Large-scale vortical structure of turbulent separation bubble affected by unsteady wake

Transcription

1 Large-scale vortical structure of turbulent separation bubble affected by unsteady wake S. Chun, H.J. Sung Experiments in Fluids 34 (2003) DOI /s Abstract The large-scale vortical structure of a turbulent separation bubble under the influence of an unsteady wake was investigated. The unsteady wake was generated by a spoked-wheel type wake generator installed in front of the separation bubble. This wake generator was rotated either clockwise or counter-clockwise at Re H = The mechanism of vortex shedding from the separation bubble was analyzed in detail by taking a conditional average as well as a phase average. Spatial box filtering (SBF) was used to extract the large-scale vortical structure from the turbulent separation bubble affected by the unsteady wake. To elucidate the influence of the unsteady wake on the large-scale vortical structure, conditional averages of the velocity, vorticity and turbulent kinetic energy were calculated. The nature of the convection of the vortical structure under the influence of an unsteady wake was analyzed. The dipole acoustic pressure level was predicted using Curle s integral of wall-pressure fluctuations. List of symbols H half-thickness of a blunt body (mm) R pp cross-correlation of wall pressure R pu cross-correlation of wall pressure and streamwise velocity R pv cross-correlation of wall pressure and wall-normal velocity R s distance from acoustic source point to observation point (mm) Re H Reynolds number, U H/m St H normalized wake-passing frequency, f p H/U T vortex shedding period (s) free-stream velocity (m/s) U Received: 26 March 2002 / Accepted: 9 January 2003 Published online: 12 April 2003 Ó Springer-Verlag 2003 S. Chun, H.J. Sung (&) Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Kuseong-dong Yuseong-gu, Daejeon, Korea hjsung@mail.kaist.ac.kr Tel.: Fax: This work was supported by a grant from the National Research Laboratory of the Ministry of Science and Technology, Korea. b width of test section (mm) f p wake-passing frequency (Hz) k turbulent kinetic energy (m 2 /s 2 ) l j cosine of angle p instantaneous wall pressure (Pa) p rms root-mean-square of wall pressure (Pa) p SBF spatial-box-filtered wall pressure (Pa) p d acoustic dipole source (Pa) p w conditionally averaged wall pressure [Pa] q dynamic pressure, 0.5qU 2 (Pa) r distance from origin to observation point (mm) u c convection velocity (m/s) time-mean reattachment length (mm) x R Greek symbols d ij Kronecker s symbol u phase angle ( ) k wavelength (mm) h inclination angle ( ) J angle between vertical axis and observation point ( ) q density (kg/m 3 ) s time delay (s) spanwise vorticity (m 2 /s) x z Abbreviations AR aspect ratio CW clockwise CCW counter-clockwise SBF spatial box filtering 1 Introduction Typically, flow past a blunt body at high Reynolds number leads to the formation of a turbulent separation bubble near the sharp corner as well as the emergence of a reattaching flow further downstream (Cherry et al. 1984; Kiya and Sasaki 1983, 1985; Chun and Sung 2002). The separation bubble is characterized by rolled-up vortices in the shear layer and their interaction with the surface (Cherry et al. 1984; Kiya and Sasaki 1983, 1985; Hwang et al. 2001). The presence of a separated flow, together with a reattaching flow, gives rise to unsteadiness, pressure fluctuations and vibrations of the structure through which the fluid is flowing. Furthermore, when a wake generator is located in front of the blunt body, the turbulent separation bubble is subjected to a periodic unsteady wake located

2 573 Fig. 1. Flow configuration of unsteady wake upstream. The flow configuration of the unsteady wake and turbulent separation bubble is shown in Fig. 1. When an unsteady wake interacts with a separated and reattaching flow, the result is a flow with extremely complex characteristics. To understand this complex flow behavior, it is necessary to understand the flow physics underlying the phenomena. Numerous studies have used conditional averaging techniques to extract large-scale vortical structure from turbulent separated and reattaching flows (Cherry et al. 1984; Kiya and Sasaki 1983, 1985; Hijikata et al. 1996; Johansson et al. 1987). Cherry et al. (1984) visualized the large-scale vortical structure of the separation bubble by using space time correlations for pressure pressure, velocity velocity and pressure velocity. As a conditional signal, two reference microphones were installed near the separation and reattachment points (Cherry et al. 1984). A strong negative correlation was captured caused by the low-frequency flapping motion of the vortex shedding (Cherry et al. 1984). Kiya and Sasaki (1985) used a surfacepressure sensor to educe the structure of large-scale vortices. A certain threshold level was assumed to provide a conditional signal whenever the measured pressure was above or below the threshold level to trigger the conditional average (Kiya and Sasaki 1985). They identified a saw-tooth like movement of the separation bubble and hairpin vortices in their conditional average (Kiya and Sasaki 1985). The majority of previous studies have used a one-point conditional signal to extract the large-scale vortical structure. To observe spatially evolving large-scale vortical structures, however, multiple-array signals were needed to resolve the spatial flow characteristics. Kiya and Sasaki (1985) found that the smearing effect caused by ill-measured pressure fluctuations could be reduced by employing pressure fluctuations at several suitably arranged positions as the conditioning signals (Kiya and Sasaki 1985). In the present study, SBF was employed from the spatial distribution of wall-pressure fluctuations (Lee and Sung 2002; Blake 1986). The SBF signals were obtained by adding or subtracting an array of the measured signals by microphones (Lee and Sung 2002). The main objective of the present study was to extract spatially evolving large-scale vortical structures that manifest when the turbulent separation bubble is affected by the unsteady wake. The SBF method was applied to the multiple-array wall-pressure measurements. In a previous study by our group (Chun and Sung 2002), the influence of an unsteady wake on a turbulent separation bubble was scrutinized in a time-average sense by altering the direction of rotation (clockwise and counter-clockwise) and the normalized passing frequency (0 St H 0.20). Here we consider the same experimental conditions, but in the present work we focus on extracting the unsteady largescale vortical structure by taking a phase average and a conditional average. The cross-correlation, coherence, mean velocity and turbulent kinetic energy were visualized to derive large-scale vortical structures in the turbulent separation bubble, and an appropriate wavelength k was defined to characterize the large-scale vortical structure. The nature of the convection of the vortical structure was analyzed under the influence of an unsteady wake. In addition, the reattachment length x R was found to vary according to a saw-tooth pattern when an unsteady wake was imposed. Conditionally averaged wall-pressure levels and the corresponding noise sources were predicted using Curle s integral of wall-pressure fluctuations. Unsteady behavior of the type described here is an important consideration in the design of turbomachines because it leads to energy loss and structural vibrations as well as the generation of sound. 2 Experimental apparatus and procedure Experiments were performed in the subsonic open-circuit wind tunnel that was employed in a previous study by our group (Chun and Sung 2002). A settling chamber, honeycomb and screens were placed in sequence. A smooth contraction fairing with a ratio of 4:1 and flow-conditioning elements inside the settling chamber ensured a high-quality inlet flow. The free-stream turbulence intensity was less than 0.6% at flow speeds of m/s. A spoked-wheel type wake generator was located between

3 574 the smooth contraction and the test section. The flow configuration of the test section and the wake generator is illustrated in Fig. 1. As shown in the front view, 24 cylindrical rods were attached to the wake generator. Each rod was 400 mm in length and 10 mm in diameter. A blunt body was installed behind the wake generator. The blunt body was a blunt-faced flat plate of which dimensions are 350 mm (width) 30 mm (thickness) 550 mm (length). The characteristic length of the blunt body (H) was defined as half of the thickness of the blunt body, i.e., H=15 mm (Cherry et al. 1984; Kiya and Sasaki 1983). The aspect ratio AR based on this value of H was 26.7 and the blockage ratio was 7.5%. The flow along the centerline of the blunt body was assumed to be two-dimensional on the basis of the work of Brederode and Bradshaw (1978). The wake Strouhal number St H was defined as Fig. 2. Perspective view of installed array microphones St H ¼ f ph U 1 ; ð1þ where f p is the wake-passing frequency, which is controlled by both the rotational speed of the cylindrical rods and the number of the rods (Chun and Sung 2002). The Reynolds number Re H is defined as Re H ¼ U 1H ; ð2þ v where H is the characteristic length of the blunt body and U is the mainstream velocity. Thus, for the value of U =6.0 m/s used in the present experiments, the Reynolds number based on the characteristic length was Re H = As mentioned above, the experimental conditions used in the present work were the same as those employed previously by our group (Hwang et al. 2001; Chun and Sung 2002). To achieve synchronized measurement of the wall pressure and velocity, an array of microphones was used with an anemometry system. As shown in Fig. 2, 16 ICPtype microphones (Soritel Inc.) were installed on the surface of the blunt body. Beginning at the position of x/h=0.8 downstream of the separation point, the microphones were installed at intervals of 0.8H (0.8 x/ H 8.8). To enhance the sensor resolution of each microphone, a pinhole of diameter 1 mm through which measurements were taken and an installation hole of diameter 10.6 mm were placed concentrically. A 16- channel differential amplifier (PCB 514A, The Modal Shop Inc., Cincinnati, Ohio) was used to amplify the microphone signals. The sensitivity of each microphone was measured by comparison with the signal from a half-inch reference microphone (B&K Type 4133, Brüel & Kjær Inc., Norcross, Ga.). Typically, the sensitivity was about 0.15 V/Pa. The magnitude error and phase delay were within ±3 db and ±3, respectively, in the frequency range of 5 Hz to 10 khz (Lee and Sung 2002). To document the turbulent velocity fluctuations, a constant-temperature anemometer (TSI IFA100/300) was used with a split film probe (TSI 1288) (TSI Inc., Shoreview, Minn.). In the experiments, the low-pass cut-off frequency of the anemometer was set to 2 khz. To systematically measure the flow velocity, 22 measurement locations at intervals of Fig. 3a, b. Flow models of cutting regime and wrapping regime 0.4H (x/h=0.4~8.8) were defined along the mainstream direction. In the wall-normal direction, 20 measurement locations were defined non-uniformly (y/h=0.13~4.0). To differentiate the u and v components of the velocity, a 90 angle adapter (TSI 1157) was used for the v component. The software LabVIEW and an A/D board (DT2839, Data Transition Inc., Marlboro, Mass.) were used to obtain the pressure velocity correlation data and to analyze them. The sampling frequency was 5 khz and a total of 102,400 data were stored. To apply a phase-averaging technique, an optical tachometer (Ono Sokki HT-5200, Ono Sokki Co. Ltd, Yokohama, Japan) was installed in front of the spoked-wheel type wake generator. A trigger signal was generated from the tachometer in every rotation of the wake generator and synchronously measured with pressure and velocity. 3 Experimental results and discussion 3.1 Phase-averaged flow field As addressed by Chun and Sung (2002), there are two regimes of the separated flow disturbed by different incoming wakes: the cutting regime and the wrapping regime. As shown in Fig. 3, the cutting regime is the regime in which the separation bubble is disturbed by the unsteady wake as it moves inward toward the blunt body, and the wrapping regime is the regime in which the interaction is characterized by the outward motion of

4 575 Fig. 4a, b. Phase-averaged velocity and vorticity at Re H =5.600 and St H =0.2 the unsteady wake prior to impact with the blunt body. The flow behavior in the wrapping regime results in the unsteady wake wrapping around the separation bubble. The motions characterizing these two regimes are evident in the sequential plots of the phase-averaged velocity field and turbulent kinetic energy shown in Figs. 4 and 5. Since the wake generator is composed of 24 rods, one passing interval of the unsteady wake is 360 /24=15. The reference phase (u=0) is obtained from the trigger signal generated by the tachometer in every rotation. Inspection of the phase-averaged velocity field in Fig. 4 reveals a significant discrepancy between the results obtained with the wake generator rotating in a clockwise (CW) direction and those obtained with it rotating in a counter-clockwise (CCW) direction. When the wake generator is rotated in the CW direction, a passing wake approaches the blunt body from the top-left corner of the flow field and moves toward the bottom, i.e., flow characteristic of the cutting regime. The upper structure observed in Fig. 4a is due to the passing wake. Closer inspection of this upper structure reveals that the unsteady wake consists of a pair of counter-rotating vortical structures. The lower structure observed in Fig. 4a is due to the influence of the separated flow near the edge (x/h=0). In contrast, when the wake generator is rotated in the CCW direction, the passing wake impinges on the blunt body from the left-bottom of the flow field with downstream convection. A passing wake approaches the blunt body from the bottom-left corner of the flow field and moves outward the blunt body as shown in Fig. 4b. Figure 5 illustrates the phase-averaged turbulent kinetic energy for the systems with the wake generator rotating CW and CCW. A region of high turbulent kinetic energy is observed inside the separation bubble. For CW rotation, a vortical structure is seen near the separation edge. This vortical structure is induced by the negative circulation of the unsteady wake at x/h@0.8 and 0 y/ H 2, which is in good agreement with the result reported in Kiya and Sasaki (1985). Strong entrainment takes place due to the positive circulation caused by the unsteady

5 576 Fig. 5a, b. Phase-averaged turbulent kinetic energy at Re H =5.600 and St H =0.2 wake. This phase coincides with the inrush of the outer irrotational fluid at high pressure towards the wall (Kiya and Sasaki 1985; Lee and Sung 2002). Thus, the incoming unsteady wake brings about regular formation of turbulent kinetic energy. For CCW rotation, however, the turbulent kinetic energy is high irrespective of the flow structure of the unsteady wake. This can be attributed to the strong interactions during the mixing in the wrapping regime, which produce additional turbulent kinetic energy (Chun and Sung 2002; Tung and Kleis 1996; Kang and Choi 2001). The enhanced mixing induces a strong streamwise vorticity which breaks down the organized spanwise vortical structure (Tung and Kleis 1996; Kang and Choi 2001). In addition, it is known that the higher turbulence intensity induced by the unsteady wake in the wrapping regime significantly affects the reduction of x R (Chun and Sung 2002; Marshall and Krishnamoorthy 1997). Accordingly, the interaction in the wrapping regime can be regarded as a source of generating streamwise vortices near the separation edge. Note that the time-mean reattachment length of the system with CCW rotation (x R /H=2.4) is much shorter than that of the CW rotating system (x R /H=4.0). 3.2 Spatial box filtering As mentioned above, SBF was utilized to extract the component corresponding to a certain wavenumber from the spatially distributed wall-pressure fluctuations (Blake 1986). The equation for obtaining the specific spatial component from the pressure field (Lee and Sung 2002) is given by, p SBF ¼ XN 1 ð 1Þ ½jH=kŠ p j j¼0 ð3þ where N is the number of microphones in the array, p j is the jth element of pressure signal, and k is the wavelength of the filtering function ()1) [jh/k]. The wavelength k is a function of N and Dx,

6 Fig. 6. Spatial box filtering k ¼ N 2 Dx; ð4þ where Dx is the sensor interval. In the present study, a value of N=10 is used for CW rotation and N=6 for CCW rotation. Since Dx is fixed at 0.8H in all cases, k=4h for CW rotation and k=2.4h for CCW rotation (Lee and Sung 2002). Figure 6 shows a schematic diagram of the SBF for the case of N=6 along the centerline of the blunt body depicted in Fig. 2. An example of the SBF is illustrated in Fig. 7. In this figure, the parameter p 1 represents the pressure signal at x/h=0.8. Relatively strong fluctuations in p 1 indicate that a strong vortical structure is passing in the early region of the separation bubble by the unsteady wake. It is clear from Fig. 7 that the pressure fluctuation levels gradually decrease on going from p 1 to p 6, indicating that the fluctuations diminish as the flow moves along the x axis. The low levels of fluctuations in p 4 ~p 6 indicate that only small-scale eddies occur at the corresponding positions. As reported in Lee and Sung (2002), p SBF is obtained by first adding or subtracting the SBF function (defined in Eqs. (3) and (4)) to each of the pressure signals measured over a period of 20 s, followed by spatial integration of the resulting transformed signals. By employing an appropriate wavelength k in the SBF, the small-scale fluctuations are filtered out substantially. Invoking Taylor s frozen field hypothesis, p SBF can be thought as a trace of large-scale vortical structure in time. To find an appropriate value of k, cross-correlation of the multi-arrayed pressure signals and corresponding conditional averaging of the wall-pressure fluctuations are calculated. The relevant spatial scale of the wall-pressure fluctuations is obtained by measuring the cross-correlation R pp. The streamwise distribution of conditionally averaged pressure fluctuations is represented by p rms /q, which is normalized by the dynamic pressure q ¼ 0:5 qu 2 1. The correlation R pp and the normalized pressure fluctuation p rms /q, which are shown in Fig. 8, are defined as: R pp ¼ hpx ð R =H; 0Þpx=H; ð 0Þi=p 2 rms ; ð5þ p rms =q ¼ hpx=h; ð 0Þi 0:5 qu1 2 j v¼ 2:5v rms : ð6þ where the subscript rms indicates a root-mean-squared value. In the above equation, p rms /q is the conditional average of the transverse velocity fluctuations when the wall-normal velocity v at (x/h, y/h)=(4.0, 0.53) exceeds )2.5v rms. The spatial periodicity of the large-scale vortical structure is determined by inspecting the local minima of R pp and p rms /q. For CW rotation, the spacing between adjacent minima is approximately k =4.0H for both R pp Fig. 7. An example of SBF Fig. 8a, b. Streamwise scale of pressure fluctuations and p rms /q. This spacing indicates the distance between consecutive large-scale vortices. For CCW rotation, the spacing is 2.4H. Note that these values coincide exactly with the corresponding reattachment lengths, x R /H=4.0 for CW rotation and x R /H=2.4 for CCW rotation. The validity of the estimation of k represented above is confirmed by calculating the cross-correlation of pressure and velocity. The definitions of R pu and R pv are R pu ¼ hpx ð R =H; 0Þux=H; ð y=hþi=p rms u rms ; ð7þ R pv ¼ hpx ð R =H; 0Þvx=H; ð y=hþi=p rms v rms : ð8þ In the system at St H =0 (Fig. 9), these correlations clearly show the spatial evolution of the correlation along the separation bubble. The spans between the maxima are 577

7 578 Fig. 9a, b. Correlations of pressure and velocity at Re H =5.600 and St H =0 approximately k=4.0h for CW rotation and k=2.4h for CCW rotation, as can be seen in Fig. 10. The y position of the high correlation at s=0 in Fig. 9 is y=0.16x R for St H =0. This is almost the same as the value of 0.18 x R reported by Kiya and Sasaki (1985). Lee and Sung (2002) stated that the maximum correlation could be regarded as a coherent vortex center. The large-scale vortical structure is elliptic rather than circular, with an inclination angle. The wall-normal locations of the large-scale vortex and the inclination angles for the CW and CCW systems are summarized in Table 1. The fact that the maximum correlation is located at y=0.25x R for CW rotation and at y=0.30x R for CCW rotation indicates that the unsteady wake in the wrapping regime causes a reduction in the distance between the developing large-scale vortices. The spatial development of large-scale vortices is affected by the enhancement of mixing in the wrapping regime, which is closely related to the role of streamwise vortices (Tung and Kleis 1996; Kang and Choi 2001). 3.3 Conditionally averaged flow field with SBF On the basis of the SBF, conditionally averaged flow structures were obtained for St H =0. Sequential plots of the vector and vorticity field and corresponding turbulence intensity over one shedding cycle are displayed in Fig. 11. Five snapshots with time differences s=)t/2, )T/4, 0, T/4, T/2 are chosen, where T is the shedding period of largescale vortices (TU /H=11.11). The first and last snapshots should be the same because they differ by a time of T. A threshold level of wall pressure was applied to conditionally sample any meaningful flow field (Kiya and Sasaki 1985; Lee and Sung 2002). In the present experiments, a threshold level of p =1.8p rms was imposed. To correctly extract the flow structure, the convection velocity of the large-scale vortical structure should be subtracted from the instantaneous conditionally averaged velocity u/u as in Lee and Sung (2002). The conditionally averaged vector, vorticity, and turbulence intensity data for St H =0, which are displayed in Fig. 11, clearly show that a large-scale flow structure is formed and convects downstream. At s=)t/2, a separation bubble is observed in the region 0 x/h 7. p ffiffi Comparison of the distribution of turbulence intensity ( k =U1 ) with that of vorticity reveals that the location of maximum vorticity coincides with that of maximum turbulence intensity. This indicates the existence of a large-scale vortex (Kiya and Sasaki 1985; Lee and Sung 2002). At s=)t/4, a strong inflow of irrotational fluid is observed in the region 7 x/h 9, along with a slightly tilted largescale vortex (4 x/h 7). The appearance of a global dividing streamline in Fig. 11 indicated by black arrows

8 579 Fig. 10a, b. Correlations of pressure and velocity for CW and CCW at Re H =5.600 Fig. 11a, b. Conditionally averaged vector, vorticity and turbulence intensity for St H =0 at Re H =5.600 Table 1. Locations of vortex and inclination angles Case Location of vortex (y/h) St H =0 0.18x R 42 St H =0.2 and CW 0.25x R 45 St H =0.2 and CCW 0.30x R 35 Inclination angle (h) suggests the existence of another large-scale vortex with high turbulent kinetic energy. This is an example of the positive peak of wall pressure with SBF, which leads to an enlargement of the separation bubble. The positive peak of wall pressure arises due to the downwash of external irrotational flow that intervenes between consecutive large-scale vortices (Kiya and Sasaki 1985; Lee and Sung 2002). The separation bubble is enlarged to the greatest extent at s=0 owing to the retarding interaction between the reattaching vortex and the wall (Lee and Sung 2002). At s=t/4, the large-scale vortex sheds from the separation bubble at (x/h, y/h)=(6.0, 1.0), with the same inclination angle as at s=)t/4. The vortex shedding clearly manifests at s=t/2 as a dividing streamline at (x/h, y/h)=(7.0, 0.5). The newly generated large-scale vortex is also located in the region 4 x/h 6ats=T/2. Now, the influence of the unsteady wake on the conditionally averaged large-scale vortical structure is considered. Figure 12 shows sequential plots of the flow fields for CW rotation of the wake generator. Compared with the

9 580 Fig. 12a, b. Conditionally averaged vector, vorticity and turbulence intensity for St H =0.2 and CW at Re H =5.600 flow structure in Fig. 11, the size of the separation bubble is significantly reduced. The period of shedding is fixed at TH/U =5.0, which is the reciprocal of the wake-passing frequency St H =0.2. At s=)t/2, a large-scale vortex with an ellipsoidal shape is shed from a separation bubble at (x/h, y/h)=(3.0, 0.5). The location of maximum vorticity coincides with that of maximum turbulence intensity. As mentioned above, this indicates the existence of a largescale vortex. Note that the lowest turbulence intensity is observed at (x/h, y/h)=(4.4, 2.5), which is just above the large-scale vortex. Between s=)t/2 and 0, the large-scale vortex convects with the constant convection velocity u c / U ~0.5. At s=t/4, another detachment of a large-scale vortex is seen at (x/h, y/h)=(2.4, 0.6), which causes the separation bubble to shrink. For CCW rotation of the wake generator, the flow pattern is the same as that observed under CW rotation, but with a much smaller vortical structure (see Fig. 13). Compared with the case of CW rotation, the size of the separation bubble is reduced by 40% in both the streamwise and the wall-normal directions. With the same frequency of the unsteady wake as the CW rotation system (St H =0.2), a large-scale vortex sheds from the separation bubble at (x/h, y/h)=(2.4, 0.6) with rapidly decreasing turbulent intensity. However, the highest turbulence intensity is still contained in the separation bubble. The turbulence intensity is highest during the initial phase of flow separation along the shear layer centered at the large-scale vortical structure. This is because, in comparison to the system with CW rotation, the direction of the unsteady wake under CCW rotation is such that there is an additional contribution to the turbulence intensity as a result of the interaction between the separation bubble and the unsteady wake (Chun and Sung 2002). The convection velocity is estimated by measuring the location of the maximum turbulence intensity (Cherry et al. 1984; Kiya and Sasaki 1985; Lee and Sung 2002). To verify the existence of the so-called saw-tooth movement of the separation bubble in these systems, plots were prepared of space time contours of the conditionally averaged streamwise velocity measured at y/h@0.13 (Fig. 14). These spatio-temporal maps of the streamwise velocity clearly show the unsteadiness of the reattaching region. The solid contour line corresponds to zero instantaneous streamwise velocity, i.e., it is a trace of the instantaneous reattachment position. According to Kiya and Sasaki (1985), the asymmetric movement of the separation bubble is caused by the shrinkage of the separation bubble, which is sudden owing to the largescale motions of the vortex shedding. Such saw-tooth motion is observed along the trace of the reattachment point (5 x/h 8) for St H =0. In the initial phase of flow separation, there is no evidence of the saw-tooth movement because of the weak interaction between the vortices and the wall (0 x/h 2). In contrast to the result for St H =0, in the system with CW rotation, the reattachment position retreats all at once with the passage of large-scale vortices by the unsteady wake at

10 581 Fig. 13a, b. Conditionally averaged vector, vorticity and turbulence intensity for St H =0.2 and CCW at Re H =5.600 tu /H~0 after a gradual advancement (Lee and Sung 2002). For CCW rotation, it is seen that the reattachment position is significantly shifted toward upstream by the unsteady wake. Space time contour plots of conditionally averaged wall-pressure fluctuations are shown in Fig. 15. For St H =0, a convective packet is clearly observed around the reattachment region (6 x/h 8). When the unsteady wake is imparted (St H =0.2 and CW rotation), the convective packet moves upstream and the packet is formed more frequently. The convective packet observed in the system with CCW rotation moves closer to the separation edge than the packet in the CW rotating system, which significantly reduces x R. On the basis of the prior wall-pressure fluctuations, the surface dipole source (p d ) is predicted using Curle s integral (Fujita and Kovasznay 1974; Smol yakov 1994). p d ðx; y; tþ ¼ 1 i S ds l j d ij p w ; R S ð9þ Fig. 14a c. Conditionally averaged streamwise velocity at y/h=0.13 and Re H =5.600 where p w is the conditionally averaged wall pressure and l j are the cosines of the angles between the normal to the surface S and the Cartesian axes, d ij is Kronecker s symbol, and R s is the distance from the sound source on the surface to the point of observation (Smol yakov 1994). The square brackets represent a retarded time. Taking into account the finite microphone positions, Eq. (9) can be discretized as follows:

11 582 Fig. 15a c. Conditionally averaged wall-pressure field at Re H =5.600 Fig. 17a c. Distributions of dipole sound pressure level Fig. 16. Coordinate system for calculating the Curle s integral ZZ i S ds l j d ij p w R S ¼ b XN r x i sin # cos # ½p w Š 4p i¼1 r 2 þ x 2 i 2rx 3=2 Dx; ð10þ i sin # where b is the width of the test section and x i is the distance from origin to ith point of sound source. The details of the coordinate system and notation are shown in Fig. 16. The conditionally averaged dipole sources calculated from Eq. (10) are shown in Fig. 17. When the unsteady wake is not imposed (St H =0), the acoustic pressure is mainly concentrated on the reattachment region. However, when the unsteady wake is imposed either through CW or CCW rotation, the pressure level becomes very strong in the vicinity of the separation edge. It is seen that the pressure level in the system with CCW rotation is aligned to a greater extent with the separation edge than that of the system with CW rotation. Eight snapshots of the acoustic pressure levels taken at intervals of T/8 in the CW and CCW systems are shown in Figs. 18 and 19 respectively. Comparison of these figures shows that the pressure levels are higher for CCW rotation than for CW rotation. The highest levels of acoustic pressure are observed near the separation edge. 4 Conclusions The large-scale vortical structures of a turbulent separation bubble affected by an unsteady wake were extracted. In this work, which builds upon a previous study by our group (Chun and Sung 2002), a spoked-wheel type wake generator with cylindrical rods was installed in front of the separation bubble. The main emphasis of the present study was the identification of the large-scale structures through consideration of the spatial distribution of surface-pressure fluctuations. A conditional averaging technique with a certain threshold level was adopted through the pressure velocity joint measurement with an array of microphones. The large-scale vortical structure was reconstructed by means of the conditional average based on the SBF. The vortex shedding of the large-scale vortical structure was delineated with respect of the conditional phase. The size

12 583 Fig. 18. Dipole sound source for St H =0.2 and CW at Re H =5.600 Fig. 19. Dipole sound source for St H =0.2 and CCW at Re H =5.600

13 584 of the separation bubble was reduced by the imposition of the unsteady wake, and the direction in which the wake generator was rotated had a significant effect on the flow structure. The large-scale vortical structure obtained using SBF revealed that the flow structure was influenced in the wrapping regime rather than in the cutting regime. The saw-tooth movement of the separation bubble was examined by reconstructing the unsteady large-scale vortical structures, and the surface sources were predicted using Curle s integral. The acoustic pressure level was stronger in the system with CCW rotation than in the system with CW rotation. References Blake WK (1986) Mechanics of flow-induced sound and vibration. Academic Press, London Brederode V, Bradshaw P (1978) Influence of the side walls on the turbulent center-plane boundary-layer in a square duct. J Fluid Eng 100:91 96 Cherry NJ, Hillier R, Latour MEMP (1984) Unsteady measurements in a separated and reattaching flow. J Fluid Mech 144:13 46 Chun S, Sung HJ (2002) Influence of unsteady wake on a turbulent separation bubble. Exp Fluids 32: Fujita H, Kovasznay LSG (1974) Unsteady lift and radiated sound from a wake cutting airfoil. AIAA J 12: Hijikata K, Suzuki Y, Iwana K (1996) Flow visualization by velocity pressure cross correlation. J Fluid Eng 118: Hwang KS, Sung HJ, Hyun JM (2001) An experimental study of largescale vortices over a blunt-faced flat plate in pulsating flow. Exp Fluids 30: Johansson AV, Her JY, Haritonidis JH (1987) On the generation of high-amplitude wall-pressure peaks in turbulent separation bubble. J Fluid Mech 175: Kang S, Choi H (2002) Suboptimal feedback control of turbulent flow over a backward-facing step. J Fluid Mech 463: Kiya M, Sasaki K (1983) Structure of a turbulent separation bubble. J Fluid Mech 137: Kiya M, Sasaki K (1985) Structure of large-scale vortices and unsteady reverse flow in the reattaching zone of a turbulent separation bubble. J Fluid Mech 154: Lee I, Sung HJ (2002) Multiple-arrayed pressure measurement toward the investigation of the unsteady flow structure of a reattaching shear layer over a backward-facing step. J Fluid Mech 463: Marshall JS, Krishnamoorthy S (1997) On the instantaneous cutting of a columnar vortex with non-zero axial flow. J Fluid Mech 351:41 74 Smol yakov AV (1994) The influence of viscous stress fluctuations in a flow on aerodynamical noise. Acoustica 80: Tung S, Kleis SJ (1996) Initial streamwise vorticity formation in a two-stream mixing layer. J Fluid Mech 319: