20th Australasian Fluid Mechanics ConferencePerth, Australia5-8 December 2016

Large Eddy Simulation of the Low Frequency Flow Oscillation over NACA0012 Aerofoil

E. M. ElJack1, I. M. AlQadi1, J. H. AlMutairi2, and J. Soria1,3

1Aeronautical Engineering DepartmentKing Abdulaziz University, Jeddah, Saudi Arabia

2Department of Mechanical PowerCollege of Technological Studies, Shuwaikh, Kuwait

3Laboratory for Turbulence Research in Aerospace and CombustionDepartment of Mechanical and Aerospace Engineering

Monash University, Melbourne, Australia

Abstract

This study examines the effect of angle of attack of an aero-foil on the low-frequency flow oscillation near stall conditions.Large eddy simulations are performed for a NACA0012 aero-foil at Reynolds number of 5× 104 and Mach number of 0.4.The simulations are carried-out at angles of attack ranging from9.0◦ to 10.1◦ with increment of 0.1◦, in addition to the anglesof attack 8.5◦, 8.8◦, 9.25◦, and 10.5◦. Time histories of aero-dynamic coefficients show large oscillations due to a switchingbetween attached and separated flow around the aerofoil. Thisis indicative that the low-frequency oscillation phenomenon iscaptured. Low frequency flow oscillation is sustained and morepronounced at the angles of attack of 9.8◦, 9.9◦, and 10.0◦.

Introduction

In the presence of strong adverse pressure gradient, a laminarboundary layer detaches and travels away from the surface cre-ating a region of separated flow near the surface. The shearlayer is highly susceptible to flow disturbances. The develop-ment of a Kelvin-Helmholtz instability breaks downs the sepa-rated shear layer and initiate transition to turbulence. The ener-gized turbulent flow reattaches to the aerofoil surface forming aseparation bubble. Laminar separation bubble (LSB) forms onaerofoils flying at moderate angles of attack and low Reynoldsnumber conditions. Such conditions are present in several ap-plications such as unmanned air vehicles (UAVs), micro air ve-hicles (MAVs), low-pressure turbines, and small wind turbines.The presence of the bubble leads to considerable degredationof the aerodynamic performance with increase in drag and lossof lift. The complex dynamics of the laminar separation bub-ble leads to undesirable effects such as flow oscillations due tobubble flapping and abrupt aerofoil stall due to bubble bursting.The lack of understanding of the physics of laminar separationbubble also hinders control of their undesirable effect.As an aerofoil approaches stall angle, the laminar separationbubble exhibits a quasi-periodic switching between a long bub-ble and a short bubble resulting in a global low-frequency flowoscillation (LFO). Although LFO has been extensively stud-ied, the underlining mechanism is not well understood. Sev-eral experimental studies were performed to investigate LFO[7, 6, 4, 5, 14, 16]. The phenomenon was initially reported byZaman et al.[17]. Low-frequency flow oscillation was observedin which the laminar separation bubble grows and shrinks be-tween a short bubble near the leading edge and a long bubbleresulting in fully separated flow. The phenomenon can causeup to 50% fluctuations in lift with a Strouhal number in therange of 0.017 to 0.03 [7, 6]. The oscillation Strouhal num-ber was observed to increase with Reynolds number as well aswith angle of attack. Rinoie and Takemura [14] also detectedthe low-frequency flow oscillation phenomenon in LDV mea-

surements of a flow field around a NACA-0012 aerofoil at aReynolds number of 1.3× 105 and α = 11.5◦. They showed,via phase-averaged measurements, that the flow switches ina quasi-periodic manner between a short laminar separationbubble and a fully separated flow resulting from bubble burst-ing. Tanaka [16] used PIV measurements to show that LFO ispresent over a range of angles of attack near stall rather than aspecific angle of attack.LFO has also been studied using numerical simlation. Sand-ham [15] used an unsteady viscous-inviscid interaction modelto simulate LFO and concluded that LFO in the lift coefficientcan be related to the unsteady behavior of the laminar separa-tion bubble near the aerofoil leading edge. Marxan and Hen-ningson [10] studied bubble bursting and its relation to aerofoilstall. They argued that changes in the transition process playa major role in bubble bursting along with the viscous-inviscidinteraction. Their hypothesis is that bursting takes place whensaturated disturbances can not reattach the flow right after tran-sition. Mary and Sagaut [11] carried out the first large eddysimulation of a laminar separation bubble around an aerofoilnear stall conditions. However, LFO was not observed. One ofthe first attempts to capture the low frequency flow oscillationphenomenon by large eddy simulation was by Mukai [12] whoobserved several aspects of the unsteady phenomenon despitethe use of a relatively coarse grid. Almutairi et al.[3] investi-gated the LFO for a higher Reynolds number of 1.3×105 at anangle of attack α = 11.5◦. They observed more regular oscilla-tions in aerodynamic characteristics compared to that observedin the study of Almutairi and AlQadi [2].

Mathematical Model and Computational Setup

The code used in this simulation is a modified version ofthe DNS code that was written and validated by Jones etal. [9]. Almutairi [1] extended the code to solve the non-dimensional Favre-filtered Navier-Stokes equations in three-di-mensional curvilinear coordinates. The code is fourth-order intime and space and it uses advanced physical and numericalboundary conditions along with a solution-stabilizing scheme.Full details of the numerical approach are provided in Almu-tairi [1].The size of the computational domain in terms of aerofoilchord c, figure 1, is Lξ = 5.0c, Lη = 7.3c, Lζ = 0.5c. Aninvestigation was performed to assess the effect of the do-main span-wise width on LFO. Five span-wise widths Lζ =0.2c,0.25c,0.5c,0.75c, and 1.0c were considered. CL signalsshowed that LFO is captured for Lζ ≥ 0.25c. Therefore, a do-main width of Lζ = 0.5c is considered sufficient for the currentReynolds number.At the far-field and downstream boundaries, the code imple-ments a characteristic type boundary condition. The aerofoil

ξ

ζ

η

ξ

ζη

Figure 1: Computational domain

surface is insulated and no-slip wall condition is applied. Theinternal branch-cut boundary is updated at each step of the tem-poral scheme.A computational grid of size Nξ ×Nη ×Nζ = 780×320×101

was generated around NACA-0012 aerofoil for each of the six-teen angles of attack in which the aerofoil is oriented such thatthe incoming freestream is always at zero angle. The currentcomputational domain is similar to the configuration of Almu-tairi [1]. However, the current grid is refined and optimized byredistributing grid points in η direction such that around 60%of the total grid points are within one chord from the aerofoilsurface. The grids were generated using hyperbolic grid gener-ator to improve grid orthogonality and minimize grid skewness.Furthermore, the wall-normal grid spacing was reduced to en-sure a wall-normal spacing of y+ ≤ 1. Figures 2 and 3 show gridresolution, at the aerofoil surface, for the attached and separatedphases of the LFO cycle at α = 9.8◦. The figures illustrate thevariation of y+, in η direction, ∆x+ in ξ direction, and ∆z+

in ζ direction on the aerofoil suction side. The maximum gridspacing values in wall-normal units, at the attached phase, arey+ = 0.5, ∆x+ = 12, and ∆z+ = 14 with 20 grid points withiny+ ≤ 10. It is noted that y+ has relatively higher values in therange 0.2 ≤ x/c ≤ 0.4, this is the region where transition to tur-bulence takes place. Having inadequate spacing in ξ directioncould affect the development of the evolving Kelvin-Helmholtzinstability and consequently the transition process. Equidistantgrid spacing with relatively smaller ∆x is adopted in the range0 ≤ x/c ≤ 0.5. The maximum grid spacing is smaller for theseparated phase as the velocity gradient is much smaller in thiscase.

Results and Discussion

Large eddy simulations were carried out for flow aroundNACA-0012 aerofoil at sixteen angles of attack (α = 9.0◦ to10.1◦ with increment of 0.1◦, in addition to the angles of at-tack 8.5◦, 8.8◦, 9.25◦, and 10.5◦). The simulation Reynoldsnumber and Mach number are Re = 5×104 and M∞ = 0.4, re-spectively. The free-stream flow direction is set parallel to thehorizontal axis for all simulations (u1 = 1, u2 = 0, and u3 = 0).The entire domain was initialized using the free-stream condi-tions. The simulations were performed with a time step of 10−4

non-dimensional time units. Aerodynamic coefficients; CL , CD ,Cf , and CM , were sampled for each angle of attack at a frequencyof 10kHz generating three million samples over a time periodof 300 non-dimensional time units. Span-wise ensemble aver-ages of pressure, velocity components, and Reynolds stressesare sampled every 50 time-steps in x− y plane. A data set of20,000 x − y planes is recorded at a frequency of 204Hz for

x/c

0.0 0.2 0.4 0.6 0.8 1.0

y+

0.0

0.2

0.4

0.6

0.8

1.0

∆x

+

0.0

2.0

4.0

6.0

8.0

10.0

12.0

y+

∆x+

∆z+ = 25 y

+

Figure 2: Grid resolution (Attached phase)

x/c

0.0 0.2 0.4 0.6 0.8 1.0

y+

0.0

0.2

0.4

0.6

0.8

1.0

∆x

+

0.0

2.0

4.0

6.0

8.0

10.0

12.0

y+

∆x+

∆z+ = 25 y

+

Figure 3: Grid resolution (Separated phase)

each angle of attack. Span-wise ensemble averages of pressureand skin friction coefficients are sampled around the aerofoilsurface every 50 time-steps. In the interest of brevity, only re-sults pertinent to the present discussion are presented.Figures 4 and 5 show isosurfaces of (Q-criterion= 200) for at-tached and separated phases of the LFO cycle. The isosurfacesare colored by the total energy per unit mass E. A local aver-age of streamlines at both phases is superimposed on the iso-surfaces to indicate the average shape and location of the sepa-ration bubble. The figures illustrate the initial development ofKelvin-Helmholtz rolls in the separated boundary layer. Then, asecondary spanwise instability develops causing helical pairingbetween adjacent spanwise vortical structures leading to the for-mation of Λ-shaped structures and the subsequent breakdown toturbulence. Figure 5, in comparison to the attached phase illus-trated in figure 4, shows the separated shear layer moving awayfrom the aerofoil surface toward the energetic freestream whilethe location of the breakdown of the 2D structures moves down-stream during separated phase.Figure 6 shows the time history of the lift coefficient for an-gles of attack 9.0◦, 9.5◦, 9.8◦, 9.9◦, 10.0◦, and 10.5◦. Thelift coefficient exhibits large oscillations due to switching be-tween attached and separated flow around the aerofoil. Theoscillations in the coefficients develop naturally and are self-sustained. However, the LFO cycles do not repeat uniformlybut rather with some degree of randomness. Such stochasticbehavior in the LFO is expected taking into consideration theunsteady nature of the transitional flow including random andfrequent break-up of the laminar separation bubble with rela-tively high oscillation amplitude. This behavior is in agreementwith the experimental measurements of Rinoie and Takemura

Figure 4: Instantaneous Q-criterion iso-surface (Q-criterion=200.0) colored by the total energy per unit mass (E): Attachedphase.

[14]. Furthermore, Tanaka [16] indicated that there were dis-turbed cycles that do not resemble other regular cycles in hisexperimental measurement.As shown in the figure, at the angle of attack 9.0◦ the flow is at-tached. However, the laminar separation bubble is present andintact since it start forming at much lower angle of attack, Jones[8]. At angle of attack α = 9.5◦ the flow field is attached for thefirst 150 non-dimensional time units after which the flow startsto separate and reattach leading to oscillation in the lift coeffi-cient. This indicates that flow oscillation can evolve naturally innumerical computations from initial uniform free stream condi-tions with no flow forcing. At higher angles of attack (α = 9.8◦,α = 9.9◦, and 10.0◦) the oscillation becomes quasi-periodicand self-sustained with larger amplitude. At an angle of attack10.5◦ the flow is mostly separated with intermittent reattach-ment. This is also consistent with the experimental observationsby Tanaka [16], who conducted a study of low-frequency flowoscillations using PIV. LFO was observed over a range of an-gles in which the oscillation starts as intermittent bursts of LSBat lower angles. As the angle of attack increased, LFO becamemore regular. At the upper limit of the range, the flow wasmostly stalled with intermittent reattachment.Figure 7 shows the pressure coefficient, CP at α = 9.8◦ aver-aged over selected subintervals of 5000 time–steps (0.5 non-dimensional time units). It is noted that at Φ1 there is a strongadverse pressure gradient near the leading edge at x/c ≈ 0.025,which causes flow separation, followed by a pressure plateauextending to x/c ≈ 0.25 that indicates the separated region ofthe laminar separation bubble. Transition to turbulence ener-gies the separated shear layer and leads to reattachment. Con-sequently, the flow reattachment causes the small decrease inthe pressure that follows pressure plateau at the end of the bub-ble. At this phase of the cycle, Φ1, the flow is attached and thelaminar separation bubble is present and intact. In the followingphases of the cycle, Φ2 to Φ5, the suction pressure is graduallydecreasing which indicates bubble bursting. The bubble con-tinue to burst until the pressure coefficient distribution becomesalmost flat which is an indication of airfoil stall at phase Φ6.Figure 8 (top) shows the averaged values of CL for all anglesof attack. As shown in the figure, CL has maximum value atα = 9.0◦ and decreases as the angle of attack increases. How-ever, the CL profile shows some degree of nonlinearity. This isin agreement with the experimental work of Ohtake et al. [13] atlow Reynolds number. Figure 8 (bottom) shows that the meandrag coefficient increases with the angle of attack.

Conclusions

This work investigated the effect of angle of attack on low-frequency flow oscillation near stall conditions. Sixteen largeeddy simulations were performed for NACA0012 aerofoil at

Figure 5: Instantaneous Q-criterion iso-surface (Q-criterion=200.0) colored by the total energy per unit mass (E): Separatedphase.

α = 9.00oC

L0.5

0.6

0.7

0.8

α = 9.50o

CL

0.5

0.6

0.7

0.8

α = 9.80o

CL

0.5

0.6

0.7

0.8

α = 9.90o

CL

0.5

0.6

0.7

0.8

α = 10.0o

CL

0.5

0.6

0.7

0.8

α = 10.5o

CL

0.5

0.6

0.7

0.8

Time

0 50 100 150 200 250 300

Figure 6: Time histories of lift coefficient at angles of attack9.0◦, 9.5◦, 9.8◦, 9.9◦, 10.0◦, and 10.5◦

Reynolds number of 5 × 104 and Mach number of 0.4. Thesimulations were carried-out at angles of attack from 9.0◦

to 10.1◦ with increment of 0.1◦, in addition to the anglesof attack 8.5◦, 8.8◦, 9.25◦, and 10.5◦. The time historiesof aerodynamic coefficients show that the low–frequencyoscillation phenomenon and its associated physics are capturedin the simulations. It is noted that the low–frequency oscillationevolves naturally from uniform free stream conditions with noflow forcing. It is also observed that the LFO is present overa range of angles of attack, which is in agreement with theexperimental observations of Tanaka [16].

x/c

0.0 0.2 0.4 0.6 0.8 1.0

Cp

-2

-1

0

1

Φ1

Φ2

Φ3

Φ4

Φ5

Φ6

Figure 7: Pressure coefficients around the aerofoil plotted ver-sus the scaled x-axis (x/c).

CL

0.55

0.65

0.75

0.85

CD

0.06

0.08

0.1

0.12

Angle of attack, α

8 8.5 9 9.5 10 10.5 11

Figure 8: Mean values of the lift and drag coefficients plottedversus the angle of attack

Acknowledgements

Computations for the study were performed on the Aziz Su-percomputer at King Abdulaziz Universitys High PerformanceComputing Center (http://hpc.kau.edu.sa). The authors wouldlike to acknowledge the computer time and technical supportprovided by the center.

References

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