International Journal of Heat and Mass Transfer 63 (2013) 434–444

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Numerical investigation of helical baffles heat exchanger with differentPrandtl number fluids

0017-9310/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.04.001

⇑ Corresponding author. Tel./fax: +86 22 27400199.E-mail addresses: xig-xiao@163.com (X. Xiao), zhanglvh@tju.edu.cn (L. Zhang).

Xiaoming Xiao a, Luhong Zhang a,⇑, Xingang Li a,b, Bing Jiang a,b, Xiaoling Yang a, Youmei Xia a

a School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, PR Chinab National Engineering Research Center for Distillation Technology, Tianjin University, Tianjin, PR China

a r t i c l e i n f o

Article history:Received 22 September 2011Received in revised form 14 May 2012Accepted 25 March 2013Available online 3 May 2013

Keywords:Heat transferHelical bafflesPrandtl numberNumerical analysisSimulationOptimisation

a b s t r a c t

The numerical simulations for helical baffles heat exchanger with different Prandtl number (Pr) fluids andthe comparison for helical baffles heat exchangers with different helical tilt angle (b) were presented inthis paper. The results reveal that, the helical baffles are used to direct the shell side fluid flow spirallyacross the tubes, and the guide function will weaken when large Pr fluids involved. The heat transfer coef-ficient per unit length pressure drop decreases with the increase of heat exchanger length, and for heatexchangers with same length, the heat transfer coefficient per unit pressure drop increases with theincrease of b. By comparing heat exchangers with same required heat transfer capacity, heat exchangercontained water as the shell side fluid achieves the best heat transfer performance when b is at 40�, andfor shell side fluid with big Pr, the small angle scheme is the optimal selection.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In the past few decades, shell and tube exchangers carry enor-mous importance in the oil refining, power generation, offshoreheat recovery and so on [1,2]. Among all the assemblies in the heatexchanger, baffle plays a significant role since it is used to directthe shell side fluid flow across the tube bundle in a suitable man-ner to improve heat transfer and maintain a reasonable pressuredrop across the exchanger. Take the most commonly used segmen-tal baffles for an example, the heat transfer is improved as the baf-fles guide the shell side fluid to flow upward and downwardsbetween the tube bundle, which enhances the turbulence intensityand the local mixing [3]. However, the segmental baffles havesome inherent defects since the structure limitations: (1) foulingformed in the stagnation zone near the shell wall and the rear ofbaffle plates; (2) large pressure drop results from baffles’ impedingto the fluid flow and the flow separation near the baffle edge; (3)significant bypass streams and leakage streams due to manufactur-ing tolerances; (4) short operational lifetime as a result of flow-induced tube vibration [4,5].

To minimize the shortcomings of shell and tube heat exchang-ers with traditional segmental baffles, many strategies have beenattempted [6–8]. In the end of 1980th, helical baffles heatexchangers was firstly invented in Czechoslovakia [9]. Instead of

perpendicularly inserting the baffles into the shell, the pseudo-cir-cular shaped baffle plates are mounted in the shell one by one in acertain angle respect to axis. The baffles could be overlapped orcontinuously adjacent, and the value of baffles tilt angle (b) variesas the change of operation conditions [10,11]. Compare to the tra-ditional segmental baffles, the application of helical baffles greatlyreduces the probability of fouling and flow-induced tube vibration,as well as decreases the proportions of bypass streams and leakagestreams in the total streams, moreover, a small increase for theheat transfer rate and a big decrease for the pressure drop willbe achieved [12].

The combination of experimental study and numerical simula-tion study is the main research method for the helical baffles stud-ies so far, most of those researches focused on the flow behaviors inthe shell side, the effect of helical tilt angle on the heat transfer, theheat transfer coefficient correlation and so forth [13–15]. But inprevious studies, some conclusions may not be practical or rigor-ous. For example, the heat transfer coefficient per unit pressuredrop was considered as the heat transfer efficiency evaluation cri-terion for heat exchangers, and the comparison was always basedon the same heat transfer areas or the same Reynolds number (Re)for different heat exchangers. However, in heat exchanger design,the heat exchanger size and the heat exchanger area are alwaysunknown, while the volumetric flow rate, the inlet temperaturefor each working mediums and the required heat transfer capacityare always known and set as inputs; plus, for helical baffles heatexchanger, the Re changes a lot with the change of b under the

Nomenclature

Latin lettersA heat transfer area, m2

B baffles spacing, mCp specific heat, J/kg KD inside diameter of shell, md tube outside diameter, mde equivalent diameter, mK total heat transfer coefficient, W/m2 KL effective length of tube, mm mass flow rate, kg/sV volumetric flow rate, m3/hN number of tubesp tube pitch, mPe Peclet numberPr Prandtl numberq volumetric flow rate, m3/hRe Reynolds numberS cross area, m2

T temperature, �Cu mean velocity, m/s

Greek lettersa shell side heat transfer coefficient, W/m2 Kb helical baffles tilt angle, �DP pressure drop, PaDTm logarithmic mean temperature difference,k thermal conductivity, W/m Kl dynamic viscosity, N s/m2

q fluid density, kg/m3

Subscriptsin inletout outlets shell sidet tube sidew wall

X. Xiao et al. / International Journal of Heat and Mass Transfer 63 (2013) 434–444 435

same shell side volumetric flow rate. Thus, compared to the com-parison of heat exchangers with same Re or same heat transferarea, the comparison of heat exchangers with same required heattransfer capacity seems to be more practical. Moreover, in previouspublications, no early research had been focus on the influence ofthe fluid characteristic on the design of helical baffles heat exchan-ger yet. For instance, in some published literatures, 40� was theoptimal baffles tilt angle since the boundary layer thickness onthe tube surface was the thinnest [4,16], but only water in turbu-lent state was tested in the original experiments and no further re-search predicted that the conclusion would be applied to otherfluids with different Prandtl number (Pr) or in different flow state.

The objective of this paper is to study the heat transfer perfor-mance for fluids with different Pr in the shell side of helical bafflesheat exchanger. The value of Pr ranges from 5 to 15,000 and thehelical baffles tilt angle varies from 10� to 50�. Firstly, the researchstudied the baffle’s influence on the velocity field and the pressurefield; Secondly, since the length of heat exchangers with differenthelical baffles tilt angle were different in order to providing thesame heat transfer capacity, we explored the effect of heat exchan-ger length on the heat transfer performance in the next section; Fi-nally the paper studied the heat transfer performance for fluidswith different Pr. Though turbulent flow was desired for most heattransfer processes, the laminar flow was also studied since the Rewas quite small for some simulation runs. The numerical approachwas employed as the primary research method as the experimentresult validation for the simulation result was conducted ahead oftime.

2. CFD modeling

2.1. Physical modeling

The geometry was drawn and meshed by using GAMBIT 2.3.16software as well as Fluent 3.2 software. The physical model was asimplified heat exchanger model with 4 � 4 tubes scheme. Thoughwithout nozzles, helical baffles with nine types of angles, sixgroups of helical baffle cycle unit numbers (stand for different heattransfer lengths), and a segmental baffle heat exchanger for flowpattern comparison were included in the model. The detailedgeometry parameters are listed in Table 1 and a sample of whichwith 25� baffles tilt angle and six baffle cycle units is shown inFig. 1. Two things should be noted for the physical model. First,

the effective tube length is equal to the baffles spacing value mul-tiplies by the baffle cycle unit number. Take the heat exchangerwith 10� baffles tilt angle for example, when baffle cycle unit num-ber was designed to be 2, the tube effective length was equal to37.12 mm, which is the double of the baffles spacing. Second, thenumbers with asterisk in Table 1 indicate that they are exclusivegeometry parameters for heat exchanger with segmental baffles.

2.2. Governing equations and boundary conditions

The commercial CFD code Fluent 6.3 was used to perform thesimulation. Since the Re number of fluid in this article was in therange from dozens to hundreds of thousands, the simulations weresolved employing the laminar flow model and the renormalizationgroup (RNG) k–e model. Choosing (RNG) k–e model as the turbu-lence model was because it involved the effect of swirl on turbu-lence, which could enhance the simulation accuracy of swirlingexisted in the heat exchanger [17]; plus, the (RNG) k–e modelhad already gained excellent utilization in some published articlesabout heat exchanger simulation [18–20]. The governing equationsfor continuity, momentum, energy, k and e for the fluid region areas follows:

Continuity:

@

@xiðquiÞ ¼ 0 ð1Þ

Momentum:

@

@xiðquiukÞ ¼

@

@xil @uk

@xi

� �� @P@xk

ð2Þ

Energy:

@

@xiðquitÞ ¼

@

@xi

kCp

@t@xi

� �ð3Þ

Turbulent kinetic energy:

@

@tðqkÞ þ @

@xiðqkuiÞ ¼

@

@xjakleff

@k@xj

� �þ Gk þ qe ð4Þ

Turbulent dissipation energy:

@

@tðqeÞ þ @

@xiðqeuiÞ ¼

@

@xjaeleff

@e@xj

� �þ C�1e

ek

Gk � C2eqe2

kð5Þ

Table 1Detailed geometry parameter for simulated heat exchangers.

Parameters Unit Value

Inside diameter of shell mm 150Tube outside diameter mm 19Effective length of tube mm 37.12–2528.09, 600⁄

Number of tubes – 16Tube layout pattern � 90Tube pass – 1Tube pitch mm 25Baffle cycle unit number – 2,4,6,8,10Baffles tilt angle � 0⁄,10,15,20,25,30,35,40,45,50Baffle spacing mm 18.56–252.81, 60⁄

Fig. 1. Schematic diagram of heat exchangers with helical baffles: (a) tube bundles arrangement in the shell side; (b) side view of heat exchanger with parameters definition.

436 X. Xiao et al. / International Journal of Heat and Mass Transfer 63 (2013) 434–444

where

leff ¼ lþ lt; lt ¼ qClk2

e; C�1e ¼ C1e �

gð1� g=g0Þ1þ bg3 ð6Þ

g ¼ ð2Eij � EijÞ1=2 ke; Eij ¼

12@ui

@xjþ @uj

@xi

� �ð7Þ

The coefficients for the (RNG) k–e model were assigned as the de-fault values in Fluent 6.3.

The flow was taken as steady, incompressible one. Non-slipboundary condition was applied on all the solid surfaces withinthe computational domain and the standard wall function wasadopted near the wall and the range of the dimensionless lengthx+ or y+ was 10 < x+(y+) < 100. The ‘‘velocity inlet’’ was served asthe shell side inlet boundary with a constant total temperaturedesigned at 343.15 K, and pressure-outlet boundary conditionwas applied on the shell outlet with back total temperature set

Table 2Thermo physical properties of the simulated materials.

Material name Density (kg/m3) Specific heat capacity (J/kg K)

Water liquid 998.20 4182.00Gasoil liquid 830.00 2050.00Ethylene glycol 1111.40 2415.00Glycerin 1259.90 2427.00Engine oil 889.00 1845.00

as constant numbers, the numbers were specific values varied withsimulation cases. The temperatures of tube walls were set as328.15 K, and other solid surfaces were set as adiabatic. Five kindsof fluids with different Pr were utilized to simulate, the thermophysical properties of those fluids are listed in Table 2.

2.3. Mesh selection and independency validation

Mesh generation was performed using Gambit. The shell volumewas meshed using unstructured tetragonal-hybrid elements andthe size function in Gambit was utilized to improve the calculationaccuracy in the regions adjacent to the tubes as seen in Fig. 2, Themesh size varied from 1,800,000 to 10,000,000 with the change ofsimulation case, and the smallest mesh size reached 2.2 � 10�10 m3.

As seen in Table 3, the grid independence tests were carried outwith adopting three different mesh size groups for the case with25� baffles tilt angle and six baffle cycle units. The differences be-tween the latter two groups were less than 3% in pressure drop aswell as the temperature. Considering, both the calculating time andsolution precisions, the second mesh system was taken for thephysical model.

2.4. Numerical method

The governing equations along with the boundary conditionswere iteratively solved by the finite volume method using SIMPLEpressure–velocity coupling algorithm [21,22]. The QUICK schemewith three-order precision was utilized for convective formulationand the SIMPLE algorithm was for pressure-velocity coupling.

The convergence criteria were 10�8 for energy and 10�5 for allother equations. The calculations were carried in a DELL towerworkstation with two Quad Core Intel� Xeon� 5590 3.33 GHz CPUs

Thermal conductivity (W/m K) Viscosity (kg/Pa s) Pr

0.600 0.00100 6.990.140 0.00332 50.410.252 0.01570 150.460.286 0.79900 6780.330.145 1.06000 13487.59

Fig. 2. Front view of meshed heat exchanger head.

Table 3Summary of grid independence checks for simulation.

Item Coarse grid Medium grid Fine grid

Nodes number 878192 1683365 3830694DP, kPa 10.24 8.96 8.69Ts,out, �C 42.98 42.90 42.92

Table 4Main geometric parameters of the experiment setup.

Parameters Unit Value

TEMA type – BEUInside diameter of shell mm 500Tube outside diameter mm 19Tube inside diameter mm 15Effective length of tube mm 6000Number of tubes – 208Tube layout pattern � 90Tube pass – 2Tube pitch mm 25Inlet nozzle diameter mm 150Outlet nozzle diameter mm 150Baffles tilt angle � 25Baffle spacing mm 638.8

X. Xiao et al. / International Journal of Heat and Mass Transfer 63 (2013) 434–444 437

and 48 GB memory. Due to the different mesh numbers, each sim-ulation case took approximately 2–10 h to converge.

2.5. Experiment setup and model validation

In order to check the simulation model validity, a pilot-scalehelical baffles heat exchanger experiment was carried out. The linediagram of the experiment setup is shown in Fig. 3. The experimentsystem contained the test helical baffles heat exchanger, the rela-tive devices and the utilities. Hot water and cold water were usedas the test fluids, the cold water ran through the tube side of thetest heat exchanger and the hot water flowed through the shellside.

Fig. 3. Line diagram of the experiment setup: 1 – hot water tank; 11 – cold water tatemperature indicator; 6 – test heat exchanger with helical baffles; 9 – heat exchanger fwater inlet; 20 – cooling water outlet.

The main geometric parameters for the test heat exchanger arepresented in Table 4. To investigate the heat transfer performancein the shell side of the test heat exchanger, several groups of exper-iments were carried out. In each run, the volumetric flow rate andthe inlet temperature of each fluid were set fixed as inputs, theoutlet temperature and the pressure drop of the shell side and tubeside were recorded. Different operation conditions were obtainedby varying volumetric flow rate of the inlets. The volumetric flowrates in the shell side and tube side ranged from 50 m3/h to150 m3/h and 50 m3/h to 90 m3/h respectively. The inlet tempera-tures of shell side and tube side were controlled at 70 �C and 40 �C.

The armored pt100 temperature sensors with a precision of0.2 �C were installed to measure the hot and cold water tempera-tures at the inlet/outlet of the heat exchanger. The pressure dropof water flowing through the test heat exchanger was measuredby pressure transmitters (Rosemount� 3051S) with the accuracyof 0.1% at a range 0–1.0 MPa. The volumetric flow rates for fluidsin the shell side and tube side were measured by two vortex flow-meters (KROHNE� OPTISWIRL 4070) with precisions of 0.75% of0–250 m3/h. The output signal for all measuring instruments were4–20 mA and a data acquisition unit (WP-R302C type color screenpaperless recorder) was used for data collecting and displaying.The experiment runs were accepted for data recording only if thesteady state conditions were verified and the deviation betweenheat loads from hot side and cold side were calculated less than10%. The time consumption for each run was probably 15 min.

The simulation model with 25� baffles tilt angle and six bafflecycle units as shown in Fig. 1 was employed to the model valida-tion. Though the scale of the simulation model and the experimentheat exchanger was different, the flow pattern and the heat

nk; 2, 12 – pump; 3, 13 – flowmeter; 4,7,14,17 – pressure indicator; 5,8,15,16 –or heating; 10 – heating steam inlet; 18 – heat exchanger for cooling; 19 – cooling

Fig. 5. Comparison of overall shell side pressure drop between the experimentalresults and simulated results.

438 X. Xiao et al. / International Journal of Heat and Mass Transfer 63 (2013) 434–444

transfer process, as well as the mathematical model were similarbetween them. As the increase of the shell side fluid velocity, thecomparison of total heat transfer coefficient and overall shell sidepressure drop between the experimental results and simulated re-sults in shell side were provided in Figs. 4 and 5. In these evalua-tions, the main aim was to compare the trends, as can be seen,the trends for both results were similar, which indicated the reli-ability of the simulation model and the mesh choosing.

2.6. Parameter definition

The definitions of Reynolds number in the shell side are asfollows:

Res ¼qsdeus

lsð8Þ

where de is the equivalent diameter derived from the tube outsidediameter d, for square tube layout, de is defined as in Eq. (9) [7]:

de ¼4p2 � pd2

pdð9Þ

The value of the fluid density qs and the dynamic viscosity ls aredetermined by the average temperature of the shell side fluid. us

is the mean velocity of fluid in the shell side defined by

us ¼qs

qSð10Þ

S ¼ 12

BD 1� dp

� �ð11Þ

where S is the cross area at the shell centerline [23–25], D is insidediameter of shell and p is tube pitch, B stands for baffles spacing,which is derived from helical baffles tilt angle b and shell insidediameter D as shown in Eq. (12):

B ¼ffiffiffi2p

D tan b ð12Þ

The total heat transfer coefficient are defined by the followingequations:

K ¼ QADTm

ð13Þ

A ¼ N � pdL ð14Þ

DTm ¼ðDTmax � DTminÞlnðDTmax=DTminÞ

ð15Þ

Fig. 4. Comparison of total heat transfer coefficient between the experimentalresults and simulated results.

DTmax ¼ maxðTw � Ts;in; Tw � Ts;outÞ ð16Þ

DTmin ¼ minðTw � Ts;in; Tw � Ts;outÞ ð17Þ

3. Results and discussion

3.1. Baffle’s effect on velocity field in the heat exchanger withsegmental and helical baffles

Fig. 6a and b illustrate the fluid flow in the shell side of heat ex-changer with segmental and helical baffles. As seen in Fig. 6a, inthe heat exchanger with segmental baffles, the baffles in the shellside work as obstacles which divide the original axial flow intocross flow, back flow and some vortex. In the zones near the edgeof baffles, the direction of velocity vector changes largely as thefluid has to climb over baffles. Compared to the velocities of themain crossflow streams, the fluid velocities near the shell wall sur-face and at the corner of baffles are rather small, where the stagna-tion flow generated. The turbulence and local mixing result fromthe segmental baffles are positive to heat transfer but rather nega-tive to forming huge pressure loss as a sudden pressure changeforms at each baffle section.

On the contrary, the function of helical baffles is used to form-ing a spiral fluid flow passage which forces the fluid to flowthrough the channels between baffles as depicted in the Fig. 6b.No obvious changes could be found for the direction and the mag-nitude of velocity vector at the near-baffle edge areas, and the uni-formity of the velocity distribution with helical baffles are muchbetter than that with segmental baffles. Since the shell side fluidin the helical baffles heat exchanger keeps moving forward spirallyas the cross plug flow with little back flow or vortex, the helicalbaffles have a similar heat transfer effect as the segmental baffles.With the help of less turbulence and local mixing, the pressuredrop could get a much smaller value than that for segmentalbaffles.

However, the function of construction spiral channels is noteffective in all situations. Fig. 7 shows the velocity field under fourdifferent situations. In Fig. 7a and b, water and glycerin were intro-duced into the shell side of heat exchanger with b at 45�, and inFig. 7c and d, water and glycerin were introduced into the shellside of heat exchanger with b at 10�. From Fig. 7a and b we cansee, though the flow patterns are similar, the velocity distributionare different. In Fig. 7a, a relatively uniform velocity distribution isfound within the cross section except the quarter circle region

Fig. 6. Stream lines in the shell side for heat exchanger with segmental and helical baffles.

X. Xiao et al. / International Journal of Heat and Mass Transfer 63 (2013) 434–444 439

where the baffle existed, indicates that the main stream of fluiddoes pass through the channels formed by the baffles. In Fig. 7b,the velocity in the centerline region is much bigger than the veloc-ities in other regions indicates the leakage stream is generated inthe centerline of the heat exchanger. With the change of shell sidefluid from water to glycerin, the Res (calculated in Eq. (8)) achievesa big change from 8000 to 10, and the flow state transits from tur-bulent flow to laminar flow. The increased wall shear stress in-duces the increase of the large boundary layers at the tube wallsurface and shell wall surface, which forces the main stream ofthe fluid in the Fig. 7b to move through the centerline of the heatexchanger, but not pass through the channels formed by the helicalbaffles. In Fig. 7c and d, the proportion of streams pass through thecenterline decreases as the result of the Re varying to 60,000 and800, respectively where fluids are in turbulent state or near turbu-lent state.

To sum up we can say the function of helical baffles as construc-tion channels does not work well if the shell fluid is in laminarstate. When laminar flow is mainly resulted from the employment

of high viscosity fluid, adopting baffles with small b could enhanceturbulence and induce the fluid flow through the channels.

3.2. Impacts of heat exchanger length on heat transfer and pressuredrop

Water was used as the simulated medium in this section andthe next section, the helical baffles tilt angle degree varied from10� to 50� and the heat baffle cycle unit numbers changed from2 to 12.

As the length of each heat exchanger adopted in the simulationis different, the unit length pressure drop (DP/L), the total heattransfer coefficient (K) as well as the heat transfer coefficient perunit length pressure drop [K/(DP/L)] are studied in order to elimi-nate the length interference effect.

Fig. 8 illustrates the unit length pressure drop (DP/L) against theheat exchanger length. As the increase of heat exchanger length,the proportion of fluid in the steady flow state in the middle sec-tion of the heat exchanger gets increased, and the negative impacts

Fig. 7. Velocity vectors in the longitudinal section plane and velocity contours in the cross section plane for heat exchanger with helical baffles (qs = 5 m3/h): (a) b = 45�,water; (b) b = 45�, glycerin; (c) b = 10�, water; (d) b = 10�, glycerin.

440 X. Xiao et al. / International Journal of Heat and Mass Transfer 63 (2013) 434–444

of inlet and outlet on the pressure drop become relatively smaller.Consequently, as shown in Fig. 8, the DP/L decreases with the in-crease of heat exchanger length for all angle schemes. Besides,for heat exchanger with same length, DP/L for small b scheme isapparently bigger than that for big b scheme, this is because thebig increase of kinetic energy loss results from the increase ofvelocity and the big increase of drag and friction resistance lossdue to the increase of baffle numbers in the small angle scheme.

The variation trend of the total heat transfer coefficient alongheat exchanger length is presented in Fig. 9. It can be clearly ob-served that K decreases with the increase of heat exchanger lengthfor all angle schemes. The reason for the falling trend for the curvesis because the temperature difference between the shell and tubeside fluids decreases with the increase of heat exchanger length,

which reduces the local driving force for heat transfer results inthe decrease of heat transfer coefficient. Apart from this major phe-nomenon, another feature can be noted from Fig. 9: Under thesame heat exchanger length, the K for the small b scheme is biggerthan that for the big b scheme in general, but the K for b = 35� isbigger than that for b = 20�, b = 25� and b = 30�. For example, whenheat exchanger length = 1000 mm, the K for b = 10� increases 66.7%than that for b = 50�, and the K for b = 35� is 5.5%, 8.2%, 3.9% biggerthan that for b = 20�, b = 25� and b = 30� respectively. The explana-tion for this character is as follows: The fluid turbulence intensityand the velocity boundary layer on the tube surface are the twomain factors impact the heat transfer in the shell side, big turbu-lence intensity and thin velocity boundary layer thickness in theshell side will lead to big K. With the increase of b, the fluid turbu-

Fig. 8. Unit length pressure drop versus heat exchanger length for different bafflestilt angles (water).

Fig. 9. Total heat transfer coefficient versus heat exchanger length for differentbaffles tilt angles (water).

Fig. 10. Total heat transfer coefficient per unit length pressure drop versus heatexchanger length for different baffles tilt angles (water).

Fig. 11. Heat transfer length versus heat transfer capacity (qs = 3.2 m3/h, water).

X. Xiao et al. / International Journal of Heat and Mass Transfer 63 (2013) 434–444 441

lence intensity has less impact on the K derived from the reductionof velocity, while the effect of velocity boundary layer growsrespectively, and the thickness of which reaches the minimum va-lue at b = 40� [12,13]. So when the tilt angle grows, the K declinesin general as a result of the decrease of fluid turbulence intensity,and the K for b = 35� is bigger than some smaller angle schemessince the thinner velocity boundary layer thickness.

In Fig. 10, the heat transfer coefficient per unit length pressuredrop against the heat exchanger length is presented. First, we cansee that the [K/(DP/L)] decreases with the increase of the heatexchanger for all angle schemes. Though both present the declinetrend as shown in Figs. 8 and 9, the numerator of [K/(DP/L)] isfalling faster than the denominator leads to the downward trendfor the curves presented in Fig. 10. Secondly, under the same heatexchanger length, [K/(DP/L)] gets bigger as the increase of b. Thephenomenon is different from the previous reports that K/DPreaches the largest value when the baffles tilt angle is in the rangeof 35� to 45� [13,16]. In their studies, the comparisons were basedon the same pressure drop or the same Re, while the heatexchangers in Fig. 10 shared the same shell side flow rate andthe comparison was based on the same heat exchanger length.

3.3. Comparison of heat transfer performance with same required heattransfer capacity

The length of heat exchangers with same heat transfer capacitycan be obtained as shown in Fig. 11. For example, the vertical coor-dinate values to the intersection points of the vertical line and thecurves represent the length of heat exchangers with helical bafflesin different tilt angle sharing the heat transfer capacity = 18,000 W,and the exact values are obtained by formula fitting andcalculation.

In Fig. 12, the variation of shell side heat exchanger lengthagainst the baffles tilt angle with heat transfer capacity rangingfrom 15,000 W to 45,000 W is reported. One can see immediatelyfor each set of heat transfer capacity, heat exchanger with b at10� has the shortest heat exchanger length, (i.e., the smallest re-quired heat transfer area), and the length value increases withthe increase of b when b < 25�, then the length value falls with b till35�. When b > 35�, the required heat exchanger length returns toincrease with b. If one merely considered the reduction of heattransfer area, b = 10� seems to be a better choice. The mechanismof fluctuated curves in Fig. 12 is explained as follows: To providethe same required heat transfer capacity, A heat exchanger withshortest length must have a bigger K. The heat exchanger length

grows with the increase of b in general is due to the decline of Kin general as discussed in Section 3.2, which is influenced mainlyby the decrease of fluid turbulence intensity. The heat exchangerlength declines when 25� < b < 35� since the K falls in this angle

Fig. 12. Heat transfer area versus baffles tilt angle for different heat transfercapacity (qs = 3.2 m3/h, water).

Fig. 14. Total heat transfer coefficient per unit pressure drop versus baffles tiltangle for different heat transfer capacity (qs = 3.2 m3/h, water).

442 X. Xiao et al. / International Journal of Heat and Mass Transfer 63 (2013) 434–444

range resulted from the reduction in the velocity boundary layerthickness on the tube surface.

Fig. 13 depicts the shell side pressure drop versus baffles tilt an-gle for different heat transfer capacity, the value of the heat trans-fer area for each heat exchanger is reported in Fig. 12. It is clear inFig. 13 that the pressure drop decreases with b for all heat transfercapacity scheme, and with the increase of b, the decreasing ten-dency becomes more and more gently, which implies that the ef-fect of b on the pressure drop is larger for small angle than bigangle. For the case heat transfer capacity = 20,000 W, the pressuredrop decreases 60% when b increases from 10� to 15�, but only re-duces 10% when b varies from 45� to 50�. When b is small, the baf-fles spacing is small which limits the channel space to increase thefluid velocity and forces the shell side fluid moving in a reinforcedzigzag way leading to severe pressure loss, the fluids have to movelonger to cross the heat exchanger derived from large backflow orvortex, consequently result in a big pressure drop. When b gets lar-ger, the baffles spacing is bigger, and the fluid could pass throughthe channels formed by the baffles easier but not crash the bafflesthemselves. Thus backflow and vortex are greatly reduced result inthe small pressure loss when b is large.

In Fig. 14 the heat transfer coefficient per unit pressure dropversus baffles tilt angle for different heat transfer capacity isshowed and a peculiar behavior is observed that among all heat

Fig. 13. Shell side pressure drop versus baffles tilt angle for different heat transfercapacity (qs = 3.2 m3/h, water).

exchangers with the same heat transfer capacity, K/DP is largestwhen b is at 40�.

From Figs. 12–14, the following conclusions to fluid water couldbe reached. Firstly, when considering heat transfer area, DP andK/DP as the main three objective functions for heat exchanger’sselection, best heat transfer performance is obtained whenb = 40�. Take the curves present heat transfer capacity = 25,000 Wfor example: although the heat transfer area value for b = 10� is25% smaller than the value for b = 40�, DP and K/DP for b = 10� is25 times and 20 times bigger than that for b = 40� respectively,similar result can be obtained when comparing b = 15� to b = 40�.For 15� < b < 50�, both heat transfer area and DP get the relativelysmall values and K/DP gets the maximum value when b = 40�. Sowhen deal with water as the shell side fluid, b = 40� is the bestchoice. The conclusion could be viewed as a additional revisionto the result of [9].

Secondly, an interesting phenomenon will be found if we goback to Fig. 12. The heat exchanger length (i.e., the required heattransfer area) increases 40% and 80%, and decreases 30% when bchanges from 40� to 50�, 25� and 10� respectively when heat trans-fer rate = 15000 W, and for heat transfer rate = 45000 W, the re-quired heat transfer area increases 35% and 30%, and decreases45% when b changes from 40� to 50�, 25� and 10� respectively. Ithas been revealed that the ascendant performance at b = 40� willbe weaken if enhanced the required heat transfer capacity.

3.4. Pr effect on heat transfer performance

As stated in the Table 2, five kind of fluids with different Pr wereutilized to simulate in this section. With the identical volumetricflow rate and temperature inlet conditions, the fluids were intro-duced into the shell side of heat exchanger with b changed from10� to 50�. To provide the same required heat transfer capac-ity = 15000 W, the lengths of heat exchangers were different witheach other and the detail of length selection is described in Section3.3.

In Fig. 15, heat exchanger length against the baffles tilt angle forfluids with different Pr is presented. For water and gasoil liquid, theheat exchanger length curves are fluctuated and the relativelysmall value are caught when b = 35�. But for curves with biggerPr, the curves are monotone increasing.

Fig. 16 depicts the shell side pressure drop versus the baffles tiltangle for different fluids. The obvious decreasing trends areobserved for all curves, and for curves with same b, the pressuredrop increases with the increase of Pr, which mainly result from

Fig. 15. Heat exchanger length versus baffles tilt angle for fluids with different Pr(qs = 3.2 m3/h, Heat transfer capacity = 15000 W).

Fig. 16. Shell side pressure drop versus baffles tilt angle for fluids with different Pr(qs = 3.2 m3/h, Heat transfer capacity = 15000 W).

Fig. 17. Total heat transfer coefficient per unit pressure drop versus baffles tiltangle for fluids with different Pr (qs = 3.2 m3/h, Heat transfer capacity = 15,000 W).

X. Xiao et al. / International Journal of Heat and Mass Transfer 63 (2013) 434–444 443

the decrease of Reynolds number in the shell side, sharing thesame conclusion as the classical theory [26].

Fig. 17 reports the heat transfer coefficient per unit pressuredrop against the helical tilt angle for different fluids. Like thecurves exhibited in Fig. 14, the curve for water (Pr = 6.99) in theFig. 17 shows an inverted U-shaped trend and reach its maximumwhen b = 40�, and K/DP decreases 10% and 15% when b varies to45� and 50�. However, other curves do not share the same curvetrend as the water curve. The curve for gasoil liquid (Pr = 50.41)keeps increasing from b = 10� to b = 40�, then the value of K/DP re-duces only 4% and 6% when b varies to 45� and 50�. The ethyleneglycol curve (Pr = 150.46) ascends gradually to reach a peak whenb = 40�, then the value of K/DP changes merely between b = 40� andb = 45�, and increases 2% at b = 50�. For the glycerin curve(Pr = 6780.33) and engine oil curve (Pr = 13487.59), the curvesare monotone increasing. The values of K/DP at b = 50� increase8% and 7% respectively in contrast with the values at b = 40�.

The reason for their difference in curve tendency could be ex-plained as follows. For fluids similar to water, a thinnest boundarylayer is obtained on the tube surface at b = 40�, which mostly de-crease the resistance to heat transmission [1,16]. For fluid withmuch bigger Pr like glycerin, ‘though the velocity boundary layercould also approach the minimum value at b = 40�, the absolutethickness is much bigger in this case, which is almost unchangedsince the original big value when b > 40�. Therefore, the reduction

for heat transfer rate is smaller than the reduction for pressuredrop results in the continual growth trend of K/DP when b > 40�.

From Figs. 15–17 we can see, for employing glycol as the shellside fluid, though the pressure drop reduces 70% when b changesfrom 10� to 50�, the heat exchanger length (i.e., the heat transferarea) increases 2.3 times, and the net increased amount of heattransfer area reaches 3 m2, besides, only a 2.1 times bigger increaseobtained for K/DP at b = 50� than that at b = 10�. Similar results canbe obtained for engine oil from Figs. 15–17. So when wecomprehensively consider K/DP, heat transfer area and DP in heatexchanger’s selection, heat exchangers with small b is the optimalchoice for shell fluid with big Pr. Furthermore, the shell side fluidvelocities in this section range from 0.20 m/s to 1.32 m/s with bchange from 50� to 10�. For fluid with big Pr, the small fluidvelocity at big b will lead to laminar flow and is harmful to the heattransfer; conversely, the relatively big fluid velocity at small b willinduce turbulent flow and improve heat transfer. From this point ofview, we can also draw the conclusion that the heat exchangerwith small b should be applied when the shell fluid has big Pr.

4. Conclusions

In this paper, the heat transfer and fluid flow performance ofheat exchangers with different baffles tilt angles were studiedusing the CFD method. After discussed the effect of baffles and heatexchanger length on heat transfer performance, a new perspectivewas provided that the heat transfer performance comparisonamong different heat exchangers is better conducted under thesame required heat transfer capacity, then five different kinds offluids were involved in the research to reveal the effect of Prandtlnumber on heat transfer characteristics. Following are the mainfindings in this article:

1. Despite causing enhancement in turbulence, the segmental baf-fles in heat exchanger work as obstacles to induce huge pres-sure loss, while the helical baffles in the heat exchangerchannel the fluid flow to generate a much smaller pressuredrop. The function of helical baffles as construction channelswill weaken when fluid with big Prandtl number involved,and the heat exchanger with small helical tilt angle couldenhance the turbulence and resume the baffle’s function.

2. The heat transfer coefficient per unit length pressure drop willreduce if lengthen the heat exchanger, the heat transfer coeffi-cient per unit length pressure drop increases with the increaseof helical tilt baffles under the same heat exchanger length.

444 X. Xiao et al. / International Journal of Heat and Mass Transfer 63 (2013) 434–444

3. When same heat transfer capacity required and adopting wateras the shell side fluid, heat exchanger with helical tilt angle at40� is the best selection, but the superiority will be less obviousif the required heat capacity increased.

4. Helical baffles tilt angle at 40� is no more the best selection ifthe Prandtl number for the shell side fluid increases. When Pra-ndtl number is large enough, heat exchanger with small bafflestilt angle reveals to be the optimal choice.

Acknowledgements

This research was supported financially by the Program for Na-tional Basic Research Program of China (No. 2009CB219905 and2009CB219907) and Chang Jiang Scholars and Innovative ResearchTerms in Universities (No. IRT0936).

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