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NUMERICAL SIMULATION OF COMBINED CONVECTION ANDRADIATION HEAT TRANSFER FROM
SINGLE CYLINDER & TUBE BANKS
Presented bySHARAD PACHPUTE
June 2011
Major Project PartII Presentation
Department of Mechanical Engg.
IIT Delhi
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OUTLINE OF PRESENTATION
1. Introduction
2. Literature Review
3. Objective
4. Problem statement
5. Governing equation
6. Numerical Simulation7. Heat transfer form single cylinder
8. Heat transfer from in-line tube bank
9. Heat transfer from staggered tube bank
10. Comparison between in-line and staggered tube banks11. Conclusion and future scope.
Keys word: cross flow, convection &radiation, participating media , DO-model.
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1. INTRODUCTION
Background:
Industrial applications-Thermal power plant boilers, small industrial boilers , heat recoverysystem and chemical plant etc.
Flow past tube bank
- complexity in the flow due to radiatively participating gases
- Radiation become significant from flue gases at high temperatures
- The effect of participating gases like CO2, H2O is considerable
QTotal = Qconvection+ Qradiation
4 4
( ) ( )fluid walltotal s fluid wall sQ hA T T A T T
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2.LITERATURE REVIEW
Re Prm n
D
hDNu C
k
The cross flow over cylinder in forced convection Nu depend on Re and Pr
Zukauskas(1986) and Churchill given correllation for different Re and Pr range
Research work carried out for unsteady case and turbulence flow.
2.3 Heat transfer from cylinder with participating medium:
2.2 Convective heat transfer from cylinder :
2.1 Flow past cylinder: Model used for Fundamental studies of fluid mechanics
D.A. Kaminski et.al(1994) studied flow and heat transfer of participating medium
at Re=500.
In this numerical model, they did not consider unsteady effects occur due to
vortex shedding and considered only half top portion of cylinder .
U
T
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2.4 Convective heat transfer from tube banks
Nusseltnumber correlation
Zukauskas(1983) : ReDmax =1000-2x105 => C ,m depends on maximum velocity
Grimison (1937) :ReDmax =2000-40000 => C, m depends on tube spacing
No correlation is available at low Reynolds number
Turbulence effect is not considered on convective Nu in correlation
2.5 Radiative heat transfer from tube bank P. Stehlik (1999) evaluated radiative component and combined heat transfer in the
thermal calculation of finned tube banks mathematically.
2.6 Conclusion from literature review
Both experimental and numerical results are available for convective heat transfer
only .
However, convective and radiative heat transfer from single cylinder and tube still
not explored well.
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3 .OBJECTIVE
To carry out numerical study on flow past a single cylinder and tube
banks and heat transfer characteristics considering radiativelyparticipating gases.
To get heat transfer correlations for single cylinder and tube banks
Fig3.1 ,Flow over single cylinderFig3.2 ,Flow over tube bank
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4.Problem Statement
Fig.4.1 Computational domain for single cylinder
Numerical simulation of flow ,convection and combined heat transfer at different Re for
Single cylinder
In-line tube bank - four different tube spacing (3x3,2x2, 1.5x1.5 ,1.25,1.25)
Staggered tube bank four different tube spacing (2x2x,1.5x1.5,3x1,1.3x3)
To carry out detail studies of radiation properties ,inlet and wall temperature for single
cylinder and tube banks
To Develop correlation for single cylinder and tube banks
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Fig.4 .1 Flow past in-line tube bank
Fig.4.2 Flow past staggered tube bank
Computational domain for flow past tube bank
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5. GOVERNING EQUATION AND MATHEMATICAL
MODELING
5.1 Governing Equation:Two dimensional incompressible viscous fluid flow in two-dimensions in the
absence of body forces and viscous dissipation
Continuity equation :
Momentum equation :
Energy equation:
Where, = divergence of radiative heat flux calculated from solving RTE
0u v
x y
2 2
2 2
1u u u p u uu v
t x y x x y
2 2
2 2
1v v v p v vu v
t x y y x y
2 2
2 2.
r
p
T T T K T T u v q
t x y c x y
r.q
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5.2 Radiation Modeling for DO Method: Radiative transpose equation(RTE) in discrete ordinate at S(x,y,z) along
in a gray medium
b
4
( ) ( . )4
m
m m mss i i
II I I I s s s d
S
bm
m
m
m
m
m
m IIz
I
y
I
x
I
In Cartesian coordinate the discrete equation
( , )
When the surface bounding the medium is gray and emits and reflects diffusely
then radiative boundary condition in x plane
at x=0 ;
at x=L,
similarly for y and z plane
0.;.)1(
0.
i
sn
jjjb snsnIwIIj
0.;.)1(
0.
i
sn
jjjb snsnIwIIj
Incident radiation(G):
, , 04 m m m
m m m
mG I d w I
GTdITq 4
4
4
44.
Divergence of radiative heat flux
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6. NUMERICAL SIMULATION
Numerical simulation is carried out using FLUENT a commercial CFD solver.
6.1 Initial and Boundary condition:In the beginning of solution process flow domain defined as u= u , V=0, T= Tin
Inlet- velocity inlet , Outlet- outflow ,top and bottom farfield/symmetry
Uniform Inlet temperature and constant cylinder wall temperature
6.2 Numerical Method :FLUENT uses FVM to solve governing equation sequentially.
Laminar flow -
Pressure discretization utilized the standard method with PISO coupling
The second order Upwind discretization for Momentum ,energy equation
Turbulent flow
SST k- turbulencemodel
Pressure discretization utilized the standard method with SIMPLEC coupling
QUICK discretization scheme for momentum- equation and energy equations
The gray radiation model- second order upwind discretization for RTE and DO intensity
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6.3 Computational Mesh
Fig.6.1 Mesh for single cylinder Fig.6.2 Details of mesh close to cylinder
Fig.6.3 Mesh for in-tube bank
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7 Result of flow over cylinder7.1 Flow Past a Single cylinder:
7.1.1 -Stream lines at four different instants of time in one shedding cycle
Re=100 (Present stream lines ) Re=100 (B.N. Rajani et al. stream lines)
Re=500
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Re=50350 (turbulent flow)
7.1.2 Stream lines for turbulent flow in one shedding cycle
Re=7190 (turbulent flow)
Re=21580 (turbulent flow)
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
100 1000 10000
Cd
Re
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.1 0.2 0.3 0.4
Cd
Flow time(s)
7.1.2 Coefficient of drag for cylinder
Re=100
0.3
0.5
0.7
0.9
1.1
1.3
1.5
0 0.2 0.4 0.6 0.8 1 1.2
Cd
Flow time (s)
Re=7190
Re=21580
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300k
400K
400K
7.2.1 Convective heat transfer in Laminar flow
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160 180
Nu
,angle(deg)
convective Nu (numerical)
Schmidt and Wenner (experimental)
Fig.7.2.1 Time averaged local Nu at Re=100
0
2.5
5
7.5
10
12.5
15
17.5
20
22.5
25
0 20 40 60 80 100 120 140 160 180
TimeaveragedNu
,angle(deg)
present Nu (numerical)
Chuns Nu (experimental)
Eskerts Nu (experimental)
Fig.7.2.2 Time averaged local Nu Re=500
Authors Num at Re=100 Num at Re=500
McAdams correlation [28] 5.23 -
Kramers correlation [29] 5.49 -
Eskert et.al (expimental)[25] 5.38 12.591
Zaukaus correlation [16] 5.10 10.778
Churchill et al.[11] 5.16 12.456
P.C.Jain et. al (numerical )[13] 5.632 -
N. Mahir et. al [30](numerical 5.179 0.003 -
Knudsen correlation [27] 5.19 -Present value (numerical) 5.183 12.169
7.2 Convective Heat transfer from single cylinder
To tal number of grids
Nu48671 74944 209396
12.1695 12.1713 12.1738
Grid test at Re=500
f f
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7.2.2 Convective heat transfer in turbulent flow
0
20
40
60
80
100
120
0 20 40 60 80 100 120 140 160 180
TimeaveragedNu
,Angle
present convective Nu (numerical)
Scholten et.al. Nu ( experimental),1997
0
50
100
150
200
250
300
0 20 40 60 80 100 120 140 160 180
ConvectiveNu
,angle (deg)
Nu for Re=7190
Nu for Re=21580
Nu for Re=50350
65.5
66
66.5
67
67.5
68
68.569
1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.4 1.41 1.42 1.43 1.44
SurfaceaveragedNu
Time(s)
convective Nu (numerical)
Fig. Validation with experimental Nu at Re=7190 Fig. Local Nu distribution
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111.25
111.3
111.35
111.4
111.45
111.5
111.55
0.8 0.85 0.9 0.95 1
SurfaceaverageNu
Flow time (s)
convective Nu at Re=21580
171.27
171.275
171.28
171.285
171.29
171.295
171.3
171.305
171.31
0.4 0.45 0.5 0.55 0.6
Surface
av
erage
Nu
Flow time (s)
convective Nu at Re=50350
ReTu
%
Circumferentially and time averaged Nuconv (Nux,t)
% difference from
experimental
Value of Scholton et
al
Present
numerical
value
K. Szczepanik et. al
numerical value [15]
Experimenta
l value of
Scholtonet.al.
Zukau
skas
7190 1.6 67.22 67.3 (steady k- model ) 51 47.3 31.8%
21580 0.46 111.45 148 (unsteady k- model ) 103.4 91.3 7.78 %
35950 0.34 142.86 - 127.5 124 12.04 %
50350 0.36 171.28 191.1 (steady k- model ) 155.1 151.7 10.56 %
Table 6.3: Comparison of present Nu for convection with experimental result
7 3 C bi d i d di i h f f li d
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7.3 Combined convective and radiative heat transfer from cylinder
7.3.1 Combined heat transfer for purely absorbing medium
Temperature distribution at Re=100
(a) Convective heat transfer (b) combined heat transfer, =1(1/m) , s=0(1/m)
7 3 1 C bi d h t t f f l b bi di (k 1 (1/ ) 0 )
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0
2
4
6
8
10
12
14
16
18
20
0 20 40 60 80 100 120 140 160 180
TimeaveragedlocalNu
,angle(deg)
convective Nu (numerical)
Nu with radiation (numerical)
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120 140 160 180
TimeaveragedNu
,angle(deg)
combined Nu (numerical)
convective Nu (numerical)
ReD 83Combined
NuRadiative Nu
100 5.183 11.8723 6.691
500 12.169 19.77 7.592
7190 67.22 74.967 7.67
21580 111.45 118.98 7.74
50350 171.28 179.91 8.62
7.3.1 Combined heat transfer for purely absorbing medium (k=1 (1/m),=0 )
7 4 Eff t f b ti d tt i ffi i t t t l N
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7.4 Effect of absorption and scattering coefficients on total Nu
(b) ReD=500 , =1 (1/m) and s=0 (1/m)
7.4.1 Temperature contour (in Kelvin) for combined heat transfer
(a)ReD=500 , =0 (1/m) and s=0 (1/m)
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ReD=500, =0 (1/m) and s=30 (1/m)(a)ReD=500 , =0 (1/m) and s=0 (1/m)
7.4.2 Temperature contour for convection and combined heat transfer
7 4 Eff t f b ti d tt i ffi i t t t l N
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0
5
10
15
20
25
30
35
40
0 20 40 60 80 100 120 140 160 180
TotalNu
,Angle( deg)
Total Nu at =0 (1/m)
Total Nu at =1 (1/m)
Total Nu at =10 (1/m)
Total Nu at =60 (1/m)
10
12
14
16
18
20
22
0 10 20 30 40 50 60
TotalN
u
absporption coefficient (1/m)
10
12
14
16
18
20
22
0 10 20 30 40 50 60
TotalNu
Scattering coefficient (1/m)
Total Nu at =1(1/m)
Total Nu at =10 (1/m)Total Nu at =0 (1/m)
0
20
40
60
80
100
120
140
160
180
200
100 20100 40100
Surface
averag
ed
Nu
ReD
convective heat transfer
Effect of radiation absrobtivity without scattering on combined Nu at ReD= 500
7.4 Effect of absorption and scattering coefficients on total Nu
7 5 Eff t f i l t d ll t t h t t f
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7.5 Effect of inlet and wall temperature on heat transfer
Re TwallConvectiv
e Nu
Total Nu
=1
(1/m)
=10
(1/m)
ReD
=500
850 12.169 19.77 16.252
900 12.205 20.702 17.151
1000 12.285 22.356 17.675
Re Tin(K)Convective
Nu
Total Nu
=1
(1/m)
=10
(1/m)
ReD =500
850 12.180 19.75 16.0157
900 12.203 20.47 16.985
1000 12.287 22.456 17.675
Constant inlet temperature condition Constant inlet temperature condition
Case-I: Tw >Tin Case-II: Tin > Tw
Temperature contours
Development of correlation for single cylinder
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0
2
4
6
8
10
12
14
16
18
20
0 200 400 600 800 1000
Nu
Re
Nu by present correlation
Nu by Zukauskas correlation
Nu by Knudsen correlation
5 21.2 10 Re 0.024 Re 0.282Nu
0.50.51ReNu
0.466 1/ 30.6831Re PrNu
Zukauskas correlation
Knudsen correlation
Present correlation
0
50
100
150
200
250
300
350
5000 25000 45000 65000 85000 105000 125000
Nu
Re
Nu by present corrrelation
Nu by Zukauskas correlation
0.60.26ReNu
5 21 10 Re 0.0032Re 46.63Nu
Correlation for Combined Nu (k=1, s=0)5 22 10 Re 0.003294Re 53.8Nu
(100
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8.Heat transfer from in-line tube bank
8.1.1 Flow features of tube bank (axb)
In-line 1.5x1.5
In-line 2x2In-line 3x3
In-line 1.25x1.25
a=ST /D , b= SL/D
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0 1 2 3 4 5 6 7 8 9 10
-10
-5
0
5
10
Y
velocity (m/s)
O r i g i n P r o 8 E v a l u a t i o n O r i g i n P r o 8 E v a l u a t i o n
O r i g i n P r o 8 E v a l u a t i o n O r i g i n P r o 8 E v a l u a t i o n
O r i g i n P r o 8 E v a l u a t i o n O r i g i n P r o 8 E v a l u a t i o n
O r i g i n P r o 8 E v a l u a t i o n O r i g i n P r o 8 E v a l u a t i o n
O r i g i n P r o 8 E v a l u a t i o n O r i g i n P r o 8 E v a l u a t i o n
O r i g i n P r o 8 E v a l u a t i o n O r i g i n P r o 8 E v a l u a t i o n
O r i g i n P r o 8 E v a l u a t i o n O r i g i n P r o 8 E v a l u a t i o n
0 2 4 6 8 10 12
-10
-5
0
5
10
Y
velocity (m/s)
Y
O r i g i n P ro 8 E v a lu a t io n O r i g i n P ro 8 E v a lu a t io n
O r i g i n P ro 8 E v a lu a t io n O r i g i n P ro 8 E v a lu a t io n
O r i g i n P ro 8 E v a lu a t io n O r i g i n P ro 8 E v a lu a t io n
O r i g i n P ro 8 E v a lu a t io n O r i g i n P ro 8 E v a lu a t io n
O r i g i n P ro 8 E v a lu a t io n O r i g i n P ro 8 E v a lu a t io n
O r i g i n P ro 8 E v a lu a t io n O r i g i n P ro 8 E v a lu a t io n
O r i g i n P ro 8 E v a lu a t io n O r i g i n P ro 8 E v a lu a t io n
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 2 4 6 8 10 12
Y
Velocity (m/s)
velocity profile at X=-1.5
velocity profile at X=0
velocity profile at X=3
8.1.3 velocity distribution
Re=500 for Inline 2x2 at X=-1.5 Re=500 ,Inline 1.5x1.5 at X=-1.25
Re=500 for Inline 2x2
X=-1.5
X=0
X=3
8 1 3 Coefficient of drag
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8.2 Temperature distribution within in-line bundle for convection only
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2
Cd
Flow time(S)
Cd for cylinder 41
Cd for cylinder 42
Cd for cylinder 43
Cd for cylinder44
(a x b)
ReD
(based on inlet
velocity)
Coefficient of drag for
first cylinder 11
3 x 3 500 1.462
2 x 2 500 1.588
1.5 x 1.5 500 2.346
1.25 x 1.25 500 2.495
8.1.3 Coefficient of drag
Re=500 , In-line2x2 Re=500 ,In-line 1.5x1.5
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8.4 Local Heat transfer from tube within inline tube bank
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140 160 180
Nu
,angle(deg)
Nu for cylinder 11
Nu for cylinder 12
Nu for cylinder 13
Nu for cylinder 14
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140 160 180
Nu
,angle (deg)
Nu for cylinder 21
Nu for cylinder 22
Nu for cylinder 23
Nu for cylinder 24
Local Nu distribution for in-line tube bank 2x2 at ReD=21580
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8.5 Mean convective heat transfer from inline bundle
0
20
40
60
80
100
120
140
100 5100 10100 15100 20100
ConvectiveNu
ReD
convective Nu for inline 3x3
Convective Nu for inline 2 x2
Convective Nu for inline 1.5x1.5
Convective Nu for inline 1.25x1.25
Re
For (3x3)
ReDmax
Convective Nu %
difference
fromZukauskas
Grimison
correlation
Zukauskas
correlation Present Nu
6000 9000 71.9295 66.09 56.5967 14.36%
14000 21000 122.166 112.88 84.5938 24.8%
20000 30000 148.531 141.11 104.28 26.04%
8 6 Combined heat transfer from in-line tube bank
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8.6 Combined heat transfer from in-line tube bank
Re=21580 inline 1.5x1.5
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0
20
40
60
80
100
120
0 5000 10000 15000 20000 25000
Nu
ReD
convective Nu
combined Nu
Convective and combined ( = 1(1/m, s=0 (1/m)) Nu for inline 22
l f l f l b b k
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8.7 Development of correlation for inline tube bank
0
50
100
150
200
250
300
350
400
450
0 50000 100000 150000 200000
Nu
ReDmax
Convective Nu by present correlation
Convective Nu by Zukauskas correlation
0.5010.595ReNu
Validation of present convective Nu with Zukauskas correlation for inline bank (a/b>0.7)
Present correlation
9 HEAT TRANSFER FROM STAGGERED TUBE BUNDLE
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9. HEAT TRANSFER FROM STAGGERED TUBE BUNDLE
9.1 Flow features of staggered tube bank
Streamlines for 2x2
Streamlines 1.3x3Streamlines 3x1
Flow features of inner cylinders
9.2 Drag of staggered tube bundles
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g gg
Staggered tube
arrangement
(axb)
ReDCoefficient of drag (CD)
for first cylinder -11
2 x 27190 1.1656
21580 0.9283
1.5 x 1.57190 1.1824
21580 0.8657
3 x 17190 1.2404
21580 0.8892
1.3 x 3
7190 1.623
21580 1.318950350 0.9798
9.3 Temperature distribution within staggered tube bundle for convection
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p gg
ReD=500,2x2ReD=7190 ,1.25x1.25
ReD=21580, 3x1 ReD=21580, 1.3 x 3
9.4 Local Heat transfer from tube within staggered bundle
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9.4 Local Heat transfer from tube within staggered bundle
0
40
80
120
160
200
240
0 20 40 60 80 100 120 140 160 180
Nu
,angle (deg)
Convective Nu for cylinder 11
Convective Nu for cylinder 12
Convective Nu for cylinder 21
Convective Nu for cylinder 22
0
40
80
120
160
200
240
0 20 40 60 80 100 120 140 160 180
Nu
,angle (deg)
Convective Nu for cylinder 11''
Convective Nu for cylinder 12''
Convective Nu for cylinder 21''
Convective Nu for cylinder22''
Local Nu distribution for tube bank 2x2 at ReD=21580
9.5 Mean convective heat transfer from staggered bundle
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9.5 Mean convective heat transfer from staggered bundle
60
75
90
105
120
135
150
1 2 3 4
ConvectiveN
u
Row number
Nu for staggered 2x2
Nu for staggered 1.3x3
Nu for staggered 3x1
ReDReDma
x
Convective Nu%
differenc
e fromGrimison
%
difference
from
Zukauskas
Grimison
correlation
Zukauska
s
correlatio
n
Present
Nu
500 1000 NA NA - - -
7190 14380 88.2341 85.407 65.07 26.2 23.8
21580 42530 NA 165.154 116.22 28.5 29.5
50350
10070
0 NA 274.57 200.4 23.03 27.01
50
100
150
200
250
5000 15000 25000 35000 45000 55000
ConvectiveNu
ReD
Convective Nu for staggered 2x2
Convective Nu at staggered1.5 x1.5
Convective Nu for staggered 3 x1
Convective Nu for stagered 1.3x3
9.6 Combined heat transfer within staggered tube bundle
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Temperature contour for combined heat transfer, bank 2x2 at ReD=21580
For (a) =0 (1/m) (b) =1 (1/m)
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staggered
arrangementReD Nuconv NuTotal Nurad
2 x2
7190 65.07 70.894 (=1) 5.824
21580 116.22 120.83115 (=1) 4.6115
50350 200.4 203.6548 (=1) 3.2548
1.5 x1.5
7190 63.376 67.66(k=1) 4.291
21580 112.828 116.793 (=0) 3.9653
21580 112.828 118.817(=1) 5.989
21580 112.828 119.3614(k=10) 6.533
50
70
90
110
130
150
170
190
210
230
0 20000 40000 60000 80000 100000
Nu
ReDmax
Convective Nu
Combined Nu
Combined heat transfer within staggered tube bundle
9.6 Development of correlation for staggered tube bundle
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9.6 Development of correlation for staggered tube bundle
For staggered tube bank 2x2 (a/b 2) 0.5650.308ReNu
0
50
100
150
200
250
300
350
400
450
0 50000 100000 150000 200000 250000
Nu
ReDmax
Nu by present correlation
Nu by Zukauskas correlation 050
100
150
200
250
300
350
400
450
500
1000 51000 101000 151000 201000
Nu
Re Dmax
Nu by present correlation
Nu by Zukauskas
correlation
(a>b)
(a
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0
50
100
150
200
250
5000 25000 45000 65000 85000 105000
N
u
ReDmax
Nu at staggered tube bank 2x2
Nu staggered tube bank 3x1
Convective Nu for case (a/b2)
10 COMPARISONS BETWEEN INLINE AND STAGGERED BUNDLES
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55
57
59
61
63
65
67
69
71
73
75
1 2 3 4
Convectiv
eNu
Tube bank row
Convective Nu for staggered bank 2X2
Convective Nu for inline bank 2x2
10.1 Mean convective heat transfer from tube bank
0
50
100
150
200
250
5000 25000 45000 65000 85000 105000
Nu
ReDmax
Convective Nu for inline 2x2
Convective Nu for staggered 2x2
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10.1 Combined heat transfer from tube bank
0
1
2
3
4
5
6
7
8
10000 30000 50000 70000 90000 110000
RadiativeNu
Re Dmax
Radiative Nu for inline 2x2
Radiative Nu for staggered 2x2
0
50
100
150
200
250
0 20000 40000 60000 80000 100000 120000
TotalNu
ReDmax
Total Nu for inline 2x2
Total Nu for staggered
2x2
11 .Conclusion and future scope
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As expected, the Nu increases with the increase of Re The effect of temperature difference on convective and radiative heat transfer
is very small
The total Nu of non-participating medium is higher than that of participating
medium cases.
The radiative heat transfer increases with increasing temperature but it
decreases with and .
p
Single cylinder
In-line tube bank
With decrease in tube spacing CD increases and wake behind cylinder increases.
The convective Nu may depends on recirculation intensity and turbulence intensity
in inter- tubular spacing, It increases with increasing Reynolds number for given in-line tube configuration.
Radiative Nu increases with increases ofRe number for low and medium tube
spacings.
Total Nu decreases slightly with absorption coefficient of participating medium
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11.3 Staggered tube bank
With decreasing longitudinal pitch CD increases as well wake behind tube
bank.The convective Nu is higher in case of tube spacing (a>b) than (a< b).
Total Nu increases with absorption coefficient of participating medium
For Staggered tube a banks, with increase in Re total Nu decreases
11.4 FUTURE SCOPE
Present numerical studies carried out considering smooth surfaces.
The scattering effects can be studied in detail for tube banks
In finned heat exchanger accurate correlations are not available, hence
there is scope for both convective and combined heat transfer
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