Visualization of a locally-forced separated flow over a backward-facing step

Transcription

1 Experiments in Fluids 25 (1998) Springer-Verlag 1998 Visualization of a locally-forced separated flow over a backward-facing step K. B. Chun, H. J. Sung 133 Abstract A laboratory water channel experiment was made of the separated flow over a backward-facing step. The flow was excited by a sinusoidally oscillating jet issuing from a separation line. The slit was connected to a cavity in which water was forced through a rigid pipe by a scotch-yoke system. The Reynolds number based on the step height (H) was fixed at Re The forcing frequency was varied in the range St at the forcing amplitude A Timeaveraged flow measurements were made by a LDV system, especially in the recirculating region behind the backwardfacing step. To characterize the large-scale vortex evolution due to the local forcing, flow visualizations were performed by a dye tracer method with fluorescent ink. The vortex amalgamation process was captured at the effective forcing frequency (St 0.477) for laminar separation. This vortex merging process enhances flow mixing, which leads to the shortening of the reattachment length. List of symbols A forcing amplitude, A (Q Q )/U f forcing frequency, Hz g slit width, g mm H step height, H 20 mm Q total velocity measured at (x/h, y/h) ( 0.02, 1.01), m/s Re Reynolds number based on H and U, Re U H/ν 0 0 St reduced forcing frequency, Strouhal number, St fh/u 0 St reduced forcing frequency based on the momentum thickness, St fθ/u 0 Received: 17 March 1997/Accepted: 31 December 1997 K. B. Chun Test & Development Team Samsung Motors Technology Center San 50, Kongse-ri, Kihung-eup, Yongin-city, Kyungki-do, , Korea H. J. Sung Department of Mechanical Engineering Korea Advanced Institute of Science and Technology 373-1, Kusong-dong, Yusong-ku, Taejon, , Korea Correspondence to: H. J. Sung U streamwise time-mean velocity, m/s u streamwise fluctuation velocity, m/s U free-stream velocity, m/s 0 (u 2)1/2 r.m.s. intensity of streamwise velocity fluctuation, m/s x reattachment length, m r x reattachment length at A 0, m r0 0 x, y distance of streamwise and vertical, respectively, m Greek symbols γ forward-flow time fraction p δ boundary layer thickness, mm δ* displacement thickness, mm μ viscosity, Ns/m2 θ momentum thickness, mm phase of local forcing, 1 Introduction Flow with separation and reattachment has long been a subject of fundamental fluid dynamics research. The presence of a separated flow, together with a reattaching flow, gives rise to increased unsteadiness, pressure fluctuations, structure vibrations and noise. Also, they enhance heat and mass transfer and augment mixing. In particular, reattaching flows cause large variations of local heat transfer coefficients (Vogel and Eaton 1985). Thus, control of separated and reattaching flows is an essential issue in practical applications. A literature survey reveals that there have been many attempts to control or lessen the unfavorable behavior associated with separated and reattaching flows. The method of an oscillating separation edge was applied by Nagib et al. (1985) and Roos and Kegelman (1986). Use of sound waves to influence the reattchment process was examined by several researchers, and the relevant flow geometry, forcing method and effective reduced frequency are summarized in Table 1. As a feasible technique, the introduction of a local forcing in the vicinity of the separation edge has been contemplated (Hasan 1992; Kiya et al. 1993; Sigurdson 1995; Chun and Sung 1996). These experimental efforts utilized a small-amplitude localized jet flow close to the separation edge. The jet flow contained a well-defined single-frequency pulsation. It was demonstrated that, by means of a small localized perturbation near the separation edge, the overall characteristics of the separated and reattaching flows were altered significantly. Recently, Chun and Sung (1996) made a wind tunnel experiment to control the separated and reattaching flow over

2 Table 1. Summary of other experiments Case Flow geometry Forcing method Effective reduced frequency 134 Nagib et al. (1985) Backward-facing step Oscillating flap St 0.06 Bhattacharjee et al. (1996) Backward-facing step Acoustic forcing St 0.35, St Roos and Kegelman (1986) Backward-facing step Oscillating flap St 0.22 Hasan (1992) Backward-facing step Acoustic forcing St Kiya et al. (1993) Blunt circular cylinder Acoustic forcing St Obi et al. (1993) Diffuser Acoustic forcing St Sigurdson (1995) Blunt circular cylinder Acoustic forcing St 2.5 Chun and Sung (1996) Backward-facing step Acoustic forcing St 0.28, St The definitions of St are: St fh/u, St fθ/u and St fd/u. a backward-facing step. They showed that the unfavorable behavior associated with separated and reattaching flows can be reduced by the introduction of a small, localized perturbation in the vicinity of the separation edge. The local forcing was produced by a single-frequency sinusoidal disturbance at the separation edge through a thin slit. The effect of local forcing on the flow structure was scrutinized by altering the forcing amplitude (0 A ) and forcing frequency (0.305 St 0.955). They clarified that the local forcing mechanism is effective for controlling the separated and reattaching flows. A small localized forcing near the separation edge enhanced the shear-layer growth rate and produced a large rolled-up vortex at the separation edge. In an effort to investigate the evolution and dynamic behavior of the large-scale vortices in the controlled separated flows, a flow visualization study has been made in a water channel. Although numerous studies of the basic flow over a backward-facing step have been conducted in wind tunnels, flow visualizations in water tunnels are relatively scarce. The present water-channel flow visualization provides an understanding of vortex merging phenomena due to the local forcing for laminar separation. A dye tracer method with fluorescent ink was employed. To measure timeaveraged flow quantities in the recirculating region, a twocomponent LDV system was utilized. For an effective flow visualization, the Reynolds number based on the step height was fixed at Re The forcing amplitude was also fixed at A due to the practical constraint of the present forcing system. The vortex amalgamation process was clearly observed at an effective forcing frequency. The initial rolled-up vortex was split into two vortices due to the local blowing, which merged downstream. These amalgamations of the rolled-up vortices are shown to invigorate flow mixing. 2 Experimental apparatus and procedure 2.1 Water channel Experiments were performed in a recirculating open water channel. The water channel, in which a diffuser, a contraction Fig. 1. Configuration of test section and flow visualization and a honeycomb were placed in sequence, was designed to provide a high-quality flow in the test section. The turbulence intensity was less than 0.7% at Re 1200, where the Reynolds number was defined based on the step height (H) of the test section and the free-stream velocity (U 0 ). As shown in Fig. 1, the dimensions of the inlet open channel were 250 mm in width, 250 mm in depth and 1200 mm in length in the streamwise direction. 2.2 Test section and local forcing A test rig of the backward-facing step was immersed and aligned with the uniform approach flow. As illustrated in Fig. 2, the test section was placed within the open flow stream. The step height was H 20 mm and the spanwise width of the backward-facing step was 250 mm. Since the aspect ratio was 12.5, the two-dimensional flow assumption is valid to a reasonable accuracy in the central portion of the test section (Brederode and Bradshaw 1978). The length of the test section plate was 300 mm long, which was deemed sufficient to accommodate the reattachment point. The front of the test section was located 200 mm downstream of the entrance of the inlet channel, and the test section was placed 50 mm apart

3 Table 2. Initial boundary layer conditions at x/h 0.2, Re 1200 δ δ* θ δ*/θ A 0 (no forcing) A Table 3. Summary of uncertainty estimates Measured quantity Uncertainty 135 Fig. 2. Test section and local forcing system x /H r U/U 0 (u 2)1/2/U from the bottom wall. The blockage ratio of the cross-sectional area of the test section to the channel was less than 12%. The local forcing was introduced by a sinusoidally oscillating jet through a spanwise thin slit along the separation line. As seen in Fig. 2, the slit was connected to a square cavity in which water was forced through a rigid pipe with a piston-andcylinder system driven by a scotch-yoke mechanism. The forced flow was passed through two screens (1 mm and and 0.5 mm in mesh sizes) and a honeycomb (2 mm in cell size and 10 mm in length) to achieve a regulated forced flow. The scotch-yoke mechanism with varying strokes produced different forcing frequencies and forcing levels (Kiya et al. 1993). Special care was exercised to minimize air bubbles inside the forcing system. The forcing amplitude (A 0 ) was defined as the ratio of the difference of total velocity (Q) caused by local forcing to the mean free-stream velocity (U 0 ), i.e., A 0 (Q Q )/U 0. The total velocity Q, which was equal to (U2 V2)1/2, was measured at the position (x/h, y/h) ( 0.02, 1.01). A coordinate system and a cross-sectional view of the test section are illustrated in Fig. 2. The x axis is taken in the main flow direction and the y axis in the vertical direction. The origin is located at a position on the bottom of the step. The time-mean velocity components in the x and y directions are denoted by U and V, the fluctuating velocity components by u and v, respectively. 2.3 Flow visualization and instrumentation The specific gravity of the dye used was The dye was injected at x/h 3 into the boundary layer along the centerline through a 0.5 mm inner diameter tube. Since the injection velocity was very low, the initial shear layer was not disturbed. A 4 W Argon-ion laser was used as a light source. To make a light sheet and to prevent the light scattering, 4 mirrors, a collimator and a cylindrical lens were installed. A detailed diagram of the flow visualization setup is shown in Fig. 1. Photographs were taken with an ASA-3200 film by a camera (Nikon FX-2). The exposure time was varied from 1/125 to 1/250 s. The moving image was captured by a CCD camera and was recorded in an S-VHS video recorder. A macro lens was used to take enlarged photographs. This image was recorded by an image printer and stored in a 586 computer after being scanned by a 1200 DPI scanner. A three-beam, two-color LDV system (TSI ) was used to measure the velocity components in the recirculating region. A dichroic color separator was employed to accomplish the color separation in transmitting optics. The beam expander included in this system had a 2.27 beam expansion, which improved the signal-to-noise ratio about five times in signal power compared to the system without a beam expansion. A frequency shifter was included in the system to shift a single color beam after two colors were separated by a dichroic transmitting optics. The receiving optics had a compact dichroic color splitter and a photomultiplier system. The processor was interfaced to a 586 computer by an A/D converter. Each beam had a Bragg cell shifted by 20 khz to eliminate the ambiguity of flow directions. Two channels were operated simultaneously with the beams aligned at 45 and 45 to the tunnel axis for the measurements of U V and U V components of velocity. The backward scattered light from particles passing through the measuring volume was detected by multiplier tubes. Signals from the photomultiplier tubes were processed in counters that performed eight periodicity checks on the signals and digitized the signals with 2 ns resolution. In order to find the reattachment length (x r ), the forwardflow time fraction (γ p ) in the vicinity of the wall (y/h 0.05) was measured by a split film probe (TSI model-1288). A cut-off frequency was fixed at 10 Hz. This was because a pseudoperiodic low frequency flapping motion can be detected, where the normalized frequency is about 0.2 Hz. A sampling frequency was fixed at 20 Hz. The overall uncertainty intervals were calculated for the 95% confidence limits using the method of Abernethy et al. (1985). These are summarized in Table 3. 3 Results and discussion As mentioned earlier, the effect of local forcing on the turbulent separated flow over a backward-facing step has been

4 136 scrutinized in the wind tunnel experiment (Chun and Sung 1996). The main aim of the present experiment is to delineate the salient vortex amalgamation process through a flow visualization in water. Accordingly, in the present study, the general flow features over a backward-facing step by local forcing are reviewed. At first, the reattachment variations by local forcing are inspected. The time-mean reattchment position (x r ) was defined as the point where the forward-flow time fraction is equal to γ p 0.5 near the bottom wall (y/h 0.05). The normalized reattachment length x r /x r0 is displayed in Fig. 3 as a function of the local forcing frequency (St fh/u 0 ). Here, x r0 denotes the time-mean reattachment length without local forcing (A 0 0). The forcing frequency was varied in the range St The lower limit of the forcing frequency was set by the practical constraints. Therefore, no experimental data were available in the present experiment when St was lower than St As seen in Fig. 3, the effect of local forcing on the reattachment length is substantial. At a particular forcing frequency, i.e., at St :0.477, the reattachment length is reduced significantly. However, as St increases further St 0.7, the reattachment length is larger than that of the unforced flow (A 0 0), i.e., x r /x r0 1. This experimental finding is consistent with the previous assertion (Chun and Sung 1996). Distributions of the forward-flow time fraction γ p on the surface are represented in Fig. 4. The point of γ p 0.5 corresponds to the reattachment point (x r ). It is shown that the reattachment length (x r /H 2.63) of the forced flow of A is much shorter than that of A 0 0 (x r /H 7.64). For the unforced flow (A 0 0), a separation point is seen near the corner (x/h 1.0). This suggests the existence of a secondary recirculation near the corner section (Chun and Sung 1996). However, for the forced flows, no secondary flows are detected near the corner region. The disappearance of the secondary separation bubble is brought about by the formation of larger and stronger Fig. 4. Distributions of the forward-flow time fraction γ p for three forcing cases, Re 1200 Fig. 5. Distributions of U/U 0 and (u 2)1/2/U 0 at x/h 0.02 Fig. 3. Normalized reattachment x r /x r0 against forcing frequency St vortices immediately downstream of the separation edge by the forcing, which will be demonstrated by flow visualization. The effect of local forcing on the initial boundary layer is shown in Fig. 5. Two cases are selected to distinguish the flow structures by local forcing. One is the case of no forcing (A 0 0). The other is the case of A , which yields a minimum reattachment length in Fig. 3. Similarly to the previous case of air flow, the turbulence intensity (u 2)1/2/U 0 by local forcing is very large near the separation edge (1.1 y/h 1.3). However, the effect of local forcing on the mean velocity profile (U/U 0 ) is insignificant. As remarked in Chun and Sung (1996), the shear layer in the vicinity of the sharp separation edge is modified by local forcing, which gives rise to large increases in entrainment close to the separation edge. The detailed initial boundary layer conditions are listed in Table 2.

5 Bhattacharjee et al. (1986) stated that the most effective non-dimensional forcing frequency (St ) is between 0.2 and 0.4. Roos and Kegelman (1986) found the natural instability frequency of the shear layer to be at St 0.4 for laminar separation. The reduced forcing frequency in the present experiment is St 0.477, which is slightly larger than those above. However, when the momentum thickness (θ) near the separation edge is used, i.e., St fθ/u, the forcing frequency is St 0.025, which is larger than the data in the literature St (Eaton and Johnston 1980; Battachrjee et al. 1986; Hasan 1992; Kiya et al. 1993). This may be caused by the fact that the present Reynolds number is lower (Re 1200) than that of the other experiments. In order to see the effect of local forcing on the timeaveraged flow, a detailed measurement was made at Re 1200 for two cases (A 0 0 and A ). Contrary to the air flow case, the measurement in the recirculating region behind a backward-facing step was possible by using the present two-component LDV system. In the prior wind tunnel experiment (Chun and Sung 1996), the hot-wire anemometer was employed, i.e., the profiles in the recirculating region could not be measured. As seen in Fig. 6a, a relatively large effect by local forcing is displayed on the development of the separated flow (1 x/h 6). In the near-region of separation (x/h 0), the mean velocity profiles are only slightly modified by local forcing. However, significant changes are detected in the shear layer region (1 x/h 3). After the reattachment (x/h 3), the flow is gradually redeveloped. Figure 6b represents the time-averaged turbulence energy levels. The influence of local forcing on the turbulence energy levels is pronounced in the recirculating region. As opposed to the mean velocity profiles in Fig. 6a, after the reattachment (x/h 3), the turbulence intensity is recovered rapidly. This suggests that the amalgamation of the rolled-up vortices induced by local forcing can increase turbulent intensity levels within the separated shear layer. Locations of the 10% free-stream velocity level are displayed in Fig. 7 as a function of the downstream position. The rate of shear layer growth is substantially changed by local forcing and the curvature toward the wall is closely connected with the shrinkage of the reattachment length due to an increase in entrainment into the recirculating region. Figure 8 represents the distribution of maximum turbulent intensity at the streamwise locations. The maximum value of turbulence intensity appears in the recirculating region. This is attributed to the entrainment of turbulent fluid transported from the reattachment region. It is known that strong enhancement of the rolled-up vortices by local forcing contributes to the increase of turbulence levels in the recirculating region. A rapid decay of turbulent intensity downstream of the reattachment region is seen. As mentioned 137 Fig. 7. Location of points of 10% free-stream velocity Fig. 6a, b. Profiles of U/U 0 abd (u 2)1/2/U 0 for two forcing cases Fig. 8. Location of points of maximum turbulence level

6 138 Fig. 9a f. Instantaneous flow visualizations for five forcing cases, Re 1200 earlier, these experimental findings are consistent with the earlier air flow case (Chun and Sung 1996). Now, the results of flow visualization are exhibited. Global pictures of the separated flow behind a backward-facing step are displayed in Fig. 9 for six local forcing cases (0 St 0.822). The pictures were taken by a snapshot. When A 0 0 in Fig. 9a, the initial boundary layer near the separation edge propagates downstream up to x/h 3. For x/h 4, the flow begins to flap. This is caused by the shear layer instability. It is seen that a large-scale vortex is formed near x/h 7, which produces a reattachment region (x/h 7 8). When the local forcing is perturbed at A and St 0.477, the vortex structure is significantly changed in the recirculating region. A pair of counter rotating vortices is clearly displayed. Due to the local forcing at the separation edge, amalgamation of the rolled-up vortices is observed in the recirculating region (0 x/h 0.3). This modified vortex structure propagates downstream, causing a large increase in entrainment close to the separation edge and resulting in an increase of turbulence levels. This process causes a substantial reduction of the reattachment length. For St 0.550, the large-scale vortices are produced by amplification of the local forcing. As St increases further (St and St 0.717), the local forcing effect is gradually attenuated. The vortices do not merge. This gives a long reattachment length, as compared with the case of St For a high local forcing frequency (St 0.822), the initial vortex merging is no longer present. As seen in Fig. 9f, the disturbed flow by local forcing cannot penetrate into the shear layer, but it is convected downstream along the dividing streamline. As a result, the reattachment length is not shortened. A sequence of pictures for one period of local forcing (0 360 ) is presented in Fig. 10 for three different forcings. These cases, respectively, are exemplary of the qualitatively distinct conditions: no forcing (A 0 0); the minimum reattachment length case (A ); and

7 139 Fig. 10. Time evolution of large-scale vortices, Re 1200 the case where x r /x r0 is larger than 1 (A ). For A 0 0, the flow at the separation edge flaps downstream due to the shear layer instability at x/h 4 5. A closer inspection near the corner step discloses that a corner flow exists near x/h 1. Moreover, a weak flow circulation is clearly displayed within the recirculating region (0 x/h 4). After the reattachment, the large-scale vortices are seen to redevelop downstream. When the effective local forcing is perturbed (A 0 0.3, St 0.477), the rolled-up vortex due to local forcing is seen at 0 x/h 1. As time elapses, the rolled-up vortex merges with the prior one and they convect downstream. However, when the forcing condition is A , the recirculating region is not influenced by the local forcing. The disturbed flow simply propagates downstream along the dividing streamline. To see the vortex amalgamation process in detail, the time evolution of the vortex structure at A is demonstrated in Fig. 11 for two periods of local forcing (0 720 ). An initial rolled-up vortex, which is generated by the local issuing jet through a thin slit, is split into two vortices with different rotations. This splitting may be caused by the shear layer force imbalance near the separation edge. The shear layer balance is destroyed by the local forcing, which is very strong at the instant of local blowing. These split rolled-up vortices propagate downstream. As time elapses, the vortex amalgamation proceeds as follows: the lower clockwise vortex grows gradually in the recirculating region; the upper vortex, which is rotating counter-clockwise, is formed as a counterpart to the lower one to satisfy circulation. As a result, its strength is weaker than that of the lower vortex. The upper vortex merges with the prior lower vortex, which is convected toward the bottom wall at x/h 1.5 by the upper one. The new lower vortex is convected downstream. The amalgamation of the rolled-up vortices can increase flow mixing. Accordingly, the turbulence level is higher than that of the unforced flow. When the local forcing promotes these vortex pairings, the reattachment length is shortened (x r /H 2 3). An enlarged view of the initial rolled-up vortex formation is displayed in Fig. 12. A closer inspection of the flow near

8 140 Fig. 11. Vortex amalgamation process due to local forcing at A the separation edge reveals that, in the local suction stage (0 90 ), a rolled-up vortex has been generated from the inlet wall layer at the separation edge. As time proceeds, this rolled-up vortex flows downstream. However, when the local blowing commences ( 105 ), the inlet rolled-up vortex is influenced by the local issuing jet. It is seen that a jet flow due to the local blowing penetrates into the initial rolled-up vortex. A new rolled-up vortex formation is shown, which is then split into a pair of vortices, i.e., the upper and lower vortex. As stated above, the upper vortex merges with the previous lower vortex, which increases flow mixing in the recirculating region. However, as the forcing frequency is further increased in

9 141 Fig. 12. Detailed evolution of initial rolled-up vortex at A 0 0.3, St Fig. 13 (A 0.822), there is no pairing process. The initial weak vortex is not merged with the local blowing, but it propagates downstream. 4 Conclusions As an extension of the prior wind tunnel experiment, a water channel experiment has been made of the separated flow over a backward-facing step. The main objective of the present flow visualization study was to delineate the vortex amalgamation process due to local forcing. The local forcing was introduced by a sinusoidally oscillating jet, which was driven by a scotch-yoke system. The overall flow characteristics were consistent with those of the wind tunnel experiment. It was found that the reattachment length has a minimum at an effective forcing frequency (A ). The effective reduced forcing frequency based on the momentum thickness was obtained at St 0.025, where the low Reynolds number flows with laminar boundary layers upstream of separation were dealt with. The vortex amalgamation process was captured in the present flow visualization. Due to the local forcing at the separation edge, the initial rolled-up vortex was split into two vortices with different rotations. The upper vortex merged with the prior lower vortex, while the new lower one was convected downstream. Amalgamation of the rolled-up vortices increased flow mixing, which resulted in shortening the reattachment length. However, for a higher local frequency, no vortex pairing occurred. The distributed flow by local forcing could not penetrate into the shear layer, but propagated downstream along the dividing streamline. Accordingly, the reattachment length was not shortened.

10 142 Fig. 13. Detailed evolution of initial rolled-up vortex at A References Abernethy RB; Benedict RP; Dowdell RB (1985) ASME measurement uncertainty. J Fluids Eng 107: Bhattacharjee S; Scheelke B; Troutt TR (1986) Modifications of vortex interactions in a reattaching separated flow. AIAA J 24: Brederode V; Bradshaw P (1978) Influence of the side walls on the turbulent center-plane boundary-layer in a squareduct. J Fluids Eng 100: Chun KB; Sung HJ (1996) Control of turbulent separated flow over a backward-facing step by local forcing. Exp Fluids 21: Eaton JK; Johnston JP (1980) Turbulent flow reattachment: An experimental study of the flow and structure behind a backwardfacing step. Report MD-39, Thermoscience Division, Mechanical Engineering, Stanford University Hasan MAZ (1992) The flow over a backward-facing step under controlled perturbation: laminar separation. J Fluid Mech 238: Kiya M; Shimizu M; Mochizuki O; Ido Y; Tezuka H (1993) Active forcing of an axisymmetric leading-edge turbulent separation bubble. AIAA paper (AIAA ), July 6 9, Orlando, FL Kiya M; Shimizu M; Mochizuki O; Ido Y (1993) The forced turbulent separation bubble. 9th Symposium on Turbulent Shear Flows, August 16 18, Kyoto, Japan Nagib HM; Reisenthel PH; Koga DJ (1985) On the dynamical scaling of forced unsteady separated flows. AIAA Shear Flow Control Conference (AIAA ), March 12 14, Boulder, Colorado Obi S; Ohizumi H; Aoki K; Masuda S (1993) Turbulent separation control in a plate asymmetric diffuser by periodic perturbation. 2nd Int Symp on Engineering Turbulence Modeling and Measurements, May 31 June 2, Florence, Italy Roos FW; Kegelman JT (1986) Control of coherent structures in reattaching laminar and turbulent shear layers. AIAA J 24: Vogel JC; Eaton JK (1985) Combined heat transfer and fluid dynamic measurements downstream of a backward-facing step. ASME J Heat Transfer 107: Sigurdson LW (1995) The structure and control of a turbulent reattaching flow. J Fluid Mech 298: