NUMERICAL INVESTIGAT ION ON HEAT TRANSFER AND FLUID F LOW OF SHELL -SIDE FOR SHELL … ·...

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http://www.iaeme.com/IJMET/index.asp 995 [email protected] International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 5, May 2017, pp. 995–1009, Article ID: IJMET_08_05_104 Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=5 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed NUMERICAL INVESTIGATION ON HEAT TRANSFER AND FLUID FLOW OF SHELL-SIDE FOR SHELL AND TUBE HEAT EXCHANGER WITH HEXAGONAL VENT BAFFLE BY USING CFD G. Vijay Teja M.Tech. Department of Mechanical Engineering, K L University, Vaddeswaram, Guntur District, AP, India Dr. K.V. Narasimha Rao Professor, Department of Mechanical Engineering, K L University, Vaddeswaram, Guntur District, AP, India ABSTRACT Shell and tube heat exchangers with many unconventional baffles are used in industrial applications to increase the efficiency of the plant. Recently tre-foil hole baffles are developed for which heat transfer coefficient is higher. In this context, research is carried out on hexagonal vent baffle and the results are noted. Streamline flow with different parameters were tested and their effects are noted on heat transfer coefficient and consistency for different positioned tubes. ANSYS Fluent CFD commercial package is used with realizable k-ε model. For method standardization, analytical investigation is carried out to validate the numerical results. The results are showing that the heat transfer coefficient is higher for hexagonalvent baffle irrespective of positions of hexagonalvent on different tubes. Pressure drop and wall temperature are found to befluctuating throughout the length in hexagonal vent and optimum hydrodynamic performance observed in this configuration. Keywords: Hexagonal-Vent baffle, shell-and-tube heat exchanger, shell side, heat transfer enhancement, hydrodynamic performance, turbulence intensity, vorticity, effectiveness. Cite this Article: G. Vijay Teja and Dr. K.V. Narasimha Rao. Numerical Investigation on Heat Transfer and Fluid Flow of Shell-Side for Shell and Tube Heat Exchanger with Hexagonal Vent Baffle by using CFD. International Journal of Mechanical Engineering and Technology, 8(5), 2017, pp. 995–1009. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=5

Transcript of NUMERICAL INVESTIGAT ION ON HEAT TRANSFER AND FLUID F LOW OF SHELL -SIDE FOR SHELL … ·...

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http://www.iaeme.com/IJMET/index.asp 995 [email protected]

International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 5, May 2017, pp. 995–1009, Article ID: IJMET_08_05_104 Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=5 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed

NUMERICAL INVESTIGATION ON HEAT TRANSFER AND FLUID FLOW OF SHELL-SIDE

FOR SHELL AND TUBE HEAT EXCHANGER WITH HEXAGONAL VENT BAFFLE BY USING

CFD G. Vijay Teja

M.Tech. Department of Mechanical Engineering, K L University, Vaddeswaram, Guntur District, AP, India

Dr. K.V. Narasimha Rao Professor, Department of Mechanical Engineering, K L University,

Vaddeswaram, Guntur District, AP, India

ABSTRACT Shell and tube heat exchangers with many unconventional baffles are used in

industrial applications to increase the efficiency of the plant. Recently tre-foil hole baffles are developed for which heat transfer coefficient is higher. In this context, research is carried out on hexagonal vent baffle and the results are noted. Streamline flow with different parameters were tested and their effects are noted on heat transfer coefficient and consistency for different positioned tubes. ANSYS Fluent CFD commercial package is used with realizable k-ε model. For method standardization, analytical investigation is carried out to validate the numerical results. The results are showing that the heat transfer coefficient is higher for hexagonalvent baffle irrespective of positions of hexagonalvent on different tubes. Pressure drop and wall temperature are found to befluctuating throughout the length in hexagonal vent and optimum hydrodynamic performance observed in this configuration. Keywords: Hexagonal-Vent baffle, shell-and-tube heat exchanger, shell side, heat transfer enhancement, hydrodynamic performance, turbulence intensity, vorticity, effectiveness.

Cite this Article: G. Vijay Teja and Dr. K.V. Narasimha Rao. Numerical Investigation on Heat Transfer and Fluid Flow of Shell-Side for Shell and Tube Heat Exchanger with Hexagonal Vent Baffle by using CFD. International Journal of Mechanical Engineering and Technology, 8(5), 2017, pp. 995–1009. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=5

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Numerical Investigation on Heat Transfer and Fluid Flow of Shell-Side for Shell and Tube Heat Exchanger with Hexagonal Vent Baffle by using CFD

http://www.iaeme.com/IJMET/index.asp 996 [email protected]

1. INTRODUCTION Heat exchangers contribute significantly to many energy conversion processes. Applications range from food processing industries, nuclear power plants, offshore industries, pharmaceutical production to aviation industries [1]. Recent developments in other exchanger geometries have come in various industry applications. However, the shell-and-tube heat exchanger by far remains the industry choice where reliability and maintainability are vital [2].Because of their feasibility of desirable design considerations and ranges now-a-days, CFD is playing very important role for parametric design process [1]. Although it is relatively simple to adjust the tube side parameters, it is very hard to get the right combination for the shell side. If possible, an ability to visualize the flow and temperature fields on the shell side can simplify the assessment of the weaknesses, thus directs the designer to the right direction. CFD can be very useful to gain that ability. Here the model made in CATIA and CFD simulation is used to investigate the heat transfer and fluid flow in Shell and tube heat exchanger with hexagonal vent baffles. Staggered tube bank with triangular pitch layout is used, which is better for heat transfer and surface area per unit length[3].Wealth of literature and theories are available to design a heat exchanger according to the requirements. A good design referred to a heat exchanger with least possible area and pressure drop to fulfil the heat transfer requirement[4].CFD is the science of predicting fluid flow, heat and mass transfer, chemical reactions and related phenomena by solving numerically the set of governing mathematical equations, which is stated in the ANSYS training module [5]. For method standardization, analytical investigation is carried out by varying other parameters to estimate performance of design using Kern method [6].

2. LITERATURE REVIEW Over the years, significant research and development efforts devoted to better understand the shell-side geometry. New geometries are been introduced for performance enhancement and improve reliability. The pioneering works published in the Trans. Institute of Chemical Engineers during May 1990, on helical baffles paved the way to a major shift from a conventional understanding of baffles in a shell-and-tube heat exchanger [2]. Helical baffles serve as guide vanes for shell-side flow as compared to creating flow channels with conventional segmented baffles. In the past decade, heat transfer has extended the understanding of the helical baffle geometry through extensive testing and development [2].Helical geometry gave better results than convectional baffles. More recently, many researchers started working in this field of redesigning of baffles modeling.

Shell-and-tube heat exchangers with trefoil-hole baffles are new type heat transfer devices and are widely used in nuclear power plants due to their special advantages, with the fluid flowing longitudinally on the shell side. However, very little related literature is available. In order to obtain an understanding of the underlying mechanism of shell-side thermal augmentation, a CFD model including inlet and outlet nozzles was proposed in the study [7].Based on the RNG k-Ɛ model, numerical investigations on shell-side fluid flow and heat transfer are conducted by using commercial CFD software FLUENT14.0. The results show that the fluid is fully developed after the first trefoil-hole baffle. The heat transfer coefficient and pressure drop vary periodically along the axial direction. Fluid velocity increases gradually and the jet flow forms in the region near baffles. The secondary flow is also produced on the two sides of baffles when the fluid flows through trefoil-hole baffle. The jet flow and secondary flow can decrease the thickness of boundary layer and then enhance the heat transfer [7].

In another paper, three-dimensional CFD simulations using the commercial software ANSYS 15.0-FLUENT, have been performed to study and compare the shell-side flow

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distribution, heat transfer coefficient and the pressure drop between the recently developed trefoil-hole, helical baffles and the conventional segmental baffles, at low shell side flow rates [8]. In this numerical comparison, the whole heat exchangers consisting of the shell, tubes, baffles and nozzles are modeled; the numerical model predicts the thermo-hydraulic performance with a considerably good accuracy, by comparing with experimental data for single segmental baffles. The model is then used to compute and compare the thermo-hydraulic performance for the same heat exchanger with trefoil-hole and helical baffles. The results show that the use of helical baffles results in higher thermo-hydraulic performance while trefoil-hole baffles has a higher heat transfer performance with large pressure drop compared to segmental baffles where thermo-hydraulic performance is high in helical baffle [8]. Hence, there is need of additional modifications in the baffle changes and comparing them each other.

In this present work, a new baffle hole geometry is designed and studied. The results are obtained by using ANSYS 15.0 and analytical investigation is carried to standardizing the analysis.

3. GEOMETRICAL MODEL AND MESHING The shell side design of a shell-and-tube heat exchanger; in particular, the baffle spacing, and shell diameter dependencies of the heat transfer coefficient and the pressure drop are investigated by numerically modeling a small heat exchanger. The flow and temperature fields inside the shell are resolved using a commercial CFD package by varying the mesh size as in Figure1to obtain optimization mesh size. Set of CFD simulations have been performed for a single shell and single tube pass heat exchanger with a variable number of baffles and turbulent flow. The results are observed to be sensitive to the turbulence model selection. The best turbulence model among the ones considered is determined by comparing the CFD results of heat transfer coefficient, outlet temperature and pressure drop with the Realizable k-ε model method results. The effect of baffle spacing to shell diameter ratio on the heat exchanger performance is investigated by varying flow rate and optimization is obtained.

Figure 1 Cold fluid outlet Temperature for different mesh densities The entry and exit points for tubes are exactly starting and ending with length of the heat

exchanger respectively, ends for shell along the length are chopped off at designed length, i.e. no D-ends or to roid ends are used for simulation purpose. Geometrical details are given in Table 1.The baffle plate thickness is kept at 4mm.Shell side fluid must flow aligned to the hot fluid tubes to accomplish this condition. Cross-section of baffles has to change in such a way

250260270280290300310320330

COLD

FLU

ID O

UTL

ET T

EMPE

RATU

RE

NUMBER OF ELEMENTS

EXPERIMENTAL

C.F.D

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Numerical Investigation on Heat Transfer and Fluid Flow of Shell-Side for Shell and Tube Heat Exchanger with Hexagonal Vent Baffle by using CFD

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that the turbulence should be kept uniform in baffle contact point on tubes. From this concept, hexagonal shape of baffles are modeled. Number of elements used is 2595539; number of nodes is 657982. Maximum Skewness obtained is 0.86 which is lesser than the acceptable limit of the overall skewness of 0.9[9].The standard deviation is found to be 0.1308,which is negligible.

Table 1 Geometrical parameter of hexagonal vent

Shell Diameter 150 mm Shell Inlet Diameter 52.5 mm Shell Outlet Diameter 52.5 mm Tube Internal Diameter 15.798 mm Tube External Diameter 19.1 mm Number of tubes, baffles 7,6 Distribution Rotated Circular Type Baffle Pitch 86 mm Tube Pitch 42 mm Baffle Type Rotated Circular Type Baffle Thickness 4 mm Vent circle radius. 13.8242 mm parallel face distance 24.053 mm

Figure 2 Geometrical view of hexagonal vent

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4. GOVERNING EQUATIONS The fluid flow assumed study-state turbulent model with incompressible fluid. The shell side fluid flows only through the hexagonal vents and it is assumed that three are no other leakages. Finite volume method is adopted to solve the model equations like Continuity equation (1) momentum equation (2) and energy equation (3). The equations are given below [10, 11]:

= 0 (1)

= − + {( + ) + } (2)

= {( + ) } (3)

To understand exact performance of flow, realizable k- model is chosen, experimental strong adverse gradient of pressure and recirculation [11], turbulent kinetic energyk (4) and dissipation (5) whichhave effect on boundary layer transport equations given below:

= + + Г − (4)

= + + Г −√

(5)

Where Г(6) represents k generation from mean velocity gradients given as:

Г = − = ( + ) (6)

The turbulent kinetic viscosity is:

= µ (7)

Realizable − model considered is varying from standard RNG − model due to functionality of µ is no more considered as constant [8]. µ depends upon mean strain,

Figure 4 geometry view after generating in ANSYS

Figure 5 geometry view after mesh

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Numerical Investigation on Heat Transfer and Fluid Flow of Shell-Side for Shell and Tube Heat Exchanger with Hexagonal Vent Baffle by using CFD

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rotation rates, angular velocity and turbulence field and empirical constants of Realizable − model [12] are given below:

C1=max [0.43,µ/(µt+5)]; C2=1.9; k =1.0; =1.2 In addition, the second order upwind scheme has been adopted for the momentum, energy,

turbulence and its dissipation rate. All the convergence residuals are considered very less. The main two variations of this realizable model are: new eddy-viscosity formula involving a variable Cµ originally proposed by Reynolds and new model equation for dissipation based on the dynamic equation of the mean-square vorticity fluctuation[12]

5. BOUNDARY CONDITIONS AND NUMERICAL METHODOLOGY Data reduction is very important to eliminate unwanted values and calculations in any engineering experiment. The calculation of experimental values for CFD simulation is carried out at mass flow rate of 1kg/s to ensure proper turbulence. Details are given in Table5.

For Hexagonalvent baffles, calculation of shell side Reynolds Number:

Re= ̇( )

(8)

Where, the turbulence intensity is calculated using equation (9) which gives the percentage of the intensity. The present investigation yielded a value of 5.5, which is just about medium turbulence case [13]:

( ) = 0.16( ) (9)

Table 2 Turbulence intensity %.

Thermo-physical Properties of hot and cold fluids

Table 3 Fluids Material Properties

Fluid properties Cold side fluid (water at NTP) Hot side fluid (water at 80°C) Density (kg/m3) 998.2 974 Cp (J/kg-K) 4178 4195.3 Conductivity (W/m-k) 0.6 0.67 Viscosity (Kg/m-s) 0.001003 0.000355

Solid Material Properties

Table 4 Solid Material Properties

Area Re TI % Hexagonal vent 4487.8979 5.5926 Tube side 15817.8284 4.7777

Solid properties Copper Steel Density (kg/m3) 8978 8030 Cp (J/kg-K) 381 502.48 Conductivity (w/m-k) 387.6 16.27

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Table 5 Boundary conditions

BC Momentum Thermal Hot Inlet 0.36576 (m/s) 353 (K) Cold Inlet 0.4673148 (m/s) 300 (K) Hot Inlet Hydraulic Dia. 15.798 mm Cold Inlet Hydraulic Dia. 52.5 mm Outlet Pressure Outlet 300 (K)

Values of momentum, pressure and energy are chosen to be 0.7, 0.7 and 0.6respectively.At different mass flow rates, the flow will affect the heat transfer coefficient and other properties of the stated problem. The mass flow rate is varied with intervals of 0.1 kg/s. Reynolds number is calculated using Eq. (8) and turbulent intensity-TI is calculated using Eq. (9). The Nusselt number correlation is used to obtain the heat transfer coefficient (Eq. 10). Prandtl number for shell-side fluid water at bulk mean temperature of 38.6960C is 4.5147. The Nusselt number correlation is given by [14]:

Nu= c (1.13 pr 0.4) Ren (10) The values of ‘c’ and ‘n’ are taken from the data book by calculating staggered ratios, St/d

and Sl/d ratio, which isfound to be 2. C is 0.482 and n is 0.556 [14]. Using these values and formula (Eq. 10), Nu number is calculated and thus heat transfer coefficient can be determined.

Heat transfer coefficient(h) = . (11)

Table 6 Data of hexagonal vent with various mass flow rates

For the configuration used in the model, the flow is laminar up to mass flow rate of 0.4

kg/s (Re<2300) and at mass flow rate of 0.5 (kg/s), transition begins and attains complete turbulence at mass flow rate of 0.9 (kg/s). Therefore, to ensure turbulence, 1kg/s mass flow rate is used in the simulation. Where the turbulence intensity is above 5%, the flow is completely developed flow due to jet kind of lay path. The heat transfer coefficients of the model values are found to be increasing with increase in mass flow rate of shell side fluid.

S.No. Mass flow rate-m(kg/s)

Re TI (%) Nu Heat transfer coefficient, h (W/m2K)

1 0.2 897.5795 6.83 42.3974 169.5895 2 0.3 1346.3693 6.50 53.1185 212.4740 3 0.4 1795.1591 6.27 62.3321 249.3284 4 0.5 2243.9410 6.09 70.5656 282.2624 5 0.6 2692.7387 5.96 78.0934 312.3736 6 0.7 3141.5285 5.84 85.0818 340.3272 7 0.8 3590.3183 5.75 91.6390 366.5560 8 0.9 4039.1081 5.66 97.8410 391.3640 9 1 4487.8979 5.59 103.7438 414.9752

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Numerical Investigation on Heat Transfer and Fluid Flow of Shell-Side for Shell and Tube Heat Exchanger with Hexagonal Vent Baffle by using CFD

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Figure 6 Mass flow rate vs heat transfer coefficient

6. RESULTS AND DISCUSSION Figure 7 shows the streamline plots of the aerodynamics of the baffle. The fluid is found to be having higher velocity at baffle opening creating wake region immediately after the baffle. Hexagonalvent having turbulence at inlet section and it is becomes more and more aligned along the length of the heat exchanger.

050

100150200250300350400450

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Hea

t tra

nsfe

r coe

ffici

ent-

h (w

/m2k

)

mass flow rate (kg/s)

Figure 7 Streamline plot

Figure 8 Vector velocity plot

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Figure 8 shows the Velocity vector plot to understand the velocity of each vector in the flow. It is clear that a secondary flow occurs in shell have less flow velocity. The flow over the tubes is fully developed immediately after every baffle. High velocity region is formed which is indicated with red colour. Figure 8 shows the velocity after baffle, which is relatively high. Recirculation zones can be indicated clearly in vector plots. Changes in direction of the flow because of the disturbance offered by baffles are responsible for this recirculation zone.

The fluid flowing inside the shell wets the outer surface of the tubes, which lead to a temperature change in the surface of the tubes. Figure 9 shows the temperature change is higher after half of the flow passed and the temperature of the surface is fluctuating throughout the length at each baffle. So, periodic transfer of heat occurs on the surface of tubes. Maximum temperature change is observed in hexagonalvent configuration in the last 40% of tube length, where, the temperature change in shell side fluid is somehow uniform along the length as shown inFigure10.Due to hexagonal vent configuration, temperature is getting decreased near to the opening of the hole pattern of baffle, it is directing the incoming flow towards the outer surface of the tubes. This change in temperature is gradually decreasing and temperature distribution in all tubes is uniform that will prevent generation of sudden thermal stresses.

Figure 11 shows that hexagonalvent baffles are generating vortex-generated area after passing through opening of the baffle plate because of sudden expansion. Shell side fluid temperature is not changing much in hexagonalvent baffles. The vent patterns to create the disturbance are functioning satisfactorily and the vortex is found to be generating from each face of each vent as shown in Figure 11. By understanding the Velocity plot (Figure8), temperature plot (Figure9) and vortex plot (Figure11), it is evident that the hexagonal vent baffles are yielding satisfactory performance.

Figure 9 Temperature plot on wetted area of tubes

Figure 10 Temperature distribution in shell side fluid

Figure 11 Temperature Plot on Vortex Core Region

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After every passage of baffle, variation takes place in the pressure of the shell side fluid (Figure12). Pressure drop took place at each baffle in six steps. Even though it is a step-wise decrease of pressure, just after passing from vent, the pressure is slightly increased for each baffle as shown in Figure 12. Along the length of the heat exchanger, the pressure drop is not very high and variation of pressure at inlet and outlet is not much different. Pressure drop in shell side fluid is showing significant changes after half of the length of the heat exchanger. The inlet pressure is 15.74 psi, which is dropped to 14.34psi at the outlet resulting in pressure drop of 1.4 psi, which is very much in the limits.

.

Figure 12 Pressure drop variation along length The shell side fluid taken at NTP, which is 300 K of water, which is coming out from

shell outlet at a temperature of 323.39 K as shown in Figure13. The raise of temperature for cold fluid is 23 Kelvin, which is acceptable for this configuration. As can be seen from the Figure 13, the shell side fluid found to be raising its temperature after travelling half of the flow length.

The Heat transfer coefficient distribution of wet surface on shell side for each tube is different which is fluctuating throughout the length, the heat transfer coefficient is different for each tube of same position (Figures 14 to 20):

100000

102000

104000

-0.1 6E-16 0.1 0.2 0.3 0.4 0.5 0.6

Pres

sure

(pas

cals)

length along heat exchanger

hexagonal vent shell side pressure drop

Figure 13 Temperature raise of shell side fluid along length

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Figure 14 Tube 1

Figure 15 Tube 2

Figure 16 Tube 3

0.00E+001.00E+032.00E+033.00E+034.00E+035.00E+036.00E+037.00E+038.00E+03

-2.00E-01 1.00E-15 2.00E-01 4.00E-01 6.00E-01

Wal

l Hea

t Tra

nsfe

r Coe

ffici

ent

[ W m

^-2

K^-

1 ]

distance along flow direction(m)

Figure 14: Tube 1

0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

-2.00E-01 1.00E-15 2.00E-01 4.00E-01 6.00E-01

Wal

l Hea

t Tra

nsfe

r Coe

ffici

ent

[ W m

^-2

K^-

1 ]

distance along flow direction(m)

Figure 15: Tube 2

0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

7.00E+03

-2.00E-01 1.00E-15 2.00E-01 4.00E-01 6.00E-01

Wal

l Hea

t Tra

nsfe

r Coe

ffici

ent

[ W m

^-2

K^-

1 ]

distance along flow direction(m)

Figure16: Tube 3

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Figure 17 Tube 4

Figure 18 Tube 5

Figure 19 Tube 6

0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

7.00E+03

-2.00E-01 1.00E-15 2.00E-01 4.00E-01 6.00E-01

Wal

l Hea

t Tra

nsfe

r Coe

ffici

ent

[ W m

^-2

K^-

1 ]

distance along flow direction(m)

Figure17: Tube 4

0.00E+001.00E+032.00E+033.00E+034.00E+035.00E+036.00E+037.00E+038.00E+039.00E+03

-2.00E-01 1.00E-15 2.00E-01 4.00E-01 6.00E-01

Wal

l Hea

t Tra

nsfe

r Coe

ffici

ent

[ W m

^-2

K^-

1 ]

distance along flow direction(m)

Figure 18: Tube 5

0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

7.00E+03

-2.00E-01 1.00E-15 2.00E-01 4.00E-01 6.00E-01

Wal

l Hea

t Tra

nsfe

r Coe

ffici

ent

[ W m

^-2

K^-

1 ]

distance along flow direction(m)

Figure 19: Tube 6

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Figure 20 Tube 7

7. CONCLUSION The hexagonal vent baffles model is performing satisfactorily as expected due to increase in turbulence and residence time of fluid in shell side. Besides, the shell side fluid gets in to better contact with tube outer surfaces, which also results in higher heat transfer rate. The streamlines of the flow pass above the tube surfaces. The thermo-hydraulic performance is moderate with a turbulent intensity of more than 5% ensures that flow will be disturbed. The velocity vectors show that velocity of flow just after the baffle vent increases compared to flow before the baffle. The vertex generation occurs from each face of hexagonal vent create a wake region around the tube that enhances the heat transfer. The temperature difference attained is acceptable for this configuration, where the temperature of the wetted area on tube shell-side increased due to decrease of thermal boundary thickness, which is caused due to flow generation over the tube. The outside surface temperature of the tube wall fluctuates throughout the flow direction. The heat transfer coefficient of the tube walls will be fluctuating along flow direction, which is different for each location and for each tube surface. The temperature change of shell-side fluid took place after travelling half of the length. The pressure drop of the system is found to be within acceptable limits.

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0.00E+00

1.00E+03

2.00E+03

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4.00E+03

5.00E+03

6.00E+03

7.00E+03

-2.00E-01 1.00E-15 2.00E-01 4.00E-01 6.00E-01

Wal

l Hea

t Tra

nsfe

r Coe

ffici

ent

[ W m

^-2

K^-

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distance along flow direction(m)

Figure 20: Tube 7

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NOMENCLATURE

Latin Symbols Across-cross-flow area at the shell centerline, mm2 Ao-heat exchange area based on the external diameter of tube, mm2 B -Baffle spacing, mm Cp-specific heat capacity, J/(kg. K) Ci -coefficients in k-ɛ model Ds-Internal shell diameter, mm Do-external tube diameter, mm Dct-outer diameter of central tube, mm h -Average heat transfer coefficient, W/(m2 K) k -Turbulent fluctuation kinetic energy, (m2/s2) L -Tube total effective length, m ṁ-mass flow rate, (kg/s) nt-number of tubes, Ncr -number of tubes in central row Pt-tube pitch, mm Pr- Prandtl number Dp-pressure drop, Pa Qave-average heat transfer rate, W Re-Reynolds number Tin-inlet temperature, K Tout-outlet temperature, K ∆ -Logarithmic mean temperature difference, K u -Average velocity, (m/s) x; y; z -Cartesian coordinate

Greek Symbols Γ-generalized diffusion coefficient ɛ -Turbulent kinetic energy dissipation rate, (m2/s3)

-Thermal conductivity, W/(m K) µ- dynamic viscosity, kg/(m.s)

-Kinematic viscosity, (m2/s) -Density, (kg/m3) -Prandtl number for k

∈-Prandtl number for ∈

Subscripts in -Inlet out -Outlet s-Shell side t -Tube side turb- turbulent