Flow and heat transfer performances of helical baffle heat exchangers with different baffle configurations

Applied Thermal Engineering 80 (2015) 328e338

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research paper

Flow and heat transfer performances of helical baffle heat exchangers with different baffle configurations Cong Dong a, b, Ya-Ping Chen a, *, Jia-Feng Wu a a b

School of Energy and Environment, Southeast University, Nanjing 210096, China School of Mechanical and Automotive Engineering, Zhejiang University of Science and Technology, Hangzhou 310023, China

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


Flow and thermal performances of four helical baffle heat exchangers are simulated.
Special slices are constructed to obtain pressure and velocity nephograms.
Local heat flux on tubes T1eT9 and tube layers N1eN4 is analyzed.
Second flow and V-notch leakage are clearly depicted.
20 TCO scheme shows the strongest competition with an anti-shortcut structure.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 April 2014 Accepted 28 January 2015 Available online 7 February 2015

The flow and heat transfer performances of four helical baffle heat exchangers were numerically simulated. The exchangers exhibited an approximate spiral pitch and different configurations, i.e., a trisection circumferential overlap baffle scheme with a baffle incline angle of 20 (20 TCO), a quadrant circumferential overlap baffle scheme with a baffle incline angle of 18 (18 QCO), a quadrant end-to-end baffle scheme with a baffle incline angle of 18 (18 QEE), and a continuous helical baffle scheme with a baffle helical angle of 18.4 (18.4 CH). Velocity vectors superimposed pressure nephogram for meridian slice M1, transverse slices f and f1, and superimposed velocity nephogram for unfolded concentric combination slices CS2 and CS3 are presented. The heat transfer enhancement mechanisms of secondary flow were analyzed. Curves describing the local average heat fluxes of heat transfer tubes T1eT9 within a 60 sector region and those of concentric heat transfer tube layers N1eN4 are presented. The results show that the 20 TCO scheme possesses the best market application value for its highest shell-side heat transfer factor jo and average comprehensive index (jo/fo). The 18.4 CH scheme performs difficulty in manufacturing with continuous helical baffle but exhibits the worse performances in terms of jo and (jo/fo). © 2015 Elsevier Ltd. All rights reserved.

Keywords: Helical baffle heat exchanger Trisection configuration Quadrant configuration Continuous configuration Circumferential overlap configuration Secondary flow

1. Introduction

* Corresponding author. Tel.: þ86 13851729402. E-mail address: [email protected] (Y.-P. Chen). http://dx.doi.org/10.1016/j.applthermaleng.2015.01.070 1359-4311/© 2015 Elsevier Ltd. All rights reserved.

Shell-and-tube heat exchangers are robust in handling hightemperature and high-pressure media fluids and flexible in meeting almost any process requirement. Thus, these exchangers are widely used in, for instance, petroleum refining, chemical

C. Dong et al. / Applied Thermal Engineering 80 (2015) 328e338

engineering, power plants, and food processing, and most are of the segment baffle type, which has many advantages, such as simple structure, ease of manufacturing, convenient installation and advanced design. However, segment baffle type heat exchangers have many fatal drawbacks, including stagnant zones with lower heat transfer coefficients, higher pressure drops, and a propensity to induce vibration and fouling. These weaknesses could be solved by applying the innovative design of quadrant helical baffle heat exchangers. Since the advent of quadrant helical baffle heat exchangers, many researchers have studied this novel type of heat exchanger, and most studies have focused on the optimum incline angle or helical angle of the sector baffles and the configurations of adjacent baffles. Lutcha et al. [1] predicted that the shell-side flow pattern in helical baffle heat exchangers is very close to that of plug flow. They also indicated that the optimum helical angle of the sector baffles is 40 and that the segment baffle scheme is the worst in terms of the behavior exhibited by the shell-side heat transfer coefficient versus pressure drop. Kral et al. [2] examined five helical baffle heat exchanger schemes and a segmental baffle scheme through waterto-water heat transfer performance experiments. Stehlik et al. [3] reviewed three helical baffle arrangements, finally they concludes that axial overlap baffles can counter to minimize the bypass stream at adjacent baffles and reduce the tube support spans. Andrews et al. [4] developed a three-dimensional CFD method based on the distributed resistance concept as well as volumetric porosity and surface permeability to simulate flow and heat transfer in helical baffle exchangers. The simulation results were compared with experimental value, which showed good agreement. Zhang et al. [5] experimentally measured the shell-side flow and heat transfer characteristics of a series of middle overlapped quadrant helical baffle heat exchangers and found that the best scheme is the one with an inclined angle of 30 . However, the four schemes of helical heat exchangers tested were of different tube lengths and cylinder diameters. Nevertheless, Nemati Taher et al. [6] numerically examined five helical baffle heat exchangers of 40 inclined angles with different baffle spaces and found the comprehensive index decreases with the increase in the axial overlap size. Because the quadrant baffle scheme is more suitable for use with square tube layouts, Chen et al. [7] proposed circumferential overlap trisection helical baffle heat exchangers for the most commonly used equilateral triangle tube layout, and the anti-shortcut baffle structure by widening the straight edges of the sector baffles with one row of tubes in the triangular area of adjacent baffles can effectively improve the heat transfer performance. Several waterewater heat transfer performance tests [8] demonstrated that the circumferential overlap trisection scheme with an inclined angle of 20 is better than the segmental baffle scheme in terms of both the shell-side heat transfer coefficient and the shell-side heat transfer coefficient per unit pressure drop for four single thread schemes with baffle inclined angles of 20 , 24 , 28 , and 32 and a dual thread scheme with a baffle inclined angle of 32 . With respect to continuous helical baffle heat exchangers, Peng et al. [9] and Wang et al. [10] experimentally studied continuous helical baffle heat exchangers compared with the non-continuous helical baffle schemes and segmental ones, and showed that the performance gain of the continuous helical baffle heat exchangers are rather limited. Zeng et al. [11] experimentally studied two continuous helical baffle heat exchangers with middle and tangential inlet/outlet, and found these two schemes performed worse than both schemes of the quadrant helix baffles and segment baffles in terms of comprehensive index. As the question what kind of baffle conjunction structure of helical baffle heat exchangers performs better, thus the question still remains [12e20]. Which schemes perform better, the

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continuous helical baffle scheme or the non-continuous scheme? The trisection baffle scheme or the quadrant baffle scheme? In this study, four helical baffle heat exchangers, such as 20 TCO, 18 QCO, 18 QEE (adjacent baffles touch at the perimeter) and 18.4 CH were compared. The heat exchangers exhibited an identical equilateral triangle tube layout and approximate spiral pitch with different baffle shapes and assembly configurations. 2. Computation model 2.1. Physical model The sample of whole geometric model for 20 TCO scheme with shell-side flow field and four kinds of baffle configurations are shown in Fig. 1. The detailed geometric parameters of four helical baffle heat exchangers are listed in Table 1. The computational domain of the helical baffle heat exchanger is simplified with only 34 heat transfer tubes, 3 rods, 10 groups of helical baffle cycle, one shell, and inlet or outlet nozzles for both shell and tube sides, as shown in Fig. 1(a). The 3D schematics of four studied baffle configurations for 20 TCO, 18 QCO, 18 QEE and 18.4 CH schemes are shown in Fig. 1(b)e(e), respectively. The TCO scheme is a design with an equilateral triangle tube layout exhibiting an anti-shortcut structure, and the straight edges of each sector baffle cut between tube rows, whereas those of both the QCO and QEE schemes are lined with partial holes, which makes the manufacture of the baffles complicated. The difficulty in manufacturing continuous helical baffles is clear, not only in forming the curve shaped of the baffles but also in drilling the holes. 2.2. Control equations [6,21e25] The computational domain of studied four helical baffle heat exchangers are numerical simulated by using commercial CFD code of software FLUENT. The conservation equations for mass, momentum and energy are stated as Equations (1)e(3). Continuity equation:

vr vðruÞ vðrvÞ vðrwÞ þ þ þ ¼0 vt vx vy vz

(1)

Momentum equations:

x  momentum

y  momentum

z  momentum

vðruÞ vp vtxx vtyx vtzx þ divðruUÞ ¼  þ þ þ þ Fx vt vx vx vy vz (2a)

vðrvÞ vp vtxy vtyy vtzy þ divðrvUÞ ¼  þ þ þ þ Fy vt vy vx vy vz (2b)

vðrwÞ vp vtxz vtyz vtzz þ divðrwUÞ ¼  þ þ þ þ Fz vt vz vx vy vz (2c)

Energy equation:


 vðrTÞ l þ divðrUTÞ ¼ div gradT þ ST vt Cp

(3)

The RNG keε turbulent viscosity model is applied to simulate fluid flow and heat transfer for helical baffle heat exchangers. The

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Fig. 1. Geometric model of helical baffle heat exchanger and four baffle structures thereof. (a) Geometric model and flow field of helical baffle heat exchanger, (b) 20 TCO scheme, (c) 18 QCO scheme, (d) scheme 18 QEE, (e) 18.4 CH scheme.

characteristics of “high streamline curvature” and “effect of swirl on turbulence” can help make the accuracy of calculation effectively improved. The RNG keε equations are as follows: Turbulent kinetic energy:

v v v ðrkÞ þ ðrkui Þ ¼ vt vxi vxj

ak meff

vk vxj

! þ Gk þ rε

(4)

Turbulent dissipation energy:

! vε ε ε2 aε meff þ C1ε Gk  C2ε r vxj k k
 εhGk 1  h=h o    k 1 þ bm3 h¼

(5)

qffiffiffiffiffiffiffiffiffiffiffiffiffi 2Sij Sij

Baffle shape Incline angle of baffle ( ) Inner diameter of shell (mm) Inner diameter of nozzle (mm) Projection diameter of baffle (mm) Baffle configuration Thickness of baffle (mm) Outer diameter of heat transfer tube (mm) Tube pitch (mm) Effective length of tubes and rods (mm) Helical baffle pitch (mm) Tube layout pattern

18 QCO 18 QEE

18.4 CH

Trisection sector Quadrant sector 20 18 18 F126 F126 F126

Continuous 18.4 F126

F40

F40

F40

F40

F123

F123

F123

F123

Circumferential overlap 3 3 F10 F10

End to end Continuous 3 3 F10 F10

17 1300

17 1300

17 1300

129

129

17 1300

129 129 Equilateral triangle

The above-referenced equations of mass conservation, energy conservation and momentum conservation as well as RNG keε turbulent viscosity can be described as a universal governing equation:

(6)

The heat transfer between hot and cold fluids was calculated by the coupled method, the computation formula can be expressed as Equation (7).

Table 1 Detailed geometric parameters of four baffle configurations of studied helical baffle heat exchangers. 20 TCO

Cm ¼ 0:0845; C1ε ¼ 1:42; C2ε ¼ 1:68; b ¼ 0:012; ho ¼ 4:38; a ¼ 1; aε ¼ 1:3:

divðrUFÞ ¼ divðGF gradFÞ þ SF

v v v ðrεÞ þ ðrεui Þ ¼ vt vxi vxj

where, meff ¼ m þ mt ; mt ¼ rCm k2 =ε; Gk ¼ 2mt Sij Sij ; k=ε; Sij ¼ 1=2ððvui =vxj Þ þ ðvuj =vxi ÞÞ.

The empirical constants for RNG keε turbulent viscosity model are assigned the following values:

  tw jb ¼ tf  ; b


  vt ¼ ho tw  tf k vn

(7)

where, U is the velocity vector, F is universal variable representing temperature T, velocity components u, v, w as well as turbulence parameters k and ε; u is horizontal component velocity; v is vertical component velocity; w is axial component velocity; t is shear stress; Gk is the generation of turbulence kinetic energy due to the mean velocity gradients; Sij is mean rate of strain tensor; mt is the turbulent viscosity; m is dynamic viscosity; b is coefficient of thermal expansion; x is x direction of position co-ordinates; y is y direction of position co-ordinates; z is z direction of position coordinates; GF and SF are generalized diffusion coefficient and generalized source term respectively; tw and tf are temperatures of both tube wall and fluid, respectively; ho is shell-side heat transfer coefficient; the subscript b is the interface between wall and fluid. 2.3. Boundary conditions For simplicity, isothermal conditions are usually adopted as the boundary conditions in conventional numerical simulations of the heat transfer tubes of heat exchangers. To make the simulation more closely approximate the heat exchanger conditions, convection heat transfer on both sides of the heat exchanger is considered in this paper.

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The working fluids within the shell and tube sides are water and incompressible, which are taken as steady and in the turbulent state. The shell-side fluid is in fully developed except the inlet and outlet cycles owing to the influence of nozzles. For the purpose of simplifying the computation, no-penetration and no-slip boundary are adopted at all wall surfaces, the outer wall of shell is assumed to be adiabatic with the heat flux is 0 kW m2, the leakage between baffle holes and tubes is ignored, the thickness of heat transfer tubes is neglected but the tube walls are still impermeable. For the purpose of improving the accuracy of calculation, the coupled thermal boundary is set for the tube walls, baffle walls and rod walls. The velocity inlet boundary conditions was served for the nozzles of shell side and tube side with the constant velocity and temperature set to Vo, in ¼ 2.82 m/s and To, in ¼ 324.9 K for the shellside cold water, corresponding to a flow rate of Go ¼ 3.57 kg/s and are set to Vi, in ¼ 1.37 m/s and Ti, in ¼ 339.4 K for the tube-side hot water and are assumed to be uniform distributions. The pressure outlet boundary conditions are applied on outlets of shell side and tube side, the pressure values of outlets are set to 0 Pa (gauge pressure). Thermo-physical properties of water are all expressed as fourth-order polynomial functions of temperature. 2.4. Grid independence Three-dimensional models of the helical baffle heat exchangers were created and calculation grids were generated by the GAMBIT software program. Because the post-processing software FLUENT is more suitable for unstructured grids, the discretization of the entire computational domain was performed by adopting unstructured tetragonal-hybrid elements of the Tgrid type for the geometric model of the heat exchangers. To maintain the grid skewness of 0.8, the smooth/swap command should be run before calculation. The grids adjacent to the tube wall were refined, and non-uniform grids were used to improve the calculation accuracy of the boundary layer, with the boundary layer effects of fluid flow taken into account, as shown in Fig. 2. The convergence of the calculations met the following requirements: 1) the residual values of u, v, w, k, and ε in the continuity equations and the energy variables in the energy equation were controlled to be less than 104 and 107; 2) the hot and cold side pressures at the inlet of the heat exchangers reached stable values. Grid independence tests were conducted using four different grid programs, as shown in Fig. 3. The computation of the 2.1  106 grids scheme was divergent. The deviation of the Nusselt number Nuo between the programs featuring a grid number of 3.9  106 and 4.5  106 was within 2% but it between the 3.2  106 and 3.9  106 was more than 5% at the same shell-side mass flow rate. Consequently 3.9  106 grids scheme is selected as computational program at last.

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Fig. 2. Grid schematic of 20 TCO scheme.

angle of 32 , and one segment baffle heat exchanger (seg) [8]. The deviations of the all six schemes are within 30% to þ20% and the variation tendencies of the curves for simulation values are in satisfactory agreement with experimental values. Generally speaking, the flow and heat transfer performances for the model of 20 TCO scheme are acceptable and credible. 2.6. Date reduction The overall heat transfer coefficient K is defined based on

K¼

ðQ1 þ Q2 Þ=2 ADtm

(8)

where Q1 and Q2 are heat transfer rates at tube-side and shell-side, respectively; A is the heat transfer area based on the outer diameter of tube; Dtm is logarithmic mean temperature difference; The tube-side heat transfer coefficient hi is obtained by DittuseBoelter equation, it is

hi ¼ 0:023

li 0:8 0:3 Re Pri di i

(9)

where li the is thermal conductivity of tube-side fluid; di is the inner diameter of tube; Rei is the tube-side Reynolds number; Pri is the Prandtl number of tube-side fluid.

2.5. Validation of results Fig. 4 gives the curves of the shell-side heat transfer coefficient and the shell-side pressure for the 20 TCO scheme. It is clearly seen that the simulation variability are agree with the measurements [8]. The average and maximum errors of the shell-side heat transfer coefficient are 26.56% and 14.88% as well as the average and maximum errors of the shell-side pressure drop 9.96% and 26.27%. To verify the accuracy and reliability of the numerical simulation, Fig. 5 shows the deviations of the shell-side heat transfer coefficient and the shell-side pressure drop between simulation variability and measurements for five circumferential overlap trisection helical baffle heat exchangers with single thread baffle incline angles of 20 , 24 , 28 , 32 and double thread baffle incline

Fig. 3. Shell-side Nusselt number Nuo versus shell-side flow rates Go for different grid programs.

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Pro is the Prandtl number of shell-side fluid; DPo is the shell-side pressure drop; L is the length of heat transfer tube; Dh is the shell-side hydraulic diameter. For the shell-side hydraulic diameter Dh and axial velocity of the shell-side fluid wo are determined as follows:

" pffiffiffi # 2 3 2 ða=do Þ  1 do Dh ¼ p wo ¼

4Go  pro D2s  Nd2o

(13)

(14)

where a is the distance between the centers of two adjacent tubes; Ds is inner diameter of shell; N is the total number of heat transfer tubes and pulling rods. Fig. 4. Comparison of simulated and measured results for the circumferential overlap scheme.

3. Numerical simulation results The shell-side heat transfer coefficient ho can be isolated from Wilson plot technique by using the overall heat transfer coefficient K and the tube-side heat transfer coefficient hi. It can be calculated as follows:

1

ho ¼

1 K



do di hi


 do do  2l ln d w

(10)

i

where lw is the thermal conductivity of tube wall; do is the outer diameter of tube. The shell-side heat transfer factor jo and friction coefficient fo are calculated by

jo ¼

ho ðPro Þ2=3 cp ro wo

(11)

fo ¼

2Dpo Dh ro w2o L

(12)

where cp is the specific heat at constant fluid pressure; ro is the density of shell-side fluid; wo is the axial velocity of shell-side fluid;

The flow and heat transfer of the four helical baffle heat exchanger schemes 20 TCO, 18 QCO, 18 QEE and 18.4 CH were numerically simulated. The four schemes all feature 10 helical cycles from C1 to C10, as shown in Fig. 6. Their inlet parameters of shell and tube sides were set to be identical to the measurements of the circumferential overlap trisection helical baffle shell-and-tube heat exchanger with a baffle incline angle of 20 . The flow and thermal performances of helical baffle heat exchangers are usually depicted along longitudinal and transverse slices. To provide a more vivid picture of the distribution of the flow pattern in the spiral channel, transverse slices f and f1 and concentric combination slices CS2 and CS3 within the fully developed region within C5eC6 were constructed as shown in Fig. 6. In this figure, slice f is situated at the interface of C5 and C6 and slice f1 is situated at the center of the following baffle plate for the non-continuous baffle schemes or 1/6 of the pitch behind slice f for the continuous baffle schemes; CS2 and CS3 are located in the gaps between concentric tube layers; T1eT9 heat transfer tubes are located along 3 rows in a 60 sector region; and N1eN4 are heat transfer tubes layers whose positions radiate from the axis to the periphery. Fig. 7(a) shows the average velocities along slices aek of the 20 TCO scheme. The average velocities along slices b to j of each scheme remain nearly unchanged, while the values along slices a

Fig. 5. Comparison of simulation results with experiment ones. (a) Shell-side heat transfer coefficient, (b) shell-side pressure drop.

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Fig. 6. Positions of special slices M1, CS2, CS3 f and f as well as tube layers N1eN4 and tube numbers T1eT9 for heat exchangers. (a) 20 TCO scheme, (b) 18 QEE scheme, (c) enlarged figure for M1, (d) left projection view of helical baffle heat exchanger.

and k are affected by the inlet and outlet as well as the structure of the initial and final sections of the heat exchangers. Fig. 7(b) shows the average pressure drops over cycles C1 to C10 of the 20 TCO scheme. The curves showing the average pressure drop as a function of pitch cycle also demonstrate a similar trend. 3.1. Flow and pressure fields The flow field is an important indicator to reflect the performance of a heat exchanger. The shell-side velocity vector distributions within one helical cycle for six schemes are shown in Fig. 8. It is clearly seen that the shell-side fluid flows along spiral channel by the guidance of helical baffles, and there are almost no stagnant zones in shell side of the four schemes. In the 18 QEE schemes, considerable amount of leakage fluid flows through the V-notches between adjacent baffles into the downstream chamber; however, in the circumferential overlap schemes (20 TCO and 18 QCO) the leakage through V-notches was significantly reduced and shell-side spiral flow characteristics were also improved; while in 18.4CH scheme, the velocity vectors distribute uniformly but their strength are the weakest. The velocity vector and pressure distributions are plotted in the same figures, which clearly describe the relationship between the velocity field and pressure field and may provide access to

important implicit information. Figs. 9 and 10 show pressure nephograms with velocity vectors superimposed for the meridian slice M1 and the transverse slices f and f1, respectively, for the four schemes. Guided by the helical baffles, the fluid flows from the high-pressure region to the low-pressure region. As shown, the flow field pattern repeats in each helical cycle, and there are outward flow vectors at the starting section and inward flow vectors at the end section of each cycle chamber. It is clear that the centripetal force of spiral flow drives the flow outward in the starting section, and the radial pressure difference supplies a centripetal force that allows the flow to reach equilibrium; finally, inward flow occurs in the end section of each cycle chamber. Thus, a single vortex secondary flow field is created. The figures show that the 20 TCO scheme has the strongest secondary vortex of the four schemes, which can strengthen the mixing of fluids, reduce the boundary layer thickness, augment the shell-side heat transfer, and prevent the tubes from fouling. The scales of these figures indicate that the 20 TCO scheme exhibits the greatest pressure drop while the 18.4 CH scheme exhibits the smallest pressure drop of the four schemes. Fig. 10 shows that the main fluid flows along the clockwise direction, but there are also flow vectors along the centrifugal, centripetal and other directions. In the sub-figures shown on the

Fig. 7. Average velocity along transverse slices aek and pressure drop within helix cycles C1eC10 of the 20 TCO heat exchanger. (a) Transverse slices aek, (b) helical cycles C1eC10.

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Fig. 8. Shell-side velocity vectors distribution of helical baffle heat exchangers. (a) 20 TCO scheme, (b) 8 QCO scheme, (c) 18 QEE scheme, (d) 18.4 CH scheme.

left-hand side of Fig. 11(a)e(c) in particular, there are reverse flow vectors at the starting line, which indicates that there is reverse leakage flow at the junctions of adjacent baffles. However, the leakage flow in the V-notch zone of the adjacent baffles could not be depicted along the longitudinal section shown in Fig. 9 because the leakage velocity vectors are perpendicular to the plane shown.

To resolve this limitation, concentric combination slices were constructed. Fig. 11 shows the flow fields of the four schemes (20 TCO, 18 QCO, 18 QEE, and 18.4 CH) in velocity vector nephograms of unfolded concentric combination slices CS2 and CS3 including two helical pitch cycles C5 and C6. It is clearly observed that the low-speed zones are mainly on the dorsal side of the

Fig. 9. Pressure nephograms with velocity vectors superimposed for the meridian slice M1 of the four schemes. (a) 20 TCO scheme, (b) 18 QCO scheme, (c) 18 QEE scheme, (d) 18.4 CH scheme.

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Fig. 10. Pressure nephograms on transverse slices f and f1 for four schemes. (a) Slices f (left) and f1 (right) of 20 TCO, (b) slices f (left) and f1 (right) of 18 QCO, (c) slices f (left) and f1 (right) of 18 QEE, (d) Slices f (left) and f1 (right) of 18.4 CH.

baffles, and the average velocity, secondary flow strength, and the V-notch leakage flow on the CS3 slices are much stronger than those on the CS2 slices for all four schemes because the CS3 slices are closer to the axis and the gaps here are larger than those of the CS2 slices. It is clearly shown that the velocity field of the 20 TCO scheme is stronger than that of other schemes. By comparing the leakage patterns at the V-notches of the 18 QCO and 18 QEE

schemes, it is shown that the leakage is restricted in the circumferential overlapped baffles of the 18 QCO scheme. The velocity field in the continuous helical channel of the 18.4 CH scheme is very uniform, and no leakage flow is observed; however, the average velocity of the 18.4 CH scheme is lower than that of the other schemes, and there is very weak secondary flow in the continuous helical channel.

Fig. 11. Velocity vector nephograms of unfolded concentric combination slices CS2 and CS3 of four schemes. (a) Combination slices CS2 (up) and CS3 (down) of 20 TCO scheme, (b) combination slices CS2 (up) and CS3 (down) of 18 QCO scheme, (c) combination slices CS2 (up) and CS3 (down) of 18 QEE scheme, (d) combination slices CS2 (up) and CS3 (down) of 18.4 CH scheme.

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Fig. 12. Local average heat fluxes at a shell-side mass flow rate of Go ¼ 3.57 kg/s. (a) Tubes T1eT9, (b) Tube layers N1eN4.

Fig. 13. Shell-side properties versus shell-side flow rate. (a) Heat transfer factors jo, (b) friction coefficients fo, (c) comprehensive index (jo/fo).

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3.2. Shell-side heat flux

simulated. Different slices were examined to demonstrate the flow field pattern and heat transfer performance. (2) The single vortex secondary flow in each helical cycle was demonstrated on pressure nephograms with velocity vectors superimposed for the meridian slice M1 and the transverse slices f and f1 of the four schemes. The secondary flow can strengthen the mixing of fluids, augment the shell-side heat transfer, and prevent the tubes from fouling. Concentric combination slices were constructed to demonstrate the reverse leakage in the V-notch of adjacent non-continuous helical baffles. It was shown that the leakage is restricted to circumferential overlapped baffles. The 20 TCO scheme exhibits the strongest secondary flow and restricted reverse leakage, whereas the 18.4 CH scheme, which exhibits a lower average velocity and almost no reverse leakage, has very weak secondary flow in the continuous helical channel. (3) The local heat flux of tubes T1eT9 in a 60 sector at a shellside flow rate Go ¼ 3.57 kg/s was presented. The local average heat flux decreases along the radial directions, and the local heat transfer factor of the central tube T1 is significantly higher than that of the external tubes. The local heat flux of the 20 TCO scheme is the highest, and that of the 18.4 CH scheme is the lowest. (4) The heat transfer factor jo and the average comprehensive index (jo/fo) of the 20 TCO scheme are the highest among those the various schemes, and the secondary flow of the 20 TCO scheme is the strongest. Conversely, the heat transfer factor jo and the average comprehensive index (jo/fo) of the 18.4 CH scheme are the lowest, even though the scheme's friction coefficient fo is the lowest and its flow field is uniform without leakage flow. Both the shell-side heat transfer factor jo and friction coefficient fo of the 18 QCO are higher than those of the 18 QEE scheme, whereas the comprehensive index shell-side friction coefficient (jo/fo) of the 18 QCO scheme is lower than that of the 18 QEE scheme.

The local average heat flux is cyclically distributed along the axial and circumferential directions and symmetrically distributed along the baffle centerlines because of the symmetric layout of the heat transfer tubes. In this study, the local average heat fluxes of nine heat transfer tubes T1eT9 within a 60 sector region were investigated. Fig. 12 shows the curves of the local average heat fluxes of tubes T1 to T9 and layers N1 to N4 for the 20 TCO, 18 QCO, 18.4 CH, and 18 QEE schemes at a shell-side flow rate Go ¼ 3.57 kg/ s. The local average heat flux on axis tube T1 or layer N1 is significantly higher than that of the external tubes or layers, and it gradually decreases along the radial direction. From top to bottom, the local average heat flux curves follow the order 20 TCO, 18 QCO, 18 QEE and 18.4 CH. 3.3. Shell-side overall performance and pressure drop characteristics Fig. 13 shows the curves of the shell-side heat transfer factor jo, shell-side friction coefficient fo and the comprehensive index of the shell-side heat transfer factor per unit shell-side friction coefficient (jo/fo) versus the shell-side flow rate Go for the 20 TCO, 18 QCO, 18 QEE, and 18.4 CH schemes. The shell-side heat transfer factor and the comprehensive index (jo/fo) of all of the schemes increase with the shell-side flow rate; however, the gradients of the two quadrant baffle schemes are lower than those of the other two schemes. Moreover, the shell-side friction coefficient decreases with the increase in the shell-side flow rate. Over the calculated mass flow rate range, the shell-side heat transfer factor jo, friction coefficient fo and average comprehensive index (jo/fo) of the 20 TCO scheme are the highest. The shell-side heat transfer factor jo and the friction coefficient fo of the 18 QCO scheme are the second highest, and the scheme's average comprehensive index (jo/fo) is the third highest. Both the shell-side heat transfer factor jo and friction coefficient fo of the 18 QEE scheme are the third highest, and the scheme's average comprehensive index (jo/fo) is the second highest. The 18.4 CH scheme exhibits the lowest shell-side heat transfer factor jo and friction coefficient fo, and its average comprehensive index (jo/fo) is the lowest. The average value of the comprehensive index of 20 TCO scheme is 1.03%, 4.98% and 9.05% higher than the average values observed for the 18 QEE, 18 QCO and 18.4 CH schemes, respectively. Because the capability for heat transfer is the primary metric used in heat exchanger applications, the 20 TCO scheme, which exhibits the highest heat transfer factor jo and is composed of fewer mechanical parts, shows the best heat transfer performance. The 18 QCO and 18 QEE schemes, which feature 25% more baffles but a lower heat transfer factor and comprehensive index than those of the 20 TCO scheme, are clearly inferior to the 20 TCO scheme in terms of market potential. Moreover, the 18.4 CH scheme, which shows great difficulty in manufacturing, exhibits the worst heat transfer performance. This poor performance may be explained by the fact that the surface of the continuous helical channel does not break; thus, the boundary layer thickness is greater, and the scheme has almost no market potential in heat exchanger applications. 4. Conclusions (1) The flow pattern and heat transfer performance for four helical baffle heat exchangers with different baffle configurations (20 TCO, 18 QCO, 18 QEE, and 18.4 CH) and an identical tube layout and helical pitch were numerically

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Acknowledgements This work is supported by the National Natural Science Foundation of China (Nos. 51276035, 51206022) and the Provincial Science and Technology Innovation and Transformation of Achievements of Special Fund Project of Jiangsu Province (BY2011155). Nomenclature A a cp Dh Ds di do fo Go ho ho,

exp

ho,

sim

jo K k L

heat transfer area based on the outer diameter of tube (m2) distance between centers of two adjacent tubes (m) specific heat at constant fluid pressure (J kg1 K1) shell-side hydraulic diameter (m) inner diameter of shell (m) inner diameter of tube (m) outer diameter of tube (m) shell-side friction coefficient shell-side flow rate (kg s1) shell-side heat transfer coefficient (kW m2 K1) experimental value of shell-side heat transfer coefficient (kW m2 K1) simulation value of shell-side heat transfer coefficient (kW m2 K1) shell-side heat transfer factor overall heat transfer coefficient (kW m2 K1) turbulence kinetic energy (m2 s2) length of heat transfer tube (m)

338

N Nuo Pri Pro Q1 Q2 q Rei SF T Ti, in To, in tf tw U u Vi, in Vo, in v w wo

C. Dong et al. / Applied Thermal Engineering 80 (2015) 328e338

total number of heat transfer tubes and pulling rods shell-side Nusselt number tube-side Prandtl number shell-side Prandtl number tube-side heat transfer rate (kW) shell-side heat transfer rate (kW) heat flux (kW m2) tube-side Reynolds number generalized source term temperature (K) inlet temperature of tube-side (K) inlet temperature of shell-side (K) temperature of fluid (K) temperature of tube wall (K) velocity vector (m s1) horizontal component velocity (m s1) inlet velocity magnitude of tube-side (m s1) inlet velocity magnitude of shell-side (m s1) vertical component velocity (m s1) axial component velocity (m s1) shell-side axial velocity (m s1)

Greek symbols generalized diffusion coefficient shell-side pressure drop (kPa) experimental value of shell-side pressure drop (kPa) simulation value of shell-side pressure drop (kPa) logarithmic mean temperature difference (K) ε turbulence kinetic energy dissipation rate (m2 s3) li thermal conductivity of tube-side fluid (kW m1 K1) lw thermal conductivity of tube wall (kW m1 K1) m dynamic viscosity, N s/m2 r density of fluid (kg m3) ro density of shell-side fluid (kg m3) F universal variable

GF Dpo Dpo, exp Dpo, sim Dtm

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