SIMULATION OF A LARGE-EDDY-BREAK-UP DEVICE (LEBU) IN AMODERATE REYNOLDS NUMBER TURBULENT BOUNDARY LAYER

Cheng ChinDepartment of Mechanical Engineering

University of MelbourneParkville, Victoria 3010, Australia

chincc@unimelb.edu.au

Jason MontyDepartment of Mechanical Engineering

University of MelbourneParkville, Victoria 3010, Australia

montyjp@unimelb.edu.au

Nicholas HutchinsDepartment of Mechanical Engineering

University of MelbourneParkville, Victoria 3010, Australia

nhu@unimelb.edu.au

Andrew OoiDepartment of Mechanical Engineering

University of MelbourneParkville, Victoria 3010, Australia

a.ooi@unimelb.edu.au

Ramis OrluLinne FLOW Centre

KTH MechanicsSE-100 44 Stockholm, Sweden

ramis@mech.kth.se

Philipp SchlatterLinne FLOW Centre

KTH MechanicsSE-100 44 Stockholm, Sweden

pschlatt@mech.kth.se

ABSTRACTA well-resolved large eddy simulation (LES) of a

large-eddy break-up (LEBU) device in a spatially evolvingturbulent boundary layer up toReθ ≈ 4300 is performed.The LEBU is a flat plate that is implemented via an im-mersed boundary method. Initial flow visualizations showsuccessful implementation of the LEBU. The LEBU is lo-cated at a wall-normal distance of 0.8δ (local boundarylayer thickness) from the wall and acts to delay the growthof the turbulent boundary layer. The LEBU serves to reduceskin friction drag up to 160δ downstream of the LEBU butno net drag reduction is found. Investigation is performedon the interactions of high and low momentum bulges withthe LEBU and the corresponding output is analysed, show-ing a ‘break-up’ of these large momentum bulges. In addi-tion, results show an attenuated turbulence intensity profiledownstream of the LEBU, which is mainly due to a reduc-tion in energy at spanwise length scales ofλ+

z < 200 and> 500.

BACKGROUNDA paradigm shift in the understanding of wall turbu-

lence took place once a certain degree of order was foundto exist in the larger eddies of turbulent flows (seee.g.Townsend, 1976). These organized, so-called coherent,structures were found to be present and significantin andtothe understanding of wall turbulence with one class beingassociated with the wall layer (Klineet al., 1967) and an-other one with the outer layer of the boundary layer (Brown& Thomas, 1977). Furthermore, the coherent processeshave been found to play a major role in the growth and evo-

lution of turbulent boundary layers (TBLs), thereby open-ing doors for the beneficial manipulation and control (Corkeet al., 1981). These lead to the birth of large-eddy break-updevices (LEBUs), which consist of one or more thin platesor airfoils 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 reduce the tur-bulence intensity for up to 100 local boundary layer thick-ness downstream the device, and were (seemingly) capa-ble of reducing the local skin friction and above all the netdrag by tens of percentage (Corkeet al., 1982). This re-sult triggered an avalanche of follow-up studies (seee.g.Walsh & Anders, 1989; Tardu & Binder, 1991, and refer-ences therein), which, however, seemed to have faded awayonce direct drag measurements in towing tanks have shownthat — while local skin friction reduction could be achieved— any substantial net drag reduction by means of LEBUsturned out to be implausible, when accounting the addi-tional device drag (Sahlinet al., 1988).

MOTIVATIONDespite the decline of interest in LEBUs or other outer

layer devices (OLDs), due to their failure in delivering thepromised net drag reduction, experimental investigationscontinued to explore their capability in locally reducing skinfriction and turbulence. With the renewed interest in thevery large-scale motions (VLSMs) (Hutchins & Marusic,2007) and their influence that extends to the wall (Mathiset al., 2009), a renewed interest in LEBUs (among otherOLDs) is at the verge. Besides the vast number of ex-perimental investigations, there is, however, a clear lack

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of numerical simulations. Recalling the apparent experi-mental difficulties in accurately measuring the skin frictionand drag, direct numerical simulations (DNS) would indeedbe the perfect tool to provide the full details needed to un-derstand the underlying mechanisms involved in turbulenceand skin friction and possibly drag reduction. Computerresources have, however, only over the last years becomepowerful enough to perform such simulations. One — andto the authors knowledge the only — work in this respectis the DNS by Spalartet al. (2006). Despite its pioneer-ing character, it was, however, limited to low Reynoldsnumbers, where the inner and outer layer are barely dis-cernible, and the observations made might not be transfer-able to higher Reynolds numbers. Recently, the Reynoldsnumbers achievable in turbulent boundary layers by meansof DNS (Schlatter &Orlu, 2010) and well-resolved large-eddy simulations (LES) (Eitel-Amoret al., 2014) have in-creased considerably and call for a reconsideration of theflow around a LEBU at a moderately high Reynolds num-ber.

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0 120 240

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yδ ⋆

o

xδ ⋆

o

zδ ⋆

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0.8δ

Flow

Figure 1. Computational domain of the turbulent bound-ary layer LES. The LEBU is imposed after a completewashthrough and performed as a separate simulation.

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980 990 1000 1010 1020x/δ ⋆

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yδ ⋆

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Figure 2. Amplitude of the forcing function around theLEBU.

NUMERICAL SETUPThe numerical simulations involve two separate setups.

The first setup is for the reference case, which is an evolv-ing turbulent boundary layer (herein we will denote the ref-erence case as RTBL). The turbulent boundary layer LES isperformed using a numerical scheme that is based on a fullyspectral method as described by Chevalieret al. (2007) withan ADM-RT (Schlatteret al., 2004) subgrid-scale model.Here the streamwise, wall-normal and spanwise directionsare denoted asx,y andz with corresponding velocities rep-resented asU + u, V + v andW +w. The inlet boundarycondition is set to be a laminar Blasius boundary layer pro-file with Reδ ⋆

o= 450, whereδ ⋆

o is the displacement thick-ness at the inlet of the computational domain. A low am-plitude forcing is imposed close to the inlet totrip the flowin order to achieve turbulent transition earlier. The compu-tational domain isLx ×Ly ×Lz = 6000δ ⋆

o ×200δ ⋆o ×240δ ⋆

oin the streamwise, wall-normal and spanwise directions re-spectively as shown in figure 1. The associated number ofspectral collocated points is 6144× 513× 512. The secondsetup is with a LEBU in the turbulent boundary layer. Thesecond simulation is essentially just imposing the LEBU de-vice into the first setup, this is achieved using an immersedboundary method, which has previously been successfullyimplemented by Brynjell-Rahkolaet al. (2013). The LEBUis modeled as a flat plate with lengthLLEBU ≈ 20δ ⋆

o , thick-ness ofTLEBU ≈ 0.165δ ⋆

o with infinite spanwise width. Thisgives an aspect ratio (L/T ) of approximately 120. TheLEBU is implemented in the boundary layer at the loca-tion x = 1000δ ⋆

o ,y = 17.6δ ⋆o (shown in figure 1), which is

at a wall-normal distance of 0.8δ99 based on local bound-ary layer thickness. The local boundary layer thickness isδ ≈ 22δ ⋆

o . At each timestep, a forcing term is computedand imposed to ensure the velocities within the grid pointsin the LEBU reduce to zero. Figure shows the smoothingfunction around the LEBU. The amplitude (A f ) of the forc-ing is applied via a smoothing function around the surfaceof the LEBU for stability of the solver. This is illustratedin figure 2, red denotes an amplitude forcing of 1 and bluedenotes no forcing applied.

RESULTS

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y/δ ⋆o

(b)

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0 1000 2000 3000 4000 5000x

δ ⋆o

y/δ ⋆o

0 1U/U∞

Figure 3. Flow visualisation of (a) TBL without LEBUand (b) TBL with LEBU.

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1000 1050 1100 1150x

δ ⋆o

LEBU

yδ ⋆

o

Figure 4. Mean velocity profiles at three different loca-tions downstream of the LEBU. Red lines denote RTBL andblue lines are for the TBL with LEBU imposed.

First we present the mean velocity flow visualizationof the two cases in figure 3. Figure 3(a) shows the referencecase (RTBL) and figure 3(b) is with the LEBU imposed, thestreamwise velocity is normalised byU∞ (free stream veloc-ity). From the plots, one could immediately observe the ef-fects of the LEBU on the boundary layer, the LEBU seemsto impede the growth of the boundary layer. In figure 4,the normalised mean velocity profiles (U/U∞) at three dif-ferent locations downstream of the LEBU are plotted. Thered line denotes the uncontrolled simulation and the bluecorresponds to the LEBU simulation. At the region behindthe LEBU, there appears to be a slight velocity deficit forthe LEBU results when compared to the RTBL case. Thevelocity deficit gradually diminishes with streamwise dis-tance, which is as expected. Also in figure 4, it is observedthat the LEBU causes the flow to accelerate in the near-wallregion, immediately downstream of the device.

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10−3

xδ ⋆

o

LEBU

c f

Figure 5. Comparison of theReθ between LEBU andTBL. Red line denote TBL and blue line is for TBL withLEBU imposed.

One of the well-known effects of a LEBU is the re-duction in skin friction drag as previously reported in litera-ture (Anderset al., 1985; Savill & Mumford, 1988; Klein& Friedrich, 1990; Iuso & Onorato, 1995; Spalartet al.,2006). Experimental reports have shown that a LEBUcauses a decrease in the skin friction drag coefficientc f

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1000 2000 3000 4000 5000x

δ ⋆o

LEBU

Reθ

Figure 6. Comparison of the coefficient of frictionc f be-tween LEBU and TBL. Red lines denote TBL and blue linesare for TBL with LEBU imposed.

up to 120δ downstream of the LEBU (Savill & Mumford,1988). Though it is not the primary aim of this paper toinvestigate the best configuration of the LEBU (i.e. the lo-cation and dimension of the LEBU) for maximum skin fric-tion drag reduction, an assessment of the performance ofthe current imposed LEBU on skin friction drag reduction iscarried out. In figure 5, a comparison of thec f for the RTBL(red line) and the LEBU case (blue line) shows a clear re-duction inc f downstream of the LEBU. The result showsa similar trend agreeing with the experimental studies men-tioned earlier. Thec f reduction seems to persist up to 3500δ ⋆

o or 160δ downstream of the LEBU, which agrees with thedrag reduction distance ofO(100)δ reported in experiments(Savill & Mumford, 1988). The maximumc f reduction forthe LEBU is approximate 10% at 25δ downstream of theLEBU, which is consistent with the results reported for asingle LEBU (Savill & Mumford, 1988; Klein & Friedrich,1990). The averagec f reduction is approximately 4%. Anadvantage of this numerical study is the accurate analysis ofthe overall net drag due to the LEBU, which would be diffi-cult to obtain with high accuracy in experiments. To obtainan indication of the overall net drag due to the LEBU, onecould essentially compare the momentum thicknessθ or theReθ between the RTBL and the LEBU case as shown in fig-ure 6. The red line represents the RTBL and the blue lineis for the LEBU case. For net drag reduction, the blue linewould have to be lower than the red line at a given stream-wise location. Here the result shows that the LEBU casehas a consistently higherReθ corresponding to a higherθdownstream of the LEBU. It is interesting to note that atstreamwise location ofx/δ ⋆

o ≈ 4800, the LEBU case ap-pears to converge back to the RTBL and subsequently fallbelow it, suggesting that there is zero net drag due to theLEBU and possibly a net drag reduction. However, as thisdrag reduction occurs near the end of the computational do-main, results might be affected. Hence, a longer domainlength would be required to confirm these findings of netdrag reduction.

One of the focus of the paper will be on the mechanismresponsible for the ‘break-up’ to further our understandingof the feasibility of utilizing LEBUs as control devices. Fig-ure 7 shows thexz plane where the LEBU is located. Here,the region where the LEBU is implemented is clearly iden-tified by zero velocity. The wake from the LEBU has in-troduced small-scale turbulence into the outer region of the

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o

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Figure 7. Instantaneousxz plane ofU/U∞ for the LEBUsimulation at the wall-normal location of the imposedLEBU.

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30(a)

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o

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xδ ⋆

o

yδ ⋆

o

-0.2 0.2uU∞

Figure 8. Instantaneousu/U∞ of the LEBU simulation attwo different spanwisexy planes. Black line represents theLEBU.

boundary layer and it is evident that large-scale motions ap-pear to diminish after the LEBU. To investigate the effectsof the LEBU better, we analyse the instantaneous fluctuat-ing velocityu at a zoomed-in region surrounding the LEBUdevice. Figure 8 shows twoxy planes of instantaneousuat two different spanwise locations, figure 8(a) shows a re-gion of high momentum in front of the LEBU and figure8(b) presents a region of low momentum. In both plots, onecould visualize shedding of vortices, which suggests that theLEBU adds vorticity to the wake of the boundary layer. Tostudy the interaction of these bulges with the LEBU, condi-tional averages of spatial and temporal data would be per-formed with emphasis before and after the LEBU, effec-tively analysing the LEBU as an input/output device.

Figures 9(a,b) show the conditional averagedu basedon high and low momentum bulges before the leading edgeof the LEBU respectively. The conditional average crite-ria is defined as having a bulge of lengthLb > 1δ with ei-ther constant± u at a distance of 1δ in front of the leadingedge. Bulges with lengthLb < 1 are discarded from the con-ditional averages. Once these streamwise-wall normal (xy)planes are identified, these samexy planes are averaged after

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-0.04 0.04uU∞

Figure 9. Conditional average ofu/U∞ based on (a) highmomentum and (b) low-momentum region in front of theLEBU. Conditional average after interaction with the LEBUat approximately 2δ downstream for (c) high momentumregion and (d) low-momentum region. Black line representsthe LEBU.

interacting and convecting approximately 2δ downstreamof the LEBU. Figures 9(c,d) shows the corresponding av-erages of figures 9(a,b) after 2δ downstream of the LEBUrespectively. It is evident from the results that the LEBUserves to ‘break-up’ these large high and low momentumregions into two separate bulges. The bottom bulge propa-gates towards the wall as they convect downstream, whichfollows the phenomenon ‘downwashing’. Thec f reductionseen in figure 5 would most likely be due to these bulgesinteracting with the near-wall region further downstream.

Next, we analyse the effects of the LEBU on otherturbulence statistics downstream of the LEBU. Figure 10presents the streamwise varianceu′+2 at an arbitrary dis-tancex ≈ 2000δ ⋆

o downstream of the LEBU. The Reynoldsnumber at this streamwise location isReτ = Uτ δ99/ν ≈700. We have chosen to scale the turbulence intensitywith the friction velocityUτ of the RTBL (symbol ‘+’ de-note scaling with RTBL friction velocity unless stated oth-erwise), as using a constant scaling allows comparison ofthe raw velocity fluctuations between RTBL and the LEBUcase. Note that scaling withU∞ would produce similar re-sults. The result from the LEBU case (blue line) clearlyshows an attenuation of energy in the near-wall region ascompared to the RTBL (red line). In contrast, at the outerregion (y+ > 350), the LEBU case appears to exhibit moreenergy. Even though theu′+2 indicates a reduction in tur-bulence energy in the near-wall region, there is no infor-mation regarding how the energy carrying length-scales are

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10−1 100 101 102 103

y+

u′+2

Figure 10. Comparison of the streamwise turbulence in-tensity for RTBL and the LEBU case at streamwise locationx ≈ 2000δ ⋆

o . Line symbols are as in figure 4.

affected. To examine the streamwise turbulence intensityfurther, we analyse the energy spectra, which provides in-formation regarding the length-scale energy contributiontothe overall turbulence energy.

102

103

(a) RTBL

λ+z

102

103

100 101 102 103

(b) LEBU

y+

λ+z

0.5 7Φ+uu

Figure 11. Comparison of the premultiplied energy spec-tra Φ+

uu at streamwise locationx/δ ⋆o = 2000. (a) TBL with-

out LEBU and (b) TBL with LEBU. Symbol white ‘⋆’ is aty+ ≈ 15,λ+

z ≈ 120.

Figures 11(a,b) shows the spanwise premultipled en-ergy spectraΦ+

uu of u at the same location as figure 10 forRTBL and the LEBU case respectively. In figures 11(a,b),

one would immediately notice a distinct peak in the energyspectra for both cases. This is indicated by a white star‘⋆’ symbol located aty+ ≈ 15,λ+

z ≈ 120. The peak for theRTBL appears stronger than the LEBU case, which explainsthe higher peak inu′+2 seen earlier. Another difference isthe presence of a secondary peak in the LEBU case at lo-cationy+ ≈ 100,λ+

z ≈ 400, which is absent in the RTBL.These results clearly provide evidence that not only are thelarge-scale motions manipulated by the LEBU, the small-scale motions are equally affected. To obtain a clearer im-age of what length scales are affected, we have subtractedthe energy spectra of the LEBU case from the RTBL.

Figure 12 shows the difference in the premultipled en-ergy spectra between the RTBL and the LEBU case. Redand blue contours indicate gain and reduction in energy re-spectively, after implementing the LEBU into the TBL. Thetwo dashed lines are atλ+

z = 200 and 500. It is clear fromthe results that the LEBU affects the length scales by caus-ing a decrease in energy atλ+

z < 200 and> 500. Within theregionλ+

z ≈ 200 to 500, the LEBU case indicates a gain inenergy across these length scales. This is probably due toboth smaller scales generated by the LEBU and the ‘breakup’ of the large-scale motions. These results also seems tosuggest that the manipulation of the length scales is inde-pendent of the wall-normal locationy+.

102

103

100 101 102 103

y+

λ+z

-2 2Φ+uu

Figure 12. Difference in the premultiplied energy spec-tra between the RTBL and the LEBU case. Red indicatesgain in energy and blue indicates reduction in energy withthe implementation of the LEBU. Black dashed lines are atλ+

y = 200 and 500.

ConclusionsA LES simulation of a LEBU imposed in a turbulent

boundary layer is performed. The LEBU is implemented ata wall-normal location of 0.8δ via an immersed boundarymethod. The LEBU clearly shows a reduction in the skinfriction drag, however, there is no evidence of net drag re-duction found in this study, thereby confirming results bySahlin et al. (1988). A conditional average is performedbased on high and low momentum bulges before the lead-ing edge, the corresponding output at 2δ downstream of thetrailing edge of the LEBU is analysed, effectively analysingthe LEBU as an input/output device. The results clearly

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show that the LEBU ‘breaks’ these high and low momen-tum bulges into two halves, which is as expected. Is it likelythat the lower-half bugles cause the skin friction reductionwhich persists overO(100δ ) downstream of the LEBU asthey interact with the near-wall while propagating down-stream. An analysis of the streamwise velocity turbulenceintensity performed at approximately 50δ downstream ofthe LEBU case exhibits an attenuated profile compared toa normal TBL. This is investigated further through spec-tral analysis to identify the range of length scales affectedor manipulated. It is evident that the LEBU causes an at-tenuation of energy across the length scalesλ+

z < 200 and> 500, while causing a gain in energy in the length scales200< λ+

z < 500. The LEBU probably acts to ‘break-up’the large-scale motions (λ+

z > 500) and redistributes the en-ergy to moderate length scales (200< λ+

z < 500). Overall,results suggest that the LEBU is effective in manipulatingthe large-scale motions.

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