Sensitivity study on the variation of a shell side heat transfer coefficient

8/13/2019 Sensitivity study on the variation of a shell side heat transfer coefficient

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a Corresponding author: [email protected]

Sensitivity study on the variation of a shell side heat transfer coefficientwith the longitudinal pitch variation in a staggered tube bank

ASHRAF ALFANDI 1, Young In Kim 2, Hyungi Yoon 2, Namgyun Jeong 2 and Juhyeon Yoon 2,a

1University of Science and Technology, Advanced Nuclear System Engineering Department, 217 Gajeong-Ro Yuseong-Gu, Daejeon, 305-350, Republic of Korea2Korea Atomic Energy Research Institute, 989-111 Daedeok-Daero, Yuseong-Gu, Daejeon, 305-353, Republic of Korea

Abstract . In designing compact heat exchangers, tube bank arrangement are of high importance since thevariation of the longitudinal and transverse pitches affects the heat transfer and pressure drop in a heatexchanger. Smaller pitches allow a high performance compact heat exchanger at the expense of a high pressuredrop. Normally the transverse tube pitch is determined by a given requirement on the pressure drop limitthrough the heat exchanger. The longitudinal pitch has a quiet different effect on heat transfer and pressuredrop depending on the in-line and staggered tube banks, respectively. In this study, the effect on a shell-sideheat transfer coefficient is investigated using the CFD code FLUENT with variation of a longitudinal pitch todiameter ratio, S L, in the range from 1.15 to 2.6 with a fixed transverse pitch to diameter ratio. For the

benchmark purpose with the available empirical correlation, typical thermal-hydraulic conditions for theZukauskas correlation are assumed. Many sensitivity calculations for different mesh sizes and turbulent modelsare performed to check the accuracy of the numerical solution. Realizable - turbulence model is found to bein good agreement with results of the Zukauskas correlation among the other turbulence models, at least for thestaggered tube bank. It was found that the average heat transfer coefficient of a crossflow over a staggered tube

bank calculated by using the FLUENT is in good agreement with the Zukauskas correlation-calculated heattransfer coefficient in the range of 1.15 2.6. For the staggered tube bank, using the Zukauskas correlationseems to be valid down to S L = 1.15.

Keywords : Heat transfer coefficient, staggered tube bank, longitudinal pitch, crossflow, turbulence model.

Nomenclatures

D diameter of tubePT transverse pitchPL longitudinal pitchST transverse pitch to diameter ratioSL longitudinal pitch to diameter ratioUmax maximum velocityRe Reynolds number

Nu Nusselt numberPr Prandtl numberPr w Prandtl number at the wall condition

Greek dynamic viscosity density turbulence kinetic energy turbulence dissipation rate specific dissipation rate

1 Introduction

The tube banks within heat exchanger can be arranged ineither staggered or in-line configurations according to theheat transfer and pressure drop design optimizationanalysis. For a compact design of a shell and tube heat

exchanger, longitudinal and transvers pitches are the mostimportant parameters in the thermal performanceoptimization point of view. Normally, using the smallerlongitudinal pitch enables to utilize more heat transferarea density and to design more compact heat exchangerwhereas the transverse pitch is determined mainly formeeting a specified pressure drop requirement of the heatexchanger. In this study, investigated is the effect on avariation of a shell side heat transfer coefficient with thelongitudinal pitch variation in a staggered tube bank.

1.1 Literature Review

Many researchers have investigated the heat transfercharacteristics in tube banks. Pierson [1] and Huge [2]have carried out many experiments on the heat transfer inin-line and staggered tube arrangements. Colburn [3] has

proposed an empirical correlation for the calculation ofheat transfer in a staggered tube bank with number ofrows more than ten. Grimison [4] has correlated theexperimental data done by Pierson [1] and Huge [2].Zukauskas [5] has suggested empirical correlations toestimate the average Nusselt number for a tube bank, as a

function of Reynolds number and Prandtl number. Khan[6] has developed an analytical model to investigate theheat transfer from tube banks in crossflow for both in-lineand staggered arrangements. Bassiouny and Wilson [7]


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Experimental Fluid Dynamics 2013

have developed a mathematical model to simulate thelaminar and turbulent flow fields in in-line and staggeredtube banks. Kim [8] has investigated numerically theeffect of the longitudinal pitch on the heat transfercharacteristics of crossflow over in-line tube banks. Lee[9] has identified the effect of an uneven horizontal pitch

in a tube bank heat exchanger and derived a generalcorrelation that can predict the individual heat transfercoefficient of each row for an arbitrary longitudinal pitchdistribution. But none of the researchers has conducted anumerical investigation to study the effect of thelongitudinal pitch variation on the heat transfer ofcrossflow over staggered tube banks.

In the present study, the effect of the longitudinal pitch variation on the heat transfer coefficient of crossflow over staggered tube banks while fixing thetransverse pitch is investigated numerically using theCFD code FLUENT [10]. The calculation is modelled asa conjugate heat transfer problem to impose non constant

wall temperature boundary condition on the tube surface.

2 Numerical modelling

2.1 Geometry and boundary conditions

Figure 1 shows a staggered tube bank that has transverseand longitudinal pitches. The transverse and longitudinal

pitch to tube diameter ratios, S T and S L, respectively, aredefined as

(1)

(2)

To study the effect of the longitudinal pitch variation,the longitudinal pitch to diameter ratio S L is changed inthe range of 1.15 2.6, but the transverse pitch todiameter ratio S T is kept constant at 1.4. Tube diameter,D, is set to 1.0 cm (see figure 1 below.)

Figure 1. Cross-sectional view of the tube bundle with thedefinition of geometrical parameters

The red-dotted box shown in figure 1 represents a twodimensional computational domain used in this study. Tosolve as a conjugate heat transfer problem, the three solid

regions shown in figure 2 are modelled to describe thetube metal thickness of 1.5 10 -5 m.

Figure 2. Computational domain and Boundary conditionsIn this study, typical thermal hydraulic parameters are

taken from a typical once-through steam generator designdata [11]. These numerical values just represent a

physically meaningful set of data.All numerical calculations are performed at a

Reynolds number equals 8.9 10 4. Having known theRe D, the maximum velocity can be calculated by

(3)In the range of 1.15 2.6 of S L, The flow will have

the maximum velocity of 1.09 m/s at the transverse crosssection [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 assumedto be constant at 297.4C. Considering the repeated

pattern of the flow at the inlet and outlet boundaries, a

periodic boundary condition is prescribed. Because of thesymmetry in the upper and lower part of thecomputational domain, symmetric boundary conditionsare applied as shown in figure 2. The working fluid in thetube side is assumed to have a constant saturationtemperature of 255.27C.

2.2 Mesh generation

Figure 3 . Computational gridAn unstructured, Quadrilateral dominant method is usedto generate a grid for the entire computational domain.Two examples of the meshes are shown in the figure 3 (a)and (b) for the two extreme cases at S L = 1.15 and 2.6,having a total number of elements 58040 and 109615,respectively.

A two-layer model is adapted to treat the wall boundary layer near the wall. Along the fluid solidinterface boundary, a maximum 25 inflation layers, as

PT = 1.4 10-2 m

PL

D = 10 -2 m


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seen in figure 4, are used to have maximum y = 2.5 10 -6 m at the first grid so that y+ ~ 0.5.

Figure 4 . Fluid solid interface boundary fine grid resolution

Mesh sensitivity study was conducted byinvestigating several cases of different grid numbers, asshown in the figure 5. The mesh was continually refineduntil the variation in the heat transfer coefficient is smallenough to be 0.15 %.

Figure 5. Mesh sensitivity studyFor pressure-velocity coupling, the SIMPLE algorithmhas been utilized. A second order upwind scheme has

been applied for convection terms of mass, momentumand energy conservation equations. All the calculationsare considered to be converged when the heat transfer

coefficient and mass flow rate reach a steady state value.

3 Results and discussion

3.1 Average heat transfer coefficient andturbulence model effect

For the purpose of benchmarking, the Zukauskascorrelation [5] has been used to estimate the heat transfercoefficient at different longitudinal pitch to diameterratios in the range of 1.15 2.6. The Zukauskascorrelation is as follow for a staggered tube bank:

(5)

where the subscript w means that the fluid property is to be evaluated at the tube wall temperature/ Other fluid properties are to be evaluated at the bulk fluidtemperature . Figure 6 shows results of the sensitivitystudy on the variation of the average heat transfercoefficient for different turbulence models including the

standard - [13], Realizable - [14], Re-NormalizationGroup (RNG) - [15], and SST -. The results of thesensitivity study demonstrate that the Realizable -turbulence model gives the same variation trend of theaverage heat transfer coefficient with that of theZukauskas correlation. In the staggered tube banks, theadverse pressure gradient field is not dominant, and theSST - turbulence model over-predicts the heat transfercoefficient values compared with the values of theZukauskas correlation [12]. The results also demonstratethat, as the longitudinal pitch to diameter ratio, S L, decreases, the flow speed becomes larger and thus theheat transfer coefficient increases, as shown in the figure

6.

Figure 6 . FLUENT calculated heat transfer coefficient atdifferent turbulence models

3.2 local heat transfer coefficient

The velocity contour in figure 7 shows that, for tube banks with smaller longitudinal pitch, the fluid velocityimpinging on the tube surface is higher compared to thatof widely spaced tube bank case. This high speedimpinging fluid velocity makes the boundary layerthickness on the head-on spot thinner in the smallerlongitudinal pitch case. The thinner laminar boundarylayer manifests the higher local heat transfer coefficientat the head-on spot as shown in figure 8.

1.60E+04

1.65E+04

1.70E+04

1.75E+04

1.80E+04

1.85E+04

1.90E+04

1.95E+04

2.00E+04

2.05E+04

0 20000 40000 60000 80000 100000 120000

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

- K

)

Grid number

SL = 1.15 SL = 2.6

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

- K

Longitudinal pitch to diameter ratio variation

Zukausckas

Realizable K-epsilon

SST k-omega

RNG k-epsilon

Standard k-epsilon

Solid

Shell-side

Tube-side

Inflationlayers


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Figure 7 . Flow velocity contour for different pitches

Figure 8 shows that the calculated local heat transfercoefficient around the tube surface is largest at thestagnation point located at the upstream region, anddecreases with distance along the tube surface as the

boundary layer thickness increases. The heat transfercoefficient reaches its minimum value after the separation

point. Beyond the separation point the local heat transfercoefficient decreases. But at the rear portion of the tube,the heat transfer coefficient increases again because ofthe considerable fluid sweeping phenomena byalternative periodic vortex shedding eddies over the rear.[16]

Figure 8 . Local heat transfer coefficient

As seen in the figure 8 above, the heat transfer to thetube is not uniform around the tube surface which meansthat it is physically not correct to assume the constantwall temperature boundary condition for the shell-sidesurface. In order to take this issue into account, all thecalculations are performed as a conjugate heat transfer

problem. Figure 9 shows that the shell-side surfacetemperature is changing around the tube surface ratherthan being constant. It is noticeable that the localtemperature profile around the tube has the same trend asthe heat transfer coefficient shown in the figure 8.

Figure 9. Wall temperature profile for different pitches

4. Conclusion

In the present study, a numerical model has beendeveloped to study the effect of longitudinal pitchvariation on the shell-side heat transfer coefficient of acrossflow over a staggered tube bank. Many sensitivitystudies are performed including different number ofmeshes and turbulence models to minimize the numericalsimulation uncertainties. Realizable - turbulence modelis found to be in good agreement with results of theZukauskas correlation among the other turbulence modelsfor a staggered tube bank case. The conjugate heattransfer principle is applied where the wall thickness ismodelled as a separate tube metal zone. Heat transfercoefficient increases as the longitudinal pitch decreasesdue to the increased fluid velocity and turbulence. The

profile of the calculated heat transfer coefficient is foundto be in a good agreement with the Zukauskas correlationheat transfer coefficient in the longitudinal pitch todiameter ratio range of 1.15 2.6. For the staggered tube

bank, using the Zukauskas correlation seems to be validdown to S L = 1.15.

4 Acknowledgement

This work has been carried out under the auspices of theJordan Research and Training Reactor Project beingoperated by Korea Atomic Energy Research Institute.

5 References

1. O. L. Pierson, Experimental investigation of theinfluence of tube arrangement on convective heattransfer and flow resistance in cross flow of gasesover tube banks , ASME 59 , 563-572 (1937).

2. E.C. Huge, Experimental investigation of effects ofequipment size on convection heat transfer and flowresistance in cross flow of gases over tube banks ,ASME, 59 , 573-581 (1937).

3. A.P. Colburn, A method of correlating forcedconvection heat transfer data and a comparison with

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

0.0E+00

5.0E+03

1.0E+04

1.5E+04

2.0E+04

2.5E+04

3.0E+04

3.5E+04

0 30 60 90 120 150 180

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 )

Angle ( )

SL = 1.15SL = 2.6

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

( C )

Angle ( )

SL = 1.15

SL = 2.6


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4. E.D. Grimison, Correlation and utilization of newdata 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 inCrossflow , 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 Transfer49 , 4831-4838 (2006).

7. M. Khalil Bassiouny, A. Safwat Wilson, Modeling ofheat transfer for flow across tube banks , Chem. Eng.Process 39 , 1-14 (2000).

8. T. Kim, Effect of longitudinal pitch on convectiveheat transfer in crossflow over in-line tube banks ,Ann. Nucl. Energy 57 , 209-215 (2013).

9. D. Lee, A. Joon, S. Shin, Uneven longitudinal pitcheffect on tube bank heat transfer in cross flow , Appl.Them. Eng 51 , 937-947 (2013).

10. Inc. Fluent, Fluent Users Guide (2006).11. J. Yoon, J.-P. Kim, H.-Y. Kim, D. J. Lee, M. H.Chang, Development of a 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 inmathematical models of turbulence. (AcademicPress, 1982).

14. T.-H. Shih, W.W. liou, A. Shibber, Z. Yang, J. Zhu, A new - eddy -viscosity model for high reynolds

number turbulent flows-Model development andvalidation, Computer Fluids 24 , 227-238 (1995).

15. V. Yakhot, S.A. Orszag, S. Thangma, T.B. Gatski,S.G. Speziale, Development of turbulent models for

shear flows by a double expansion technique , phys.Fluids A 4, 1510-1520 (1992).

16. J.E. Bardina, P.G. Huang, T.J. Coakley, Turbulencemodelling validation, testing, and development.

NASA TM 110446 , (1997).

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Sensitivity study on the variation of a shell side heat transfer coefficient