lengani paper

Experimental Thermal and Fluid Science 35 (2011) 1505–1513

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Experimental Thermal and Fluid Science

journal homepage: www.elsevier .com/locate /et fs

Turbulent boundary layer separation control and loss evaluation of low profilevortex generators

Davide Lengani a,1, Daniele Simoni a,⇑, Marina Ubaldi a, Pietro Zunino a, Francesco Bertini b

a DIMSET, Università di Genova, Via Montallegro 1, I-16145 Genova, Italyb Avio R.D., Via I Maggio, 99 I-10040 Rivalta (TO), Italy

a r t i c l e i n f o a b s t r a c t

Article history:Received 7 March 2011Received in revised form 30 June 2011Accepted 30 June 2011Available online 8 July 2011

Keywords:Turbulent separationVortex generatorDeformation workTotal pressure lossesTurbine intermediate ductDissipation mechanisms

0894-1777/$ - see front matter � 2011 Elsevier Inc. Adoi:10.1016/j.expthermflusci.2011.06.011

⇑ Corresponding author. Tel.: +39 010 353 2447; faE-mail address: [email protected] (D. Simon

1 Present address: Institute for Thermal TurbomachGraz University of Technology, Austria.

The present paper analyses the results of a detailed experimental study on low profile vortex generatorsused to control the turbulent boundary layer separation on a large-scale flat plate with a prescribedadverse pressure gradient, typical of aggressive turbine intermediate ducts. This activity is part of a jointEuropean research program on Aggressive Intermediate Duct Aerodynamics (AIDA). Laser Doppler Veloc-imetry and a Kiel total pressure probe have been employed to perform measurements in the test sectionsymmetry plane and in cross-stream planes to investigate the turbulent boundary layer, with and with-out control device application.

Velocity fields, Reynolds stresses, and total pressure distributions are analysed and compared for thecontrolled and non controlled flow conditions to characterize the mean flow behaviour. The detail andthe accuracy of the measurements allow the evaluation of the deformation works of the mean motionin the test section symmetry plane. Normal and shear contributions of viscous and turbulent deformationworks have been analysed and employed to explain the distribution of the total pressure loss. For thecontrolled flow the discussion of the flow field is extended considering the effects of the vortex generatedin the cross-stream planes. The experimental data allow the evaluation of the global amount of losses,considering a balance of total pressure fluxes in the different measuring planes.

� 2011 Elsevier Inc. All rights reserved.

1. Introduction tion. Control devices can be passive, requiring no auxiliary power,

In the last 30 years many efforts have been done to apply flowcontrol devices inside a real environment in a reliable and efficientway. Even though the concept of boundary layer control was intro-duced by Prandtl [1] at the beginning of the 20th century, onlyrecently it has been thought to ‘‘control’’ the flow inside complexmachines such as aeroengines. For a modern turbomachine, oneof the most interesting applications of boundary layer control isthe prevention of flow separation. Boundary layer separation is infact one of the main causes of total pressure losses and, therefore,the prevention of separation may have a positive impact on turbo-machinery efficiency, or the suppression/delay of separation mayallow the application of more aerodynamically loaded airfoilsand ducts, without decay of aerodynamic performances [2]. Forthese reasons, the investigation of boundary layer separationcontrol methods applied to internal aeroengine flows becomes ofprimary importance.

For external aerodynamics, different flow control devices havebeen proposed and often employed to avoid boundary layer separa-

ll rights reserved.

x: +39 010 353 2566.i).inery and Machine Dynamics,

or active, requiring energy expenditure [3]. Up to now, one of themost tested passive devices are the vortex generators (VGs), thanksto their relatively easy applicability. They consist of ‘‘little wings’’embedded in the boundary layer, which generate a tip vortex ableto apply momentum transfer from the outer to the inner region ofthe boundary layer. Until the1980s their height (VGs characteristicdimension) was of the order of the boundary layer thickness [4], butlater, in order to reduce parasitic drag, different authors [5–7] intro-duced sub-boundary layer VGs, also called low profile VGs (heightapproximately 20% of the boundary layer thickness). Recently,VGs have been applied to internal flows, in particular to diffusingducts, with two different purposes: secondary flow control andmixing enhancement. Reichert and Wendt [8,9] carried out testson circular S-ducts with tapered-fin VGs. Sullerey et al. [10] exper-imentally investigated the effects of various vortex generator con-figurations in reducing the exit flow distortion and improvingpressure recovery in two-dimensional S-duct diffusers.

Flow simulation of vortex generators effects has been carriedout using two different numerical approaches: VGs may be in-cluded in the computational domain modelling their geometry,or VGs may be replaced by volume forces that create vortices inan analogous way VGs do. This last approach seems computation-ally more efficient than the first one and it has been implementedin several works (e.g. [11–14]). Most of these works came out from

Nomenclature

Cf skin frictionCpt total pressure coefficient = pt0�pt

0:5qU20

(Dn)Tx deformation work operated by the Reynolds normalstresses along the x direction

(Dt)Tx deformation work operated by the Reynolds shear stres-ses along the x direction

(Dn)Ty deformation work operated by the Reynolds normalstresses along the y direction

H0 test section inlet heightH12 boundary layer shape factorl VGs lengthp static pressurept total pressureRe inlet Reynolds number = U0H0/mReh momentum thickness Reynolds number = U0h/mTu turbulence intensity

u streamwise velocityu0v 0 Reynolds shear stress in the (x,y) planerms(u0) streamwise velocity fluctuations root mean squareU0 inlet free-stream velocityv velocity normal to the wallx axial coordinatey coordinate normal to the wallz cross-stream coordinated boundary layer thicknessdloss loss coefficientd0loss loss coefficient as a function of cross-stream coordinateh boundary layer momentum thicknessl dynamic viscositym kinematic viscosityq density

Fig. 1. Experimental test section.

1506 D. Lengani et al. / Experimental Thermal and Fluid Science 35 (2011) 1505–1513

the necessity to determine the optimal VGs geometry for differentflow conditions. In the last years the aforementioned CFD works,theoretical models (e.g. Smith [15] and Velte et al. [16]), as wellas extensive experimental parametric analyses (such as Wendt[17]) produced a large amount of data concerning global perfor-mance evaluation parameters (as reviewed by Lin [18]), whichmay allow a relatively easy and efficient implementation of VGsin common applications. Nevertheless, for the design and predic-tion of flow control in more complex environments more dataare required on turbulence and loss generation mechanisms.

In the present work, which is part of the European researchproject AIDA (Aggressive Intermediate Duct Aerodynamic forCompetitive and Environmentally Friendly Jet Engines), loss gen-eration mechanisms are analysed with and without VGs in a lin-ear diffuser, the pressure gradient of which is typical for newlydesigned aeroengine intermediate ducts. Since in aeroengineintermediate ducts the boundary layer is fully turbulent andprone to separation, this condition has been imposed at the inletof the diffuser test section. In previous works [19,20], carried outin the same test rig, the effectiveness of low-profile VGs was dem-onstrated and the mechanism by which VGs modify the flowstructure was explained by means of complementary measure-ment techniques.

The results presented herein concern a measurement cam-paign carried out by means of LDV and a Kiel total pressure probeaimed at understanding the loss production mechanisms in a sep-arating boundary layer in both controlled and uncontrolled cases.Measurements have been performed in the test section symmetryplane with and without VGs, and in two cross-stream planes lo-cated downstream of the VGs. Reynolds stresses and velocity gra-dients in the meridional plane have been adopted to evaluate theturbulent deformation works contributing to loss generation. Theresults confirm some important features of the non-controlled,fully separated boundary layer (for an extensive review of turbu-lent boundary layer separation see Simpson [21]). For thecontrolled flow some important differences in loss generationmechanism are revealed, although the deformation work termsin the symmetry plane are only partially suitable to justify the to-tal pressure distribution, because of the three-dimensional flow.The distributions of the total pressure coefficient in the cross-stream planes are explained by analyzing the effects of thecross-stream vortex action. A quasi-3D method of the overall lossevaluation from the velocities and the total pressure measured inthe meridional and the cross-stream planes is proposed andadopted for the controlled case. In this method overall losses

are evaluated from the balance of the total pressure fluxes andnot, as classically, as a mass-weighted total pressure loss coeffi-cient, since this last approach seems to be questionable for a sep-arated boundary layer.

2. Experimental apparatus and methodology

2.1. Facility

A detailed description of the open-loop low-speed wind tunnelused for this study is given in Canepa et al. [19].

The test section (Fig. 1) was designed to provide several adversepressure gradients typical for aeroengine diffusers. The boundarylayer develops on a large-scale flat plate 1700 mm long and400 mm wide with the leading edge located about 600 mm up-stream of the test section inlet (x = 0). The inlet test section heightH0 is 196 mm. Before the test section inlet, the lateral and top wallboundary layers are sucked to avoid inlet section blockage and toobtain a two-dimensional flow inside the test section. Further-more, on the inclined top wall, the boundary layer was controlledapplying suction, to avoid interaction with the lower plate bound-ary layer, where the experiments were performed.

For the experiment analysed in this paper the test section topwall was inclined by 16�, which corresponds to an ideal overallacceleration factor K value of �3.16 � 10�7. This parameter repre-sents the non dimensional velocity gradient of an ideal one-dimen-sional flow between the inlet and the outlet of the test section. Themean velocity at the test section inlet was kept constant for allexperiments at the value of 28.1 m/s. The boundary layer parame-ters and free-stream turbulence intensity in the inlet section arereported in Table 1.

Table 1Inlet section flow parameters.

d (mm) h (mm) H12 Reh Cf Tu

80 56 1.24 11000 0.0032 0.01

Table 2Vortex generators: geometrical parameters.

VGs no. h = c (mm) l (mm) s (mm) a (�) b (�)

6 16 (0.2d) 64 (4/5d) 80 (d) 23 25

D. Lengani et al. / Experimental Thermal and Fluid Science 35 (2011) 1505–1513 1507

2.2. Control device configuration

In order to control boundary layer separation, low-profile vortexgenerators are employed. A brief description of their geometricalparameters is reported here, while a more comprehensive explana-tion of their choice may be found in Canepa et al. [19]. The VGs arearranged in a co-rotating pattern at an angle a = 23� to the incomingflow and the tunnel centreline provides a plane of symmetry for theconfiguration, as shown in Fig. 2. The VGs geometrical dimensions,as defined in this picture, are reported in Table 2. The VGs axial loca-tion which was most effective in delaying separation was estab-lished in the previous work by Canepa et al. [19]. It resulted to be95 mm (x/H0 = 0.48) upstream of the detachment point, that wasdetected without VGs at x = 385 mm (x/H0 = 1.93).

2.3. Measuring techniques

Total pressure measurements were performed by means of aminiaturized Kiel total pressure probe. The transducer outputwas sampled at a frequency of 1 kHz by means of a Metrabyte A/D converter board with a 12 bit resolution. The total number ofsamples collected for each position was 10,000.

A four-beams two-colour Laser Doppler Velocimeter (Dantec Fi-ber Flow), in backward scatter configuration, was employed for thevelocity measurements [20]. The probe consists of an optical trans-ducer head of 60 mm diameter, with a focal length of 300 mm and abeam separation of 38 mm, connected to the emitting optics and tothe photomultipliers by means of optic fibres. The probe volumedimensions are 0.09 mm � 0.09 mm � 1.4 mm. The flow wasseeded with mineral oil droplets with a mean diameter of 1.5 lm.To process the bursts, two Dantec Enhanced Burst Spectrum Ana-lysers were employed. For each measurement point 30,000 sampleswere collected with a maximum record length in time of 120 s.

2.3.1. LDV experimental uncertaintyA specific evaluation of errors for LDV frequency domain proces-

sors is given by Modarress et al. [22]. For the present experimentthe uncertainty of the instantaneous velocity was evaluated to be

Fig. 2. Vortex generat

less than 1%. Statistical moments were weight-averaged with tran-sit time to avoid statistical bias. Statistical uncertainty in mean andrms velocities depends on the number of independent samples, theturbulence intensity based on the local velocity and the confidenceinterval. Thanks to the large number of samples (30,000) the statis-tical uncertainty on the mean velocity was estimated lower than 4%for a probability of 95% and a local turbulence intensity of 100%,which may occur in the near wall region. In order to obtain highaccuracy also in the boundary layer separating region, where theintegral time scale of the flow increase, the data rate has been re-duced acting on the photomultiplier voltage, while the acquirednumber of samples has been kept constant. Thus, according toGeorge [23] and Satta et al. [24] the sampling period has been al-ways kept larger than 1000 times the integral time scale of the flow.

2.3.2. Experiment organizationThe boundary layer developing over the flat plate was surveyed

along traverses normal to the wall. For the case without VGs, mea-surements were performed only in the symmetry plane, while forthe case with VGs measurements were performed in the symmetryplane and in two cross-stream planes, as depicted in Fig. 3, whichshows the Kiel miniaturized total pressure probe measurementgrid.

For the LDV analysis each normal to the wall traverse was con-stituted of 103 measurement points along the normal to the walldirection. The first point was located at 50 lm from the wall (cor-responding to y+ ffi 2 at flow separation position) and the distancebetween adjacent points was progressively increased in the outerflow region.

The probe volume was oriented with the larger dimension alongthe plate spanwise direction z in order to have better spatial reso-lution in the x and y directions. The LDV probe was moved using athree-axis computer controlled traversing mechanism with a min-imum linear translation step of 8 lm. The measurements of thetwo velocity components were performed in coincidence mode.Typical data rate was 2000 Hz. As mentioned before, to take intoaccount the increase of the flow integral time scale, the data ratewas reduced to about 50 Hz in the separating flow region.

ors configuration.

x [mm]

0100

200300

400500

600

y[m

m]

0

50

100

150

z [mm]

050

100150

Fig. 3. Streamwise and cross-stream measurement grid.


For the total pressure measurements, each normal to the walltraverse was constituted of 71 measurement points along the nor-mal direction. The first point was located at 1 mm from the wallwith a distance between adjacent points of 1 mm in the region ofthe boundary layer close to the wall, that was progressively in-creased in the outer part.

Results from total pressure measurements are presented interms of a non dimensional total pressure loss coefficient:

Cpt ¼pt0 � pt

0:5qU20

ð1Þ

where pt0 is the total pressure in the undisturbed flow at x = 0 mm,pt is the local total pressure, and the pressure difference is normal-ized by the inlet dynamic pressure.

3. Results and discussion

3.1. Flow analysis in the meridional plane

The baseline flow evolution is reported on top of Fig. 4; thedecelerating flow detaches at x = 385 mm, as shown by the timemean velocity vectors. The boundary layer profile at x = 385 mm(x/H0 = 1.93) is in fact characterized by a zero mean velocity gradi-ent in y direction at the wall. From the PIV measurements analysedin Canepa et al. [19] it was found that the detachment position ischaracterized by back-flow for a fraction of time equal to 50%, inagreement with Simpson [21]. The beginning of backflow events

Fig. 4. Mean velocity vector plots and rms velocity colour plots: baseline case (top)and controlled case (bottom).

was identified at x = 300 mm, where the maximum of rms(u0) startsto depart from the wall. Moving downstream along the duct theseparated flow area extends in the direction normal to the walland the maximum of the velocity standard deviation moves awayfrom the wall. This maximum may be identified within the sepa-rated shear layer just above the zero mean velocity line.

With VGs application, the boundary layer separation is delayed(Fig. 4, bottom). The most relevant differences with respect to thebaseline case can be observed dowstream of the VGs position(x = 350). Here, the flow is accelerated close to the wall sincestreamwise momentum is transferred from the outer to the innerpart of the boundary layer. This streamwise momentum migrationtoward the wall prevents separation, as analyzed in detail by Sattaet al. [20]. This flow transfer is one of the main effects of the vor-tices generated by the control device [19] and represents the mainmechanism through which the flow overcomes separation. At thesame time these vortices induce coherent velocity fluctuations[13] and, as a consequence, high Reynolds shear stresses u0v 0 whichare much larger than for the baseline case, as shown in Fig. 5.

The distributions of the total pressure loss coefficient Cpt areshown in Fig. 6. For the baseline flow the total pressure loss in-creases rapidly in the y direction around the detachment position(x = 385 mm), showing a behaviour similar to the velocity standarddeviation. On the contrary, near to the wall the value of Cpt is lowerafter the boundary layer has separated. As discussed in Satta et al.[20], in this region the wall shear stress is reduced due to lowvelocity and low turbulence occurring within the separated regionand thus, the total pressure loss is reduced as well.

When VGs are applied the total pressure loss growth is reduced(Fig. 6, bottom). The acceleration of the flow induced by the VGsleads to a significant reduction of the total pressure loss coefficientnear to the wall with respect to the baseline case, but even with re-spect to the boundary layer development upstream of the VGslocation. Losses start to increase again further downstream, butat the exit plane the coefficient Cpt is about 10% lower comparedto the uncontrolled case in the boundary layer outer region, andit is further reduced up to 20% in the near wall region.

3.1.1. Deformation works without boundary layer controlThe distribution of the total pressure loss coefficient may be

better explained taking into account the viscous and turbulent con-tributions to the overall deformation work of the mean motion.The present LDV results are suitable for evaluating the deformationworks operated by the normal and shear Reynolds stresses with areasonable accuracy which is of the order of 10%.

Fig. 5. Reynolds shear stress colour plots: baseline case (top) and controlled case(bottom).

Fig. 6. Total pressure loss coefficient: baseline flow (top), controlled flow (bottom).


�u@ð�u2=2Þ@x

þ �v @ð�u2=2Þ@y

þ�uq@p@x

¼ 1q@

@x�u l @

�u@x� qu02

� �� 1

q@�u@x

l @�u@x� qu02

� �

þ 1q@

@y�u l @

�u@y� qu0v 0

� �� 1

q@�u@y

l @�u@y� qu0v 0

� �ð2Þ

�u@ð�v2=2Þ@x

þ �v @ð�v2=2Þ@y

þ�vq@p@y

¼ 1q@

@y�v l @

�v@y� qv 02

� �� 1

q@�v@y

l @�v@y� qv 02

� �

þ 1q@

@x�v l @

�v@x� qu0v 0

� �� 1

q@�v@x

l @�v@x� qu0v 0

� �ð3Þ

~U � rpt

q¼ � 1

q@�u@x

l @�u@x� qu02

� �� 1

q@�u@y

l @�u@y� qu0v0

� �

� 1q@�v@y

l @�v@y� qv 02

� �� 1

q@�v@x

l @�v@x� qu0v 0

� �þ TDþ VW

ð4Þ

Considering a two-dimensional incompressible flow, the meanflow energy equations along the x and y directions may be writtenas Eqs. 2 and 3, respectively [25]. The sum of these two equations(Eq. 4) leads, on the left hand side, to the convective derivative ofthe total pressure. The dissipation terms, appearing on the righthand side of Eq. 4, have been computed from the LDV velocity re-sults, while the remaining terms, which represent the turbulentdiffusion (TD) and the work done by the viscous forces (VW) onthe control volume, have not been evaluated, because of their neg-ligible contribution according to Moore et al. [26].

The terms lð@�u=@xÞ2; lð@�u=@yÞ2; lð@�v=@yÞ2 and lð@�v=@xÞ2

represent the deformation work of the mean motion due to the vis-cous stresses. All these terms appear with a negative sign andconsequently they reduce the global amount of the mean flowmechanical energy. These contributions are not negligible only inthe region close the wall upstream of the separation onset, wherehigh velocity gradients normal to the wall are present. Down-stream of the detachment point the viscous terms are negligibledue to the moderate strain rate of the flow.

The major contributions to the dissipation of the mean flow to-tal pressure are due to the deformation work operated by the Rey-

nolds stresses. These terms �qu0iu0j@ �ui=@xj

� �, appearing on the right

side of Eq. 4, are also involved in the turbulent kinetic energytransport equation [25], but with opposite sign. They act exchang-

ing energy between mean flow and turbulence and, if positive, theydissipate the mean flow total pressure and increase the turbulentkinetic energy.

The terms more relevant in the total pressure loss productionrate have been found to be the deformation work operated bythe Reynolds normal and shear stresses along the x direction(ðDnÞTx ¼ �qu02@�u=@x and ðDtÞTx ¼ �qu0v 0@�u=@y, respectively) andthe deformation work operated by Reynolds normal stress alongthe y direction ððDnÞTy ¼ �qv 02@�v=@yÞ. Their distributions are re-ported for the uncontrolled condition in Fig. 7.

Up to x = 300 mm, the near wall losses are increased mainly bythe term (Dt)Tx. After this position, both near wall velocity gradi-ents @�u=@y and Reynolds shear stress u0v 0 decrease in the separat-ing boundary layer (Fig. 5), thus reducing the term (Dt)Tx, whichvanishes at the separation onset location. On the contrary, thedeformation work operated by the Reynolds normal stress alongthe x direction (Dn)Tx starts to generate significant losses atx = 200 mm. After the back flow begins (x = 300 mm) the term(Dn)Tx shows a steep increase due to the large flow oscillations,and it becomes the main responsible of loss generation.

Consequently, the distributions of the terms (Dt)Tx and (Dn)Tx

clearly show that the classical assumption that the normal compo-nent of the deformation work is negligible cannot be applied for aseparating turbulent boundary layer. On the contrary, in this con-dition it is the shear contribution to be negligible. The large valuesof the term (Dn)Tx depend on the velocity fluctuations generated bythe low frequency phenomena, which occur on the edge of the sep-arated flow region. The contour plot shown on the middle of Fig. 7is, in fact, very similar to the contour plot of rms(u0) (Fig. 4, top).Above the separated flow region the energy subtracted to the mainflow by (Dn)Tx is converted in turbulent kinetic energy and this factjustifies the large increase of Cpt observed in Fig. 6.

Inside the region of the reverse flow, both mechanisms of lossgeneration are almost negligible (top and middle of Fig. 7). Thus,as it came out from total pressure measurements, the total pres-sure losses do not increase in magnitude (Fig. 6).

The only non-negligible contribution to the total pressure dissi-pation rate along the y direction is given by the deformation workoperated by the Reynolds normal stress (Dn)Ty (Fig. 7 on bottom).This term is due to the channel divergence that forces fluid to moveaway from the wall, and to the normal velocity fluctuations. Thedistribution of this term resembles that one of the normal dissipa-tion term acting along the x direction and starts to be significant asbackflow appears, but shows negative values. It means that theterm (Dn)Ty performs a mean flow re-energization due to the posi-tive gradient of the normal velocity along the y direction. Hence, ittends to increase the mean flow energy subtracting it from theturbulence.

3.1.2. Deformation works with boundary layer controlThe contributions to loss generation due to (Dt)Tx, (Dn)Tx and

(Dn)Ty, evaluated with VGs installed in the test section, are reportedin Fig. 8. These terms give the greater contributions to the totalpressure loss also with boundary layer control. In this case, the vis-cous terms are not negligible downstream of the VGs due to thestrong normal velocity gradients induced by the momentum trans-ferred towards the wall. However, their effects are limited to thevery near wall region and therefore they are not shown.

The deformation work operated by the Reynolds shear stressalong the x direction (Dt)Tx (Fig. 8, top), downstream of x =350 mm, is larger than for the baseline flow. As previously de-scribed, VGs modify significantly the boundary layer shape intro-ducing distortions along the y direction, as well as largerReynolds shear stress u0v 0 compared to the uncontrolled case, asit has been discussed in Section 3.1. As a consequence, also (Dt)Tx

is larger for the controlled flow.

Fig. 7. Deformation works operated by Reynolds shear stress (top) and Reynolds normal stresses (middle and bottom) without boundary layer control.

Fig. 8. Deformation works operated by Reynolds shear stress (top) and Reynolds normal stresses (middle and bottom) with boundary layer control.


Hoverer, the Reynolds normal stress contribution (Dn)Tx (middleof Fig. 8) is characterized by the largest values and consequentlyprovides the greater contribution to the increase of total pressurelosses observed in Fig. 6. Fluctuations of the streamwise velocity,that are responsible for the growth of (Dn)Tx, are mainly generatedby the instationary vortices induced by VGs. Anyway, velocity fluc-tuations are smaller as compared with the uncontrolled conditionwhere backflow occurs (Fig. 4, top), thus (Dn)Tx is reduced as well.This justifies the considerable reduction of Cpt observed at the testsection exit plane with flow control as compared with the uncon-trolled case (Fig. 6).

The presence of VGs modifies also the shape of (Dn)Ty with re-spect to the uncontrolled condition (Fig. 8, bottom). In fact theVGs, as previously discussed about Fig. 4, transfer fluid towardthe wall producing a negative time-averaged normal velocity.The term (Dn)Ty downstream of VGs is positive near the wall,where the downward motion decrease and hence @�v=@y is nega-tive. That contributes to increase the total pressure dissipationrate close to the wall. On the contrary, above y = 18 mm the term(Dn)Ty returns negative (as observed for the uncontrolled condi-tion) due to the positive @�v=@y imposed by the channeldivergence.

Fig. 9. Overall deformation work distributions without (top) and with (bottom) boundary layer control.


The distributions of the overall dissipation work due to viscousand turbulent terms for both uncontrolled and controlled condi-tions are reported in Fig. 9. The overall deformation work andhence the induced dissipation rate appear, for the controlled case,evidently smaller at the duct exit plane. Whereas, downstream ofVGs the overall dissipation rate appears slightly larger than forthe uncontrolled case close to the wall. This fact seems apparentlyin contrast with the total pressure results which show a reductionof losses in the near wall region (Fig. 6, y < 18 mm) just dowstreamof the VGs. This discrepancy cannot be explained by analysing theflow only in the meridional symmetry plane, because the presenceof VGs induces a 3D flow.

Fig. 10. Cross-stream velocity vectors, streamwise velocity and total pressure losscoefficient contour plots in the cross-stream plane at x = 350 mm.

0 5 10 15 20 25

u [m/s]

0

40

80

120

160

y [m

m]

VGs z=0mm

VGs z=25mm

VGs z=60mm

No VGs

Fig. 11. Streamwise velocity profiles for the baseline and controlled cases atx = 350 mm.

3.2. Three-dimensional effects of VGs

The three-dimensional effects of the vortices generated by theVGs on velocity and total pressure losses are shown in Fig. 10.The comparison between the velocity profiles at selected transver-sal positions and the profile for the uncontrolled flow is reported inFig. 11.

The VGs generate vortices that rotate counter-clockwise, asindicated by the velocity vectors superimposed to the colour plotof the streamwise velocity component on the left of Fig. 10. Thevortex centre, which may be identified at y = 18 mm andz = 25 mm, is characterized by low velocity magnitude. However,at the wall, the controlled boundary layer profile is fuller thanthe baseline one, as depicted in Fig. 11 (z = 25 mm). In the upwardmotion (on the right side with respect to the vortex centre) thevortex concentrates and lifts low momentum fluid from the wallregion. This vortex action leads to an almost separated boundarylayer in a small and confined region around z = 40 mm. Anyway,at the right boundary of the vortex (z = 60 mm) the VGs effect ispositive, and the boundary layer has higher momentum comparedto the uncontrolled flow (Fig. 11). In the region of downwash, nearthe test section symmetry axis, the boundary layer appearsstrongly attached, and the largest difference with respect to theuncontrolled case may be observed (Fig. 11, z = 0 mm).

The region in the cross-stream plane characterized by high totalpressure loss coefficient Cpt (Fig. 10 on the right) is the result of twodistinct phenomena associated with the cross-stream vortex action.A loss core, correlated to the low velocities of the vortex, may beidentified in the proximity of the vortex centre. Furthermore, a localloss increase, due to the upwash of the vortex, may be observedclose to the wall on the right with respect to the vortex centre.

Far downstream of the VGs trailing edge, in the cross-streamplane at x = 600 mm, the flow distortions induced by the vorticesare almost completely disappeared and the flow is almost two-dimensional, as it was shown in [19]. Consequently, due to the mix-

ing process, the total pressure distribution in this downstreamplane (not shown in the paper) presents an almost uniform pattern.

3.3. Total pressure losses

3.3.1. Without boundary layer controlIn this case the global losses between inlet and outlet sections

may be evaluated on the meridional plane (x,y) where the

0 20 40 60 80

z [mm]

0

0.005

0.01

0.015

0.02

0.025

loss

(x=3

50)

VGsBaseline

Fig. 13. Loss of total pressure with vortex generators at x = 350 mm.


measurements of total pressure and velocity have been performed.The presence of a boundary layer in the inlet section and reverseflow in the outlet section makes the classical approach based onthe integration of the mass-weighted total pressure loss coefficientnot suitable to evaluate overall losses. With the 2D-flow assump-tion, since no work is done inside the test section and no massflowpasses through the bottom wall, the total pressure loss in the con-trol volume may be evaluated from the following balance of totalpressure fluxes across the boundaries of the 2D measuring domain:

pt losses ¼Z ~y

0ðu0ðyÞpt0ðyÞÞdy�

Z ~y

0ðu~xðyÞpt~xðyÞÞdy

�Z ~x

0ðv~yðxÞpt~yðxÞÞdx ð5Þ

However, because of the turbulent flow separation, the trans-versal velocity component �w is not negligible within the reverseflow region [27]. The massflow ’’ exiting ’’ from the meridionalplane in the transverse direction was computed via a massflow bal-ance in the same rectangular domain considered for the balance oftotal pressure fluxes. The massflow exiting at x = 450 mm is lessthen the 1% of the inlet massflow, while at x = 600 mm this contri-bution is around the 8% of the inlet massflow. Since the total pres-sure is low inside the separated region (Fig. 6), the global amountof the total pressure flux exiting in z direction is relatively small(less then 4%).

The loss of total pressure has been computed for the baselineflow at different axial coordinates considering a rectangular do-main with a fixed height ~y ¼ 150 mm and a variable position ~x ofthe exit section. The loss coefficient dloss is defined as follows:

dloss ¼pt losses

1=2qU30H0

ð6Þ

where the denominator is representative of the inlet inviscid flowpower.

The evolution of dloss along the axial coordinate is shown inFig. 12. An abrupt loss increase may be observed afterx = 300 mm where backflow begins. In particular, from this posi-tion to the outlet of the test section the loss coefficient increasesof almost 6 times.

3.3.2. With boundary layer controlThe presence of VGs induces an evident three-dimensional flow,

as previously mentioned in Section 3.2. Therefore, losses may beevaluated only through a proper balance of the total pressurefluxes in a 3-D domain. This balance is written in Eq. (7) wherethe double overbar indicates the integral average along the z direc-

0 200 400 600

x [mm]

0

0.005

0.01

0.015

0.02

0.025

loss

VGsBaseline

Fig. 12. Evolution of the loss coefficient along the axial coordinate for the baselineand controlled flows.

tion. The first two terms on the right hand side represent the totalpressure flux entering and leaving the control volume along thestreamwise direction, respectively. The third term represents thetotal pressure flux through the top side, while the two latter termsaccount for the net total pressure flux through the boundaries ofthe measuring domain normal to the z direction. Thus, if the meanvelocity component w is zero on the lateral planes of the controlvolume (z = 0 and z ¼ ~z), the two latter terms in Eq. 7 do not con-tribute to the balance. On the basis of previous results reported inCanepa et al. [19], the lateral domain boundaries (z = 0 and z ¼ ~z)have been chosen in order to satisfy this assumption.

3D pt losses ¼Z ~y

0ð�uptÞdy

��0

�Z ~y

0ð�uptÞdy

��~x

�Z ~x

0ð�vptÞdx

��~y

þ 1~z

Z ~x

0

Z ~y

0ð �wptÞdxdy

��0

�Z ~x

0

Z ~y

0ð �wptÞdxdy

��~z

!

ð7Þ

With these considerations the quasi 3D balance of the cross-stream averaged total pressure fluxes along x and y may give a rep-resentative estimation of the losses for the controlled case.

The coefficient d0loss, defined in Eq. 8, represents the contributionto the overall losses for a given z transversal position. The cross-stream averaged value of d0loss is equal to dloss and it is reportedfor comparison in Fig. 12 (red2 symbols). The distribution of d0loss

in the cross-stream plane at x = 350 mm is shown in Fig. 13.

d0loss ¼

R ~y0 ð�uptÞdy

��~x�R ~y

0 ð�uptÞdy��

0þR ~x

0 ð�vptÞdx��~y

1=2qU30H0

ð8Þ

In this plane, just downstream of VGs, a local maximum oflosses is located around the vortex centre. Here d0loss for the con-trolled case appears slightly larger than dloss for the uncontrolledcondition. The larger beneficial effects induced by VGs may be ob-served near the symmetry axis, where the local total pressure lossis extremely small. In fact high momentum fluid has been trans-ported from the outer region of the boundary layer in this positionby the cross-stream vortex, as it has been shown in Fig. 10. Also onthe right side of the vortex centre (z > 40 mm) losses are smallerthan the ones measured for the uncontrolled flow. The superposi-tion of the upwash and downwash motions produced by adjacentvortex generators, installed in a co-rotating pattern, locally reduceslosses with respect to the uncontrolled case.

2 For interpretation of colour in Figs. 2–13, the reader is referred to the web versionof this article.


Moving downstream the mixing out process of the VGs vorticesinduces a significant loss increase. From x = 350 mm to x = 600 dloss

increases from 0.0048 to 0.0120 (Fig. 12). However, global losses atx = 600 mm remain 50% lower as compared with the uncontrolledcase, since the separation is considerably reduced.

4. Conclusions

A detailed experimental study of loss mechanism in a separat-ing turbulent boundary layer controlled by low profile vortex gen-erators has been carried out on a large-scale flat plate with aprescribed adverse pressure gradient. The boundary layer withand without VGs has been investigated in the meridional andcross-stream planes: velocity fields have been surveyed by meansof LDV, while the distribution of the total pressure has been mea-sured by means of a Kiel probe.

In the baseline uncontrolled configuration the flow is affectedby a turbulent boundary layer separation. The momentum transferinduced by VGs suppresses the separation and the total pressureloss in the symmetry plane is highly reduced with respect to thebaseline case.

The dissipation mechanisms for both the separated uncon-trolled condition and the controlled case have been in depth inves-tigated through the analysis of the viscous and turbulentcontributions to the overall deformation work. Losses are mainlyproduced by three terms: the deformation work of the Reynoldsshear stress acting in the streamwise direction ((Dt)Tx) and thedeformation works of the Reynolds normal stresses acting alongboth the streamwise ((Dn)Tx) and the normal ((Dn)Ty) directions.

The largest contribution to the overall dissipation rate of themean flow mechanical energy may be identified within the sepa-rated shear layer and it is due to the term (Dn)Tx. The energy sub-tracted from the main flow by (Dn)Tx is converted in turbulentkinetic energy and justifies the large increase of both Cpt andstreamwise velocity fluctuations observed in this region. It isimportant to note that the classical assumption of negligible nor-mal component of the deformation work cannot be applied for aseparating turbulent boundary layer. On the contrary, in this con-dition it is the contribution to the overall deformation work due tothe Reynolds shear stress to be negligible: it vanishes downstreamof the detachment position since the strain rate of the mean flow isalmost disappeared.

The only non-negligible contribution to the total pressure dissi-pation rate along the y direction is given by the deformation workoperated by the Reynolds normal stress ((Dn)Ty). Due to the channeldivergence it has been found negative for the uncontrolled case.Hence the term (Dn)Ty tends to increase the mean flow mechanicalenergy subtracting kinetic energy to the turbulence.

For the controlled flow the overall deformation work and hencethe induced dissipation rate appear smaller than for the baselinecase. In particular, the dissipation term (Dn)Tx is substantially re-duced by VGs.

The presence of VGs induces cross-stream vortices able to sup-press the separation and consequently the large flow oscillations,responsible for the loss increase, that characterize the separatedshear layer. These cross-stream vortices induce a non uniform totalpressure distribution in the cross-stream plane: a total pressureloss core is located at the vortex centre and another one close tothe plate surface where the vortex induces upward motion.

Due to the intrinsically three-dimensional structure of the flowfield in the controlled case, the overall total pressure losses havebeen computed through a balance of the total pressure fluxes ina 3D domain. The boundaries of the domain have been properlychosen in order to evaluate a total pressure balance from the 2Dvelocity field measured in the cross-stream planes.

For the baseline uncontrolled condition the total pressure lossesshow a steep increase where the flow detaches. A strong reductionof the aerodynamic losses has been found with the boundary layercontrol applied. Losses for the controlled condition are in fact, atthe test section exit plane, reduced by 50% with respect to theuncontrolled separated case.

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