European Journal of Mechanics B/Fluids 30 (2011) 218–235

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European Journal of Mechanics B/Fluids

journal homepage: www.elsevier.com/locate/ejmflu

Performance of transition model for predicting low Re aerofoil flowswithout/with single and simultaneous blowing and suctionM. Serdar Genç a,∗, Ünver Kaynak b, Hüseyin Yapici ca Department of Energy Systems Engineering, Erciyes University, 38039, Kayseri, Turkeyb Department of Mechanical Engineering, TOBB University of Economics and Technology Ankara, Turkeyc Department of Mechanical Engineering, Erciyes University, 38039, Kayseri, Turkey

a r t i c l e i n f o

Article history:Received 25 January 2010Received in revised form19 July 2010Accepted 2 November 2010Available online 11 November 2010

Keywords:Laminar separation bubbleFlow separation controlBlowingSuctionHot-wire anemometerTransition

a b s t r a c t

Transition-sensitive, single point eddy viscosity models are fairly new and performance assessment ofthese models is required. In this study, the performance of transition and turbulence models is firstevaluated for predicting low Re number flows having laminar separation bubbles that are traditionallyquite difficult to predict for RANS-based CFD methods. Second, suppression of the laminar separationbubbles using blowing and/or suction is investigated for a single aerofoil. A prior experimental studyusing hot-wire anemometry for a clean (no jet) NACA 2415 aerofoil at α = 8° at a Reynolds numberof 2 × 105 shows the presence of a laminar separation bubble. For this flow, the recently developedk–kL–ω transitionmodel is first shown to accurately predict the location and extent of the experimentallymeasured separation bubble. Following this, the same transition model was used to predict the flow overthe NACA 2415 aerofoil using single or simultaneous blowing or suction. In the single blowing or suctioncases, the separation bubble is not completely eliminated, but either abated or moved downstream.Smaller blowing velocity ratios cause more effective suppression of the separation bubble than largerblowing ratios, independent of the blowing locations. In contrast, larger suction velocity ratios are betterthan smaller suction ratios for the suppression. Moreover, the lift/drag ratios increase as the jet locationmoves from the leading edge to a downstream direction in both cases. In the simultaneous blowing andsuction cases, the k–kL–ω transition model is shown to suppress the separation bubble by using a mix ofjet parameters which result in increased lift/drag ratios.

Crown Copyright© 2010 Published by Elsevier Masson SAS. All rights reserved.

1. Introduction

Separation bubbles are quite commonly encountered in severalengineering applications, e.g. aerofoils, wind turbine or gas turbineblades and curved surfaces in general. Their presence has oftenundesirable effects for some low Reynolds number applicationssuch as the human powered aircraft [1] or high altitude UnmannedAir Vehicle (UAV) applications. Typical air speeds for Micro-AirVehicles (MAV), UAVs, and low air speeds for wind turbines orlow pressure gas turbine stages involve a transitional Reynoldsnumber (Re) regime where laminar separation bubbles appearon the suction surface. Delaying, eliminating or controlling suchseparation bubbles are important aerodynamic design issues; andmeasuring,modeling and predicting themare challenging researchproblems. Control of flow separation or transition point can bedone by passive means such as changing the aerofoil geometry,

∗ Corresponding author. Tel.: +90 352 437 49 01/32132; fax: +90 352 437 57 84.E-mail addresses: musgenc@erciyes.edu.tr (M.S. Genç), ukaynak@etu.edu.tr

(Ü. Kaynak), yapici@erciyes.edu.tr (H. Yapici).

0997-7546/$ – see front matter Crown Copyright© 2010 Published by Elsevier Massodoi:10.1016/j.euromechflu.2010.11.001

thereby changing the pressure gradient, or by active means suchas a small energy input via a blowing/suction jet [2–5].

For instance, high-lift systems are designed for changing thefluid dynamic behaviour of wings, and methods have been pro-posed to predict boundary layer separation and transition underthe stall conditions [6–8]. An alternativemethod to actively controland increase the lift is the addition of a suction or blowing systemover the suction surface of the aerofoils [2–5]. A recent applica-tion in the commercial aircraft industry proposes a system wherethe circulation pattern of a wing is actively controlled by a grid ofsmall oscillating jets with blowing and suction at different magni-tudes and frequencies to weaken the upper surface normal shockwave which results in reducing the drag [9].

Experimental requirements are quite substantial for producingdata in the blowing/suction flow control area. Obtaining finermea-surements for sensitive and smaller scale flows require the ad-dition of finer instrumentation and increased complexity of theflow that will lead to further experimental error [2]. In such cases,repeating experiments for a wide range of parameters will nat-urally be an expensive endeavor. Thus, numerical experimenta-tions using a range of CFD methods such as Reynolds Averaged

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Nomenclature

α = angle of attack of the main aerofoilβ = angle between the freestream velocity direction and

the local jet surfacec = aerofoil chord lengthCf = skin friction coefficientCP = pressure coefficientCL = lift coefficientε = turbulent dissipationk = turbulent kinetic energykL = laminar kinetic energyω = specific turbulence dissipation rateγ = intermittency factorReθ t = transition onset momentum thickness Reynolds

numberµ = molecular viscosityµT = eddy viscosityNACA = National Advisory Committee for Aeronauticsp = pressureRe = Reynolds numberV∞ = free stream velocityTu = turbulence intensity, %x = axis parallel to the chord liney+

= normal distance in wall coordinatesz = axis normal to the chord lineθjet = Jet angleLjet = Jet location (x/c) from the leading edgeVjet = Jet velocityRjet = Ratio of jet velocity to freestream velocity (Vjet/V∞)

Navier–Stokes (RANS) and/or Direct Numerical and/or Large EddySimulation (DNS/LES) methods arise as viable alternatives to ex-perimentation. Huang et al. [2,3] and Huang [4] investigated a sin-gle jet with a width of 2.5% of the chord length that is placed ona NACA 0012 aerofoil’s upper surface simulating the blowing andsuction control under Re = 500,000 and angle of attack 18°. Wuet al. [10] investigated control effects on a NACA 0012 aerofoilwith a local unsteady forcing (2.5% chord length width) located atx/c = 0.05 from the leading edge at angle of attacks 18°–35° us-ing a 2-D RANS approach. Catalin [11] studied control effects ona NACA 0012 aerofoil with synthetic jet array (10% width) locatedat x/c = 0.1 from the leading edge at the angle of attack of 13°.Hassan et al. [12] studied a synthetic jet located at x/c = 0.13 fromthe leading edge at the angle of attack of 0° and 5°. All of these stud-ies indicate that the use of synthetic jets and forcing or non-forcing(oscillatory/steady) suction or blowing at an aerofoil leading edgecan increase lift and decrease drag.

As for the higher order theoretical methods, You and Moin [13]conducted a Large-Eddy Simulation (LES) of turbulent flowseparation over a NACA 0015 aerofoil at Re = 896,000 andinvestigated the effectiveness of synthetic jets. The large-eddysimulation for this flow demonstrated that synthetic-jet actuationcould effectively delay the onset of flow separation and causea significant increase in the lift coefficient. Shan et al. [14,15]and Deng et al. [16] used the Direct Numerical Simulation (DNS)method to study the flow separation and control of the separationover a NACA 0012 aerofoil using vortex generators and pulsedand blowing jets. Segawa et al. [17] studied the performance ofan alternating suction/blowing array of jet actuators for a rangeof Reynolds numbers from 3.8 × 105 to 5.7 × 105, and theyshowed that clockwise and counterclockwise longitudinal vorticesappeared to be formed side-by-side in the nearwall region. Robertsand Yaras [18] studied the Large-Eddy Simulation (LES) of the

transition process in a separation bubble over a flat plate underlow freestream turbulence conditions.

Among all these numerical methods, the RANS based methodsare more efficient for design purposes as cost of calculations inthe DNS/LES often become quite prohibitive. Today, high perfor-mance computing capabilities make it possible to routinely useRANS based CFDmethods for simulating transitional and turbulentflows. The state of the art RANS solvers frequently include practi-cal one- or two-equation turbulence closure models [19] for fullyturbulent flow calculations. In parallel, transition predictions havealso progressed by means of the eN method [20,21], two-equationlow Re-number turbulence models [22], and some early [23] andmodern [24,25] methods based on experimental correlations. TheeN method has been quite successful in practice and more or lesshas become the industry standard [20]. The so-called correlation-based models [23–25] have become helpful tools for industry ow-ing to their use of integral (or global) boundary layer parameters.Recently, transport equation models [26–29] which rely on (lo-cal) information to circumvent some complicated procedures inthe early methods, have been introduced. These transport equa-tion models solve several ‘‘transport’’ partial differential equationswritten for various transition quantities in addition to the base-line turbulence models. Some of these models have been madeavailable in a number of commercial CFD codes [26,28], and as-sessment of transport equation models has been made by differ-ent authors including trials of different user-dependent transitioncorrelations [30–33].

Transition-sensitive, single point eddy viscosity models arefairly new, and performance assessments of these models arerequired. The first aim of this study is to evaluate the performanceof transition and turbulence models for the prediction of low Renumber flows which have a laminar separation bubble, whichis traditionally very difficult for RANS-based CFD. The secondaim is to investigate the suppression of the laminar separationbubble using a single or simultaneous boundary layer blowingand/or suction. This investigation was computationally carriedout over a NACA 2415 aerofoil under Re = 2 × 105 at 8°angle of attack using the k–kL–ω transition model, due to thefact that the experimental requirements are quite heavy forproducing data in the blowing/suction flow control area. Prior tosimulating the effects of blowing and/or suction, an experimentalstudy using a hot-wire anemometry for the clean NACA 2415aerofoil is conducted that shows a laminar separation bubblebetween x/c = 0.1–0.36 over the upper surface of the aerofoil.First, a range of different RANS based turbulence or transitionmodels are used to simulate this flow as a validation step.Among the models, the recently developed k–kL–ω transitionmodel is shown to accurately predict both the location and extentof the experimentally determined separation bubble. After thevalidation, both single andmultiple jets with a width of 2.5% of thechord length are placed on the aerofoil’s upper surface to simulatethe single or simultaneous blowing and suction effect.

2. Experimental study

2.1. Wind tunnel set-up

Successive experiments were carried out at a Reynolds num-ber of 2 × 105 in the open-circuit wind tunnel at the Universityof Bath Aerospace Laboratory for pressure distributions and flowvisualizations, and in the closed-circuit wind tunnel of the TOBBUniversity of Economics and Technology (TOBB-ETU) Fluid Me-chanics Laboratory [7,8] for velocity profiles, turbulence intensi-ties and force measurements. The University of Bath open-circuitwind tunnel has a test section of 910mm(length), 350mm(height)and 300 mm (width) and the NACA 2415 test wing has a chord of

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Fig. 1. NACA 2415 aerofoil and hot-wire anemometer set-up in the TOBB ETU low speed close circuit wind tunnel [8].

127 mm that spans the entire width of the test section. The winghas 33 pressure tappings on the upper and lower surfaces whichare flush along the mid span, and the pressure distribution is mea-sured by a computer controlled scanivalve unit and transducers.The TOBB-ETU low speed close-circuit wind tunnel has a test sec-tion of 1000mm (length), 300mm (height) and 300mm (width) asdepicted in Fig. 1. The velocity profiles over the NACA 2415 aerofoilwere measured by using the DANTEC (55M10) constant temper-ature hot-wire anemometer and a computer controlled two-axistraversing mechanism which enabled automatic traversing duringmeasurements. The aerodynamics forces were measured by a bal-ance system. The DANTEC 55P11 normal hot-wire probe was usedto measure the turbulence intensity and a 55P15 boundary layerprobe was used to measure the turbulence intensity in the TOBB-ETU wind tunnel. The turbulence intensity of the TOBB-ETU windtunnelwasmeasured to be around 0.1%. In allmeasurements, 4096data points were sampled at 1 kHz. The velocity calibration errorsassociated with experimental uncertainties were less than 5% forvelocity profiles.

2.2. Oil flow visualization

Oil flow visualization is a relatively simple way of examiningsurface flow patterns. The oil flow experiment conducted in theUniversity of Bath open-return circuit wind tunnel has identified alaminar separation bubble on the suction surface of the NACA 2415aerofoil [7,8]. The upper surface oil flow patterns for the airfoil atα = 8° are shown in Fig. 2. The dense area of pigment indicatesthat the separation bubble occurs around x/c = 0.26.

3. Numerical method

3.1. Flow solver

Calculations are performed over the NACA 2415 aerofoil usingblowing/suction to study control of the laminar separation bub-ble and the transition location. The commercial RANS based codeFLUENT [34] was used in this study which offers a range of fullyturbulent and transport equation based transition models includ-ing the k–ε RNG and the low Reynolds k–ω SST (full) turbulencemodels, and the recently developed k–kL–ω and k–ω SST transi-tionmodels. In earlier work [7,8], baseline calculations using someclean aerofoil configurations (without blowing/suction) providedconfidence in the subject CFD solvers by comparing the numeri-cal results with the experiment. In the simulations, second orderupwind discretization in space is used, and the resulting system ofequations is then solved using the SIMPLE coupled solution proce-dure until a convergence criteria of O(5) reduction in all dependent

Fig. 2. Oil flow visualization over the NACA 2415 aerofoil at α = 8° [7,8].

variable residuals is satisfied. Free stream boundary conditions areused in the upstream, downstream and outer boundaries. No-slipboundary conditions are used at solid surfaces and transpirationboundary conditions are used at determined jet locations to sim-ulate blowing/suction. Low free stream turbulence levels are usedto match the wind tunnel characteristics. A free stream turbulencelevelwas used as Tu = 0.1% and the ratio of the turbulent tomolec-ular viscosities is set to µT/µL = 1 in the FLUENT calculations.

3.2. Turbulence models

There are a number of two-equation eddy-viscosity type tur-bulent transport models incorporated within the FLUENT code. Inthis study, the k–ε RNG turbulence model [35] and the Menterk–ω SST model [36] are used as the standard baseline models.The k–ε RNG turbulence model is derived from the instantaneousNavier–Stokes equations usingmathematical techniques called the‘‘Re-NormalizationGroup’’methods.While the standard k–εmodel

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Fig. 3. Structured grid of NACA 2415 aerofoil without and with jet at x/c = 0.1 for CFD analysis.

Table 1The lift and drag coefficients of the NACA 2415 aerofoil at α = 8° versus grid size based on the transition models.

α = 8° Bath-Exp. k–kL–ω k–ω SST25,000 35,000 45,000 25,000 35,000 45,000

CL 1.06 0.93 1.030 1.031 0.87 0.98 0.97CD 0.047 0.02 0.027 0.027 0.017 0.021 0.023

Table 2Test configurations of single jets.

Case Ljet Rjet θjet

Single blowing or suction

Before bubble (x/c = 0.1)

0.003 ±30°, ±45°,±90°0.016 ±30°, ±45°,±90°0.032 ±30°, ±45°,±90°0.064 ±30°, ±45°,±90°0.156 ±30°, ±45°,±90°

Center of bubble (x/c = 0.26)

0.003 ±30°, ±45°,±90°0.016 ±30°, ±45°,±90°0.032 ±30°, ±45°,±90°0.064 ±30°, ±45°,±90°0.156 ±30°, ±45°,±90°

After bubble (x/c = 0.36)

0.003 ±30°, ±45°,±90°0.016 ±30°, ±45°,±90°0.032 ±30°, ±45°,±90°0.064 ±30°, ±45°,±90°0.156 ±30°, ±45°,±90°

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Fig. 4. The distribution of CP over the NACA 2415 aerofoil at α = 8° versus gridsize based on the transition models.

is a high Reynolds number model, the k–ε RNG model was chosenhere as theRNG theoryprovides an effective viscosity that accountsfor low Reynolds number effects. The Menter k–ω SST model isthe shear stress transport (SST) variant of the original Wilcox k–ωmodel [22]. This is essentially a hybrid turbulence model that cou-ples the standard k–ε and Wilcox k–ω models with low Reynoldsnumber effects in an efficient manner in which the k–ω model(in the near-wall region) and the standard k–ε model (in the far-field region) are blended together, including the modeling of shearstress transport (SST) via a modified definition of the turbulentviscosity. The low Reynolds number version of the standard k–εmodel is chosen for its ability to mimic the low Reynolds numbereffects by using wall damping terms [36].

3.3. Transition models

Recent introduction of the so-called ‘‘transport equation mod-els’’, which are basically newer variants of the early correlationmodels have helped to incorporate certain benchmark experimen-tal data that were expressed in terms of global boundary layerparameters into current RANS based solvers. Some of these mod-els are the intermittency transport equation models of Suzen andHuang [24,25] and the correlation-based k–ω SST transitionmodelof Menter et al. [26]. More recently truly single point RANS ap-proaches such as the k–kL–ω transition model of Walters andLeylek [28] which essentially eliminate the need for the intermit-tency, and a variant of the SST model called the k–ω–γ model ofFu and Wang [29] have been introduced. Such models are suitablefor straightforward implementation within RANS methods as theysolve additional transport equations for predicting transition phe-nomena that rely on local information only, in contrast with theglobal information, as used in the early methods.

Fig. 6. Experimental and numerical lift and drag coefficients of the NACA 2415 atRe = 2 × 105 [8].

In this study, the k–ω SST transition model of Menter et al. [26]and the k–kL–ω transition model of Walters and Leylek [28]are used as they are incorporated into FLUENT. Presently, bothmethods are used selectively in the literature and are shown toproduce successful results [7,8,30–32,37]. The k–ω SST transitionmodel is based on two additional transport equations beyond k andω: the first is an intermittency equation (γ -equation) that is usedto trigger the transition process; and the second is the transitiononset momentum thickness Reynolds number (Reθ t-equation)which is forced to follow experimentally-determined correlationswith some lag. In this model, the Shear Stress Transport (SST)feature is linked to the transition model by coupling it with thek–ω SST turbulence model [36]. Transition correlations are userdependent data retrieved from benchmark experiments obtainedat different laboratories. A number of investigators have tried todevelop their own correlations of the model parameters againstdifferent experimental cases [29,30] as the original parameter setremains proprietary [26].

The k–kL–ω model [28] is considered as a three-equation eddy-viscosity type, which includes transport equations for turbulentkinetic energy (k), laminar kinetic energy (kL), and specificdissipation rate (ω).According to the authors’ private communicationwith K. Walters, the kL is more like a pre-transitional kinetic

Fig. 5. Blowing/suction control parameters [8].

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Fig. 7. Numerical and experimental velocity profiles using hot-wire anemometry over the upper surface of the NACA 2415 aerofoil (Re = 2 × 105 , α = 8°) [8].

Fig. 8. Numerical and experimental turbulent intensities over the upper surface of the NACA 2415 aerofoil using hot-wire anemometry (Re = 2 × 105 , α = 8°) [8].

energy. In their original paper, Walters and Leylek [28] statedthat ‘‘as the free-stream turbulence is increased, the mean velocityprofile distorts in the pre-transitional region and high-amplitude

streamwise fluctuations occur. Mayle and Schulz [38] stated thatthese streamwise fluctuations were not turbulence in the usual senseof that word and they proposed a laminar-kinetic-energy equation to

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Fig. 9. Comparison of numerical and experimental coefficient of pressure for thesingle element NACA 2415 aerofoil at α = 8° [7,8].

describe the development of such fluctuations. Structurally they arevery different from turbulent fluctuations, since the energy is almostentirely contained in the streamwise component. Their dynamics arealso considerably different. The dynamics of laminar kinetic energyproduction are not entirely understood at present. Actually, a betterdescription of it would be energy due to streamwise fluctuations thathave a structure which is substantially different from equilibriumshear layer turbulence. For example, the Klebanoff modes in the pre-transitional boundary layer are different from the classical turbulence.Moreover, in the beginning stages of separated flow transition, thefluctuations have considerably less three-dimensionality than fullydeveloped turbulence. The separated flow transition process can beconsidered as energy transferred to not-fully-turbulent fluctuations(mean flow energy to kL) followed by a nonlinear breakdown into fullydeveloped three-dimensional turbulence (kL to k).’’ Consequently,one can think that the term ’laminar kinetic energy’ may be abit of a misnomer and the kL can be named as pre-transitionalkinetic energy. This model, which is essentially a single-pointtechnique, combines the advantages of the prior correlationmethods and eliminates the need for intermittency. In this model,the turbulent energy is assumed in the near-wall region to be splitinto small scale turbulent energy, which contributes directly toturbulence production, and large scale turbulent energy, whichcontributes to production of laminar kinetic energy through thesplat mechanism [28]. Walters and Leylek [28] assumed thattransition initiates when the laminar streamwise fluctuations aretransported a certain distance from the wall, where that distanceis determined by the energy content of the free stream, and thekinematic viscosity.

As for the the wall boundary conditions, the k–kL–ω transitionmodel uses a Neumann type boundary condition which specifiesthe normal derivative of the function on a surface, whereas the k–ωSST transition model uses Dirichlet type wall boundary conditionswhich gives the value of the function on a surface. The wallboundary conditions can be seen in detail in the study of Menterand Rumsey [39] for the k–ω SST transition model and in thestudies of Walters and Leylek [28,40] for the k–kL–ω transitionmodel. It appears that the Menter’s k–ω SSTmodel and the k–kL–ωmodel stipulate quite different methods for treating the near wallturbulence.

It is understood (via private communication with K. Walters) thatWalters and Leylek had also tried using Dirichlet conditions withkT = kL = ω = 0 at the wall, and the results had not changed verymuch. With a model like Menter’s, the wall value of ω dictates the

Fig. 10. Numerical and experimental skin-friction coefficient for the single elementNACA 2415 aerofoil at α = 8° [7,8].

Table 3Test configurations of simultaneous jets.

Case Jet Ljet Rjet θjet

Blowing and suction Blowing x/c = 0.1 0.003 30°Suction x/c = 0.36 0.156 −90°

Suction and blowing Suction x/c = 0.1 0.156 −90°Blowing x/c = 0.36 0.003 30°

destruction of turbulence in the near-wall region. In the k–kL–ωmodel, the wall destruction terms that contain gradients of sqrt(k)and sqrt (kL) dictate the destruction of turbulence in that region. Assuch, the value of ω near the wall has little impact on the results.Recently Cutrone et al. [30] proposed to use a combination of thetwo conditions for ω in the case of separated flows.

3.4. Solution grid

AC-type structured grid used for the single aerofoil is generatedby the GAMBIT [34] program is shown in Fig. 3 [7,8]. The gridextends from −10 chords upstream to 20 chords downstream andthe upper and lower boundary extends 10 chords from the profile.As accurate prediction of transition necessitates good resolution inthe boundary layer, the wall coordinate y+ of the first grid pointoff the body is ensured to be less than 1. Different sized grids areused to ensure grid independence of the calculated results. Thisis achieved by obtaining solutions with an increasing number ofgrid nodes until a stage is reached where the solution exhibitsnegligible change with a further increase in the number of nodes.Consequently, the grid size giving the grid independent results areselected. In this study, different sized grids with 25,000, 35,000and 45,000 nodes were used to ensure grid independence of thecalculated results. This was achieved by obtaining solutions withan increasing number of grid size until a stage was reached wherethe solution exhibited negligible change with a further increasein the number of cells as shown as an example in Table 1 andFig. 4. In Table 1, the distribution of numerical data obtained fromthe transition models and experimental data in terms of lift anddrag coefficients of the NACA 2415 aerofoil at α = 8° versus gridsize was given. Fig. 4 shows the distribution of CP over the NACA2415 aerofoil at α = 8° versus grid size based on two transitionmodels. According to Table 1 and Fig. 4, the grid size giving a gridindependent result was selected to be 35,000.

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Fig. 11. The streamlines and k and kL distributions over the NACA 2415 aerofoil at α = 8° using the k–kL–w transition model.

3.5. Modeling of blowing and suction

In this study, three blowing/suction jet control cases (onlyblowing, only suction and simultaneous blowing and suction)werecomputationally investigated by using three parameters as shownin Fig. 5. These parameters are the jet location, Ljet, jet velocity ratio,Rjet, and the jet angle, θjet. Here, θjet is the angle between the localjet surface and jet entrance velocity direction in which a negativeθ represents suction condition and positive θ indicates blowingcondition. The jet entrance velocity is defined as

u = Vjet cos(θjet + β)

v = Vjet sin(θjet + β)

whereβ is the angle between the freestream velocity direction andthe local jet surface. A single jet with a width of 2.5% of the chordlength is placed on the aerofoil’s upper surface to simulate theblowing/suction jet to control the laminar separation bubble underthe conditions Re = 2 × 105 and 8° angle of attack. The jet widthwas chosen as 2.5% chord length following the recommendation byDannenberg andWeiberg [41] who showed that the lift would notincrease significantly for suction areas beyond 2.5% of the chordlength. In this study, the following values for single blowing orsuction cases shown in Table 2 were investigated: the jet locationsof Ljet (x/c = 0.1—before bubble, x/c = 0.26—center of bubble,x/c = 0.36—after bubble), the jet velocity ratios of Rjet (0.003,0.016, 0.032, 0.064, 0.156), and the jet angles of θjet (±30, ±45,±90°).

Furthermore, effects of simultaneous blowing and suction overthe NACA 2415 aerofoil for Re = 2 × 105 at 8° are investigated.These cases are summarized in Table 3 such that Ljet values aregiven as x/c = 0.1-before the bubble and x/c = 0.36-after thebubble, Rjet values are given as 0.003 for blowing and 0.156 forsuction, and θjet values are given as 30° for blowing and −90° forsuction. First, a blowing jet with Rjet=0.003 and θjet = 30° wasplaced at x/c = 0.1 location and a suction jetwith Rjet = 0.156 andθjet = −90° was placed at x/c = 0.36. Second, a suction jet withRjet = 0.156 and θjet = −90° was placed at x/c = 0.1 locationand a blowing jet with Rjet = 0.003 and θjet = 30° was placed atx/c = 0.36 location.

4. Results and discussion

4.1. Performance of transition models for the NACA 2415 aerofoilwithout blowing or suction

Fig. 6 shows the lift and drag coefficients versus angle of attackdata for twowind tunnels and the numerical calculations obtainedby using FLUENT at Re = 2 × 105. The maximum lift coefficientdefines the angle at which the aerofoil will stall and this is shownto vary with the wind tunnel. The stall occurred at an angle ofattack of 12°with CLmax = 1.33 in University of Bath experiments,whereas it occurred at an angle of attack of 14° with CLmax =

1.35 in TOBB-ETU. These solutions include full turbulence modelswith some lowReynolds number capability and transport equation

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Fig. 12. Comparison of the experimental pressure distribution (no jet) over theNACA 2415 aerofoil and the numerical pressure distributions with (a) blowing (b)suction [8].

based transition models. First, the k–ε RNGmodel and the k–ω SSTmodels were used as the baseline turbulence models to predictthe performance of the low Re capability. Second, the k–ω SSTtransition and the k–kL–ω transition models were used to predictthe transition effects under the transport model assumption. InFig. 6, all numerical methods give reasonably good results againstthe experiment in the linear region, whereas the discrepancyincreases as the stall is approached. There are mixed results fromdifferent models: the low Re number k–ω SST turbulence andk–ω SST transition models underpredict, and the fully turbulentk–ε RNG overpredict the stall. The k–kL–ω transition model isrelatively in better agreement with the experimental data. In thek–kL–ω transition model, the stall occurred at an angle of attackof 14° with CLmax = 1.38. Overall, the k–kL–ω model seems tofare better than other transition models for predicting the lift.As for the drag coefficients, although the experimental CD valuesare somewhat less than the numerical CD values, there is a quitegood agreement between the experiment and computation forlow angles of attack. However, as the stall angle is approached,the numericalmodels systematically underpredict the experiment,due to a general fact that as the Reynolds number gets smaller, thenumerical turbulence models’ ability degrades.

a

b

Fig. 13. Comparison of the experimental Cf distributions (no jet) over the suctionsurface of NACA 2415 aerofoil and the numerical Cf distributions with (a) blowing(b) suction [8].

Fig. 7 shows the numerical and experimental velocity profilesusing a hot-wire anemometer over the upper surface of the NACA2415 aerofoil (Re = 2 × 105, α = 8°). Individual figures clearlyshow the separation bubble and the reverse velocity profilesat various chordwise positions. Both transition models and thek–ω SST turbulence model predict more pronounced reverse flowregions, but the k–ε RNG turbulence model misses the separationbubble. As shown, the wall velocity gradient and the wall shearstress are zero at the start of the separation (x/c = 0.15). Beyondthat location (the profiles from x/c = 0.2 to x/c = 0.3), thereis reverse flow in the boundary layer. Transition from laminar toturbulent flowwithin the bubble also involves a noticeable changein the shape of the boundary layer velocity profile. As shown atthe x/c = 0.35 station, turbulent profiles are flatter, have largervelocity gradients at the wall, and produce larger boundary layerthickness than do the laminar profiles (x/c = 0.1). It appearsthat the k–kL–ω transition model better depicts the transitionfrom laminar to turbulent flow with more pronounced velocityprofiles and changing thickness of the separation bubble withinthe boundary layer. Fig. 8 shows the numerical and experimentalturbulence intensities over the upper surface of the NACA 2415aerofoil. The turbulence intensities are reduced in the near-wallregion, but there is more pronounced increase in the outer layer inthe k–kL–ω transition model.

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Fig. 14. CL and CD coefficients of NACA 2415 aerofoil at α = 8°with blowing using the k–kL–ω transition model [8].

Fig. 15. CL and CD coefficient ratios of NACA 2415 aerofoil at α = 8°with suction using the k–kL–ω transition model [8].

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Fig. 16. L/D ratios of NACA 2415 aerofoil at α = 8°with (a) blowing (b) suction using the k–kL–ω transition model [8].

In order to complete the overall discussion regarding the val-idation, the coefficients of pressure and skin-friction given in theearlier work [7,8] are repeated in Figs. 9 and 10 respectively. Fig. 9shows the comparison for the numerical and experimental pres-sure distributions over the single element NACA 2415 aerofoil atα = 8° [7,8]. In Fig. 9, the fully turbulent calculations underpre-dict the pressure while the transport equation transition modelsquite successfully capture the transition effects in the bubble. In-spection of the pressure coefficient provides further evidence ofthe separation bubble followed by re-attached flow, as observedin the oil flow picture (Fig. 2). A very slight increase and subse-quent decrease in the experimental pressure curve is noticeable inthe figure, which suggests first the detachment of the flow due toa high adverse pressure gradient followed by an injection of highvelocity due to flowmixingwith subsequent reattachment. The po-sition along the chord of this pressure peak is x/c = 0.32, similarto the location identified in Fig. 2.

The numerical and experimental Cf for the single elementNACA2415 aerofoil at α = 8° is given in Fig. 10. In the Cf graph,the negative region points out the separation and the locationand extent of the separation bubble. The k–ω SST transitionmodel completely fails in the prediction of the separation andreattachment point, whereas the k–kL–ω gives a good predictionof the reattachment point, but shows a very large error in theseparation point. The k–ω SST turbulence model provides the bestresult, in terms of both separation and reattachment point, anaccurate recovery of the turbulent Cf after the reattachment, whilethe k–kL–ω and the k–ω SST transition model underpredicts andoverpredicts the recovery of the turbulent Cf , respectively.

Based on the above given pressure, velocity, turbulence inten-sity and skin friction comparisons between different transitionand turbulence models, although none of the models shows clearsuperiority, the k–kL–ω transition model stands out as a reason-able choice for this low Re transitional flow. Its overall value is em-phasized by its ability, for example, to clearly generate higher Tufurther upstream compared to the other models, more accurateprediction of transition from laminar to turbulent flow near thereattachment, and reasonable pressure and lift curves up to thestall. To this end, the k–kL–ω transition model was used as a rea-sonable choice in the remaining numerical calculations for the con-trol of flow over the NACA 2415 aerofoil using blowing and/orsuction.

Finally, to shedmore light onto the discussion, Fig. 11 shows thestreamlines and k and kL distributions over the NACA 2415 aerofoilat the angle of attack of 8° using the k–kL–ω transition model.This figure illustrates the region of laminar separation, transitionto turbulence where the k and kL starts to increase, and turbulentreattachment. Also, the transition from laminar to turbulent occursat the maximum bubble height [42]. By means of the increasein the turbulent kinetic energy after the transition point, theflow overcomes the adverse pressure gradient and a subsequentturbulent reattachment happens. In this way, the bubble of fluidis trapped under the separated shear layer between the separatedand reattachment points. However, the values of kL are larger thanthe values of k. It was known that the laminar kinetic energy levelswere supposed to be smaller than the turbulent energy levels. Ascan be seen by the higher levels of kL than k, the term of ’laminarkinetic energy’ for kL is shown to be a misnomer.

M.S. Genç et al. / European Journal of Mechanics B/Fluids 30 (2011) 218–235 229

Fig. 17. Streamlines of NACA 2415 aerofoil at α = 8°with (a) blowing for Rjet = 0.003 (b) suction for Rjet = 0.156 at Ljet = 0.26c with different jet angles using the k–kL–ωtransition model [8].

Table 4Test conditions for single jets simulated.

Case Ljet Rjet θjet

Blowing-1 x/c = 0.26 0.003 30°Blowing-2 x/c = 0.26 0.156 30°Suction-1 x/c = 0.26 0.003 −30°Suction-2 x/c = 0.26 0.156 −30°

4.2. Numerical results for the NACA 2415 aerofoil using blow-ing/suction

Unfortunately, no experimental work with blowing/suction forthis aerofoil is available for the above flow conditions. As detailedexperiments with different jet parameters would be very costly,the subsequent CFD calculations using the k–kL–ω model are donewithout referring to an experiment. However, it is expected thatthe effects of blowing/suction would be to energize the flow andto alleviate the extent of the laminar separation bubble. Therefore,similar to earlier work such as Huang et al. [2,3] and Huang [4],the underlying blowing/suction control mechanism is expected tobe the suppression or postponement of the separation bubble andthe reduction of the upper surface pressure coefficients to increasethe lift and decrease the drag. Having validated the presentlyavailable k–kL–ω transition against the experiment in the previoussection, we may now embark on the numerical study of theblowing/suction jets in this low Reynolds number regime.

Fig. 12 shows the experimental pressure distribution over theNACA 2415 aerofoil without blowing/suction with the numericalpressure distributions with blowing/suction effects. As seen in

Table 4, two blowing cases, Blowing-1 (Rjet = 0.003) and Blowing-2 (Rjet = 0.156), are given in Fig. 12-a for a jet located at Ljet =

0.26c with an angle θjet = 30°. Similarly, two suction cases,Suction-1 (Rjet = 0.003) and Suction-2 (Rjet = 0.156), are givenin Fig. 12-b for a jet located at Ljet = 0.26c , but with the angleθjet = −30°. In this figure, there is a peak where the blowingor suction applies. Fig. 12-a shows that the k–kL–ω transitionmodel with blowing does not eliminate the separation bubble.However, theCP becomes less negative due to blowingwhen the jetvelocity increases. In Fig. 12-b, the k–kL–ω transition model usingthe smaller suction jet velocity does not completely eliminatethe bubble; it has just abated the bubble. The larger suction jetvelocity delays the separation bubble towards trailing edge up tox/c = 0.6. The results of suction cases might be assumed as agood point of view for flow control due to the fact that suction, ingeneral, has an effect of delaying the bubble. The experimental skinfriction coefficient distributions (no jet) over the suction surfaceof NACA 2415 aerofoil and the numerical skin friction coefficientdistributions with the blowing/suction are given in Fig. 13. Theabove discussion for pressures is further supported by the skin-friction coefficients as shown in this figure. As the negative regionpoints out the location and extent of the separation bubble, theeffects of the blowing and suction to the separation bubble areclearly seen in Fig. 13. According to this transitionmodel, the effectof high blowing rate causes a completely detached flow on theentire suction surface downstream of about x/c = 0.3. This similarbehavior was reported in the literature for high blowing rates byHuang et al. [2–4]. Consequently, the smaller jet velocity is betterthan the larger jet velocity in the blowing case while the larger

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Fig. 18. Streamlines of NACA 2415 aerofoil at α = 8°with suction for Rjet = 0.156 at Ljet = 0.26c with different jet angles using the k–kL–ω transition model [8].

jet velocity is better than the smaller jet velocity in the suctionfor postponement of the laminar separation bubble. Moreover,suction is better than blowing for abatement or postponement ofthe bubble in general.

Figs. 14–16 shows the numerical lift, drag and lift/drag ratioswithout (no jet) and with the blowing/suction at different jetangles, velocity ratios and locations using the k–kL–ω transitionmodel. As seen in Fig. 14, the lower blowing velocity ratios have

M.S. Genç et al. / European Journal of Mechanics B/Fluids 30 (2011) 218–235 231

Fig. 19. kL and k contours of the NACA 2415 aerofoil at α = 8°without and with Blowing-1 using the k–kL–ω transition model.

Fig. 20. kL and k contours of the NACA 2415 aerofoil at α = 8°with Suction-1 using the k–kL–ω transition model.

lower CD ratios and slightly bigger CL ratios, while the largerblowing velocity ratios have larger CD ratios and lower CL ratios.Obviously, it is shown that CP distribution of Blowing-1 in Fig. 12-ais almost the same with no jet case which means almost the samelift, whereas Cf distribution of Blowing-1 after blowing locationis decreasing according to no jet case (Fig. 13-a), which meanslower drag. However, Blowing-2 has less -CP distribution than nojet and Blowing-1 cases in Fig. 12-a over suction surface of theNACA 2415 aerofoil and more-Cf than other cases in Fig. 13-a,which cause lower L/D ratios (Fig. 16). As seen in Fig. 15, all casesof suction have lower CD ratios due to the fact that the suction

removes decelerated fluid particles, delays the transition and theturbulent flow. It is noteworthy that the smaller blowing velocityratios are better than larger blowing ratios, while the larger suctionvelocity ratios are better than smaller suction ratios, independentof the blowing/suction jet locations. These results are qualitativelyquite consistent with some earlier numerical predictions [2–4]. Asfor the jet location, the lift/drag ratios increase as the jet locationmoves away from the leading edge in both cases. Moreover, theperpendicular jet angles raise the lift/drag ratios in the suctioncases while the jet angle does not considerably affect the lift/dragratios in the blowing cases.

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Fig. 21. Comparison of the experimental pressure distribution (No jet) over theNACA 2415 aerofoil and the numerical pressure distributions for simultaneousblowing and suction cases.

Fig. 17 shows the streamlines around the NACA 2415 aerofoil atα = 8° with single blowing under the conditions Rjet = 0.003,Ljet = 0.26c and suction under the conditions Rjet = 0.156,Ljet = 0.26c with different jet angles. It seems that the separationhas been eliminated in Fig. 17. Conversely, Fig. 18 shows thestreamlines of the NACA 2415 aerofoil at α = 8° with suctionwith different jet angles under the conditions Rjet = 0.156, Ljet =

0.26c. As seen, the k–kL–ω transition model does not completelyeliminate the separation bubble, but moves it toward the trailingedge. Moreover, as the jet angle gets more perpendicular to theaerofoil surface, the bubble moves closer to the trailing edge of theaerofoil.

Figs. 19 and 20 compare the kL and k levels at blowing andsuction locations. The blowing produces more kL levels than nojet case as the blowing jet velocity increases whereas the suctionabsorbs the streamwise fluctuations in the pre-transitional region.The blowing produces more dramatic kL levels than suction thatmay be the cause of creating larger bubbles. Moreover, as seen inthe suction case in Fig. 20, the k level is larger than the kL level

where suctionmay be absorbing the streamwise fluctuations in thepre-transitional region.

4.3. Numerical results for the NACA 2415 aerofoil using simultaneousblowing and suction

The effects of simultaneous blowing and suction over the NACA2415 aerofoil under the conditions of Re = 2×105 and α = 8° areinvestigated in this section. In the case of simultaneous blowingand suction, the location Ljet, intensity Rjet, and the angle θjet areselected as the values which give the best results for the single jetsin the previous section. First, a blowing jet is placed at x/c = 0.1with Rjet = 0.003 and θjet = 30° and a suction jet is placed atx/c = 0.36 with Rjet = 0.156 and θjet = −90° (named as Blowingand Suction in Table 3). Then, a suction jet is placed at x/c = 0.1with Rjet = 0.156 and θjet = −90° and a blowing jet is placedat x/c = 0.36 with Rjet = 0.003 and θjet = 30° (named asSuction and Blowing in Table 3). Previous analysis reports [43] thatthe k–kL–ω and k–ω SST transition models perform close to eachother in terms of eliminating the separation bubble and the (L/D)increase in such case. Here,more detailed analysis is offered for thek–kL–ω transition model including the comparison of laminar andturbulent kinetic energy profiles.

Figs. 21 and 22 show the experimental (no jet) and computa-tional values of the pressure and skin-friction distributions withsimultaneous blowing and suction. Unfortunately, as detailed ex-periments with different jet parameters are very costly, the ex-perimental values only reflect the no jet conditions and are givenas reference values in the above figures. As shown in Fig. 23, thesequence of blowing and suction arrangements in reverse ordereliminates the separation bubble in both cases. Comparing thekL and k counterparts for the above cases (Figs. 24 and 25), itappears that the leading edge blowing combination yields moredramatic production of kL and k than the leading edge suction com-bination. In these cases, the blowing adds the energy and thusstreamwise fluctuations to the flow and the suction absorb thefluctuations, which eliminates the separation bubble. However,in the suction and blowing case, the blowing after suction addsenergy and streamwise fluctuations to the flow which increasesthe k and produces more drag than other simultaneous case. Thecombined action of blowing and suction jets appear to offset eachother’s influence such that attached flow prevails in the end.

Fig. 22. Comparison of the experimental Cf distributions (No jet) over the NACA 2415 aerofoil and the numerical Cf distributions for simultaneous blowing and suctioncases.

M.S. Genç et al. / European Journal of Mechanics B/Fluids 30 (2011) 218–235 233

Fig. 23. Streamlines and turbulence kinetic energy distributions over the NACA 2415 aerofoil with simultaneous blowing and suction.

Fig. 24. kL and k contours of the NACA 2415 aerofoil at α = 8°with blowing and suction case.

234 M.S. Genç et al. / European Journal of Mechanics B/Fluids 30 (2011) 218–235

Fig. 25. kL and k contours of the NACA 2415 aerofoil at α = 8°with suction and blowing case.

Table 5Comparison of the L/D ratios with single or multi jets.

Case (L/D)/(L/D)no jet

Single blowing at x/c = 0.1 0.86Single blowing at x/c = 0.36 1.32Single suction at x/c = 0.1 1.09Single suction at x/c = 0.36 1.49Simultaneous blowing at x/c = 0.1–suction at x/c = 0.36 1.12Simultaneous suction at x/c = 0.1–blowing at x/c = 0.36 1.10

Table 5 gives the overall view of all cases including the singleor simultaneous blowing/suction multi jets for the lift/drag ratios(L/D)/(L/D)no jet. It includes the numerical values for the previouslygiven best cases for the single and the present simultaneous blow-ing/suction multi jets. Notice that simultaneous blowing/suctionjets are not giving as much help to lift/drag ratios as one would ex-pect. For instance, the lift/drag ratios (L/D)/(L/D)no jet are 1.12 in theBlowing and Suction case, and 1.10 in the Suction andBlowing case.Again, it appears that the blowing and suction offset each other’snegative influence with a net result of little change in the lift/dragratios. Overall, the best results are obtained with the single suctionjet cases, intermediate results are obtained with the multi jets andthe worst results are obtained with the blowing jets.

5. Conclusions

In this study, the performance of the k–kL–ω transition modelis evaluated for predicting low Re number flows including laminarseparation bubble without/with a single or simultaneous blowingand suction. The transition simulations were done for NACA 2415

airfoil at Re = 2 × 105 and α = 8°. First, the model is successfullyvalidated against prior hot-wire measurements for a single airfoilwithout jets. As detailed experimentswith different jet parameterswould be very costly, the subsequent CFD calculations usingthe k–kL–ω model are done without referring to an experiment.In the single blowing and suction simulations, the separationbubble is not completely eliminated, but either abated or moveddownstream. In general, the blowing jet flow control is found tobe worse than the suction case as the blowing jet dramaticallyalters the upper surface flow in negative ways especially for jetswith larger velocity ratios and perpendicular angles. Finally, theseparation bubble is eliminated for the simultaneous blowing andsuction cases resulting in some marginal increase in the lift anddecrease in drag. Overall, the best results are obtained with thesingle suction jet cases, intermediate results are obtained with themulti jets and the worst results are obtained with the blowing jets.

Acknowledgements

M. Serdar GENÇ thanks the Foundation of Erciyes Universityfor the funding of visiting the North Dakota State University asan academic visitor. Moreover, the authors thank the ScientificResearch Projects Unit of Erciyes University for scientific researchfunding under the contract no: FBD-08-400, and Dr. Y. Bora SUZENfor helping with the modelling of blowing/suction.

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