Some ideas on the control of near wall eddies

The near-wall region of bounded turbulent flows They concluded that rotating, streamwise structures do occur consists of streamwise vortices, low speed streaks, intense shear in the wall region and they often occurred in counter-rotating layers, inflectional velocity profiles, oscillations and ejections pairs. of low speed fluid out into the logarithmic layer. A mass of data has accumulated over the past 25 years concerning this The cumulative evidence from these researchers important chain of e,ents,-howeverthe general picture is still suggests that streamwise vortices inhabit the wall region rather suggestive rather than conclusive. Some proposals are although they do not necessarily occur in counter-rotating offered as means of interacting with and/or interrupting the pairs. By using the velocity correlation in the wall region from sequence of these events in the wall region. . direct numerical simulations, Moser and Moin(1984) have argued that since R (Az) does not have a minimum at y*,30, Wall layer structure single vortices must be more predominant than counterrotating pairs. Guezennec et al.(1989) have found that The eddy structure near the wall in bounded shear '', structures do not occur in pairs of equal magnitude. The flows has usually been referred to as the "bursting sequence" vortices have diameters that grow from 10 to 40'/u, and they or the "bursting phenomenon'.I This series of events, depicted migrate away from the wall during their lifetime such that in figure I, indicates their sequence of occurrence as discussed their centers range from 10 to 50v/u, from the wall. These below. It is suggested that there may be a feed back mechanism vortices may be a part of a larger vortex structure, such as a between the large scale outer eddies in the shear flow and the hairpin or horseshoe vortex, that extends further into the wall layer events which may be important in attempts to logarithmic region; in which case, the streamwise vortices manipulate this structure. would be composed of some w Yand w as well as w .No evidence is presently available to indicale the length oA" the Streamwise Vortices vortices and their origin remains a mystery. The existence of streamwise vortices in the near wall Low Speed Streaks region has been conjectured by many authors. In its simplest hypothetical case, these vortices appear as vortex tubes aligned The low speed streaks(denoted as LSS) are the most with the streamwise direction as sketched by ubiquitous aspect of the bursting processand were rirststudied Blackwelder(1978). Kline et al.(1967) assumed such vortices by Kline et al.(1967). An experimental observation of the low existed within the flow field. Kim et al.(1971) showed some speed streaks is shown in figure 2. The data were taken by a hydrogen bubble visualization photographs that had rotation spanwise hot-wire rake at y*=15 in a turbulent boundary layer. consistent with streamwise vortices with the vortices inclined The time record from the twelve sensors has been converted to away from the wall. Bakewell and Lumley(1967) and more a streamwise spatial distance by Taylor's hypothesis to provide recently Aubry et al.( 1988) used the proper orthoganal a continuous record over 0<x*<4000. Constant velocity decomposition in the near wall region and determined that a contours for u(x,z) k[U(y) urm(y)| are plotted for k = -I pair of counter-rotating streamwise vortices containing the and -2. The lower speed fluid appears inside the elongated largest amount of energy. Lee, et al. measured the velocity regions which have spanwise scales of typically 20v/u and gradients on the wall and ascribed their results to alternating streamwise scales of several hundred viscous scales. The 'ITA regions of streamwise vorticity. Blackwelder and technique was applied to the same data and its detection Eckelmann( 1979) measured the two stress components on the locations are also indicated. Note that the technique picks up wall and found that the most probable stress pattern conformed the strong shear layers at the sides of the streaks and has a to counter-rotating vortices also. Smith and Schwartz(1983) preference for locations where there is a strong spanwise photographed hydrogen bubbles in the y-z 2 plane and found velocity. The significance of this observation is still under significant streamwise rotation in the wall region for y*<10. investigation. A similar plot of the streaks in figure 3a is from They observed frequent counter-rotating structures and the numerical data of the Center for Turbulence suggested that they were associated with the low speed streaks. Research/NASA Ames supplied by Robinson(1988). Moin and Kim(1982) showed that neither the v, w. nor the pressure had an elongated streaky Structure anywhere in the wall region. I. In the earliest research on the subject, this structure was However the vorticity displays a streaky structure due to its referred to simply as a "burst' as in Kline et al.(1967). In view strong teu/z gcadients as seen in figure 3bs of our increased knowledge, it is more descriptive to use the term "burst' only as an adjective in describing this sequence of A simplified sketch of the low speed streaks is found events. in figure 4. The streaks are shown with equal spacing in the spanwise direction but in nature they have a random spanwise 2. The usual boundary layer coordinates Of xy and z with the distribution. Also the streaks meander during their downstream velocity components u, v and w will be used in the streamwise, migration. This motion has deliberately been eliminated to normal and spanwise directions, respectively, simplify the figure although may be important in the production of turbulence. Lee et a1.(1974) found that their 'Professor Amost probable spacing is 80/u. and their average spacing is o oAerospce Engineering-Associate Fellow AIAA 100/u, very near the wall. Talmon et al.(1986) showed that their average width is only 20-40u/u,. Nakagawa and Nezu(1981) suggested that the spanwise spacing, AV is Copyright © 9199 by the American Institute of Aeronautics lognormal and showed that the spacing increased as one and A tronautics. Ic. No copyright is asserted in the approached the logarithmic region. In one of the more United States under rile 17, U.S. Code. The U.S. Governcomprehensive studies of these eddies, Smith and ment has a royalty.free license to exercise all rights under Metzler(1983) found that the streaks prsisted for At 500 the copyright claimed herein for Governmental purposes. on the average but times up to 2500-/u, were observed. Even All other rights are reserved by the copyright owner. with a moderate convection velocity of 5u . this observation will be enveloped by an inflection surface. Thus it is useful to indicates that the streaks are several thousand viscous scales think of this surface as surrounding the low speed regions of long. They also showed that the structure of the LSSs is fluid. The stochastic nature of the flow indicates that the independent of the Reynolds number over the range inflectional surfaces are random in space and time. Of course 700<Re <5800 agreeing with the data compiled from different the surfaces can end in the fluid where the inflectional profiles investigators by Hirata et al.(1982). no longer exist. The origin of the streaks is still unknown. Assuming The inflectional U(y) profiles have been observed by the streamwise vortices exist on the scales indicated above, many investigators. Kim et al.(1971) found that the U"(y)=0 their induced motion could be sufficient to explain the was a common feature of all cases of lift up observed. observation of the streaks. Since the streaks lie in a region of Willmarth and Lu(1972) found that the bursting phenomenon strong velocity gradient, the streamwise vorticity need not be occurred when the velocity profile first became inflectional. very strong to create the streaks. An alternative suggestion is Grass( 1971 ), Kline et a.(1967), Blackwelder and Kaplan(1976) that the streaks are a manifestation of the strong shear in the and others have concurred. wall region. Lee et al.(1987) showed that when homogeneous turbulence was subjected to a strong uniform shear comparable An Instability Mechanism and Oscillations to that found in the wall region, low speed streaks resulted. This mechanism would also amplify the existing w due to The importance of the inflectional profiles is that they stretching and hence the streaky structure may "still be seem to set up the necessary conditions for an inviscid Kelvinassociated with w eddies. Streaks have also been observed by Helmholtz instability within the fluid. Michalke(1965) has Nakagawa and i"ezu( 1981) and Smith and Metzler(1983) to analyzed this problem in detail for the hyperbolic tangent merge and divide in the wall region, however this happens profile with a spatial scale of A. He found that the most rapidly infrequently and can not be considered as a generation growing disturbance had a wavelength of 14A and the growth mechanism. Chu and Falco(1988) have suggested that small rates of the linear instability are extremely large. Michalke's eddies moving toward the wall may generate the LSSs. results apply to a flow field that is parallel, steady and twodimensional, but Blackwelder and Swearingen(1989) have Lift-up of the LSSs shown that these constraints are satisfied for the inflections within the wall region. Another factor that could influence the At some point in the bursting process, the low speed results from Michalke's theory is the proximity of the wall. streaks are lifted up away from the wall. This is described by Huerre(1983) has shown that Michalke's results are unaffected Klineetal.(1967)as a gradual process during which the streaks as long as the wall is more that l.2A away from the wall. marked with hydrogen bubbles appear to become thinner as Nishioka et al.(1980) support this result. they move away from the wall. Based upon motion p