STUDY OF SHOCK MOVEMENT AND UNSTEADY PRESSURE ON 2D GENERIC MODEL

Transcription

1 STUDY OF SHOCK MOVEMENT AND UNSTEADY PRESSURE ON D GENERIC MODEL Davy Allegret-Bourdon Chair of Heat and Power Technology Royal Institute of Technology, Stockholm, Sweden davy@energy.kth.se Torsten H. Fransson Chair of Heat and Power Technology Royal Institute of Technology, Stockholm, Sweden fransson@energy.kth.se Abstract A flexible generic model has been developed at the Chair of Heat and Power Technology in order to perform flutter experiments in a more fundamental fashion. It is made of engineered flexible material and oscillate in a controlled way at non-uniform amplitude and variable frequencies. Time-resolved measurements of the unsteady surface pressures, the instantaneous model geometry as well as unsteady Schlieren visualizations are performed in order to study the shock wave motion and the aerodynamic load acting over this flexible generic bump. The model oscillates at reduced frequencies from. to.9 at transonic flow condition. The mode shapes of such a flexible bump strongly depends on the excitation frequency of the generic model. Schlieren pictures are obtained for an operating point characterized by an inlet Mach number of.63. Moreover, the presented results demonstrate that the phase of shock wave movement towards bump local motion shows a decreasing trend for the third bending mode shapes at reduced frequency higher than k=.7. At the pressure taps located after the shock wave formation, the phase of pressure fluctuations towards bump local motion presents the same decreasing trend. Keywords: Fluid-structure interaction, Schlieren, Long line probe, shock wave movement, Unsteady static pressure, first bending mode shape, Flexible generic model

2 Nomenclature c ax [mm] Axial chord of the generic model C p [-] Unsteady pressure coefficient, Cp = Ps P t P s. h bump D [mm] Test section width E [MPa] Young modulus f [Hz] Excitation frequency H [mm] Test section channel height y [mm] Local generic bump height y max [mm] Maximum generic bump height h bump [-] Bump bending amplitude, dimensionless with channel heigth h shock [-] Shock wave amplitude, dimensionless with bump amplitude k [-] Inlet reduced frequency based on the half chord, k = π.f.c ax/v ax M iso [-] Inlet isentropic Mach number, M iso = M iso [-] Outlet isentropic Mach number, M iso = ( ) / ( P s P t ) γ ) / ( ( P s P t ) γ P s [kpa] Local static pressure on the bump surface P s [kpa] Upstream static pressure P s [kpa] Downstream static pressure P t [kpa] Upstream stagnation pressure Q [kg/s] Mass flow Re [-] Reynolds number t [s] Instantaneous time t [-] Time dimensionless with the excitation period, t = t T T [s] Period of excitation T t [K] Stagnation temperature v ax [m/s] Axial flow velocity x [m] Bump chord wise location φ bump [Deg.] Largest phase difference of bump motion for one mode shape φ shock [Deg.] Phase lead of shock wave movement towards bump motion φ p [Deg.] Phase lead of pressure fluctuation towards bump motion. Introduction Structure oscillating phenomena occur in many industrial applications in the field of energy technology. Under certain conditions a curved shape located in an uniform flow, such as a blade, an airfoil or the surface of a nozzle, can enter into a self-excited vibration known as flutter. Under flutter condition, aerodynamic loads can rapidly increase the amplitude of vibration of a structure until its failure. Experiments on controlled vibrating models have been performed by several researchers to investigate such aerodynamic loads and observe the shock wave motion related to it. Kobayashi et al. [99] studied this relationship on an annular blade row oscillating in torsional mode with interblade phase angle. They drew the conclusion that at an inlet Mach number of.9 the shock wave movement significantly changed between the reduced frequencies of. and.36, and that after this range of reduced frequencies the unsteady force damps the blade oscillation. Fujimoto et al. [997] studied this unsteady fluid structure interaction on a transonic compressor cascade oscillating in a controlled pitching angle vibration. They noticed that although the amplitude of the shock wave displacement did not change much within the range of this experiment, the phase lag relative to the blade oscillation increases up to almost 9 as the blade oscillation reduced frequency increases to.8. Later, Hirano et al. [] performed other experimental campaigns on this transonic compressor cascade oscillating in a controlled pitching angle vibration. They conclude that the shock wave movement has a large effect on the amplitude and the phase angle of unsteady pressures on the blade surfaces; the amplitude of unsteady pressure becomes large upstream of the shock wave but decreases rapidly downstream;

3 Study of Shock Movement and Unsteady Pressure on D Generic Model 3 the phase angle across the shock wave changes largely for the surfaces facing the flow passages adjacent to the oscillating blade, the amplitude of shock wave movement increases following the increase of the reduced frequency, and the phase angle relative to the blade displacement lags almost linearly as the reduced frequency increases. In such kind of experiments, a driving system is creating an artificial oscillation of the rigid structure, whose amplitude and frequency can be controlled. The compressor blade of Lehr and Bölcs [], for example, is made oscillating in a controlled plunging mode by a hydraulic excitation system. The high-speed pitching vibrator of Hirano et al. [] is able to reach a Hz frequency of a D mode shape controlled oscillation in a linear cascade. In most of the cases, the vibrating structures are designed in metal to be close to real applications. Thus, large amplitudes of vibration at high oscillation frequencies prompt the failure of the structures. Moreover, recent research has presented a D blade harmonically driven in a 3D mode shape controlled vibration such as in Queune et al. []. To date, this kind of flutter experimental investigations have been limited to stiff models made of metal, which oscillate in a pitching mode. Rather than studying the complex geometry of a turbomachine and specific industrial applications, the here presented generic experiments are voluntarily not taking into account inertial effects, radial geometry, numerous blades or 3D aspect of the flow occurring in industrial applications. Thus a generic oscillating flexible model is studied in order to reach a better understanding of the physics of the flutter phenomenon under transonic operating conditions.. Objectives The objective is to show the variations of amplitudes and phase lead towards bump motion of both the shock wave movement and the unsteady static pressure relatively to the reduced frequencies characterizing this experimental study. 3. Description of the experimental set-up The test facility features a straight rectangular cross section. The oscillating model used in the here presented study is of D prismatic shape and has been investigated as non-vibrating in previous studies (Bron et al. [],Bron et al. [3]), from where extensive baseline data are available. In order to introduce capabilities for the planned fluid-structure tests, a flexible version of the model was built. Figure shows the way the generic model oscillates in the test section and presents the optical access offered by this test facility. The flow entering the test section can be set to different operating conditions characterized by different inlet Mach number, Reynolds number and reduced frequency (Table ). The generic model is molded of polyurethane, at defined elasticity (E=36. 6 MPa) and hardness (8 shore), by vulcanization over a steel metal bed. As shown in Figure, it includes a fully integrated mechanical actuator allowing smooth surface deformations. This oscillating mechanism actuates the flexible model (bump) in a first bending controlled mode shape. While the highest point located at 7% of the chord vibrates in a sinusoidal motion of.mm amplitude, the two edges of the chord stay fixed. A D laser sensor measures the model movement through the optical glass top window in one direction with a bandwidth of khz and a resolution of +/-.mm. Time-resolved pressure measurements are performed on the oscillating surface using pressure taps and Kulite fast response transducers. To achieve this, Teflon tubes are directly moulded in the D flexible generic model and plugged to the Kulite transducers mounted with the long line probe technique far from the oscillating measured surface (Schäffer and Miatt [98], see Table ). These fast response transducers deliver signals with delays and large damping but exempt of resonance effect. The delays, damping, tubes vibrations and tubes

4 Figure. Test facility composition and optical access. Table. Operating flow parameters. Mass flow (bar, 33K) Stagnation temperature Test section height Test section width Generic model axial chord Oscillating frequency range Isentropic Mach number at the inlet of the test section Q=.7kg/s 33K T t 33K H=mm D=mm c ax =mm Hz f Hz.6 M iso.67 (subsonic) (transonic) Reynolds number for a characteristic length of 6mm 3. 3 Re 7. 6 Reduced frequency based on the half chord for M iso =.63. k.66

5 Study of Shock Movement and Unsteady Pressure on D Generic Model Table. Long line probe measurements performed. Encoder accuracy on the position of the camshaft ±.8Deg. Inner diameter of the Teflon tubes.9mm Length of the Teflon tubes.m Number of Kulite fast response transducers Inner diameter of the long lines.3mm Length of the long lines m Amplitude of the first bending mode shape ±.mm Average maximum height of the generic model h max =mm Tested excitation frequencies range Hz f Hz Tested reduced frequency based on the half chord for M iso =.63. k.9 Figure. Cut view of the generic model (bump). elongations have been carefully calibrated. All components of this test facility are fully described in Allegret-Bourdon et al. []. The test section offers optical access from three sides (Figure ). While the instantaneous model shape is scanned using the geometry measurement system through the top window, Schlieren measurement can be performed using the access through two sides windows. A high-speed video camera produces the Schlieren videos with a sampling frequency of 8kHz.. Experimental results. Description of the operating condition In these experiments, inlet and outlet time averaged isentropic Mach numbers are set and a time averaged lambda shock wave is generated over the generic model surface at 67% (+/-%) of the bump chord. Figure 3 shows a typical shape of the shock wave created during those experiments. To define this operating condition, the stagnation pressure and the stagnation temperature of the flow are measured (P t = 9kPa at T t = 3K) at ten chords upstream and the corresponding isentropic inlet Mach number is calculated

6 6 + : M iso at bump upper position; x : M iso at bump lower position; : M iso from Bron et al. []. M iso y/h Figure 3. Schlieren picture of the shock wave created in the test section (M iso =.63, M iso =.6) and isentropic Mach number profile at upper and lower bump positions. h bump y/h x 3 k=. k=.37 k=.7 k=. k=.7 k=. k= Shock wave mean location at y/h= φ bump st stripe mode nd stripe mode 3rd stripe mode k Figure. Description of the bump oscillations for all operating flow conditions.

7 Study of Shock Movement and Unsteady Pressure on D Generic Model 7 (M iso =.63). The downstream static pressure is measured on the ground wall and allows calculation of a downstream isentropic Mach number M iso =.6 at two chords after the generic model. Figure shows the chord wise distribution of local static pressures for the same operating condition. The generic model acts as a contraction of the channel. M iso decreases until % of the chord and then increases until % of the chord where the flow speed is maximal. Then M iso decreases through the shock wave formation. Because of the manufacturing method, the pressure taps are not exactly perpendicular to the surface and thus do not measure the exact static pressure profile as well as the unsteady pressure fluctuations. Figure describes the way the generic model is oscillating. A regular repartition of the amplitudes along the bump half chords shows a maximal deformation at =.7. Due to its flexible nature, a first bending mode shape at k=. changes in a second bending mode shape at k=.7, and reaches a third bending mode shape at higher reduced frequencies. At the mean shock wave location =.67, the local geometry presents a phase towards bump top motion. This phase is Deg. at k=., Deg. at k=.37, Deg. at k=.7, -8Deg. from k=. to k=.7, -Deg. at k=. and -9Deg. at k=.9.. Schlieren pictures over one period of shock wave oscillation At this operating condition, the generic bump is controlled-oscillated in bending mode shapes at frequency between and Hz. For each oscillating frequency, the synchronized data of the bump motion, shock wave movement and static pressure fluctuations are acquired. The shock wave motion is measured at one vertical location corresponding to mm (y/h =.) over the top of the bump neutral position (it is symbolized by the white dashed arrows in Figure 3). Figure b shows successive pictures of this shock wave oscillating at Hz oscillation frequency. A reference line indicates the mean location of the shock wave (67% of the bump chord). From t = to t =., the shock wave moves through its mean position in an upstream direction. From t =. to t =.7, the shock wave moves again through its mean position in a downstream direction. Due to the sinusoidal oscillation of the bump, the shock wave stays a longer time in the two extreme positions (upstream and downstream) and crosses quickly its mean position during one period at Hz bump oscillatory frequency. Figure a shows in the same way one oscillation of the vertical part of the shock wave at Hz excitation frequency. These pictures demonstrate a movement close to be sinusoidal..3 Power spectra of pressure fluctuation, bump motion and shock wave movement Time-variant signals and corresponding power spectra of pressure fluctuations, bump top motions and shock wave movements are shown in Figure 6 for three bump oscillatory frequencies (Hz, 7Hz and Hz). Both pressure fluctuation and shock wave motion signals seem to follow the shape of the sinusoidal signal generated by the bump displacement at the oscillatory frequencies of Hz, 7Hz and Hz. At these three excitation frequencies, the pressure fluctuation and shock wave motion power spectra show the same clear fundamental harmonic. The bump top location movement power spectra contains one supplementary higher harmonic component that is not shown here. It does not exist in the power spectra of the pressure fluctuation and shock wave motion signals. It is interpreted as being linked to external mechanical vibrations coming from the oscillation drive train and the wind tunnel. All three oscillations seem to be of a sinusoidal type after ensemble averaging posttreatment.

8 8. Schlieren visualization results Figure 7 characterized the measured oscillations of the shock wave up to k=.9. The mean location of the shock stays the same for all excitation frequencies. Moreover one can notice that the amplitude of the shock wave oscillations increases slightly from. to.9. The first bending mode shape at k=. is characterized by a phase lag towards bump motion close to 3Deg., and the phases range between 3Deg. and 9Deg. for the second bending mode shape from k=.3 to k=.7. The phase decreases significantly from 7Deg. to almost Deg. at reduced frequencies higher than k=.89 for what has been considered as a third bending mode shape.. Unsteady pressure results The unsteady pressure fluctuations are measured along the bump and the corresponding unsteady pressure coefficient and phase leads towards bump motion are deduced for five chosen pressure taps. The amplitudes of the unsteady pressures fluctuations shift significantly at the reduced frequency k=. for the pressure taps located % upstream and downstream of the bump axial chord as shown in Figure 8. Moreover the unsteady pressure coefficients remain stable and range between and for the three pressure taps located within % to 8% of the bump axial chord. The phase lead towards bump motion of the static pressure fluctuations range between 9Deg. and 8Deg. for the pressure taps located before the bump max height, and between -8Deg. and 9Deg. for the pressure taps located after the max bump height. At the pressure tap located close to the shock wave mean location (67% of the bump chord) and at y/h=., the phase leads towards bump motion follow the same decreasing trend. In comparison with the shock wave motion phase variation, a global decrease in phase close to 7Deg. is observed for the pressure taps located after the shock wave. Figure. Schlieren pictures of the shock wave oscillation cycle at a) f=hz and b) f=hz perturbation frequencies.

9 Study of Shock Movement and Unsteady Pressure on D Generic Model 9 h bump x 3 geometry motion..... pressure fluctuation... f = Hz x 8 6 C p f = Hz h shock..... shock wave movement..... time (s) h bump x 3 geometry motion...3 pressure fluctuation.... f = Hz f (Hz) f = 7Hz 6 8 x 8 6 C p f = 7Hz...3 shock wave movement 6 8 h shock. f = 7Hz...3 time (s) h bump x 3 geometry motion.. pressure fluctuation 6 8 f (Hz).. f = Hz x C p f = Hz.. shock wave movement h shock.. f = Hz.. time (s) f (Hz) Figure 6. Time-variant and power spectra of static pressure, shock wave movement and bump top motion at Hz, 7Hz and Hz perturbation frequencies.

10 Figure 7. Variation of shock wave movement towards bump motion against the inlet reduced frequency. y/h.. =. =. = shock contact with the bump surface = shock mean location at y/h =. = C p k φ p (Deg.) k Figure 8. Chord wise static pressure fluctuations at reduced frequencies from k= to k=.9 at M iso =.63.

11 Study of Shock Movement and Unsteady Pressure on D Generic Model. Conclusion Phase relations among oscillatory bump motion, shock wave movement and unsteady pressure fluctuations are investigated in the case of a flexible generic model controlledoscillated in bending mode shapes at an inlet Mach number of.63, over a range of reduced frequencies from. to.9. The following conclusions are drawn: The mode shapes of such a flexible bump strongly depends on the excitation frequency of the generic model. The phase of shock wave movement towards bump local motion shows a decreasing trend for the third bending mode shapes at reduced frequency higher than k=.7. At the pressure tap located after the shock wave formation (67% of the bump chord), the phase of pressure fluctuations towards bump local motion presents the same decreasing trend as for the shock wave movement analysis. For those same pressure taps, lower and stable pressure coefficients are also observed. Acknowledgements The present research was accomplished with the financial support of the Swedish Energy Agency research program entitled Generic Studies on Energy-Related Fluid-Structure Interaction with Dr. J. Held as technical monitor. This support is gratefully acknowledged. The authors would also like to thank O. Bron and D. Vogt of the Chair of Heat and Power Technology in KTH for their advices related to this project. References Allegret-Bourdon, D., Vogt, D. M., Fransson, T. H. [] A New Test Facility for Investigating Fluid- Structure Interactions Using a Generic Model, Proceedings of the 6th Symposium on Measuring Techniques in Transonic and Supersonic Flow in Cascades and Turbomachines, Cambridge, UK. Bron, O., Ferrand P., Fransson T. H., Atassi H. M., [] Non linear Interaction of Acoustic waves with Transonic Flows in Nozzle, 7th AIAA/CEAS Aeroacoustics Conference Maastricht, 8-3 May,. AIAA--7. Bron, O.; Ferrand P.; Fransson T. H.; [3] Experimental and numerical study of Non-linear Interactions in D transonic nozzle Flows, Proceedings of the th International Symposium of Unsteady Aeroacoustics, Aerodynamics and Aeroelasticity of Turbomachines, Durham, USA. Fujimoto, I., Hirano, T., Tanaka, H., [997] Experimental Investigation of Unsteady Aerodynamic Characteristics of Transonic Compressor Cascades, Proceedings of the 8th International Symposium of Unsteady Aeroacoustics, Aerodynamics and Aeroelasticity of Turbomachines, Stockholm, Sweden. Hirano, T., Tanaka, H., Fujimoto, I., [] Relation between Unsteady Aerodynamic Characteristic and Shock Wave Motion of Transonic Compressor Cascades in Pitching Oscillation Mode, Proceedings of the 9th International Symposium of Unsteady Aeroacoustics, Aerodynamics and Aeroelasticity of Turbomachines, Lyon, France. Kobayashi, H., Oinuma, H., Araki, T., [99] Shock Wave Behaviour of Annular Blade Row Oscillating in Torsional Mode with Interblade Phase Angle, Proceedings of the 7th International Symposium on Unsteady Aerodynamics and Aeroelasticity of Turbomachines, Fukuoka, Japan. Lehr, A., Bölcs, A., [] Investigation of Unsteady Transonic Flows in Turbomachinery, Proceedings of the 8th International Symposium of Unsteady Aeroacoustics, Aerodynamics and Aeroelasticity of Turbomachines, Lyon, France. Queune,O.J.R.,Ince,N.,Bell,D.,He,L.,[]Three Dimensional Unsteady Pressure Measurements for an Oscillating Blade with Part-Span Separation, Proceedings of the 8th International Symposium of Unsteady Aeroacoustics, Aerodynamics and Aeroelasticity of Turbomachines, Lyon, France. Schäffer, A., Miatt, D. C., [98] Experimental evaluation of heavy fan high-pressure compressor interaction in three-shaft engine; Part - experimental set-up and results, Journal Eng for Gas Turbines and Power 7: