cases of physical phenomena have to be considered:

− Rigid-body aerodynamics: it combines inertial and aerodynamic forces, the static aspects of the loading on the structure are considered. Such situation meets in external aerodynamic (lift, control and stability of the aircraft).

DYNAMIC AEROELASTICITY RIGID-BODY

AERODYNAMICS

MECHANICAL VIBRATIONS

STATIC AEROELASTICITY

Inertial Forces

Elastic Forces Aerodynamic Forces

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− Structural dynamics: it combines inertial and elastic forces. No fluid acts around the structure. This case is related to the mechanical vibrations that is to say the structure vibrates only under the inertial and elastic forces.

− Static aeroelasticity: it appears when aerodynamic forces and elastic forces act together. No vibrations are implied. The steady aerodynamic load is responsible of the deformation or the displacement of the structure.

− Dynamic aeroelasticity that takes into account all three forces. A more accurate terminology would be “aero-elasto-dynamics” but the shorter term “aeroelasticity” is the usual terminology whereas it should only be used for what is generally known as “static aeroelasticity”.

2.2 Dynamic aeroelasticity and flutter phenomenon

The dynamic aeroelasticity field covers many different phenomena:

− Aerodynamic interaction between different parts of the system (vortex-shedding, buffeting).

− Forced response (gust).

− Flutter (different kinds of specific flutter exist that are explained further).

− Other flow-induced vibrations such non-integral engine order, acoustic resonance, rotating stall, surge.

Flutter is an instability phenomenon described as a self-excited vibration. Indeed in certain circumstances a curved surface such a blade, a wing or the surface of a nozzle can enter into a self-excited vibration, that is to say vibrations with no external excitation. Flutter usually appears above a critical flow velocity, gives large vibration amplitudes and can damage the blade in a short period of time until its breakdown.

Flutter must be distinguished from forced response like rotor/stator interaction or from unsteady natural phenomena like vortex-shedding. Indeed, it is necessary that the structure undergoes an instantaneous displacement around its steady equilibrium position in such a way that an instantaneous perturbation of the flow appears. As a result, an exchange of energy between fluid and structure with their own energy level is created and, according to the direction of this energy exchange, will lead to either a stable steady equilibrium or an unsteadiness (periodic with exponential evolution). Actually the flutter phenomenon strongly depends on the flexibility of the structure and appears when the mechanical work is lower than the aerodynamic work, i.e. when the mechanical damping is small to overcome the aerodynamic excitations.

In external flows, it appears when two vibrating modes (usually bending and torsion) interact together at distinct frequencies. In internal flows, for instance in turbomachines, with an higher blade stiffness, flutter often occurs due to the interaction between a vibrating mode (bending or torsion) and an unstable aerodynamic behaviour, like a boundary layer separation, a strong shock motion or a shock/boundary layer interaction.

That is why it is difficult to predict which phenomenon originates flutter. Thus the reader has to keep in mind that there are different sources responsible for inducing flutter. For instance an interblade phase lag favourable to an amplification of any structural vibration can induce flutter. But in any case, flutter exists because of strong interaction or coupling between the instant motion of the blade and the instant aerodynamic forces.

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Flutter is characterized by self-excitation that comes from the phase shift between the blade motion and the pressure on the blade which is also called “force phase angle”.

Several kinds of flutter are defined, each with its own characteristics. Fig. 2-2 shows where each kind of flutter occurs in the plane “mass flow / pressure ratio” and the flow structure related to.

Fig. 2-2: Operating map of a multistage compressor.

First of all two kinds of flutter are depicted. Subsonic stall flutter, related to a leading edge stall, is not necessarily associated to a coupling between blades oppositely of the other types of flutter where shock waves create interdependence. As a result interblade phase angle can be very significant.

In Fig. 2-2:

− The cases 1 and 2 associated to subsonic and transonic stall flutters respectively occur when the compressor is operating near surge. The flow conditions are characterized by high incidence angles and separated flow. The vibratory modes are bending and torsion as well as coupled modes [Srinivasan, 1947].

− The case 3 related to choke flutter is encountered during part speed operation when the blades are operating at negative incidence angles. The vibratory modes associated are bending and torsion modes [Srinivasan, 1947]. It is characterized by choked flow, separation and shock waves.

− The supersonic started flutter at low back pressure (case 4), under supersonic and attached flow conditions, occurs on fan blades. The vibratory modes are bending and pitching.

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− The supersonic started flutter at high back pressure (case 5) occurs in fan blades of compressors during high-speed operation. The blades are highly loaded and strong shocks appear.

− Finally the case 6 deals with classical flutter that occurs near the operating point, for small incidence angles. There is also the so called potential flow flutter, which involves the phase lag shift between the blade motion and the pressure on the blade.

Flutter is illustrated in Fig. 2-3 from an energy point of view. The energy of the system, given by Eq. 2-1 is indeed positive when both the aerodynamic force F(t) acting on the body, i.e. the pressure, and the body motion represented by ∂δh ∂t involves phase lag between 0 and 180 degrees.

Energy = F(t).dδh = F(t). δhdt t

∂

∫ ∫

∂ ^{Eq. 2-1}

time t

amplitude

∂∂∂∂δδδδh/∂∂∂∂t F(t)

φφφφ

time t

amplitude

Energy (_φφφφ=0)

Fig. 2-3: Classical flutter illustrated by “force phase angle” Φ.

2.3 Reduced frequencies

One solution to avoid flutter in turbomachines is to stiffen the blades or to add a part-span shroud on it. Using the definition of the reduced frequencies, the designers can also use the following empirical rule: the reduced frequency must not be less than 0.33 for bending and 1.6 for torsion in order to avoid stall flutter [Armstrong et al., 1960]. The reduced frequency is defined, based on the full chord, by the following equation (Eq. 2-2).

s 2

u ax

T c

k f

T π v

= = Eq. 2-2

It gives a measure of unsteadiness through a correlation between the axial flow velocity vax, the blade chord c and the oscillation frequency f . It is also a ratio between two time scales, one related to steady phenomenon and a second one to unsteady phenomenon, Ts and T_u respectively. T_u is associated to the natural frequency f_u of the structure; it represents the characteristic time of the studied unsteadiness. On the other hand, V being the convection velocity of the flow, T_s is the time taken for a fluid particle to travel through the blade row characterized by the chord, hence T_s =V c. If the time for one blade oscillation is long enough, the flow can be considered as quasi-steady state insofar as the

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flow is able to adapt to the changing conditions. Thus, quasi-steady and unsteady states can be described via the reduced frequencies as following:

− k <<1: quasi-steady phenomenon.

− k ≅1: strong couplings.

− k >>1: predominant unsteady phenomenon that often occurs in rotor-stator interaction.

Fig. 2-4 shows an interpretation of reduced frequency from Platzer and Carta [Srinivasan, 1947]. By dividing the chord by the wavelength λ, a new form of k is derived (Eq. 2-3):

π λ^c

k = Eq. 2-3

Fig. 2-4: Graphical interpretation of the reduced frequency.

2.4 Acoustic blockage

In order to introduce the acoustic blockage theory, consider a blade row in a turbomachine and assume that excitation comes from the structure at given Inter-Blade Phase Angle (IBPA). Excitation will thus propagate both upstream and downstream of the excitation source as waves that can either be damped or not. There are modes that are purely propagative without any decaying behaviour: these are cut-on modes. Other modes can be exponentially decaying; they are defined as cut-off modes. This concept is particularly important in the analysis of the flutter mechanisms by giving important information about the system perturbations. Waves can indeed brutally change in mode and hence they produce strong discontinuities on the unsteady flow. The ability of the flow to damp or to amplify the blade motion is strongly affected by how unsteady perturbations are propagated from the cascade to the far-field.

Atassi et al [1994] has reported results explaining why transonic flows, and high subsonic flows as well, exhibit a rise of the unsteady pressure magnitude along the surface of a cascade blade, or of an airfoil, such that a significant bulge appears near the shock location. For such flows, upstream propagating acoustic disturbances are blocked and amplified: the near-sonic velocity acts as a barrier, known as acoustic blockage, which is similar to the shock in transonic flow preventing acoustic disturbances from propagating upstream. Bron et al. [2004] has investigated on a transonic convergent-divergent nozzle and confirmed the acoustic blockage theory. It has been showed that there exist critical behaviours such that down- and upstream there is a cut-off mode and cut-on mode respectively: outlet pressure perturbations are magnified when propagating into the near sonic flow region and can lead to the excitation of shock wave. This interaction creates a shift in the shock position and contributes to the system stability: it has a strong effect on

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the overall unsteady forces affecting the flutter boundary as well and thus causing large local stresses which may result in high cycle fatigue failure.

2.5 Experimental investigations

Many research efforts intended to improve the understanding of aeroelastic phenomena which occur in turbomachines have taken place. The author does not intend to present an exhaustive list of all experimental setups but many campaigns based on using rigid blade models in order to be closer to the actual physical conditions in turbomachines. In previous research works with 2D rigid models representing actual blades, i.e. with high stiffness, it was shown that from an experimental point of view, both high amplitude and high frequency cannot be reached together. For more details the reader can refer to Allegret- Bourdon [2004]. For this reason, the use of a 2D non-rigid flexible generic model is completely justified as it can reach high frequency and high amplitude at the same time.

The following sub-chapters have to be considered as the state-of-the-art of the work presented here and especially regarding the facility used. The reader should thus feel that there still need investigations on that facility and that the current study is the logical next step. This section hence only focuses on the investigations performed by Bron [2004] and Allegret-Bourdon [2004] on a 2D non-oscillating model and a 2D oscillating flexible model respectively. Rather than modelling the complex geometry of a turbomachine, this facility and experimental campaigns intend to avoid complex phenomena such as radial geometry or 3D aspect of the flow.

2.5.1 Non-oscillating model (rigid model)

Bron [2004] designed a rigid bump in order to verify acoustic blockage theory, to understand phenomena associated to travelling waves in non-uniform transonic flows and how they affect the unsteady pressure distribution on the surface as well as the far field radiated sound. Steady and unsteady states on both 2D and 3D nozzle geometries were discussed both numerically¹ and experimentally. Fig. 2-5 shows the modular test section used. Different test objects can be put in. Moreover the facility was designed in such a way that it allows access for optical measures and instrumentation (visualizations, laser measurements, etc) by means of large openings both on the upper and lower walls as well as the side walls without inserting apparatus inside.

1 The CFD software used solves the fully 2D and 3D compressible RANS equations via a finite volume formulation and a linear two-equation turbulent model. More details can be found in Bron [2004].

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Fig. 2-5: The VM100 test section, dimensions in mm, [Bron, 2004].

The studies consisted of analysing the interaction between a downstream propagating pressure disturbance and an oscillating shock in 2D and 3D geometries with a shape of a bump representing a convergent-divergent. Such a simple geometry is used in order to avoid complex phenomena (leading and trailing edges influences, inter-rows region interactions) and to be able to separate the different mechanisms. In similitude with axial turbomachines, the setup can be considered as reproducing potential interactions, rotor- stator interaction for instance, by imposing periodic back pressure fluctuations downstream of the flow. The shock wave is then expected to interact with the boundary layer. Still in similitude with axial turbomachines, this configuration corresponds to the SBLI on the suction side of the blades that can reach the pressure side of the adjacent blades and hence the interblade passage is thus affected for a particular operating point as the one suggested Fig. 2-2 with the case 3 corresponding to the choke flutter configuration. The physical issue is the following: the non-linear interaction leads to shock wave oscillations that induce oscillations of the aerodynamical force acting on the blade. Both aerodynamical and mechanical damping will therefore interact with each other that will conduct to either stable or unstable behaviour. The setup also offers the possibility to investigate different kind of flutter: subsonic stall flutter, transonic stall flutter and classical flutter (potential flutter) corresponding to the cases 1, 2 and 6 respectively (Fig. 2-2).

The 3D bump design is schematically depicted in Fig. 2-6 and the test object is presented in Fig. 2-7. It has been designed such that it allows studying the pressure amplification mechanisms on blades surface and the phase lags between the shock motion and the pressure distribution. In other words the goal was to create a flow structure which is both exciting and attenuating at different location with respect to the shock motion and the amplification of back pressure fluctuations.

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Fig. 2-6: Flow configuration over the 3D bump, [Bron, 2004].

A simpler 2D bump presented Fig. 2-8 was also designed in order to simplify analysis and to investigate the two dimensionality of the flow as well as side walls influence and corner effects. So to be able to compare both test objects with each other, the 2D bump was manufactured by keeping the same mean flow gradient, i.e. the main curvature characteristics.

Fig. 2-7: 3D bump, [Bron, 2004].

Fig. 2-8: 2D bump manufactured in aluminium, [Bron, 2004].

Comparison between experiments, 2D RANS and 3D RANS calculations on the 2D bump shows fairly good agreement for weak shocks (Fig. 2-10) until a certain streamwise position which corresponds to a rise of the boundary layer thickness due to the interaction between the adverse pressure gradient and the curvature. As shown in Fig. 2-9 the 2D RANS calculations do not catch the entire physical phenomena meaning that the flow is not fairly 2D. Indeed the interaction between the shock and the side wall boundary layers is actually strong enough to create large vortices which contribute to decrease the two- dimensionality of the flow. Fig. 2-10 shows that 3D RANS calculations gives better results for the same operating point.

Fig. 2-11, Fig. 2-12 and Fig. 2-13 illustrate such a CDF deficiency in the prediction. They show a numerical under-estimation of the boundary layer thickening that is equivalent to an “effective section” reduction. Notwithstanding a disparity of inlet boundary conditions

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because the numerical studies were performed first and there were no experimental data to initialize the calculations; a fairly good agreement for weak shock configuration between experiments and numerical simulations was established but also an under-estimation of the losses for strong SBLI. When the shock reaches a critical value such that it creates a significant region of flow separation, experimental and numerical results show very different behaviours, for both steady and unsteady states. A limit of the numerical models validity appears clearly here.

Fig. 2-9: Experimental and 2D RANS results comparison in 2D nozzle. (Same operating point,P_s₂ =112kPa), [Bron, 2004].

Fig. 2-10: Experimental, 2D RANS and 3D RANS results comparison in 2D nozzle, [Bron, 2004].

Schlieren (P_s₂ =112kPa) 3D RANS (P_s₂ =112kPa) 2D RANS (P_s₂ =116kPa) Fig. 2-11: Steady state weak shock structure in 2D nozzle, [Bron, 2004].

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Schlieren (P_s₂ =106kPa) 3D RANS (P_s₂ =108kPa) 2D RANS (P_s₂ =110kPa) Fig. 2-12: Steady state strong shock structure in 2D nozzle, [Bron, 2004].

Shock position Separation region location

Fig. 2-13: Comparison between experiments, 2D RANS and 3D RANS (Shock position and Separation region location), [Bron, 2004].

Fig. 2-14 presents comparison between experiments and 3D RANS on the 3D bump with similar trends but more pronounced due to higher mean flow gradients so larger separations with the formation of the sonic pocket according to the acoustic blockage theory (Fig. 2-15). The under-estimation of the boundary layer thickening and the separation region is thus higher.

Fig. 2-14: Experiments and 3D RANS comparison on the 3D bump, 2D plot at mid channel, P_s₂ =112kPa, [Bron, 2004].

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Fig. 2-15: Sonic pocket and streamlines within the separated flow region,P_s₂ =112kPa, [Bron, 2004].

It was shown that the unsteady pressure distribution, both on the bump surface and within the channel, results from the superposition of upstream and downstream propagating waves. Bron suggested that “outlet pressure perturbations propagate upstream in the nozzle, interact in the high subsonic flow region according to the acoustic blockage theory, and are partly reflected or absorbed by the oscillating shock, depending on the frequency of the perturbations and the intensity of the SBLI”.

A parametric study was led in order to evaluate influences of perturbation frequency, shock location, perturbation amplitude on the evolutions of unsteady pressure amplification, unsteady pressure phase angle. Relating to the 2D bump this parametric study has shown the following:

− The mean shock location and the perturbation frequency exert influence on amplification and phase-angle of the unsteady pressure distribution on one hand, on amplitude and phase-angle of the unsteady shock motion on the other hand.

− The motion amplitude of the shock wave decreases with the perturbation frequency.

− On the surface underneath the shock location a phase shift occurs increasing with both the strength of the shock and the perturbation frequency (Fig. 2-16) and participating to the unsteady aerodynamic force on the surface of the bump. This phase shift is particularly of our interest as it affects the stability of the airfoil.

− For weak shocks a linear increase of the phase-lag with the perturbation frequency was found. As to strong shocks the opposite tendency that is an advance of the shock motion compared to the incoming pressure perturbations was observed.

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Fig. 2-16: Experimental phase shift underneath shock location, [Bron, 2004].

2.5.2 2D oscillating non-rigid model (flexible model)

A new test facility was presented in order to investigate fluid-structure interactions by using a generic flexible model. This 2D oscillating flexible bump is a dynamic version of the same static generic model used by Bron [2004]. The main difference is that the unsteadiness is caused by the oscillations of the model itself with the aim of reaching a better understanding of the bending flutter phenomenon. Closer to reality for studying aeroelasticity this experimental configuration is focussed on particular types of flutter (subsonic flutter and transonic shock induced flutter). An integrated mechanical oscillating mechanism was designed [Vogt, 2001] such as it allows oscillations in a controlled way.

Fig. 2-17 shows a section of the mechanical actuator.

Fig. 2-17: Section view of the mechanical actuator with prismatic cam.

The bump can oscillate with the help of a rotating camshaft, driven by a motor and composed of three identical prismatic cams manufactured as part of a cylindrical stunted steel axle. Those three cams are in contact with two bearing plates mounted in an actuator casing. Thus for one rotation, the camshaft creates three vertical oscillations of the actuator and so three oscillations of the top of the bump. Therefore, a rotational speed of the camshaft of 10,000 rpm produces an oscillating frequency of 500 Hz of the flexible model top. The 2D generic model moulded of a flexible material that allows smooth deformations of the curved surface (Fig. 2-18) is 290mm long and is made for oscillating along 120mm that defines the chord. A view of the overall facility is presented in Fig. 2-19.

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Fig. 2-18: Composition of the flexible bump, [Allegret-Bourdon, 2004].

Fig. 2-19: View of the overall test facility with optical accesses, [Allegret-Bourdon,

2004].

The investigations by Allegret-Bourdon [2004] at various reduced frequencies (Table 2-1) showed a strong dependence of the bump modes shape towards the oscillation frequency.

The main objective was to maintain the first bending mode shape until a reduced frequency of 0.3.

Parameters Symbols Units Values

Upstream stagnation pressure P_t₁ kPa 159

Upstream stagnation

temperature T^t¹ K 305

Upstream static pressure P_s₁ kPa 116

Downstream static pressure P_s₂ kPa 104

Inlet isentropic Mach number M_iso₁ - 0.69

Outlet isentropic Mach number M_iso₂ - 0.80

Absolute frequencies f Hz 10, 25, 50, 75, 150, 200

Reduced frequencies k - 0.015, 0.037, 0.074, 0.11, 0.221, 0.294

Table 2-1: Operating conditions and reduced frequencies.

Two generic models were considered. The first one was manufactured with lateral gaps along its deforming chord in order to avoid friction between the structure and the side windows. Regarding the shock wave motion the results obtained were not expected even if that configuration showed a better 2D flow in CFD. Indeed by comparing the data with Bron´s data there were noticeable differences for the same operating point. For this reason a second 2D bump was manufactured in order to avoid gap leakages as well. Thus better results according to previous studies were achieved and those related to the first bending mode shape are summarized below for the operating point presented in Table 2-1:

− In the quasi-static case the shock wave movement follows the bump motion (Fig. 2-22).

− The first bending mode shape (k=0.015) is characterized by a phase difference of 135º relatively to the quasi-static case (Fig. 2-20). Furthermore, it is shown that the amplitude of the shock wave motion increases with the frequency until about k=0.088;

then it remains almost constant whereas Bron presented results indicating clearly the amplitude of the shock motion decreases with the frequency (Fig. 2-21).

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− Similar trends downstream of the shock wave were observed that is to say an increase of the unsteady pressure coefficient until the end of the chord for the overall range of the reduced frequencies. More specifically a phase difference of 180º from upstream to downstream of the chord relating to the phase of unsteady pressure towards the bump local deformation was noticed (Fig. 2-22).

Fig. 2-20: Variation of ensemble averaged shock wave movement towards bump motion, [Allegret-Bourdon, 2004].

Fig. 2-21: Experimental shock motion for strong shock configuration (P_s₂ =106kPa) and high perturbation amplitude (amp= ±2.12kPa), [Bron, 2004].

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Fig. 2-22: Chordwise repartition of unsteady pressure coefficient and phase lead of static pressure towards bump local deformation, [Allegret-Bourdon, 2004].

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3 OBJECTIVES AND METHOD OF ATTACK

A better understanding of the mechanisms responsible of the phase lag which lead to instabilities will permit to develop aerodynamic rules in order to predict the flutter limit.

Travelling pressure waves, outlet disturbances, shock motion and fluctuating turbulent boundary layers interact and yield to complex unsteady transonic flows. Complex phenomena in such flows rise in the shock/boundary layer region by producing phase lags and high time harmonics.

From a general point of view the overall objective is to enhance the knowledge related to fluid-structure interaction phenomena which occur in transonic flows. The present study is strongly based on previous works performed both at HPT for the experimental part and at ECL for the numerical part. It is clearly obvious that a deeper understanding comes also through both experimental and numerical investigations by comparing them with each other.

In this framework a new flexible generic model was designed by Andrinopoulos et al.

[2008] with which both high amplitude (0.5mm) and high frequencies (300Hz) can be reached by maintaining the first bending mode during oscillations. Dedicated to study flutter phenomenon under subsonic and transonic flow conditions this new bump was manufactured with the aim of better understanding:

− steady and unsteady pressure distribution over the bump surface,

− causes of force phase angle between vibrating structure and unsteady aerodynamic forces,

− phase lags between shock motion and unsteady pressure distribution on the bump surface,

− transition from stable to unstable operation.

As previously done, the present work also concentrates on “subsonic flutter” and

“transonic shock induced flutter”. These particular types of flutter should be investigated by the measure of surface pressure fluctuations. Moreover the “transonic shock induced flutter” is also related to the shock motion and its interaction with the boundary layer.

On the other hand those results might also serve to calibrate and validate future CFD models, more specifically with regard to the “unsteady boundary conditions”. Indeed nowadays, with the computer power growth, simulations are increasingly accurate and permit to study flows with many parameters. However, in the case of fluid structure interaction problems for both external and internal flows, there is a large need for accurate experimental data in order to validate the numerical models developed. This sometimes shows very good agreement and some other times large discrepancies, without researchers so far understanding why.

In summary, the objectives are the following ones:

− geometry measurements on the polyurethane bump for a check of repeatability and reproducibility results,

− unsteady pressure measurements on the polyurethane bump for one operating point,

− setup of the new aluminium bump for dynamic geometry measurements.

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Investigations are achieved by using simple and basic models (Fig. 3-1). Thus complex phenomena like influences of both leading and trailing edges are avoided. A test object, having the profile shape of a bump, reproduces a convergent-divergent geometry. The bump was manufactured in such a way that its shape creates a contraction in order to induce a shock wave.

A geometry measurement system using the laser triangulation principle is used to measure the dynamic flexible geometry in order to relate the pressure measurements to the structure deformations. Unsteady pressure measurements for one operating point are performed based on the use of recessed-mounted pressure transducers with Kulite fast response sensors. After post-processing the data, interpretation and comparison can be done for analysing the interaction between the flow and the generic surface motion.

Bending mode shape of the blade Generic flexible model (bump)

Fig. 3-1: From blades to bump.

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4 DESCRIPTION OF THE TEST FACILITY AND THE MEASUREMENT TECHNIQUES

4.1 Overall facility

The VM100 wind tunnel facility consists of a screw compressor driven by a 1MW electric motor. The maximum mass flow available is about 4.7Kg/s at 4bar and 303K. A set of valves allows redirecting the flow either in a test turbine or in exchangeable wind tunnel facility, as depicted in Fig. 4-1.

Fig. 4-1: Overall facility at HPT.

The air exhaust temperature of the compressor is approximately 453K and can be adjusted down to 303K by an air-cooling system. Another set of three valves allows controlling both the mass flow and the pressure level in the test section (Fig. 4-2).

Fig. 4-2: Sketch of the wind tunnel flow control.

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By opening the inlet valve or closing the bypass valve, the mass flow can be increased inside the test section. Closing the outlet valve has the effect of increasing the pressure level and decreasing the mass flow. As a result, a long and sensitive set up of different valves is necessary to adjust both the inlet Mach number and the Reynolds number in the wind tunnel channel. In order to compensate for the pressure losses in the different pipes between the compressor and the exhaust, a fan sucks the air downstream of the test section out to the atmosphere. As a result, the pressure level can be below atmosphere to increase the mass flow.

The wind tunnel VM100 is 1.6m long and is located just after a settling chamber. A lateral section of the wind tunnel is shown in Fig. 4-3. The airflow is accelerated in a symmetrical contraction just before entering in the test section (Fig. 4-4), which was designed with three optical accesses at the top and both sides that are closed by Plexiglas windows. The test section is 120mm height and 100mm width.

Fig. 4-3: Lateral section of the wind tunnel.

The airflow inside the wind tunnel can be set at different operating conditions characterized by different inlet and outlet isentropic Mach numbers, Reynolds numbers and reduced frequencies. These parameters are constant during the experiments and are used to define the different operations points of the various experimental campaigns.

Fig. 4-4: Test section.

test section Flow

Inlet

Outlet

test object

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4.2 The flexible generic models

The test section was equipped with a 2D bump in order to create a contraction of the channel. A shock wave is then expected to occur and interact with the incoming boundary layer. Andrinopoulos et al [2008] designed a new flexible model in aluminium (Fig. 4-5) and performed a finite element analysis to simulate the response of the new bump in order to ensure that it can reach frequencies up to 300Hz while remaining in the first bending mode. Indeed, the goal is that the flexible model undergoes controlled forced oscillations with amplitude of 0.5mm for a frequencies range from 0Hz to 300Hz with maintaining the first mode shape. The new bump was designed and manufactured with the same outer dimensions and shape than the ones used in the previous campaigns. The axial chord is defined as the length of the model that is deforming, i.e. 120mm long, and note that it corresponds to the channel height as well.

Fig. 4-5: Flexible generic models (top): polyurethane bump (left) and aluminium bump (right) and its schematic representation (bottom).

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The different bumps have been manufactured with different designs and materials. Their mechanical properties are listed in Table 4-1 following remarks:

− steel was used for the bearing plates for both the polyurethane and the aluminium bump.

− Titanium was only used for the actuator casing of the polyurethane bump. The actuator casing for the second bump was in aluminium.

PARAMETERS

Young’s modulus E [MPa]

Poisson’s ratio ν

shear modulus G [MPa]

density, ρ [kg/m²]

MATERIALS

Polyurethane 36.00 0.49 12.0810 1030

Titanium 1.00e5 0.36 3.6800e4 4500

Steel 20.68e5 0.29 8.0200e4 7820

Aluminium

(AI7075-T6) 7.00e4 0.34 2.6119e4 2700

Table 4-1: Mechanical properties of the bumps.

4.3 The geometry measurement system

The instantaneous dynamic geometry is measured with a traverse system using time- resolved laser triangulation principle. Fig. 4-6 shows a schematic representation of the measurement setup. Through the top optical glass window the laser beam covers the bump. A red light beam is thus projected on one point of the surface of the bump. The reflected light is then projected back and a lens is used to create an image on a plane located on a positive sensitive detector (PSD). When the distance between the bump and the laser sensor changes, that is to say when the test object is moving, the angle between the laser beam and the reflected light also changes. The traverse system is controlled by a LabView program with which both space and time steps can be entered as an input data.

The accuracy regarding the position from the traverse system is ±0.01mm. The main source of inaccuracy in such a measurement system is related to the laser spot on the beam surface in term of size. Firstly, since the laser beam goes though the top optical Plexiglas window and secondly, since the bump surface quality may introduce changes in terms of size and reflexivity. Furthermore, in order to deduce the dynamic geometry, the geometry measurement and the bump motion are synchronised in time using an incremental shaft encoder. This encoder is directly connected to the camshaft that drives the bump oscillations and gives its angular position by delivering an output reference signal of 1 pulse per revolution. Both data from the laser and the encoder were stored using the KT8000 that is a digital high-speed data acquisition system. The system features 32 channels with programmable amplifiers, 14bit A/D conversion for each channel and a maximum sampling rate for all 32 channels simultaneously of 200kHz. The sampling settings were adjusted in such a way to have a constant sampling rate equal to 200 periods for each studied frequency. The post-treatment consisted of ensemble-averaging the data from each measurement position.

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Fig. 4-6: Illustration of the laser triangulation measurement, [Allegret-Boudon, 2004].

4.4 Pressure measurements

The test facility is instrumented such that both steady state and unsteady measurements can be achieved. Steady state aims at describing the structure of the mean flow. Time- resolved pressure measurements have been performed on the oscillating bump using pressure taps and 6 Kulite fast response transducers. The signals from the sensors were acquired with the KT8000.

4.4.1 Steady state pressure measurement

The steady state pressure measurement has been carried out by using a 16-channels PSI9016 system with an accuracy of 0.04% full scale. First it consists in reaching the desired operating point and then start acquiring data in order to characterise the mean flow and latter to be able to analyse the unsteady flow field. Hence both the inlet and the outlet static pressures are respectively measured up- and downstream of the bump. P_s₁ is measured at 1.5 chords upstream and P_s₂ at 2 chords downstream of the generic model.

The total pressure P_t₁is evaluated by a total pressure probe located in the settling chamber. Fig. 4-7 illustrates the different measurement positions.

Fig. 4-7: Pressure measurements locations in the wind-tunnel.

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4.4.2 Static calibration of Kulite transducers

Calibration is the establishment of a known relation (transfer function) between the input (driving function) and the output (response function). Static calibration of fast response transducers consists in checking the linearity of the transducers, in evaluating the 2 coefficients (Eq. 4-1) that determine the transfer function between voltage V and pressureP. These 2 coefficients have to be evaluated over the full pressure range. The experimental procedure of static calibration is to measure the output voltage of each transducer for different pressure values over the full pressure range of the transducers.

V a a

P= 0 + 1× Eq. 4-1

Fig. 4-8 depicts such functions for the different sensors used (the legend specifies the references of each of them). A static calibration has been performed at six points on all transducers.

100 120 140 160 180 200

0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12

pressure [kPa]

voltage [V]

60117420 56531A64 60117403 60117411 60117415 60117437

Fig. 4-8: Static calibration of the Kulite transducers.

4.4.3 Dynamic calibration

Unsteady pressure is measured by means of capillarity tubes due to space constraints and practical reasons: the instrumentation is such that Kulite transducers are mounted at any location underneath the test object since they are very sensitive to acceleration of the model as well as temperature. The purpose is to evaluate the damping and the phase lag though pressure holes. The dynamic calibration of capillarity tubes was performed using a calibration unit [Vogt, 2001] (Fig. 4-9) and it is based on the technique of recessed- mounted pressure transducers [Vogt, 2004]. It consists of a nozzle air jet impacting on a rotating wheel with holes illustrated in Fig. 4-9. The air pressure jet and the rotating speed of the motor can be controlled and thus allows a fine adjustment over the amplitude and frequency. The signals from the sensor are treated such as to yield complex dynamic transfer properties in the frequency domain (magnitude ratio and phase) that represents an estimation of the transfer function of the pressure fluctuations through each capillarity tube. The process consists in applying a periodic fluctuating pressure on the surface of the

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instrumented bump and then measuring both the input and output signals. The dynamic calibration has been performed in the range from 2Hz to 200kHz with respect to the bump excitation frequency of 500Hz. Fig. 4-10 shows the transfer properties for the 51 taps though the amplitude ratio defined as the measured pressure amplitude over the pressure amplitude of reference.

Fig. 4-9: Dynamic calibration unit (top right), the fluctuating pressure generator (top left) and the calibration head (bottom).

0 500 1000 1500 2000

0 0.5 1 1.5

amplitude ratio [-]

0 500 1000 1500 2000

0 10 20 30

frequency [Hz]

phase [°]

Fig. 4-10: Dynamic transfer properties: magnitude ratio (up) and phase (down).

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Fig. 4-11 shows different transfer characteristics in the range of interest (0-350Hz) for 5 axial positions corresponding to the taps 10, 20, 30, 40 and 50. One can notice that the amplitude ratio is slightly lower in the fore and aft parts of the bump (tap 10 and tap 50 respectively) that is to say the attenuation decreases.

0 50 100 150 200 250 300 350

0.5 1 1.5

amplitude ratio [-]

0 50 100 150 200 250 300 350

0 5 10

frequency [Hz]

phase [°]

tap10 tap20 tap30 tap40 tap50

Fig. 4-11: Transfer characteristic at 5 different axial positions.

An amplitude ratio of 1 means that the measured amplitude and the amplitude at the tap are equal. An amplitude ratio higher than 1 indicates an amplitude magnification. Finally, an amplitude ratio smaller than 1 denotes an amplitude damping: the measured amplitude is smaller than the amplitude at the tap. The amplitude ratio depicts two peaks at about 80Hz and 270Hz that typically represent a resonance phenomenon. The two peaks do appear at the resonance frequency of the system due to waves. The next sub-section focuses on it by studying the influence of capillarity tube length.

4.4.4 About quality

Several tests were performed in order to evaluate the quality of the dynamic calibration.

Influence of the length of the capillarity tube

Fig. 4-12 presents the amplitude ratio and the phase for two different length of the capillarity tube: the standard one, representing the length of each tube, and a longer one.

The amplitude ratio plot shows 3 increases that correspond to acoustic resonance. The setup can be modelled as Helmholtz resonator with the below frequency:

LVc

a d f 2 4

2π

=π Eq. 4-2

The sensor cavity volume remaining constant, if the tube length increases the resonance frequency decreases as it is showed in Fig. 4-12. As a result a less tube length induces better pressure measurements. For a given diameter, a longer tube produces smaller resonance peaks at lower resonance frequency.

Experimental Campaign on a Generic Model for Fluid-Structure Interaction Studies