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M.Tech. Project Progress Report
Enhancement Of Heat Transfer Through Air Jet
Impingement By Using Axisymmetric Detached Ribs.
Submitted by
Rohan Arun Gulavani
2009AME3486
Under the guidance of
Prof. Anupam Dewan Prof. Sanjeev Sanghi
Department of Applied Mechanics
Indian Institute of Technology Delhi
Hauz Khas, New Delhi
November 2010
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Abstract
As we know, heat transfer enhancement is getting increasing importance since last
few years as it increases performance of any system which uses thermal energy at any
point of operation, such as, internal combustion engines, food processing equipments,
textiles, films and papers, processing of some metals and glass, etc. As impingement
of any fluid on the surface certainly increases the heat transfer than the natural
convection, researchers are concentrating over impingement with modified surface.
One way to modify the surface is use of ribs. The function of rib is to make the flow
turbulent, which results in enhancement of heat transfer. So in this project I am going
to study various dimensional parameters of axisymmetric detached ribs which are
certainly affects the heat transfer. Computational study is the main part of this project
and for which, commercial CFD software FLUENT and GAMBIT is used.
In this report, I simulate the air jet impingement over the flat plate as well as on plate
with detached rib. Grid independence study, selection of turbulence model, boundary
conditions, effect of impingement on heat transfer, and the effect of turbulent intensity
and length scale on heat transfer and rib clearance effect ( c/d ) are the main content
of the report.
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Contents
Abstract ................................ ................................ ................................ ..................... ii
List of Figure ................................ ................................ ................................ ............ iv
Chapter 1. Introduction ................................ ................................ .......................... 1
Chapter 2. Literature Review ................................ ................................ ................. 2
Chapter 3. Governing Equations ................................ ................................ ............ 5
Chapter 4. Geometry, Boundary Conditions and Grid ................................ ............ 7
Chapter 5. Results and Discussion ................................ ................................ ....... 10
Chapter 6. Conclusions and Future Scope ................................ ............................ 16
References ................................ ................................ ................................ ............... 17
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List of Figure
Figure 4:1 Experimental geometry considered by (Prabhu and Katti )................................ .... 7
Figure 4:2 Computational domain................................. ................................ ........................ 8
Figure 4:3 Grid considered in the present study................................ ................................ ..... 9
Figure 5:1 Grid independence study................................ ................................ .....................10
Figure 5:2 Comparisons of results using the RNG and standard k- models......................... 11
Figure 5:3 Effect of detached rib on Nusselt number................................ ............................ 12
Figure 5:4 Effect of turbulent intensity on Nusselt number................................ ................... 13
Figure 5:5 Effect of turbulent length scale on Nusselt number................................ ..............14
Figure 5:6 Effect of rib clearance ( c/d ) on heat transfer................................ ...................... 15
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Chapter 1. IntroductionAs we know, heat transfer enhancement is getting increasing importance since last
few years as it increases performance of any system which uses thermal energy at any
point, such as, internal combustion engines, food processing engines, etc. During past
few years many investigations dealing with impingement heat transfer enhancement
have been reported in the literature. In this case, fluid under high pressure impinges
on the surface over which we want to enhance heat transfer. Due to high pressure
difference, the flow becomes turbulent and consequently heat transfer increases. Such
processes have become popular in some industrial applications, such as, drying of
food products, textiles, films and papers, processing of some metals and glass, cooling
of gas turbine blades and outer wall of the combustion chamber, cooling of electronic
equipments, etc.
With impinging jets, to increase heat transfer, some scientists have used modified
surfaces, e.g., they have used surface roughners, attached ribs, detached ribs. Based
on several experimental studies reported in the literature, it can be concluded that in
all situations, these techniques enhance heat transfer. In the present project, a
computational study to consider the effect of axisymmetric detached rib on heat
transfer from a smooth surface has been reported.
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Chapter 2. Literature ReviewAs already mentioned, turbulence has significant effect on heat transfer, Gardon and
Akfirat (1965) studied the effect of turbulence on the heat transfer between two-
dimensional jet and flat plate. They also studied the effect of impingement on two
dimensional flat-plate. Hoogendoorn (1977) has proposed Nusselt number variation at
stagnation point and nearby region. He said that for low nozzle to plate distance
(z/d
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in the heat transfer coefficient for the dimpled surface as compared to the smooth
surface. Gau and Lee (1992, 2000) reported the heat transfer augmentation to slot jet
impinging on square ribbed and triangular ribbed walls, respectively. They performed
both the flow visualization and local Nusselt number measurement. They found that
reduction in heat transfer in case of triangular rib due to formation of air bubble
enclosing cavities near stagnation point which was lower than that in case of flat
plate. They stated that if impingement is used, flow becomes turbulent and it easily
penetrates the cavities resulting in an increase in the heat transfer. They reported that
square ribs are superior to triangular ribs. Gao et al. (2003) studied the effect of
various parameters on heat transfer such as nozzle to plate distance, number of arrays
of tabs. They found that 6 tabs array produce 6 distinct regions of high heat transfer
while 10 and 16 tabs array produce only 5 and 8 regions, respectively. They also
stated that for large nozzle to plate distance, Nusselt number distribution is quite
uniform and tabs plays an important role in making the flow turbulent and enhancing
the heat transfer.
Some researchers have reported the detached rib experiments. Liou and
Wang (1995) and Liou et al. (1995) studied different configurations of detached ribs
on the walls in internal flows and reported improved thermal performance compared
to the attached ribs. The flow visualization results of Liou et al. (1998) showed the presence of recirculating flow immediately behind the detached rib. They also
observed an asymmetric wake behind the rib because of asymmetric flow area across
the rib. The vortex shedding promotes the mixing of fluid and hence leads to a higher
level of heat transfer distributions. Tsia and Hwang (1999) studied the effect of
thermal conductivity of the attached ribs in internal flow using thermally active
material (aluminum ribs) and thermally non-active turbulators (wood ribs). They
concluded that higher enhancements with thermally active ribs are attributed to the rib
conduction effects. Their experiments with fully detached ribs show that enhancement
in heat transfer due to enhancement in turbulence. They speculated the flow over the
detached ribs and reported shedding of vortices from the detached rib and the wall jets
ejecting from the rib clearance.
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Prabhu and Katti (2008) studied the effect of axisymmetric detached rib
by normal impingement of circular jet. They studied various parameters such as
nozzle to plate distance (z/d), clearance of rib from the plate (c/d), height of the rib
(e/d), width of the rib (w/d), rib distance from axis of nozzle, etc. They concluded that
there is a continuous enhancement in Nusselt numbers from stagnation point till the
first detached rib for all the ribbed configurations studied. This behavior may be
attributed to fluid accelerations created in the stagnation region by the clearance under
the first rib. This result is supported by lower wall static pressure under the rib,
compared with smooth surface.
Yuling Shi et. al. (2002) has done computational study for impingement
heat transfer for 2D model. They compare the results between RSM and standard k-
turbulence model. They come to conclusion that results obtained by standard k-
model and RSM model has very little difference and results are very well agreement
with experimental results. They studied the effect of turbulence intensity on heat
transfer and they come to conclusion that as intensity increases heat transfer and
hence Nusselt number increases. Pathak et al. (2006) studied different turbulence
models for slightly heated jet discharged in a crossflow. They also commented on the
value of y+
in the computation. They concluded that for the flow which is not much
affected by the side wall, it is preferable to keep the value of y
+
between 20-30. Theyconcluded that for three-dimensional flow computations Reynolds stress transport
model is seen to be performing better than the standard k- model. Saket. al. (2007)
has investigated the effect of turbulent length scale and turbulent intensity on forced
convection heat transfer.
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Chapter 3. Governing EquationsContinuity equation:
0jj
Ux
Vx
!x
- - - - - - - - - - - - - - - - - - - - (3.1)
Momentum equation:
, ,jii j i j j i j j i
UUPU U u u
x x x x x V Q V
xxx x x! x x x x x -
- - - - - - - - - - - - - - - - - - - (3.2)
Energy equation:
? A .( ) ( ) ( )Pr
p t
i i ij eff
j j t j
c TU E p k U
x x x
QV X
x x x !
x x x - -- - - - - - - - - - - - - - - - - - (3.3)
Where,
2( )
3
j i kij eff eff eff ij
i j k
U U U
x x xX H
x x x
x x x
Viscous heating term plays important role in the compressible flow computations.
Turbulent model used for computation is k- model
Standard k- model:
,i
x x x
ti k b M
k
kku G G Y
Q V Q VI
W
x x x
x x x - - - - - - - - - - - - - - - - - - (3.4)
2
,
1 3 2
i x x x
ti k b
u C G C G C k k
I I I
I
Q I I I VI Q V
W
x x x
x x x - - - - - - - - - - - - (3.5)
Where,
tQ denotes the turbulent viscosity and is modeled as
2
t
kC
QQ V
I!
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In these equations,
kG represents the generation of turbulent kinetic energy due to mean velocity gradient
bG represents the generation of turbulent kinetic energy due to buoyancy
MY represents the contribution of fluctuating dilatation in compressible turbulent to the
overall dissipation rate
The values of the model constants used in above equations are
1 2 31.42, 1.68, 0.09, 1.0, 1.3
kC C C
I I I I W W! ! ! ! !
,kI
are the turbulent Prandtl numbers for I and k respectively.
RNG k- model
,i
x x xi k eff k b M k
kku G G Y S V E Q VI
x x x!
x x x - - - - - - - - - - - - - - - (3.6)
2
,
1 3 2
i x x x
i eff k bu C G C G C S Rk k
I I I I I I
I I I VI E Q V
x x x!
x x x - - - -- - - - - (3.7)
Where,
RI
is the value contributing in the constant2
CI
All other nomenclatures are same as standard k- equations
The model constants are
1 2 31.42, 1.68, 0.09, 1.0, 1.3
kC C C
I I I I
! ! ! ! !
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Chapter 4. Geometry, Boundary Conditions and GridThe arrangement for plate, nozzle and rib is described in Fig. 4.1.
Figure 4:1 Experimental geometry considered by (Prabhu and Katti )
Fig. 4.1 shows the nature of geometry of problem considered for computational
purpose. Here a nozzle of diameter 15.00 mm and is impinging air at 1.5 bar pressure.
Steel plate of dimension 160 x 80 x 0.06 mm acts as the heater which is continuously
provides a heat flux of 5000 W. Different dimensions of ribs and other geometries are
considered. We will look at the effect of (1) nozzle to plate distance (z/d);
(2) clearance (c); (3) thickness of rib (e); (4) width of the rib (w); and (5) pitch of the
rib (p).
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B ondi ions
Fi 4: C t ti l domai
Boundary conditions assi ned to t e computational domain are shown in Fi 5.1. The
values to the di erent parameters are taken directly from the experimental data of
(Prabhu and Katti .
1) Velocity inlet ( avg. velocity = 20 m/s)
2) Pressure outlet: atmospheric pressure
3) Wall: heat flux 5000 W;thickness: 0.06 mm; wall material: Steel
4) Reynolds number (Re) = 20000
5) Fluid: Air
Properties of air at 300 k:
i) Density = 1.225 kg/m3
ii) Specific heat CP = 1006.43 J/kg-K
iii) Thermal conductivity = 0.0242 W/m-k
iv) Viscosity = 1.7894 X 10-5 kg/m-s
Velocity Inlet (d= 15 mm)
Pressure OutletPressure Outlet
Wall (160mm)
z
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Grid
A picture of grid used for computationalis shown in Fig. 4.3. This grid is based on the
grid independence study. Itis refined till y+ value atthe wallis reduces to less than 5.Successive ratio used in grid is 1.05.
Figure 4:3 Grid considered in the present study
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Chapter 5. Results and DiscussionGrid Independence Study
This study was carried out using three different mesh si es. Experimental data shows
that Nusselt number values increases first and then reduces continuously from peak
Nusselt number point to the wall of nozzle. The same trend was obtained using the
fine mesh with y+ value ofthe grid point equalto 4.0. The simulation was carried out
using the standard k- model with enhanced wall function approach. According to the
theory for the temperature law of the wall y+ value at the first grid point should be
less than 13.2. Therefore accordingly mesh size was reduced so that y+
reaches up to
4.0. A further refinementin mesh did not change the results.
Figure 5:1 Grid independence study
0
50
00
50
200
250
300
0 05
5 2 2
5
Nu
r/d
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Comparison between Standard k- and RNG k- models
Fig. 5.2 shows that results depend on turbulence model used. The predictions using
the standard k-
model are in good agreement with experimental results than those bythe RNG k- model. One reason forthis conflictis assumption made in formulation of
these models. In standard k- model formulation is done with assumption that flow is
fully turbulent in other way in RNG k- ,low Re flow is the assumption. Maximum
percentage deviation for Standard k- modelis 11.95 %, while forRNG k- modelit
is 20.65 %
Figure 5:2 Comparisons of results using the RNG and standard k- models.
0
0
100
1
0
200
2
0
300
0 0!
1 1!
2 2!
r/d
Nu
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E ect of detached rib
As we see in last section, Standard k- method gives much better results than RNG
k- method. So for further analysis we are going to use standard k- turbulence model.And we tried to keep y+ value less than 5.
In this section, effect of detached rib is examined. In following graph, Nusselt
number is compared in both the cases. It is found that in the case of detached rib,
Nussult numberincreases in nozzle region ( r/d = 0 to 0.5 mm). So we can definitely
say that, detached ribs are much effective to increase heattransfer from flat plate.
Following results are obtained forthe-
1) z/d =0.5 (distance of nozzle from plate)
2) w/d= e/d= 0.23 (width and height of rib)
3) c/d = 0.067 (clearance from the flat surface)
4) r1/d = 0.5 (distance of first rib from axis of nozzle)
5) p/e = 4.0 (pitch ofthe rib)
Figure 5:3 Effect of detached rib on Nusselt number
0
50
100
150
200
250
300
0.000 0.500 1.000 1.500 2.000 2.500
Smooth plate
Plate with rib
r/d
Nu
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If we analyse above graph, Peak nusselt numberis achieved atjust behind the
first detached ri b from the centre of the nozzle. The reasons that mentioned in
literature, due to turbulence, and minimum clearance, flow trying to escape from the
space available. Because ofthis, wake region is createdjust behind the first rib. This
wake region is responsible for highly turbulent flow and resulting into high heat
transfer and hence high Nusselt number.
Effect ofturbulentlength scale (l)and turbulentintensity
Turbulent length scale and turbulent intensity are the main parameter of turbulence.
These parameters have direct impact on turbulent kinetic energy and its dissipation
rate. Hence, it has measure influence on heattransfer. Following results are obtainedforthe dimensions as mentioned in previous section.
1) Turbulentintensity:It is given by the ratio of square root of mean fluctuations to the mean
velocity. i.e. The intensity is directly be the measure ofturbulence. More the
intensity more will be the turbulence and hence the heat transfers from the
surface.
Figure 5:4 Effect ofturbulentintensity on Nusselt number
0
50
100
150
200
250
300
0.000 0.500 1.000 1.500 2.000 2.500
Turbulent intensity = 4.7 %
Turbulent intensity= 8 %
turbulent intensity = 10 %
"
'uI
U
!
Nu
r/d
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From graph, it is clear that, as turbulent intensity increases, peak Nusselt
number increases. Hence our objective is to increase turbulent intensity i.e.
Fluctuations in the flow.
2) Turbulentlength scale ( l) :-Turbulent length scale is inversely proportional to energy dissipation rate.
Hence more the turbulentlength scale minimum is the turbulent kinetic energy
dissipation rate. Energy dissipation rate has direct impact on heat transfer.
Hence more is dissipation rate more is the heattransfer.
Hence from graph, Peak Nusselt number is larger for length scale
1.05mm than lenth scale 4.2 mm and 5.6 mm.
Figure 5:5 Effect ofturbulentlength scale on Nusselt number
0
50
100
150
200
250
300
0.000 0.500 1.000 1.500 2.000 2.500
Turbulent length scale, l= 1.05 mm
Turbulent length scale, l= 4.2 mm
Turbulent length scale, l=5.6 mm
Nu
r/d
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Effect ofrib clearance (c)
Following graph clearly shows that, for rib clearance (c) 1.0 mm, Nusselt number
reaches to 247.3. which is larger than for clearance of 0.5, 1.5 and 2.0 mm. Thisvalues are obtained by Standard k- method, keeping y+ value around 3.8 i.e. less
than 5. At stagnation point, as clearance increases, Nusselt numbertends to increases,
but away from nozzle it shows less values. Allthe curves in the graph has maximum
percentage deviation from experimental results is less than 15%.
Figure 5:6 Effect of rib clearance ( c/d ) on heattransfer
0
#0
100
1#
0
200
2$ 0
300
0.000 0.500 1.000 1.500 2.000 2.500
rib clearence c= 0.5mm
rib clearence c= 1 mm
rib clearence c=1.5 mm
rib clearence c = 2.0 mm
r/d
Nu
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Chapter 6.
Conclusions and Future Scope
The following conclusions may be drawn based on the results obtained thus far
1) The problem of air impingement can be modeled with standard k- model
with a good agreement between experimental and computational results.
2) Sufficiently low values of y+
can be obtained by successive mesh refinement
using successive ratio 1.05 and interval size 0.09. y+ value should be less than
5 for enhanced wall treatment.
3) Turbulent intensity and turbulent length scale are the parameter of turbulence
and have influence on Nussul number i.e. heat transfer through flat plate
4) Distance, at which ribs are placed, has impact on heat transfer. For clearance
of 1 mm (c/d = 0.067) will give more heat transfer than any other clearance.
In future the effect of rib on the heat transfer by air impingement will be studied. The
effect of parameter under considerations is
1) Nozzle to plate distance (z/d)
2) Height of the rib (e/d)
3) Width of the rib (w/d)
4) Distance of first rib from axis of nozzle.
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References
1. C. J. Hoogendoorn, 1977. The effect of turbulence on heat transfer at a
stagnation point. Int. J. Heat Mass Transfer, Vol. 20, pp. 1333-1338.
2. C. Sak, R. Liu, D.S.-K. Ting, G. W. Rankin, 2007, Role of turbulent length
scale and turbulent intensity on forced convection from a heated horizontal
circular cylinder, Experimental thermal and fluid sciences, vol. 31, pp. 279-
289.
3. FLUENT Inc., Fluent 6.3 Documentation, http://www.fluent.com, 2006.
4. Gardon, R., Akfirat, C., 1965. The role of turbulence in determining the heat
transfer characteristics of impinging jet. Int. J. Heat Mass Transfer Vol. 8, pp.
12611272.
5. Gao, N., Sun, H., Ewing, D., 2003. Heat transfer to impinging round jets with
triangular tabs. Int. J. of Heat Mass Transfer Vol.46, pp.25572569.
6. Gau, C., Lee, I.C., 2000. Flow and impingement cooling heat transfer along
triangular rib-roughened walls. Int. J. Heat Mass Transfer Vol.43, pp. 4405
4418.7. Hansen, L.G., Webb, B.W., 1993. Air jet impingement heat transfer from
modified surfaces. Int. J. Heat Mass Transfer Vol.36, pp. 989997.
8. Katti V.V., Prabhu, S.V., 2008. Experimental study and theoretical analysis of
local heat transfer distribution between smooth flat surface and impinging air
jet from a circular straight pipe nozzle. Int. J. Heat Mass Transfer Vol.51, pp.
4480-4495
9. Katti V.V., Prabhu, S.V., 2008 Heat transfer enhancement on a flat surface
with axisymmetric detached ribs by normal impingement of circular air jet Int.
J. Heat Mass Transfer. Vol. 29, pp. 1279-1294
10.K Kanokjaruvijit and R F Martinez-Botas, 2004, An experimental
investigation of the heat transfer due to multiple jets impinging normally on a
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dimpled surface. J. Mechanical Engineering Science. Vol. 218 Part C,
pp.1337-1347.
11.Manabendra Pathak, Anupam Dewan, Anoop K. Dass, 2006, Computational
prediction of a slightly heated turbulent rectangular jet discharged into a
narrow channel crossflow using two different turbulence models, Int. J. Heat
Mass Transfer. Vol. 49, pp.3914-3928
12. S. Sugawara, T. Sato, H. Komatsu and H. Osaka, 1988. Effect of free stream
turbulence on the flat plate heat transfer, Int. J. Heat Mass Transfer, Vol. 31,
pp. 5-12.
13.Yuling Shi, M. B. Ray and A. S. Mujumdar, 2002, Computational study of
impingement heat transfer under a turbulent slot jet, Ind. Eng. Chem. Vol. 41,
pp. 4643-4651.