Three-dimensional coherent structure in a separated and reattaching flow over a backward-facing step

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1 Three-dimensional coherent structure in a separated and reattaching flow over a backward-facing step I. Lee, S. K. Ahn, H. J. Sung Experiments in Fluids 36 (2004) DOI /s Abstract An experimental study was carried out to elucidate the large-scale vortical structure in a separated and reattaching flow over a backward-facing step. The Reynolds number based on the step height (H) was Re H =33,000. The large-scale vortical structure was probed by means of three-dimensional velocity measurements performed at the recirculation zone (x/h=4.0) and the reattachment zone (x/h=7.5). A 32-channel microphone array extending in the streamwise and spanwise directions was used for sensing the wall pressure fluctuations. The relationship between the flow field and the relevant spatial mode of the pressure field was determined by examining the spatial box filtering. From the relevant spatial mode of the wall pressure fluctuations, a conditional averaging technique was employed to characterize the coherent structure. In addition, the cross-correlation between velocity and wall pressure fluctuations was calculated to identify the structure and the length scale of the large-scale vortex. The cross-correlation results revealed that the large-scale hairpin vortices have a three-dimensional structure, in agreement with previous findings. The present results clearly show the growth and downstream elongation of the hairpin vortices. List of symbols H step height, m k turbulent kinetic energy, m 2 /s 2 q freestream dynamic pressure, Pa Re H Reynolds number based on U 0 and H,U o H/m U 0 freestream velocity, m/s U c convection velocity, m/s X 0 streamwise coordinate of the measurement origin, m time mean reattachment length, m x R Received: 19 June 2002 / Accepted: 19 March 2003 Published online: 21 January 2004 Ó Springer-Verlag 2004 I. Lee, S. K. Ahn, H. J. Sung (&) Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Kusong-dong, , Yusong-ku, Taejon, Korea hjsung@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. Greek symbols c p forward flow time fraction q cross-correlation coefficient s time delay, s x vorticity, m 2 /s 1 Introduction The characterization of unsteady coherent structure in a separated and reattaching flow process is a longstanding problem that has been investigated in numerous experimental as well as numerical studies. Many studies have been performed to find an intrinsic unsteady feature in separated and reattaching flows (Eaton and Johnston 1981, 1982; Cherry et al. 1984; Kiya and Sasaki 1985; Driver et al. 1987; Devenport and Sutton 1991; Heenan and Morrison 1998). Particular attention has been given to the identification of coherent structure by means of a conditional average of the flow field based on pressure fluctuations in the reattachment region. For example, Cherry et al. (1984) characterized the nature of the unsteadiness in a separated shear layer through measurements of wall pressure fluctuations, and Kiya and Sasaki (1983, 1985) deduced a three-dimensional hairpin vortical structure in the reattaching region from conditionally averaged velocity vectors and turbulent intensity contours. However, past studies in which the flow structures were reconstructed from the conditional average employed temporal information of the local pressure fluctuations measured at a single point as a conditioning signal. The so-called temporal scheme can cause blurring of the structure due to the effects of local, small-scale events that are not associated with the large-scale vortical structure. This blurring phenomenon has been demonstrated by Lee and Sung (2002), who utilized spatial information of the pressure fluctuations measured by an array of microphones. In Lee and Sung (2002), the pressure velocity joint measurement was performed on a centerplane in a flow over a backward-facing step. From the space time information of the pressure fluctuations, an effective means of extracting a relevant spatial mode due to the large-scale vortical structure was introduced and discussed. This was termed spatial box filtering (SBF) with a specific discrete spatial wavelength. Emphasis was placed on the specific SBF mode of pressure, with the wavelength corresponding to the length scale of the large-scale vortical structure. This mode then turned out to be well correlated 373

2 374 with the flow field of the vortical structure. This result provided evidence that the pressure fluctuations are mainly due to the vortical structure in the shear layer. The success of SBF derives from the fact that it furnishes coherent-structure-oriented conditioning information for filtering out irrelevant small-scale eddies. Regarding the modulated behavior of the coherent structure by the flapping motion, the relation between the lowpass-filtered pressure and the periodic shrinkage/enlargement motion of the separation bubble was established. It was then pointed out that there are still unsolved questions regarding more detailed three-dimensional flow structures. The three-dimensional nature of the large-scale vortical structure in a separated and reattaching shear layer has been corroborated in a variety of studies (Kiya and Sasaki 1985; Le and Moin 1994; Silveira Neto et al. 1993; Shih and Ho 1994). However, experimental visualizations of the three-dimensional vortical structure have been scarce. The main objective of the present study, which follows on from the work of Lee and Sung (2002), was to investigate the three-dimensional large-scale vortical structure in a separated and reattaching shear layer, with the emphasis on the vortical structure in the spanwise direction. To achieve this objective, a series of conditional averages of the threedimensional flow field were performed on velocity and wall pressure fluctuation data. The SBF of Lee and Sung (2002) was employed to obtain a conditioning signal from an array of microphones aligned along both the streamwise and the spanwise directions. Surface pressure fluctuation data were obtained as a function of both space and time, and were then processed to extract a meaningful flow structure from the measured velocity data. Conditionally averaged velocity vector fields and contours of vorticity and turbulence intensity are presented. In order to elucidate the three-dimensional coherent structure, the cross correlation between spatially filtered wall pressure fluctuations and velocity fluctuations is obtained. The spacevarying characteristics of the large-scale vortical structure were examined by comparing the results from independent data set measured at x/h=4.0 (recirculation region) and x/h=7.5 (reattaching region). This study aims to elucidate the three-dimensional coherent structure of the turbulent separated and reattaching flow over a backwardfacing step. 2 Experimental apparatus A subsonic open-circuit wind tunnel, which was originally constructed as part of the work of Chun and Sung (1996), was slightly modified for the present experiments. A detailed description of the wind tunnel can be found in Lee and Sung (2001). The dimensions of the inlet channel were 630 mm (width) 100 mm (height) 1,000 mm (length). The free-stream turbulence intensity which was measured on the centerline of the inlet channel at 100 mm upstream of the channel exit was less than 0.6% at speeds of 5 25 m/s. The step edge was attached to the end of the inlet channel, which was 1,000 mm downstream of the trip wire at the entrance of the inlet channel. At this location, a constant-area rectangular duct of dimensions 630 mm (width) 150 mm (height) 2,500 mm (length) was constructed to act as the backward-facing step. The step height H of the backward-facing step was 50 mm, and the aspect ratio (AR) was For this experimental apparatus, a two-dimensional flow assumption can be made with reasonable accuracy, at least for much of the central portion of the test section. An AR greater than 10 was recommended by de Brederode and Bradshaw (1978) to avoid significant side-wall effects in the vicinity of the centerline of the channel. Therefore, the flow is assumed to maintain two-dimensionality along the centerline of the test section. In the present study, an arrayed-microphone system (Soritel Inc., Seoul, Korea, Model TMS160A) was used to sense the wall pressure fluctuations. This system consists of 32 electret condenser microphones of diameter mm and height 25.4 mm, connection cables and a 32-channel differential amplifier (Model 514A). The pressure sensing system was calibrated using the procedure described in Lee and Sung (2001); the calibration results indicated that the magnitude error and the phase delay were so small that no further compensation procedure of the output was required. The microphones were installed in the test section of the wind tunnel to form a crossshaped two-dimensional array, as illustrated in Fig. 1. This setup enabled the simultaneous measurement of the spatial behavior of wall pressure fluctuations in both the streamwise and spanwise directions. The array consisted of 17 microphones in the streamwise direction and 13 microphones in the spanwise direction, with a uniform interval of 0.25H between adjacent microphones. Thus, the array spanned 4H in the streamwise direction and 3H in the spanwise direction. The center of the cross-shaped array was considered to be the origin of measurement. In the present work, the measurement origin X 0 was varied between X 0 /H=4.0 and X 0 /H=7.5, with the whole array being moved accordingly. The origins of X 0 /H=4.0 and X 0 /H=7.5 correspond to the measurements for the recirculation region and the reattaching region, respectively. For the joint velocity-pressure measurement, the velocity time history was measured on the y z plane located at x=x 0. In this plane, velocity measurement grids were defined and a split film probe was traversed to measure the time history of all three velocity components. The usual hot-wire technique was used together with a constant temperature anemometer (TSI-IFA300). The velocity measurement grid of points extended over 0.01 y/h 2.0 and )2.0 z/h 2.0. The y z plane was selected for the velocity measurement plane in order to focus upon the three-dimensional flow structure in that plane. The measurement of each velocity component was performed independently using different hot-wire probes. As in Lee and Sung (2002), split films (TSI model 1288 and 1287) were employed for the u and v components, respectively. For the w component, the TSI model 1288 was rotated 90 with respect to the support axis, making the split plane coincide with the x y plane. For every velocity time history measurement, the pressure time histories were simultaneously acquired from a total of 29 microphones using a 32-channel A/D converter DT2839 (Data Translation Inc., Marlboro, Mass.) with an effective sampling frequency of Hz. Originally, all data

3 375 Fig. 1. Experimental setup of backward-facing step Fig. 2a, b. Wall pressure fluctuations and correlations at X 0 /H=4.0: a streamwise direction; b spanwise direction were oversampled four times with a sampling frequency of 1, Hz, after which one out of every four pressure readings was recorded in order to reduce the interchannel sampling delay. Since the original sampling frequency was sufficiently high to neglect the high-frequency pressure components, an anti-aliasing filter was not required. Instead, a digital lowpass filter was employed prior to the selection of a single data point from every four samples. Each pressure or velocity time history contained 163,840 data points, which were stored on a Pentium personal computer for further data processing. In the present experiments, the Reynolds number based on the step height is Re H =33,000, which is the same as in the experiments of Chun and Sung (1996). When rescaled using the momentum thickness, this corresponds to Re h =1,300. Of the various data that can be used to represent the backward-facing step flow, the reattachment length x R has been frequently employed as a representative quantity in a time-mean sense. The reattachment length was estimated by measuring the forward-flow time fraction c p in the vicinity of the wall using the split film probe (TSI model 1288). The point of reattachment was then defined as the point where the forward-flow time fraction has the value c p =0.5. The reattachment length obtained using this approach was x R =7.4H. 3 Experimental results 3.1 Spatial box filtering The SBF in the present study has its theoretical origin in the wave vector filter developed by Maidanik and Jorgensen (1967). The wave vector filter was devised for discriminating wall pressure fluctuations of different spatial scales in the measurement of underwater acoustics. Lee and Sung (2002) demonstrated the effectiveness of SBF in the extraction of a coherent structure featuring signal out of complicated spatio-temporal distribution of pressure fluctuations. A detailed description of SBF is given in

4 Lee and Sung (2002). In brief, the ith SBF mode ~p ðþ i, which corresponds to a spatial component with a discrete wavelength k i, is defined from the following equation ~p i ðþ ¼ XN 1 k¼0 ½ ð 1Þ kh=k iš pk ð1þ where p k corresponds to the pressure at the kth sensor, and N is the number of sensors. The notation [...] represents a truncation to the nearest smaller integer. The step height H is used for the non-dimensionalization of k i. The wavelength k i is given by k i =2 1 i ND, where D=0.25H is the interval between adjacent sensors. For the streamwise array (N=16), this gives k i =2 3 i H. A closer inspection of Eq. (1) discloses that SBF does not require temporal information, i.e., the memory of past flow states. This kind of signal processing method is particularly advantageous when a diagnosis tool for the 376 Fig. 3a, b. Wall pressure fluctuations and correlations at X 0 / H=7.5: a streamwise direction; b spanwise direction Fig. 4a, b. Conditionally averaged vector field (u,v) and turbulent intensity plot at z/h=0: a X 0 /H=4.0; b X 0 /H=7.5

5 feedback control is used. Note that the microphones are installed not only in the streamwise direction but also in the spanwise direction (Fig. 1). Hence, a specific spanwise mode as well as a streamwise mode can be investigated simultaneously. The present arrangement of microphones was designed to allow velocity measurements in three dimensions. This ability to measure the velocity in three dimensions represents the most conspicuous distinction of the present work. As shown in Lee and Sung (2002), the use of SBF should be preceded by the estimation of a proper length scale of the large-scale vortical structure. This length scale is taken to be the wavelength k i, and the appropriate order i of SBF is then calculated. Figure 2 shows the conditionally averaged distributions of wall pressure fluctuations normalized by the inflow dynamics pressure q ¼ 1=2qU0 2 and the cross-correlation coefficient q pp ðþ¼ x px; ð tþpx ð 0 ; tþ= fp rms ðþp x rms ðx 0 Þg of the pressure in the recirculation 377 Fig. 5a, b. Conditionally averaged vector field (u,w) and contour plots of turbulent intensity at y/h=0.92. a X 0 / H=4.0; b X 0 /H=7.5 (dashed arrow for visual aid only) Fig. 6a e. Conditionally averaged vector field (u,w) and contour plots of vorticity x x H/U 0 and turbulent intensity at y/h=0.92: a s=)t/4; b s=)t/8; c s=0; d s=t/8; e s=t/4

6 378 region (X 0 =4.0H). Note that Fig. 2 a and b is for the streamwise and spanwise directions, respectively. The conditional averages of the pressure in both directions are synchronized with the times at which the transverse velocity fluctuations v at (x,y)=(7.5h,1.0h) exceed )2.5v rms. This condition is such that the inrush of the outer irrotational fluid between the large-scale vortices occurs near the time-mean reattachment point x R =7.4H. The same data measured in the reattaching region (X 0 =7.5H) are displayed in Fig. 3. Examination of Fig. 2 indicates that the wavelengths in the streamwise and the spanwise directions are 3H and 2H, respectively. Similarly, the relevant wavelengths are 4H and 2.5H in the reattaching region (Fig. 3). 3.2 Conditionally averaged flow field From the previous section, it becomes clear that the SBF 1st mode of pressure p ðþ 1 with the streamwise wavelength of 4H is the most pertinent mode in the streamwise direction. In this section, the conditionally averaged flow field based on the conditioning signal ~p ðþ i is examined in detail. The conditionally averaged vector field and the contour plots of turbulence intensity in a virtual x y plane are displayed in Fig. 4. The turbulence intensity plotted in this section is defined as the short-time moving average of 1/2(u 2 +v 2 +w 2 ) during one-quarter of the shedding cycle T/4, where T represents the shedding period of large-scale vortices, TU 0 /H= These plots are synchronized with the time instant when ~p ðþ i attains a minimum exceeding )2.5 times the rms value. This choice was made in light of the work of Lee and Sung (2002), who established that the negative peak is closely related to the passage of a largescale spanwise vortical structure near the time-mean reattachment point. In the present study, the streamwise distribution of the velocity field was not measured due to practical limits on the volume of data that could be managed. The temporal information can be obtained from the Taylor hypothesis. Thus, the abscissas in Figs. 4 and 5 are su c /H, which is interpreted as x X 0, where either X 0 =4.0H (setup for recirculation region) or X 0 =7.5H (setup for reattaching region). In addition, the convection velocity of U c =0.6U 0 obtained in Lee and Sung (2001) is employed. The flow fields obtained using the Taylor hypothesis show characteristic features of either a plane shear layer in the recirculation region (Fig. 4a) or a vortical structure in the reattaching region (Fig. 4b). Although the large-scale flow structures are in general accordance with those observed in Lee and Sung (2002), there are discrepancies in the small-scale motions. These discrepancies are attributable to the effect of flow inhomogeneity along the streamwise direction. The three-dimensional flow structure is readily identifiable in Fig. 5, which shows the velocity vector fields and Fig. 7a e. Conditionally averaged vector field (v,w) and contour plots of vorticity x x H/ U 0 and turbulent intensity at X 0 /H=7.5. a s=)t/4; b s=)t/8; c s=0; d s=t/8; e s=t/4

7 contours of turbulence intensity obtained in the x z plane located at y/h=0.92. The transverse coordinate y/h=0.92 roughly corresponds to the center of the large-scale vortices. Note that both the vector plots measured at X 0 /H=4.0 (Fig. 5a) and at X 0 /H=7.5 (Fig. 5b) show a similar pattern of counter-rotating flow structures. The center of the counter-rotating system coincides with a region of high turbulence intensity. The rotating pattern is stronger in the recirculation region (Fig. 5a) than in the reattaching region (Fig. 5b), which may be due to the downstream growth and subsequent diffusion of the coherent structures. The growth and deformation of the large-scale vortical structure will be dealt with later in this paper. The counter-rotating flow pattern observed in Fig. 5 is very similar to that reported by Kiya and Sasaki (1985). Further investigation of Fig. 5a discloses that the centers of the rotating system are located at (x,z)(4.6h,1.0h) and (x,z)(3.3h, 0.9H). Similarly, the centers in the reattaching region are at (x,z)(7.4h,1.0h) and (x,z)(7.4h, 1.2H). Again, the relation x=x 0 su c /H is employed to calculate the center coordinates. The interval between the centers in the spanwise direction gives the spanwise length scales of 1.9H and 2.2H in the recirculation and reattaching regions, respectively. These values are in good agreement with the spanwise wavelengths of 2H and 2.5H obtained in the previous section. The flow behavior observed in the y z plane, in which all the flow components are measured with an explicit spatial and temporal dependence, clearly reflects the spatio-temporal three-dimensional flow structure. Figures 6 and 7 show representative sequential plots of the conditionally averaged velocity vector (v,w) and contour plots of streamwise vorticity component x x H/U 0 and turbulence intensity for the recirculation region and the reattaching region, respectively. The turbulence intensity plotted here is 1/2(v 2 +w 2 ), because the dominant contribution from the streamwise component tends to obscure the three-dimensionality. Each sequence of plots comprises five snapshots, with time differences s=)t/4, )T/8, 0, T/8, T/4. The zero time difference corresponds to the negative peak of ~p ðþ i with a magnitude greater than 2.5 times the rms value. The time differences were selected on the basis of the observation by Lee and Sung (2002) that the conditionally averaged flow field begins to deviate from the large-scale vortical structure for s >T/4 (Lee and Sung 2002). In both Figs. 6 and 7, a pair of counterrotating vortices are clearly discernible at the zero time delay, i.e., the passage of the large-scale spanwise roller. The centers of the vortices are located at (y,z)(0.94h,)0.63h) and (y,z)(0.82h,0.87h) in the recirculation region, and at (y,z)(0.80h,)1.02h) and (y,z)(0.73h,1.01h) in the reattaching region. The spanwise length scales calculated from the vortex centers are 1.5H and 2.03H, respectively. These values are in turn comparable with those observed in the (x,z) plane. The similarity in the length scales and the locations of the 379 Fig. 8a e. Pressure velocity correlation pu: a s=)t/4; b s=)t/8; c s=0; d s=t/8; e s=t/4

8 380 features observed in the x z and y z planes, together with the common relationship with p ðþ 1, strongly suggest that the counter-rotating vortex pairs observed in these planes are traces from a single entity. 3.3 Pressure velocity cross correlation In order to elucidate the three-dimensional coherent structure, the cross correlation between spatially filtered wall pressure fluctuations and velocity fluctuations is obtained. This is because the pressure velocity cross correlation demonstrates an averaged spatial pattern of flow structure. The usefulness of pressure velocity correlation in the eduction of large-scale vortical structure was shown by Kiya and Sasaki (1983). Hijikata et al. (1996) visualized the large-scale vortical structure using pressure velocity cross correlation. The cross-correlation coefficient between the pressure p(t) at an arbitrary position and the u velocity field is defined as q pu ðy; z; sþ ¼pt ðþuy; ð z; t þ sþ= ðp rms u rms Þ, where s is a time difference. By definition, a positive value of s indicates that the velocity field lags the pressure. In a similar manner, q pv (y,z,s) can be calculated. Lee and Sung (2002) demonstrated that the pressure velocity correlation is enhanced when the ordinary pressure at a single point is replaced with the SBF mode pressure. This was attributed to the high degree of regularity of the SBF mode pressure. This characteristic of SBF is utilized here to investigate more closely the three-dimensional structure in this section. The SBF 1st pressure mode ~p ðþ 1 obtained from the streamwise array is employed in the calculation of q pu (y,z,s) andq pv (y,z,s). For the spanwise velocity component, however, the SBF mode pressure from the spanwise array is used because the spanwise velocity component is well correlated with the SBF mode pressure in the spanwise direction. For simplicity, the notation pv is used for the correlation coefficient instead of q pv (y,z,s). Sequential contour plots of the cross-correlation coefficient pu for X 0 /H=4.0 and X 0 /H=7.5 are shown in Fig. 8. The time differences between these plots are the same as in Figs. 6 and 7. In both the recirculation and reattaching regions, a maximum positive correlation is observed at s=0. The location of the maximum correlation in each region is close to the location of the center of the counter-rotating vortices mentioned in the previous section. In addition, the spanwise extents of the high correlation region are 2.0H and 2.4H for the recirculation region and the reattaching region, respectively. These values are in good agreement with the spanwise length scales measured from the pressure correlations and the conditionally averaged velocity vector fields. Figure 9 shows the sequential contour plots of the pressure velocity correlation pv for X 0 /H=4.0 and X 0 /H=7.5. These plots exhibit pronounced negative minima at s=0. A similar negative correlation between pressure and v velocity has been pointed out by Kiya and Sasaki (1985). The pressure Fig. 9a e. Pressure velocity correlation pv: a s=)t/4; b s=)t/8; c s=0; d s=t/8; e s=t/4

9 velocity correlation exhibits positive maxima of pv at s=)t/4, indicating that there is a downstream region of positive correlation. In Figs. 6 and 7, however, no active three-dimensional structures are observed for s=)t/4. Thus, the positive correlation region in Fig. 9 is not directly associated with the large-scale vortices, but may arise from the velocity field that is induced to satisfy the continuity. The cross-correlation coefficients between the spanwise velocity component and the SBF spanwise mode pressure are displayed in Fig. 10. Again, a similar distribution is observed for X 0 /H=4.0 and X 0 /H=7.5. The correlation between the two quantities is strong throughout the entire y z plane, even in the near-wall region for most of time instants. This tendency of pw stands in contrast to the localized maxima observed for pu and pv. For s=0, the y z plane is divided into halves characterized by positive and negative correlations. This is consistent with the presence of counter-rotating vortices of the type observed in Fig. 5. It is also notable that the y z distribution is exactly reversed between s=)t/8 and s=t/8. This observation is closely associated with the threedimensional coherent vortex structure, which will be shown below. Figure 11 shows three pressure velocity correlations at X 0 /H=7.5 in the x y centerplane (z=0). The correlations exhibit many local extrema, which are connected by virtual line segments in the figure. In addition, some of the extrema are labelled with A, O, and B. The extrema O and A for pu are located at (7.58H,0.98H) and (8.65H,0), respectively. These locations are in good agreement with those reported by Lee and Sung (2002). The coordinates of the extrema O and A define an angle of 46 with the x axis, which is very close to the angle of 45 observed by Kiya and Sasaki (1985) for the major axis of the elliptical streamlines in the mid-span plane of the hairpin vortices. Furthermore, the abscissa of the maximum (7.58H,0.98H) corresponds to 0.13x R, which is comparable with the 0.18x R reported by Kiya and Sasaki (1985). Taken together, the above results indicate that this maximum can be regarded as a coherent vortex center. Similarly, the line segment OB for pw has an angle of 55 with the x axis, which matches the value of 56 reported previously for the minor axis of the elliptical streamlines in the mid-span plane of the hairpin vortices (see Fig. 8 in Kiya and Sasaki 1985). Finally, the three-dimensional structure of the coherent hairpin vortex is visualized in Figs. 12 and 13 by means of the isosurfaces of the cross correlations. It is evident that the large-scale vortices take the form of a hairpin vortex, which agrees well with the results of numerous previous studies (Kiya and Sasaki 1985; Silveira Neto et al. 1993; Shih and Ho 1994). The isosurfaces in Fig. 12 for the recirculation region represent the head of the hairpin vortex. In the downstream reattaching region, the hairpin is elongated in the streamwise direction by shear, thereby giving rise to the form in Fig Fig. 10a e. Pressure velocity correlation pw: a s=)t/4; b s=)t/8; c s=0; d s=t/8; e s=t/4

10 382 Fig. 11. Pressure velocity correlations at X 0 /H=7.5 Fig. 12. Iso-surface of pressure velocity correlation coefficient pw at X 0 /H=4.0. The white surface for pw ¼ 0:1 and the black surface for pw ¼ 0:1 4 Conclusions An experimental study was carried out to extract the threedimensional large-scale vortical structure in a separated and reattaching flow at Re H =33,000. Based on the close interrelation between the velocity field and the wall pressure fluctuations, the two-dimensional wall pressure field and three-dimensional velocity field were simultaneously measured. These measurements were performed at the recirculation zone (x/h=4.0) and reattachment zone (x/ H=7.5). To measure the wall pressure fluctuations over a turbulent backward-facing step, a cross-shaped twodimensional 32-channel microphone array was installed. This microphone array covered both the streamwise and the spanwise directions. The size of the large-scale vortex was obtained from the measurements of the pressure field. In addition, a conditional averaging technique was employed to characterize the large-scale vortical structure in greater detail. The relationship between the flow field and the relevant spatial mode of the pressure field was determined by examining the SBF. A cross-correlation between velocity and pressure fluctuations was performed to identify the structure and the length scale of the largescale vortex. Inspection of the conditionally averaged flow field revealed the presence of a counter-rotating vortex Fig. 13. Iso-surface of pressure velocity correlation coefficient pwat X 0 /H=7.5. The white surface for pw ¼ 0:1 and the black surface for pw ¼ 0:1 pair in both the x z and y z planes. The streamwise and spanwise length scales of the coherent structures in the recirculation region were measured to be 3H and 2H, respectively. The corresponding scales in the reattaching region were 4H and 2.5H, indicating that the coherent structures grow as they move downstream. The threedimensional iso-surface of pressure velocity correlation, along with the presence of the counter-rotating vortex pair, shows a hairpin-like coherent structure. The present results show that the spatial box filtering, in combination with the two-dimensional measurement of wall pressure fluctuations, is an effective technique for detecting the complicated three-dimensional structure of the separated and reattaching flow over a backward-facing step. References Brederode V de, Bradshaw P (1978) Influence of the side walls on the turbulent center-plane boundary-layer in a squareduct. 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 KB, Sung HJ (1996) Control of turbulent separated flow over a backward-facing step. Exp Fluids 21:

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