numerical simulation of combined heat transfer from tube bank and single cylinder (mtech sharad...

8/4/2019 Numerical simulation of combined heat transfer from tube bank and single cylinder (MTech Sharad Pachpute Presentation 2011)

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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




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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)


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)


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)


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)




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


25/47

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


27/47

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







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







-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




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 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)


40/47

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 Zukauskas correlation 050

100

150

200

250

300

350

400

450

500

1000 51000 101000 151000 201000

Nu

Re Dmax


Nu by Zukauskas

correlation

(a>b)

(a


42/47

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


44/47

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


45/47

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


46/47

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


47/47

numerical simulation of combined heat transfer from tube bank and single cylinder (mtech sharad...

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