influence of a large-eddy-breakup-device on the turbulent...
TRANSCRIPT
Influence of a Large-Eddy-Breakup-Device on the
Turbulent Interface of Boundary Layers
C. Chin1, N. Hutchins1, A. Ooi1, R. Örlü2, P. Schlatter 2 and J. P. Monty11Dept of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
2Linné FLOW Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
Abstract
This paper investigates the e�ects of implementing alarge-eddy break-up device (LEBU) on the growth ofthe boundary layer. The LEBU is placed at a wall-normal distance of 0.8” (local boundary layer thickness)from the wall. A detail analysis of the interaction be-tween the LEBU and the turbulent/non-turbulent inter-face (TNTI) is performed and the LEBU is found to todelay the growth of the turbulent boundary layer. At thenear-wall, the LEBU acts to reduce global skin frictiondrag. It is found that the structures along the TNTI isdi�erent between that of the LEBU and a normal de-veloping turbulent boundary layer, where the structuresappear smaller in length and width in the LEBU case.In addition, the LEBU disrupts the entrainment of thefreestream high momentum flow into the boundary layer.
1 Introduction
Coherent structures have been found to play a majorrole in the growth and evolution of turbulent boundarylayers (TBLs) Townsend(1956), thereby opening doorsfor the beneficial manipulation and control Corke(1981).These lead to the birth of large-eddy break-up devices(LEBUs), which consist of one or more thin plates orairfoils placed parallel to the wall emerged in the outerpart of turbulent boundary layers, and act to ‘break up’the ‘large-eddies’. These devices were found to be ca-pable of reducing the local skin friction by tens of per-centage, however, no clear physical explanation of themechanism has been presented. With the renewed inter-est in the very large-scale motions (VLSMs) as reportedby Hutchins and Marusic (2007) and their influence thatextends to the wall (Mathis et al 2009), re-examinationof LEBUs (and other OLDs) seems pertinent, especiallygiven recent advances in our ability to simulate develop-ing turbulent boundary layers. One area of interest is inthe turbulent/non-turbulent interface (TNTI), where itis defined as a line or surface that separates the turbu-lent region from the non-turbulent region. The TNTI isan important parameter in the study of boundary layersas it characterises the growth of the boundary layer andthe entrainment process of high momentum flow fromthe free stream into the turbulent region of the bound-ary layer. Since the primary purpose of the LEBU is tobreak up large eddies, this work investigates the influ-ence of the LEBU on the largest-scales located at theturbulent/non-turbulent interface (TNTI).
Figure 1: Computational domain of the turbulent bound-ary layer LES. The LEBU is imposed after a completewashthrough and performed as a separate simulation
2 Methodology
The TBL and LEBU numerical datasets are taken fromChin et al (2015). The dataset is a well-resolved largeeddy simulation (LES) of a large-eddy break-up (LEBU)device in a spatially evolving turbulent boundary layerup to Re
◊
¥ 4300 is performed. Here the streamwise,wall-normal and spanwise directions are denoted as x, yand z with corresponding velocities represented as U +u,V + v and W + w. The inlet boundary condition isset to be a laminar Blasius boundary layer profile withRe
”
ı
o
= 450, where ”ı
o
is the displacement thickness atthe inlet of the computational domain. A low amplitudeforcing is imposed close to the inlet to trip the flow in or-der to achieve turbulent transition earlier. The LEBU isa flat plate that is implemented via an immersed bound-ary method as shown in figure 1. The LEBU is placedat a wall-normal location of 0.8”, where ” is the localboundary layer thickness and at a streamwise locationof x/” ¥ 45 downstream from the inlet. The computa-tional domain is L
x
◊ Ly
◊ Lz
= 6000”ı
o
◊ 200”ı
o
◊ 240”ı
o
in the streamwise, wall-normal and spanwise directionsrespectively (or L
x
/” ◊Ly
/” ◊Lz
/” ¥ 272◊9◊11). Theassociated number of spectral collocated points is 6144◊ 513 ◊ 512.
3 Results
It was previously reported by Chin et al (2015) that themaximum skin friction (c
f
) reduction for the LEBU isapproximate 12% at x/” ¥ 25 downstream of the LEBUshown in figure 2. The red line denotes the TBL andthe blue line is for the LEBU c
f
profiles. There are
10 ERCOFTAC Bulletin 108
Figure 2: Comparison of the (a) skin friction coe�cientc
f
and (b) Reynolds number Re◊
based on free-streamvelocity and momentum thickness between LEBU andTBL. Red line denotes TBL and the blue line is LEBU
three regions of interest to investigate for the LEBU case,namely (i) x/” around the vicinity of the LEBU; (ii)x/” ¥ 25, which is the location of maximum c
f
reductionand (iii) x/” ¥ 160, where the c
f
appears to collapseback to the TBL profile. Since the LEBU is located atclose to the edge of the boundary layer, the e�ects ofthe interaction of the LEBU and the boundary layer arefurther investigated.
The TNTI is detected using the instantaneous heightof the boundary layer at U = 0.99UŒ. The TNTI ob-tained using this method has been compared to the de-tection method using kinetic energy by Chauhan et al(2014) and found to be similar. Hence we adopted theidentification of the TNTI to be U = 0.99UŒ. Figure 3shows an illustration of the method employed. The whitecontour denotes the instantaneous height H (the fluctu-ation is defined as h) of the TNTI at various streamwiselocation for a given timestep and the black line indi-cates the mean boundary layer thickness. Figure refT-NTI compares the fluctuation of the TNTI height h nor-malised by the local boundary layer thickness ”
L
of theTBL (top figure) and the LEBU (bottom figure). In theTBL case, the h/”
L
profile exhibits consistent fluctua-tion values across the entire x/”. It is observed thatthese fluctuations steadily increase in size (length andwidth) as x/” increases. This increase in size is consis-tent with increasing Reynolds number as the boundarylayer develops from left to right. In the LEBU case, theblack solid line denoted the streamwise location of theLEBU, prior to the LEBU, the h/”
L
profile is similar tothe TBL. However, immediately behind the LEBU, thefluctuation is severely attenuated. This e�ect persistsfor a streamwise distance of x/” ¥ 25 downstream of theLEBU (indicated by the black dash-line in the LEBUcase). Subsequently, the h/”
L
profile appears to revertback to that of the TBL, one might notice the length-scales of these h/”
L
fluctuations are slightly weaker andshorter than that of the TBL.
Figure 5 displays the rms profile of h for both TBLand LEBU as a function of streamwise distance. Here itis immediately clear that after the LEBU, there is severeattenuation of the fluctuation intensity h. The e�ect ofthis attenuation persists for a streamwise distance x/” ¥100 downstream of the LEBU before collapsing back tothe TBL profile. It is interesting to note that this dis-tance of x/” ¥ 100 corresponds to the distance we notice
Figure 3: Detection method for the turbulent/non-turbulent interface. The interface wall-normal height(H) is defined as 0.99UŒ. The white contour is atU = 0.99UŒ, black contour is the mean boundary layerthickness
drag reduction in the cf
(see figure 2). The results sug-gest that apparently the generation of vortices from thetrailing edge of the LEBU does not add to the fluctuationof the TNTI. The LEBU seems to creates a shear layer(due to the wake) that stabilises the TNTI by prevent-ing entrainment of the non-turbulent region containinglarge amount of energy and momentum into the turbu-lent boundary layer. This might be the mechanism thatcauses skin friction drag reduction seen in figure 2.
Next, the two point correlation will be utilised to in-vestigate the di�erence in structure size in the TNTI.Two point correlation have been used to understand av-erage structure characteristics and help identify coherentstructures (see Brown and Thomas 1977). the correla-tion equation is given in (1).
RIJ
= I(x, y, z)J(x + �x, y + �y, z + �z)‡
I
‡J
, (1)
where I and J correspond to the signals of interest. If I= J it is a two-point correlation, and when I ”= J it isa cross correlation. Here ‡ refers to the standard devi-ation, and �x, �y and �z are the spatial distances inthe streamwise and wall-normal and spanwise directionsrespectively. The overbar denotes the spatial and tem-poral average. Figure 6 presents the cross correlationcontours of h for TBL and LEBU at various locationsx/” ¥ 25, 100 and 160 downstream of the LEBU. Theleft column presents the results for the LEBU and theright column is for the TBL. Note that the x and y axesare normalised by the local boundary layer thickness atits corresponding streamwise location.
Figure 6(a,b) is at x/” ¥ 25, which is where the max-imum c
f
reduction occurs. It is clear that the aver-age structure at the TNTI for the LEBU is narrowerand shorter. This is most likely due to the wake ofthe LEBU that is interacting with the boundary layer.Further downstream at x/” ¥ 100 (figure 6 c,d), it ap-pears that the structures are similar between TBL andLEBU. However, upon closer inspection near the peakcorrelation contours, the LEBU is slightly narrower inwidth as compared to the TBL. At distance x/” ¥ 160downstream of the LEBU, where the c
f
profile of theLEBU collapses back to the TBL, the structures remaindi�erent. The structure in the TBL still is longer andwider when compared to the LEBU. Across the di�erentstreamwise locations, there is evidence to suggest thatthe LEBU acts to permanently alter the TNTI.
To further investigate the e�ects of the LEBU on the
ERCOFTAC Bulletin 108 11
Figure 4: Contour plots of the TNTI fluctuating height h for TBL (top) and LEBU (bottom). The black solid linedenotes the streamwise location of the LEBU. The black dash-line is at x/” ¥ 25 downstream of the LEBU
Figure 5: Comparison of the rms of h between TBL andLEBU. The red line denotes TBL and the blue line isLEBU. The black dash-line denotes the location of theLEBU
entrainment process, correlation between h and u is com-puted for various wall-normal distances of u. This allowsthe study of the direct relationship and influence of theTNTI on the velocity at a given wall-normal height. Herewe have chosen the wall-normal locations of y/”
L
¥ 0.1,0.5 and 0.8, represented by red, blue and black lines re-spectively in figure 7. Figure 7(a) shows the results forthe TBL and (b) for the LEBU, the LEBU location isdenoted by the solid grey line. The results from the TBLshow that there is consistently strong influence (constantcorrelation coe�cient, R
hu
¥ 0.4) of the TNTI on thevelocity profile at wall-normal location of y/”
L
¥ 0.8 asthe boundary layer develops. The influence of the TNTIon the velocity field at y/”
L
¥ 0.5 appears relativelyweak with R
hu
¥ 0.1, which displays a somewhat linearincrease in R
hu
with x/”. This is expected as the fluctu-ation of the TNTI will increase in strength as Reynoldsnumber increases with x/”. Within the logarithmic re-gion y/”
L
¥ 0.1, there seems to be negligible influenceof the TNTI on the velocity field. In the LEBU casepresented in figure 7(b), a similar trend to the TBL isnoticed for R
hu
at wall-normal distance of y/”L
¥ 0.1.The result for y/”
L
¥ 0.5 appears similar to that of theTBL except at the streamwise location where the LEBUis located. At this location, there is a sudden mild spikein the correlation coe�cient (blue line). As the TNTIfluctuates in the wall-normal direction. This is probablydue to the presence of the LEBU that increases the in-termittency at y/”
L
¥ 0.5 leading to the increase in Rhu
.The most interesting result is at y/”
L
¥ 0.8. The cor-
relation Rhu
is similar to that of the TBL preceding theLEBU, however, at the LEBU, there is sudden decreasein correlation. This can again be explained by the wall-normal location of the LEBU (at y/”
L
¥ 0.8), which hasessentially zero velocity. Immediately after the LEBU,the TNTI clearly does not correlate with the sheddingof vortices at the trailing edge of the LEBU, hence thelow R
hu
. The wake seems to dissipate relatively quicklyand the R
hu
collapses back to match the TBL profile atx/” ¥ 100. This agrees with the earlier discussion thatthe wake disrupts the entrainment process. This is fur-ther evidence that the entrainment process is critical tounderstanding the drag reduction seen in c
f
.
4 Conclusions
A detail investigation on the e�ects of the LEBU on theturbulent boundary layer is performed using high fidelitynumerical simulation dataset. The results are comparedto a spatially evolving turbulent boundary layer. TheLEBU acts to permanently change the characteristics ofthe TNTI resulting in a shorter and narrower dominantstructure at the interface and attenuates the fluctuationintensity of the TNTI. Further correlation results showthat the LEBU clearly disrupts the entrainment of thehigh momentum flow in the freestream into the turbulentboundary layer. There is evidence to support that themechanism for skin friction drag reduction is due to thedisruption of the entrainment process. Future work willbe focused on the near-wall statistics to investigate howthe turbulent structures are alter in the presence of theLEBU.
Acknowledgments
This research was undertaken with the assistance of re-sources provided at the NCI NF through the NationalComputational Merit Allocation Scheme supported bythe Australian Government. Computer time was alsoprovided by SNIC (Swedish National Infrastructure forComputing). The simulations were run at the Centrefor Parallel Computers (PDC) at the Royal Institute ofTechnology (KTH). The authors also acknowledge thefinancial support of the Australian Research Council.
12 ERCOFTAC Bulletin 108
Figure 6: Cross correlation (Rhh
) contour map of the TNTI fluctuation height (h) at a streamwise location of x/” ¥25 (a,b); x/” ¥ 100 (c,d) and x/” ¥ 160 (e,f) downstream of the LEBU. Left: TBL; Right: LEBU. The x-y axes arenormailsed by the local boundary layer thickness ”
L
(¥ 30”ı
o
, 53”ı
o
& 69”ı
o
respectively). Contour levels begin at Rhh
= 0.1 with increments of 0.1
Figure 7: Cross correlation (Rhu
) of h and u for (a) TBLand (b) LEBU. Red line denotes correlation of h with uat y/”
L
¥ 0.1; blue line is for correlation of h with u aty/”
L
¥ 0.5 and black line is for correlation of h with u aty/”
L
¥ 0.8. The grey solid line denotes the streamwiselocation of the LEBU
References
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Chin, C., Monty. J., Hutchins, N. Ooi, A., Örlü, R. andSchlatter, P. (2015) Simulation of a large-eddy-break-updevice (LEBU) in a moderate Reynolds number turbu-lent boundary layer, TSFP 9, Paper 1A-3.
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