UNSTEADY AERODYNAMICS, AEROACOUSTICS AND AEROELASTICITY OF TURBOMACHINES Episode 9 pdf

Study of Shock Movement and Unsteady Pressure on 2D Generic Model 411 of 0.102 and 0.136, and that after this range of reduced frequencies the un- steady force damps the blade oscillation. Fujimoto et al. [1997] studied this unsteady fluid structure interaction on a transonic compressor cascade oscillat- ing in a controlled pitching angle vibration. They noticed that although the am- plitude 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 90 ˇ r as the blade oscillation reduced frequency increases to 0.284. Later, Hirano et al. [2000] 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; 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 re- duced 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 oscil- lation of the rigid structure, whose amplitude and frequency can be controlled. The compressor blade of Lehr and Bölcs [2000], for example, is made oscil- lating in a controlled plunging mode by a hydraulic excitation system. The high-speed pitching vibrator of Hirano et al. [2000] is able to reach a 500Hz frequency of a 2D 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 fre- quencies prompt the failure of the structures. Moreover, recent research has presented a 2D blade harmonically driven in a 3D mode shape controlled vi- bration such as in Queune et al. [2000]. 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. 2. Objectives The objective is to show the variations of amplitudes and phase lead to- wards bump motion of both the shock wave movement and the unsteady static 412 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 2D prismatic shape and has been investigated as non-vibrating in previous studies (Bron et al. [2001] ,Bron et al. [2003]), from where extensive baseline data are available. In order to intro- duce capabilities for the planned fluid-structure tests, a flexible version of the model was built. Figure 1 shows the way the generic model oscillates in the test section and presents the optical access offered by this test facility. The flow Figure 1. entering the test section can be set to different operating conditions character- ized by different inlet Mach number, Reynolds number and reduced frequency (Table 1). The generic model is molded of polyurethane, at defined elasticity (E=36.10 6 MPa) and hardness (80 shore), by vulcanization over a steel metal bed. As shown in Figure 2, 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 57% of the chord vibrates in a sinusoidal motion of 0.5mm amplitude, the two edges of the chord stay fixed. A 1D laser sensor measures the model movement through the optical glass top window in one direction with a bandwidth of 20kHz and a resolution of +/-0.01mm. Time- Test facility composition and optical access Study of Shock Movement and Unsteady Pressure on 2D Generic Model 413 Table 1. Mass flow (4bar, 303K) Q=4.7kg/s Stagnation temperature 303K≤T t ≤353K Test section height H=120mm Test section width D=100mm Generic model axial chord c ax = 120mm Oscillating frequency range 10Hz≤f≤500Hz Isentropic Mach number at the inlet of the test section 0.6≤M iso1 ≤0.67 (subsonic) (transonic) Reynolds number for a characteristic length of 650mm 43.10 3 ≤Re≤27.10 6 Reduced frequency based on the half chord for M iso1 =0.63 0.01≤k≤0.66 Table 2. Encoder accuracy on the position of the camshaft ±10.8Deg. Inner diameter of the 15 Teflon tubes 0.9mm Length of the 15 Teflon tubes 0.5m Number of Kulite fast response transducers 15 Inner diameter of the 15 long lines 1.3mm Length of the 15 long lines 5m Amplitude of the first bending mode shape ±0.5mm Average maximum height of the generic model h max =10mm Tested excitation frequencies range 10Hz≤f≤200Hz Tested reduced frequency based on the half chord for M iso1 =0.63 0.015≤k≤0.294 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 2D flexible generic model and plugged to the Kulite transducers mounted with the long line probe technique far from the os- cillating measured surface (Schäffer and Miatt [1985], see Table 2). These fast response transducers deliver signals with delays and large damping but exempt of resonance effect. The delays, damping, tubes vibrations and tubes elonga- tions have been carefully calibrated. All components of this test facility are fully described in Allegret-Bourdon et al. [2002]. The test section offers op- tical access from three sides (Figure 1). 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. Operating flow parameters Long line probe measurements performed 414 Figure 2. 4. Experimental results 4.1 Description of the operating condition In these experiments, inlet and outlet time averaged isentropic Mach num- bers are set and a time averaged "lambda" shock wave is generated over the generic model surface at 67% (+/-1%) of the bump chord. Figure 3 shows a typical shape of the shock wave created during those experiments. To de- fine this operating condition, the stagnation pressure and the stagnation tem- perature of the flow are measured (P t = 159kPa at T t = 305K)atten chords upstream and the corresponding isentropic inlet Mach number is cal- culated (M iso1 =0.63). The downstream static pressure is measured on the ground wall and allows calculation of a downstream isentropic Mach number M iso2 =0.61 at two chords after the generic model. Figure 4 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 iso2 decreases until 10% of the chord and then increases until 50% of the chord where the flow speed is maximal. Then M iso2 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 4 describes the way the generic model is oscillating. A regular repar- tition of the amplitudes along the bump half chords shows a maximal defor- mation at x/c ax =0.47. Due to its flexible nature, a first bending mode shape Cut view of the generic model (bump) Study of Shock Movement and Unsteady Pressure on 2D Generic Model 415 0 0.2 0.4 0.6 0.8 1 1.2 0.75 x/c ax 0 0.2 0.4 0.6 0.8 1 1.2 −0.1 y/H Figure 3. Schlieren picture of the shock wave created in the test section (M iso1 =0.63, M iso2 y/H 0.015 0.037 0.074 0.11 0.147 0.221 0.294 0 ∆φ bump k Figure 4. =0.61) and isentropic Mach number profile at upper and lower bump positions Description of the bump oscillations for all operating flow conditions 416 at k=0.015 changes in a second bending mode shape at k=0.074, and reaches a third bending mode shape at higher reduced frequencies. At the mean shock wave location x/c ax =0.67, the local geometry presents a phase towards bump top motion. This phase is 20Deg. at k=0.015, 45Deg. at k=0.037, 120Deg. at k=0.074, -180Deg. from k=0.11 to k=0.147, -45Deg. at k=0.221 and -90Deg. at k=0.294. 4.2 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 10 and 200Hz. 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 mea- sured at one vertical location corresponding to 15mm (y/H =0.25) over the top of the bump neutral position (it is symbolized by the white dashed arrows in Figure 3). Figure 5b shows successive pictures of this shock wave oscillat- ing at 10Hz oscillation frequency. A reference line indicates the mean location of the shock wave (67% of the bump chord). From t’=0 to t’=0.250, the shock wave moves through its mean position in an upstream direction. From t’=0.500 to t’=0.750, the shock wave moves again through its mean position in a down- stream direction. Due to the sinusoidal oscillation of the bump, the shock wave Figure 5. Schlieren pictures of the shock wave oscillation cycle at a) f=200Hz and b) f=10Hz perturbation frequencies Study of Shock Movement and Unsteady Pressure on 2D Generic Model 417 stays a longer time in the two extreme positions (upstream and downstream) and crosses quickly its mean position during one period at 10Hz bump os- cillatory frequency. Figure 5a shows in the same way one oscillation of the vertical part of the shock wave at 200Hz excitation frequency. These pictures demonstrate a movement close to be sinusoidal. 4.3 Power spectra of pressure fluctuation, bump motion and shock wave movement Time-variant signals and corresponding power spectra of pressure fluctua- tions, bump top motions and shock wave movements are shown in Figure 6 for three bump oscillatory frequencies (10Hz, 75Hz and 200Hz). Both pres- sure fluctuation and shock wave motion signals seem to follow the shape of the sinusoidal signal generated by the bump displacement at the oscillatory fre- quencies of 10Hz, 75Hz and 200Hz. 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 con- tains 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 vibra- tions coming from the oscillation drive train and the wind tunnel. All three oscillations seem to be of a sinusoidal type after ensemble averaging posttreat- ment. 4.4 Schlieren visualization results Figure 7 characterized the measured oscillations of the shock wave up to k=0.294. 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 0.015 to 0.294. The first bending mode shape at k=0.015 is characterized by a phase lag towards bump motion close to 315Deg., and the phases range between 30Deg. and 90Deg. for the second bending mode shape from k=0.03 to k=0.074. The phase decreases signif- icantly from 270Deg. to almost 0Deg. at reduced frequencies higher than k=0.089 for what has been considered as a third bending mode shape. 4.5 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=0.221 for the pressure taps located 20% upstream and downstream of the 418 h´ Figure 6. Time-variant and power spectra of static pressure, shock wave movement and bump top motion at 10Hz, 75Hz and 200Hz perturbation frequencies Study of Shock Movement and Unsteady Pressure on 2D Generic Model 419 bump axial chord as shown in Figure 8. Moreover the unsteady pressure co- efficients remain stable and range between 2 and 4 for the three pressure taps located within 40% to 80% of the bump axial chord. The phase lead towards bump motion of the static pressure fluctuations range between 90Deg. and 180Deg. for the pressure taps located before the bump max height, and be- tween -180Deg. and 90Deg. 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=0.25, 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 270Deg. is observed for the pressure taps located after the shock wave. 5. Conclusion Phase relations among oscillatory bump motion, shock wave movement and unsteady pressure fluctuations are investigated in the case of a flexible generic model controlled-oscillated in bending mode shapes at an inlet Mach number of 0.63, over a range of reduced frequencies from 0.015 to 0.294. The follow- ing conclusions are drawn: • The mode shapes of such a flexible bump strongly depends on the exci- tation frequency of the generic model. Figure 7. Variation of shock wave movement towards bump motion against the inlet reduced frequency 420 y/H Figure 8. Chord wise static pressure fluctuations at reduced frequencies from k=0 to k=0.294 at M iso1 • 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=0.074. • At the pressure tap located after the shock wave formation (67% of the bump chord), the phase of pressure fluctuations towards bump local mo- tion 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. =0.63 [...]... Mode, Proceedings of the 9th International Symposium of Unsteady Aeroacoustics, Aerodynamics and Aeroelasticity of Turbomachines, Lyon, France Kobayashi, H., Oinuma, H., Araki, T., [ 199 4] 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,... T., Tanaka, H., [ 199 7] 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., [2000] Relation between Unsteady Aerodynamic Characteristic and Shock Wave Motion of Transonic Compressor... upstream Mach number value of 0.75, a total pressure of 1108121 Pa, and a total temperature of 299 .8 Kelvin The steady angle -of- attack of the fl is 3 degrees The ow chord of the profile is 0.3 meter The profile is moving in pitch at a frequency of 40Hz, with an amplitude of 0.25 degree Navier-Stokes steady and unsteady computations were run using the turbulence model of Michel and that of Spalart-Allmaras We... 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., [2000] Three Dimensional Unsteady Pressure Measurements for an Oscillating Blade with Part-Span Separation, Proceedings of the 8th International Symposium of Unsteady Aeroacoustics, ... Interaction of Acoustic waves with Transonic Flows in Nozzle, 7th AIAA/CEAS Aeroacoustics Conference Maastricht, 28-30 May, 2001 AIAA-2001-2247 Bron, O.; Ferrand P.; Fransson T H.; [2003] Experimental and numerical study of Non-linear Interactions in 2D transonic nozzle Flows, Proceedings of the 10th International Symposium of Unsteady Aeroacoustics, Aerodynamics and Aeroelasticity of Turbomachines, ... radius of the fan is about 0 .9 m A Navier-Stokes grid of moderate size has been built in order to run Spalart steady and unsteady computations It is made up with 6 blocks, and its total number of nodes is 397 044 The first grid layer thickness at the wall is about 5.e-06 m A view of the grid and of its multi-block topology is given in the next figure Numerical Unsteady Aerodynamics for Turbomachinery Aeroelasticity. .. International Symposium on Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, pages 830–840 Lyon, PUG Girodroux-Lavigne, P., and Dugeai, A (2003) Transonic aeroelastic computations using NavierStokes equations International Forum on Aeroelasticity and Structural Dynamics, Amsterdam, June 4-6 Jameson, A., Schmidt,W , and Turkel, S ( 198 1) Numerical Solution of the Euler Equation by... 343-3 49 Spalart P., and Allmaras, S ( 199 2) One Equation Turbulence Model for Separated Turbulent Flows 30th Aerospace Science Meeting, AIAA Paper 92 -04 39, Reno (NV) Vuillot, A.-M., Couailler, V., and Liamis N ( 199 3) 3D Turbomachinery Euler and NavierStokes Calculation with Multidomain Cell-Centerd Approach AIAA/SAE/ASME/ASEE 29th Joint propulsion conference and exhibit, Monterey (CA), USA, AIAA Paper 93 -2573... formulation of the linearised equations is similar to the methods presented by Clark & Hall [2] and Sbardella & Imregun [3] 437 K C Hall et al (eds.), Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 437–448 © 2006 Springer Printed in the Netherlands 438 The main difference between the current method and the previous methods is the use of GMRES with preconditioning instead of pseudo-time-stepping... Navier-Stokes unsteady turbomachinery computations for more complex configurations References Batina, J.T ( 198 9) Unsteady Euler airfoil solutions using unstructured dynamics meshes 27th Aerospace sciences meeting, AIAA Paper 89- 0115 Dugeai, A., Madec, A., and Sens, A S (2000) Numerical unsteady aerodynamics for turbomachinery aeroelasticity In P., Ferrand and Aubert, S., editors, Proceedings of the 9th International . Proceedings of the 9th International Symposium of Unsteady Aeroacoustics, Aero- dynamics and Aeroelasticity of Turbomachines, Lyon, France. Kobayashi, H., Oinuma, H., Araki, T., [ 199 4] Shock Wave. Experimental and numerical study of Non-linear Interactions in 2D transonic nozzle Flows, Proceedings of the 10th International Symposium of Unsteady Aeroacoustics, Aerodynamics and Aeroelasticity of Turbomachines, . [2000] Investigation of Unsteady Transonic Flows in Turbomachinery, Pro- ceedings of the 8th International Symposium of Unsteady Aeroacoustics, Aerodynamics and Aeroelasticity of Turbomachines, Lyon,