A KIND OF FAST CHANGING COHERENT STRUCTURE IN A TURBULENT BOUNDARY LAYER*

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ACTA MECHANICA SINICA (English Series), Vol.15, No.3, Aug. 1999 The Chinese Society of Theoretical and Applied Mechanics Chinese Journal of Mechanics Press, Beijing, China Allerton Press, INC.

1 ACTA MECHANICA SINICA (English Series), Vol.15, No.3, Aug The Chinese Society of Theoretical and Applied Mechanics Chinese Journal of Mechanics Press, Beijing, China Allerton Press, INC., New York, U.S.A. ISSN A KIND OF FAST CHANGING COHERENT STRUCTURE IN A TURBULENT BOUNDARY LAYER* Lian Qixiang (~f!l~) (Institute of Fluid Mechanics, Beijing Univ. of Aero. & Astro, Beijing , China) ABSTRACT: Coherent structures of a turbulent boundary layer were investigated by hydrogen bubble method. A kind of fast changing structure was observed. That is a spot in which all the hydrogen bubbles vanish much faster than in other regions. This investigation verified that dark-spot is formed by a strong sweep from outer layer. Inside a dark-spot the local instantaneous flow speed might be four times of its neighboring high-speed streaks. Comparing with the low/high speed streaks, both dark-spot and the vortical structures around it are changing very fast. Around darkspot intensive shear layers are formed and indications of the generation of small-scale structures could be observed. KEY WORDS: turbulent boundary layer, coherent structure, small-scale structure 1 INTRODUCTION The investigation of the coherent structures is important for the deeper understanding of the mechanism of turbulence and for the researches on the control of turbulent flows [1]. The high/low speed streak, sweep, ejection, burst and various vortical structures are generally considered as coherent structures in a turbulent boundary layer. These structures have certain geometric shape and are varying with time. Except the burst, other structures are generally varying slowly and moving with the fluid entraining them. Since the discovery of high/low-speed streaks and burst by Kline et alfl '3], a model is widely accepted that between the two legs of a hairpin vortex low-speed streak is lifting from the wall and burst is generated. This model is also used for the explanation of the formation of sweep by Smith & Walker[4]. Sweeping fluid transfers the energy of the free stream to the near wall region, it is the main source of energy for the balance of the turbulence dissipation, Brodkey and his colleagues in Ohio State University[ 5] ~bserved flow structures in outer and inner regions of turbulent boundary layers using tracer and stereoscopic visual method. They considered that the sweeps generate ejection and burst. Unfortunately, the pictures in their papers are stereoscopic graphs, hence the observed structures were presented by hand sketch. Talmon et a1.(1986) [6] in their hydrogen visualized plan views of a turbulent boundary layer first noted a spot in which all hydrogen bubbles disappeared. They called it 'dark-spot' and considered that it is closely related with ejection. Dark-spot appears frequently in ~he Received 2 February, 1999 * The project supported by the National Natural Science Foundation of China (No ) and the National Climbing Project

2 194 ACTA MECHANICA SINICA (English Series) 199g near wall plan views in turbulent boundary layers with adverse pressure gradient. They have not attracted much attentions in the past. The present paper shows that it is generated by a strong sweep. At the beginning, its shape is similar to a common high-speed streak. Yet it expands very fast. The flow speed inside a dark-spot is generally several times of that of a high-speed streak. Generally there are vortical structures and fast lifting fluid formed around it. It is the most active and fast changing structure in the near wall region. Some traces of the generation of small-scale structures were observed around dark-spot. These observations might offer some hints on the mechanism of the generation of smaller scale structures in relation to large coherent structure. 2 EXPERIMENTAL FACILITIES The experiment was conducted in a recirculating water channel of the Beijing University of Aeronautics and Astronautics. Its test section is 0.4 m wide, 0.4 m deep and 6.8m long. The flat plate for test is 6 m long, 0.4 m wide and 1 cm thick, made of Plexiglas. It is set up along one side of the test section. Along the opposite side, a two-dimensional curved wall is set up. A two~dimensional convergent-divergent channel was formed. The flow parameters are the same as the experiment carried out by the author in [7]. The flow parameters in the divergent section are shown in Fig.1. The observation on the flow structures on the test flat plate was conducted in the divergent section. At the inlet of the divergent section the angle of divergence is the largest. It decreases along stream as the thickness of the boundary layer increases. So that large adverse pressure gradient might be obtained without causing separation. 20~ 1500 '7, 10 ~ 1ooo R~ x/m 1.0 ~ U...~.~ c~ c5 1.0m Fig.1 Sketch of the set-up of the test flat plate and the flow parameters in the diverging channel

Vo1.15, No.3 Lian Qixiang: A Kind of Fast Changing Coherent Structure 195 Hydrogen bubble method was used for the observation of coherent structures.

3 Vo1.15, No.3 Lian Qixiang: A Kind of Fast Changing Coherent Structure 195 Hydrogen bubble method was used for the observation of coherent structures. Coherent structures are moving with fluid entrained them. They have Lagrangian feature. The hydrogen bubbles in the present tests have average diameter of about 10 micron. They could follow the coherent structures and reveal their variations. Coherent structures in turbulent boundary layers, such as high/low speed streaks, long streaks, streamwise and transverse vortices, were discovered by hydrogen bubble visualization [2,3]. Hydrogen bubble method was also used for further investigations on coherent structures [5~7]. Generally, plan views and side views are used, in the former the platinum wire is parallel to the plate surface and normal to free stream; in the latter the platinum wire is normal to the surface of plate. In this experiment, the diameter of the platinum wire is mm. The frequency of the pulsation current for generating time-lines is fixed to 12 Hz. Films taking at 16 frames per second recorded the flow structures. 3 TEST RESULTS AND DISCUSSIONS In the plan views, some unique spots could frequently be observed, in which the hydrogen bubble time-lines are becoming dim and vanishing gradually. Talmon et al.[ 6] noted it and called it 'dark-spot'. They considered it as closely related with the ejection of fluid from the wall. The following test results will verify that dark-spot is formed by strong sweep from outer layer. At beginning the shape of time-lines inside a dark spot is similar to those in a high-speed streak. Yet several unique features appear afterwards. First, the width and the spacing of the time-lines increase rapidly and become much wider than those in high-speed streaks. Second, the time-lines inside it become dim and disappear gradually. Third, its area expands both in streamwise and in spanwise direction. Fourth, its spanwise dimension is close to its streamwise dimension. Generally the streamwise dimension of a high-speed streak is much larger than its spanwise dimension. The last two features are more obvious in the near wall plan views. Figure 2 shows the plan views of a dark-spot visualized by a platinum wire at y Inside the dark-spot there are 3 hydrogen bubble time-lines, marked by 'a, b and c' in Fig.2. Its most downstream point is marked by 'f'. In Fig.2(a), the magnitude of width and spacing of these time-lines is only a little greater than those of an ordinary high-speed streak. Yet the width and the spacing increase very rapidly. In Fig.2(c), the spacing between time-line 'a' and 'b' is increased to 7 mm (the real scale); meanwhile the spacing in a high-speed streak over 'H' is only 1.6 mm. The former is 4.4 times of the latter. That means the flow speed inside this dark-spot is about 4.4 time of the flow in that high-speed streak. Generally, the flow speed in a dark-spot is much larger than that in high-speed streaks. The second feature of a dark-spot is show in Fig.2(a),~2(d). The hydrogen bubble lines inside this dark-spot become dim gradually. They almost disappear in Fig.2(d). This spot appears as a black region, while the surrounding bubble lines are still bright. So it is call 'dark-spot'. The hydrogen bubbles after issued from the platinum wire are dissolving continuously into water. Therefore every b.ubble has only a finite life span. The life span of hydrogen bubble time-lines was first discussed in [7], and further investigations were made in [8]. The dissolving rate is inversely proportional to the local concentration of hydrogen in water. The increase of the spacing between time-lines decreases the average local density of hydrogen[8]; hence shorten the life of local hydrogen bubbles. In Fig.2(a),~2(c), the

196 ACTA MECHANICA SINICA (English Series) 1999 Fig.2 The plan views of a typical dark-spot. Platinum wire at x = 300 mm, y+ = 7 width and spacing of time-lines inside the dark-spot increase rapidly.

4 196 ACTA MECHANICA SINICA (English Series) 1999 Fig.2 The plan views of a typical dark-spot. Platinum wire at x = 300 mm, y+ = 7 width and spacing of time-lines inside the dark-spot increase rapidly. The average distance between bubble increases, so that the density of hydrogen around the bubble decreases. Therefore the life span of these bubbles decreases. The third and fourth features of dark-spot are shown in Fig.2(a)-~2(e). The area of dark-spot expands rapidly. At the same time all the new bubbles issued from the platinum wire accumulate to bubble line 'c'. All hydrogen bubbles along the front and lateral border of the dark-spot are consisted of the same bubbles as in Fig.2(a). From the original films, the streamwise stretching and spanwise stretching of the dark-spot could be measured as shown in Fig.3. Figure 3(a) shows the streamwise position of the most downstream point (x/) and the middle point (xc) of the bubble line c. Figure 3(b) shows the spanwise stretching rate ebb and the streamwise stretching rate efc. Both ebb and eft are greater than zero. So that cqw/oz > 0 and Ou/Ox > 0. Due to equation of continuity, Ov/Oy. < 0. On the surface of the plate y = 0, v : 0. In the near wall region v is approximately equal to (Ov/cgy)dy, therefore v < 0. The local flow is toward the plate. That means it is a sweep, which generates the

Vol.15, No.3 24! 2o 16 12 Lian Qixiang: A Kind of Fast Changing Coherent Structure 00'.0 ' 0:2 " 0:4 ' "0:6 ' 0'.

5 Vol.15, No.3 24! 2o Lian Qixiang: A Kind of Fast Changing Coherent Structure 00'.0 ' 0:2 " 0:4 ' "0:6 ' 0'.8 t/s (a) the foremost point x/--x and the most (b) streamwise stretching efc~a and spanwise rear line xc--h- with time t stretching ebb--v with time t Fig.3 The stretching features of the dark-spot in Fig.2, measured from original films dark-spot. From Fig.2(c),-~2(e), the front edge and the lateral edge of this dark-spot form an arc, somewhat elliptical. Similar shape might appear when an oblique circular jet impinging on a flat plate. The fluid impinging on the wall expands toward downstream and laterally, at the same time blocks the upstream fluid to flow into the dark-spot. The plan views shown in Fig.2 is formed very close to wall, at y+ = 7. Dark-spot could also be observed at higher distance from the wall. Their shape is not so regular as in Fig.2, and their expansion is also not so distinct as the near wall dark-spots. Figure 4 shows the plan views at y+ = 45. In Fig.4(a), the symbol [] is inside a dark-spot. The local time-lines near [] are becoming wider, dim and vanishing. The expansion of its area is not so distinct as that in Fig.2. Yet the hydrogen bubbles are vanishing rapidly. The sweeping fluid makes these time-lines stretching towards wall. Therefore the life span of these bubble lines are shortened. Such stretching could not be observed in the plan view. A side view could reveal such stretching as shown later in Fig.5. Around a dark-spot very close to wall, the formation of vortices was not observed. The formation of vortex could be observed around a dark-spot at higher distance from wall. In Fig.4, the symbol V points a vortex- The sweeping fluid is decelerated as it is impinging on the wall. The shear layer in a decelerating fluid has the tendency to accumulate into vortex[ 9]. The strong sweep, which produces a dark-spot, could be observed in side view as in Fig.5. In Fig.5(a), the symbol V points several patches of hydrogen bubbles, which are the remains of time-line broken by the sweep. These patches are moving downward to the wall, as shown in, Fig.5(a).~5(c). In Fig.5(c) the patches pointed by V are very close to wall. The speed of these patches measured from the films is about 0.9U, which is close to the free stream speed. In Fig.5(b) and 5(c) the sweep forms a black region over the symbol V, in which all hydrogen bubbles disappear. Accompanied with the sweep, there are lifts of fluid both in the upstream and the downstream of the sweep, as shown by the symbol A. In Fig.5(a) the lift shown by A is at the downstream of the sweep. In Fig.5(c) and 5(d) the lift shown by A is at the upstream of the sweep. In the lifting fluid the time-lines are curved convex upward. The spacing between the lifting time-lines is rather large. In Fig.5(d), the spacing at the place of A is equal or greater than the spacing of outer layer, shown by the time-lines at the upper side of these photos. The lifting speed measured from spacing is about 0.8U. The lifting speed is close to the sweeping speed. The coherent structures in turbulent boundary layers are generally large-scale structures. The generation of small-scale structures from large-scale structures is important for "~ f"~/'~ / o.s.2 o.0 :... o o.s 0.7 t/s 197

198 ACTA MECHANICA SINICA (English Series) 1999 Fig.4 The plan views of a dark-spot and the vortices around it visualized by a platinum wire at ~ = 300 ram, y+ = 45 the production of turbulence.

6 198 ACTA MECHANICA SINICA (English Series) 1999 Fig.4 The plan views of a dark-spot and the vortices around it visualized by a platinum wire at ~ = 300 ram, y+ = 45 the production of turbulence. Burst might produce small-scale structures. The papers on burst are abundant. Most of them studied various methods for detecting burst frequency from temporal data. The change of spatial structure in burst is still an unclear phenomenon. In Fig.4 and Fig.5, the strong sweep and lifting produce some phenomena, which might indicate the generation of small-scale fluctuations. At first, an analysis was made for the appearance of small-scale structures on the hydrogen bubble visualized pictures. The shape of hydrogen bubble time-lines might be distorted to various shapes due to large structures. Yet the edge of each bubble line would remain clear and sharp. The radius of curvature of each bubble line would be large, about the same order of the length scale of the structure. The bubble time-lines of high/low speed streaks have such appearances. If there are fluctuations with length scale smaller than the width of the bubble line, the bubble line

7 Vo1.15, No.3 Lian Qixiang: A Kind of Fast Changing Coherent Structure 199 Fig.5 The side views visualized by a platinum wire at x ram, a dark-spot and the vortices around it are visualized might be distorted into zigzag shape. Further finer fluctuations might change the bubble lines into misty patches and dispersed. In Fig.4 the symbol V points a vortex, it is forming in Fig.4(a) and formed in Fig:4(b). In Fig.4(c) this vortex nearly disappears, yet the remains could be observed. In Fig.4(d) the remains, pointed by V, were changed to a zigzag curved line. A part of the line is misty. The time interval between Fig.4(b) and Fig.4(c) is only second. The bubble lines around the vortex change very much and almost disappears in this short interval. Meanwhile the shape of the bubble lines around this dark-spot remain almost unchanged. Therefore some smail-scaie fluctuations might be generated in this place, which cause the local bubble lines dispersed and dissolved quickly. These small-scaie fluctuations exist only in a small region; therefore the neighboring bubble lines remain smooth without much change in shape. In Fig.5(a) at the downstream side of the sweep, the lifting bubble line marked by A becomes chaotic and dispersed into small irregular patches shown in Fig.5(c), also marked by A. In Fig.5(c) and Fig.5(d) at the upstream side of the sweep, at the left side of the lifting fluid marked by A, there is a vortical structure, appeared as twisted bubble lines incline about 45 degree in Fig.5(d). In the numerical simulations of Xu et al.[ l~ and Brooke & Hanratty[ 11] sweep with spanwise expansion flow in the wall region could be observed in the y-z plan. It is similar to the spanwise expansion of the dark-spot in Fig.2. Yet the indications of the fluctuations of small structures do not appear in these numerical simulations. 4 CONCLUSIONS Dark-spot is a very active structure in the near wall region. It changes very fast, much faster than the high/low speed streaks and streamwise vortices. The flow speed inside a

8 200 ACTA MECHANICA SINICA (English Series) 1999 dark-spot is much faster than the flow in high-speed streaks. Dark-spot is formed by a strong sweep. Around the sweep forming a dark-spot there are lifting fluid with high upward speed. Between the downward sweep and the upward lift an intensive shear layer is formed. It might be rolled into large vortex or break into small scale structures with intensive fluctuations. It might be an important source of the generation of turbulent energy. The indication of such fluctuations was observed in Fig. 4 and Fig. 5. REFERENCES 1 Cantwell B. Future direction in turbulence research and the role of organized motion. In Lumley JL ed. Whither Turbulence? Turbulence at Crossroads. Proc of a Workshop on Turbulence, Cornell University, March 22~24, New York: Springer-Verlag ~131 2 Kline S J, Reynolds WC, Schranb FA, Runstadler PW. Structures of turbulent boundary layer. J Fluid Mech, 1967, 37:741,~773 3 Kim HT, Kline SJ, Reynolds WC. The production of turbulence near a smooth wail in a turbulent boundary layer. J Fluid Mech, 1971, 50:133-~160 4 Smith CR, Walker DA. Sustain mechanism of turbulent boundary layer: The role of vortex development and interactions. In Panton RL ed. Advances in Fluid Mechanics. Vol.15. Boston, USA: Computational Mechanics Publications, ,,~47 5 Praturi AK, Brodkey RS. A stereoscopic visual study of the coherent structures in turbulent shear flow. J Fluid Mech, 1978, 89:251~272 6 Taimon AM, Kunen JMG, Oom G. Simultaneous flow visualization and Reynolds-stress measurement in a turbulent boundary layer. J Fluid Mech, 1986, 163:459,~478 7 Lian QX. A visual study of the coherent structure of turbulent boundary layer in flow with adverse pressure gradient. J Fluid Mech, 1990, 215:101,, Lian QX, Su TC. The applications of the hydrogen bubble method in the investigations of complex flows. Atlas of Visualization, 1996, 2:105,~115 9 Lian QX, Su TC. Large vortex in front stagnation region of a square plate induced by a fine interference wire. Science in China (Series A), 1994, 37:469,,, Xu C, Zhang Z, den Tooder JMJ, Niewstadt FTM. Origin of high kurtosis in the viscous sublayer. Phys Fluids, 1996, 8(7): 1938~ Brooke JW, Hanratty TJ. Origin of turbulence producing-eddies in a turbulent channel flow. Phys Fluids A., 1993, 5(4): 1011,,~1022

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