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

Transcription

1 Report Number: EKV / 725 Experimental Campaign on a Generic Model for Fluid-Structure Interaction Studies Hakim Ferria Master of Science Thesis Energy Technology 27 KTH School of Energy and Environmental Technology Heat and Power Technology SE-1 44 STOCKHOLM

2 Master of Science Thesis / Hakim Ferria Page 2 Master of Science Thesis EGI 28: 725 Experimental Campaign on a Generic Model for Fluid-Structure Interaction Studies Hakim Ferria Approved 28-4 Examiner Prof. Torsten Fransson Commissioner Supervisor Nikos Andrinopoulos Contact person

3 Master of Science Thesis / Hakim Ferria Page 3 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 5Hz. 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 25Hz by remaining in the first bending mode shape. The one in polyurethane can even reach frequency up to 35Hz; however, amplitude is higher than the theoretical one fixed to.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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5 Master of Science Thesis / Hakim Ferria Page 5 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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7 Master of Science Thesis / Hakim Ferria Page 7 TABLE OF CONTENTS ABSTRACT... 3 ACKNOWLEDGEMENTS... 5 TABLE OF CONTENTS... 7 LIST OF FIGURES... 9 LIST OF TABLES NOMENCLATURE INTRODUCTION BACKGROUND AEROELASTICITY DYNAMIC AEROELASTICITY AND FLUTTER PHENOMENON REDUCED FREQUENCIES ACOUSTIC BLOCKAGE EXPERIMENTAL INVESTIGATIONS Non-oscillating model (rigid model) D oscillating non-rigid model (flexible model) OBJECTIVES AND METHOD OF ATTACK DESCRIPTION OF THE TEST FACILITY AND THE MEASUREMENT TECHNIQUES OVERALL FACILITY THE FLEXIBLE GENERIC MODELS THE GEOMETRY MEASUREMENT SYSTEM PRESSURE MEASUREMENTS Steady state pressure measurement Static calibration of Kulite transducers Dynamic calibration About quality Conclusion DYNAMIC GEOMETRY POLYURETHANE BUMP Sinusoidal signal Dynamic geometry results ALUMINIUM BUMP Sinusoidal signal Finite element analysis Ping test Checking of two dimensional shape Rotational speed of the motor Repeatability Dynamic results CONCLUSION STEADY STATE RESULTS UNSTEADY STATE RESULTS EXPERIMENTAL RESULTS... 63

8 Master of Science Thesis / Hakim Ferria Page SOME ELEMENTS FOR FUTURE INVESTIGATIONS CONCLUSION AND PERSPECTIVES REFERENCES... 77

9 Master of Science Thesis / Hakim Ferria Page 9 LIST OF FIGURES Fig. 2-1: Collar s aeroelastic triangle Fig. 2-2: Operating map of a multistage compressor Fig. 2-3: Classical flutter illustrated by force phase angle Φ Fig. 2-4: Graphical interpretation of the reduced frequency Fig. 2-5: The VM1 test section, dimensions in mm, [Bron, 24] Fig. 2-6: Flow configuration over the 3D bump, [Bron, 24] Fig. 2-7: 3D bump, [Bron, 24] Fig. 2-8: 2D bump manufactured in aluminium, [Bron, 24] Fig. 2-9: Experimental and 2D RANS results comparison in 2D nozzle. (Same operating point, Ps 2 = 112kPa ), [Bron, 24] Fig. 2-1: Experimental, 2D RANS and 3D RANS results comparison in 2D nozzle, [Bron, 24] Fig. 2-11: Steady state weak shock structure in 2D nozzle, [Bron, 24] Fig. 2-12: Steady state strong shock structure in 2D nozzle, [Bron, 24] Fig. 2-13: Comparison between experiments, 2D RANS and 3D RANS (Shock position and Separation region location), [Bron, 24] Fig. 2-14: Experiments and 3D RANS comparison on the 3D bump, 2D plot at mid channel, P 2 = 112kPa, [Bron, 24] s Fig. 2-15: Sonic pocket and streamlines within the separated flow region, Ps 2 = 112kPa, [Bron, 24] Fig. 2-16: Experimental phase shift underneath shock location, [Bron, 24] Fig. 2-17: Section view of the mechanical actuator with prismatic cam Fig. 2-18: Composition of the flexible bump, [Allegret-Bourdon, 24] Fig. 2-19: View of the overall test facility with optical accesses, [Allegret-Bourdon, 24] Fig. 2-2: Variation of ensemble averaged shock wave movement towards bump motion, [Allegret-Bourdon, 24] Fig. 2-21: Experimental shock motion for strong shock configuration ( Ps 2 = 16kPa ) and high perturbation amplitude ( amp = ± 2.12kPa ), [Bron, 24] Fig. 2-22: Chordwise repartition of unsteady pressure coefficient and phase lead of static pressure towards bump local deformation, [Allegret-Bourdon, 24] Fig. 3-1: From blades to bump Fig. 4-1: Overall facility at HPT Fig. 4-2: Sketch of the wind tunnel flow control Fig. 4-3: Lateral section of the wind tunnel Fig. 4-4: Test section Fig. 4-5: Flexible generic models (top): polyurethane bump (left) and aluminium bump (right) and its schematic representation (bottom) Fig. 4-6: Illustration of the laser triangulation measurement, [Allegret-Boudon, 24] Fig. 4-7: Pressure measurements locations in the wind-tunnel Fig. 4-8: Static calibration of the Kulite transducers Fig. 4-9: Dynamic calibration unit (top right), the fluctuating pressure generator (top left) and the calibration head (bottom) Fig. 4-1: Dynamic transfer properties: magnitude ratio (up) and phase (down) Fig. 4-11: Transfer characteristic at 5 different axial positions Fig. 4-12: Influence of the capillarity tube length

10 Master of Science Thesis / Hakim Ferria Page 1 Fig. 4-13: Transfer characteristic for the tap4 with 6 sensors Fig. 4-14: Influence of the pressure jet Fig. 4-15: Signal reconstruction (7Hz) Fig. 5-1: Sinusoidal shape of the oscillations (5Hz) of the polyurethane bump Fig. 5-2: Instantaneous amplitude (top) and phase (bottom) of the polyurethane bump Fig. 5-3: Sinusoidal shape of the oscillations (5Hz) of the aluminium bump Fig. 5-4: 3D mesh of the aluminium bump Fig. 5-5: First normal mode of the aluminium bump Fig. 5-6: Pin test for the aluminium bump Fig. 5-7: Positions of the laser beam for each side of the aluminium bump Fig. 5-8: Instantaneous amplitude of the aluminium bump for 2 spanwises Fig. 5-9: Checking of the constant velocity of the motor Fig. 5-1: Clockwise and counter clockwise speed of the motor Fig. 5-11: Repeatability for the laser measurement (aluminium bump 1Hz) Fig. 5-12: Repeatability for the laser measurement (aluminium bump 2Hz) Fig. 5-13: Instantaneous amplitude (top) and phase (bottom) of the aluminium bump at 5Hz, 1Hz, 25Hz, 3Hz and 32Hz Fig. 5-14: Amplitude magnification of the aluminium bump Fig. 5-15: Amplitude magnification normalized showing 3 behaviours of the bump Fig. 5-16: Schematic representations of the polyurethane bump (top) and the aluminium bump (bottom) Fig. 6-1: Steady state pressure measurement layout on the bump Fig. 6-2: Pressure in terms of Ps (a) and Cp (b) and isentropic Mach number distributions along the bump surface Fig. 6-3: Operating conditions in Bron s 2D experiments, [Bron, 24] Fig. 6-4: Steady state shock induced separation, [Bron, 24] Fig. 6-5: Particular aerodynamic points Fig. 6-6: Shock location (Schlieren and 3D NS simulation) for Ps 2 = 14kPa, [Bron, 24]. 61 Fig. 7-1: Instantaneous amplitude (a), unsteady pressure coefficient (b) and phase of unsteady pressure towards the bump motion (c) at frequencies 1Hz, 25Hz and 5Hz Fig. 7-2: Instantaneous amplitude (a), unsteady pressure coefficient (b) and phase of unsteady pressure towards the bump motion (c) at frequencies 75Hz, 1Hz and 15Hz Fig. 7-3: Instantaneous amplitude (a), unsteady pressure coefficient (b) and phase of unsteady pressure towards the bump motion (c) at frequencies 25Hz and 3Hz Fig. 7-4: Relative variations of the section (left) and relative variations of the velocity (right) Fig. 7-5: Pressure and velocity perturbations ratio at the throat Fig. 7-6: Velocity gradient (a) and coefficient G k (b) versus the reduced frequency Fig. 7-7: Module of K Fig. 7-8: Module of the shock motion amplitude and its phase Fig. 7-9: Mach number gradient... 73

11 Master of Science Thesis / Hakim Ferria Page 11 LIST OF TABLES Table 2-1: Operating conditions and reduced frequencies Table 4-1: Mechanical properties of the bumps Table 6-1: The operating conditions Table 6-2: Pressure rise location on the bump surface Table 6-3: Aerodynamic throat and shock localisations Table 7-1: Reduced frequencies of the full frequency range

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13 Master of Science Thesis / Hakim Ferria Page 13 NOMENCLATURE Latin letters a A C p C ˆ p c f k M ˆP P Q T V speed of sound theoretical amplitude of the bump oscillations steady pressure coefficient unsteady pressure coefficient blade chord frequency reduced frequency Mach number complex pressure pressure mass-flow temperature 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 3D AC CFD DFSD ECL HPT KTH KT8 OP PSD RANS SBLI Two Dimensional Three Dimensional Alternative Current Computational Fluid Dynamics Discrete Fourier Series Decomposition Ecole Centrale de Lyon Heat and Power Technology Kungliga Tekniska Högskola (Royal Institute of Technology) Kaiser Threde 8 system Operating Point Position Sensitive Detector Reynolds Averaged Navier Stokes Shock Boundary Layer Interaction

14 Master of Science Thesis / Hakim Ferria Page 14 VM1 Wind Tunnel Facility at HPT

15 Master of Science Thesis / Hakim Ferria Page 15 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 [24] and Allegret- Bourdon [24]. 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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17 Master of Science Thesis / Hakim Ferria Page 17 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). Inertial Forces RIGID-BODY AERODYNAMICS MECHANICAL VIBRATIONS DYNAMIC AEROELASTICITY Aerodynamic Forces Elastic Forces STATIC AEROELASTICITY 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).

18 Master of Science Thesis / Hakim Ferria Page 18 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.

19 Master of Science Thesis / Hakim Ferria Page 19 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.

20 Master of Science Thesis / Hakim Ferria Page 2 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 δ h t involves phase lag between and 18 degrees. δh Energy = F(t).dδh = F(t). dt t Eq. 2-1 φ amplitude amplitude Energy (φ=) time t δh/ t F(t) time t 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.33 for bending and 1.6 for torsion in order to avoid stall flutter [Armstrong et al., 196]. The reduced frequency is defined, based on the full chord, by the following equation (Eq. 2-2). Ts c k = = 2π f Eq. 2-2 T v u It gives a measure of unsteadiness through a correlation between the axial flow velocity v ax, 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, T s 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 ax

21 Master of Science Thesis / Hakim Ferria Page 21 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): k = π c Eq. 2-3 λ 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. [24] 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

22 Master of Science Thesis / Hakim Ferria Page 22 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 [24]. 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 [24] and Allegret-Bourdon [24] 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 Non-oscillating model (rigid model) Bron [24] 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 numerically 1 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 [24].

23 Master of Science Thesis / Hakim Ferria Page 23 Fig. 2-5: The VM1 test section, dimensions in mm, [Bron, 24]. 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, rotorstator 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 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.

24 Master of Science Thesis / Hakim Ferria Page 24 Fig. 2-6: Flow configuration over the 3D bump, [Bron, 24]. 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, 24]. Fig. 2-8: 2D bump manufactured in aluminium, [Bron, 24]. Comparison between experiments, 2D RANS and 3D RANS calculations on the 2D bump shows fairly good agreement for weak shocks (Fig. 2-1) 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 twodimensionality of the flow. Fig. 2-1 shows that 3D RANS calculations gives better results for the same operating point. Fig. 2-11, Fig and Fig 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

25 Master of Science Thesis / Hakim Ferria Page 25 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 2 = 112kPa ), [Bron, 24]. s Fig. 2-1: Experimental, 2D RANS and 3D RANS results comparison in 2D nozzle, [Bron, 24]. Schlieren ( P 2 = 112kPa ) 3D RANS ( P 2 = 112kPa ) 2D RANS ( P 2 = 116kPa ) s s Fig. 2-11: Steady state weak shock structure in 2D nozzle, [Bron, 24]. s

26 Master of Science Thesis / Hakim Ferria Page 26 Schlieren ( P 2 = 16kPa ) 3D RANS ( P 2 = 18kPa ) 2D RANS ( P 2 = 11kPa ) s Fig. 2-12: Steady state strong shock structure in 2D nozzle, [Bron, 24]. s s Shock position Separation region location Fig. 2-13: Comparison between experiments, 2D RANS and 3D RANS (Shock position and Separation region location), [Bron, 24]. Fig 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 2 = 112kPa, [Bron, 24]. s

27 Master of Science Thesis / Hakim Ferria Page 27 Fig. 2-15: Sonic pocket and streamlines within the separated flow region, Ps 2 = 112kPa, [Bron, 24]. 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.

28 Master of Science Thesis / Hakim Ferria Page 28 Fig. 2-16: Experimental phase shift underneath shock location, [Bron, 24] D 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 [24]. 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, 21] such as it allows oscillations in a controlled way. Fig 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 1, rpm produces an oscillating frequency of 5 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 29mm long and is made for oscillating along 12mm that defines the chord. A view of the overall facility is presented in Fig

29 Master of Science Thesis / Hakim Ferria Page 29 Fig. 2-18: Composition of the flexible bump, [Allegret-Bourdon, 24]. Fig. 2-19: View of the overall test facility with optical accesses, [Allegret-Bourdon, 24]. The investigations by Allegret-Bourdon [24] 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.3. Parameters Symbols Units Values P kpa 159 Upstream stagnation pressure t1 Upstream stagnation temperature t1 Upstream static pressure s1 Downstream static pressure s2 Inlet isentropic Mach number iso1 Outlet isentropic Mach number iso2 T K 35 P kpa 116 P kpa 14 M -.69 M -.8 Absolute frequencies f Hz 1, 25, 5, 75, 15, 2 Reduced frequencies k -.15,.37,.74,.11,.221,.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=.15) is characterized by a phase difference of 135º relatively to the quasi-static case (Fig. 2-2). Furthermore, it is shown that the amplitude of the shock wave motion increases with the frequency until about k=.88; then it remains almost constant whereas Bron presented results indicating clearly the amplitude of the shock motion decreases with the frequency (Fig. 2-21).

30 Master of Science Thesis / Hakim Ferria Page 3 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 18º 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. 2-2: Variation of ensemble averaged shock wave movement towards bump motion, [Allegret-Bourdon, 24]. Fig. 2-21: Experimental shock motion for strong shock configuration ( Ps 2 = 16kPa ) and high perturbation amplitude ( amp = ± 2.12kPa ), [Bron, 24].

31 Master of Science Thesis / Hakim Ferria Page 31 Fig. 2-22: Chordwise repartition of unsteady pressure coefficient and phase lead of static pressure towards bump local deformation, [Allegret-Bourdon, 24].

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33 Master of Science Thesis / Hakim Ferria Page 33 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. [28] with which both high amplitude (.5mm) and high frequencies (3Hz) 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.

34 Master of Science Thesis / Hakim Ferria Page 34 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.

35 Master of Science Thesis / Hakim Ferria Page 35 4 DESCRIPTION OF THE TEST FACILITY AND THE MEASUREMENT TECHNIQUES 4.1 Overall facility The VM1 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 33K. A set of valves allows redirecting the flow either in a test turbine or in exchangeable wind tunnel facility, as depicted in Fig Fig. 4-1: Overall facility at HPT. The air exhaust temperature of the compressor is approximately 453K and can be adjusted down to 33K 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.

36 Master of Science Thesis / Hakim Ferria Page 36 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 VM1 is 1.6m long and is located just after a settling chamber. A lateral section of the wind tunnel is shown in Fig 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 12mm height and 1mm width. Outlet Inlet Flow test object test section 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.

37 Master of Science Thesis / Hakim Ferria Page 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 [28] 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 3Hz while remaining in the first bending mode. Indeed, the goal is that the flexible model undergoes controlled forced oscillations with amplitude of.5mm for a frequencies range from Hz to 3Hz 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. 12mm 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).

38 Master of Science Thesis / Hakim Ferria Page 38 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. MATERIALS Young s modulus E [MPa] PARAMETERS Poisson s ratio ν shear modulus G [MPa] density, ρ [kg/m 2 ] Polyurethane Titanium 1.e e4 45 Steel 2.68e e4 782 Aluminium (AI775-T6) 7.e e4 27 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 timeresolved 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 ±.1mm. 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 KT8 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 2kHz. The sampling settings were adjusted in such a way to have a constant sampling rate equal to 2 periods for each studied frequency. The post-treatment consisted of ensemble-averaging the data from each measurement position.

39 Master of Science Thesis / Hakim Ferria Page 39 Fig. 4-6: Illustration of the laser triangulation measurement, [Allegret-Boudon, 24]. 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. Timeresolved 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 KT Steady state pressure measurement The steady state pressure measurement has been carried out by using a 16-channels PSI916 system with an accuracy of.4% 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 Pt 1 is 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.

40 Master of Science Thesis / Hakim Ferria Page 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 pressure P. 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. P = a + a1 V 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. voltage [V] A pressure [kpa] Fig. 4-8: Static calibration of the Kulite transducers 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, 21] (Fig. 4-9) and it is based on the technique of recessedmounted pressure transducers [Vogt, 24]. It consists of a nozzle air jet impacting on a rotating wheel with holes illustrated in Fig 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

41 Master of Science Thesis / Hakim Ferria Page 41 instrumented bump and then measuring both the input and output signals. The dynamic calibration has been performed in the range from 2Hz to 2kHz with respect to the bump excitation frequency of 5Hz. Fig. 4-1 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). amplitude ratio [-] phase [ ] frequency [Hz] Fig. 4-1: Dynamic transfer properties: magnitude ratio (up) and phase (down).

42 Master of Science Thesis / Hakim Ferria Page 42 Fig shows different transfer characteristics in the range of interest (-35Hz) for 5 axial positions corresponding to the taps 1, 2, 3, 4 and 5. One can notice that the amplitude ratio is slightly lower in the fore and aft parts of the bump (tap 1 and tap 5 respectively) that is to say the attenuation decreases. amplitude ratio [-] phase [ ] 1 5 tap1 tap2 tap3 tap4 tap frequency [Hz] 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 8Hz and 27Hz 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 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 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: f π d 2 π = a Eq LV c The sensor cavity volume remaining constant, if the tube length increases the resonance frequency decreases as it is showed in Fig 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.

43 Master of Science Thesis / Hakim Ferria Page 43 Repeatability amplitude ratio [-] phase [ ] TAP 23 "standard" length longer length frequency [Hz] Fig. 4-12: Influence of the capillarity tube length. The repeatability consists in achieving the same successive measurements under the same conditions. All sensors were hence used for the same tap (tap4) in order to check whether an influence of the sensors exists. Fig presents the amplitude ratio and the phase for each transducer at the same tap and shows a good agreement. Others tests should be performed still from a repeatability point of view; for instance, to use the same transducer for different taps. amplitude ratio [-] phase [ ] A frequency [Hz] Fig. 4-13: Transfer characteristic for the tap4 with 6 sensors. Influence of the pressure jet value The amplitude of the pressure perturbation can be adjusted. In Fig the transfer characteristic for 3 different values of this amplitude for the tap5 is plotted. It shows a good agreement with no dependence with the amplitude from the calibration unit.

44 Master of Science Thesis / Hakim Ferria Page 44 amplitude ratio [-] TAP 5 2kPa 4kPa 6kPa phase [ ] frequency [Hz] Fig. 4-14: Influence of the pressure jet. Inverse process This sub-section aims at reconstructing the pressure signal. The signal at the tap is thus reconstructed from the sensor signal by using the inverse transfer function as it is depicted in Fig It shows a very good agreement between the reference and the reconstructed signals. Higher harmonics in the reconstructed signal do not appear because of the lowpass filter behaviour of the reconstruction process. 1.5 x reference signal reconstructed signal tap signal pressure amplitude time Fig. 4-15: Signal reconstruction (7Hz) Conclusion The technique used for the unsteady pressure measurement shall give good results regarding the calibrations and the different check that have been performed. Rather than putting transducers at the desired location this technique was used in order to keep the sensors far from strong efforts like acceleration or high temperature. Moreover it thus allows the use of the same Kulite transducers for measuring unsteady pressure at different locations.

45 Master of Science Thesis / Hakim Ferria Page 45 Results have shown similar trends for all the pressure taps except for the taps 11 and 47 that exhibit a higher damping but still having the same behaviour (see Fig. 4-1). The amplitude ratio strongly depends on the perturbation frequency; however, in the targeted frequency range the damping do remain above.5 meaning that the capillarity tube damps the measured pressure signals until 5% (at worst) of the reference signal. Concerning the phase, results have shown an almost linear variation with the perturbation frequency. In the present work, only one operating point has been investigated. It is determined by setting up the inlet stagnation pressure and temperature, and the outlet static pressure as well. The OP is reached by controlling the pressure level and mass flow within the section by the mean of different valves that do work such that a slight change in the outlet valve position induces a large change in the outlet static pressure. As a result, to achieve the desired OP is rather difficult; moreover, the accuracy of each above measurements has also to be taken into account in the setting of the OP.

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47 Master of Science Thesis / Hakim Ferria Page 47 5 DYNAMIC GEOMETRY In this chapter dynamic considerations for both the polyurethane and the aluminium bumps are described. As mentioned previously the dynamic geometry of the first model has been performed by Allegret-Bourdon [24] and will be carried out again in order to check whether the setup well run. Then the mechanical characteristics of the new aluminium bump are presented. 5.1 Polyurethane bump Sinusoidal signal The bump has been designed in such a way to have a sinusoidal shape regarding the deformation with amplitude at the top of.5mm. It has been moulded with polyurethane material by vulcanisation over a metal bed. Knowing that the polyurethane is a material of which mechanical properties change with time especially the Young s modulus a first examination of the oscillation shape is presented in Fig Raw signal - Expected frequency: 5Hz.3 Fourier Transform - Expected frequency: 5Hz 4.25 amplitude [V] amplitude [V] time [s] frequency [Hz] Fig. 5-1: Sinusoidal shape of the oscillations (5Hz) of the polyurethane bump. After setting the desired vibration frequency, the laser beam is positioned on the top of the bump at one fixed point and the data acquisition can start by using the KT8. A Fourier transform is then carried by post-treating the raw from the unsteady data acquisition, system. Raw signal and its Fourier transform are here exposed for a frequency of 5Hz. Other frequencies have been carried out and for all of them good sinusoidal shapes have been found Dynamic geometry results The dynamic geometry is measured along the chord during the oscillation of the bump for the frequency range [1Hz-35Hz]. The results, amplitude and phase, are plotted in Fig. 5-2 for 5Hz, 1Hz, 25Hz, 32Hz and 35Hz. The phase is calculated with the mean of an encoder that can deliver both 1 pulse and 15 pulses signal per revolution; it is connected via the camshaft and thus it is supposed that the phase is equal to zero at the actuator position. Hence the phase is taken to zero at that location. Firstly one can notice that the targeted.5mm-amplitude of the oscillation is only reached for a frequency above

48 Master of Science Thesis / Hakim Ferria Page 48 32Hz. Until 2Hz, the amplitudes stay at.4mm. Furthermore it appears a symmetric pattern with respect to the actuator position. The measured shape corresponds to a first bending mode according to the shape of amplitude, i.e. no inflection points, and the shape of the phase as well. The strong variations of the phase below 8mm and above about 18mm do not make any sense since the corresponding amplitudes are small. amplitude [mm] position of the actuator x [mm] phase [ ] position of the actuator x [mm] Fig. 5-2: Instantaneous amplitude (top) and phase (bottom) of the polyurethane bump. 5.2 Aluminium bump Sinusoidal signal

49 Master of Science Thesis / Hakim Ferria Page 49 As previously, it is interesting to check the good shape of the oscillation. Fig. 5-3 shows both the raw signal and its Fourier transform at 5Hz and depicts good results. Raw signal - Expected frequency: 5Hz.1 Fourier Transform - Expected frequency: 5Hz amplitude [V] amplitude [V] time [s] frequency [Hz] Fig. 5-3: Sinusoidal shape of the oscillations (5Hz) of the aluminium bump Finite element analysis A 3D finite element analysis has been performed on the bump in order to obtain the first natural frequency of the model and thus to be able to compare with further tests. This analysis has been performed with the commercial software I-Deas 12. Fig. 5-4 shows the 3D mesh (25646 nodes, 2419 elements) with the appropriate boundary conditions that is to say, as the actual model is fixed on the test section, that all degrees of freedom are restrained in all directions on the bottom surface and on each side as well. Fig. 5-4: 3D mesh of the aluminium bump. The first natural frequency appears at 29Hz. It corresponds to the first bending mode as depicted in Fig The results confirm the ones got by Andrinopoulos [28] both in 3D and 2D configurations. The second natural frequency (torsion mode) appears at 38Hz and the third one (second bending mode) at 521Hz.

50 Master of Science Thesis / Hakim Ferria Page 5 Fig. 5-5: First normal mode of the aluminium bump Ping test The ping test consists of exciting the natural frequencies in an experimental way by hitting the surface of the bump. The way to reach such data is the following: the laser signal is projected at one steady point located here in the aft part of the bump, the bump surface is then hit close to its highest point and in the same time readings from the laser are stored using the data acquisition system KT8 with high sampling frequency. Applying the Fourier transform on the raw signal the two first one harmonic have been found equal to 195Hz and 29Hz respectively (Fig. 5-6) amplitude [mm] frequency [Hz] Fig. 5-6: Pin test for the aluminium bump. The actual natural frequency of the all setup shall be modified whether bearing plates and actuator are considered in.

51 Master of Science Thesis / Hakim Ferria Page Checking of two dimensional shape The bump is a 2D model. All the measurements, related to the geometry and the use of the laser, do carry out at position called spanwise1; it is here the standard position. This sub-section aims at verifying whether the bump presents a well 2D dynamic shape by performing measures at location called spanwise2 as described in Fig The results, plotted in Fig. 5-8 and representing the amplitude of the bump movement in function of the position in the spanwise direction have not shown a good agreement. The shapes seem to be the same but shifted mainly in the fore part of the bump where it has been found a difference of.19mm that represents about 38% of the theoretical amplitude (.5mm). The best fitting occurs close to the actuator position that makes sense. Fig. 5-7: Positions of the laser beam for each side of the aluminium bump. magnitude [mm] spanwise 1 -- spanwise 2 1Hz 2Hz 3Hz 1Hz 2Hz 3Hz x [mm] Fig. 5-8: Instantaneous amplitude of the aluminium bump for 2 spanwises Rotational speed of the motor The camshaft that allows the bump to oscillate is driven by an AC servomotor. The power is transmitted from the motor to the actuator by a system of belts and pulleys. In this sub-

52 Master of Science Thesis / Hakim Ferria Page 52 section the constant velocity of the motor is checked by using the encoder signal. Fig. 5-9 shows the deviation from the constant velocity with respect to the frequency. At 5Hz a deviation of 6.5% from the constant speed assumption is observed. For low frequencies, below 3Hz, the assumption of constant speed has to be discussed. To explain why such a variation occur a qualitative argument is proposed. Force is the result of the product of a mass with acceleration, i.e. the time derivative of the speed, In order to achieve the.5mm amplitude oscillation of the bump, a minimal force is needed. The force is here not strong enough to oblige the bump to oscillate. The bump stiffness acts as a break regarding the oscillation mechanism which is more controlled by the bump stiffness than the motor speed. 7 Deviation from the constant velocity [%] frequency [Hz] Fig. 5-9: Checking of the constant velocity of the motor. The direction of rotation, i.e. clockwise or counter clockwise, can be set up in the software that controls the speed of the motor. Fig. 5-1 presents for three different frequencies the amplitude of the oscillations along the bump in clockwise and counter clockwise configurations. It shows a good agreement except for the frequency of 3Hz in the aft part of the bump behind the actuator where a maximum difference of.25mm has been found that represents 5% of the theoretical amplitude (.5mm). amplitude [mm] Hz 2Hz 3Hz ClockWise -- CounterClockWise x [mm] Fig. 5-1: Clockwise and counter clockwise speed of the motor.

53 Master of Science Thesis / Hakim Ferria Page Repeatability The measurements for checking repeatability of the laser measurements for both 1Hz and 2Hz are plotted in Fig and Fig show very good agreement. Expected Frequency 1Hz Expected Frequency 2Hz.5.5 amplitude [mm] amplitude [mm] x [mm] Fig. 5-11: Repeatability for the laser measurement (aluminium bump 1Hz) x [mm] Fig. 5-12: Repeatability for the laser measurement (aluminium bump 2Hz) Dynamic results The dynamic geometry is presented in Fig where amplitude and phase are plotted. It shows that for frequencies below 22Hz the bump remains in the first bending mode shape with respect to the target design (neither inflection point nor phase shift meaning second bending mode shape). However for frequencies above 24Hz the amplitude in the aft part of the bump increases gradually until reaching very high value at 32Hz almost.8mm that represents 16% of the theoretical amplitude (.5mm). The value of 32Hz has not been exceeded as the amplitude in the aft part increases exponentially that could lead to fatigue failure right behind the actuator. For having a view of how each point on the bump behaves regarding the oscillation frequency, the amplitude magnification has been plotted in Fig Each curve corresponds to one point on the bump surface from x=42mm to x=252mm that represents the traverse along the laser measurement. First in the vicinity of the actuator (located at x=122mm) the amplitude remains almost constant and equals to the theoretical one. Then the aft part of the bump has such a shape probably due to its length regarding the fore part that is shorter. Furthermore according to the results from the finite element analysis (a torsion mode was found at 38Hz), such a behaviour denotes a bump motion that combines both bending and torsion modes.

54 Master of Science Thesis / Hakim Ferria Page position of the actuator amplitude [mm] x [mm] phase [ ] position of the actuator x [mm] Fig. 5-13: Instantaneous amplitude (top) and phase (bottom) of the aluminium bump at 5Hz, 1Hz, 25Hz, 3Hz and 32Hz.

55 Master of Science Thesis / Hakim Ferria Page 55 amplitude [mm] Amplitude magnification amplitude [mm] Amplitude magnification frequency [Hz] (a) Amplitude magnification from the beginning to the actuator position frequency [Hz] (b) Amplitude magnification of the aft part. Fig. 5-14: Amplitude magnification of the aluminium bump. The amplitude magnification plots show different trends depending on the position. Upand downstream the actuator position the amplitude decreases and increases respectively with increased frequency. Fig focuses on three regions: a fore position located at x=52mm, the actuator position (x=122mm) and an aft position (x=192mm). The amplitudes presented are relative to the amplitude of each point at 5Hz. The amplitude magnification in the aft part of the bump reveals typical resonance behaviour at a frequency that is different from the natural ones as the experimental configuration do not refer to a freevibration but a controlled forced vibration. 2 amplitude normalized [-] fore part actuator position aft part frequency [Hz] Fig. 5-15: Amplitude magnification normalized showing 3 behaviours of the bump.

56 Master of Science Thesis / Hakim Ferria Page Conclusion The mechanical behaviour is highly required to achieve the aeroelastic behaviour of the system. Two different bumps have been studied with identical shapes but different materials and hence different properties. The geometric goal is the same; however the shapes that have been established are totally distinct. The mechanical study shows that the actuator plays an important role regarding the mechanical behaviour of the bump. The overall bump can be modelled as two beams that are linked with each other via the actuator which has to be seen as an inflexible solid with respect to both the fore and the aft part of the bump: The shape of amplitude for the aluminium bump could be explained by the fact that the aft part of the bump modelled as a beam is longer than the fore part. Hence it implies a higher flexibility. The shape of amplitude for the polyurethane bump that is symmetric regarding the actuator position could be explained by the fact that the flexibility is the same in each side of the actuator position. That flexibility of the aft part is not so much different from the fore part in this case compared to the aluminium bump because of the size of the slot as depicted in Fig Fig. 5-16: Schematic representations of the polyurethane bump (top) and the aluminium bump (bottom).

57 Master of Science Thesis / Hakim Ferria Page 57 6 STEADY STATE RESULTS All the results regarding the pressure measurements were carried out with a second version of the polyurethane bump. Although these two bumps are in theory strictly identical, it should be noted that the dynamic geometry on that second bump was not measured. This second bump was instrumented with Kulite transducers at discrete locations corresponding to 51 taps at midspan along the bump (Fig. 6-1): 13 taps were only used for the steady static pressure (taps 1, 2, 7, 13, 17, 22, 27, 32, 37, 42, 45, 47 and 51), 48 taps for the unsteady static pressure, from tap 3 to tap pressure taps steady measurement 12 width y [mm] tap 1 tap length x [mm] Fig. 6-1: Steady state pressure measurement layout on the bump. The operating point is reached by adjusting the pressure level within the test section with the different valves. The operating conditions, obtained by averaging the flow conditions, are defined in Table 6-1. The isentropic Mach number is calculated from the measured pressure values, it is based on the ratio between stagnation and static pressures as given by Eq Parameters Symbols Units Values inlet stagnation pressure P t1 Pa inlet stagnation temperature T t1 K 36 inlet static pressure P s1 Pa outlet static pressure P s2 Pa 1436 inlet isentropic Mach number M iso outlet isentropic Mach number M iso mass flow Q kg/s 3.83 Table 6-1: The operating conditions.

58 Master of Science Thesis / Hakim Ferria Page γ 1 2 P γ t M 1 1 iso = Eq. 6-1 γ Ps The steady state is highly necessary to analyse the unsteady results by superimposing them. The steady flow field has thus to be described as well as possible. In that purpose comparisons will be done with respect to previous studies [Bron, 24] in order to have a better appreciation on the shock wave position as only pressure measurements (i.e. no visualization) have been done in the current work. The defined OP is such that it produces a shock wave over the bump. Fig. 6-2 shows the static pressure and the isentropic Mach number distributions at mid-channel along the model as well as the steady pressure coefficient defined by Eq. 6-2; the inlet section is here considered as the reference. Data from Bron s experiment base line [24] are also displayed (Fig. 6-2) whose OP is defined in Fig We focus on the case of the outlet static pressure value of 14kPa (highlighted with red box). Even though the operating conditions are not in line with each other, the results collapse rather well. Note the following differences between the two configurations: Concerning the total inlet static pressure, there is a difference of 1.215kPa. With such a difference, the same trend is still observed. The inlet isentropic Mach number is higher in Bron s experiment. The mass flow and the temperature are higher in our experiment. C p = P Ps P t, ref s, ref Eq. 6-2 Steady static pressure distribution At this operating point a sonic pocket appears and a shock wave develops in the divergent-convex part of the nozzle. All the presented values were measured on the bump surface that is to say underneath the turbulent boundary layer. A pressure rise can be observed over the bump that seems more extended in our experiment than in Bron s one (see Table 6-2). This is due to the resolution of the steady pressure measurement stations distribution. Except from observing the boundary layer is rather thick given the strong shock configuration, it is erroneous to assume that the boundary layer is thicker for our OP if we compare with [Bron, 24]. Experiment Pressure rise start Pressure rise end Pressure rise Length Bron x=136mm x=146mm x=1mm Ferria x=127mm x=15mm x=23mm Table 6-2: Pressure rise location on the bump surface. The pressure rise length gives information first about the boundary layer thickness and second about the real shock location. This boundary layer acts as a diffuser; as a result the strong discontinuity related to the shock spreads out over a larger area. The shock position is thus considered as the pressure rise start point.

59 Master of Science Thesis / Hakim Ferria Page bump shape Ferria Bron pressure [kpa] x [mm] M iso (a).5 bump shape Ferria Bron Cp [-] M iso (b) x [mm] Fig. 6-2: Pressure in terms of Ps (a) and Cp (b) and isentropic Mach number distributions along the bump surface..5 Experiment Aerodynamic throat Shock location (mm) (mm) Bron x=1 x=146 Ferria x= x 15 Table 6-3: Aerodynamic throat and shock localisations. Isentropic Mach number The isentropic Mach number displayed in Fig. 6-2 decreases until 25% of the measurement field. Such a trend is due to the concave surface of the model in subsonic flow. Then it reaches a maximum value equal to about 1.33 and located at about 43% (the current resolution is not high enough for strongly concluding about the different areas). Then it decreases brutally in the divergent part. There exists a supersonic area that

60 Master of Science Thesis / Hakim Ferria Page 6 represents about 52.5% of the axial chord (from x=98mm to x=161mm). According to the isentropic Mach number distribution, the shock is located downstream the location given by the steady static pressure. The reader has indeed to keep in mind that the isentropic Mach number is calculated with the isentropic formula based on the static pressure and the isentropic hypothesis assumes the stagnation pressure as constant that is incorrect for transonic flows with strong wave. Downstream the shock, the isentropic Mach number is slightly higher in our experiment than in Bron s one. The flow is thus more accelerated meaning that the section is smaller. The boundary may finally be slightly thicker right behind the shock. Moreover as stated in the previous section, the measurements were performed on the bump surface where the pressure rise is diffused within the boundary layer. It is even more difficult to conclude on the exact location of the shock. The locations of the separation and the reattachment points as well as the pressure rise region from [Bron, 24] are plotted in Fig Note the difference with respect to the axial coordinate: the reference in Bron [24] is such that the zero is taken 7mm downstream of the bump start. Fig. 6-4 shows that the pressure rise start is located at about 65mm that corresponds in our experiments to 135mm. Moreover the separation flow starts from about 7mm until 12mm representing a 5mm-separated-region. Regarding our experiment, the relation is such that the separation and reattachment points are at 14mm and 19mm respectively. Fig. 6-5 summarises the aerodynamic particular points of interest that is to say the sonic point, the pressure rise start, the pressure rise end and the shock position. Fig. 6-3: Operating conditions in Bron s 2D experiments, [Bron, 24]. Fig. 6-4: Steady state shock induced separation, [Bron, 24]. amplitude [mm] aerodynamic throat geometric throat pressure rise start shock position pressure rise end reattachment point x [mm] Fig. 6-5: Particular aerodynamic points.

61 Master of Science Thesis / Hakim Ferria Page 61 In the following chapter the same nomenclature regarding these particular aerodynamic points will be considered and plotted. Moreover according to the good consistency with Bron s steady results we will also consider the same position of the shock as in Bron s experiment. Fig. 6-6 presents both the Schlieren picture and the 3D NS simulation of the shock wave created within the test section with an outlet static pressure of 14kPa (taken from [Bron, 24]). The configuration is such that the nozzle flow is chocked: perturbations from downstream can no longer propagate upstream. The Schlieren visualisation (Fig. 6-6 a) suggests that the shocks impacts the bump surface between about x=65mm and x=71mm, whereas the 3D NS simulation (Fig. 6-6 b) gives a shock at about 78mm. (a) Schlieren visualisation (b) Isentropic Mach number at mid-channel Fig. 6-6: Shock location (Schlieren and 3D NS simulation) for P 2 = 14kPa, [Bron, 24]. s