optimized vortex generator in the flow separation control around naca 0015

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Porto, Portugal, 30 June - 2 July 2014

A. Cunha, E. Caetano, P. Ribeiro, G. Mller (eds.) ISSN: 2311-9020; ISBN: 978-972-752-165-4

3219

ABSTRACT: This study concerns the flow control using a new vortex generators (VGs) shape with counter-rotating vortices, obtained by modifying a configuration already investigated. The experiments were performed in order to determine the VGs answer when they were placed at 10% from the leading edge on the suction face of an airfoil Naca 0015 to improve the lift and drag coefficients. An optimized geometry form is given in this paper by using the experimental designs method. The aerodynamic measurements were accomplished in wind tunnel for several Reynolds numbers. The obtained results are analyzed according to several parameters such as the VG height, the aperture, the space between the same VG pair and the additional factor. A three-dimensional controlled flow pressure field was also displayed at different velocities, attack angles and taking into account the additional element effect. The results show a profit brought by the passive devices estimated at about 14% in relative lift increase and 16% of drag decrease.

KEY WORDS: Vortex Generators (VGs); Airfoil; Lift; Drag; Design of Experiments (DoE); Pressure coefficient.

1 INTRODUCTION The development of flow control devices design to improve the airfoil performance in terms of lift and drag coefficient is of great importance for the aircraft industries. Since the introduction of the boundary-layer concept by Prandtl, there has been a constant challenge faced by scientists and engineers to minimize its adverse effects and control it to advantage.

Flow separation control, by means of passive devices, is today the less expensive and the fastest solution to implement. Vortex Generators [1, 2] have been rigorously investigated and also used in practice with a various degree of success. Passive VGs are simple use and known to bring momentum in the boundary layer which leads to the delay or suppression of the flow separation [3]. Several parametric investigations have been conducted on the VGs by a number of researchers [4-6].

The configurations studied in this present investigation are of the same form as the ones used by Lin [6]; the only difference is in the c element addition (figure 4). The reply of these vortex generators on the Naca 0015 profiles upper surface resulted in improvement of the aerodynamic coefficients in terms of lift increase and drag reduction.

Traditionally, a researcher conducts experiments sequentially by varying parameter one after the other. This method gives results but it is time consuming and requires a large number of experiments. The data analysis method used allows collecting, summarizing and presenting data in order to obtain maximum information for further experiments. To conduct a planned experimental research, the methodology of experimental design is used [7] in order to have the optimized configuration.

More and more authors are interested in the use of these experimental designs in order to perform their tests in various areas. Zeng and al [8] analyzed by numerical method using experimental design the influence of various parameters on

the heat transfer and flow friction characteristics of a heat exchanger with Vortex Generators fins. The parameters of vortex generator fin-and-tube heat exchangers were optimized using the Taguchi method [9].

A development of models which allows surface quality determination of mechanical parts obtained through turning processes was carried out by Puertas Arbizu and al [10] using experimental designs, in particular the response surface methodology.

Lundstedt and al [11] present a tutorial which aims to give a simple and easily understandable introduction to experimental design and optimization. The screening methods described in their paper are factorial and fractional factorial designs. This has been carried out in an efficient way and without having to perform a large number of experiments.

The aim of the present paper is to provide an optimized geometry for vortex generators with counter-rotating vortices by using a full factorial design based on the principal form already used by other authors in particular those reported recently [6]. Various velocities of the flow were tested in wind tunnel in order to determine the Reynolds number effect on the control parameters. The results are analyzed in several parameters such as the VG height, the aperture, the space between the same VG pair and the additional factor effect.

A comparative study is also made between the proposed optimal vortex generators geometry and the same one without element c. The aim of the addition is to determine the utility in improvement of the aerodynamic performances, and moreover the state of the controlled flow is explored through the measurement of three dimensional pressure field.

2 EXPERIMENTAL SETUP

2.1 Wind tunnel and acquisition system The tests were performed in a DeltaLab type open circuit subsonic wind tunnel. The tunnel is one meter long with a

Optimized vortex generators in the flow separation control around a NACA 0015 profile

H. Tebbiche1, M.S. Boutoudj1, 2 1Dpartement de Gnie Mcanique, Facult du Gnie de la Construction, Universit Mouloud Mammeri, 15 000

Tizi-Ouzou, Algrie 2Laboratoire dEnergtique, Mcanique et Matriaux LEMM ; Universit Mouloud Mammeri, 15 000 Tizi-Ouzou, Algrie

Emails: [email protected], [email protected]

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

3220

cross-section area of 0,3m x 0,3m equipped with a 2-axis strain gauge balance to measure the lift and drag coefficients.

The data acquisition is obtained with a Pulse software developed by Brel & Kjr for Sound and Vibration Measurement, after adapting this device to the balances transducer (Strain gauges). Each test is repeated three times and averaged. The time of acquisition is 60 s with a 500 Hz frequency.

The speed and the static pressure distribution along the airfoil were measured respectively using a Pitot tube and a differential manometer connected via capillary tubes.

2.2 Airfoil The airfoil used is an academic Naca 0015 profile (chord length 154 mm and spanwise length 200 mm). The model is equipped with fourteen pressure taps in the longitudinal direction; the locations of the pressure taps and the VGs position from the leading edge are illustrated more explicitly in figure 7.

Figure 1 shows the experimental setup with the airfoil assembled in the wind tunnel.

Figure 1. Measurement setup.

The same profile is designed to complete two kind of measurement: - statement of the wall static pressure, - drag and lift forces.

3 GLOBAL SETTINGS The use of shape factor (H12) informs us about the state of the boundary layer. It allows the determination of the turbulent laminar transition as well as precise positioning from the location of turbulent boundary layer separation; its expression is given by:

1122

H = (1) With:

10

1 u dyU

= (2) 2

0

1u u dyU U

= (3)

Where: 1 : Displacement thickness (m), 2 : momentum thickness

(m), U : Freestream velocity (m/s), u : velocity component tangential to the surface (m/s).

These quantities (2 and 3) were determined by integration up to the tangential speed maximum value of the calculated profile [12].

The dimensionless coordinate normal to the airfoil y+ is similar to local Reynolds number, often used in CFD to describe how coarse or fine a mesh is for a particular flow. The non-dimensional wall parameter is defined as:

2fyU Cy

+ = (4) Where: y : Normal distance to the profile (m), fC : Skin friction

coefficient, : Kinematic viscosity (m2s-1). By assimilating the airfoil to a flat plate, the skin friction

coefficient can be estimated from the following empiric relation [13]:

0.22 0.037Ref LC (5)

With ReL is the Reynolds number related to the chord length. The measured forces (lift and drag) are respectively linked

to the aerodynamics coefficients by:

212

yL

FC

U S = (6) And

212

xd

FCU S = (7)

With: xF : Drag force (N), yF : Lift force (N), : Volumic weight

(Kg/m3), S : Surface profile (m2). The pressure coefficient Cp is provided by the expression:

0212

P PCpU = (8)

With: P : Wall static pressure,

0P : Upstream reference pressure.

4 PRELIMINARY NUMERICAL STUDY

Turbulent flow around two-dimensional profile NACA 0015 was analyzed with incompressible steady Reynolds Averaged Navier-Stokes (RANS) equations approximated by finite volume method. The calculation was conducted at Reynolds number equals to 2.6 105. The turbulence was approached by the k SST model and required maintaining the neighboring adimensional distance from the wall at 2.5y+ .


3221

This numerical study is an essential step to make the dimensionless form of VGs factor by using boundary layer thickness ( ) .

Figure 2 illustrates the evolution of the shape factor versus the chord length X/L. According to the state of the boundary layer, the 12H factor takes a characteristic value for each position along the chord. The separated flow to the upper surface is characterized by the shape factor increase which exceeds 12 2.3H = [14] at X/L = 0.4 to the chord.

Figure 2. H12 versus X/L, = 13, - - CFD.

The boundary layer global characteristics deduced from the velocity profile corresponding to the VGs height position are shown in the following table:

Table 1. Boundary layer characteristics, =13, CFD.

/X L 1( )U ms ( )m 41 10 ( )m 42 10 ( )m 12H 0.187 24.84 0.010 9.906 5.080 1.95

The numerical results validation was undertaken by overlaying the evolution of both numerical and experimental data (figure 3). It is supposed that the slight difference between the two results is caused by the airfoils guard-plates effect which do not exist in the idealistic case considered in the numerical simulation.

Figure 3. Pressure coefficient distribution versus X/L,

=13, Experimental data, - - CFD.

5 ORGANIZATION OF TESTS BY EXPERIMENTAL DESIGNS

5.1 Formalization of the problem The need for employing a rational step [15] to carry out research has encouraged the engineers and researchers to employ the statistical methods. The experimental designs have for main goal obtaining the maximum information at lower

cost. The desired information is in general to qualify the influence of several parameters (or factors) on a given phenomenon. Based on this information, it will be possible to determine the behavior of the studied system in the various possible configurations, and thus to optimize the answer. To reach this result, the experimental designs technique proposes a strategy of tests having a principal characteristic to minimize the tests number to be realized [7].

The aim of this work is to provide an optimized geometry for vortex generators with counter-rotating vortices by using the experimental designs based on the principal form already used by some authors in particular Lin [6] who proposed a complete review on the recent contributions on the subject [2]. Several authors [4, 16] did a detailed study of the flow around VGs inspired from his vortex generators type. These VGs are plates of triangular shape, placed normal to the suction surface and at a lateral angle to the flow.

The configurations studied in this present investigation are of the same form than that used by Lin [6]; the only difference is in the addition of the element c as shows in figure 4. The various parameters of the geometry to be optimized are given as follows: l : Vortex generators length, b : Distance between two passive devices, a : Space between the same VG, h : Vortex generator height, c : Vortex generator additional element, : Vortex generator aperture angle.

Figure 4. Passive VGs parameters

Only four elements ( , , , )a h c related to the VGs geometry are used. The other parameters such as the ratios /l h and

/b c are maintained constant (l/h =2.6, b/c = 3). Level of each factor is shown in the following table, where level 1 and level 2 represents respectively the low and high values.

Table 2. Variation level on each factor.

Code Factor Level 1 Level 2 Units A a/ 0.55 0.70 - B c/ 0.30 0.45 - C h/ 0.35 0.55 - D 30 48 ()

5.2 Experimental design selection Using a full factorial design with four factors k and two

variation levels justifies making sixteen experiments (2k=16). In the framework of this comparative study, we limit the number of VGs pairs to six. The lift coefficient was selected as objective function.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1.6

1.8

2

2.2

2.4

2.6

2.8

H12

X/L

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-5

-4

-3

-2

-1

0

1

X/L

Cp


3222

Level 1:-1 Level 2:+1

Table 3. A 24 factorial experiment.

Exp. no. Variables A B C D

01 - - - - 02 + - - - 03 - + - - 04 + + - - 05 - - + - 06 + - + - 07 - + + - 08 + + + - 09 - - - + 10 + - - + 11 - + - + 12 + + - + 13 - - + + 14 + - + + 15 - + + + 16 + + + +

The table above shows the experiences organization and the

factor levels for each test.

5.3 Tests procedure The tests were performed by way of the described devices above (figure 1) at Reynolds number of 2.6 105. The obtained results for the references state (without vortex generators) indicate that the airfoils stall angle is observed at 15 degrees (figure 5).

Figure 5. Lift coefficient versus angle of attack.

The experimental response chosen corresponds to an incidence in post-stall (16 degrees) for best understanding the factors effects in improvement of the aerodynamic coefficient

LC and deducing the most influential parameters.

Table 4. Response of the lift coefficient at 16 degrees.

Exp. no. Variables Answer A B C D YCL

01 - - - - 0.8699 02 + - - - 1.0479 03 - + - - 1.1267 04 + + - - 1.0846 05 - - + - 1.1668 06 + - + - 1.1810 07 - + + - 1.2113 08 + + + - 1.2370 09 - - - + 1.0220 10 + - - + 1.0693 11 - + - + 0.9416 12 + + - + 1.1439 13 - - + + 1.1259 14 + - + + 1.1157 15 - + + + 1.1198 16 + + + + 1.1457

5.4 Analysis of the results The effects (interactions) are obtained via the calculation matrix given by this expression [17]:

1 tE X yN

= (9) With: E: Effect-vector, N: Number of experiments, Xt: The transposed matrix of the effects calculation, y: Response-vector. By calculating the effects values of principal factors and

interactions, it is possible to make a relative factors study with respect to their influence to the response. Thus, simply, by the effects examination, the factors can be classified according to their capacity to vary the studied answer. This study is often translated graphically, by histograms. The Paretos law is a simple mean to classify the phenomenon [18]. In this case, 34.78% of causes represent 80% of effects; the Pareto law can be used [19] with precaution.

The Pareto diagram is used here to identify the relative importance of the different factors in order to focus on some key cases that have the greatest impact, rather than getting lost in the treatment of a variety causes that have less effect. To solve the problem with maximum efficiency, we will act on 80% of the effects, so it was deemed necessary to take into account only the influence of the following elements (C, A, B, ABD, BD, ABCD, CD, AC and D) and neglect the rest. Graphical analysis highlighted the importance of the C-factor, represented by the vortex generators height, which means the most influential factor with a contribution ratio of 22%. Following the analysis of the results (Table 4), the C-values taken on +1 ( 0.55)h = perform better than those on -1 ( 0.35)h = . Moreover, the sixteen configurations tested have confirmed the great role of the C-factor.

With a single contribution of 10%, the factor A is also considered a major element. Several researchers have

6 8 10 12 14 16 18 20 220.5

0.6

0.7

0.8

0.9

1

1.1

1.2

CL


3223

investigated the importance of the VGs spacing [4, 20] which justifies the interesting position in the following ranking. Thirdly, there is the B-Factor with a contribution of 9% which is not negligible. So adding this item to the basic triangular configuration [1, 2, 4, 5] is very beneficial for the control through a passive device. A great interest is given to this factor; moreover; a comparative study will be devoted in order to detect its efficiency.

Another equally important finding is covered on D-factor. Treated alone; it has practically no effect but it may interact with the other factors. Then, the combined contribution (ABD, BD, CD and D) operates on 39% of the significant effects.

Figure 6. Pareto diagram applied at 16 degrees, - -- -

cumulated ratio, effects contribution.

The analysis results performed concerned only the classification of the factors and interactions as well as their contribution rates. A more comprehensive interpretation of the test results will be undertaken in the following sections.

The comparison made between the results from baseline and those obtained after the control by experimental designs gives the optimized geometrical parameters of the vortex generators summarized in the following table:

Table 5. Optimized geometrical parameters.

Factors a/ c/ h/ Levels 0.70 0.45 0.55 30

6 EXPERIMENTAL RESULTS

6.1 Position of the vortex generators The vortex generators were positioned in line at 10% from the leading edge (figure 7); the measurements of the aerodynamic forces were performed for several incidences. When the flow is not controlled, separation is two-dimensional [21]; only one measurement of the pressure fields is sufficient to obtain the pressure distribution around the profile. On the other hand, when control intervenes, the flow will be three-dimensional. A complete sweeping of span Z is necessary and was possible by relocating the VGs along the Z axis (figure 14).

Figure 7. VGs disposition: (1) perspective view; (2) top view.

6.2 Lift, drag and pressure measurements

6.2.1 Reynolds number effect The lift and drag coefficients resulting from the flow around the airfoil without vortex generators versus the incidence angle (uncorrected for wind tunnel blockage) are shown in figure 8 at two Reynolds numbers. We observe that at low incidence both LC and dC evolutions have a linear behavior.

Its also noted that the progressive incidence increase causes a sudden drop in the lift related to a profile stall. This fall is accompanied by an expansion of the induced drag caused by the fluid separation.

Figure 8. Lift and drag coefficient versus angle of attack (left:

Re=1.58 105, right: Re=2.6 105).

Furthermore, stall angles corresponding to Reynolds

numbers of 1.58 105 and 2.6 105 are respectively 13 and 15 degrees. The flow is more resistant to the stall at high Reynolds number.

The pressure distribution on upper and lower airfoil surfaces is, as well known, no longer the same. The Cp values become more and more negative as the attack angle increases till (=13, =15) respectively (Re=1.58 105, Re=2.6 105) when a sudden increase occurs. This is due to the flow separation on the upper surface.

Figure 9 represents the pressure distribution along the chord. This figure shows that the flow carried at lofty Reynolds number is strongly accelerating just after the leading edge where a depression peak is observed. On the other hand, with regard to the other value, one notices the formation of a plate which is characteristic in the unhooking profile.

C A B ABD BD ABCD CD AC D BCD BC ACD ABC AD AB0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Factors & interactions

Effe

cts

con

trib

utio

n

Cu

mu

late

d r

atio

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 5 10 15 20 0 5 10 15 200

0.2

0.4

0.6

0.8

1.0

1.2

1.4

CL,

Cd

CL

Cd


3224

Figure 9. Pressure coefficient versus X/L, =14.

6.2.2 Optimized vortex generators in improvement of the aerodynamic coefficients

The purpose of this experiment is to demonstrate the vortex generators ability to change the natural flow on the upper surface of the airfoil. Figure 10 shows the lift coefficient without and with the control geometry given in table 5. For both speeds studied, lift increase is noticed. At Reynolds number equal to 1.58 105, the control effect on the lift coefficient is less effective than the case when Reynolds equals 2.6 105. One can see a relative lift increase of 14% in the case (B) and only 5% for the case (A). The results also show an improvement in the stall angle of two degrees for the two cases.

The analysis of the drag curves (figure 11) reveals more efficiency of the vortex generators on the drag reduction at low velocity flow. The drag decrease dC is about 16% at low Reynolds number (C) and 11% for the high speed (D).

However, the L dC C ratio is increased by 28.3% for Re=2.6 105 and 23.6% for Re=1.58 105, respectively at 17 and 15 degrees.

Figure 10. Lift coefficient versus angle of attack, (A):

Re=1.58 105, (B): Re=2.6 105.

Figure 11. Drag coefficient versus angle of attack, (C):

Re=1.58 105, (D): Re=2.6 105.

6.2.3 Comparative study of the added B-factor contribution

A comparative study was made between the proposed vortex generators geometry and the same one without the factor B in order to determine its influence in the improvement of the aerodynamic performances. About 2% of lift increase is noticed in figure 12 when the VGs are equipped with the factor B for the incidences smaller than the stall angle. Figure 13 indicates an increase of about 3% at the maximum lift.

Figure 12. Lift coefficient versus attack angle, Re=1.58 105.

Figure 13. Lift coefficient versus angle of attack, Re=2.6 105.

When the control is applied, the flow becomes three-

dimensional, different from the two-dimensional one without

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-5

-4

-3

-2

-1

0

1

X/L

Cp

Re=1.58x105

Re=2.6x105

0 5 10 15 20 0 5 10 15 200.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

CL

(A) (B)

Baseline

VG Control

0 5 10 15 20 0 5 10 15 200.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Cd

(C) (D)

Baseline

VG Control

0 5 10 15 200.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

CL

[Re=1.58x105]

Baseline

VGs with factor "B"VGs without factor "B"

0 5 10 15 200.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

CL

[Re=2.60x105]

Baseline

VGs with factor "B"VGs without factor "B"


3225

the VGs. The wall pressure field was investigated in order to study the VGs impact on the pressure evolution.

The following curves show this pressure field on the upper airfoil surface. The measurements were performed at five pressure taps locations along the Z space (figure14). Curve smoothing was carried out by interpolation to find the intermediates values by using MATLAB software.

Figure 14. Pressure taps positions.

a) Case with factor B:

Figure 15-a. 3D pressure coefficient, Re=1.58 105, =15.

Figure 15-b. 3D pressure coefficient, Re=2.6 105, =16.

Figure 16-a. Iso-values of the pressure field coefficients,

Re=1.58 105, =15.

Figure 16-b. Iso-values of the pressure field coefficients,

Re=2.6 105, =16.

Pressure field outlined in figures above shows a periodic distribution of the wall pressure on the upper profile surface. A strong depression is observed in the spacing defined by the factor A (figure 15-a). The control highlights the presence of a vortices pair which extends to a very large distance from the leading edge. The flow is not only affected downstream of the vortex generators as shown in the iso-values distribution (figures: 16-a. 16-b) but also upstream of VGs. The created vortices may thus accelerate the fluid and create a low pressure zone. This energy supply revitalizes the previously separated boundary layer and delays the stall angle.

b) Case without factor B:

Figure 17-a. 3D pressure coefficient, Re=1.58 105, =15.

Figure 17-b. 3D pressure coefficient, Re=2.6 105, =16.

Figure 18-a. Iso-values of the pressure field coefficients,

Re=1.58 105, =15.

Figure 18-b. Iso-values of the pressure field coefficients,

Re=2.6 105, =16.

-2

-1

0

1

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Z/h

X/L

-2

-1

0

1

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-3.74

-3.74

-3.48

-3.48-3.22

-3.22

-2.97

-2.97

-2.71

-2.71

-2.45

-2.19

-1.93

-1.68

-1.42

-1.16

-0.9

-0.642

-0.383

Z/h

X/L

-2

-1

0

1

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-3.99

-3.7-3.42-3.14

-2.86

-2.58

-2.3

-2.01

-1.73

-1.45

-1.45

-1.17

-0.889

-0.607

-0.326

Z/h

X/L

-2

-1

0

1

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-3.71

-3.71

-3.45

-3.45

-3.19

-3.19

-2.93

-2.93

-2.67

-2.41

-2.15

-1.89

-1.63

-1.37

-1.11

-0.845

-0.585

Z/h

X/L

-2

-1

0

1

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-4.3-4.01

-4.01

-3.71

-3.42

-3.42

-3.12

-3.12-2.83

-2.83

-2.53

-2.23

-1.94

-1.64

-1.35

-1.35

-1.05

-0.757-0.461

-0.461

Z/h

X/L


3226

Figures (17. 18) illustrate the pressure field coefficient at two different velocities and two attack angles in the case without the factor B. Compared with the optimized shape; we notice an asymmetrical distribution of the pressure field. This can be also seen in the iso-values representations.

On the other hand, the boundary layer reenergized process is more efficient in the presence of the factor B in terms of the pressure field distribution and lift/drag ratio enhancement (figures 12 and 13).

7 CONCLUSION The experimental investigation enabled us to carry out tests relating to the control of aerodynamic unhooking by setting up an optimization step of the vortex generators shape parameters by the means of the experimental designs. The obtained results highlighted the importance of the C-factor represented by the vortex generators height which is the most influential factor with a contribution ratio of 22%. The optimized VGs geometry showed an improvement of 14% relative lift compared to maxLC and 16% of drag reduction.

The Reynolds number effect was also performed; it shows that the flow at high velocity is more effective in increasing the Lift/Drag ratio.

Comparative efficiency of the studied VGs highlighted a significant improvement on the flow control when the vortex generators are equipped with factor B. This result is confirmed by the three-dimensional representation of the pressure field as well as the iso-values curves.

REFERENCES [1] C. Bak, P. Fuglsang, J. Johansen and I. Antoniou, Wind tunnel test of

the NACA 63 415 and a modified NACA 63 415 Airfoil, Riso R-1193, Riso National Laboratory, Roskilde, Denmark, 2000.

[2] J. C. Lin, Review of research on low-profile vortex generators to control boundary-layer separation, Progress in Aerospace Sciences, 38: 389-420, 2002.

[3] A. C. Brown, H. F. Nawrocki, P.N. Paley, Subsonic diffusers designed integrally with vortex generators, J Aircr, 5(3): 221-9, 1968.

[4] G. Godard and M. Stanislas, Control of decelerating boundary layer. Part 1: Optimization of passive vortex generators, Aerospace Science and Technology, 10: 181-191, 2006.

[5] T. K. Zhen, M. Zubair and K. A. Ahmad, Experimental and Numerical Investigation of the Effects of Passive Vortex Generators on Aludra UAV Performance, Chinese Journal of Aeronautics, 24: 577-583, 2011.

[6] J. C. Lin, Control of turbulent boundary layer separation using micro-vortex generators, AIAA Paper, 3404, 1999.

[7] D. C. Montgomery, Design and analysis of experiments, John Wiley & Sons, New York, third edition, 1991.

[8] M. Zeng. L. H. Tang.M. Lin. Q. W. Wang, Optimization of heat exchangers with vortex-generator fin by Taguchi method, Applied Thermal Engineering, 30: 1775-1783, 2010.

[9] G. Taguchi, Taguchi on robust technology development, Bring Quality Engineering (QE) Upstream, ASME, 1991.

[10] I. Puertas Arbizu, C. J. Luis Prez, Surface roughness prediction by factorial design of experiments in turning processes, Journal of Materials Processing Technology, 143-144: 390-396, 2003.

[11] T. Lundstedt and al, Experimental design and optimization, Chemometrics and Intelligent Laboratory Systems, 42: 3-40, 1998.

[12] B. Thwaites, Incompressible aerodynamics: an account of the theory and observation of the steady flow of incompressible fluid past aerofoils, wings, and other bodies, Dover Publication, Inc, 1987.

[13] A. Gerasimov, Modeling Turbulent Flows with FLUENT, Europe, ANSYS, Inc, October 2006.

[14] P. Bradshaw, The response of a constant-pressure turbulent boundary layer to the sudden application of an adverse pressure gradient, A.R. C.R. & M. 3575, 1967.

[15] G. Sado and M. C. Sado, Les plans dexpriences, de lexprimentation lassurance qualit, Collection AFNOR, 1991.

[16] J. G. Betterton and al, Laser Doppler anemometry investigation on sub-boundary layer vortex generators for the flow control, in: 10th Intl. Symp. On Appl. of Laser Tech. to Fluid Mech., Lisbon, July 10-13 2000.

[17] J. Goupy, La mthode des plans dexpriences-Optimisation du choix des essais & de linterprtation des rsultats, Ed Dunod, 1996.

[18] V. Pareto, Cours dconomie politique, Droz, 1896. [19] R. Koch, the 80/20 Principle: The Secret of Achieving More with Less,

Nicholas Brealey Publishing, 2001. [20] K. A. Ahmad, J. K. Watterson, J. S. Cole, et al, Sub-boundary layer

vortex generator control of a separated diffuser flow, AIAA paper, 4650, 2005.

[21] D. C, McCormick, Boundary layer separation control with directed synthetic jets, AIAA paper, 0519, 2000.

optimized vortex generator in the flow separation control around naca 0015

Documents