Comparison of heat transfer performances of helix baffled heat exchangers with different baffle configurations☆

Cong Dong ,Yaping Chen *,Jiafeng Wu

1 School of Energy and Environment,Southeast University,Nanjing 210096,China

2 School of Light Industry,Zhejiang University of Science and Technology,Hangzhou 310023,China

Keywords:Helix baffled heat exchanger Trisection baffle Quadrant baffle Continuous baffle Circumferential overlap baffle Secondary flow Heat transfer Numerical simulation

ABSTRACT Numerical simulations were performed on flow and heat transfer performances of heat exchangers having six helical baffles of different baffle shapes and assembly configurations,i.e.,two trisection baffle schemes,two quadrant baffle schemes,and two continuous helical baffle schemes.The temperature contour or the pressure contour and velocity contour plots with superimposed velocity vectors on meridian,transverse and unfolded concentric hexagonal slices are presented to obtain a full angular view.For the six helix baffled heat exchangers,the different patterns of the single vortex secondary flow and the shortcut leakage flow were depicted as well as the heat transfer properties were compared.The results show that the optimum scheme among the six configurations is a circumferential overlap trisection helix baffled heat exchanger with a baffle incline angle of 20°(20°TCO)scheme with an anti-shortcut baffle structure,which exhibits the second highest pressure drop Δp o,the highest overall heat transfer coefficient K,shell-side heat transfer coefficient h o and shell-side average comprehensive index h o/Δp o.

1.Introduction

The shell-and-tube heat exchangers are widely used in petroleum re fining,chemical engineering,power plants and food processing,and most of them are segment baffle type.However,segment baffle type heat exchangers have many drawbacks,including stagnant zones with lower heat transfer coefficients,higher pressure drops,and a propensity to induce vibration and fouling.These problems could be ameliorated by installing helical baffles in the shell side.

Since the advent of quadrant helix baffled heat exchangers developed by Lutcha and Nemcansky[1],many researchers have studied helix baffled heat exchangers.Lutcha and Nemcansky[1]indicated that the optimum incline of the sector baffles is 40°by the chart of heat transfer coefficient hoversus pressure drop Δpo.Stehlik et al.[2]suggested using axial overlap baffles to reduce the support span of the tubes and the leakage between adjacent plates.Andrews and Master[3]developed a 3D CFD method for numerical simulation of the helix baffled heat exchangers.Zhang et al.[4]experimentally measured four middle overlapped schemes of helix baffled heat exchangers with different tube lengths and cylinder diameters,and found that the best scheme is the one with an inclining angle of30°,and it also demonstrated that all the tested helix baffled heat exchangers have 10%-40%less heat transfer coefficients than that of the segmental baffle one.Zhang et al.[5]also simulated several shell-and-tube heat exchangers with middle overlapped helical baffles and continuous baffles,and the results agree with the experimental data.Chen[6]noticed that the V-notch of adjacent baffles at the periphery of the axial overlap scheme opens a leakage shortcut to the downstream chamber and it might affect the heat transfer of the mainstream flow.Cao et al.[7]numerically verified this speculation,and found that both the shell-side heat transfer coefficient and pressure drop decrease with the increase in the overlap size at certain mass flow rates.Song and Pei[8]constructed an “anti-shortcut”baffle structure by widening the straight edges of the sector baffles in the circumferential overlapping area of the adjacent baffles for improving heat transfer performance.Peng et al.[9]discovered experimentally that the continuous helical baffle schemes performed more poorly than both quadrant helical baffle and segmental baffle schemes in terms of the shell-side heat transfer coefficient and comprehensive index of shell-side heat transfer coefficient per unit pressure drop.

Considering most heat exchangers adopting an equilateral triangle tube layout,Chen[6]proposed a modified design of so called trisection helix baffled heat exchangers,thus the edges of sector baffles could be situated in the gaps between tube rows.The results of water-water heat transfer performance tests[10,11]demonstrated that the circumferential overlap trisection scheme with an inclined angle of 20°is better than other heat exchangers including the segmental one in terms of both the shell-side heat transfer coefficient and the shell-side heat transfer coefficient per unit pressure drop.So far,different schemes were studied by a variety of researchers[12-19],but there emerged the question which one performs better,the continuous helical baffle scheme or the non-continuous one,the quadrant baffle scheme or the trisection baffle one?

Experimental research is an indispensable step before a new type of heat exchanger is put into use;however,numerical simulation plays a crucial role in explaining how structural factors influence the flow and heat transfer of a heat exchanger[20,21].In this study,six helix baffled heat exchangers exhibiting an identical equilateral triangle tube layout and approximate spiral pitch with different baffle shapes and assembly configurations,i.e.,two trisection baffle schemes of a 20°incline angled circumferential overlap baffle one(20°TCO)and a 36.2°incline angled axial middle overlap baffle one(36.2°TMO),two quadrant baffle schemes of a 18°incline angled circumferential overlap baffle one(18°QCO)and a 18°incline angled end-to-end baffle one(18°QEE),and two continuous helical baffle schemes with helix angles of 18.4°(18.4°CH)and 16.8°(16.8°CH),were numerically simulated.The former five schemes have a spiral pitch of 129 mm while the latter one has a decreased spiral pitch of 117 mm,in the shell side with a 123 mm diameter.

2.Computational Models

Geometric models of six helix baffled heat exchangers are shown in Fig.1,and the geometric parameters are listed in Table 1.The components of each physical model include a shell,tubes,tube plates,helical baffles,rods,and inlets and outlets for both fluid sides.The shell-side channel consists of 10 helical cycles,and there are 34 heat exchange tubes and 3 rods,consistent with the test piece of circumferential overlap trisection helix baffled heat exchanger scheme with 20°inclineangle.Models of six schemes 20°TCO,36.2°TMO,18°QCO,18°QEE,18.4°CH and 16.8°CH are shown in Fig.1(b)to(g)respectively.

Table 1 Geometric parameters of shell and tube of helix baffled heat exchanger

Fluid flow and heat transfer follow the three basic laws of conservation of mass,momentum and energy.The RNG k-ε turbulent viscosity model is used to provide an improved flow field with high streamline curvature for helical heat exchangers;the options“enhanced wall treatment”and “thermal effects”are enabled in this model to achieve the accurate spiral flow in the shell side.The equations mentioned here are expressed as the following general formula[3,5,12]:

where U is the velocity vector,Φ is the universal variable representing temperature T,velocity components u,v,w,or turbulence parameters k andε,andΓΦand SΦare the generalized diffusion coefficient and generalized source term,respectively.

The commercial CFD software FLUENT was used for numerical simulation.The SIMPLE algorithm was adopted to address the coupling between velocity and pressure.The residual values of conservation equations on u,v,w,k andεwere controlled to be less than 10?4and the counterpart for“energy”was below 10?7,respectively.

Fig.1.Geometric model of helix baffled heat exchanger and baffle structures of six schemes.

Convective heat transfer on both sides of the heat exchanger is considered to make the simulation more close to real heat exchanger conditions.The following assumptions were made:(1)the fluids within the shell helical passages and tubes are incompressible,fully developed in turbulence and steady;(2)the heat loss of the shell wall is ignored;and(3)the leakage between baffles and the inner shell wall is considered,but that between baffles holes and tubes is ignored.

The following boundary conditions were employed:(1)The temperature inlet and velocity inlet boundary conditions of both the shell and tube sides for the six schemes are set to be identical to the measured test values of the 20°TCO scheme[9];(2)pressure outlet boundary conditions are applied,and both the shell and tube sides values are set to 0 Pa(gauge);(3)adiabatic boundary conditions are used at the shell wall,inlet and outlet tube walls,and no-slip,no-penetration and coupled boundary conditions are adopted at the heat transfer tube walls and the helical baffle walls,while the thickness of the tube walls is omitted;and(4)the physical parameters of fluid medium on both tube and shell sides are all expressed as the fourth-order polynomial functions of the temperature.

3D models of the helix baffled heat exchangers were created and calculation grids were generated by the GAMBIT software,as shown in Fig.2.Grid independence tests were conducted and the deviation of the shell-side heat transfer coefficient hobetween the programs featuring a grid number of 3.9 million and 4.5 million was within 2%at the same shell-side mass flow,therefore,3.9 million grid cells were adopted.Fig.3 shows the comparison results of shell-side heat transfer coefficient and pressure drop of the numerical simulation with the experimental data[10]of the 20°TCO scheme.The average deviations of the heat transfer coefficient and pressure drop are approximately 14.88%and 9.96%,respectively.It can be concluded that the deviations are acceptable and the computational accuracy of mathematical model is reasonable.

3.Numerical Simulation Results

The medium on the tube side was hot water,and the inlet velocity and temperature were Vi,in=1.37 m·s?1and Ti,in=339.4 K,respectively;while the inlet velocity and temperature of the shell-side cold water were Vo,in=2.82 m·s?1and To,in=324.9 K,respectively,corresponding to a flow rate of Go=3.57 kg·s?1and a shell-side axial Reynolds number of Rez,o=6887.

Fig.2.Grid on longitudinal section.

Fig.3.Comparison of simulated and measured results of the 20°TCO scheme.

To provide a more vivid picture of the distribution of the flow pattern in the spiral channel,the meridian slice M1,transverse slices f and f1 and concentric hexagon slices H2 and H3 within the fully developed region between the fifth(C5)and sixth(C6)helix cycles were constructed as shown in Fig.4.

3.1.Temperature field

Fig.5 shows temperature contours on the meridian slice M1 and transverse slice f between helical cycles C5 and C6 for the 20°TCO,18°QEE,36.2°TMO and 18.4°CH schemes,respectively.On each meridian slice M1,the temperature increases uniformly along the flow direction from left to right,and the temperature is higher at axis than that at periphery.It is clearly seen that the temperature at the front of the helical baffle is lower than that at dorsal regions,which implicates the difference of thermal boundary layer thickness.Also it shows that the temperature difference of the 20°TCO scheme is greater than that of the other schemes,which reflects its higher shell-side heat transfer coefficient ho.

3.2.Flow and pressure fields

Fig.6 shows pressure contours with velocity vectors superimposed on the meridian slice M1 for the six schemes respectively.Guided by the helical baffles,the fluid flows from the high-pressure region to the low-pressure region,the flow field pattern repeats in each helix cycle that the centrifugal force of spiral flow drives the flow outward in the starting section,and the radial pressure difference supplies a centripetal force that allows the flow to reach equilibrium; finally,inward flow occurs in the end section of each cycle chamber,thus,a single vortex secondary flow is created.It is also showed that the 20°TCO scheme has the strongest secondary flow of the six schemes,which can enhance the mixing of fluids,reduce the boundary layer thickness,augment the shell-side heat transfer,and prevent the tubes from fouling.On the other hand,the 36.2°TMO and 18.4°CH schemes exhibit relatively lower secondary flow among the six schemes.

Fig.7 shows pressure contours with velocity vectors superimposed on the transverse slices f and f1 for the schemes of 20°TCO and 18.4°CH respectively.It shows that the main fluid flows along the clockwise direction,but there are also flow vectors along the centrifugal,centripetal and other directions.In the slice f for the 20°TCO scheme shown on Fig.7(a)in particular,there are reverse flow vectors at the starting line,which indicates that there is reverse leakage flow at the conjunctions of adjacent baffles.However,the leakage flow in the V-notch zone of the adjacent baffles could not be depicted along the longitudinal section because the leakage velocity vectors are perpendicular to the plane shown.To view this leakage,the concentric hexagonal slices were constructed.

Fig.4.Special slices in shell side of heat exchanger.

Fig.5.Temperature fields on meridian slice M1 and transverse f of four schemes.

Fig.6.Pressure contours with velocity vectors superimposed for the meridian slice M1 of six schemes.

Fig.7.Pressure contours on transverse slices f and f1 for 20°TCO and 18.4°CH schemes.

Fig.8 shows the velocity vector fields of the six schemes in unfolded hexagonal slices H2 and H3 including two spiral pitch cycles C5 and C6.It is clearly observed that the low-speed zones are mainly on the dorsal side,and the average velocity,secondary flow strength,and the V-notch leakage flow on the H3 slices are much stronger than those on the H2 slices for all of the four non-continuous baffle schemes,because the H3 slices are closer to the axis and the gaps here are larger than those of the H2 slices.It is clearly showed that the velocity magnitude of the 20°TCO scheme varies more drastically than that of the other schemes.By comparing the leakage patterns at the V-notches of the 18°QCO and 18°QEE schemes,it reveals that the leakage is restricted in the circumferential overlapped baffles of the 18°QCO scheme.The velocity fields in the 36.2°TMO scheme and the two continuous helical schemes 18.4°CH and 16.8°CHare very uniform,but there are very weak secondary flows in the helical channels of these schemes,and the average velocities of these schemes are lower than that of the other schemes.There is no leakage flow in the two continuous helical schemes;however,on the H2 slice(Fig.8(b))of the 36.2°TMO scheme,the short-cut leakage is observed from the concurrent gaps to the next down-stream ones.

3.3.Heat transfer performances

From the above simulated data,the overall heat transfer coefficient K is calculated as

The tube-side heat transfer coefficient hican be estimated by Dittus-Boelter equation:

Then,the shell-side heat transfer coefficient hocan be calculated as follows:

Here Q is the average heat transfer rate through the tube;Aois the shell-side heat transfer area;Δtmis the logarithmic mean temperature difference;hoand hiare the shell-side and tube-side heat transfer coefficients respectively;Reiis the tube-side Reynolds number;doand diare the outer and inner diameters of tubes;Priis the Prandtl number of tube-side fluid;and λiand λ are conductivities of tube-side fluid and tube wall respectively.

Fig.9 shows the curves of the overall heat transfer coefficient K,shell-side heat transfer coefficient ho,shell-side pressure drop Δpoand the comprehensive index of shell-side heat transfer coefficient per unit pressure drop ho/Δpoversus the shell-side flow rate Gofor the six schemes.Over the shell-side mass flow rate range,the overall heat transfer coefficient K,shell-side heat transfer coefficient hoand average comprehensive index ho/Δpoof the 20°TCO scheme are the highest.The 18.4°CH scheme exhibits the second lowest overall heat transfer coefficient K,shell-side heat transfer coefficient hoand pressure dropΔpo,and its average comprehensive index ho/Δpois the third lowest.The 16.8°CH scheme increases indeed the overall heat transfer coefficient K and heat transfer coefficient ho,but its pressure drop Δpoincreases even more quickly and ranks the first,making ho/Δpodeclined to the lowest.The average value of comprehensive index ho/Δpoof the 20°TCO scheme is 13.45%,3.76%,1.21%,9.09%and 14.99%higher than that observed for the 36.2°TMO,18°QCO,18°QEE,18.4°CH and 16.8°CH schemes respectively.The 36.2°TMO scheme exhibits the lowestshell-side heattransfer coefficient hoand pressure drop Δpo,and its average comprehensive index ho/Δpois the second lowest.

Because the heat transfer capability is the primary requirement in heat exchanger applications,the 20°TCO scheme,which exhibits the highest heat transfer coefficients K and ho,shows the best application potential.The 18°QCO and 18°QEE schemes,which feature 25%more baffles but lower heat transfer coefficients K and hoand comprehensive index ho/Δpo,are inferior to the 20°TCO scheme.Moreover,the 36.2°TMO,18.4°CH and 16.8°CH schemes present difficulty in baffle manufacturing for greater inclined angle or curve shaped plates,exhibiting the worse performance features,and they are not recommended for application.

4.Conclusions

(1)The single vortex secondary flow in each helical cycle was demonstrated on the meridian slice M1 and the transverse slices f and f1 of the six schemes,which can strengthen the mixing of fluids,augment the shell-side heat transfer,and prevent the tubes from fouling.Concentric hexagonal slices were constructed to demonstrate the “reverse leakage”in the V-notch of adjacent non-continuous helical baffles.

(2)The 20°incline angled trisection circumferential overlap baffle scheme(20°TCO)exhibits the strongest secondary flow and restricted reverse leakage,whereas the two continuous helical baffled schemes 18.4°CH and 16.8°CH,which exhibit a lower average velocity and almost no reverse leakage,have very weak secondary flow in the continuous helical channel.

Fig.8.Velocity vector contours of unfolded hexagonal slices H2 and H3 of six schemes.

(3)The overall heat transfer coefficient K,the shell-side heat transfer coefficient hoand the average comprehensive index ho/Δpoof the 20°TCO scheme are the highest among the six schemes;conversely,the overall heat transfer coefficient K,the shell-side heat transfer coefficient hoand the average comprehensive index ho/Δpoof the middle axial overlapped scheme 36.2°TMOand the continuous helix schemes 18.4°CH and 16.8°CH are the three lowest ones,despite the difficulty in their baffle manufacturing.

Nomenclature

G flow rate,kg·s?1

h heat transfer coefficient,kW·m?2·K?1

k turbulence kinetic energy,m2·s?2

p pressure,Pa

Re Reynolds number

T temperature,K or°C

U velocity vector

u horizontal component velocity,m·s?1

V velocity,m·s?1

v vertical component velocity,m·s?1

w axial component velocity,m·s?1

Δp pressure drop,Pa or kPa

ε turbulence dissipation rate,m2·s?3

λ thermal conductivity,W·m?1·K?1

μ dynamic viscosity,Pa·s

ρ density of fluid,kg·m?3

Subscripts

i tube side

in inlet

o shell side

z axial

Fig.9.Heat transfer properties.