numerical study of passive and active flow separation control over a naca0012 airfoil

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Computers & Fluids 37 (2008) 975–992

Numerical study of passive and active flow separation controlover a NACA0012 airfoil

Hua Shan a,*, Li Jiang a, Chaoqun Liu a, Michael Love b, Brant Maines b

a Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, United Statesb Lockheed Martin Aeronautics Company, Fort Worth, TX 76101, United States

Received 30 December 2006; received in revised form 12 June 2007; accepted 5 October 2007Available online 5 December 2007

Abstract

This paper is focused on numerical investigation of subsonic flow separation over a NACA0012 airfoil with a 6� angle of attack andflow separation control with vortex generators. The numerical simulations of three cases including an uncontrolled baseline case, a con-trolled case with passive vortex generator, and a controlled case with active vortex generator were carried out. The numerical simulationsolves the three-dimensional Navier–Stokes equations for compressible flow using a fully implicit LU-SGS method. A fourth-order finitedifference scheme is used to compute the spatial derivatives. The immersed-boundary method is used to model both the passive and activevortex generators. The characteristic frequency that dominates the flow is the natural frequency of separation in the baseline case. Theintroduction of the passive vortex generator does not alter the frequency of separation. In the case with active control, the frequency ofthe sinusoidal forcing was chosen close to the natural frequency of separation. The time- and spanwise-averaged results were used toexamine the mean flow field for all three cases. The passive vortex generators can partially eliminate the separation by reattachingthe separated shear layer to the airfoil over a significant extent. The size of the averaged separation zone has been reduced by more than80%. The flow control with active vortex generator is more effective and the separation zone is not visible in the averaged results. Thethree-dimensional structures of the flow field have also been studied.� 2007 Elsevier Ltd. All rights reserved.

1. Introduction

At low Reynolds number, the boundary layer on theupper surface of an airfoil at incidence remains laminarat the onset of pressure recovery. As laminar flow is lessresistant to an adverse pressure gradient, flow separationmay occur near the leading edge of the airfoil. The sepa-rated shear layer is inviscidly unstable and vortices areformed due to the Kelvin–Helmholtz mechanism [1]. Thedetached shear layer may also undergo rapid transitionto turbulence and the separated flow may reattach to thewall surface because of the increased entrainment associ-ated with the turbulent flow [11] and form an attached tur-bulent boundary layer. The formation of the separationbubble depends on the Reynolds number, the pressure dis-

0045-7930/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compfluid.2007.10.010

* Corresponding author. Tel.: +1 817 272 5685.E-mail address: [email protected] (H. Shan).

tribution, the surface curvature, and freestream turbulencelevel. The location and the extent of flow separation coulddirectly affect the airfoil performance or the efficiency ofthe turbo-machinery. The flow separation over a wing inflight results in the loss of lift and increase of drag as wellas generation of aerodynamic noise.

Flow control through boundary layer manipulation toprevent or postpone separation can significantly reducethe pressure drag, enhance the lift, and improve the perfor-mance of the aircraft. Traditionally, flow separation controlis implemented through airfoil shaping, surface cooling,moving walls, tripping early transition to turbulence, andnear-wall momentum addition. Given an imposed pressurefield, the kernel in separation postponement is to addmomentum to the very near-wall region [11].

Among the near-wall momentum addition methods,steady or pulsed blowing jets and vortex generators (VG)have been widely used. The experiments conducted by

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976 H. Shan et al. / Computers & Fluids 37 (2008) 975–992

Bons et al. [6] have shown that steady Vortex GeneratorJets (VGJ) have the effect of reducing or entirely eliminat-ing the separation zone on the suction surface of the bladeat low Reynolds number, while the pulsed VGJs produce acomparable improvement to that for steady VGJs but withan order of magnitude less required mass-flow. In contrastto steady blowing, the oscillatory blowing takes advantageof inherent local instabilities in the near-wall shear layerthat causes the selective amplification of the input oscilla-tion frequency. These amplified disturbances convectdownstream along the airfoil as coherent large structuresthat serve to mix the boundary layer flow and delay sepa-ration [25]. A comprehensive review of flow separationcontrol by periodic excitation in various forms includinghydrodynamic, acoustic, and blowing/suction methods,can be found in [14]. The conventional passive vortex gen-erator was first developed by Taylor [36] in 1947 to preventboundary layer separation in wind tunnel diffuser. The firstsystematic study of vortex generations and their effects onthe boundary layer was performed by Schubauer andSpangenberg [30] in late 1950s. Since then the vortex gener-ators have been successfully applied to lifting surfaces inmany aeronautical applications for control of flow separa-tion and reduction of drag in a turbulent boundary layer[7,16,20]. The vortices created by vortex generators transferlow energy fluid from the surface into the mainstream, andbring higher energy fluid from the mainstream down to thesurface where the higher kinetic energy level is able to with-stand a greater pressure rise before separation occurs.Another mechanism introduced by the vortex generator isassociated with the excitation of the local instability wavesthat lead to an early transition to turbulence, which delaysthe flow separation and reduces the size of the separationzone.

Generally, vortex generators are designed as either pas-sive or active devices. The effectiveness of a passive vortexgenerator, whose size, position, and orientation are fixedon the surface, is limited to a narrow operational range.Lin [21] gave an in-depth review of boundary layer flowseparation control by the passive low-profile vortex gener-ators. More recently, Godard and Stanislas [12] conductedan experimental study to optimize the standard passivevane-type vortex generators over of bump in a boundarylayer wind tunnel, which mimics the adverse pressuregradient on the suction side of an airfoil at the verge ofseparation. Two types of VG configurations that produceco- and counter-rotating longitudinal vortices were tested,and the counter-rotating device appears to be more effec-tive. On the other hand, the active vortex generator, devel-oped from the concept of dynamic flow control is capableof changing its size, position, and orientation accordingto different flow conditions. The basic experimental studiesof Shizawa and Mizusaki have revealed the response offlow behind the active vortex generators over a flat plate[34,35]. Other experimental research has also shown thatthe active control using deployable vortex generatorsenhances the momentum mixing and energizes the bound-

ary layer so that the flow separations is delayed [27]. It isalso interesting to find experimentally that the high-fre-quency deployable micro vortex generator system (HiM-VG) producing an oscillatory flow field at frequenciesranging from 30 to 70 Hz is very effective in mitigating flowseparation on the upper surface of a deflected flap [26].However, the mechanism of flow control with active vortexgenerators is still unclear due to lack of systematic studies.

In cases of flow separation, instability and laminar-turbulent transition may take place in the detached freeshear layer. It is widely accepted that the instability in theseparation zone is driven by the Kelvin–Helmholtz mecha-nism if the disturbance level of freestream is low. In thiscase, transition takes place due to nonlinear breakdownof spatially growing traveling waves in the separated freeshear layer [37]. When the shear layer becomes turbulent,the detached shear layer may reattach to the surface, creat-ing a separation bubble and forming an attached turbulentboundary layer. Yarusevych et al. [40] studied the boundarylayer separation on a NACA0025 airfoil via hot-wire ane-mometry and surface pressure measurements and foundthe fundamental frequency associated with flow separation.

Flow transition in separation bubbles is a classic topicwhich has been studied both theoretically and numericallyfor many years [5]. Among the different approaches usedfor the study of flow instability, there are the linear stabilitytheory (LST) [9], the parabolized stability equations (PSE)method [4], and direct numerical simulation (DNS) andlarge eddy simulation (LES). LST is mainly a local analysiswith assumption of parallel base flow. PSE assumes asteady base flow with no elliptic part. These assumptionsdo not apply for the case of flow separation and transitionaround an incident airfoil. With the development of com-puter resources and efficient numerical methods, high reso-lution and high accuracy DNS/LES has become feasiblefor the study of transition in separated flows and flowseparation control. Early efforts of the authors includethe numerical simulations of two-dimensional flow separa-tion, three-dimensional separation and transition over aNACA0012 airfoil with 4� angle of attack [31,32], flow sep-aration control on a NACA0012 airfoil with pulsed blow-ing jets [19], and numerical simulation of flow behind a pairof active vortex generators over a flat plate [33].

The objective of current work is to study the feasibilityof simulating the flow separation control with vortex gen-erators using a technique that combines the body-fittedmesh for the airfoil in a curvilinear coordinate systemand the immersed-boundary method for modeling the vor-tex generator. Direct numerical simulations of the follow-ing three cases were performed on a NACA0012 airfoil at6� angle of attack: (1) uncontrolled flow separation (base-line case); (2) flow control with passive vortex generators(Case 1); and (3) flow control with active vortex generators(Case 2). The organization of the remaining part of thispaper is as follows. In Section 2, we briefly introduce themathematical model and numerical methods. Section 3presents the layout of the vortex generators and problem

H. Shan et al. / Computers & Fluids 37 (2008) 975–992 977

formulations for the baseline case, and the two controlledcases. Section 4 shows the numerical results for all threecases. Conclusions are given in Section 5.

2. Mathematical model and numerical methods

2.1. Governing equations

The three-dimensional compressible Navier–Stokes equ-ations in generalized curvilinear coordinates (n,g,f) arewritten in conservative form as

1

JoQotþ oðE � EvÞ

onþ oðF � F vÞ

ogþ oðG� GvÞ

of¼ 0:

The vector of conserved quantities Q, inviscid flux vectors(E,F,G), and viscous flux vectors (Ev,Fv,Gv) are defined by

Q ¼

q

qu

qv

qw

Et

0BBBBBB@

1CCCCCCA; E ¼ 1

J

qU

qUuþ pnx

qUvþ pny

qUwþ pnz

UðEt þ pÞ

0BBBBBB@

1CCCCCCA;

F ¼ 1

J

qV

qVuþ pgx

qVvþ pgy

qVwþ pgz

V ðEt þ pÞ

0BBBBBB@

1CCCCCCA; G ¼ 1

J

qW

qWuþ pfx

qWvþ pfy

qWwþ pfz

W ðEt þ pÞ

0BBBBBB@

1CCCCCCA;

Ev ¼1

J

0

sxxnx þ syxny þ szxnz

sxynx þ syyny þ szynz

sxznx þ syzny þ szznz

Qxnx þ Qyny þ Qznz

0BBBBBB@

1CCCCCCA;

F v ¼1

J

0

sxxgx þ syxgy þ szxgz

sxygx þ syygy þ szygz

sxzgx þ syzgy þ szzgz

Qxgx þ Qygy þ Qzgz

0BBBBBB@

1CCCCCCA;

Gv ¼1

J

0

sxxfx þ syxfy þ szxfz

sxyfx þ syyfy þ szyfz

sxzfx þ syzfy þ szzfz

Qxfx þ Qyfy þ Qzfz

0BBBBBB@

1CCCCCCA;

where J ¼ oðn;g;fÞoðx;y;zÞ is the Jacobian of the coordinate transfor-

mation between the curvilinear (n,g,f) and the Cartesian(x,y,z) frames, and nx,ny,nz,gx,gy,gz,fx,fy,fz are coordi-nate transformation metrics. q is the density. The threecomponents of velocity are denoted by u, v, and w. Et isthe total energy given by

Et ¼p

c� 1þ 1

2qðu2 þ v2 þ w2Þ:

The contravariant velocity components U, V, and W aredefined as

U � unx þ vny þ wnz;

V � ugx þ vgy þ wgz;

W � ufx þ vfy þ wfz:

The terms Qx, Qy, andQz in the energy equation are definedas

Qx ¼ �qx þ usxx þ vsxy þ wsxz;

Qy ¼ �qy þ usxy þ vsyy þ wsyz;

Qz ¼ �qz þ usxz þ vsyz þ wszz:

The components of the viscous stress tensor and heatflux are denoted by sxx,syy,szz,sxy,syz,sxz and qx,qy,qz,respectively.

In the dimensionless form, the reference values forlength, density, velocities, temperature, pressure and timeare Lr; qr;U r; T r; qrU

2r ; and Lr/Ur, respectively, where the

subscript ‘‘r” denotes the reference quantities. The dimen-sionless parameters, including the Mach number M, theReynolds number Re, the Prandtl number Pr, and the ratioof specific heats c, are defined as follows:

M ¼ U rffiffiffiffiffiffiffiffiffiffifficRgT

p ; Re ¼ qrUrLr

lr; Pr ¼ Cplr

kr; c ¼ Cp

Cv;

where Rg is the ideal gas constant, Cp and Cv are specificheats at constant pressure and constant volume, respec-tively. Viscosity is determined according to Sutherland’slaw in dimensionless form

l ¼ T 3=2ð1þ SÞT þ S

and S ¼ 110:3KT1

:

The governing system is completed by the equation of state

cM2p ¼ qT :

The components of the viscous stress tensor and the heatflux in their non-dimensional form are as follows:

sij ¼l

Reoui

oxjþ ouj

oxi

� �� 2

3dij

ouk

oxk

� �and

qi ¼ �l

ðc� 1ÞM2RePr

oToxi

:

2.2. Numerical algorithms and parallel computing

The numerical simulation solves the three-dimensionalcompressible Navier–Stokes equations in generalized cur-vilinear coordinates using the implicit LU-SGS method[41]. A second-order fully implicit Euler backwardscheme is used for the temporal discretization. The spa-tial derivatives appearing in the residual term are com-puted using the fourth-order finite difference scheme inthe interior of the domain. A sixth-order filter is appliedat regular intervals in the simulation to suppress numer-ical oscillation.


The nonreflecting boundary conditions [18] are derivedbased on characteristic analysis. The modified Navier–Stokes equations are applied to the domain boundaryand solved implicitly with the equations of interior pointsto ensure numerical stability. Viscous terms are takeninto account by including the viscous effect near the wall.The computation of the characteristic variables appearedin the modified Navier–Stokes equations depends on thedirection of characteristic waves at the boundary. Thecorresponding characteristic variables of outgoing charac-teristic waves are computed from the interior nodes. Thecharacteristic variables of incoming waves are determinedby the boundary conditions. In the case of subsonic flowaround airfoils, there are four incoming waves and onlyone outgoing wave at the inflow boundary. Thus, thefreestream velocity and temperature are specified at thisboundary, while the density is computed from interiorpoints. Similarly, the nonreflecting boundary conditionsalso apply to the far-field, downstream, and no-slipadiabatic wall boundaries. More details of the mathemat-ical model and numerical method can be found in[17,18,32].

The numerical simulation is performed using parallelcomputing with the Message Passing Interface (MPI)libraries. The computational domain is partitioned into n

equal-sized sub-domains along the streamwise direction(n-direction) and each sub-domain is assigned to one pro-cessor. The implicit LU-SGS algorithm is implementedthrough a blockwise iteration within each processor andthe solution data on the sub-domain interfaces areexchanged with neighboring processors at the end of itera-tion. The parallel computer code has been thoroughlytested on different platforms with the performance scalingalmost linearly over a large number of processors.

2.3. Immersed-boundary method

The immersed-boundary method developed by Peskin[28] has been widely applied to numerical simulation ofvarious flow problems. More recently, this method hasbeen used for the simulation of three-dimensional flowsby Goldstein et al. [13], Saiki and Biringen [29], Arthurset al. [3], and Grigoriadis et al. [15]. The latest review isgiven by Mittal and Iaccarino [23]. The basic differencebetween the immersed-boundary method and conventionalapproach lies in the way the solid boundaries are defined.Instead of using structured or unstructured boundary-fit-ting grids to define the geometrical configuration, theimmersed-boundary method actually mimics the presenceof solid bodies by means of suitably defined body forces.There are two different ways to impose the body forces:the continuous forcing approach and the discrete forcingapproach. In the first approach, which is suitable for solv-ing flow problems with immersed elastic boundaries, theforcing term, usually formulated as a distribution function,is incorporated into the continuous momentum equation.In the second approach the forcing is introduced after the

governing equations are discretized. The second approachis more attractive for flow problems involving solid bound-ary, which is tracked as a sharp interface. The introductionof forcing terms in the discrete forcing approach can be for-mulated in two methods: the indirect and direct boundarycondition impositions. The indirect imposition still needs asmooth distribution function to distribute the forcing overseveral nodes near the interface. The implementation ofthe direct imposition is very straightforward, where theboundary conditions are directly imposed at immersedboundaries.

The focus of this work is to study the vortex generatorinduced large coherent vortical structures that convectdownstream and introduce high momentum into boundarylayer flow to eliminate or delay flow separation. The accu-racy of numerical solution in resolving the vortex genera-tor’s self boundary layer has trivial effect on theconvection and diffusion of streamwise vortical structuresin the downstream [38]. Therefore, the immersed-boundarymethod is an ideal technique for this case. In the presentwork, the discrete forcing approach with direct boundarycondition imposition is used.

To validate the immersed-boundary method, in particu-lar the discrete forcing approach with direct boundary con-dition imposition, numerical experiments were performedon two test cases: the backward-facing step flow, and theflow past a circular cylinder. A detailed investigation onapplication of immersed-boundary technique to these twoexamples can be found in [38] and [22]. In our test caseof backward-facing step flow, the 22h � 2h domain is par-titioned by a non-uniform Cartesian grid with 220 � 65points, where h is step height. Fig. 1 shows the mesh andthe immersed boundary. The mesh is clustered near the sur-face of the step in both horizontal and vertical directionsand near both top and bottom walls. The no-slip boundarycondition is directly imposed on grid nodes located on theimmersed boundary without interpolation and zero-veloc-ity is specified at the interior nodes of the step. The Rey-nolds number based on the step height is 100corresponding to a steady flow field. Fig. 2 shows the con-tours of streamwise velocity. The negative value is shownby dashed contours. The reattachment length is about3.7h, which is consistent with the experimental data [2]and numerical results with various immersed-boundarymethods [38].

In the test case of flow past the circular cylinder, insteadof using a Cartesian grid, the 56D � 17D domain is parti-tioned by a curvilinear mesh with 364 � 259 grid points,where D is the diameter of the cylinder. The mesh isdesigned properly such that the immersed boundary (sur-face of the cylinder) conforms to the grid line and the meshis clustered near the surface of the cylinder, as shown inFig. 3.

The purpose of this is to avoid numerical interpolationin the immersed-boundary method, thus the no-slip condi-tion can be directly imposed on grid nodes that representthe surface of the cylinder. Zero-velocity is specified at

Fig. 1. Mesh near backward-facing step.

Fig. 2. Contours of streamwise velocity in backward-facing step flow.


the interior nodes of the cylinder. The Reynolds numberbased on freestream and diameter of the cylinder is 40 cor-responding to the steady flow.

The contours of streamwise velocity are plotted inFig. 4, where the negative contours are dashed. Fig. 5shows the streamlines of the steady flow, where a, b, L,and h represent the characteristic parameters used todescribe the size and location of the recirculation zone.Comparison of the present results with other computa-tional [10,22] and experimental [8] results at the sameReynolds number is given in Table 1. CD is coefficient

Fig. 3. Mesh around cylinder a

of drag. Our numerical results agree very well withothers.

To further test the feasibility of simulating active vortexgenerator with the immersed-boundary method. A numer-ical simulation of flow behind a pair of active vortex gener-ators over a flat plate was performed [33] and satisfactoryagreement was found when the numerical results were com-pared with experimental data [34]. Fig. 6 shows the con-tours of instantaneous streamwise velocity behind thevortex generators at their fully deployed and retracted posi-tions during the first working duty cycle. In Fig. 6a, the

nd the immersed boundary.

Fig. 4. Contours of streamwise velocity in steady flow past a circular cylinder.

Fig. 5. Streamline of steady flow past a circular cylinder.

Table 1Comparison of present result with other computational/experimentalresults

L a b h CD

Present result 2.25 0.759 0.589 53.9� 1.53Linnick and Fasel [22] 2.28 0.72 0.60 53.6� 1.54Coutanceau and Bouard [8] 2.13 0.76 0.59 53.8� –Fornberg [10] 2.24 – – 55.6� 1.50

Fig. 6. Contours of instantaneous streamwise velocity beh


large scale streamwise vortical structures created by thevortex generators can be seen on the cross-sections (y–z

plane). On x–y plane, the high-speed streaks appear atthe downwash side of the streamwise vortices that bringhigh momentum fluid into the near-wall region. InFig. 6b, the streamwise vortices disappear in the immediatedownstream region after the vortex generators are fullyretracted.

ind a pair of active vortex generator over a flat plate.


3. Problem formulation

This study focuses on numerical simulation of flow sep-aration and control over a NACA0012 airfoil at a 6� angleof attack. The characteristic scaling parameters for non-dimensionalization include the freestream velocity U1,the freestream pressure p1, the freestream temperatureT1, and the chord length of the airfoil C. The characteris-tic time is defined as C/U1. Fig. 7a shows the layout of apair of vortex generators on the surface of the airfoil, sim-ilar to the experiment of [34] except that the flat plate usedin the experiment is replaced by the NACA0012 airfoil.The width of the airfoil is set to 0.1C in the simulation.The circular wing lip type vortex generator has a radiusof 0.01675C and a thickness of 0.001C. The vortex genera-tor can rotate about its circular center (apex of the vortexgenerator) with a pitch angle ranging from 0� to 30.96� as

Fig. 7. NACA0012 airfoil and vortex generator: (a

Fig. 8. Perspective view of the a

shown in Fig. 7b. The 0� pitch angle is corresponding to thefully retracted position and 30.96� to the fully deployedposition. The maximum pitch of the vortex generator givesit a maximum height of 0.0086C normal to the airfoil sur-face. On the surface of the airfoil, the apex of the vortexgenerator is located at x = 0.1C, as shown in Fig. 7c. Thedistance between the mid-chord points of the vortex gener-ators is 0.02C. The angle of yaw to the freestream flow is18�. In the passive flow control simulation (Case 1), thevortex generators were deployed to their maximum height.In the active flow control simulation (Case 2), the motionof two vortex generators was synchronized and controlledby a predefined duty cycle, which was set to a single sinu-soidal function of time with a specified period in this study.

The body-fitted mesh is used to partition the domainaround the NACA0012 airfoil as displayed in Fig. 8. Inthe n–f plane of the curvilinear coordinate system, the

) perspective view; (b) side view; (c) top view.

irfoil and mesh in n–f plane.

Fig. 9. Vortex generator and mesh on the upper surface of the airfoil and in n–f plane.


C-type mesh is generated numerically using an elliptic gridgeneration algorithm, where n, g, and f represent thestreamwise, spanwise, and wall-normal directions, respec-tively. The layout of mesh on the centerline plane and air-foil surface near the vortex generators is shown in Fig. 9.The upstream boundary of the computational domain is3.5C from the leading edge of the airfoil. The outflowboundary is located at 5C downstream of the trailing edge.Because the nonreflecting boundary conditions are used, itis not necessary to use very large domain. The spanwiselength of the domain is 0.1C. Since the numerical simula-tion is not designed to study the effect of an array of vortexgenerator pairs with redefined distance between each pair,a symmetry boundary condition is used on the boundaryto avoid imposing a particular period in the spanwisedirection.

The flow parameters used by the numerical simulationare summarized in Table 2. The Reynolds number basedon the freestream velocity and the chord length is 105.The freestream Mach number is 0.2. The body-fitted meshhas 840 � 90 � 120 grid points. Based on the wall unit offully developed turbulent boundary layer flow, the grid sizeon the upper surface of the airfoil downstream of the vor-tex generator is Dx+ � 18, Dy+ � 6, and Dz+ � 0.75. Thetime step size is Dt = 1.09 � 10�4C/U1.

Table 2Computational parameters

Angle ofattack, a

Reynolds number,Re = U1C/t1

Machnumber, M

Grid nodes,Nn � Ng � Nf

6� 105 0.2 840 � 90 � 120

Fig. 10. Isosurface of instantaneou

4. Numerical results

The numerical simulations include three cases: uncon-trolled flow separation (baseline case), flow separation con-trol with a pair of passive vortex generators (Case 1), andflow separation control with a pair of active vortex gener-ators (Case 2). The flow conditions and mesh used areexactly the same for all three cases. The numerical simula-tion results are summarized and compared in the followingsubsections.

4.1. Baseline case

In the baseline case, the vortex generators are at theirfully retracted position. The typical feature of the flow fieldcan be seen from a side view of the isosurface of instanta-neous spanwise vorticity with xy = 30 as depicted inFig. 10. The separation of free shear layer from the airfoilsurface, vortex shedding from the separated shear layer,reattachment of the shear layer, and breakdown to turbu-lence in the boundary layer can be seen clearly in the figure.

Fig. 11 shows the time- and spanwise-averaged velocityvectors at every third streamwise grid location and the con-tours of streamwise velocity. The time-average was per-formed over a time period of 15C/U1. The contours ofthe reversed flow with negative streamwise velocity areplotted in a dark color. The mean flow field in Fig. 11 indi-cates that the separation starts at x = 0.06C near the lead-ing edge of the airfoil. The separated flow reattaches nearx = 0.285C. The average length of the separation bubbleis about 0.225C. The streamlines of the mean flow field

s spanwise vorticity (xy = 30).

Fig. 11. Time and spanwise-averaged velocity vectors and contours of baseline case (Every third streamwise grid location is shown).

Fig. 12. Time- and spanwise-averaged streamlines of baseline case.

Fig. 14. Mean skin friction coefficient of baseline case.


are plotted in Fig. 12. Besides the location of the mean sep-aration and reattachment points, Fig. 12 also shows thecenter of the mean recirculation bubble in the separationzone. The characteristic length of the separation regionLsep, defined as the distance between the separation pointand the center of the mean recirculation bubble [24], isabout 0.18C in the baseline case.

Fig. 13 shows the mean pressure coefficient Cp of the air-foil calculated from the time- and spanwise-averaged result.Near the leading edge, the strong adverse pressure gradienton the upper surface causes the separation of the boundarylayer near the leading edge. The suction plateau that fol-lows the suction peak corresponds to the separation bub-ble. The skin friction coefficient Cf of the mean flow onthe upper surface of the airfoil is shown in Fig. 14. The neg-ative value of Cf between x = 0.06C and x = 0.285C, indi-cates the near-wall reversed flow in the separation bubble.Both Figs. 13 and 14 confirm the observation in Figs. 11and 12 in terms of the location and length of the separation

Fig. 13. Mean pressure coefficient of baseline case.

bubble. The abrupt recovery of Cf from its negative peak toa positive peak between x = 0.25C and x = 0.35C corre-sponds to transition and reattachment of the separatedflow.

The chord-wise distribution of peak turbulence kineticenergy k is displayed in Fig. 15. The ‘peak’ means the max-imum k at each streamwise location. The abrupt increase ofk at x � 0.24C indicates the starting point of transition toturbulence, which is also shown by the sharp increase of Cf

displayed in Fig. 14. It is clear that transition occurs beforethe separated flows reattaches, because the mean reattach-ment point is at x = 0.285C while transition starts atx � 0.24C.

The three-dimensional isosurfaces of the instantaneousstreamwise, spanwise, and wall-normal components of vor-ticity over the upper surface of the airfoil are shown inFig. 16. The three-dimensional vortical structuresappear after the transition and reattachment as shown in

Fig. 15. Chord-wise distribution of peak turbulence kinetic energy ofbaseline case.


Fig. 16a–c, where the contours of streamwise vorticity xx,spanwise vorticity xy, and wall-normal vorticity xz are dis-played. The separated shear layer can be seen from the iso-

Fig. 16. Three-dimensional isosurface of compone

surface of the spanwise vorticity in Fig. 16b. Near theleading edge of the airfoil, a two-dimensional shear layeris detached from the surface and no three-dimensionalstreamwise vortical structure can be seen near the separa-tion point. Therefore, the separated shear layer is initiallya two-dimensional laminar flow. Then slight distortionsbecome visible on the isosurface of the spanwise vorticityand the three-dimensional fluctuations start to grow rap-idly and eventually lead to the shedding of vortices indicat-ing that the separated shear layer undergoes transition,which is followed by reattachment of the separated shearlayer, and breakdown of small-scale three-dimensionalstructures in the immediate downstream region of reat-tachment. Fig. 16a also indicates that the downstreamregion of the reattachment point between x = 0.25C andx = 0.5C is the most active area that contains more vorti-cal structures.

nts of instantaneous vorticity of baseline case.


In order to identify the natural frequency of flow sepa-ration in the baseline case, spectrum of pressure fluctua-tions was computed from simulation data at severalstreamwise stations. Fig. 17 shows the spectra of pressurefluctuations at x = 0.163C and x = 0.217C on the center-line plane and near the upper surface of the airfoil.Fig. 17a has a small peak at f � 15U1/C which becomesthe dominant spectrum at the downstream location ofx = 0.217C as shown in Fig. 17b. The peak spectrum atf � 15U1/C reflects the natural characteristic frequencyof the flow separation region (fsep), a frequency at whichvortices are shedding from the separated shear layer [24].A careful examination of the animated flow structures fromsimulation data also confirms this conclusion. Apparentlyfsep is the dominant frequency in the baseline case.Fig. 17b also indicates that fsep is not an isolated spectrumpeak and a broad and strong spectrum of other frequenciesappears as a wave packet centered at fsep. The similar wavepackets have also been observed in the experiments of Yar-usevych et al. [40].

4.2. Case 1 – flow separation control with passive vortex

generators

In this case, a pair of static vortex generators is used forpassive flow separation control. The details of the layout ofvortex generators were presented in Section 3. It is worth tonote that the apex of the vortex generator is located at

Fig. 17. Spectra of pressure flu

Fig. 18. Time and spanwise-averaged velocity vectors and contou

x = 0.1C, which is very close to the location of the meanseparation point at x = 0.06C in the uncontrolled baselinecase. The vortex generators are fully deployed to their max-imum height which is about two times the local boundarylayer thickness. It should be pointed out that geometricparameters of the vortex generators, such as size, pitchand yaw angles, distance between vanes, and streamwiselocation, are not to be optimized in this study.

Fig. 18 shows the time- and spanwise-averaged velocityvector and contours of streamwise velocity. The time-aver-age was performed over a time period of 25C/U1. Fig. 19plots the streamlines of the time- and spanwise-averagedflow field. Compared with the uncontrolled baseline caseshown in Fig. 11, the strong recirculation and the size ofseparation bubble has been substantially reduced. Twosmall separation bubbles can be identified in the mean flowdisplayed in Fig. 18. The first bubble starts at the naturalseparation point near x = 0.06C and is forced to reattachat about x = 0.11C. Then the mean flow remains attachedbehind the vortex generators over a significant extent of theairfoil until x = 0.21C, the starting point of a second sepa-ration which reattaches near x = 0.25C forming a smallseparation bubble with a length of about 0.04C. Thenumerical results indicate that the passive vortex generatorleads to a more than 80% reduction in the length of sepa-ration bubble compared with the baseline case.

The mean pressure coefficient Cp is shown in Fig. 20 incomparison with that of the baseline case. The suction

ctuations of baseline case.

rs of Case 1 (Every third streamwise grid location is shown).

Fig. 19. Time- and spanwise-averaged streamlines of Case 1.

Fig. 20. Mean pressure coefficient of Case 1 in comparison with baselinecase.


plateau has been significantly reduced. The Cp curves fromboth cases almost coincide with each other downstream ofreattachment, indicating that the vortex generator hasminor effect on mean pressure distribution downstreamof the reattachment (x > 0.4C). The comparison betweenthe friction coefficientCf of the two cases is displayed inFig. 21. The Cf of Case 1 remains positive except for thetwo segments corresponding to the small separation bub-bles that appear in Figs. 18 and 19. There is a sharpincrease in Cf immediately downstream of the vortex gener-ator indicating that the friction is increased due to the highmomentum fluid brought by the vortex generator into thenear-wall region.

Fig. 21. Mean skin friction coefficient of Case 1 in comparison withbaseline case.

Fig. 22 shows the chord-wise distribution of the peakturbulence kinetic energy k of Case 1 in comparison withthat of the baseline case. In Case 1, k increases sharply atx � 0.24C, about the same location in the baseline case.It should be noted that the passive vortex generators onlyreduce the size of the natural separation bubble and thereare still two small separation bubbles remaining in the timeand spanwise-averaged result as shown in Fig. 18. In thiscase, the high momentum transferred from the freestreamby vortices created by the passive vortex generators reat-taches the separated laminar flow forming the first bubblebetween x = 0.06C and x = 0.11C. But the reattached lam-inar flow is not able to resist the adverse pressure gradientdownstream and it separates again from the airfoil surfacenear x = 0.21C. The separated shear layer undergoes tran-sition which leads to reattachment at x = 0.25C formingthe second bubble as shown in Fig. 18. In this case, as dis-played in Fig. 22, transition in the second separated shearlayer occurs at approximately the same location as in thebaseline case. It is possible that the vortices created bythe passive vortex generators bring more energy to thetransition process such that the maximum peak k is almostthree times higher than that of the baseline case.

Fig. 23 shows the three-dimensional isosurfaces of theinstantaneous streamwise, spanwise, and wall-normalvorticity over the upper surface of the airfoil. The passivevortex generators at x = 0.1C produce a pair of counter-rotating streamwise vortices in the immediate downstreamregion, see Fig. 23a. These vortices are the only three-dimensional structures upstream of x = 0.2C. They bringhigh momentum fluid into the near-wall region andreattach the separated flow as shown in Fig. 23b. The

Fig. 22. Chord-wise distribution of peak turbulence kinetic energy of Case1 in comparison with baseline case.

Fig. 23. Three-dimensional isosurface of components of instantaneous vorticity of Case 1. (a) streamwise vorticity (dark color: xx = 100; light color:xx = � 100); (b) spanwise vorticity (xy = 30); (c) wall-normal vorticity (dark color: xz = 50; light color: xz = � 50).


reattached flow separates again at about x = 0.2C which isvery close to the mean separation point The animated flowfield also shows a steady location of the second separationpoint. The animation also shows that the instantaneousreattachment point wanders between x = 0.25C andx = 0.3C. At the instant shown by Fig. 23, the reattach-ment occurs at about x = 0.3C. Fig. 23 also shows the mostactive vortical structures between x = 0.3C and x = 0.5C

which is consistent with the distribution of peak turbulencekinetic energy in Fig. 22.

The time- and spanwise-averaged results have shownthat the second separation starts at x = 0.21C and transi-tion occurs at x = 0.24C. The spectrum of pressure fluctu-

ations was computed from simulation data to identify thefrequency of flow separation..The spectra of pressure fluc-tuations at x = 0.163C and x = 0.217C are displayed inFig. 24. Compared with in Fig. 17a, the peak spectrumf � 15U1/C that appears in the uncontrolled baseline caseis not visible in Fig. 24a, as the separated shear layer reat-taches due to streamwise vortices created by the passivevortex generators. However, at x = 0.217C within the sec-ond separation bubble, a spectrum peak is found atf � 15U1/C as shown in Fig. 24b. This frequency equalsfsep – the natural characteristic frequency of flow separa-tion in the baseline case. It is also confirmed by the ani-mated flow visualization of the simulation data that

Fig. 25. Time and spanwise-averaged velocity vectors and contours in Case 2 (Every third streamwise grid location is shown).

Fig. 26. Time- and spanwise-averaged streamlines of Case 2.

Fig. 27. Mean pressure coefficient of Case 2 in comparison with baselineand Case 1.

Fig. 24. Spectra of pressure fluctuations of Case 1.

Fig. 28. Mean skin friction coefficient of Case 2 in comparison withbaseline and Case 1.


Fig. 29. Chord-wise distribution of peak turbulence kinetic energy of Case2 in comparison with baseline case.


vortices are shedding from the second separated shear layerat a frequency of fsep, indicating that mechanism of flowtransition in Case 1 is similar to that of baseline case.

Fig. 30. Three-dimensional isosurface of components of instantaneous vorticxx = � 100); (b) spanwise vorticity (xy = 30); (c) wall-normal vorticity (dark

Despite the similarity, the spectra of these two cases haveobvious difference that Case 1 has a standalone and smallerpeak at fsep and the baseline case has a stronger wavepacket centered at fsep, see Figs. 17b and 24b. A possibleexplanation is as follows: In the baseline case, the initialseparation occurs at x = 0.06C. The instability in the sepa-rated shear layer develops and evolves into an amplifieddisturbance involving more frequencies such that the spec-trum at x = 0.217C shows a wave packet with a higherpeak centered at fsep. In Case 1, the second separation bub-ble starts at x = 0.21C, and it is not surprise that its spec-trum at x = 0.217C has an isolated peak at fsep.

4.3. Case 2 – flow separation control with active vortex

generators

In controlled case 2, a pair of oscillating vortex genera-tors was used for active flow separation control. The vortex

ity of Case 2. (a) streamwise vorticity (dark color: xx = 100; light color:color: xz = 50; light color: xz = � 50).


generator layout can be found in Section 3. The location ofthe vortex generators is the same as in controlled case 2.The motion of two vortex generators was synchronizedand controlled by a sinusoidal duty cycle with a frequencyof fe = 15U1/C that equals the natural frequency of theseparation region in the baseline case. It has been reportedthat the range of effective frequency of excitation includesbands of naturally amplified frequencies centered at fsep

and the normalized frequency of excitation should beF+ = fe/fsep = O(1) [24,39]. Given the length of natural sep-aration bubble XB = 0.225C in the uncontrolled baselinecase, there is an alternative way to normalize fe as feXB/U1 = 3.4, which is consistent with the general range of0.3 6 feXB/U1 6 4 obtained by experiments [14].

A time- and spanwise-average was performed over thesimulation data with a time period of 30C/U1. Fig. 25shows the averaged velocity vector and contours of stream-wise velocity. The separation is not visible in the mean flowfield as it is also confirmed by plotting the mean streamlinesin Fig. 26. Compared with Case 1, the active vortex gener-ator with an excitation frequency equaling the natural fre-quency of separation is more effective than the passivevortex generator in terms of controlling the size of separa-tion bubble.

Fig. 31. Spectra of pressure

The comparison of mean pressure coefficient Cp of con-trolled case 2 with the baseline case and controlled case 1 isshown in Fig. 27. Case 2 produces a more desirable Cp

curve, because the suction plateau is removed. The Cp

curves from all three cases almost coincide with each otherdownstream for x > 0.4C, indicating that the active vortexgenerator has minor effect on the average pressure distribu-tion over the aft portion of the airfoil at this angle ofattack. The friction coefficient Cf of all the three cases isshown in Fig. 28. In Case 2, there is a sharp increase inCf immediately downstream of the active vortex genera-tors, which brings in extra kinetic energy to the flow fieldand leads to an early transition.

A comparison of the chord-wise distribution of peakturbulence kinetic energy k of all three cases is given inFig. 29. It is obvious that the active vortex generatorslocated at x = 0.1C have triggered immediate transitiondownstream as there is an abrupt rise in k starting atx = 0.1C. The mechanism of transition and separation con-trol in this case is probably different from that of the base-line case and Case 1, where the transition occurs in theseparated shear layer due to amplification of the Kelvin–Helmholtz type instability. In Case 1, the reduction in bub-ble size is caused by the streamwise vortices created by the

fluctuations of Case 2.


passive vortex generators. The momentum transferred bythe vortices enforces the separated flow to reattach. Butin further downstream region, the reattached flow fails toresist the pressure rise and separates again, followed bythe transition in separated shear layer and reattachment.In Case 2, the early transition process triggered by theactive vortex generators must play an important role ineliminating the separation bubble. Otherwise the reat-tached flow would separated again as it happens in Case1, because the streamwise vortices created by the periodicmotion of the active vortex generators do not sustain afterthe vanes are fully retracted during a duty cycle. Also com-pared to the passive vortex generators that stay at theirmaximum height all the time, the active vortex generatorshave less capability of bringing high momentum into thelower boundary layer. On the other hand, transitionincreases entrainment and enables momentum transferfrom mainstream to boundary layer. Therefore, it mustbe the early transition triggered by the active vortex gener-ators that eliminates the separation bubble.

Fig. 30 shows the three-dimensional isosurfaces of theinstantaneous streamwise, spanwise, and wall-normal vor-ticity over the upper surface of the airfoil. Transitionoccurs in the immediate downstream region of the activevortex generators located at x = 0.1C. The periodically cre-ated streamwise vortices travel downstream and form atrain of vortex tubes that are still visible up to x = 0.5C

as shown in Fig. 30a. As one looks carefully at the furtherdownstream region with x > 0.5–0.6C, the instantaneousflow fields of all three cases are qualitatively similar to eachother, see Figs. 16, 23, 30. It appears also in the averagedresults that the Cp and Cf curves of all three cases overlapin the downstream region, as shown in Figs. 27 and 28.

In Case 2, the excitation frequency is fe = 15U1/C. Thespectra of pressure fluctuations at x = 0.163C, x = 0.217C,x = 0.312C, and x = 0.577C on the centerline plane nearthe upper surface of the airfoil are displayed in Fig. 31.The first peak from the left corresponds to fe. The spectrumpeaks corresponding to its harmonics at 30U1/C, 45U1/C,60U1/C, and 70U1/C are also seen in Fig. 31a–c. The har-monic peaks of fe disappear in the spectrum at x = 0.577C

as shown in Fig. 31d. Fig. 31 indicates that the flowbetween the vortex generators and mid-chord is dominatedby fe and its harmonics.

5. Concluding remarks

We have studied the flow separation control with vortexgenerators using an approach that combines the body-fit-ted mesh for the airfoil in a curvilinear coordinate systemand the immersed-boundary method for the vortex genera-tor in the context of direct numerical simulation. Our studyincludes the following three cases: (1) uncontrolled flowseparation (baseline case), (2) flow separation control withpassive vortex generators (Case 1), and (3) flow separationcontrol with active vortex generated (Case 2) over aNACA0102 airfoil at a 6� angle of attack. In the uncon-

trolled baseline case, the naturally separated flow is domi-nated by fsep � 15U1/C, which represents the frequency ofvortex shedding from the separated shear layer. In Case 1,the time- and spanwise averaged results have shown thatthe passive vortex generators are able to reattach the sepa-rated flow in the immediate downstream region over anextent of 0.1C. However, the reattached flow separatesagain and the separated shear layer undergoes transitionand reattachment forming the second separation bubble.Thus, the passive vortex generators reduce the size of theseparation zone by more than 80%. The simulation of Case2 has shown that active vortex generators are more effectivethan the passive ones because the separation is not visiblein the time- and spanwise averaged mean flow. At the smallangle of attack simulated in this study, flow separation con-trol does not produce significant gain in lift or reduction indrag, but it does provide a first step leading toward a morethorough understanding of flow control with active vortexgenerators. The future work should emphasis on numericalsimulations of flow separation and control over airfoils atlarger angles of attack (e.g. P15�).

Acknowledgement

The presented research work was supported in part bythe Lockheed Martin Aeronautic Company.

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numerical study of passive and active flow separation control over a naca0012 airfoil

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