The Study of Turbulent Boundary Layer Characteristics Downstream of Different Shaped Transverse Grooves

Transcription

1 Proceedings of the International Conference on Fluid and Thermal Energy Conversion 2009 FTEC 2009 Tongyeong, South Korea, December 7 10, 2009 ISSN The Study of Turbulent Boundary Layer Characteristics Downstream of Different Shaped Transverse Grooves Laboratorium of Fluid Mechanics, Mechanical Engineering Department FTI ITS, Surabaya, Indonesia Contact Person: Mechanical Engineering Department FTI ITS Surabaya, 60111, Indonesia Phone: , Fax: , sutardi@me.its.ac.id Abstract The characteristics of turbulent boundary layers downstream of three different shaped transverse grooves (square (SQ), semi-circular (SC), and (triangular (TR)) were studied experimentally at a momentum thickness Reynolds number (R θ ) of The groove size of 20mm, and depth to width (d/w) ratio of unity was used in the study. The experimental results shows that the effects of the TR-groove on (u /U 0 ) max is the most pronounced compared to the effects of the SQ- and SC-grooves. On the contrary, The effects of SQgroove on v /U 0 is the more significant than that of the TR- and SC-grooves. Data for Reynolds stress (<-uv>/(u 0 ) 2 ) show quite scatter that results in difficulty to distinguish the effect of the grooves on <-uv>/(u 0 ) 2. The streamwise and wall-normal turbulence intensities (u'/u 0 and v'/u 0 ) are increased in the near-wall region downstream of the + groove. Next, there is a small increase in the bursting frequency ( f B ) for the square groove compared to the smooth-wall case, while the SC- and TR-grooves do not have any + apparent effect on f B. Ejection and inflow processes are clearly identified using flow visualization study. Keywords: Transverse groove, turbulent boundary layer, hot-wire anemometry, smokeflow visualization. 1 INTRODUCTION There have been many studies on the turbulent boundary layers on the smooth-wall and on the roughwalls. The augmentation of heat and momentum transfers over the rough surface has been well documented in the literature. An effort to modify the near-wall turbulent structures in order to reduce the skin friction has been performed using transversal riblet surfaces. For example, Walsh [1] investigated the turbulent boundary layer over a transverse convex curvature riblet surface where the rib cross-section is semicircular. A little drag reduction was reported, especially at low freestream velocity (~ 11m/s, R θ 900), but the drag characteristic on the riblet surface at higher velocity (~ 40m/s, R θ 4500) does not differ from the corresponding smooth-wall

2 The effect of an impulsive step on the turbulence measures in a turbulent boundary layer has also been studied. For example, Andreopoulus and Wood [2] studied a turbulent boundary layer altered by a short length of surface roughness. Next, Webster et al. [3] also investigated the effect of a 2D bump on a turbulent boundary layer. It was found that streamwise and wall-normal turbulence intensities (u' and v') and the Reynolds stress (<-uv>) downstream on the steps are significantly shifted up from the smooth-wall values [2,3]. In the same way, the C f on the step and at downstream of the step deviates significantly from the smooth-wall C f. The studies of turbulent boundary layers on the transverse square groove [4,5,6] and on the transverse V-groove [7,8] had also been performed. In those studies, it was shown that there is a periodic exchange between the fluid within the groove and the outer flow. It was found a small sudden decrease in C f (~ 3.5%) just downstream of a groove of size d/δ 0 = 0.4 [4]. The C f relaxed back to the smooth-wall value at x/d 100 (x/δ 0 40) downstream of the groove. For a groove with smaller d/δ 0 (0.125 and 0.17), it was found a significant increase in C f (about 100% and 200%, respectively) just downstream of the groove [5,6]. The sudden increase was followed by a decrease below the smoothwall value (by about 50%), and an oscillatory relaxation to the smooth-wall value beyond x/δ 0 = 2. They speculated that the intense local pressure gradient emanating from the downstream edge of the groove was responsible for the sudden increase in C f, and the reduction in C f was due to the weakening of the streamwise vorticity due to the removal of the wall. In the studies of [7,8], however, it was not mentioned about the effect of the presence of the transverse V-shaped groove on the distribution of C f downstream of the groove. It is conjectured that the distribution of C f is strongly correlated with the turbulence intensity and turbulence bursting. From this conjecture, Wahidi et al. [9] studied intensively the C f behavior downstream of the groove. In the recent numerical study, it is shown that the groove width relative to the rib width corresponds to the shear stress distribution in turbulent channel flow over periodic grooves, resulting the heat transfer behavior differs significantly to that over the smooth surface [10]. It is now fairly well established that the near-wall turbulence structures can be controlled through the use of different surface geometry's to reduce skin friction drag [11]. A greater understanding of the interaction between the near-wall turbulence structure and the surface can only be achieved by studying how the turbulent boundary layer responds to different types of surface modification/roughness. The nature of relaxation of the turbulent boundary layer downstream of the groove needs to be understood in order to optimize the geometry and size of the groove. It is very little known, however, on the effect of the ratio w/δ on the structure of the near-wall layer. For instance, it is showed that the ratio w/δ is an important parameter and should be much smaller than unity [12]. The objective of this study is to determine the effect of different shaped transverse grooves (square (SQ-groove), semi-circular base (SC-groove), and tri-angular (TR-groove)) on a zero-pressure gradient turbulent boundary layer. The effects of the groove on the mean velocity and turbulence intensities downstream of the groove are studied. The Reynolds stress and quadrant analysis are also presented in this paper. Finally, a smoke visualization of vortical motion inside grooves is also presented. 2 EXPERIMENTAL DETAILS Experiments were performed in an open circuit low speed wind tunnel, where the test section is 0.91m 0.91m and is over 20m long. The roof of the tunnel is adjusted to maintain a zero pressure gradient along the test section. The air passes through a screened diffuser and a large settling chamber with three single-piece precision screens and is accelerated into the test section through a 5:1 contraction. The freestream turbulence intensity is less than 0.5 percent at all velocities. The velocity in the test section is changed using motorized variable angle inlet vanes on the blower. The experiments were performed at a freestream velocity of 2.0 m/s, which correspond to Reynolds number, based on the momentum thickness just upstream of the groove, of R θ =1000. The measurements were made on a smooth-wall flat plate and with three different shaped transverse grooves located 2.5m from the leading edge (Figure 1). The shaped-grooves are square (SQ), semi-circular (SC), and triangular (TR). The groove depth to width ratio (d/w) is unity with the groove depth (d) is 20mm. The boundary layer was tripped at the leading edge of the plate using a roughness strip consisting of 100mm wide 000 2

3 The Study of Turbulent Boundary Layer Characteristics Downstream of Different Shaped Transverse Grooves sandpaper (series 0811) and a 1.5mm diameter cylindrical rod. The flat plate is made of 25mm thick acrylic and is mounted horizontally on the floor of the wind tunnel. The present experimental conditions and flow parameters together with related previous studies are given in Table 1. The groove depth (d) is also presented normalized using δ and u τ just upstream of the groove. Figure 1a. A schematic of test-plate showing a single transverse groove. Figure 1b. Groove shapes on the test surface. i) Square (SQ), ii) semi-circular base (SC), iii) triangular (TR). Mean velocity and turbulence measurements were made using 5μm diameter Platinum-plated tungsten (Pt-plated tungsten) single normal (SN) and X-wire probes. DANTEC 55M01 standard bridges were used for the velocity measurements. The hot-wires were calibrated in the core of the wind tunnel, where the lowest achievable velocity is approximately 0.6m/s. A third order polynomial is used to curve fit the calibration data, which includes the zero velocity point. The hot-wire signals were digitized using a 16 channel 12 bit Keithley 570 system analog to digital (A/D) converter at sampling rates of 4 khz. The hot-wire probe is traversed in the wall-normal direction using a specially designed traversing mechanism using a Mitutoyo height gauge. The traverse is installed on rails mounted on the roof of the tunnel, and has a maximum span of approximately 46cm and a minimum linear division of 0.01mm. The second wind tunnel, which is smaller than the aforementioned, has a test section of 0.16m x 0.31m x 0.9m, with a maximum freestream velocity of approximately 6.5 m/s. The freestream turbulence intensity of this tunnel is approximately 0.6% at all freestream velocities. Flow visualization is at R θ = 63 using smoke tunnel and utilizing a high-speed camera having a speed up to 8000 frames per second. To illuminate smoke in the test section, a laser sheet is used for obtaining 000 3

4 better images. A red-laser beam from a He-Ne laser generator with a wave length of 633 nm is passed through a cylindrical length to obtained a thin laser sheet. Table 1. Experimental conditions and flow parameters Square groove [3] Square groove [4] Square groove [5] Present study: Square, Semi-circular base, and Tri-angular grooves *) Based on δ at 50 mm upstream of the groove leading edge. d (mm) U 0 (m/s) R θ d/δ 0 d + = u τ d /ν d/w ~ *) A second wind tunnel, which is smaller than the aforementioned, has a test section of 0.16m x 0.31m x 0.9m, with a maximum freestream velocity of approximately 6.5 m/s. The freestream turbulence intensity of this tunnel is approximately 0.6% at all freestream velocities. Flow visualization is at R θ = 63 using smoke tunnel and utilizing a high-speed camera having a speed up to 8000 frames per second. To illuminate smoke in the test section, a laser sheet is used for obtaining better images. A red-laser beam from a He-Ne laser generator with a wave length of 633 nm is passed through a cylindrical length to obtained a thin laser sheet. 3 RESULTS AND DISCUSSIONS 3.1 Mean Velocity Mean velocity profiles downstream of three different shaped grooves (SQ-, SC-, and TRgrooves) at seven representative x-locations normalized using outer variables (U 0 and δ) are presented in Figure 2. The profiles for the corresponding smooth-wall (with no groove) are also presented in the figure for comparison. It can be seen that the effect of all three grooves on U/U 0 is marginal. A small decrease, up to ~ 10%, in U/U 0 downstream of the SC- and TR-grooves over the corresponding smooth-wall U/U 0 profile is discernible in the range 0.02 y/δ 0.05 at the first location closest to the groove. For the SQ-groove, on the contrary, the U/U 0 profile increases up to ~ 8% above the smoothwall U/U 0 profile in the inner region at this x-location. Though at x/δ 0 = a small deviation of the U/U 0 profiles for the three grooves is still discernible, the deviation is well within the experimental uncertainties. 3.2 Turbulence Intensities The streamwise turbulence intensity (u'/u 0 ) profile downstream of the different shaped grooves is presented in Figure 3. There is a significant increase in u'/u 0 downstream of the three groove shapes up to x/δ 0 = in the region y/δ Also, an increase in the maximum value of u'/u 0 ([u'/u 0 ] max ) over the corresponding smooth-wall value for the TR-groove at x/δ 0 = is discernible. The [u'/u 0 ] max for the TR-groove reaches up to ~15% of the smooth-wall value, whereas [u'/u 0 ] max for the SQ- and SC-grooves are not significantly different from the corresponding smooth-wall value. Beyond x/δ 0 = 0.067, the [u'/u 0 ] max for the three grooves are not distinguishable from the corresponding smooth-wall value, although some scattered data for the SQ- and TR-grooves are seen up to x/δ 0 = The effect of the TR-groove on u'/u 0 are more pronounced than the SQ- and SC-grooves, which [u'/u 0 ] max for the TR-groove clearly increases above the smooth-wall peak value of u'/u 0. The relaxation process in u'/u 0 seems slower than in U/U 0. Even at x/δ 0 = 1.867, small increase in u'/u 0 due 000 4

5 The Study of Turbulent Boundary Layer Characteristics Downstream of Different Shaped Transverse Grooves to the presence of the grooves is still discernible in the region y/δ 0.02, which means that u'/u 0 for all three grooves has not relaxed back completely at this streamwise location. Figure 2. Streamwise mean velocity profiles. Δ, TRgroove; ο, SC-groove;, SQ-groove; , smooth-wall. Figure 3. Streamwise turbulence intensity profiles. Δ, TR-groove; ο, SC-groove;, SQ-groove; , smooth-wall. Next, there is a slightly greater effect of the grooves on (v'/u 0 ) than on (u'/u 0 ). For example, (v'/u 0 ) is increased by up to about 50% for the SQ-groove case in the region y/δ 0.1 at x/δ 0 = (Figure 4), compared to a corresponding increase of about 30% for (u'/u 0 ). The increase in (v'/u 0 ) for the SQ-groove is less pronounced further downstream, and the relaxation of v'/u 0 downstream of the groove looks similar to the relaxation in u'/u 0, with the increase still discernible in the region 0.04 y/δ 0.1 at x/δ 0 = (it is not clearly seen on the figure since the profile overlaps with v'/u 0 from the other grooves). The effect of the SC- and TR-grooves on v'/u 0 is less intense than that of the SQgroove at the first x-location. As x increases, the effect of the three grooves on v'/u 0 is not distinguishable, and the deviation of v'/u 0 from the smooth-wall case are alike. Similar to the v'/u 0 downstream of the SQ-groove, the v'/u 0 downstream of the SC- and TR-grooves has not relaxed till x/δ 0 = It can be speculated that the sudden absence of the solid wall due to the groove is the cause for the amplification in v'/u Reynolds Stress The Reynolds stress (<-uv>/(u 0 ) 2 ) downstream of the three different shaped transverse grooves for the groove size of 20mm are presented in Figure 5. The data are highly scattered in the region y/δ 0.1 but they are less scattered in the region y/δ 0.1. Due to this scattered data, it is very difficult to distinguish the distribution of <-uv>/(u 0 ) 2 for the three different shaped grooves. Although 000 5

6 the data are highly scattered, a certain pattern is clearly seen. As the downstream distance increases, the <-uv>/(u 0 ) 2 in the region y/δ 0.1 increases above the corresponding smooth-wall values, and the increase is more pronounced for the TR-groove case than that for the SQ- and SC-groove cases. Even at the location at x/δ 0 = 1.867, the <-uv>/(u 0 ) 2 has not relaxed to the smooth-wall value for all three groove shapes. It is found in [2] that the maximum increase in <-uv>/(u 0 ) 2 was occurred at x/δ 0 3.5, instead of at just downstream of the step change. It is found in [3] that the maximum increase in <-uv>/(u 0 ) 2 was occurred even farther downstream of the step change, i.e. at x/δ The relaxation process in <-uv>/(u 0 ) 2 seems longer than the relaxation process in u'/u 0 and v'/u 0 [3]. Figure 4. Wall-normal turbulence intensity profiles. Δ, TR-groove; ο, SC-groove;, SQ-groove; , smooth-wall. Figure 5. Reynolds stress profiles downstream of three different shaped-grooves. Δ, TR-groove; ο, SC-groove;, SQ-groove; , smooth-wall. It is now clear that the effects of the grooves on the streamwise and wall-normal turbulent intensities (u'/u 0 and v'/u 0 ) and Reynolds stress (<-uv>/(u 0 ) 2 ) are not negligibly small. The grooves affect the u'/u 0, v'/u 0, and <-uv>/(u 0 ) 2 most effectively in the region close to the wall. The downward shift in the u' in the inner region from the corresponding smooth-wall value, which is observed in the present study, were also observed in [13,14,15]. Moreover, it is found an increase in the u' on the rough walls [14]. The location of the increase in u', however, is slightly different from that is found in the present study. They found that the increase in u' occurs in the region 0.15 y/δ 0.6, while in present study, the increase in u' is observed in the region y/δ A significant increase in the v' in the region closer to the wall was also found in the studies of [14,15]. In both studies, the increase in v' is also more pronounced than the increase in u'. The increase in <-uv> downstream of the grooves as shown in Figure 5 (up to y/δ 0.5) is somewhat similar to the finding of [14] for the case of the wire mesh type rough wall (up to y/δ 0.6). In the study of [15], on the contrary, it is found a decrease in the Reynolds stress in the region y/δ 0.2 and followed by the increase in it in the region 000 6

7 The Study of Turbulent Boundary Layer Characteristics Downstream of Different Shaped Transverse Grooves 0.3 < y/δ < 0.9 for the k-type rough wall. Moreover, Krogstad and Antonia [14] argued that the v' and <-uv> are more sensitive to the change in the wall geometry than u'. 3.4 Quadrant Analysis of Reynolds Stress Figures 6 and 7 show the distribution of the ejection and sweep (q 2 + and q 4 + ) events across the layer normalized by (u τ ) 2 for three different shaped transverse grooves at a location just downstream of the grooves (x/δ 0 = 0.013). The corresponding smooth-wall results for those two events are also shown in the figures for comparison. A small decrease in q 2 + and q 4 + due to the presence of the TR-groove compared to the smooth-wall value is clearly seen in the region 20 y (0.04 y/δ 0.4), but this groove causes an increase in q 2 + in the closet distance from the wall (say y + 20 or y/δ 0.04). The effects of the SQ- and SC-grooves on the ejection and sweep events, on the contrary, are to increase these two events in the region y + 60 (y/δ 0.12), at this instance. In the region y (y/δ 0.5), the ejection and sweep events are similar between the events on the smooth-wall and those on the three different shaped grooves. Figure 6. Contribution of the second quadrant (q 2 + ) to the Reynolds stress downstream of the different shaped grooves. Δ, TR-groove; ο, SC-groove;, SQgroove;, smooth-wall. Figure 7. Contribution of the second quadrant (q 4 + ) to the Reynolds stress downstream of the different shaped grooves. Symbols as in Figure 6. Figure 8. Contribution of the second quadrant (q 1 + ) to the Reynolds stress downstream of the different shaped grooves. Symbols as in Figure 6. Figure 9. Contribution of the second quadrant (q 3 + ) to the Reynolds stress downstream of the different shaped grooves. Symbols as in Figure 6. The distributions of the first and third quadrants (q 1 + and q 3 + ) are shown in Figures 8 and 9, respectively, together with the data obtained from the smooth-wall. For instance, the effect of the SQgroove on q 1 + and q 3 + is the most pronounced, followed by the effects of the SC- and TR-grooves consecutively. The effect of the grooves on q 1 + is more significant than on q 3 + and penetrates farther away from the wall. For example, the increase (in negative sign) in q 1 + due to the presence of the SQ

8 B and SC-grooves is clearly seen up to (y or y/δ 0.1), while the increase (in negative sign) in q 3 due to the presence of the grooves is limited up to y + 25 or y/δ On the other words, in general all four quadrants contributing to the total Reynolds stress (<-uv>) are affected the most by the presence of the SQ-groove, followed by the SC- and TR-grooves, consecutively. The bursting frequency (f B ) downstream of the different shaped grooves is calculated using the second quadrant method as described by [16] and is presented in Figure 10. The f is obtained at y/δ BB 0.02 (y + 14) at each x-location, and are presented normalized using inner variables (ν and u τ ). On average, f + (f + 2 ν f B /(u B τ) ) over the TR-, SC-, and SQ-grooves are approximately 9%, 16%, and 20%, respectively, higher than f + over the smooth-wall case. While for the SQ-groove f + shows a significant peak point at about x/δ 0 0.3, the f + over SC- and TR-groove show less clear peak points. The maximum increase in f + is the most pronounced for the SQ-groove and followed by the SC-groove, and the least increase in f + is for the TR-groove. Also, the location of the maximum value of f + for the SQ-groove occurs at a location farther downstream of the groove compared to the locations of the maximum value of f + for the SC- and TR-grooves. + Figure 10. Distribution of bursting frequency ( f B = ν f B B /(uτ) 2 ). Δ, d = 5mm;, d = 10mm;, d = 20mm;, smooth- wall. 3.5 Flow Visualization The flow visualization results of the present study, where the visualization study was performed at lower fluid velocity than that was using for quantitative measurement, are shown in Figures 11 and 12 for the SQ- and TR-grooves, respectively. The visualization results for the SC-groove are qualitatively similar to that of the SQ- and TR-grooves. The quality of the results, is however, not as clear as that of the SQ- and TR-grooves, and the results are not presented here. Ejection and inflow processes are clearly identified using smoke visualization obtained for a plane perpendicular to the wall [17]. The features of the ejection and inflow were also obtained in a similar study using transversal square groove [5,18]. A quasi-stable vortex is formed inside the groove, and temporarily ejected from the groove. Events inside the groove can have sequences as follow. First, an inflow of the outer stream into the groove initiates the process. Next, a quasi-stable vortex inside the groove is formed, and finally the fluid is ejected from the groove. The time-mean duration of one ejection process is approximately 20 ν/u* 2, 15 ν/u* 2 and 12 ν/u* 2, for the SQ-, SC-, and TR-grooves, respectively (Table 2). In this study, u* is the friction velocity and defined as (τ w /ρ) 1/2, where ν is the fluid kinematic viscosity. Elavarasan et al. [5] conjectured that the ejection process is triggered by the passing of quasi-streamwise vortices over the groove. Table 2. Time-mean duration of one ejection process for SQ-, SC, and TR-grooves Groove t + = t.u* 2 /ν SQ 20 SC 15 TR

9 The Study of Turbulent Boundary Layer Characteristics Downstream of Different Shaped Transverse Grooves Figure 11a. Fluid ejection at initial process. Flow is from the right to the left. Figure 11b. Fluid inflow at initial process. Flow is from the right to the left. Figure 12a. Fluid ejection at t = 72 msec. after the initial process of the ejection. Figure 12b. Fluid inflow at initial process. 4 CONCLUSION The effect of three different shaped transverse grooves (square (SQ), semi-circular base (SC), and triangular (TR)) on a zero pressure gradient turbulent boundary layer has been studied at R θ = 1000 using hot-wire anemometry. The groove size corresponds to d/δ 0 = 0.27 (d + = 128). The main conclusions can be summarized as follows: (1) The effect of all three grooves on U/U 0 is less significant. (2) There are significant effects (an increase and a small decrease) in u'/u 0 in the near-wall region immediately downstream of the groove. The increase is more pronounced for the TR-grooves than that for the SQ- and SC-groove, and the increase in (u'/u 0 ) max for the TR-groove reaches up to ~15%. (3) The effect of the grooves on v'/u 0 is slightly more significant than that on u'/u 0. The increase in v'/u 0 for the SQ-groove over the smooth-wall value immediately downstream of the groove is almost 50%, compared to 30% for u'/u 0. (4) The effect of the TR-groove on the Reynolds stress is slightly more pronounced than the effects of the SQ- and SC-grooves. (5) The SQ- and SC-grooves increase significantly to all quadrants contributing to the Reynolds stress. The effect of the TR-groove to those quadrants, on the other hand, is to reduce q 2 + and q 4 + in the region 20 y (0.04 y/δ 0.4) and to increase q 1 + and q 3 + in the region y + 20 (or y/δ 0.04). The average bursting frequency immediately downstream of the TR-, SC- and SQgrooves are approximately 9%, 16% and 20%, respectively, higher than that over the corresponding smooth-wall

10 (6) Ejection and inflow processes are clearly identified using flow visualization study, with the mean time between two consecutive ejections is approximately 20, 15, and 12 ν/u* 2. for SQ-, SC, and TR-groove, respectively. REFERENCES [1] Walsh, M. J., Viscous drag reduction in boundary layers, Prog Astro Aero (Eds: DM Bushnell and JN Hefner), 123, pp , [2] Andreopoulus, J. and Wood D. H., The response of a turbulent boundary layer to a short length of surface roughness, J Fluid Mech, 118, pp , [3] Webster, D. R., Degraaff, D. B., and Eaton, J. K., Turbulence characteristics of a boundary layer over a two-dimensional bump, J Fluid Mech, 320, pp , [4] Choi, K. -S. and Fujisawa, N., Possibility of drag reduction using d-type roughness, Applied Scientific Research, 50, pp , [5] Elavarasan, R., Ching, C. Y., and Antonia, R. A., Turbulent boundary layer over a smooth wall with widely separated transverse square cavities, Applied Scientific Research, 55, pp , [6] Pearson, B. R., Elavarasan, R., and Antonia, R. A., The response of a turbulent boundary layer to a square groove, J. Fluids Engineering, 119, pp , [7] Timin T., Esmail, M. N., and Trass, O., Momentum exchange between turbulent flow sublayers and rough surfaces, Proc 9th Canadian Cong Appl Mech. CANCAM83, University of Saskatchewan, Saskatoon, Canada. May 30 June 03, pp , [8] Tantirige, S. C., Iribarne, A. P., Ojha, M., and Trass, O., The turbulent boundary layer over single V-shaped grooves, Int. J. Heat Mass Transfer, 37(15), pp , [9] Wahidi, R., Chakroun, W., and Al-Fahed, S., The behavior of the skin-friction coefficient of a turbulent boundary layer flow over a flat plate with differently configured transverse square grooves, Exp. Thermal Fluid Sci., 30, pp , [10] Smith, E. and Pongjet, P., Numerical study on heat transfer of turbulent channel flow over periodic grooves, Int. Com. Heat and Mass Transfer, 35, pp , [11] Coustols, E. and Savill, A. M., Turbulent skin friction drag reduction by active and passive means, Special course on Skin Friction Drag Reduction, AGARD Report, 786, pp , [12] Haugen, R. L. and Dhanak, A. M., Momentum transfer in turbulent separated flow past a rectangular cavity, J App Mech, 33, pp , [13] Djenidi, L., Elavarasan, R., and Antonia, R. A., The turbulent boundary layer over transverse square cavities, J Fluid Mech, 395, pp , [14] Krogstad P.-Ǻ. and Antonia, R. A., Surface roughness effects in turbulent boundary layers, Expts. Fluids, 3, pp , [15] Keirsbulck, L., Labraga, L., Mazouz, A., and Tournier, C., Surface roughness effects on turbulent boundary layer structures, J Fluids Engg., 124, pp , [16] Bogard, D. G. and Tiederman, W. G., "Burst detection with single-point velocity measurements", J Fluid Mech, 162, pp , [17] Ari Susanto, Experimental Study on the Turbulent Boundary Layer Characteristics in the Vicinity of a Single Transverse V-Groove, Tugas Akhir (in Indonesian), Mech. Eng. Dept., FTI- ITS, [18] Nuch, M., Experimental Study on the Turbulent Boundary Layer Characteristics downstream of a Transverse Square Groove, Tugas Akhir (in Indonesian), Mech. Eng. Dept., FTI-ITS,