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CHAPTER 4

Shell-and-Tube Heat Exchangers with Helical Baffles

G.D. Chen, M. Zeng, Q.Y. Chen, B.T. Peng & Q.W. WangKey Laboratory of Thermo-Fluid Science and Engineering, MOE, Xi’an Jiaotong University, Xi’an, Shaanxi, China.

Abstract

Helical baffl es are increasingly used to improve the heat transfer performance for shell-and-tube heat exchangers (STHXs) in recent years. In order to make good use of helical baffl es, serial improvements have been made by the group of Novel Heat Transfer Technologies and Compact Heat Exchangers of Xi’an Jiaotong University. In this present chapter, the heat exchangers with discontinuous helical baffl es (DCH), with continuous or combined helical baffl es, and with the helical baffl ed combined multiple (CMH) shell pass are present. Extensive results from experiments and numerical simulations indicate that the helical baffl ed STHXs have better fl ow and heat transfer performance than the conventional segmental baffl ed (SG) STHXs.

Keywords: Heat transfer enhancement; helical baffl e; multiple shell-pass; combine helical baffl e; shell-and-tube heat exchanger

1 Introduction

Heat exchangers play an important role in many engineering processes such as oil refi ning, chemical industry, environmental protection, electric power generation, refrigeration. Among the different types of heat exchangers, the shell-and-tube heat exchangers (STHXs) have been commonly used in industries [1]. It was reported that more than 35–40% of the heat exchangers are of the shell-and-tube type, because of their robust construction geometry as well as easy maintenance and

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90 EMERGING TOPICS IN HEAT TRANSFER

possible upgrades [2, 3]. To meet the special requirements of modern industries, various ways were adopted to enhance the heat transfer performance while main-taining a reasonable pressure drop for the STHXs [4]. One useful method is using baffl es to change the direction of fl ow in the shell side of the STHXs to enhance turbulence and mixing.

For many years, various types of baffl es have been designed, for example, the conventional segmental baffl es with different arrangements, the defl ecting baffl es, the overlap helical baffl es, and the rod baffl es [5–10]. The most commonly used segmental baffl es make the fl uid fl ow in a tortuous, zigzag manner across the tube bundle in the shell side, as shown in Fig. 1. It improves the heat transfer by enhanc-ing turbulence and local mixing on the shell side of heat exchanger. However, the traditional segmental baffl ed STHXs have many disadvantages, such as (1) high pressure drop on the shell side due to the sudden contraction and expansion of fl ow, and fl uid impinging on the shell wall caused by segmental baffl es; (2) low heat transfer effi ciency due to the fl ow stagnation in the so-called stagnation regions, which are located at the corners between baffl es and shell wall; (3) low shell-side mass velocity across the tube bundle due to the leakage between baffl es and shell wall caused by inaccuracy in manufacturing tolerance and installation; (4) short operation time due to the vibration caused by shell-side fl ow normal to tube bundle. When the traditional segmental baffl es are used in STHXs, higher pumping power is often needed to offset higher pressure drop for the same heat load. During the past decades, the defl ecting baffl es, the rod baffl es, and the disk-and-doughnut baffl es have been developed to solve these shortcomings of segmental baffl es. However, none of the above baffl e arrangements can solve all the principal aforementioned problems. New designs are still needed to direct the fl ow in a plug-fl ow manner, to provide adequate support to the tubes, and to have a better thermodynamic performance.

The STHXs with helical baffl es are usually called helixchanger [11–15]. This heat exchanger was invented in Czech Republic and commercially produced by ABB Lummus Heat Transfer [16] (as shown in Fig. 2) with some improved design (as shown in Fig. 3). Helical baffl es offer a possible alternative to segmental baffl es

Figure 1: Flow manner in segmental baffl ed STHX.


SHELL-AND-TUBE HEAT EXCHANGERS WITH HELICAL BAFFLES 91

by circumventing the aforementioned problems of conventional segmental baffl es and are accepted by their outstanding advantages including (1) improved shell-side heat transfer rates/pressure drop ratio; (2) reduced bypass effects; (3) reduced shell-side fouling; (4) prevention of fl ow-induced vibration; (5) reduced mainte-nance. In the past decades, the helixchangers have been continuously developed and improved and have been widely accepted by engineers.

In this chapter, we shall be concerned with some developments and improve-ments conducted on helixchangers, and in particular, with the discontinuous heli-cal baffl es, single-shell-pass continuous helical baffl es and combined helical baffl es, and combined multiple-shell-pass helixangers with continuous helical baffl es, as well as their fl ow and heat transfer performance. Before introducing different types of helical baffl es, there is a separate section that explains the fl ow and heat transfer enhancement mechanism of the helixchangers.

2 Flow and Heat Transfer Enhancement Mechanism of Helixchangers

Compared with segmental baffl ed STHXs, most helical baffl es are formed by four quadrant-shaped plates, as shown in Fig. 4. These plates are arranged at a cer-tain angle to the tube axis in a sequential pattern, creating a helical fl ow path through the tube bundle. The helical fl ow path through the tube bundle provides the necessary characteristics to reduce the fl ow dispersion and generate near plug fl ow conditions necessary for high thermal effectiveness. It also ensures a certain

Figure 2: Structure of helical baffl ed STHX (ABB Lummus).

Figure 3: Structure of STHX with continuous helical baffl es.



Figure 4: Helixchanger tube bundle in fabrication.

Figure 5: Different layouts of discontinuous helical baffl es [17].

amount of crossfl ow to tubes to achieve high heat transfer coeffi cients. Different arrangements of helical baffl es form different constructions of helixchangers (as shown in Fig. 5), that is, baffl es touch at the perimeter, overlapping baffl es, double helical baffl es [17].

2.1 Flow characteristics of helixchangers

Hydrodynamic tests were carried out on a clear plastic heat exchanger model to verify the fl ow characteristics of the helical baffl ed exchanger. Tests were con-ducted with different baffl e arrangements – for the segmental and helical baffl es, the experimental method was based on a standard stimulus–response technique. The stimulus was a delta function (pulse dye tracer injection in inlet shell-side nozzle) and the response was tracer output signal(C curve registered as a change of voltage on photoelectric cell installed in the outlet nozzle). Thus, a residence time distribution was obtained.



Figure 6 shows that the curve for conventional segmental baffl es has a long trail, which indicates that the dead space in the exchanger is large. Its consid-erable deviation from plug-fl ow curve indicates signifi cant amount of back mixing. The curve for helical baffl es approaches of plug fl ow curve more closely, indicating low degree of back mixing. It also shows the nearly negli-gible dead volume in the exchanger. Wang [18] carried an experimental study on the fl ow fi eld of STHXs with helical baffl es using laser Doppler anemom-etry. The experimental results confi rmed that increased turbulence and local mixing occurred due to the induced azimuthal component of the velocity in the shell cross section by the helical baffl es. Numerical studies were also carried out to study the longitudinal component of velocities on discontinuous helical baffl es [19].

2.2 Heat transfer enhancement mechanism of helixchangers

Lutcha and Nemcansky [17] explained that large differences in heat exchanger effectiveness are a result of different fl ow patterns, that is, perfect mixing fl ow and perfect plug fl ow, and this situation is depicted in Fig. 7. They indicated that the perfect plug fl ow has signifi cant advantages in heat transfer than that of per-fect mixing fl ow, because mixing fl ow has substantial reduction of local driving force for heat transfer, that is, the temperature difference between the two fl uids. Therefore, a proper baffl e arrangement should result in a fl ow pattern, which is close to plug fl ow. A comparison of the helical baffl e arrangement and segmental baffl e arrangement approaching plug fl ow conditions was made, and the results suggested that helical baffl e arrangement induced a fl ow pattern more close to the plug fl ow pattern than segmental baffl e arrangement (Fig. 8).

Figure 6: Curves for different baffl e arrangement [17].



Figure 7: Comparison of heat exchanger effectiveness for mixing fl ow and plug fl ow [20].

Figure 8: Heat exchanger effectiveness for segmental baffl es and helical baffl es [20].

Kral et al. [20] reported that the convective heat transfer across a tube bundle decreased with the increasing velocity angle if the free stream was homogenous (Fig. 9a), while the heat transfer coeffi cient on Nusselt number of helical baffl ed heat exchanger was signifi cantly dependent on the helix angle. At small helix angles, the fl ow of working fl uid resembled that of a cross-fl ow. In the range of 25–40°, the heat transfer coeffi cient increases with larger helix angles. Beyond 40°, the Nusselt number drops rapidly (Fig. 9b) [21–23].

The principle of fl ow and heat transfer enhancement mechanism of helixchang-ers can be concluded as follows [17]:

(a) The helical shell-side fl ow approaches the plug fl ow conditions more closely, which results in improved effective MTD due to the reduction of back mixing.

(b) The velocity gradient within the helical fl ow channel favorably affects the boundary layer heat transfer, which contributed to increased heat transfer coef-fi cient.



(c) The smooth helical fl ow passage through the tube bundle eliminates unnecessary pressure losses.

(d) The negligible dead volume within the helical shell space along with uniform shell-side fl ow velocities provides considerably reduced fouling tendencies.

3 STHXs with Di scontinuous Helical Baffles

3.1 Structure of the discontinuous helical baffles

The discontinuous helical baffl es (or overlapped baffl es) are formed by over-lapped fans or oval-shaped plates, each fan or plate occupies certain place of heat exchanger shell cross section and is angled to the axis of heat exchanger. Adja-cent baffl es may touch each other to form a continuous helix at the periphery of outer shell side (Fig. 10). These discontinuous helical baffl es can be manufactured and installed easily in the shell side of STHXs. In the helical baffl ed STHX, the quadrant plates on the shell side can create a close helical fl ow pattern, which has higher conversion of pressure drop to heat transfer on an optimal helix angle.

Figure 9: Ratio of Nusselt numbers versus velocity angle [19].



Besides, this helix-fl ow manner can achieve near-plug fl ow conditions, which can reduce fouling, fl ow-induced vibration signifi cantly, and can prolong the run lengths of working fl uid in the shell side.

3.2 Flow and heat transfer performance

STHXs with discontinuous helical baffl es have better performance than STHXs with segmental baffl es and were proven on test units and in industry applica-tions [24–28]. Actually, fl ow and heat transfer performance of STHXs with discontinuous helical baffl es are greatly affected by many parameters, such as baffl e styles, heat exchange tubes, helical angle, and blocking plates. Lei et al. [29] studied the single-helical baffl es, double-helical baffl es, and segmental baffl es numerically and experimentally and concluded that the double discon-tinuous helical baffl ed STHX had obviously higher heat transfer effectiveness (10%) than that of single ones. Van Der Ploeg and Master [30] reported that large feed/effl uent exchangers were typically designed with a helix angle up to 45° in double helical baffl e arrangement and it had a more effective and fl exi-ble conversion of pressure drop. Besides, the double helical baffl ed tube bundle had the lowest total installed cost and the shortest payback than the other baffl e arrangements, which were segmental baffl e arrangement, rod baffl e arrange-ment, and plate heat exchanger. Zhang and co-workers [31, 32] experimentally studied the discontinuous helical baffl ed heat exchangers combined with two-dimensional or three-dimensional fi nned tubes. Experimental results showed that for the heat exchanger with rib-shaped fi n tubes, the shell-side Nusselt and Euler numbers were augmented by 90–130% and 10%, respectively. The increase in heat transfer is signifi cantly greater than that in pressure drop for rib-shaped fi n tubes. Detailed studies on helical angles and block plates are presented as follows.

3.2.1 Effect of helical anglesH elical angle has great effect on heat and fl ow performance of heat exchangers with discontinuous helical baffl es, because it can determine the minimum fl ow area and the gradient of the velocities in the shell side. Andrews and Master

Figure 10: Schematic of discontinuous helical baffl es.



[33, 34] used the distributed resistance approach for the three-dimensional modeling of a helixchanger. Pressure drops from ABB Lummus heat transfer correlation results were used to validate the simulations, which reasonably agreed well with the computed results. Two fl ow regimes have been identifi ed in the numerical simulations: an inner region fl ow that exhibits a fl ow reversal due to a backward-facing (relative to the fl ow) gap,and an outer region that shows a ‘plug’-like fl ow. The inner region of the 40° helix shows a smaller reverse fl ow and a more desirable ‘plug’-like fl ow.

Zhang et al. [35–37] carried out careful experimental and numerical studies on segmental baffl ed STHXs and discontinuous (middle overlapped) helical baffl ed STHXs with different helical angles. Specially, the material of the heat exchange tubes and the shell of the STHXs is 0Cr18Ni9 and hot oil fl ows through the shell side and cold water fl ows through the tube side in the experiments. The results indicated that, for the same volume fl ow rate, the shell-side NuPr1/3 of the STHXs with discontinuous helical baffl es is lower than that of the STHX with segmental baffl es, while the shell-side friction factors f of the former is far lower than that of the later. The optimal helix angle was 40° and the discontinuous helical baffl ed STHX has the best comprehensive performance, which evaluated by heat transfer coeffi cient per pressure drop. The results are consistent with the results of previous studies [17, 20, 21], see Figs 11–13.

3.2.2 Effect of block platesIn the discontinuous helical baffl ed STHXs, the ‘triangle zones’ exist in the shell side (as shown in Fig. 10). Because of the ‘triangle zones’ between two overlapped plates, fl uid may leak from these ‘triangle zones’. The leakage phenomenon has been confi rmed by both visualization experiments and numerical simulations [38, 39]. Zhang et al. [39] have studied the fl ow performance in shell side of STHXs with overlapped helical baffl es using the computational fl uid dynamic

Figure 11: Heat transfer performance of discontinuous helical baffl es [35].



method. The leakages in the ‘triangle zones’ were apparent and seriously affected the helical fl ow in the shell side (as shown in Fig. 14).

One useful method to solve this problem is inserting block plates in these tri-angle zones. Experiments have been carried out to study the infl uences of inserting block plates on heat transfer performance and pressure drop in the STHXs with overlapped helical baffl es [40–43].

In the experiments, all of the geometrical parameters expect that the baffl e style and baffl e distance were kept the same. The results showed that, for the same mass fl ow rate, the block plates may increase the heat transfer coeffi cient and pressure drop by about 15% and 100%, respectively. For the same pressure drop, the heat transfer coeffi cients of STHX without block plates were higher than that with block plates by about 12%, as shown in Fig. 15. These can be explained as follows:

Figure 13: Comprehensive performance of discontinuous helical baffl es [35].

Figure 12: Flow performance of discontinuous helical baffl es [35].



Figure 14: Flow fi eld in the heat exchangers with overlapped helical baffl es [39].

Figure 15: Block plates effects on heat transfer performance [40].

the block plates were set in the direction upright the fl ow direction, the fl ow rushes the block plates vertically and it would induce much bigger pressure drop. Further-more, zones that were similarly like the ‘dead zones’ in the segmental baffl ed STHXs existing in certain place can make the comprehensive performance of dis-continuous helical baffl ed STHXs decrease.

The correlations for heat transfer and pressure drop of the STHXs with discon-tinuous helical baffl es are listed in Table 1.

3.3 Shell Side Design method for STHXs

It can be found that both heat transfer and fl ow performance of discontinuous helical baffl ed STHXs are different from traditional segmental baffl ed heat exchangers, which result in many diffi culties in design these heat exchangers. In order to simply the design process, The Delaware method of heat exchanger design [44, 45] is used as a basis for determining correction factors. Stehlik et al. [46] carried out a study of correction factors for STHXs with segmental baffl es as compared to helical baffl es. The results of the study shown that helical baffl e STHXs, when properly designed, offered a signifi cant improvement in



Tabl

e 1:

C

orre

latio

ns f

or h

eat t

rans

fer

and

pres

sure

dro

p of

the

STH

Xs

with

dis

cont

inuo

us h

elic

al b

affl e

s.

Res

earc

hers

Baf

fl e s

tyle

Flui

dC

orre

latio

nsR

ange

Lei

et a

l. [2

9]

Sing

le d

isco

ntin

uous

hel

ical

baf

fl e

oil

Nu s

= 0

.275

Re s

0.55

Pr1/

350

< R

e s <

1,0

00

f s =

20.

06R

e s-0

.56

f s =

11.

34R

e s-0

.47

400

≤ R

e s40

0 <

Re s

< 1

,000

Zha

ng e

t al.

[34]

Mid

dle-

over

lapp

ed h

elic

al b

affl e

b =

20°

oil

Nu s

= 0

.275

Re s

0.54

2 Pr1/

310

0 <

Re s

< 8

00

f s =

11.

0Re s

–0.7

5110

0 <

Re s

< 8

00

b =

30°

oil

Nu s

= 0

.365

Re s

0.51

6 Pr1/

311

0 <

Re s

< 4

80

f s =

13.

5Re s

–0.7

7411

0 <

Re s

< 4

80

b =

40°

oil

Nu s

= 0

.455

Re s

0.48

8 Pr1/

319

0 <

Re s

< 7

50

f s =

34.

7Re s

–0.8

0619

0 <

Re s

< 7

50

b =

50°

oil

Nu s

= 0

.326

Re s

0.51

2 Pr1/

315

0 <

Re s

< 5

00

f s =

47.

9Re s

–0.8

4915

0 <

Re s

< 5

00

Zha

ng a

nd F

ang.

[31

]

Dis

cont

inuo

us h

elic

al b

affl e

Peta

l-sh

aped

fi n

tube

oil

Nu s

= 0

.026

Re s

0.8 Pr

1/3

Unk

now

n

Inte

gral

low

-fi n

tube

oil

Nu s

= 0

.029

Re s

0.8 Pr

1/3

Unk

now

n

Zha

ng e

t al.

[32]

Dis

cont

inuo

us h

elic

al b

affl e

Low

-fi n

tube

soi

lN

u s =

0.0

3(R

e sPr

)0.71

512

5,00

0<R

e sPr

<50

0,00

0

Eu s

= 1

9.3(

Re s

Pr)–0

.058

125,

000<

Re s

Pr<

500,

000

Rib

-sha

ped

fi n tu

beoi

lN

u s =

0.0

17(R

e sPr

)0.82

310

0,00

0<R

e sPr

<42

5,00

0

Eu s

= 5

4.6(

Re s

Pr)–0

.132

100,

000<

Re s

Pr<

425,

000



heat transfer while providing a reduced cost in pressure drop. In designing and optimizing of helixchangers, pitch angle, baffl e’s arrangement, and the space between two baffl es are important parameters. Zhang et al. [47] have replaced the curve-type factors in the literature by mathematical expressions for the con-venience of engineering design. Jafari Nasr and Shafeghat [48] proposed a rapid design algorithm for helical baffl ed heat exchangers. The general idea behind that design algorithm consists of creating a simp le relationship between pres-sure drop, heat transfer coeffi cient, and heat exchanger area for each side, that is, Δp = f (h, A). Here, the correction design method proposed by Stehlik et al. [46] was introduced in detail.

3.3.1 Correlations for heat transfer coefficient in shell sideThe average Nu number for the shell side of discontinuous helical baffl es [46] is determined by

Nus = + +0 62 0 3 2 22 3 4 7 8 9 10. ( . )Nu Nu Y Y Y Y Y Y Ylam turb

(1)

where

Nu Relam = 0 664 0 5 0 33. Pr. . (2)

Nu

Returb =

+ −−0 037

1 2 443 1

0 7

0 1 0 67

. Pr

. Re (Pr

.

. . (3)

In eqn (1) coeffi cients Yi are the correction factors. Their physical meanings are defi ned as follows [46]: Y2 accounts for the thermal-physics properties effects; Y3 accounts for the scale-up from a single tube row to a bundle of tubes; Y4 accounts for the adverse temperature gradient; Y7 accounts for the bundle-shell bypass streams; Y8 accounts for the baffl e spacing in inlet and outlet sections; Y9 accounts for the change in the cross-fl ow characteristics in heat exchanger; and Y10 accounts for the turbulent enhancement.

Average heat transfer coeffi cient for shell side [46] is

hNu

ss s

l=

l (4)

l

d=

p 0

2 (5)

where do is the outside diameter of the tube; and ls is thermal conductivity of shell-side fl uid. The application ranges of eqns (1–5) are 10 < Re < 106, 10 < Pr < 103, nrc > 10, and 5° ≤ b ≤ 4 5°

n n nrc rp p= −( )1 (6)

nrp is the number of tube rows in the cross section of heat exchanger; and np is the number of baffl es.



3.3.2 Correlations for pressure drop in shell sideThe pressure drop cross the bundle per unit cycle without bypass fl ow can be determined by [46]

Δ =p n ut r01

221

2 22

2 6 72l r Z Z Z (7)

The pressure drop cross the whole bundle zone with bypass fl ow is [46]

Δ = Δp p

l

Bt tt

0 01 0

3Z (8)

where lt0 is the effective length of heat exchanger eliminating the inlet and outlet parts and B is the baffl e pitch.

The pressure drop in the inlet and outlet zones [46] is

Δ = Δp ptn t 01

5Z (9)

where nr1 is the number of tube rows on the center stream line within one cycle. λ22 is the friction factor of ideal cross-fl ow through tube bundle, lto is the baffl ed length of tube bundle. In eqns (7–9) correction factors are defi ned as mentioned in and are as follows [46]: Z2 accounts for the thermal- physics properties effects; Z3 accounts for the bundle-shell bypass streams; Z5 accounts for the baffl e spacing in inlet and outlet sections; Z6 accounts for the change in the cross-fl ow characteristics in heat exchanger; and Z7 accounts for the turbulent enhancement.

The pressure drop in the inlet and outlet nozzles can be calculated by [49, 50]

2

.0.5nozzle s nozzlep vxrΔ = (10)

where z is taken as 1.5 or 2.0.The overall pressure drop of the shell-side fl uid:

Δ = Δ + Δ + Δp p p pnozzle tn t0 (11)

3.3.3 Determina tion of factorsFrom the above presentation it can be seen that the determination of factors Yi and Zi is the key issue to obtain the shell-side fl uid heat transfer coeffi cient and pres-sure drop.

(1) Y2 and Z2

⎛ ⎞

= ⎜ ⎟

⎝ ⎠

0.14

2,

Y s

s w

hh

(12)

0.14

2,

Z s

s w

hh

−

⎛ ⎞

= ⎜ ⎟

⎝ ⎠

(13)



where hs,w is the dynamic viscosity at average temperature of tube wall. The determination of average temperature of tube wall is conducted by

, ,,

1

s avg t avgw t avg

ts

t tt t

hh

⎛ ⎞−⎜ ⎟

= + ⎜ ⎟+⎜ ⎟⎝ ⎠

(14)

where tt,avg and ts,avg are the averaged inlet and outlet temperatures of tube side and shell side in the heat exchanger, respectively. ht and hs are heat transfer coeffi cients for tube side and shell side, respectively.

(2) Y3, Y7 and Z3 For in-line arrangement

3 1.5 2

0.7 / 0.3Y 1( / 0.7)

b ab ae

−= +

+

( 15)

For staggered arrangement

3

2Y 13b

= + (16)

where a is the ratio of distance between the tube normal to the fl ow direction and the central tube pitch, b is the ratio of distance between tube in the fl ow direction and the central tube pitch. The parameter e is determined by

b 1: 1

4aπ

ε≥ = − (17)

b 1: 1

4abp

e< = − (18)

Y7 and Z3 are functions of ttnpt /D1 and Sss /S2z .These curves (as shown in Figs 16, 17) have been fi tted to the equations (where x = tt npt /D1 and y = Sss /S2z) by Zhang et al. [47].

0.338

7Y exp 1.343 (1 (2 )x y⎡ ⎤= − −⎣ ⎦

(19)

0.363

3Z exp 3.56 (1 (2 )x y⎡ ⎤= − −⎣ ⎦

(20)

1 02 1 0S 0.5( / cos ) ( )z p i t

t

D dB s D D t d

tb⎡ ⎤−

= − − + −⎢ ⎥

⎣ ⎦

(21)

In eqns (19)–(21), tt is the tube pitch, D1 is the inner diameter of shell, Sp is the thickness of baffl e, Stt is distance between the two tubes’ outside surfaces, npt is the number of stealing strip pairs, and Ds is the diameter of tube bundle.



Figure 16: Bundle-to-shell by-pass heat transfer correction factor.

Figure 17: Bundle-to-shell by-pass pressure drop correction factor.

(3) Y8 and Z5

Y8 and Z5 are functions of (lt c−lto)/ltc and B/D1 . The curves (as shown in Figs 18 and 19) have been fi tted to the equations [where x = (ltc−lto)/ltc and y = B/D1] by Zhang et al. [47].

0.0487 0.301 1.2

8Y 1.079 0.445y y x−= − (22)

1.2

5Z ( 0.0172 0.0899 )y x −= − + (23)



(4) Y9 and Z6

Y9 and Z6 are only infl uenced by helical angle. The curves (as shown in Figs 20 and 21) have been fi tted to following equations (x = b ) by Zhang et al. [47]:

x ≤ 18°

9Y 1= (24)

18° < x ≤ 45°

2

9Y 0.997 0.00445 0.0001821x x= + − (25)

4 5 2

6Z 0.289 5.06 10 4.53 10x x− −= − × − × (26)

Figure 18: Inlet/outlet region heat transfer correction factor.

Figure 19: Inlet/outlet region pressure drop correction factor.



Figure 20: Heat transfer correction factor accounting for changes in the cross-fl ow characteristics.

Figure 21: Pressure drop correction factor accounting for changes in the cross-fl ow characteristics.

(5) Y10 and Z7

Y10 and Z7 are also only infl uenced by the helical angle. The following curves (as shown in Figs 22 and 23) have been fi tted into the equations are obtained (x = b) by Zhang et al. [47]:

x ≤ 25°

10Y 1= (27)

25° < x ≤ 45°

2 3 4 4

10Y 56.39 8.28 0.46 0.012 1.64 10x x x x−= − + − + − × (28)

x ≤ 22°

7Z 1= (29)

22° < x ≤ 45°

= − + −2

7Z 5.411 0.379 0.00402x x (30)



According to the available results of experiments and numerical simulations mentioned previously, the STHXs with discontinuous helical baffl es have higher heat transfer coeffi cients per pressure drop h/Δp for the same shell-side pressure drop. However, they still have their shortcomings, for example, the discontinuous helical baffl ed STHXs usually have relatively lower heat transfer coeffi cient than the conventional segmental baffl ed STHXs for the same baffl e distance and identi-cal shell-side mass fl ow rate. It means that the shell-side mass fl ow rate has to be increased to obtain the same heat transfer rate, if the helical baffl ed STHX is cho-sen to replace segmental baffl ed STHX under the same free fl ow area; in other words, this replacement will not be advisable unless the various modifi cations in terms of number of shell passes are considered. However, increasing mass fl ow rate is not always acceptable in some practical situations. In addition, the leakage percentage of discontinuous helical baffl es may be relatively large in the triangle

Figure 22: Heat transfer correction factor accounting for turbulence enhancement.

Figure 23: Pressure drop correction factor accounting for turbulence enhancement.



zones when the mass fl ow rate is small, which will reduce the comprehensive heat transfer performance. Furthermore, the triangle zone area will become quite large when the shell diameter increases in large-scale STHXs. In order to overcome these problems, the STHXs with continuous helical baffl es and combined helical baffl es have been introduced.

4 Single Shell -Pass STHXs with Continuous Helical Baffles

4.1 Structure of the Continuous Helical Baffles

The continuous helical baffl es (Fig. 24) are manufactured by linking several sets of continuous helical cycles [51]. One continuous helical cycle is lengthened to one screw pitch along the length (axial) direction and rotated 2ϖ angle along the circum-ferential direction, and several continuous helical cycles are linked end to end to form continuous helicoids. This method overcomes the diffi culties in manufacturing whole continuous helicoids at one time and reduces the manufacture cost signifi cantly.

One major diffi culty related to the manufacturing of continuous helical baffl es is drilling holes on the surface of the continuous helical baffl es. If the holes on the baffl es are drilled in the same size as the tubes in initially plain plates, and then the pitch is varied by stretching the spiral in or out, the tube will not see a round hole rather an elliptic one. Therefore, it is impossible to pass a round tube through an elliptic hole. To solve this problem, a die is used to hold the helical cycle at the required pitch, and then the required holes can be drilled on the baffl es (Fig. 25) [51, 52].

Figure 24: Confi guration of shell-and-tube heat exchanger with continuous helical baffl es [51].

Figure 25: Dies for drilling tube holes [51].



4.2 Flow and heat transfer performance of continuous helical baffled heat exchangers

The fl uid fl ow in the shell side of STHX with continuous helical baffl es is a com-plete helix in nature. This fl ow pattern can avoid abrupt turns of fl ow direction and maintain constant rush on the heat exchange tubes. It can have superior advantages in decreasing pressure drop, preventing leakage, mitigating fouling, and increas-ing heat transfer coeffi cient.

In order to study the fl ow and heat transfer performances of continuous helical baffl ed heat exchangers, two heat exchangers – one is set up with segmental baf-fl es (SG-STHX) and another is equipped with continuous helical baffl es ( CH-STHX) (as shown in Fig. 26) – were tested on the on an oil/water–water/water test stand [52–56]. The experimental system consists of two loops: the hot oil loop and cooling water loop, as shown in Fig. 27.

Figure 27: Experimental loops.

Figure 26: Layout of heat exchangers baffl es.



4.2.1 Heat transfer and pressure dropExperimental results (as shown in Fig. 28) suggested that continuous helical baffl es enhance heat transfer coeffi cient and pressure drop by 43–53% and 64–72% than the segmental baffl ed heat exchanger, respectively [57]. It confi rms that the CH-STHX has better heat transfer performance than the SG-STHX. The reasons for the better heat transfer performance can be explained as follows: fi rst, the completely helical fl ow manner is closer to ‘plug fl ow’ and it can increase the temperature difference to drive heat transfer process; second, the helical fl ow man-ner avoids local ‘dead zones’ and can make the heat transfer process more evenly and in higher effi ciency, in particular the baffl e pitch of the continuous helical baffl es is much smaller than the segmental baffl es; third, the minimal fl ow area of the CH-STHX has been greatly decreased and the velocity, turbulence, and mixing have been greatly increased.

The data on heat transfer coeffi cients and pressure drops for different mass fl ow rates obtained from the experiments are used to fi t correlations between the Nusselt numbers Nuo, friction factors fo and Reynolds numbers Reo, as shown in Figs 29 and 30). The reduction results are fi tted into the following correlations:

1-1/3

o o 1m

oNu Pr c Re= (31)

2

o 2 o= mf c Re (32)

It is also indicated that the present experimental results for CH-STHX are much bigger than those in the previous work [52]. What should be emphasized here is that the helical angle in [20] is b = 9.5°, while that in the present work is b = 8.5°. Smaller helix angle means smaller fl ow area, which can result in higher velocities, turbulence, and better heat transfer performance. The experi-mental results also indicate that the SG-STHX has better heat transfer perfor-mance than the CH-STHX for the same Reynolds number. When comparing with the results for DCH-STHX obtained by Zhang et al. [35], the CH-STHX also has higher Nusselt number than the DCH-STHX in the higher Reynolds number region.

Figure 28: Heat transfer rate and heat transfer coeffi cient performance [57].



The experimental results also indicate that the SG-STHX has higher friction factors than the CH-STHX and DCH-STHX for the same Reynolds number. The higher friction factors of the SG-STHX results from sudden contraction and expansion of the fl ow in the shell side, and the fl uid impinging on the shell walls caused by segmental baffl es. It is also suggested that both the SG-STHX and CH-STHX have higher friction factors than the previous correlations [52]. This is because the effects of inlet and outlet sections are included in the present study, while those in [52] are excluded.

4.2.2 Entropy generation number and energy lossesIn order to evaluate the comprehensive performance of the two STHXs, entropy generation number and energry losses, which are based on second-law thermody-namic analysis, are introduced. The entropy generation rate for a heat exchanger is defi ned as [58, 59]

o,out w,outo p,o s w p,w

o,in w,in

o,out w,outo s w t

o,in w,in

( ) ln( ) ( ) ln( )

( ) ln( ) ( ) ln( )

seg tT T

S s m c m cT T

p pm R m R

p p

= + −′

−

(33)

500 1000 1500 2000 2500 30001

10

100

Reo

Nu oPr o-1

/3

discontinuous helical bafflecontinuous helical baffle

SG-STHX SG-STHX(Peng et al.[52]) CH-STHX CH-STHX(Peng et al.[52]) DCH-STHX(Zhang et al.[35])

segmental baffle

500 1000 1500 2000 2500 300010-3

10-2

10-1

100

segmental baffle

Reo

f o

SG-STHX SG-STHX(Peng et al.[52]) CH-STHX CH-STHX(Peng et al.[52]) DCH-STHX(Zhang et al.[35])

discontinuous helical baffle

continuous helical baffle

Figure 30: Friction factor versus Reynolds number [57].

Figure 29: Nusselt number versus Reynolds number [57].



where the fi rst two terms on the right side represent the shell-side and tube-side heat transfer irreversibility and the last two terms represent the shell-side and tube-side pressure drop irreversibility. What should be emphasized is that the pressure drop at the inlet and outlet in both sides used here are the total pressure drop ini-tially; however, it is diffi cult to measure them and static pressure drops at the inlet and outlet in both sides are used instead in eqn (33).

The entropy generation number is defi ned as [58, 59]

segs

min

min w p,w o p,o

( )

( ) min[ , ]p

p

SN

mc

mc m c m c

′

=

=

(34)

Energy losses are the amount of work obtained at the end of the reversible pro-cess. The relationship between the irreversible production and entropy generation can be expressed as

e segI T S=′ ′ (35)

The vari ation of the entropy generation number Ns with the shell-side Reynolds number Reo is shown in Fig. 31. It can be seen that the entropy generation number of the SG-STHX is obviously higher than that of the CH-STHX for the same Reynolds number, which indicates that the SG-STHX has higher irreversibility losses of the heat transfer and pressure drop. In comparison, the CH-STHX decreases the entropy generation number by 30% on average than the SG-STHX. The total energy losses, including the temperature difference and pressure drop in both sides, have similar trend as Ns with the Reynolds number and the CH-STHX decreases the energy losses by 68% on average [57]. From the results mentioned above, it can be concluded that the test CH-STHX has better heat tran sfer quality than the SG-STHX.

4.3 Maxi mal velocity ratio design method

In the practical industries, the tube bundle of STHXs sometimes needs to be redesigned or replaced, because of failure or improving its heat transfer effi ciency.

Figure 31: Entropy generation number and energy loss [57].



How to design new tube bundle and baffl e arrangements to make the CH-STHX has better performance than the original SG-STHX in the same shell structure is very important for designers. From the correlations mentioned above, it can be concluded that the maximal velocity in the minimum fl ow area, which determines the Reynolds number, can affect the heat transfer performance greatly. In order to enhance heat transfer performance of the CH-STHX, one effective method is to increase the maximal velocity in the shell side for the same mass fl ow rate. The maximal velocity ratio, R, is defi ned when the CH-STHX and the SG-STHX have the same heat transfer coeffi cient in the shell side.

CH,max

SG,max

uR

u=

(36)

where uCH,max and uSG,max are the maximal velocities in the minimum fl ow area for helical baffl ed heat exchangers and segmental baffl ed heat exchangers.

As shown in Fig. 32, the maximal velocity rates decrease with the increase of the heat transfer coeffi cient in the shell side. When the maximal velocity rates are above the line with circle points (R > 2.4), the heat transfer coeffi cient of CH-STHX will be higher than that of SG-STHX. By contrast, the corresponding fric-tion factor rates between the CH-STHX and the SG-STHX keep almost constant fo,CH/fo,SG = 0.28 with the increase of heat transfer coeffi cient in the shell side[57].

4.4 Effect of the inlet and outlet locations

Peng and coworkers [52, 54] carried out experimental investigations on the continuous helical baffl ed STHXs with two different inlet/outlet shell-side confi gurations, that is, side-in/side-out and middle-in/middle-out, as shown in Fig. 33.

The results indicated that the heat transfer coeffi cient of the heat exchanger with the side-inlet/side-outlet shell design is about 2% higher than that with the middle-inlet/middle-outlet shell design and it also has better comprehen-sive performance. Two reasons account for why the performance of side-inlet/side-outlet shell design is better than that of middle-inlet/middle-outlet shell design. First, the side-inlet/side-out design is more effective in forcing the

Figure 32: Maximal velocity rates versus heat transfer coeffi cient.



fl uid to fl ow in a helical passage, hence resulting in a higher local heat transfer coeffi cient. Second, the middle-inlet/middle-outlet design causes the fl uid to impinge perpendicularly to the shell wall, hence resulting in higher local pressure drop.

4.5 Applications example

In order to have a further understanding of the heat transfer performance of STHX with helical baffl es, continuous helical baffl es have been applied in a shell-and-tube evaporator of an air condition system to replace the conven-tional segmental baffl es (Fig. 34), the detail parameters of the evaporator are shown in Table 2. In the evaporator, water fl ows through the shell side and is cooled by refrigerants fl owing through the tube side. All structure param-eters and working conditions were kept the same except the baffl e style of the evaporators. The test result suggests that the STHX with continuous helical

F igure 34: Direct expanding evaporator with continuous helical baffl es for [60].

Figure 33: Middle inlet/middle outlet and side inlet/side outlet confi guration.



baffl es has much better performance than STHX with segmental baffl es. For the same heat transfer area, the refrigerating output of the evaporator with con-tinuous helical baffl es is 4.9% higher than that of the conventional evaporator with segmental baffl es; the coeffi cient of performance of the evaporator with continuous helical baffl es is 5.4% higher than that of conventional evaporator with segmental baffl es [60].

In order to further enhance heat transfer of STHXs with helical baffl es, improved heat exchange fi nned tubes were used by researchers. Zhang et al. [61–63] experimentally and numerically studied the continuous helical baffl ed heat exchangers combined with three-dimensional fi nned tubes. Experimental results showed that for the heat exchanger with petal-shaped fi nned tubes, the shell-side Nusselt numbers were obviously higher than the smooth tubes. The increase in heat transfer is signifi cantly greater than that in pressure drop for rib-shaped fi nned tubes. Numerical simulation results agreed well with the experimental data.

The correlations for heat transfer and pressure drop of the STHXs with continu-ous helical baffl es can be seen in Table 3.

There are also some problems that existed for the STHXs with continuous heli-cal baffl es. The fi rst one is manufacturing continuous helical surface. The helical baffl e surface becomes relatively steep at portions close to the central axis when the pitch is large, especially in the STHXs with large shell diameters. In such situ-ations, the continuous helical baffl e surfaces will have bigger twist rate and are quite diffi cult to be manufactured, as shown in Fig. 35.

In the STHXs with continuous helical baffl es, a central tube has to be used to fi t the helical structure inside the shell. On one hand, heat exchange tubes cannot be arranged at the place where the central tube is located, thus the heat transfer area of the heat exchanger will be decreased; on the other hand, part

Table 2: Compared results of direct expanding evaporators with continuous helical and segmental baffl es [60].

Item LS195Z LS195Z II

Compressor type SRF-3Number of the condenser’ tubes 90 90Total heat transfer area of

condenser/m2 10.52

Baffl e style Segmental Continuous helicalNumber of tubes 196 196Heat transfer area/m2 23.99 23.91Refrigeration capacity/kW 185.8 195.0 (+4.9%) Coeffi cient of performance 3.57 3.75 (+5.4%) Heat fl ux on the outer

surface/kW m–27.74 8.23

Total heat transfer coeffi cient/Wm–2 K–1 1,545 1,613 (+4.4%)



Tabl

e 3:

Cor

rela

tions

for

hea

t tra

nsfe

r an

d pr

essu

re d

rop

of th

e ST

HX

s w

ith c

ontin

uous

hel

ical

baf

fl es.

Res

earc

hers

Baf

fl e s

tyle

Flui

dC

orre

latio

nsR

ange

Peng

et a

l. [5

2]

Con

tinuo

us h

elic

al b

affl e

Side

-in/

side

-out

oil

Nu s

= 0

.059

9Re s

0.66

9 Pr1/

3

Re s

≤ 1

,960

1,96

0 <

Re s

f s =

3.7

6Re s

-0.5

78

f s =

0.3

16R

e s-0

.251

Mid

dle-

in/m

iddl

e-ou

toi

l

Nu s

= 0

.045

1Re s

0.69

9 Pr1/

3

Re s

≤ 2

,757

2,75

7 <

Re s

f s =

1.4

0Re s

-0.4

37

f s =

0.2

26R

e s-0

.206

Wan

g et

al.

[55]

Con

tinuo

us h

elic

al b

affl e

Side

-in/

side

-out

oil

Nu s

= 0

.053

3Re s

0.68

8 Pr1/ 3

unkn

own

f s =

1.6

4Res-

0.4 5

Mid

dle-

in/m

iddl

e-ou

toi

lN

u s =

0.0

323R

e s0.

742 Pr

1/3

unkn

own

f s =

0.6

3Re s

-0.3

3

Wan

g et

al.

[57]

Con

tinuo

us h

elic

al b

affl e

Mid

dle-

in/m

iddl

e-ou

toi

lN

u s =

0.0

001R

e s1.

602 Pr

1/3

1,30

0< R

e s <

2,6

90oi

lf s

= 1

0.55

4Re s

-0.5

341,

300<

Re s

< 2

,690

Zha

ng e

t al.

[61]

Con

tinuo

us h

elic

al b

affl e

with

pe

tal-

shap

ed fi

nned

tube

soi

lN

u s =

0.0

26R

e s0.

8 Pr1/

3un

know

n

Zha

ng e

t al.

[62,

63]

Con

tinuo

us h

elic

al b

affl e

with

sm

ooth

tube

oil

Nu s

= 0

.030

Re s

0.8 Pr

0.4

10,0

00 <

Re s

< 2

0,00

0

Con

tinuo

us h

elic

al b

affl e

with

pe

tal-

shap

ed fi

n tu

beoi

l

Nu s

= 0

.062

Re s

0.8 Pr

0.4

10,0

00 <

Re s

< 2

0,00

0N

u s =

0.0

63R

e s0.

8 Pr0.

410

,000

< R

e s <

20,

000

Nu s

= 0

.058

Re s

0.8 Pr

0.4

10,0

00 <

Re s

< 2

0,00

0N

u s =

0.0

59R

e s0.

8 Pr0.

410

,000

< R

e s <

20,

000

Nu s

= 0

.060

Re s

0.8 Pr

0.4

10,0

00 <

Re s

< 2

0,00

0



of heat exchanger volume is occupied by the central tube and cannot be used for heat exchange, which will result in the decreasing of STHX compactness. Because of these above reasons, the SHTX with combined helical baffl es has been proposed to solve part of problems existed in continuous helical baffl es by Wang et al. [64].

5 Single Shell-Pass STHXs with Combined Helical Baffles

5.1 Structure of the combined helical baffles

The combined helical baffl e is a combination of discontinuous helical baffl es and continuous helical baffl es (Fig. 36). Discontinuous helical baffl es are installed in the central region, while the continuous helical baffl es are used in most part of the outer space of the shell side. The discontinuous helical baffl es and continuous heli-cal baffl es worked together to form a whole continuous helicoids. This combined helical baffl e simplifi es the manufacture process and takes advantages of both discontinuous helical baffl es and continuous helical baffl es. In addition, it can save more space and increase the heat exchangers compactness.

Fi gure 35: Twist rate with different inner helix diameter.

F igure 36: Schematic of single shell-pass STHXs with combined helical baffl es [64].



5 .2 Flow streamlines

In order to study the fl ow manners of the combined helical baffl es, numerical studies have been carried out by Chen et al. [65]. The streamlines in the shell side of these STHXs with different helical baffl es (discontinuous helical baffl es/DCH-STHX, continuous helical baffl es/CH-STHX and combined helical baffl es/CMH-STHX) are shown in F ig. 37a–c.

From F ig. 37a, it can be observed that in the outer part of the shell pass of the DCH-STHX, the fl uid passes though the tube bundles in an approximately helical pattern and there are seriously leakages from the ‘triangle zones’. The leaking fl uid passes through the shell side without rushing across the tube bundle, which can result in lower heat transfer performance and lower pressure drop. It can be observed in Fig. 37b that the fl uid passes though the tube bundles with much less leakage in the shell side of the CMH-STHX compared to the DCH-STHX, because the ‘triangle zones’ formed by discontinuous helical baffl es are decreased. As to Fig. 37c, the continuous helical baffl es (CH-STHX) form a completely helix fl ow in the shell side, and there is no leakage. These advantages may contribute to its outstanding performance on heat transfer.

The velo city fi elds of these STHXs obtained by whole heat exchanger simula-tion are shown in Fig. 38. It can be observed that in the outer part of the shell pass of the CMH-STHX, where the continuous helical baffl es are located, the velocities are distributed in an even and smooth way. The difference of the velocities in each helix cycle is small. But in the inner part of the shell pass, the velocities change greatly and the leakage in the triangle zones still exists. How-ever, the areas of the triangle zones are decreased compared to the DCH-STHX (as shown in Fig. 38c), the effect of the leakage in the triangle zones is decreased. As to Fig. 38b, the continuous helical baffl es (CH-STHX) form a completely helix fl ow in the shell side, and the distributions of velocities in different helix cycles are same and there is no triangle zone. In the shell side of the conven-tional SG-STHX (as shown in Fig. 38d), there are many ‘stagnation regions’ and fl uid fl ow is in a ‘zigzag’ manner.

Figu re 37: Shell-side streamlines for different STHXs.




Chen et al. [66] studied the STHXs with combined helical baffl e by computational fl uid dynamics method. The numerical results suggested that for the same mass fl ow rate and identical layout of heat exchanger tubes in the shell side, the overall pressure drop of the combined helical baffl ed STHX (CMH-STHX) is about 50% lower than that of heat exchanger with segmental baffl es (SG-STHX) and its heat transfer coeffi cient per pressure drop h/Δp was 81.7% higher than that of the heat exchangers with segmental baffl es.

Chen et al. [65, 67] also numerically studied the heat transfer and fl ow perfor-mance of STHXs with discontinuous helical baffl es (DCH-STHX), combined helical baffl es (CMH-STHX), and continuous helical baffl es (CH-STHX) by adopting periodic boundary conditions. In the study, experiments were carried out to validate the numerical predictions. It can be concluded that, for the same Reyn-olds number, the Nusselt numbers of the CMH-STHX and CH-STHX are about 37.6%, 78.2% higher than that of the DCH-STHX (Fig. 39), whereas the friction

Figure 3 8: Velocity distributions.



factor of the CH-STHX is about 14.8% and 150.2% higher than that of CMH-STHX and DCH-STHX.The following correlations were fi tted by the numerical results:

CH-STHX:

-1/3 0.5613

o o o oPr = 0.1293Re 960 Re 3720Nu ≤ ≤ (37)

-0.2591

o o o= 0.1554Re 973 Re 3720f ≤ ≤ (38)

CMH-STHX:

≤ ≤-1/3 0.5354

o o o oPr = 0.1399Re 710 Re 3180Nu (39)

-0.0787

o o o= 0.0278Re 717 Re 3182f ≤ ≤ (40)

CMH-STHX:

-1/3 0.3509o o o oPr = 0.4229Re 700 Re 3060Nu ≤ ≤ (41)

-0.0203

o o o= 0.0088Re 700 Re 3060f ≤ ≤ (42)

Whole heat exchanger simulations also carried out by Chen et al. [68]. The results indicate that the heat transfer rate of the CMH-STHX is about 25% and 11% higher than that of the SG-STHX and DCH-STHX on average (as shown in Fig. 40). However, it is still 10% lower than that of the CH-STHX. Figure 41 illus-trates the differences of heat transfer rate and mass fl ow rate between different STHXs under the identical overall pressure drop (Δp = 1,500 Pa). Compared with the SG-STHX, the heat transfer rates of CH-STHX, CMH-STHX, and DCH-STHX are 30.6%, 26.8%, and 20% higher, respectively. While the mass fl ow rates of CH-STHX, CMH-STHX, and DCH-STHX are 22.2%, 45.5%, and 46% higher than that of SG-STHX, respectively. A higher heat transfer rate can be achieved by enhancing mass fl ow rate under the same pressure drop in all STHXs with helical baffl es (CH-STHX, CMH-STHX, and DCH-STHX) and the CMH-STHX has a better performance than DCH-STHX.

Figure 39: Nusselt number and friction factor versus Reynolds number.



5.4 Maximal velocity ratio

In heat exchanger design, one of the key factors affecting heat transfer is the maxi-mal velocity in the minimum free fl ow area for the same mass fl ow rate. It can be inferred that reasonable velocity designs in the shell side can make the CMH-STHX and DCH-STHX have the same heat transfer performance as the CH-STHX. If the CH-STHX, CMH-STHX, and DCH-STHX have the same Nusselt number for the same mass fl ow rate in the shell side, we call that they have identical heat transfer effi ciency and the corresponding velocity ratios can be defi ned as follows [65]:

DCH, max

DCH, CHCH, max

uR

u= (43)

CMH,maxCMH,CH

CH,max

uR

u= (44)

where uDCH,max, uCMH,max, and uCH,max are the maximal velocities of DCH-STHX, CMH-STHX, and CH-STHX in the minimum free fl ow area, respectively.

Figure 40: Variations of heat transfer rate versus pressure drop.

Figure 41: Difference of Qm and M between different STHXs (Δp = 1,500 Pa).



Reasonable velocity ratios of RCMH,CH and RDCH,CH design can make CMH-STHX and the DCH-STHX have higher Nusselt numbers than the CH-STHX at the same mass fl ow rate in the studied range of Nusselt number (Fig. 42). Three different helical baffl ed STHXs design by the maximal velocity ratios are designed to validate the maximal velocity ratios.

In general, the single shell-pass STHXs with helical baffl es have lower heat transfer coeffi cients than the segmental baffl ed STHXs for the same free fl ow area and tube layout conditions, although they also have much lower pressure drops. To further enhance heat transfer performance of STHXs, the multiple shell-pass STHXs with helical baffl es have been introduced.

6 Comb ined Multiple Shel l-Pass STHXs with Helical Baffles

6.1 Structure of the combined multiple shell-pass SHTXs with helical baffles

The combined multiple shell-pass STHX (Fig. 43) has been invented and studied by Wang et al. [69–74] to further enhance the shell-side heat transfer performance. The main improvements are as follows: there are two or more shell passes in the shell side of STHXs, where the outer shell passes are set up with continuous helical baffl es and the inner pass can be equipped with other kinds of baffl es (Fig. 18c). Taking the two shell-pass STHX with helical baffl es as an example, the shell has two shell passes, the inner shell pass and the outer shell pass, which are separated by a sleeve tube. The baffl es in the inner shell pass could be some traditional baffl es such as segmental baffl es, discontinuous helical baffl es, disk-doughnut baffl es, rod baffl es, and so on, which could be manufactured and installed easily.

The outer shell pass is constructed by complete continuous helical baffl es. Because of the inner sleeve tube, the inner shell-pass baffl es and outer shell-pass helical baffl es do not need to be fi xed on the same helical surface. The inner shell pass and the outer shell pass are joined together at one end of the shell side. If the working fl uid fl ows through the inner and outer shell pass simultaneously, the STHX is called parallel combined multiple shell-pass helical baffl ed STHX

Figure 42: Maximal velocity ratios versus Nusselt number [65].



(Fig. 43a), and if the working fl uid fl ows through the inner and outer shell passes sequentially, the STHX is called series combined multiple shell-pass STHX with helical baffl es (Fig. 43b).


The shell of the parallel combined multiple shell-pass STHX with helical baffl es and the series combined multiple shell-pass STHX with helical baffl es have been separated into several individual shell passes. As to each individual shell pass, the cross-sectional fl ow area is reduced, and thus the velocity of the fl uid could be

Figure 43: Schematic of combined multiple shell-pass STHXs with helical baffl es [69–74].



increased for the same mass fl ow rate, and therefore the heat transfer performance can be expected to have a great improvement. In addition, the combined multiple shell-pass STHXs with helical baffl es avoid the diffi culties in manufacturing con-tinuous helical baffl es with a small size inner helix and increases its compactness.

Numerical studies have been conducted on the series combined multiple shell-pass STHX with helical baffl es by Wang et al. [75, 76]. It was found that the pres-sure drop of combine d double shell-pass STHX with helical baffl es was lower than that of segmental baffl ed STHX by about 13% for the same mass fl ow rate and same heat transfer rate (Fig. 44c). For the same overall pressure drop in the shell side, the overall heat transfer rate of the combined double shell-pass STHX with helical baffl es is nearly 5.6% higher than that of conventional segmental baffl ed STHX and the mass fl ow rate in the double shell-pass STHX with helical baffl es is

Figure 44: Numerical results of combined multiple shell pass STHX with helical baffl es [75].



about 6.6% higher than that in the STHX with segmental baffl es [75]. The velocity distributions and temperature distributions of the numerical results can be seen in Fig. 44a and b. Chen et al. [77] studied the combined multiple shell-pass STHXs with continuous helical baffl es in the outer shell-pass and different forms of baffl es (segmental baffl es, discontinuous baffl es and disk-and-doughnut baffl es) in the inner shell pass with computational fl uid dynamics method. The results indicated that for the same mass fl ow rate and overall heat transfer rate, the double shell-pass STHX with discontinuous helical baffl es in the inner shell pass has the lowest pres-sure drop in the shell side.

7 Concluding Remarks

This chapter demonstrates a general review of the STHXs different baffl es, such as discontinuous helical baffl es, continuous and combined helical baffl es has been presented, from the points of heat transfer enhancement mechanism, improve-ments on baffl e structure, and industrial applications. Some conclusions can be drawn as follows:

1. For the same geometrical structure and same baffl e number, all single shell-pass STHXs with helical baffl es (discontinuous helical baffl es, continuous heli-cal baffl es, and combined helical baffl es) have higher heat transfer coeffi cients per pressure drop h/Δp than the segmental baffl ed STHXs. However, for the same mass fl ow rate, the segmental baffl ed STHXs still have higher heat trans-fer coeffi cients and much higher pressure drop.

2. The single shell-pass STHX with continuous helical baffl es is superior to the heat exchanger with segmental baffl es or discontinuous helical baffl es, but it is diffi cult to be manufactured, especially when a STHX with large-scale shell diameter is needed.

3. The single shell-pass STHXs with combined helical baffl es make good use of advantages of both discontinuous helical baffl es and continuous helical baffl es, and can simplify the manufacturing process.

4. Compared with the single shell-pass STHXs with segmental baffl es or helical baffl es, the combined multiple shell-pass STHXs with helical baffl es in the outer shell passes can enhance the comprehensive heat transfer performance.

5. Both the combined single shell-pass and combined multiple shell-pass STHXs can simplify the manufacture and installation of heat exchangers. They can be used to replace the conventional segmental baffl ed STHXs in industries.

Acknowledgments

This work is supported by National Natural Science and Foundation of China (Grant Nos. 50776068 and 51025623) and the National Basic Research Program of China (973 Program, No. 2012CB720402).



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