Heat transfer in staggered tube banks

8/13/2019 Heat transfer in staggered tube banks

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Sensitivity study on the variation of a shell side heat transfer

coefficient with longitudinal pitch variation in a staggered tube bank

ASHRAF ALFANDI

University of Science and Technology, Advanced Nuclear System EngineeringDepartment, 217 Gajeong-Ro Yuseong-Gu, Daejeon, 305-350, Republic of Korea

[email protected]

Young In Kim, Hyungi Yoon, Namgyun Jeong and Juhyeon Yoon

Korea Atomic Energy Research Institute, 989-111 Daedeok-Daero, Yuseong-Gu,

Daejeon, 305-353, Republic of Korea

[email protected], [email protected], [email protected]

The corresponding author: [email protected]

Abstract

In designing compact heat exchangers, the tube bank arrangement is of high

importance since the variation of the longitudinal and transverse pitches affects the

heat transfer and pressure drop in a heat exchanger. Smaller pitches allow a high

performance compact heat exchanger at the expense of a high pressure drop.

Normally, the transverse tube pitch is determined by the given requirement on the

pressure drop limit through the heat exchanger. The longitudinal pitch has a quite

different effect on the heat transfer and pressure drop depending on the in-line and

staggered tube banks, respectively. In this study, the effect on a shell-side heat

transfer coefficient is investigated using the CFD code FLUENT with a variation in

longitudinal pitch to diameter ratio, SL, in the range of 1.15 to 2.6 with a fixed

transverse pitch to diameter ratio. For the benchmark purposes with the available

empirical correlation, typical thermal-hydraulic conditions for the Zukauskas

correlation are assumed. Many sensitivity calculations for different mesh sizes and

turbulent models are performed to check the accuracy of the numerical solution. A

realizable κ -ε turbulence model was found to be in good agreement with results of the

Zukauskas correlation among the other turbulence models, at least for the staggeredtube bank. It was found that the average heat transfer coefficient of a crossflow over a

staggered tube bank calculated using FLUENT is in good agreement with the

Zukauskas correlation-calculated heat transfer coefficient in the range of 1.15 – 2.6.

For a staggered tube bank, using the Zukauskas correlation seems to be valid down to

SL = 1.15.

Keyword: Heat transfer coefficient, staggered tube bank, longitudinal pitch,

crossflow, turbulence model.



1. Introduction

The tube banks within the heat exchanger can be arranged in either staggered or

in-line configurations according to the heat transfer and pressure drop design

optimization analysis. For a compact design of a shell and tube heat exchanger,

longitudinal and transvers pitches are the most important parameters from a thermal

performance optimization point of view. Normally, using a smaller longitudinal pitch

enables more heat transfer area density to be utilized and to design a more compact

heat exchanger, whereas the transverse pitch is determined mainly for meeting a

specified pressure drop requirement of the heat exchanger. In this study, the effect on

a variation of a shell side heat transfer coefficient with the longitudinal pitch variation

in a staggered tube bank is investigated.

1.1 Literature Review

Many researchers have investigated the heat transfer characteristics in tube banks.Pierson [1] and Huge [2] have carried out many experiments on the heat transfer in

in-line and staggered tube arrangements. Colburn [3] proposed an empirical

correlation for the calculation of the heat transfer in a staggered tube bank with more

than ten rows. Grimison [4] has correlated the experimental data done by Pierson [1]

and Huge [2]. Zukauskas [5] suggested empirical correlations to estimate the average

Nusselt number for a tube bank, as a function of Reynolds number and Prandtl

number. Khan [6] developed an analytical model to investigate the heat transfer from

tube banks in a crossflow for both in-line and staggered arrangements. Bassiouny andWilson [7] developed a mathematical model to simulate the laminar and turbulent

flow fields in in-line and staggered tube banks. Kim [8] investigated numerically the

effect of the longitudinal pitch on the heat transfer characteristics of the crossflow

over in-line tube banks. Lee [9] identified the effect of an uneven horizontal pitch in a

tube bank heat exchanger and derived a general correlation that can predict the

individual heat transfer coefficient of each row for an arbitrary longitudinal pitch

distribution. Few researchers have conducted a numerical investigation to study the

effect of longitudinal pitch variation on the crossflow heat transfer of over-staggered

tube banks.

In the present study, the effect of the longitudinal pitch variation on the heat transfer

coefficient of a cross flow over staggered tube banks while fixing the transverse pitch

is investigated numerically using the CFD code FLUENT [10]. The calculation is

modeled as a conjugate heat transfer problem to impose a non-constant wall

temperature boundary condition on the tube surface.

2. Numerical Modeling





In this study, typical thermal hydraulic parameters are taken from typical

once-through steam generator design data [11]. These numerical values just represent

a physically meaningful set of data.

All numerical calculations are performed at a Reynolds number of 8.9×104. Having

known ReD, the maximum velocity can be calculated by

= (3)

In the range of 1.15 – 2.6 of SL, the flow will have a maximum velocity of 1.09 m/s at

the transverse cross section [12] because

√ () ()

(4)

At the inlet boundary, the hot water flow rate is set to 1.59 kg/s and the upstream bulk

temperature is assumed to be constant at 297.4ᵒC. Considering the repeated pattern ofthe flow at the inlet and outlet boundaries, a periodic boundary condition is prescribed.

Because of the symmetry in the upper and lower parts of the computational domain,

symmetric boundary conditions are applied, as shown in figure 2. The working fluid

in the tube side is assumed to have a constant saturation temperature of 255.27ᵒC.

2.2 Mesh generation

Figure 3 Computational grid

An unstructured, the quadrilateral dominant method is used to generate a grid for the

entire computational domain. Two examples of the meshes are shown in figures 3 (a)

and 3 (b) for the two extreme cases at SL = 1.15 and 2.6, having a total number of

elements of 58,040 and 109,615, respectively.

A two-layer model is adapted to treat the wall boundary layer near the wall. Along the

fluid – solid interface boundary, a maximum of 25 inflation layers, are used to have a

maximum y = 2.5×10-6 m at the first grid so that y+ ~ 0.5.

A mesh sensitivity study was conducted by investigating several cases of different

grid numbers, as shown in figure 4. The mesh was continually refined until a variationin the heat transfer coefficient is small enough to be 0.15 %.





results also demonstrate that, as the longitudinal pitch-to-diameter ratio, SL, decreases,

the flow speed becomes larger, and thus the heat transfer coefficient increases, as

shown in figure 5.

Figure 5 FLUENT – calculated heat transfer coefficient at different turbulence models

3.2 local heat transfer coefficient

The velocity contour in figure 6 shows that, for tube banks with a smaller longitudinal

pitch, the fluid velocity impinging on the tube surface is higher compared to that of a

widely spaced tube bank case. This high-speed impinging fluid velocity makes the

boundary layer thickness on the head-on spot thinner in the smaller longitudinal pitch

case. The thinner laminar boundary layer manifests the higher local heat transfer

coefficient at the head-on spot, as shown in figure 7.

Figure 6 Flow velocity contour for different pitches

14000

15000

16000

17000

18000

19000

20000

21000

22000

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

H e a t t r a n s f e r c o e f f i c i e n t W m ² - K

Longitudinal pitch to diameter ratio variation

Zukausckas

Realizable K-epsilonSST k-omega

RNG k-epsilon

Standard k-epsilon





Figure 8 Wall temperature profile for different pitches

4. Conclusion

In the present study, a numerical model was developed to study the effect of

longitudinal pitch variation on the shell-side heat transfer coefficient of a crossflow

over a staggered tube bank. Many sensitivity studies were performed including

different numbers of meshes and turbulence models to minimize the numerical

simulation uncertainties. The Realizable κ -ε turbulence model was found to be in

good agreement with the results of the Zukauskas correlation among the other

turbulence models for a staggered tube bank case. The conjugate heat transfer

principle is applied where the wall thickness is modelled as a separate tube metal zone.

The heat transfer coefficient increases as the longitudinal pitch decreases owing to the

increased fluid velocity and turbulence. The profile of the calculated heat transfer

coefficient was found to be in a good agreement with the Zukauskas correlation heat

transfer coefficient in the longitudinal pitch-to-diameter ratio range of 1.15 – 2.6. For

a staggered tube bank, using the Zukauskas correlation seems to be valid down to SL

= 1.15.

5. Acknowledgement

This work has been carried out under the auspices of the Jordan Research and

Training Reactor Project being operated by Korea Atomic Energy Research Institute.

6. References

1. O. L. Pierson, Experimental investigation of the influence of tube arrangement on

convective heat transfer and flow resistance in cross flow of gases over tube banks,

ASME 59, 563-572 (1937).

2. E.C. Huge, Experimental investigation of effects of equipment size on convection

heat transfer and flow resistance in cross flow of gases over tube banks, ASME,59, 573-581 (1937).

276

278

280

282

284

286

288

290

0 30 60 90 120 150 180

T e m p e r a t u r e ( ᵒ C

)

Angle (ϕ)

SL = 1.15

SL = 2.6



3. A.P. Colburn, A method of correlating forced convection heat transfer data and a

comparison with fluid friction, Trans. Am. Inst. Chem. Eng. 29, 174-210 (1933).

4. E.D. Grimison, Correlation and utilization of new data on flow resistance and

heat transferfor cross flow of gases over tube banks, ASME 59, 583-594 (1933).

5. A.A. Zukauskas, Heat Transfer from Tubes in Crossflow, Adv. Heat Transfer 8,

93-160 (1972).

6. W.A. Khan, J.R. Culham, M.M. Yovanovich, Convection heat transfer from tube

banks in cross flow: Analytical approach, Int. J. Heat Mass Transfer 49,

4831-4838 (2006).

7. M. Khalil Bassiouny, A. Safwat Wilson, Modeling of heat transfer for flow across

tube banks, Chem. Eng. Process 39, 1-14 (2000).

8. T. Kim, Effect of longitudinal pitch on convective heat transfer in crossflow over

in-line tube banks, Ann. Nucl. Energy 57, 209-215 (2013).9. D. Lee, A. Joon, S. Shin, Uneven longitudinal pitch effect on tube bank heat

transfer in cross flow, Appl. Them. Eng 51, 937-947 (2013).

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computer code, ONCESG, for thermal-hydraulic design of a once-through steam

generator, J. Nucl. Sci. Technol 37, 445-454 (2000)

12. F. Kreth, M.S. Bohn, Principles of heat transfer (Books/Cole, Thomas Learning,

2001).13. B.E. Launder, D.B. Spalding, Lectures in mathematical models of turbulence.

(Academic Press, 1982).

14. T.-H. Shih, W.W. liou, A. Shibber, Z. Yang, J. Zhu, A new κ -ε eddy-viscosity model

for high reynolds number turbulent flows-Model development and validation,

Computer Fluids 24, 227-238 (1995).

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turbulent models for shear flows by a double expansion technique, phys. Fluids A

4, 1510-1520 (1992).

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Heat transfer in staggered tube banks