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Experimental investigation of the interaction between incoming wakes and instability mechanisms in a laminar separation bubble
Experimental Thermal and Fluid Science 50 (2013) 54–60
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Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Experimental investigation of the interaction between incoming wakes and instability mechanisms in a laminar separation bubble Daniele Simoni ⇑, Marina Ubaldi, Pietro Zunino DIME – Università di Genova, Via Montallegro 1, I-16145 Genova, Italy
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Article history: Received 8 November 2012 Received in revised form 25 March 2013 Accepted 12 May 2013 Available online 23 May 2013 Keywords: Separated flow transition Incoming wakes Kelvin–Helmholtz instability Ultra-High-Lift turbine blade
a b s t r a c t The present paper reports the results of a detailed experimental study on the interaction process between incoming wakes and a laminar separated boundary layer. Experimental investigations have been carried out, for a low Reynolds number case, over a flat plate installed within a double contoured test section designed to produce an adverse pressure gradient typical of Ultra-High-Lift turbine blade profiles. Measurements have been performed by means of a single-sensor hot-wire anemometer. The phase-locked ensemble averaging technique, synchronized with the wake frequency, has been adopted to reconstruct the boundary layer space–time evolution in terms of ensemble-averaged velocity and velocity root mean square. These experimental data have been exploited in order to investigate how the unsteady incoming flow interacts with the instability mechanisms of the boundary layer to drive transition. Two main effects of wake passage were found. The low frequency disturbance associated with the wake passage triggers the Kelvin–Helmholtz instability process developing in the shear layer in the time interval between wakes. Moreover, the temporary reduction/suppression of the separation bubble observed when the incoming wake reaches the separated flow region has been found to be driven by linear stability mechanisms, which promote a quick amplification of the high frequency velocity fluctuations carried by wakes. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction The physical understanding of the separated flow transition mode is of primary importance for Low Pressure Turbine (LPT) applications. Indeed, such components must face the problem of boundary layer laminar separation, especially when high-lift profiles operating at low Reynolds number conditions are considered. Boundary layer separation gives rise to a separated shear layer whose transition process typically forces reattachment, generating a laminar separation bubble (e.g. [1–3]). Under steady inflow conditions, the amplification of unstable waves within the separated shear layer, and in particular along the velocity profile inflection line, has been found to be the dominant mechanism that drives transition (e.g. [4–6]). Recent studies [7–10] showed that vortical structures are generated above the flow stagnation region by the roll up of the free shear layer induced by a Kelvin–Helmholtz instability process. The transition of the separated shear layer is forced by the breakdown to turbulence of these large scale coherent structures, which promotes the boundary layer reattachment [11,12].
⇑ Corresponding author. Tel.: +39 010 353 2447; fax: +39 010 353 2566. E-mail address: [email protected] (D. Simoni). 0894-1777/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2013.05.004
On the other hand, in a real engine the rotor–stator aerodynamic interaction tends to modify the boundary layer separation and transition processes. Wakes shed from upstream rows induce periodic (low frequency) and stochastic (high frequency) velocity fluctuations within the suction side boundary layer altering both the transition and the separation processes as compared with the steady inflow case. Several numerical and experimental studies were carried out in the past to characterize the migration across turbine and compressor rows of unsteady wakes shed from upstream. Michelassi et al. [13] and Wu et al. [14] numerically analyzed the dynamics of unsteady wakes that travel from the inlet to the outlet planes of turbine cascades. Stieger and Hodson [15] experimentally analyzed, by means of a laser Doppler velocimeter, the migration of incoming wakes within an highly loaded low pressure turbine cascade. All these works highlight that the traveling wakes are stretched and bowed by the velocity gradients induced by the cascade geometry along the streamwise and normal to the wall directions. The velocity defect characterizing the wake region tends to be reoriented and pushed toward the suction side of the blade, generating the so called ‘negative-jet’, as described in [16]. This apparent jet carries not only momentum within the suction side boundary layer but also high frequency velocity fluctuations, which further contribute to the periodic boundary layer separation suppression. The turbulence (high frequency fluctuations)
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introduced within the suction side boundary layer by the incoming wakes alters the boundary layer development largely than the low frequency fluctuations associated with the periodic wake passage, as found in the work of Lou and Hourmouziadis [17]. Therefore, an unsteady transition from laminar to turbulent condition occurs, which is favorable for the reduction of the separation bubble extension [18–20]. Anyway, a laminar separation bubble may grow periodically between wakes, as well described in [21]. This implies that a separated shear layer, which is intrinsically unstable according to the linear stability theory [22], is periodically generated. The analysis of the interaction between this strongly unstable flow region and the incoming wake velocity fluctuations represents the main target of the present work. The present paper reports the results of a detailed experimental investigation on the transition/separation processes of the boundary layer under unsteady inflow conditions. A summary of the results obtained in the same test section under steady inflow [8,23] is reported to allow comparisons between the two inflow conditions. The analysis of the results under unsteady inflow is aimed at characterizing the interaction between the separated shear layer developing between wakes and both the low and the high frequency velocity fluctuations carried by wakes. Firstly the phaselocked ensemble averaged quantities are reported to survey the overall behavior of the separated flow region when perturbed by the incoming wakes. Then the propagation of the velocity fluctuations introduced within the separated shear layer by the incoming wakes is analyzed, with the aim of verifying if linear instability mechanisms affect the periodic transition/reattachment processes of the boundary layer. For this purpose, a Lagrangian approach has been adopted in order to characterize the amplification process of velocity fluctuations within the separated shear layer and to highlight the analogies with the separated flow transition mode developing under steady inflow conditions.
2. Experimental apparatus and measuring techniques Measurements have been performed in the low speed blow down wind tunnel of the Laboratory of Aerodynamics and Turbomachinery of Genova University. As shown in Fig. 1, the test section consists of a thick flat plate with a (8:1) regular elliptic leading edge and a sharp trailing edge. The flat part of the plate, including the leading edge, is L = 200 mm long and 300 mm wide. The plate is located between two contoured walls designed to impose the prescribed adverse pressure gradient, typical of UltraHigh-Lift turbine profiles. The test section throat is located at x/ L = 0.285. The endwall geometry is scaled from the Lou and Hourmouziadis test case [17]. The boundary layer developing along the rear part of the plate was surveyed by means of 13 traverses normal to the wall (from x/L = 0.30 up to x/L = 1.0). Each traverse was constituted of 31 points along the direction normal to the wall, with smaller spacing close to the wall. Measurements have been carried out only at midspan of the plate, hence any three dimensional structures along the spanwise direction, such as streamwise streaks or Goertler
x/L=1 moving bars
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Fig. 1. Test section.
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vorticies, cannot be identified. These spanwise structures have been found to contribute to the overall amount of velocity fluctuations in the former part of the separated flow region, as shown for example in Coull and Hodson [24], Lardeau et al. [25] and Marxen et al. [26], A three-axis computer controlled traversing mechanism with a minimum linear translation step of 8 lm has been employed to allow high movement precision and spatial resolution. The boundary layer development has been investigated for a low Reynolds number condition (Re = 70,000). The corresponding test section inlet velocity U0 was 5.5 m/s and the inlet turbulence intensity was Tu = 1.5%. The presence of incoming wakes has been simulated by means of a moving bar system. The bars are moved upstream of the plate leading edge, in a plane located at a distance of 60 mm from it, with a peripheral velocity of Uwake = 7.8 m/s. The flow coefficient for the unsteady inflow tests was chosen in order to be representa tive of real engine operating conditions u ¼ UU0 ¼ 0:7 . The bar wake pitch was set equal to 356 mm in order to obtain a typical reduced L frequency of f þ ¼ fwake ¼ 0:8. The bar diameter (d = 3 mm) was choU0 sen so that the wakes generated by the bars give the same losses as those generated by a typical low-pressure turbine row. The total pressure loss coefficient for the bars (x ¼ Dpt =0:5qU 20 , with Dpt the total pressure drop across the bars) was evaluated to be 3.3% from total pressure measurements. A Dantec single-sensor miniature boundary layer hot-wire probe (type 55P15) has been employed for the velocity measurements. The anemometer output voltages were sampled using a Metrabyte DAS 58 sample and hold AD converter board, 12 bits resolution and 1 MHz maximum sampling frequency. Flow direction in a separation bubble cannot be determined with a single sensor hot-wire, but the rectification of the velocity profile close to the wall usually indicates the reversed flow region. Since the experimental velocity records contain both periodic fluctuations associated with the incoming wake frequency, and other velocity fluctuations due to turbulence and unsteadiness not at the wake frequency, the phase-locked ensemble average technique has been employed to distinguish between the periodic velocity fluctuations and all the other velocity fluctuations called in the following unresolved unsteadiness. Four contiguous incoming wake periods have been analyzed. Each period was subdivided in 100 time steps; thus, each record was constituted of 400 data. In order to obtain a satisfactory statistical accuracy, 500 records were acquired and used for the ensemble average.
3. Results and discussion 3.1. Reference steady inflow case The main results obtained in the same test section at the same Reynolds number for the reference steady case by means of different measuring techniques (single sensor hot-wire anemometer, Particle Image Velocimetry (PIV) and Laser Doppler Velocimetry (LDV)), discussed in detail in previous authors’ papers [8,23], are here summarized for a better interpretation of the unsteady inflow results. The main conclusions of these works can be summarized, with assistance of Fig. 2, as follows. – A laminar separation bubble occurs from x/L = 0.39 up to x/ L = 0.69 (time–mean reattachment position), with the bubble maximum thickness localized at x/L = 0.58. – Velocity fluctuations coming from upstream are amplified within the separated shear layer (along the velocity profile inflection line) with exponential growth rate through linear instability mechanisms.
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– Velocity fluctuations in the Kelvin–Helmholtz frequency range are detected, which induce a sinuous oscillation of the separated shear layer up to the bubble maximum thickness position (see the vector map contained in the blue1 box in the middle of Fig. 2), where saturation of the velocity fluctuations takes place. – The large amplitude oscillations associated with saturation induce the separated shear layer roll-up. – Large scale vortical structures are shed close to the maximum bubble thickness position as a consequence of the shear layer roll-up (see the vector map contained in the red box in the middle of Fig. 2). – The breakdown of these large structures to smaller scales induces the separated shear layer transition, thus the separation bubble reattachment. 3.2. Periodic separation bubble evolution induced by incoming wakes Data concerning the unsteady inflow condition are analyzed in order to understand how the incoming wakes modify the separated-flow transition process described above for the steady inflow reference case. To this purpose, color plots of the ensemble averaged velocity and unresolved unsteadiness distributions, for different time instants in the wake passage period, are reported in Fig. 3 in order to obtain a global view of the time-varying boundary layer behavior for the unsteady inflow case. Results have been here reported only for the time interval 0.0 6 t/T 6 0.7 during which the incoming wake – separated shear layer interaction phenomena occur. Later, for 0.7 6 t/T 6 1.0, since the incoming wake has left the measuring domain, the separation bubble behavior doesn’t show significant variations. The velocity profile inflection line (where @ 2hui/@y2 = 0) has been superimposed to the plots for each instant in order to highlight locations where inviscid instability phenomena may occur. In Fig. 3 a coarse time step (Dt/T = 0.1) has been adopted to show the unsteady development of the separation bubble in an almost complete wake passage period. A finer time step (Dt/T = 0.04) has been used in Fig. 5 for a better description of the amplification 1 For interpretation of color in Figs. 2–5 and 7, the reader is referred to the web version of this article.
mechanisms of flow oscillations during the incoming wake – separated shear layer interaction in the time interval 0.2 6 t/T 6 0.4. Referring to Fig. 3 the wake is entering the measuring domain at t/T = 0.2, as revealed by the large free-stream unresolved unsteadiness. Before the wake arrival time the laminar boundary layer separates and a separated flow transition process occurs, as shown by both velocity and unresolved unsteadiness distributions from t/ T = 0.0 to t/T = 0.2. In this time interval the laminar separation bubble evolves with dynamics similar to that characterizing the steady inflow case: velocity fluctuations grow along the velocity profile inflection line up to reach their maximum value just behind the bubble maximum displacement position. The large unresolved unsteadiness core observable at x/L = 0.60 and y/L = 0.01 is associated with the occurrence of Kelvin–Helmholtz large scale coherent structures, as it will be demonstrated in the following section. At t/T = 0.2 downstream of x/L = 0.60 velocity fluctuations propagate toward the wall promoting transition, and thus the reattachment of the boundary layer. Overall, the dynamics of the transition/reattachment processes here described for the time period between 0.0 6 t/T 6 0.2 closely agrees with that observed under steady inflow conditions by Simoni et al. [8]. At t/T = 0.2 the wake appears on the left of the measuring domain inducing large velocity fluctuations in the free-stream region. At t/T = 0.3 the fluctuations associated with the incoming wake appear strongly amplified within the separated shear layer, exactly along the velocity profile inflection line, up to x/L = 0.50. On the other hand, quite low values of the unresolved unsteadiness characterize the near wall region, which is not affected, at this time instant, by the velocity fluctuations carried by wakes. Thus, in the initial stage of the interaction, fluctuations carried by wakes do not penetrate up to the wall, coherently with the results shown in [27]. For larger t/T values the further increase of the velocity fluctuations within the separated shear layer strongly reduces the thickness of the separation bubble up to around x/L = 0.50, as revealed by the velocity color plots at t/T = 0.4. At t/T = 0.5, the high velocity fluctuation core decays and moves downstream promoting the suppression of the separation bubble. As the incoming wake travels further downstream (t/T = 0.6), the separation bubble in the front part of the measuring domain rises again and then progressively grows. After t/T = 0.7 the separated flow region keeps growing up to assume the structure already observed during the time interval between t/T = 0.0 and t/ T = 0.2. 3.3. Detection of the Kelvin–Helmholtz vortices in the time interval between wakes In the previous section the large unresolved unsteadiness core observable near the maximum bubble displacement for 0.0 6 t/ T 6 0.2 has been ascribed to the presence of Kelvin–Helmholtz vortices. This vortex shedding phenomenon can indeed be highlighted by means of the ensemble averaged velocity and unresolved unsteadiness time–space plots (Fig. 4) obtained at the axial position where the unsteady bubble maximum displacement occurs (x/L = 0.54, slightly upstream with respect to the steady inflow case). In these plots the incoming wake passages are revealed by the large unresolved unsteadiness values, characterizing the freestream region, at t/T = 0.25 + n (with n the wake passage index). At this streamwise position the separated flow thickness grows after the first wake passage from t/T = 0.65 up to t/T = 1.25, generating inflected velocity profiles. The bubble maximum thickness occurs at around t/T = 1.25, just before the subsequent wake arrival time, as revealed by the velocity distribution. Small distinct cores of large unresolved unsteadiness can be observed along the velocity profile inflection line, which moves away from the wall from t/ T = 0.65 up to t/T = 1.25 due to the progressively increased
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thickness of the separation bubble in the period between two wake passages. These cores, which appear with a well defined period DtKH (corresponding to a frequency f ffi 470 Hz) where the velocity profile is inflected, are the traces of the large scale vortical structures generated by the inviscid Kelvin–Helmholtz instability mechanism. In order to confirm the occurrence of the Kelvin–Helmholtz instability the Monkewitz and Huerre [28] dimensionless frequency parameter can be evaluated. The separated shear layer can be interpreted as the interface between two distinct layers (the separated flow region and the external flow) characterized by two different velocities u1 and u2 (for the present case u1 ’ 0 represents the velocity at the bottom edge of the separated shear layer, while u2 = Ue represents the velocity at its top). The velocity ¼ ðu2 þ u1 Þ=2 difference Du = u2 u1 and the averaged velocity u can be introduced to describe the velocity distribution. Moreover the vorticity thickness of the separated shear layer can be determined by dw = Du/(ou/@y)max. Thus, by means of these parameters and the vortex street frequency (f = 470 Hz) it is possible to . The calculate the dimensionless frequency x ¼ 0:25dw ð2pf Þ=u dimensionless vortex shedding frequency results to be x = 0.21, which is very close to the value obtained for the steady case (x = 0.220, see [29]), and well agrees with the range numerically predicted by Yang and Voke [3] 0.206 < x < 0.231. Therefore, the unresolved unsteadiness cores detected in the present investigation for the unsteady inflow condition may be considered as the effect of the Kelvin–Helmholtz shedding vortex phenomenon. Furthermore, due to the local acceleration and deceleration that
Kelvin–Helmholtz vortices induce in the boundary layer in correspondence of their top and bottom sides, respectively, vortex traces are also observable in the ensemble averaged velocity distribution (red and blue vertical stripes on the left of Fig. 4). It is worth explaining the reason for which the visualization of these vortices is possible in the ensemble averaged results. Indeed, flow structures that were not locked to the dominant forcing frequency (the incoming wake frequency) would be smeared out spatially by the ensemble-averaging procedure, as explained in [27]. Since in the present experiments the high unresolved unsteadiness cores survive to the ensemble-averaging process, the low frequency incoming wake passage results to be the ‘‘triggering source’’ or, in other words, the wake locks the relative phase of the Kelvin–Helmholtz vortex shedding phenomenon of the laminar separation bubble growing between wakes. Similar triggering effects induced by the periodic wake passage on a separation bubble were also found in the numerical simulations of Wissink [30] and Wissink et al. [31], as well as in the case of laminar separation bubbles perturbed by periodic external excitations [32,33]. 3.4. Effects of the high frequency velocity fluctuations carried by wakes In order to provide a more in depth analysis of the interaction process between the high frequency velocity fluctuations carried by wakes and the separated shear layer, ensemble-averaged velocity and unresolved unsteadiness distributions are reported in Fig. 5 with a finer time step (Dt/T = 0.04) for the time interval 0.2 < t/ T < 0.4.
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The sequence of the unresolved unsteadiness color plots of Fig. 5 (t/T = 0.2, t/T = 0.24 and t/T = 0.28) clearly reveals that the velocity fluctuations introduced within the boundary layer by the incoming wakes are amplified along the velocity profile inflection line. Maximum values of the unresolved unsteadiness within the separated shear layer increase with time (see the different frames) and move in space (along the velocity profile inflection line). These results suggest the occurrence of convective linear instability mechanisms that act amplifying the velocity fluctuations carried by wakes when they are propagating downstream. The occurrence of linear instability mechanisms during the incoming wake – separated shear layer interaction is supported by the spatial evolution of the mean kinetic energy of velocity fluctuations reported in Fig. 6. Data reported in this plot have been obtained along the velocity profile inflection line following, in both time and space (i.e. in a lagrangian frame), the propagation of velocity fluctuations introduced into the boundary layer by the incoming wake at x/L = 0.30 and t/T = 0.16. This time instant at the measuring grid inlet has been chosen in order to select a fluid portion pertaining to the leading front of the wake, which is characterized by small velocity fluctuations. Thus, Fig. 6 shows the amplification of an initial ‘‘small-amplitude’’ oscillation carried by wakes. The convection speed of velocity fluctuations within the separated shear layer has been assumed equal to the flow velocity at the inflection point. This assumption is good if the wall proximity effects on the propagation speed are negligible, as it occurs for a thick separation bubble [34]. The propagation speed value was verified in [8,29] for steady and unsteady inflows, respectively. Furthermore, also the works of Stieger et al. [35] and Gompertz and Bons [27] show structures generated during the incoming wake – boundary layer interaction that propagate at around a half of the local free-stream velocity (thus with a velocity very close to that at the inflection line). Filled dots on Fig. 5, connected by straight lines, help to identify the correspondence between the spatial positions and the time instants at which the mean kinetic energy of flow oscillations have been evaluated to construct the diagram of Fig. 6. The straight line shape of the experimental curve plotted in log scale in Fig. 6 reveals that the velocity fluctuation kinetic energy is exponentially amplified, as it typically occurs when linear instability mechanisms set in, in the time period 0.16 < t/T < 0.28, moving from x/L = 0.3 to x/L = 0.45. Downstream of x/L = 0.45 the amplification rate of velocity fluctuations departs from the exponential growth and saturation takes place. Saturation is associated with
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f [Hz] Fig. 7. Phase-locked velocity profile measured at x/L = 0.44 for t/T = 0.2 (top); freestream velocity power density spectra at x/L = 0.30 (bottom). Maximum amplified frequency, indicated on the bottom plot, has been computed for the piecewise linear profile depicted on the top.
the occurrence of finite amplitude oscillations within the flow, which induce the generation of higher frequency waves, as described in [4], that contribute to the separated shear layer transition and reattachment processes. Indeed, as previously observed referring to Figs. 3 and 5, from t/ T = 0.32 the thickness of the separation bubble front part progressively decreases up to the almost complete suppression of the bubble observable at t/T = 0.5. Thus, taking into account the results of Fig. 6, we can deduce that the separation bubble starts to be sensibly reduced where (and when) the linear stability mechanisms have amplified the high frequency velocity fluctuations carried by wakes up to induce the saturation of the growth rate, thus the beginning of the separated shear layer transition. Finally, the interaction process between incoming wakes and the separated shear layer can be summarized and further explained as follows. – Boundary layer separation rising between wakes generates inflection points in the velocity profiles that make the separated shear layer intrinsically unstable to velocity oscillations (see the phase-locked velocity profile on the top of Fig. 7, obtained at x/ L = 0.44 just before the wake arrival time). The maximum amplified frequency predicted by the inviscid linear stability theory for the piecewise linear profile approximating the experimentally measured one (black straight line) is f ffi 470 Hz. – Incoming wakes are low frequency disturbances that carry small scale (high frequency) velocity fluctuations. Indeed, the spectrum characterizing the unsteady inflow case obtained in the free-stream region at x/L = 0.30 (bottom of Fig. 7) shows
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not only the occurrence of distinct peaks associated with fundamental and higher order harmonics induced by the traveling periodic wakes, but also larger energy with respect to the steady inflow case for frequency f > 20 Hz, due to the turbulence carried by wakes. Thus, oscillations carried by wakes contain significant energy also in the surround of the most unstable frequency of the separated shear layer (marked with a cyan arrow in the spectral diagram of Fig. 7). – Thus, when the incoming wake is traveling over the separated flow region, the high frequency velocity oscillations introduced into the boundary layer by the incoming wakes match a strongly unstable separated shear layer, which induces an exponential amplification of the velocity fluctuations (Fig. 6). – Consequently, a rapid transition process of the separated shear layer occurs, which induces the localized and temporary reattachment of the separation bubble. 4. Conclusions The experimental data concerning the evolution of a laminar separation bubble under unsteady inflow have been analyzed in order to highlight the role played by the separated shear layer instability in the promotion of the transition, which induces the temporary separation bubble suppression during the incoming wake-boundary layer interaction. Low frequency wake passage events induce a periodic evolution of the separation bubble and influence the separated shear layer Kelvin–Helmholtz instability mechanisms in the time interval between wakes. In this interval a laminar separation bubble is generated and the transition process of the separated shear layer develops in a configuration similar to the steady case: velocity fluctuations start to grow along the velocity profile inflection line, where the boundary layer is intrinsically unstable according to the inviscid instability theory, up to reach their maximum values just behind the bubble maximum displacement position. The incoming wake passage events trigger the occurrence of the Kelvin–Helmholtz instability process, which induces a vortex shedding phenomenon behind the bubble maximum displacement position. Downstream of this position the separated shear layer transition induces the boundary layer reattachment. Otherwise, when the incoming wake reaches the separated flow region, the high frequency velocity fluctuations carried by wakes strongly interact with the separated shear layer which grows between wakes. These high frequency oscillations contain energy at the most unstable frequency of the separated shear layer, thus an exponential amplification of the velocity fluctuations is induced. Convective linear instability mechanisms act amplifying the high frequency velocity fluctuations carried by wakes, up to induce a quick localized transition process of the separated shear layer in the forward part of the bubble, which then leads to the almost complete suppression of the separated flow region. Acknowledgements The authors gratefully acknowledge the financial support of the European Commission as part of the research project TATMo, ‘‘Turbulence And Transition Modeling for Special Turbomachinery Applications’’. It is also acknowledged the financial support of the Italian Ministry for Instruction, University and Research (PRIN 2007). References [1] O. Marxen, D.S. Henningson, The effect of small-amplitude convective disturbances on the size and bursting of a laminar separation bubble, J. Fluid Mech. 671 (2011) 1–33.
[2] L.L. Pauley, P. Moin, W.C. Reynolds, The structure of two-dimensional separation, J. Fluid Mech. 220 (1990) 397–411. [3] Z. Yang, P.R. Voke, Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature, J. Fluid Mech. 439 (2001) 305–333. [4] A. Dovgal, V. Kozlov, A. Michalke, Laminar boundary layer separation: Instability and associated phenomena, Prog. Aerosp. Sci. 30 (1994) 61–94. [5] O. Marxen, M. Lang, U. Rist, S. Wagner, A combined experimental/numerical study of unsteady phenomena in a laminar separation bubble, Flow Turbul. Combust. 71 (2003) 133–146. [6] B. McAuliffe, M. Yaras, Transition mechanisms in separation bubbles under low- and elevated-freestream turbulence, ASME J. Turbomach. 132 (2010) 011004–011010. [7] M. Lang, U. Rist, S. Wagner, Investigations on controlled transition development in a laminar separation bubble by means of LDA and PIV, Exp. Fluids 36 (2004) 43–52. [8] D. Simoni, M. Ubaldi, P. Zunino, D. Lengani, F. Bertini, An experimental investigation of the separated-flow transition under high-lift turbine blade pressure gradients, Flow Turbul. Combust. 88 (2012) 45–62. [9] S. Burgmann, W. Schröder, Investigation of the vortex induced unsteadiness of a separation bubble via time-resolved and scanning PIV measurements, Exp. Fluids 45 (2008) 675–691. [10] R. Hain, C. Kähler, R. Radespiel, Dynamics of laminar separation bubbles at low-reynolds-number aerofoils, J. Fluid Mech. 630 (2009) 129–153. [11] S.D. Sourabh, O. Ramesh, On the origin of the inflectional instability of a laminar separation bubble, J. Fluid Mech. 629 (2009) 263–298. [12] C.P. Häggmark, C. Hildings, D.S. Henningson, A numerical and experimental study of a transitional separation bubble, Aerosp. Sci. Technol. 5 (2001) 317– 328. [13] V. Michelassi, J.G. Wissink, W. Rodi, Analysis of DNS and LES of flow in a lowpressure turbine cascade with incoming wakes and comparison with experiments, Flow Turbul. Combust. 69 (2002) 295–329. [14] X. Wu, R. Jacobs, J.C.R. Hunt, P.A. Durbin, Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage, J. Fluid Mech. 446 (2001) 199–228. [15] R.D. Stieger, H.P. Hodson, The unsteady development of a turbulent wake through a downstream low-pressure turbine blade passage, ASME J. Turbomach. 127 (2005) 388–394. [16] R. Howell, O. Ramesh, H. Hodson, N. Harvey, V. Schulte, High-lift and aft loaded profiles for low-pressure turbines, ASME J. Turbomach. 123 (2001) 181–188. [17] W. Lou, J. Hourmouziadis, Separation bubbles under steady and periodicunsteady main flow conditions, ASME J. Turbomach. 122 (2000) 634–643. [18] H. Hodson, R. Howell, The role of transition in high-lift low pressure turbines for aeroengines, Prog. Aerosp. Sci. 41 (2005) 419–454. [19] W.P. Jeon, T.C. Park, S.H. Kang, Experimental study of boundary-layer transition on an airfoil induced by periodically passing wake, Exp. Fluids 32 (2002) 229–241. [20] F. Satta, D. Simoni, M. Ubaldi, P. Zunino, Experimental investigation of separation and transition processes on a high-lift low-pressure turbine profile under steady and unsteady inflow at low reynolds number, J. Therm. Sci. 19 (2010) 26–33. [21] M. Talan, J. Hourmouziadis, Characteristic regimes of transitional separation bubbles in unsteady flow, Flow Turbul. Combust. 69 (2002) 207–227. [22] P.J. Schmid, D.S. Henningson, Stability and transition in shear flows, Springer, 2001. [23] D. Simoni, M. Ubaldi, P. Zunino, F. Bertini, Loss production mechanisms in a laminar separation bubble, Flow Turbul. Combust. 89 (2012) 547–562. [24] J.D. Coull, H.P. Hodson, Unsteady boundary-layer transition in low-pressure turbines, J. Fluid Mech. 681 (2011) 370–410. [25] S. Lardeau, M. Leschziner, T. Zaki, Large eddy simulation of transitional separated flow over a flat plate and a compressor blade, Flow Turbul. Combust. 88 (2012) 19–44. [26] O. Marxen, M. Lang, U. Rist, O. Levin, D.S. Henningson, Mechanisms for spatial steady three-dimensional disturbance growth in a non-parallel and separating boundary layer, J. Fluid Mech. 634 (2009) 165–189. [27] K.A. Gompertz, J.P. Bons, Combined unsteady wakes and active flow control on a low-pressure turbine airfoil, AIAA J. Propul. Power 27 (2011) 990–1000. [28] P.A. Monkewitz, P. Huerre, The influence of the velocity ratio on the spatial instability of mixing layers, Phys. Fluids 25 (1982) 1137–1143. [29] D. Simoni, M. Ubaldi, P. Zunino, F. Bertini, Transition mechanisms in laminar separation bubbles with and without incoming wakes and synthetic jet effects, Exp. Fluids 53 (2012) 173–186. [30] J.G. Wissink, DNS of separating, low reynolds number flow in a turbine cascade with incoming wakes, Int. J. Heat Fluid Flow 24 (2003) 626–635. [31] J.G. Wissink, W. Rodi, H.P. Hodson, The influence of disturbances carried by periodically incoming wakes on the separating flow around a turbine blade, Int. J. 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Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Experimental investigation of the interaction between incoming wakes and instability mechanisms in a laminar separation bubble Daniele Simoni ⇑, Marina Ubaldi, Pietro Zunino DIME – Università di Genova, Via Montallegro 1, I-16145 Genova, Italy
a r t i c l e
i n f o
Article history: Received 8 November 2012 Received in revised form 25 March 2013 Accepted 12 May 2013 Available online 23 May 2013 Keywords: Separated flow transition Incoming wakes Kelvin–Helmholtz instability Ultra-High-Lift turbine blade
a b s t r a c t The present paper reports the results of a detailed experimental study on the interaction process between incoming wakes and a laminar separated boundary layer. Experimental investigations have been carried out, for a low Reynolds number case, over a flat plate installed within a double contoured test section designed to produce an adverse pressure gradient typical of Ultra-High-Lift turbine blade profiles. Measurements have been performed by means of a single-sensor hot-wire anemometer. The phase-locked ensemble averaging technique, synchronized with the wake frequency, has been adopted to reconstruct the boundary layer space–time evolution in terms of ensemble-averaged velocity and velocity root mean square. These experimental data have been exploited in order to investigate how the unsteady incoming flow interacts with the instability mechanisms of the boundary layer to drive transition. Two main effects of wake passage were found. The low frequency disturbance associated with the wake passage triggers the Kelvin–Helmholtz instability process developing in the shear layer in the time interval between wakes. Moreover, the temporary reduction/suppression of the separation bubble observed when the incoming wake reaches the separated flow region has been found to be driven by linear stability mechanisms, which promote a quick amplification of the high frequency velocity fluctuations carried by wakes. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction The physical understanding of the separated flow transition mode is of primary importance for Low Pressure Turbine (LPT) applications. Indeed, such components must face the problem of boundary layer laminar separation, especially when high-lift profiles operating at low Reynolds number conditions are considered. Boundary layer separation gives rise to a separated shear layer whose transition process typically forces reattachment, generating a laminar separation bubble (e.g. [1–3]). Under steady inflow conditions, the amplification of unstable waves within the separated shear layer, and in particular along the velocity profile inflection line, has been found to be the dominant mechanism that drives transition (e.g. [4–6]). Recent studies [7–10] showed that vortical structures are generated above the flow stagnation region by the roll up of the free shear layer induced by a Kelvin–Helmholtz instability process. The transition of the separated shear layer is forced by the breakdown to turbulence of these large scale coherent structures, which promotes the boundary layer reattachment [11,12].
⇑ Corresponding author. Tel.: +39 010 353 2447; fax: +39 010 353 2566. E-mail address: [email protected] (D. Simoni). 0894-1777/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2013.05.004
On the other hand, in a real engine the rotor–stator aerodynamic interaction tends to modify the boundary layer separation and transition processes. Wakes shed from upstream rows induce periodic (low frequency) and stochastic (high frequency) velocity fluctuations within the suction side boundary layer altering both the transition and the separation processes as compared with the steady inflow case. Several numerical and experimental studies were carried out in the past to characterize the migration across turbine and compressor rows of unsteady wakes shed from upstream. Michelassi et al. [13] and Wu et al. [14] numerically analyzed the dynamics of unsteady wakes that travel from the inlet to the outlet planes of turbine cascades. Stieger and Hodson [15] experimentally analyzed, by means of a laser Doppler velocimeter, the migration of incoming wakes within an highly loaded low pressure turbine cascade. All these works highlight that the traveling wakes are stretched and bowed by the velocity gradients induced by the cascade geometry along the streamwise and normal to the wall directions. The velocity defect characterizing the wake region tends to be reoriented and pushed toward the suction side of the blade, generating the so called ‘negative-jet’, as described in [16]. This apparent jet carries not only momentum within the suction side boundary layer but also high frequency velocity fluctuations, which further contribute to the periodic boundary layer separation suppression. The turbulence (high frequency fluctuations)
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introduced within the suction side boundary layer by the incoming wakes alters the boundary layer development largely than the low frequency fluctuations associated with the periodic wake passage, as found in the work of Lou and Hourmouziadis [17]. Therefore, an unsteady transition from laminar to turbulent condition occurs, which is favorable for the reduction of the separation bubble extension [18–20]. Anyway, a laminar separation bubble may grow periodically between wakes, as well described in [21]. This implies that a separated shear layer, which is intrinsically unstable according to the linear stability theory [22], is periodically generated. The analysis of the interaction between this strongly unstable flow region and the incoming wake velocity fluctuations represents the main target of the present work. The present paper reports the results of a detailed experimental investigation on the transition/separation processes of the boundary layer under unsteady inflow conditions. A summary of the results obtained in the same test section under steady inflow [8,23] is reported to allow comparisons between the two inflow conditions. The analysis of the results under unsteady inflow is aimed at characterizing the interaction between the separated shear layer developing between wakes and both the low and the high frequency velocity fluctuations carried by wakes. Firstly the phaselocked ensemble averaged quantities are reported to survey the overall behavior of the separated flow region when perturbed by the incoming wakes. Then the propagation of the velocity fluctuations introduced within the separated shear layer by the incoming wakes is analyzed, with the aim of verifying if linear instability mechanisms affect the periodic transition/reattachment processes of the boundary layer. For this purpose, a Lagrangian approach has been adopted in order to characterize the amplification process of velocity fluctuations within the separated shear layer and to highlight the analogies with the separated flow transition mode developing under steady inflow conditions.
2. Experimental apparatus and measuring techniques Measurements have been performed in the low speed blow down wind tunnel of the Laboratory of Aerodynamics and Turbomachinery of Genova University. As shown in Fig. 1, the test section consists of a thick flat plate with a (8:1) regular elliptic leading edge and a sharp trailing edge. The flat part of the plate, including the leading edge, is L = 200 mm long and 300 mm wide. The plate is located between two contoured walls designed to impose the prescribed adverse pressure gradient, typical of UltraHigh-Lift turbine profiles. The test section throat is located at x/ L = 0.285. The endwall geometry is scaled from the Lou and Hourmouziadis test case [17]. The boundary layer developing along the rear part of the plate was surveyed by means of 13 traverses normal to the wall (from x/L = 0.30 up to x/L = 1.0). Each traverse was constituted of 31 points along the direction normal to the wall, with smaller spacing close to the wall. Measurements have been carried out only at midspan of the plate, hence any three dimensional structures along the spanwise direction, such as streamwise streaks or Goertler
x/L=1 moving bars
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Fig. 1. Test section.
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vorticies, cannot be identified. These spanwise structures have been found to contribute to the overall amount of velocity fluctuations in the former part of the separated flow region, as shown for example in Coull and Hodson [24], Lardeau et al. [25] and Marxen et al. [26], A three-axis computer controlled traversing mechanism with a minimum linear translation step of 8 lm has been employed to allow high movement precision and spatial resolution. The boundary layer development has been investigated for a low Reynolds number condition (Re = 70,000). The corresponding test section inlet velocity U0 was 5.5 m/s and the inlet turbulence intensity was Tu = 1.5%. The presence of incoming wakes has been simulated by means of a moving bar system. The bars are moved upstream of the plate leading edge, in a plane located at a distance of 60 mm from it, with a peripheral velocity of Uwake = 7.8 m/s. The flow coefficient for the unsteady inflow tests was chosen in order to be representa tive of real engine operating conditions u ¼ UU0 ¼ 0:7 . The bar wake pitch was set equal to 356 mm in order to obtain a typical reduced L frequency of f þ ¼ fwake ¼ 0:8. The bar diameter (d = 3 mm) was choU0 sen so that the wakes generated by the bars give the same losses as those generated by a typical low-pressure turbine row. The total pressure loss coefficient for the bars (x ¼ Dpt =0:5qU 20 , with Dpt the total pressure drop across the bars) was evaluated to be 3.3% from total pressure measurements. A Dantec single-sensor miniature boundary layer hot-wire probe (type 55P15) has been employed for the velocity measurements. The anemometer output voltages were sampled using a Metrabyte DAS 58 sample and hold AD converter board, 12 bits resolution and 1 MHz maximum sampling frequency. Flow direction in a separation bubble cannot be determined with a single sensor hot-wire, but the rectification of the velocity profile close to the wall usually indicates the reversed flow region. Since the experimental velocity records contain both periodic fluctuations associated with the incoming wake frequency, and other velocity fluctuations due to turbulence and unsteadiness not at the wake frequency, the phase-locked ensemble average technique has been employed to distinguish between the periodic velocity fluctuations and all the other velocity fluctuations called in the following unresolved unsteadiness. Four contiguous incoming wake periods have been analyzed. Each period was subdivided in 100 time steps; thus, each record was constituted of 400 data. In order to obtain a satisfactory statistical accuracy, 500 records were acquired and used for the ensemble average.
3. Results and discussion 3.1. Reference steady inflow case The main results obtained in the same test section at the same Reynolds number for the reference steady case by means of different measuring techniques (single sensor hot-wire anemometer, Particle Image Velocimetry (PIV) and Laser Doppler Velocimetry (LDV)), discussed in detail in previous authors’ papers [8,23], are here summarized for a better interpretation of the unsteady inflow results. The main conclusions of these works can be summarized, with assistance of Fig. 2, as follows. – A laminar separation bubble occurs from x/L = 0.39 up to x/ L = 0.69 (time–mean reattachment position), with the bubble maximum thickness localized at x/L = 0.58. – Velocity fluctuations coming from upstream are amplified within the separated shear layer (along the velocity profile inflection line) with exponential growth rate through linear instability mechanisms.
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– Velocity fluctuations in the Kelvin–Helmholtz frequency range are detected, which induce a sinuous oscillation of the separated shear layer up to the bubble maximum thickness position (see the vector map contained in the blue1 box in the middle of Fig. 2), where saturation of the velocity fluctuations takes place. – The large amplitude oscillations associated with saturation induce the separated shear layer roll-up. – Large scale vortical structures are shed close to the maximum bubble thickness position as a consequence of the shear layer roll-up (see the vector map contained in the red box in the middle of Fig. 2). – The breakdown of these large structures to smaller scales induces the separated shear layer transition, thus the separation bubble reattachment. 3.2. Periodic separation bubble evolution induced by incoming wakes Data concerning the unsteady inflow condition are analyzed in order to understand how the incoming wakes modify the separated-flow transition process described above for the steady inflow reference case. To this purpose, color plots of the ensemble averaged velocity and unresolved unsteadiness distributions, for different time instants in the wake passage period, are reported in Fig. 3 in order to obtain a global view of the time-varying boundary layer behavior for the unsteady inflow case. Results have been here reported only for the time interval 0.0 6 t/T 6 0.7 during which the incoming wake – separated shear layer interaction phenomena occur. Later, for 0.7 6 t/T 6 1.0, since the incoming wake has left the measuring domain, the separation bubble behavior doesn’t show significant variations. The velocity profile inflection line (where @ 2hui/@y2 = 0) has been superimposed to the plots for each instant in order to highlight locations where inviscid instability phenomena may occur. In Fig. 3 a coarse time step (Dt/T = 0.1) has been adopted to show the unsteady development of the separation bubble in an almost complete wake passage period. A finer time step (Dt/T = 0.04) has been used in Fig. 5 for a better description of the amplification 1 For interpretation of color in Figs. 2–5 and 7, the reader is referred to the web version of this article.
mechanisms of flow oscillations during the incoming wake – separated shear layer interaction in the time interval 0.2 6 t/T 6 0.4. Referring to Fig. 3 the wake is entering the measuring domain at t/T = 0.2, as revealed by the large free-stream unresolved unsteadiness. Before the wake arrival time the laminar boundary layer separates and a separated flow transition process occurs, as shown by both velocity and unresolved unsteadiness distributions from t/ T = 0.0 to t/T = 0.2. In this time interval the laminar separation bubble evolves with dynamics similar to that characterizing the steady inflow case: velocity fluctuations grow along the velocity profile inflection line up to reach their maximum value just behind the bubble maximum displacement position. The large unresolved unsteadiness core observable at x/L = 0.60 and y/L = 0.01 is associated with the occurrence of Kelvin–Helmholtz large scale coherent structures, as it will be demonstrated in the following section. At t/T = 0.2 downstream of x/L = 0.60 velocity fluctuations propagate toward the wall promoting transition, and thus the reattachment of the boundary layer. Overall, the dynamics of the transition/reattachment processes here described for the time period between 0.0 6 t/T 6 0.2 closely agrees with that observed under steady inflow conditions by Simoni et al. [8]. At t/T = 0.2 the wake appears on the left of the measuring domain inducing large velocity fluctuations in the free-stream region. At t/T = 0.3 the fluctuations associated with the incoming wake appear strongly amplified within the separated shear layer, exactly along the velocity profile inflection line, up to x/L = 0.50. On the other hand, quite low values of the unresolved unsteadiness characterize the near wall region, which is not affected, at this time instant, by the velocity fluctuations carried by wakes. Thus, in the initial stage of the interaction, fluctuations carried by wakes do not penetrate up to the wall, coherently with the results shown in [27]. For larger t/T values the further increase of the velocity fluctuations within the separated shear layer strongly reduces the thickness of the separation bubble up to around x/L = 0.50, as revealed by the velocity color plots at t/T = 0.4. At t/T = 0.5, the high velocity fluctuation core decays and moves downstream promoting the suppression of the separation bubble. As the incoming wake travels further downstream (t/T = 0.6), the separation bubble in the front part of the measuring domain rises again and then progressively grows. After t/T = 0.7 the separated flow region keeps growing up to assume the structure already observed during the time interval between t/T = 0.0 and t/ T = 0.2. 3.3. Detection of the Kelvin–Helmholtz vortices in the time interval between wakes In the previous section the large unresolved unsteadiness core observable near the maximum bubble displacement for 0.0 6 t/ T 6 0.2 has been ascribed to the presence of Kelvin–Helmholtz vortices. This vortex shedding phenomenon can indeed be highlighted by means of the ensemble averaged velocity and unresolved unsteadiness time–space plots (Fig. 4) obtained at the axial position where the unsteady bubble maximum displacement occurs (x/L = 0.54, slightly upstream with respect to the steady inflow case). In these plots the incoming wake passages are revealed by the large unresolved unsteadiness values, characterizing the freestream region, at t/T = 0.25 + n (with n the wake passage index). At this streamwise position the separated flow thickness grows after the first wake passage from t/T = 0.65 up to t/T = 1.25, generating inflected velocity profiles. The bubble maximum thickness occurs at around t/T = 1.25, just before the subsequent wake arrival time, as revealed by the velocity distribution. Small distinct cores of large unresolved unsteadiness can be observed along the velocity profile inflection line, which moves away from the wall from t/ T = 0.65 up to t/T = 1.25 due to the progressively increased
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Fig. 5. Phase-locked velocity and unresolved unsteadiness distributions (temporal zoom).
thickness of the separation bubble in the period between two wake passages. These cores, which appear with a well defined period DtKH (corresponding to a frequency f ffi 470 Hz) where the velocity profile is inflected, are the traces of the large scale vortical structures generated by the inviscid Kelvin–Helmholtz instability mechanism. In order to confirm the occurrence of the Kelvin–Helmholtz instability the Monkewitz and Huerre [28] dimensionless frequency parameter can be evaluated. The separated shear layer can be interpreted as the interface between two distinct layers (the separated flow region and the external flow) characterized by two different velocities u1 and u2 (for the present case u1 ’ 0 represents the velocity at the bottom edge of the separated shear layer, while u2 = Ue represents the velocity at its top). The velocity ¼ ðu2 þ u1 Þ=2 difference Du = u2 u1 and the averaged velocity u can be introduced to describe the velocity distribution. Moreover the vorticity thickness of the separated shear layer can be determined by dw = Du/(ou/@y)max. Thus, by means of these parameters and the vortex street frequency (f = 470 Hz) it is possible to . The calculate the dimensionless frequency x ¼ 0:25dw ð2pf Þ=u dimensionless vortex shedding frequency results to be x = 0.21, which is very close to the value obtained for the steady case (x = 0.220, see [29]), and well agrees with the range numerically predicted by Yang and Voke [3] 0.206 < x < 0.231. Therefore, the unresolved unsteadiness cores detected in the present investigation for the unsteady inflow condition may be considered as the effect of the Kelvin–Helmholtz shedding vortex phenomenon. Furthermore, due to the local acceleration and deceleration that
Kelvin–Helmholtz vortices induce in the boundary layer in correspondence of their top and bottom sides, respectively, vortex traces are also observable in the ensemble averaged velocity distribution (red and blue vertical stripes on the left of Fig. 4). It is worth explaining the reason for which the visualization of these vortices is possible in the ensemble averaged results. Indeed, flow structures that were not locked to the dominant forcing frequency (the incoming wake frequency) would be smeared out spatially by the ensemble-averaging procedure, as explained in [27]. Since in the present experiments the high unresolved unsteadiness cores survive to the ensemble-averaging process, the low frequency incoming wake passage results to be the ‘‘triggering source’’ or, in other words, the wake locks the relative phase of the Kelvin–Helmholtz vortex shedding phenomenon of the laminar separation bubble growing between wakes. Similar triggering effects induced by the periodic wake passage on a separation bubble were also found in the numerical simulations of Wissink [30] and Wissink et al. [31], as well as in the case of laminar separation bubbles perturbed by periodic external excitations [32,33]. 3.4. Effects of the high frequency velocity fluctuations carried by wakes In order to provide a more in depth analysis of the interaction process between the high frequency velocity fluctuations carried by wakes and the separated shear layer, ensemble-averaged velocity and unresolved unsteadiness distributions are reported in Fig. 5 with a finer time step (Dt/T = 0.04) for the time interval 0.2 < t/ T < 0.4.
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0.05 t/T=0.32
0.1
x/L=0.44; t/T =0.20
0.03
piecewise linear profile
y /L
t/T=0.28
t/T=0.24
0.01
0.04 t/T=0.36
0.02
0.01
t/T=0.20
l
t/T=0.16
0.3
0.35
0
0.4
0.45
0.5
0.55
0
0.2
0.6
0.8
1
/Uref
x/L 0.1
Fig. 6. Evolution along the inflection line of the mean kinetic energy of velocity fluctuations induced by wake at x/L = 0.30 and t/T = 0.16.
0.01
Maximum amplified frequency as predicted by Linear Stability Theory
0.001
pds [m2/s2]
The sequence of the unresolved unsteadiness color plots of Fig. 5 (t/T = 0.2, t/T = 0.24 and t/T = 0.28) clearly reveals that the velocity fluctuations introduced within the boundary layer by the incoming wakes are amplified along the velocity profile inflection line. Maximum values of the unresolved unsteadiness within the separated shear layer increase with time (see the different frames) and move in space (along the velocity profile inflection line). These results suggest the occurrence of convective linear instability mechanisms that act amplifying the velocity fluctuations carried by wakes when they are propagating downstream. The occurrence of linear instability mechanisms during the incoming wake – separated shear layer interaction is supported by the spatial evolution of the mean kinetic energy of velocity fluctuations reported in Fig. 6. Data reported in this plot have been obtained along the velocity profile inflection line following, in both time and space (i.e. in a lagrangian frame), the propagation of velocity fluctuations introduced into the boundary layer by the incoming wake at x/L = 0.30 and t/T = 0.16. This time instant at the measuring grid inlet has been chosen in order to select a fluid portion pertaining to the leading front of the wake, which is characterized by small velocity fluctuations. Thus, Fig. 6 shows the amplification of an initial ‘‘small-amplitude’’ oscillation carried by wakes. The convection speed of velocity fluctuations within the separated shear layer has been assumed equal to the flow velocity at the inflection point. This assumption is good if the wall proximity effects on the propagation speed are negligible, as it occurs for a thick separation bubble [34]. The propagation speed value was verified in [8,29] for steady and unsteady inflows, respectively. Furthermore, also the works of Stieger et al. [35] and Gompertz and Bons [27] show structures generated during the incoming wake – boundary layer interaction that propagate at around a half of the local free-stream velocity (thus with a velocity very close to that at the inflection line). Filled dots on Fig. 5, connected by straight lines, help to identify the correspondence between the spatial positions and the time instants at which the mean kinetic energy of flow oscillations have been evaluated to construct the diagram of Fig. 6. The straight line shape of the experimental curve plotted in log scale in Fig. 6 reveals that the velocity fluctuation kinetic energy is exponentially amplified, as it typically occurs when linear instability mechanisms set in, in the time period 0.16 < t/T < 0.28, moving from x/L = 0.3 to x/L = 0.45. Downstream of x/L = 0.45 the amplification rate of velocity fluctuations departs from the exponential growth and saturation takes place. Saturation is associated with
0.4
0.0001 1E-005 1E-006
unsteady steady
1E-007 1E-008
Incoming wake frequency 1
10
100
1000
f [Hz] Fig. 7. Phase-locked velocity profile measured at x/L = 0.44 for t/T = 0.2 (top); freestream velocity power density spectra at x/L = 0.30 (bottom). Maximum amplified frequency, indicated on the bottom plot, has been computed for the piecewise linear profile depicted on the top.
the occurrence of finite amplitude oscillations within the flow, which induce the generation of higher frequency waves, as described in [4], that contribute to the separated shear layer transition and reattachment processes. Indeed, as previously observed referring to Figs. 3 and 5, from t/ T = 0.32 the thickness of the separation bubble front part progressively decreases up to the almost complete suppression of the bubble observable at t/T = 0.5. Thus, taking into account the results of Fig. 6, we can deduce that the separation bubble starts to be sensibly reduced where (and when) the linear stability mechanisms have amplified the high frequency velocity fluctuations carried by wakes up to induce the saturation of the growth rate, thus the beginning of the separated shear layer transition. Finally, the interaction process between incoming wakes and the separated shear layer can be summarized and further explained as follows. – Boundary layer separation rising between wakes generates inflection points in the velocity profiles that make the separated shear layer intrinsically unstable to velocity oscillations (see the phase-locked velocity profile on the top of Fig. 7, obtained at x/ L = 0.44 just before the wake arrival time). The maximum amplified frequency predicted by the inviscid linear stability theory for the piecewise linear profile approximating the experimentally measured one (black straight line) is f ffi 470 Hz. – Incoming wakes are low frequency disturbances that carry small scale (high frequency) velocity fluctuations. Indeed, the spectrum characterizing the unsteady inflow case obtained in the free-stream region at x/L = 0.30 (bottom of Fig. 7) shows
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not only the occurrence of distinct peaks associated with fundamental and higher order harmonics induced by the traveling periodic wakes, but also larger energy with respect to the steady inflow case for frequency f > 20 Hz, due to the turbulence carried by wakes. Thus, oscillations carried by wakes contain significant energy also in the surround of the most unstable frequency of the separated shear layer (marked with a cyan arrow in the spectral diagram of Fig. 7). – Thus, when the incoming wake is traveling over the separated flow region, the high frequency velocity oscillations introduced into the boundary layer by the incoming wakes match a strongly unstable separated shear layer, which induces an exponential amplification of the velocity fluctuations (Fig. 6). – Consequently, a rapid transition process of the separated shear layer occurs, which induces the localized and temporary reattachment of the separation bubble. 4. Conclusions The experimental data concerning the evolution of a laminar separation bubble under unsteady inflow have been analyzed in order to highlight the role played by the separated shear layer instability in the promotion of the transition, which induces the temporary separation bubble suppression during the incoming wake-boundary layer interaction. Low frequency wake passage events induce a periodic evolution of the separation bubble and influence the separated shear layer Kelvin–Helmholtz instability mechanisms in the time interval between wakes. In this interval a laminar separation bubble is generated and the transition process of the separated shear layer develops in a configuration similar to the steady case: velocity fluctuations start to grow along the velocity profile inflection line, where the boundary layer is intrinsically unstable according to the inviscid instability theory, up to reach their maximum values just behind the bubble maximum displacement position. The incoming wake passage events trigger the occurrence of the Kelvin–Helmholtz instability process, which induces a vortex shedding phenomenon behind the bubble maximum displacement position. Downstream of this position the separated shear layer transition induces the boundary layer reattachment. Otherwise, when the incoming wake reaches the separated flow region, the high frequency velocity fluctuations carried by wakes strongly interact with the separated shear layer which grows between wakes. These high frequency oscillations contain energy at the most unstable frequency of the separated shear layer, thus an exponential amplification of the velocity fluctuations is induced. Convective linear instability mechanisms act amplifying the high frequency velocity fluctuations carried by wakes, up to induce a quick localized transition process of the separated shear layer in the forward part of the bubble, which then leads to the almost complete suppression of the separated flow region. Acknowledgements The authors gratefully acknowledge the financial support of the European Commission as part of the research project TATMo, ‘‘Turbulence And Transition Modeling for Special Turbomachinery Applications’’. It is also acknowledged the financial support of the Italian Ministry for Instruction, University and Research (PRIN 2007). References [1] O. Marxen, D.S. Henningson, The effect of small-amplitude convective disturbances on the size and bursting of a laminar separation bubble, J. Fluid Mech. 671 (2011) 1–33.
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