EXPERIMENTAL INVESTIGATION OF A FLAPPING MOTION DOWNSTREAM OF A BACKWARD FACING STEP. θ Momentum thickness, m ν Kinematic viscosity, m 2 /s

Transcription

1 Proceedings of 9th International Symposium on Fluid-Structure Interactions, Flow-Sound Interactions, Flow-Induced Vibration & Noise July 8-, 8, Toronto, Ontario, Canada FIV8-4 EXPERIMENTAL INVESTIGATION OF A FLAPPING MOTION DOWNSTREAM OF A BACKWARD FACING STEP Zhuoyue Li School of Aeronautics and Astronautics Dalian University of Technology Linggong Road, Dalian, China,64 sanjkfhk@63.com Nan Gao School of Aeronautics and Astronautics Dalian University of Technology Linggong Road, Dalian, China,64 gaonan@dlut.edu.cn ABSTRACT The flow field downstream of a backward facing step with Reynolds numbers of were studied using stereoscopic particle image velocimetry (PIV) with fieldof-views perpendicular to the incoming flow. It was found that the separated shear layer underwent a flapping motion with a frequency of f H/U o.4, much smaller than the shedding frequency ( f H/U o.) for Reynolds number larger than. Here H is the step height and U o is the freestream velocity. The low frequency flapping motion appeared to be coherent in the spanwise direction. The cause of the flapping motion is still not clear. NOMENCLATURE F uu,f vv,f ww, Power spectra of the streamwise, vertical and spanwise fluctuating velocity u, v and w F yy Power spectra of the instantaneous shear layer location y.5 f Frequency, Hz f s Sample frequency, Hz H Step height, m n Samples of each data block, m Re Reynolds number, U o H/ν T Sampling time per block, s U o Freestream velocity, m/s W Step width, m x,y,z Spatial coordinates, m y.5 Position where velocity is.5u o, m Coherence of the instantaneous shear layer location γ yy y.5 θ Momentum thickness, m ν Kinematic viscosity, m /s INTRODUCTION The interests over the dynamic behaviours of the flow separated from a backward facing step are increasing recently [ 5]. Large scale structures were found to roll up downstream of the step corner due to the Kelvin-Helmholtz instability at a characteristic frequency scaled with the initial momentum thickness θ o and the freestream velocity, f θ o /U o. [6]. The characteristic frequency of the flow structures decreases to f H/U o. (or f X r /U o.6 to. where X r is the mean reattachment length) near the mean reattachment point [7 ]. The characteristic frequency further decreased to f H/U o. downstream of the reattachment point [8, 3]. The motion with the frequency

2 f H/U o. was referred to as the shedding mode in refs. [3 5] or wake mode in refs. [6, 7]. Besides unsteady modes discussed above, Hasan [6] noticed that the initial part of the shear layer flapped in the vertical direction with a frequency one order of magnitude lower than the shedding frequency. The existence of the low frequency flapping instability was later confirmed by a wavelet analysis on the fluctuating streamwise component of velocity vector [9] and fluctuating skin friction [8]. Based on flow visualizations, Hasan [6] argued that the low frequency flapping motion in the initial part of the shear layer was self-sustained, i.e. the reaction of the shear layer to the upstream travelling disturbances is a positive feedback to the disturbances. Similarly, Heenan and Morrison [9] argued that the flapping motion was a global instability driven by the impingement of the large structures and upstream propagating disturbances based on a passive flow control study using a perforated bottom wall. The three dimensional nature of the flow structures free of the side wall effects was also studied. It was described by Simpson [] citing Pronchick [] that structures are initially two dimensional in a flow over a backward facing step with an laminar initial boundary layer. The spanwise coherence of the flow structures starts to break down about three step heights downstream of step, and the flow structure becomes fully three dimensional n- ear the reattachment point. The critical Reynolds number for the onset of three dimensionality is Re c 7 found by Kaiktsis et al. [] in a three dimensional DNS study. The spanwise correlations of the wall pressure decreased drastically when Reynolds number increases from 8 to. Beaudoin et al. [3] found that the onset of the 3D structures was due to a centrifugal instability and appeared to link to the curvature of the reattaching flow. Recently, Statnikov et al. [4] and Scharnowski et al. [5] performed PIV measurements and LES simulation on a transonic flow over a backward facing step with a free-stream Mach number of.8 and a Reynolds number of Re H of.8 5. They found that there were two dominant global modes in the shear layer: the first mode with f H/U o. corresponding to slow growth and collapse of the recirculation bubble and a second mode with f H/U o.7 corresponding to rolling up and shedding of a large scale structure from the shear layer. Their LES simulation [4] suggested these two modes were both three dimensional, i.e. their velocities varied Flow W z y Ls x L H Laser F.O.V. Bottom wall Camera Side wall (a) Camera (b) FIGURE : Schematics of the experimental facility. sinusoidally in the spanwise direction with a spanwise wavelength λ z /H.. So far, there has not been any direct measurement of the spanwise wave motion in a separated and reattaching flow using a time-resolved technique. In this study, we focused on a time-resolved stereoscopic PIV measurement of the flow in the recirculation bubble of a low speed backward facing step flow. Instantaneous locations of the shear layer will be extracted from each PIV snapshot and analyzed. The experimental methodologies will be discussed in the next section, followed by results and discussion and concluding remarks. EXPERIMENTAL METHODOLOGIES Measurements were performed in a recirculation water tunnel with a test section of cm 3cm 6cm (width, height, length). A two dimensional contraction section was used with a contraction ratio of 6.. A pump with a 3kW motor was used to deliver the water. The maximum velocity in the test section was.4 m/s. A 5 cm long, 4 mm diameter honeycomb flow straightener was used in the delivery plenum upstream of the contrac-

3 tion section. The turbulence level in the test section was less than.%, evaluated using PIV and a fiber-film hotfilm sensor(7µm diameter,.5mm long, Dantec). The water velocity in the test section can be varied manually by adjusting the frequency drive. A step model made of PLA plastic with a height of H = mm and a width of W = 5mm was created using 3D printing technique, shown in Fig. (a). The model was composed of three sections: the section I is the leading part ( to 3.3% chord length) of an Eppler 334 airfoil with a chord length of 67.6mm and a thickness of mm; the section II has a flat top and a length of 85.mm; the section III has a length of 55.mm. Two 3mm long and mm tall side walls were attached to the two ends of the step model to ensure the two dimensionality. The aspect ratio was W/H = 5.. The model was mounted on a traversing mechanism with a stepper motor so that it could be moved in the test section to allow measurements at x/h =.5 to 5. with a x/h =.5. The surface of the step model was polished and could be considered to be s- mooth. The initial boundary layer at the separation point (step corner) was not measured and was likely in a laminar state as the Reynolds number was much lower than the critical Reynolds number for the transition to occur. A LaVision stereoscopic particle image velocimetry system was used to measure the flow velocities on planes perpendicular to the freestream velocity. Water was seeded using silver coated hollow glass spheres with a nominal diameter of µm (Dantec S-HGS-). A mj dual-head Nd-YAG pulse laser system (Litron Nano) was used to illuminate the tracer particles, the laser sheet plane was perpendicular to the incoming flow and was positioned at a fixed location in the tunnel. Two LaVision supplied Highspeedstar cameras with a 768 * 5 pixel resolution and Scheimpflug adapters were used to capture the images. Cameras were mounted behind a mm plexiglass window at the end of the water tunnel, as shown in Fig. (a) and (b). The LaVision supplied DaVis 8.3 software package was used for image acquisition and postprocessing. Calibration was performed by using a type- target plate(.mm diameter mark). Self-Calibration method was used to correct the large misalignments between calibration plate and laser sheet. The time interval between two exposures was 5µs. Vectors were computed using image cross correlations with 4 * 4 and 6 * 6 pixel interrogation windows and a 5% overlap in the first and second passes, respectively. A total of 3 y/h x/h (a) Mean streamwise velocity for Re = 8, dashed line denotes position with y.5, + denotes the position velocity spectra were studied. F uu F uu F uu F vv (b) Re = 5 F vv (c) Re = 8 F vv (d) Re = 389 F ww F ww FIGURE : Distributions of (a) the mean streamwise velocity; and the velocity spectra F uu, F vv and F ww measured on the center plane = at positions -6 for (b) Re = 5,(c) Re = 8 and (d) Re = 389. Spectra were cascaded by one decay for clarity. F ww 3 3 3

4 snapshots were acquired at a rate of 5 Hz. According to the method in [6], the uncertainty of PIV velocity fields were less than ±% for a 95% confidence level. RESULTS AND DISCUSSIONS The contours of the steamwise velocity on the center plane (z = ) are shown in Fig. (a). A recirculation region can be seen downstream of the step. The mean velocity was zero at X r /H = 4.7 at y/h =., closest position to the wall, and was regarded as the mean reattachment position. The power spectra of the streamwise, vertical and spanwise fluctuating velocity, F uu, F vv and F ww, at six different locations (marked in Fig., a) on the center plane = were computed. Positions -3 were at y/h =. and positions 4-6 were at y = y.5 where the streamwise velocity was U =.5U o. The velocity spectra for three different Reynolds numbers are shown in Fig. (b,c & d), respectively. The frequency resolution of spectra was δ f = /T, where T was the sampling time in each data block. The spectrum was computed by breaking the PIV time record into N = blocks with T = s data in each block in case with Re = 5 and in N = 4 blocks with T = s data in each block in cases with Re 8, resulting in a frequency resolution of δ f H/U o =.5,.5 and.5 for Re = 5, 8 and 389, respectively. For low Reynolds number case Re = 5 (Fig., b), a prominent peak at f H/U o. can be identified in F vv at positions x/h 3.(x/X r.65). The spectra F uu and F ww were rather flat and no prominent peak could be found. The peak in F vv was likely linked to the shedding of large scale structures and this shedding occurred in the region x/x r.65, in agreement the results in the literature [3, 3, 6]. In the case with a larger Reynolds number Re = 389 (Fig., d), there was a sharp peak with f H/U o.35 at position 5 and relative smaller peak with f H/U o. at position 6. These two peaks were likely caused by a same flow motion which quickly decreased in characteristic frequency after reattachment to the wall. Moreover, a peak with a very low frequency f H/U o.4 can be seen in spectra F vv at positions -6, as well as F uu at positions 4-6 and F ww at positions -, suggesting a very low frequency motion emerged inside of the recirculation bubble at this Reynolds number. This motion appears to be a three dimensional motion suggested by the large low frequency peak in F ww. y/h (a).6.4. (b) FIGURE 3: (a) An instantaneous snapshot of the streamwise velocity for Re = 389 at x/h = 4.. The dashed line denotes y.5, the position with a streamwise velocity of.5u o and (b) illustration of the spanwise variations in the instantaneous reattachment location for a shear layer. F yy u/u o (a) (b) (c) FIGURE 4: Power spectra of the instantaneous shear layer location (y.5 ) at z = for x/h =.5 to 5. (from bottom to top) and a Reynolds number of (a) 5,(b) 8 and (c) 389. Spectra were cascaded by one decay for clarity. In order to understand the three dimensional motion better, the spanwise distributions of the instantaneous position of the shear layer were extracted from PIV snapshots by finding y.5, the position with a streamwise x/h

5 Re = 5 Re = o.9 fh/u.8 Re = (a) x/h =.(x/xr =.) Re = 5 Re = 8 Re = fh/u.5. o.8.. (b) x/h = 3.(x/Xr =.65) Re = 5 Re = o.8.9 Re = 389. fh/u... (c) x/h = 5.(x/Xr =.) FIGURE 5: Coherence of the instantaneous shear layer location γyy (x, zo, z, f ) for Re = (left) 5, (middle) 8 and (right) 389 for x/h = (a)., (b) 3. and (c) 5., the reference position is zo =. 5

6 velocity of.5u o. An typical snapshot of the streamwise velocity is shown in Fig. 3 (a), with y.5 marked using a dashed line. Regions with a negative streamwise velocity can be seen in the snapshot. These regions corresponded to the upstream travelling flow illustrated in Fig. 3 (b). The spatial and temporal variations of y.5 (x,z,t) were used to study the large scale organized motion in the s- panwise direction. Power spectra of the instantaneous shear layer location, y.5, atz = and x/h =.5 to 5. for different Reynolds numbers are shown in Fig. 4. The spectrum F yy F yy (x,z, f ) = ŷ.5(x,z, f )ŷ.5 (x,z, f ) T () was computed by breaking the time record into N = blocks in case with Re = 5 and in N = 4 blocks in cases with Re 8. Here, ŷ.5 (x,z, f ) is the Fourier transform of the instantaneous y.5 (x,z,t), represents conjugate, the overline denotes time average. For flow with Re = 5, a small sharp peak at f H/U o. can be i- dentified at x/h =.5 to 4., while for flow Re = 389, the small sharp peak at f H/U o. was less evident and a large peak at f H/U o.4 emerged at x/h =.5 to 5. suggesting again a low frequency motion dominated the flow fluctuations at this Reynolds number. The spanwise characteristics of the shear layer at different frequencies was studied using the coherence of y.5 measured at different spanwise location z γ yy (x,z o,z, f ) = F yy (x,z o,z, f ) Fyy (x,z o,z o, f )F yy (x,z,z, f ), () where z o = is a reference position. Distributions of γ yy for three Reynolds numbers are shown in Fig. 5 (ac), respectively, for streamwise positions of x/h =., 3. and 5. (x/x r =.,.65 and., respectively). In the flow with Re = 5, the spanwise coherence was poor at all the frequencies and every position. The spanwise coherence became very large in the case with large Reynolds number Re = 389 in the low frequency range f H/U o.4 at x/h = and 5. The coherence was particularly large at x/h = 3 suggesting the low frequency motion appeared at this Reynolds number was coherent in the spanwise direction. The phase relations at the frequency of f H/U o.4 for Re = 389 will be studied in the future. CONCLUSIONS Time resolved stereoscopic PIV measurements were performed on a flow downstream of a backward facing step with Re = 5 to 389 in a water tunnel to study coherent motion in the spanwise direction. It is found that a very low frequency flapping motion existed in the flows when the Reynolds number was larger than, and the flapping motion became stronger as Re increased to 4. The shear layer over the whole recirculation bubble flapped up and down and the motion appeared to be coherent in the spanwise direction. The exact spanwise length scale was not determined due to the limited size of measurement domain and will be studied in the future. ACKNOWLEDGEMENTS The research was funded by Natural Science Foundation of China (975, 5778) and 973 Plan (4CB744). REFERENCES [] Ma, X., and Schröder, A., 7. Analysis of flapping motion of reattaching shear layer behind a twodimensional backward-facing step. Physics of Fluids, 9, p. 54. [] Ma, X., Geisler, R., and Schröder, A., 7. Experimental investigation of separated shear flow under subharmonic perturbations over a backward-facing step. Flow, Turbulence and Combustion, 99(), Jul, pp [3] Chovet, C., Lippert, M., Foucaut, J.-M., and Keirsbulck, L., 7. Dynamical aspects of a backwardfacing step flow at large reynolds numbers. Experiments in Fluids, 58(), Oct, p. 6. [4] Berk, T., Medjnoun, T., and Ganapathisubramani, B., 7. Entrainment effects in periodic forcing of the flow over a backward-facing step. Phys. Rev. Fluids,, Jul [5] Hu, R., Wang, L., and Song, F., 5. Review of backward-facing step flow and separation reduction (in Chinese). Sci Sin-Phys Mech Astron, 45() [6] Hasan, M., 99. The flow over a backward-facing step under controlled perturbation: laminar separation. J Fluid Mech, 38, pp [7] Driver, D., Seegmiller, H., and Marvin, J.,

7 Time-dependent behavior of a reattaching shear layer. AIAA J, 5, pp [8] Eaton, J., and Johnson, J., 98. Turbulent flow reattachment : An experimental study of the flow and structure behind a backward-facing step. Tech. Rep. MD-39, Thermosciences Div., Dept. of Mech. Eng., Stanford University. [9] Heenan, A., and Morrison, J., 998. Passive control of pressure fluctuations generated by separated flow. AIAA J, 36, pp. 4. [] Liu, Y., Kang, W., and Sung, H., 5. Assessment of the organization of a turbulent separated and reattaching flow by measuring wall pressure fluctuations. Exp Fluids, 38(4), pp [] Le, H., Moin, P., and Kim, J., 997. Direct numerical simulation of turbulent flow over a backwardfacing step. J Fluid Mech, 33, pp [] Eaton, J., and Johnson, J., 98. Low frequency unsteadyness of a reattaching turbulent shear layer. In Proceedings of the Third Symposium on Turbulent Shear Flows, L. B. et al., ed., Vol. 3 of Turbulent Shear Flows, Springer, pp [3] Wee, D., Yi, T., Annaswamy, A., and Ghoniem, A., 4. Self-sustained oscillations and vortex shedding in backward-facing step flows: Simulations and linear instability analysis. Phys Fluids, 6, pp [4] Lee, I., and Sung, J.,. Multiple-arrayed pressure measurement for investigation of the unsteady flow structure of a reattaching shear layer. J Fluid Mech, 463, pp [5] Dejoan, A., and Leschziner, M., 4. Large eddy simulation of periodically perturbed separated flow over a backward-facing step. Int J Heat Fluid Fl, 5, pp [6] Hudy, L., Naguib, A., and Humphreys, W., 7. Stochastic estimation of a separated-flow field using wall-pressure-array measurements. Phys Fluids, [7] Sampath, R., and Chakravarthy, S. R., 4. Proper orthogonal and dynamic mode decompositions of time-resolved piv of confined backward-facing step flow. Exp Fluids, 55(9), p. 79. [8] Spazzini, P., Iuso, G., Onorato, M., Zurlo, N., and Di-Cicca, G.,. Unsteady behavior of backfacing step flow.. Exp Fluids, 3, pp [9] Heenan, A., and Morrison, J., 998. Passive control of backstep flow. Exp Therm Fluid Sci, 6, pp. 3. [] Simpson, R., 989. Turbulent boundary-layer separation. Annu Rev Fluid Mech,, pp [] Pronchick, S., 983. Experimental investigation of the turbulent flow behind a backward facing step. PhD Thesis, Stanford University, Standford, CA. [] Kaiktsis, L., Karniadakis, G., and Orszag, S., 99. Onset of three-dimensionality, equilibria, and early transition in flow over a backward-facing step. J Fluid Mech, 3, p. 5C58. [3] Beaudoin, J., Cadot, O., Aider, J., and Wesfreid, J., 4. Three-dimensional stationary flow over a backward-facing step. European Journal of Mechanics - B/Fluids, 3(), pp [4] Statnikov, V., Bolgar, I., Scharnowski, S., Meinke, M., Kähler, C., and Schröder, W., 6. Analysis of characteristic wake flow modes on a generic transonic backward-facing step configuration. Eur J Mech B-Fluid, 59, pp [5] Scharnowski, S., Bolgar, I., and Kähler, C., 7. Characterization of turbulent structures in a transonic backward-facing step flow. Flow Turbul Combust, 98, pp [6] Wieneke, B., 5. PIV uncertainty quantification from correlation statistics. Meas Sci Technol, 6, p