Effect of Winglet Vortex Generators Orientation on Heat ...ijens.org/Vol_18_I_01/181201-7575-IJMME-IJENS.pdf · i j e n s s i

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:18 No:01 8

181201-7575-IJMME-IJENS © February 2018 IJENS I J E N S

Effect of Winglet Vortex Generators Orientation on

Heat Transfer Enhancement Khudheyer S. Mushatet Iltifat lazim edan

Mech. Eng. Dept. Mech. Eng. Dept.

College of Engineering College of Engineering

Thi-Qar University Thi-Qar University

E-mail:[email protected] E-mail: el _la [email protected]

Abstract-- experimental; and numerical investigation of

three dimensional turbulent flow and heat transfer; inside a

rectangular channel equipped with array of winglet vortex

generators. Three pairs array of winglet vortex generators of

different geometrical configuration as rectangular , triangular

, semi circle and parabolic are considered. The array of winglet

vortex generators is formed and distributed on the bottom hot

surface with a facility for changing the angle of attack from (0°

to 60°). ANSYS Fluent C ode (15.0) based on a fi nite volume

method is used to obtain the numerical results while a k-

turbulence model is used to model the tur bulent .The Reynolds

number range is from 10000 to 50,000 under a constant heat

flux boundary condition.. Two cases of winglet vortex

generators array are included. The first case is anti stream

common flow up. The second case is the combined anti and

with stream common flow up. The two cases are tested for

different values of angle of attack, the stream wise and span

wise position between the vortex and Reynolds number. The

obtained results show that the suggested arrangement of

common ;flow up (anti and with stream) for vortex generator

offers superior in heat transfer enhancement and overall

thermal performance rated by 240% and 170% respectively.

In addition, A signification increase in heat transfer

enhancement , and overall thermal performance is found as the

angle of attack and the positions between vortex generator

increases .

Index Term— winglet vortex generators, turbulent channel

flow, CFD

1. INTRODUCTION

The vortex generators are considered as a kind of passive

heat transfer enhancement dev ices. This system is used for

thermal equipment such as heat exchanger and internal

cutting edge cooling of a gas tu rbine. The system o f heat

tran sfer enhancement is based o n fl ow part ition a nd

reattachment. In ge neral, flow reatt achment intro duces a

strong shear flow o n the sur face beh ind each winglet or rib,

resu lting in an effe ctive distur bance of the ther mal boundary

layer and in this way the heat transfer is improved [1]. A

vortex generator is usually a small triangular or rectangular

plate that is mounted on a surface at an angle to the

incoming flow. Experim ental investigate b y Feib ig et al. [2]

sho wed the avera ge heat tran sfer in lam inar chan nel-flow

was enhan ced by more than 50% and the corresp onding

increase of drag coef ficient was up to 45% by delta and

rectan gular wings and win glets. Further expe riment with

double rows of de lta winglets in transiti onal channel flow

by Tiggelb eck et al. [3]stated th at the increa se ratio of heat

trans fer enhan cement and drag incre ase was larger for

higher Rey nolds nu mbers. Torii et al. [4] proposed a

common-flow up delta winglet arrangement, which was

effective in delaying boundary layer separation from the

tube, redu cing form drag,

and rem oving zon es of poor heat tran sfer fr om the n ear-

wake of the t ube. Jain e t al. [5] stu died a comm. on flow-up

configu ration delta win glet that causes impo rtant separ ation

delay, reduced form drag and rem oves the zones of poor

heat tran sfer. Under some conditions, the increase of

pressure drop can be even 2-4 times higher than the heat

transfer augmentation by LVGs [6-8], which debilitates the

advantages of longitudinal vortex generators. Gen try and

Jac obi [9,10] experime ntally stu died heat tran sfer

enhancement chara cteristics of delta wing vortex generators

in a flat-pl ate chan nel flow. Results showed that the average

heat could be enhanced by 50–60% at low Reynolds number

in compa rison with the original arrangement. Liou et al. [11]

prese nted comparative stud ies in terms of heat transfer

augm entation and fr iction loss on 12 different

configurations of longitudinal vortex generators. It was

found that direction and strength of the secondary flow are

the more significant fluid dyn amic factors affecting heat

transfer, followed impor tance by fluid velocity, and then

turbu lent kinetic ene rgy. D u et al. [12] numerically studied

the flow structure and heat transfer enhancement of LVGs

applied in direct air e cooled con denser using RNG k-ε

model and found that the delta winglet pair with attack angle

of 25° could reach the best thermal and flow performances.

Habchi et al. [13] numerically investigated the performance

of trapez oidal wing with excavation at the bottom. The

results sho wed the conv ective heat tran sfer bet ween the

vortex gene rator and the surround ding fluid is decreased.

Therefore, the si ze of the ca vity should be opti mized to

maximize the ef fect of heat tran sfer enhancement and flow

resistance decrease. Wu and Tao [14] a lso did numerical

study on ther mal hydraulic perfor mance of rectangular

winglets with pun ched holes at the chan nel wall and fo und

that the ca se with pun ched holes had slightly higher average

Nu number (about 1.1%) and slightly lower average friction

factor (about 1.2%) compared with the case without

punched holes. Zhou and Ye [15]exper imentally

investigated the heaat tran sfer perfo r mance of a n ew vortex

gener ator called curved tra pezoidal winglet and compared

rectan gular winglet. Wang et al. [16]fou nd that longi tudinal

vortex generator conf igurations play an imp ortant role in

heat tran sfer enhan cement that can gre atly imp rove heat

transfer ra tes by 10–45%. Furthermore, heat transfer

perform ance of chan nels with LVGs on both si des is better

than th ose just on one. The results from studies by Biswas et

al. [17,18] showed that the flow loss due to the winglet-pair

was less than that due to the wing, and the zone of poor heat



transfer as it was observed with the wing could be avoided

by using winglet- pair. The use of winglet-pair appeared to

be a more attractive augmentation technique .Min et al. [19]

deve loped a modified recta ngular longitu dinal vortex

generator (LVG) obtain ned by cut ing of f the four corn ers

of a rect angular wing. Their experimental results of this

longitudinal mounted in rectangular channel proposed that

the modified rectangular wing pairs of the modified

rectangular wing pairs have better flow and heat transfer

characteristics than those of rectangular wing pair. Zhang et

al. [20] exam ined num erically the thermal enhancement

and flow resistance character ristics in a rectangular channel

with new makeup of double delta winglets and double delta

winglet with ho les. The double delta winglets with larger

angle could make more effective heat transfer improvement.

Caliskan [21] studied the heat tran sfer enhancement of

punched LVGs using the infrared thermal image technique.

He reported 23-55% increase in heat tra nsfer perfor mance

and correl ations for Nu were developed for corresponding

LVGs.

In the work currently being done, a numerical and

experimental study for three –dimensional turbulent flow

and heat transfer in a channel with common flow up and

combined anti and with stream wise common flow up

arrangement of winglet vortex generator is performed. Three

pairs array of winglet vortex generators of different

geometrical configuration as rectangular ,triangular ,semi-

circle and parabolic are used. In addition a parabolic

winglet type is tested as new suggested configuration under

low and high Reynolds number rang (Re =103 to 5×103).

Different values of stream wise distance which

dimensionlized with channel height as Xr= 1.5,2 and 3 are

studied. 2. PROBLEM DESCRIPTION

The geometry consists of three dimensional

rectangular channel with winglet vortex generators array. As

shown in Fig. (1). Four types of winglet vortex generators as

Triangular , Rectangular, Semi circle, and parabolic are

tested. Different angles of attack(ß=0⁰ ,30⁰ ,45⁰ and

60⁰ )for vortex generators are studied.

The channel of length (L =1.08 m) ,height ( H =0.06m) and

width(W =0.18m). Different sizes of vortex generators are

considered while the ratio of area of the vortex generator

with respect to the area of the channel inlet (Ar) is kept

constant. Three values of area ratio (Ar ) as

0.0740,0.0370,and 0.0231 are considered. Different values

of stream wise distance which dimensionlized with channel

height as Xr= 1.5,2 and 3 are tested. In addition ,the spine

wise dimensionless distance as Zr=1,1.5 is included. The

distance from the channel inlet to the first pair of vortex

generators is kept constant at (0.18) cm for the studied

geometrical parameters.

Case 1.Anti stream wise common up.

Case 2. Combined anti and with stream wise common up.

Flow

x

z y

Flow



Fig. 1. Schematic diagram of the physical problem.

3-EXPERIMENTAL WORK

The sche matic diagram of the test rig is depicted in

Fig.2.This system consisting of the rectangular channel is

fabricated from galvanize steel material. The channel has a

length (L=108 cm),height (H=6 cm) and width (w=18 cm)as

shown in Fig.( 3).It consists of four walls, the two side walls

are made of plexi glass to see clearly the vortex generators

and consequently ensuring that they are in their specified

positions. The top and bottom walls are fabricated from

galvanized steel.A heater of (3000)W is imposed to the

bottom channel surface to generate a constant heat

flux(q=1000W/m2). A glass wool insulation is used to

insulate the bottom hot surface in order to prevent the heat

dissipation to the outside the channel .The exp erimental

parts of the te st rig is depicted in Fig.1.

Table I

shows the experimental parts of the test rig.

1 Rectangular channel 6 Pitot tube

2 Computer 7 Digital manometer

3 Variac 8 Voltmeter

4 Data logger

5 Magrfhelic different pressure gauge 9 Blower

Fig.2. schematic dia gram of the test rig.

4.THE THEORETICAL WORK

To mo del the thermal and flow characteristics of this model, the following assumptions are made:

1. Incompressible flow.

2. The fluid is stagnant and Newtonian air.

3.Non slip flow.

4. The dissipation of heat is assumed to be neglected.

5.Steady state.

6. The gravity effect is neglected .

7. Three dimensional analysis.

8. Constant physical properties for the fluid .



9.The enfluence of thickness of vortex generators is assumed to be neglected.

The governing equation for the continuity ,momentum and energy based on the above assumptions are as follows.

∂u

∂x+

∂v

∂y+

∂w

∂z= 0 (1)

X-Direction

(∂u2

∂x+

∂uv

∂y+

∂uw

∂z) = −

1

𝜌

∂P

∂x+

∂

∂x(ʋ

∂u

∂x) +

∂

∂y(ʋ

∂u

∂y) +

∂

∂z(ʋ

∂u

∂z)

+∂

∂x(−u2 ) +

∂

∂y(−uv ) +

∂

∂z(−uw )(2)

Y-Direction

(∂vu

∂x+

∂vv

∂y+

∂vw

∂z) = −

1

𝜌

∂P

∂y+

∂

∂x(ʋ

∂v

∂x) +

∂

∂y(ʋ

∂v

∂y) +

∂

∂z(ʋ

∂v

∂z)

+∂

∂x(−uv ) +

∂

∂y(−v2 ) +

∂

∂z(−vw ) (3)

z-direction

(∂wu

∂x+

∂wv

∂y+

∂w2

∂z) = −

1

𝜌

∂P

∂z+

∂

∂x(ʋ

∂w

∂x) +

∂

∂y(ʋ

∂w

∂y) +

∂

∂z(ʋ

∂w

∂z)

+∂

∂x(−uw ) +

∂

∂y(−vw ) +

∂

∂z(−w

2 ) (4)

4-1 Boundary Conditions

The boundary conditions are specified for each zone of the computational domain as follow:

At inlet:

Uniform inlet velocity ,U=Uin .

The flow is isothermal (T=Tin=300K).

At walls :

1- On the channel walls and vortex generators, the velocity is taken to be zero (no slip), u=v=w=0 .

2- A constant heat flux (q=1000W/m2) is imposed on the bottom surface.

3- 𝜕𝑝

𝜕𝑛 = 0 ,where n is a normal unit vector .

4- 𝑘 = 0 and = 0

At outlet :

1-A zero gage pressure is specified at the outlet domain.

2- Smooth exit for dependent variable (𝜕𝑈

𝜕𝑥 =

𝜕𝑉

𝜕𝑥=

𝜕𝑊

𝜕𝑥= 0) are assumed.



5-NUMERICAL METHOD

A fin ite volu me method is used to discretised the gov erning flow and heat equations. A Fluent code with Work bench is

adopted to get the required results.

5.1 Grid independency It is important to have a good fine mesh which must have a good distribution cells in order to have an accurate solution, for

this reason, a grid independence study is made to choose the optimum grid to get a better solution. Table (2) shows the

specified grid for all studied shapes. Grid independence tests are carr ied out in the following method before further numerical

work. three sets of grid numbers, i.e.( 1244398, 1676622, 2543513 ) are adopted to examine the influence of the grid number

on the calculation with vortex generators. grid number of 2543513 is applied in simulation to keep a moderate accuracy while

saving computation time.

5-RESULTS AND DISCUSSION

The numerical results.

5.1 Validation with published results

A model validation must be performed to ensure that the present approach is reliable and applicable. This validation is

done by comparing the results of the present model with results of anshuman and Singh.[22]as shown in Fig.(3). Acceptable

agreement is obtained where the deviation does not exceeds 2% for Re=10000.

a-ß=30° b- ß=45°

0 0.5 1 1.5 2

0

10

20

30

40

50

Anshumanand Singh.[49]

0 0.5 1 1.5 2

X

0

10

20

30

40

50

Sp

an

wis

e N

ua

vg

Present result

0 0.5 1 1.5 2

0

10

20

30

40

50

Anshuman and Singh[49]

0 0.5 1 1.5 2

X

0

10

20

30

40

50

Sp

an

ew

ise N

uavg

present result



c- ß=60°

Fig. 3. Comparison of the present result with the published result of the Anshuman and Singh [22]

The discussion of numerical results are listed

according to the studied cases as follows.

Case 1:anti stream wise common flow up

Fig. (4) shows the variation of average Nusselt

number with Reynolds number for different shapes of vortex

generators for ß=45° and Xr=1.5 . Generally ,it can be noted

that the Nusselt number increases with the increasing

Reynolds number because of the increasing the velocity

which increases the heat transfer coefficient. It can be seen

that, the rectangular vortex generators (R.V.G) provides a

higher average Nusselt number than the semi-circle vortex

generators (S.V.G), triangular vortex generators (T.V.G)

and parabolic vortex generators (P.V.G) for all considered

Reynolds number values. This behavior due to the sudden

expansion after the vortex generator. where of the RVG has

the sharpest expansion with respect to the other shapes,

which they have a gradual expansion. The sharpest

expansion inducing the strongest longitudinal vortices and

the higher flow obstruction, This configuration creates a

stronger reverse flow as compared with those of other

shapes, leading to better mixing between the core and the

wall flows.

a.Ar=0.0740 b.Ar=0.0370

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

Plane channel

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

T.V.G

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

10000 20000 30000 40000 50000 60000

Re

0

50

100

150

200

250

Nu

avg.

S.V.G

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

R.V.G

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

Plane channel

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

P.V.G

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

T.V.G

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

S.V.G

10000 20000 30000 40000 50000 60000

Re

0

50

100

150

200

250

Nu

avg

.

R.V.G

0 0.5 1 1.5 2

0

10

20

30

40

50

Present result

0 0.5 1 1.5 2

X

0

10

20

30

40

50

sp

an

wis

e N

ua

vg

Anshuman and Singh[49]



c.Ar=0.0231

Fig. 4. Variation of average Nusselt number with Reynolds number for different shapes of vortex generators for ß=45° and Xr=1.5.

Fig.(5) shows the average skin friction coefficient distribution

with Reynolds number for different shapes of vortex generators

for ß=45° and Xr=1.5. Generally, it can be seen that the average

skin friction coefficient decrease with increasing Reynolds

number. The friction factor enduced by using vortex generators

is observed to be higher than that of the plane channel for all

studied vortex generators shapes, This attributed to the

suppression of the viscous sub-layer. This trend is increased as

vortex generators area ratio increases. The increased drag is

always associated with extra pressure loss. When the area ratio

increases ,the strength of longitudinal vortices are increases

result in a reverse flow leading to noticeable increase in friction

factor as compared with plane channel.

a.Ar=0.0740 b.Ar=0.0370

10000 20000 30000 40000 50000 60000

0.01

0.02

0.03

Plane channel

10000 20000 30000 40000 50000 60000

0.01

0.02

0.03

P.V.G

10000 20000 30000 40000 50000 60000

0.01

0.02

0.03

T.V.G

10000 20000 30000 40000 50000 60000

0.01

0.02

0.03 R.V.G

10000 20000 30000 40000 50000 60000

Re

0.01

0.02

0.03

Cf

S.V.G

10000 20000 30000 40000 50000 60000

0.01

0.02

0.03

Plane channel

10000 20000 30000 40000 50000 60000

0.01

0.02

0.03

P.V.G

10000 20000 30000 40000 50000 60000

0.01

0.02

0.03

T.V.G

10000 20000 30000 40000 50000 60000

0.01

0.02

0.03 R.V.G

10000 20000 30000 40000 50000 60000

Re

0.01

0.02

0.03

Cf

S.V.G

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

Plane channel

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

P.V.G

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

T.V.G

10000 20000 30000 40000 50000 60000

0

50

100

150

200

250

S.V.G

10000 20000 30000 40000 50000 60000

Re

0

50

100

150

200

250

Nu

avg

. R.V.G



c.Ar=0.0231

Fig. 5. Variation of average skin friction factor with Reynolds number for different shapes of vortex generators for ß=45° and Xr=1.5

The fig.(6) shows the variation of average Nusselt number with Reynolds number for different angle of attack for

Xr=1.5 and Ar=0.0370. This figure illustrates the maximum average Nusselt number were obtained at ß=45°,Re=50000. The

averaged Nusselt number of every shapes gradually increases with increasing Reynolds number. But, the R.V.Gwith ß=45°

perform better in heat transfer. It is found that ß=0° gives minimum average Nusselt numberfollowed by 03°, 60°, 45°

successively. This is because of the attack angle (ß ) that influences both the form and intensity of vortices. The R.V.G with

smaller ß produce mainly longitudinal vortices which last over a long distance along the downstream direction. However, the

smaller ß means smaller area facing the air flow, and the intensity of vortices generated is weaker. The R.V.G with larger

ßcreate mainly transverse vortices which influence only the local area of R.V.G. Attack angle of ß=45°is of the optimum

configuration for the best heat transfer performance in the present study. This trend is found for all tested shapes of vortex

generators The optimum averaged Nusselt number is found for R.V.G. at Ar=0.0370, ß = 45° and Re = 50000. The optimum

increase in Nusselt number is( 31.6 % ) as compared with plane channel. The attack angle makes the vortex generators

disturb the boundary layer more effectively and provide better air flow mix. and thus enhancing heat transfer.

a-T.V.G b-P.V.G

10000 20000 30000 40000 50000 60000

0

20

40

60

80

100

120

140

160

180

200

ß=0

10000 20000 30000 40000 50000 60000

0

20

40

60

80

100

120

140

160

180

200

ß=30

10000 20000 30000 40000 50000 60000

0

20

40

60

80

100

120

140

160

180

200

ß=45

10000 20000 30000 40000 50000 60000

Re

0

20

40

60

80

100

120

140

160

180

200

Nu

avg.

ß=60

10000 20000 30000 40000 50000 60000

0

20

40

60

80

100

120

140

160

180

200

ß=0

10000 20000 30000 40000 50000 60000

0

20

40

60

80

100

120

140

160

180

200

ß=30

10000 20000 30000 40000 50000 60000

0

20

40

60

80

100

120

140

160

180

200

ß=60

10000 20000 30000 40000 50000 60000

Re

0

20

40

60

80

100

120

140

160

180

200

Nu

avg.

ß=45

10000 20000 30000 40000 50000 60000

0

0.004

0.008

0.012

0.016

0.02

T.V.G

10000 20000 30000 40000 50000 60000

0

0.004

0.008

0.012

0.016

0.02

P.V.G

10000 20000 30000 40000 50000 60000

0

0.004

0.008

0.012

0.016

0.02

S.V.G

10000 20000 30000 40000 50000 60000

0

0.004

0.008

0.012

0.016

0.02 R.V.G

10000 20000 30000 40000 50000 60000

Re

0

0.004

0.008

0.012

0.016

0.02

Cf

Plane channel



c-S.V.G d-R.V.G

Fig. 6. Variation of average Nusselt number with Reynolds number for different effect angles of attack at the area ratio (0.0370)and Xr=1.5

Fig.(7)shows the overall efficiency versus Reynolds numbers with different shapes and size of winglet vortex generators.It can

be seen that the overall efficiency (η) are above unity for all the vortex generators. The enhancement factor tended to decrease

with the rise in the Reynolds number values for all vortex generators. It is worth noting that the overall efficiency (η) of the

R.V.G shape were higher than of those other shapes for all Reynolds number values. In addition , the minimum overall

efficiency is noticed at the parabolic vortex generators. This indicated that the use of R.V.G leads to the advantage over that of

P.V.G. where the maximum overall efficiency (η) is about 1.88 at Xr =1.5 and ß=45°.

a.Ar=0.0740 b.Ar=0.0370

10000 20000 30000 40000 50000 60000

0

40

80

120

160

200

ß=0

10000 20000 30000 40000 50000 60000

0

20

40

60

80

100

120

140

160

180

200

ß=30

10000 20000 30000 40000 50000 60000

0

20

40

60

80

100

120

140

160

180

200

ß=45

10000 20000 30000 40000 50000 60000

Re

0

20

40

60

80

100

120

140

160

180

200

Nu

avg

.

ß=60

10000 20000 30000 40000 50000 60000

0

20

40

60

80

100

120

140

160

180

200

ß=0

10000 20000 30000 40000 50000 60000

0

20

40

60

80

100

120

140

160

180

200

ß=30

10000 20000 30000 40000 50000 60000

Re

0

20

40

60

80

100

120

140

160

180

200

Nu

avg.

ß=60

10000 20000 30000 40000 50000 60000

0

40

80

120

160

200

ß=45

10000 20000 30000 40000 50000 60000

1

1.5

2

2.5

3

T.V.G

10000 20000 30000 40000 50000 60000

1

1.5

2

2.5

3

S.V.G

10000 20000 30000 40000 50000 60000

Re

1

1.5

2

2.5

3

eff

.

R.V.G

10000 20000 30000 40000 50000 60000

0.8

1.2

1.6

2

P.V.G

10000 20000 30000 40000 50000 60000

0.8

1.2

1.6

2

T.V.G

10000 20000 30000 40000 50000 60000

0.8

1.2

1.6

2

S.V.G

10000 20000 30000 40000 50000 60000

Re

0.8

1.2

1.6

2

eff

.

R.V.G



c.Ar=0.0231

Fig. 7. Variation of the overall efficiency with Reynolds number for different shapes of vortex generators for ß=45° and Xr=1.5

Fig. (8) shows the comparison between the experimental and numerical results of the plane channel.It can be illustrates

that the numerical results agree well with the experimental results, with the mean deviation being about 11%. The agreement

between the numerical and experimental results prove that the model and methods used in the present study are feasible and

the numerical results are reliable.

Fig. 8. The comparison between the experimental and numerical results of the channel

Fig. (9) shows the comparison between numerical and experimental results of overall efficiency for the channel with

T.V.G. This figure displays thatthe deviation percentage was about (5-6%) between the experimental and numerical results

.This deviation value verifies that a good approach is followed for experimental and numerical work.

10000 20000 30000 40000 50000 60000

20

40

60

80

100

120

140

160

Num.

10000 20000 30000 40000 50000 60000

Re

20

40

60

80

100

120

140

160

Nu

avg

Expt.

10000 20000 30000 40000 50000 60000

0.8

1

1.2

1.4

P.V.G

10000 20000 30000 40000 50000 60000

0.8

1

1.2

1.4

T.V.G

10000 20000 30000 40000 50000 60000

0.8

1

1.2

1.4

S.V.G

10000 20000 30000 40000 50000 60000

Re

0.8

1

1.2

1.4

eff

.

R.V.G



Fig. 9.

Comp

arison betwe

en the

overall

efficie

ncy experi

menta

lly and

numer

ically result

s for

many

value

of

Reynolds number for T.V.G shape and Ar=0.0370, Xr=3.

Fig.(10) shows the comparison between numerical and experimental results of average Nusselt number against Reynolds

number for ß=45° and Ar=0.0370 and Xr=3. The deviation percentage for T.V.G was found to be about (7% ) between the

experimental and numerical result. while the R.V.G was about (4.7%),(4.4%)for S.V.G and P.V.G about (4.9%). These

deviation values verifies that a good approach is followed for experimental and numerical work.

a-T.V.G b-P.V.G

10000 20000 30000 40000 50000 60000

0.8

1.2

1.6

2

exp.ß=0

10000 20000 30000 40000 50000 60000

Re

0.8

1.2

1.6

2

eff

num.ß=0

10000 20000 30000 40000 50000 60000

0.8

1.2

1.6

2

num.ß=30

10000 20000 30000 40000 50000 60000

Re

0.8

1.2

1.6

2

eff

exp.ß=30

10000 20000 30000 40000 50000 60000

20

40

60

80

100

120

140

160

180

200

220

240

Num.

10000 20000 30000 40000 50000 60000

Re

20

40

60

80

100

120

140

160

180

200

220

240

Nu

avg

Expt.

10000 20000 30000 40000 50000 60000

Re

20

40

60

80

100

120

140

160

180

200

220

240

Nu

avg

Expt.

10000 20000 30000 40000 50000 60000

20

40

60

80

100

120

140

160

180

200

220

240

Num.

10000 20000 30000 40000 50000 60000

0.8

1.2

1.6

2

num.ß=60

10000 20000 30000 40000 50000 60000

Re

0.8

1.2

1.6

2

eff

exp.ß=60

10000 20000 30000 40000 50000 60000

Re

0.8

1.2

1.6

2

eff

num.ß=45

10000 20000 30000 40000 50000 60000

Re

0.8

1.2

1.6

2

exp.ß=45



c-S.V.G d-R.V.G

Fig. 10. Comparison between the average Nusselt number experimentally and numerically results for many value of Reynolds number for ß=45° and

Ar=0.0370, Xr=3.

Case 2 Combine anti and with stream wise common flow up:

The variation of average Nusselt number with Reynolds number for different shapes of vortex generators for ß=45°

and Xr=1.5 is shown in Fig. (11) . From this figure, it can be seen that the Nusselt number increases with the increasing

Reynolds number because of the increasing the velocity which increases the heat transfer coefficient. It can be seen that, the

rectangular vortex generators (R.V.G) provides a higher average Nusselt number than the semi-circle vortex generators

(S.V.G), triangular vortex generators (T.V.G) and parabolic vortex generators (P.V.G) for all considered Reynolds number

values. This behavior due to the sudden expansion after the vortex generator. where of the RVG has the sharpest expansion

with respect to the other shapes, which they have a gradual expansion. The sharpest expansion inducing the strongest

longitudinal vorticesand the higher flow obstruction, This configuration creates a stronger reverse flow as compared with

those of other shapes, leading to better mixing between the core and the wall flows. This trend is found for all tested sizes of

vortex generators, however increasing the vortex generator size (represented here by Ar) leads to increase the average Nusselt

number. The optimum averaged Nusselt number is found for R.V.G. at Ar=0.0740, ß = 45° and Re = 50000. The optimum

increase in Nusselt number is 10% as compared with plane channel. Increasing the size of vortex leads to increase the flow

restriction creating strong longitudinal vortices and thus enhancing heat transfer. The second case gives the higher than the

first case about 17 % .

a-Ar=0.0740 b-Ar=0.0370

10000 20000 30000 40000 50000 60000

Re

20

40

60

80

100

120

140

160

180

200

220

240

Nu

avg

Expt.

10000 20000 30000 40000 50000 60000

20

40

60

80

100

120

140

160

180

200

220

240

Num.

10000 20000 30000 40000 50000 60000

20

40

60

80

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120

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160

180

200

220

240

Num.

10000 20000 30000 40000 50000 60000

Re

20

40

60

80

100

120

140

160

180

200

220

240

Nu

avg

Expt.

10000 20000 30000 40000 50000 60000

80

120

160

200

240

Plane

10000 20000 30000 40000 50000 60000

80

120

160

200

240

P.V.G

10000 20000 30000 40000 50000 60000

80

120

160

200

240

T.V.G

10000 20000 30000 40000 50000 60000

80

120

160

200

240

R.V.G

10000 20000 30000 40000 50000 60000

Re

80

120

160

200

240

Nu

avg

S.V.G

10000 20000 30000 40000 50000 60000

80

120

160

200

240

Plane

10000 20000 30000 40000 50000 60000

80

120

160

200

240

P.V.G

10000 20000 30000 40000 50000 60000

80

120

160

200

240

T.V.G

10000 20000 30000 40000 50000 60000

80

120

160

200

240

S.V.G

10000 20000 30000 40000 50000 60000

Re

80

120

160

200

240

Nu

avg

R.V.G



c-Ar=0.0231

Fig. 11. Variation of average Nusselt number with Reynolds number for different shapes of vortex generators for ß=45° and Xr=1.5

The variation of thermal enhancement ratio (Nuwith/Nuwithout) with Reynolds number for different angle of attack is

depicted in figure(12). It can be seen that the thermal enhancement ratio significantly increases with presence of vortex

generators as compared with plane channel. This increase is noticed for any specified Reynolds number. For each vortex

generator, it is decreased as Reynolds number increase . The introduction of VGs generates the longitudinal vortices and

secondary flow, which breaks the boundary layer development. The boundary layer is thinner and the heat transfer is

enhanced.As fact, the disturbing and mixing of flow would change the original field of flow and temperature and the flow

separation point and the recirculation zone are delayed for the streamlined configuration. The higher area ratio of the winglet

vortex generators greats more disturbance of the boundary layer and provides a better air flow mixing. Hence, the heat

transfer is enhanced. The heat transfer enhancement from the rectangular vortex generator was significant more than those of

other shapes vortex generators. The optimum increase is formed at an angle of attack (ß=45°). The thermal enhancement ratio

varied from 1.6 to 2.8 with Re increasing. The reason of the above difference is described as follows. The winglet vortex

generators make a hindrance in the main flow stream with a pressure difference in upstream and downstream of the vortex

generators. This mechanism creates a strong longitudinal vortices. These vortices extend for a large distance behind the

winglet vortex generators and vanish slowly in stream wise flow direction .This flow interaction accelerating the mixing

process between the cold and hot fluid and thus increasing the thermal enhancement ratio. The optimum enhancement ratio is

pointed at the rectangular vortex generators while the minimum at parabolic vortex generators. This trend is founded for all

tested sizes of vortex generators, however increasing the vortex generator size (represented here by Ar) leads to increase the

thermal enhancement ratio. The optimum thermal enhancement ratio is founded for R.V.G. at Ar=0.0073, ß = 45° and Re =

50000. The second case gives the higher than the first case about 20 % .

10000 20000 30000 40000 50000 60000

80

120

160

200

Plane

10000 20000 30000 40000 50000 60000

80

120

160

200

P.V.G

10000 20000 30000 40000 50000 60000

80

120

160

200

T.V.G

10000 20000 30000 40000 50000 60000

80

120

160

200

S.V.G

10000 20000 30000 40000 50000 60000

Re

80

120

160

200

Nu

avg

R.V.G



a-T.V.G b-S.V.G

c-R.V.G d-P.V.G

Fig. 12. Variation of the Nusselt number ratio Nwith/Nwithout(enhancement ratio) with Reynolds number for different angle of attack and Xr=1.5

The variation of average Nusselt number against Reynolds number due to the change in vortex generator angles of attack is

depicted in Figure(13) for Ar =(0.0370) and Xr=1.5. Generally ,it can be observed that increasing the angle of attack leads to

increase the average Nusselt number as compared with plane channel. It is found the angle of attack affect the average

Nusselt number variation ,where it increase as the angle of attack increase up to ß= 45° and them for all the considered vortex

generators decreases. The Nusselt number at ß= 45° is marginally larger than that at ß= 60° Hence, the T.V.G gives the

optimum Nusselt number at ß= 45°. The attack angle makes the T.V.G disturbs the boundary layer more effectively and

provide better air flow mix.

The average Nusselt number of the channel with semi-circle vortex generators ( S.V.G ) is clearly increased in comparison

with those of the plane channel. The Nusselt number at ß= 45° is marginally larger than that at ß= 60°and angle of attack

ß=60 is greater than (ß=30°,0°). Hence, the ß=45° attack angle is the more optimal angle for the S.V.G. The second case

gives the higher than the first case about 17 % .

10000 20000 30000 40000 50000 60000

0

0.4

0.8

1.2

1.6

2

Ar=0.0704

10000 20000 30000 40000 50000 60000

0

0.4

0.8

1.2

1.6

2 Ar=0.0370

10000 20000 30000 40000 50000 60000

Re

0

0.4

0.8

1.2

1.6

2

Nu

with / N

u w

itho

ut

Ar=0.0231

10000 20000 30000 40000 50000 60000

0

0.5

1

1.5

2

2.5

ß=0

10000 20000 30000 40000 50000 60000

0

0.5

1

1.5

2

2.5 ß=45

10000 20000 30000 40000 50000 60000

0

0.5

1

1.5

2

2.5

ß=60

10000 20000 30000 40000 50000 60000

Re

0

0.5

1

1.5

2

2.5

Nu

with / N

uw

itho

ut

ß=30

10000 20000 30000 40000 50000 60000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

ß=0

10000 20000 30000 40000 50000 60000

0

0.2

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1

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1.6

1.8

2

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2.4

Re

ß=30

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0

0.2

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0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

Nu

with

/ N

uw

ith

out

ß=60

10000 20000 30000 40000 50000 60000

Re

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

ß=45

10000 20000 30000 40000 50000 60000

0

1

2

3

Ar=0.0370

10000 20000 30000 40000 50000 60000

Re

0

1

2

3

Nu

with /N

u w

ith

ou

t

Ar=0.0231



a-T.V.G b-P.V.G

c-S.V.G d-R.V.G

Fig. 10. Variation of average Nusselt number with Reynolds number for different effect angles of attack at the area ratio (0.0370)and Xr=1.5

6-Conclusions

The potential using of winglet vortex generators array with different shapes, and arrangements in a three dimensional

plane channel turbulent flow been conducted experimentally and numerically .The conclusions obtained from this

investigation has been listed as follows:

1-It was found that the strength of the two longitudinal vortices induced by rectangular winglet vortex generators is higher as

compared with other tested shapes.

2-Utilizing rectangular winglet vortex generators array indicated the optimum heat transfer enhancement with modest

pressure drop.

3- The stream wise distance between winglet vortex generators has more effect on heat transfer and pressure drop as

compared with span wise distance.

4-The stream wise distance(Xr)represents the optimum distance for enhancing the heat transfer .

10000 20000 30000 40000 50000 60000

80

120

160

200

240

ß=0

10000 20000 30000 40000 50000 60000

80

120

160

200

240

ß=30

10000 20000 30000 40000 50000 60000

80

120

160

200

240

ß=45

10000 20000 30000 40000 50000 60000

Re

80

120

160

200

240

Nu

avg

ß=60

10000 20000 30000 40000 50000 60000

80

120

160

200

240

ß=0

10000 20000 30000 40000 50000 60000

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120

160

200

240

ß=30

10000 20000 30000 40000 50000 60000

80

120

160

200

240

ß=45

10000 20000 30000 40000 50000 60000

Re

80

120

160

200

240

Nu

avg

ß=60

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160

200

240

ß=0

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240

ß=30

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160

200

240

ß=45

10000 20000 30000 40000 50000 60000

Re

80

120

160

200

240N

uavg

ß=60

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80

120

160

200

240

ß=0

10000 20000 30000 40000 50000 60000

80

120

160

200

240

ß=30

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80

120

160

200

240

ß=60

10000 20000 30000 40000 50000 60000

Re

80

120

160

200

240

Nu

avg

ß=45



5-Increasing the vortex generator angle of attack (ß), increase the thermal performance with considerable increase in pressure

drop.

6- Enhancement of heat transfer for rectangular ,triangular ,semi circle and parabolic winglet vortex generators is enhanced

by (146%-200%),(141%-71%),(144%-181%) and(134%-169%)respectively as compared with plane channel.

NOMENCLATURE

Symbol Definition SI

Units

Ach Channel area m2

Ar Area ratio

As Surface area m2

Av Vortex area m2

Cf Skin friction coefficient -

Cp Specific heat capacity J / kg.

K

CV Control volume -

Dh Hydraulic diameter

(4A/Per.) m

f/fo Friction factor ratio

h Height of vortex m

H Channel height m

HD Dynamic head mm

k Thermal conductivity W/m.

K

L Channel length m

Nu Nusselt number -

Nuavg Average Nusselt

number -

Nuwith/Nuwit

hout

Thermal enhancement

ratio

P Pressure Pa

PD The dynamic pressure Pa

q Heat Flux W/m2

Re Reynolds number -

T Temperature K

Symbol Definition SI

Units

Tb Bulk temperature K°

Tw Wall temperature K°

u Velocity in x-direction m/s

U Bulk inlet velocity m/s

v Velocity in y-direction m/s

W Channel width m

w Velocity in z-direction m/s

X1

The distance from the

channel inlet to the first

pair of vortex

generators

m

Xr Streamwise distance

y Transverse coordinate m

z Span wise coordinate m

Zr Span wise distance



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[1] S. Caliskan “Experim ental investigation of heat tran sfer in a chan nel with new winglet-ty pe vortex generators”, Int ernational Journal of Heat and

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[3] St. Tiggelbeck, N.K. Mitra, M. Fiebig, Exper imental investigations of heat tran sfer enhancement and flow lo sses in a cha nnel with double ro ws of longitudinal vortex gene rators, Int. J. Heat Mass Transf. 36 (9) (1993) 2327-2337.

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multifunctional heat exchangers, Appl. Therm. Eng. 38 (2012) 14-25. [14] J.M. Wu, W.Q. Tao, Nume rical study on lam inar convection heat tran sfer in a rectan gular chan nel with longi tudinal vortex generator. Part A:

verific ation of field syner gy princi ple, Int. J. Heat Mass Transf. 51 (2008) 1179-1191. [15] G. Zhou, Q. Ye, Experi me ntal investing ations of thermal and flow chara cteristics of cu rved trapezoidal win glet ty pe vortex generators, Appl. The

rm. Eng. 37 (2012) 241–248.

[16] Q. Wang, Q. Chen, L. Wang, M. Zeng, Y. Huang, Z. X iao, Exper imental study of heat tran sfer enhan cement in na rrow rectangular chan nel with long itudinal vo rtex gener ators, Nu clear Engineering Des ign 237 (2007) 686–693.

[17] G. Bisw as, P. Deb, S. Biswas, Genera t ion of longitu dinal stre am wise vortices––a dev ice for improve ing heat exch anger design, Jou rnal of Heat

Transfer 116 (1994) 588–597. [18] G. Biswas, K. Torii, D. Fujii, K. Nishi no, Numeri cal and experimental determination of flow structure and heat transfer effects of longitudinal

vortices in a channel flow, InternationalJournal of Heat and Mass Transfer 39 (16) (1996) 3441–3451.

[19] C.H. Min, C.Y. Qi, X.F. Kong, J.F. Dong, Expe rimental study of rectan gular chan nel with modified rectangular longitudinal vortex generators, Int. J. Heat Mass Transf. 53 (15-16) (2010) 3023-3029.

[20] Zhang, T. Zhe Q. Huang, Xiao B. Zhang and Chun J. Liu," Numerical investigation of heat transfer using a novel punched vortex

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[21] Caliskan S. Experimental investigation of heat transfer in a channel with new winglet-type vortex generators. Int J Heat Mass Transf

2014;78:604-14.

[22] Anshu man Pra tap Singh1, Dr. N. K. Sing h," Numer ical analysis of heat tran sfer in turbul ent channel fl ow with long itudinal vortex gen erators", International Journal of Res e arch in Management, Sci ence & Techn ology, 2014, Vol. 2, No. 2,pp. 2321-3264.

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