Numerical investigation of conjugate heat transfer and flowperformance of a fin and tube heat exchanger with vortex

generators

Shobhana Singh Kim Sørensen

Department of Energy Technology, Aalborg University, Pontoppidanstræde 111, 9022, Aalborg, Denmark,{ssi,kso}@et.aau.dk

AbstractVortex generator is considered as an effective device foraugmentation of the thermal-hydraulic performance of aheat exchanger. The aim of present study is to examinethe influence of vortex generators on a double fin andtube heat exchanger performance. Vortex generator ofrectangular winglet type is chosen and investigated atdifferent angles of attack 0◦, −10◦ and −20◦ with theflow direction. Three-dimensional numerical model isdeveloped and simulations are performed for a Reynoldsnumber range 5000 ≤ Re ≤ 11000 taking conjugate heattransfer into account. The heat transfer and pressure losscharacteristics are determined and analyzed for an in-lineconfiguration of a fin and tube heat exchanger. In order toevaluate the enhancement in the performance on anequitable basis, the heat exchanger with plain fin surfaceis considered as a reference design. Results show that theangle of attack of a vortex generator has a significantimpact on the volume goodness factor, and enhance thethermal performance of a fin and tube heat exchanger incomparison to the design with plain fin. The vortexgenerator at an angle of attack −10◦ is found to performsuperior over the Reynolds number range studied. AtRe = 5000, the vortex generator with an angle of attack−10◦ increases the volume goodness factor by 32% withrespect to the baseline heat exchanger design.Keywords: Fin and tube heat exchanger, vortex generator,conjugate heat transfer, volume goodness factor

1 IntroductionFin and tube heat exchangers are one of the mostcommonly used thermal engineering systems due to thelarger heat transfer area provided by the extended surfaceintegrated tubes. In the process industry, vortexgenerators (VGs) are being increasingly incorporated inmodern multi-functional heat exchangers to enhance heatand mass transfer and to increase energy efficiency(Ghanem et al. , 2013). The enhancement by vortexgenerators shows a great promise in reducing the size ofheat exchangers (Biswas et al. , 1994). They areintegrated into a surface by means of embossing,stamping, punching, or by other attachment processes.

Wide range of application and design flexibility havemade vortex generators an effective mode of performanceenhancement. In fin and tube heat exchanger oftennegligible heat transfer takes place in the downstream ofthe circular tube due to a low velocity fluid which can beenhanced by several hundred percent by placing VG inthe wake region behind the tubes (Biswas et al. , 1994;Joardar and Jacobi , 2008). Several experimental andnumerical studies on different configurations of VGs havebeen carried out over the last two decades (Turk andJunkhan , 1986; Joardar and Jacobi , 2008; Tiggelbeck etal. , 1992, 1993; Jacobi and Shah , 1995; Jang et al. ,2013) including fin and tube heat exchangers (Fiebig ,1995; Fiebig et al. , 1994, 1993). However, most of thestudies are commonly based on convective heat transferanalysis.

In majority of engineering applications, for example,waste heat recovery, heating and cooling, aerospaceengineering etc., physical phenomena usually combinesboth heat transfer in solid and fluids. For accuratepredictions of improved performance for a givenapplication, numerical simulations with coupledtemperature fields in solids and fluids are essential. It ispragmatic in testing different design configurations withvortex generators. Due to the lack of sufficient data onthe impact of VGs on doubled fin and tube heatexchangers, present study work aims to investigate theeffect of VGs with different angles of attack (α) on theheat transfer and pressure loss characteristics. Theanalysis is performed by developing a three-dimensional(3D) numerical model that includes conjugate heattransfer in solid and fluid domains simultaneously.

2 Numerical Model2.1 Computational Geometry: Fin and Tube

Heat Exchanger with Vortex GeneratorsFigure 1a shows a double fin and tube heat exchangerwith plain fin and with VGs as investigated in the presentstudy. The double fin and tube heat exchanger isgenerally designed for a wide range of applications suchas marine exhaust gas boilers for waste heat recoveryfrom coal-fired boilers (Singh et al., 2016a,b, 2017) due

DOI: 10.3384/ecp1713813 Proceedings of the 58th SIMS September 25th - 27th, Reykjavik, Iceland

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Plain fin

(a) Plain fin

Fin with vortex generators

(b) Fin with vortex generator

Figure 1. Illustration of fin and tube heat exchanger design

to good anti-wear and anti-fouling performance, compactdesign, stability (Chen and Lai, 2012; Jin et al., 2013,2016). To investigate the effectiveness of VGs,rectangular winglet vortex generator (RWVG) areselected considering their heat transfer enhancementperformance better than delta winglets (Li et al., 2015).Two pairs of RWVGs each of height 0.004 m and length0.019 m are placed longitudinally on the fin surface in thedirection of the flow. The rectangular winglets can beeasily manufactured by punching out off the fin surface atan angle of 90◦ as shown in Fig.1b. Figure 2 illustratesthe design details of the rectangular vortex generator atan angles of attack α with the incoming flow direction.Table 1 lists the design parameters of the heat exchangerconsidered in the study.

2.2 Governing Equations

Based on flow velocity and Reynolds number (≥ 5000),Shear Stress Transport (SST) turbulence model is adoptedto simulate the fluid flow in the domains of interest(Menter, 1994; Menter et al., 2003; Woelke, 2007).

The governing equations of mass, momentum, and

Table 1. Dimensions of the computational geometry simulatedin the present study

Parameter ValueLength of the fin, L f 0.145 mWidth of the fin, Wf 0.032 mThickness of the fin base, δ f 0.002 mWidth of the gap between fins, d f 0.006 mFin pitch, p f 0.015 mInner diameter of the tube, Di 0.030 mOuter diameter of the tube, Do 0.038 mTube pitch, pt 0.075 mLength of the gas domain, Lg 0.150 mWidth of the gas domain, Wg 0.075 mThickness of the gas domain, p f

2 0.0075 mLength of RWVG, lV G 0.019 mHeight of RWVG, hV G 0.004 mThickness of RWVG, δV G 0.002 mAngle of attack of RWVG, α 0◦, −10◦,−20◦

energy conservation can be written as:

∂ρ

∂ t+∇(ρU) = 0 (1)

∂ (ρU)

∂ t+∇(ρU⊗U)−∇(µe f f −∇U) =−∇p

+∇(µe f f −∇U)T +F (2)

where U is the averaged flow velocity field [m/s], ρ isthe density [kg/m3],⊗ is the outer vector product, p is thepressure [Pa], F is the total body force [N/m3], µe f f is theeffective viscosity coefficient [Pa.s].

∂ (ρCpT )∂ t

+∇(ρCpU)T =−∇(q)+τ : ∇U− p∇U+Q(3)

∂ (ρCpT )∂ t

=−∇(q)+Q (4)

where Cp is the specific heat capacity at constant pressure[J/kgK], q is the heat flux by conduction [W/m2],~τ : ∇~Uis the viscous heating term and is assumed negligible, Qis the heat source [W/m3].

The transport equations of SST model in terms of k andω can be written as:

∂ (ρω)

∂ t+∇(ρωU) = ∇

[(µ +

µt

σω,1

)∇(ω))

]+

γ2

[2ρSi j.Si j−

23

ρω∂Ui

∂x jδi j

]−β2ρω

2+2ρ

σω,2ω

∂k∂xk

∂ω

∂xk

(5)

where ω is the turbulent frequency [1/s] and µt = ρkω

isthe eddy viscosity.

DOI: 10.3384/ecp1713813 Proceedings of the 58th SIMS September 25th - 27th, Reykjavik, Iceland

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hVG

δVG

lVG

Rectangular winglet

Punched hole

in the fin

lVG

Axis of rotation

Fin surface

hVG

Axis of winglet

Axis of winglet

90,0°

90,0°

Flow direction

α

Angle of attack

y-axis

x-axis

Figure 2. Schematic illustration of rectangular winglet vortex generator

∂ (ρk)∂ t

+∇(ρkU) = ∇

[(µ +

µt

σk

)∇(k))

]+Pk

−β∗ρkω (6)

where k is the rate of turbulent kinetic energy [m2/s2].The rate of production of turbulent kinetic energy which

is given as:

Pk =

(2µtSi j.Si j−

23

ρk∂Ui

∂x jδi j

)(7)

2.3 Solution ProcedureIn most of the numerical problems, Computational FluidDynamics (CFD) based tool solves the governingtransport equations faster under specified conditions andpredicts the physical processes such as fluid flow, heattransfer etc. with reliable accuracy. In the present work,Ansys CFX v.17.1.(Ansys , 2017) is used to develop thefinite volume model and simulate steady state flow withcoupled conjugate heat transfer. Control surface approachis used to perform the coupling between the fluid andsolid grid interface. To gain the time savings and reducedcomputational power, symmetric boundary conditions areemployed as shown in the Fig.3. The computationalgeometry has faces set as a plane of symmetry andperiodic inlet and outlet. The boundary conditions atdifferent faces of the computational domain are describedin Table 2. Due to a high complexity design includingVGs, unstructured mesh is generated with a fineboundary layers. Meshes with ≈ 7000000 and≈ 13000000 average number of grid elements areselected for plain fin and fin with VG to achieve thereliable numerical solution, respectively. Theconvergence is obtained when the maximum residual ofobjective variables (i.e. temperature, pressure andvelocity components) accomplished 10−4.

2.4 Model ValidationIn order to validate the model, the Nusselt number andEuler number values from the correlations of Chen et al.

Table 2. Boundary conditions used to solve the numerical model

Boundary ConditionsPeriodic ˙m = minWall U · n = 0; k = 0;

[limlω→0 ω = 6µ

ρβ lw2]

Symmetry U.n =0; ∇.k = 0; ∇.ω= 0

Inner tube wall T = TwOperating ConditionsGas temperature, Tin 573.15 KInner tube wall temperature, Tw 453.15 K

(2014) are compared with the present numerical results asshown in Fig.4. The standard deviation of predictedvalues of Nusselt and Euler numbers from the valuesobtained from the correlations values vary from 0.004 to5.150, respectively. The deviation can be justified by theassumptions made in model parameters in addition to theexperimental error in developing the correlations. Thelower standard deviation in the numerical values indicatesthe reliability and validity of the computational modelunder given operating conditions.

3 Data Analysis and PerformanceEvaluation

In this section, the heat transfer and flow characteristicsare defined to evaluate the performance enhancement inthe fin and tube heat exchanger by RWVGs.

Reynolds number in the present study is determined as:

Re =uinDo

ν(8)

where Re is the Reynolds number [-], uin is the inlet flowvelocity [m/s], Do is the outer tube diameter [m] and ν isthe kinematic viscosity of the air [m/s].

The overall avergae heat transfer coefficient of the finand tube heat exchanger is calculated as:

h =Q

At∆Tlm(9)

DOI: 10.3384/ecp1713813 Proceedings of the 58th SIMS September 25th - 27th, Reykjavik, Iceland

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Figure 3. Computational geometry simulated in the present study

0

0,05

0,1

0,15

0,2

0,25

0

10

20

30

40

50

60

70

4000 6000 8000 10000 12000

Eule

r num

ber

[-]

Nusselt n

um

ber

[-]

Reynolds number [-]

Nusselt number (Numerical)

Nusselt number (Experimental)

Euler number (Numerical)

Euler number (Experimental)

Figure 4. Numerical model validation based Nusselt numberand Euler number correlations

where h is the overall heat transfer coefficient [W/m2 ·K], At is the total heat transfer area [m2], and Q is the totalheat transferred calculated as:

Q = mCp(Tin−Tout) (10)

where m is the mass flow rate [kg/s], Cp is the specificheat capacity [J/kg · K], Tin and Tout are the massaveraged air temperature at the inlet and outlet [K]. ∆Tlmis the logarithmic mean temperature difference which iscalculated as:

∆Tlm =(Tin−Tw)− (Tout −Tw)

ln( Tin−Tw

Tout−Tw

) (11)

where Tw is the inner tube wall temperature [K].In order to determine heat transfer characteristic,

average Nusselt number which is calculated as:

Nu =hDo

k(12)

Colburn-j factor is calculated based on average Nusseltnumber and is expressed as:

j =Nu

RePr1/3 (13)

where ρ is the density of the fluid [kg/m3], Pr is thePrandtl number [-], and Nu is the

In addition to the heat transfer characteristics, pressurelosses are be evaluated using the Euler number, Eu and thefriction factor, f as:

Eu =∆p

12 ρu2

max(14)

f =∆p

12 ρu2

in× Do

Lg(15)

where, ∆p is the pressure loss [Pa] and Lg is the length ofthe gas domain in the computational geometry [m]

Due to a number of possible enhancement methods,operating conditions and available designs, comparisonof performance on equitable basis can be challenging. Inthe present study, a factor called Volume goodness factoras proposed by Kays and London (1998) is utilized topredict the overall performance. It considerssimultaneous effect of heat transfer and pressure loss and,therefore, useful in several practical applications.

jf 1/3 =

NuRePr1/3(

∆p12 ρu2

in× Do

Lg

)1/3 (16)

DOI: 10.3384/ecp1713813 Proceedings of the 58th SIMS September 25th - 27th, Reykjavik, Iceland

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4 Results and Discussion4.1 Heat Transfer EnhancementThe influence of angle of attack (α) on Nusselt numbercan be seen in Fig.5a. It is clear that heat exchanger withRWVG has higher Nusselt number than that of baselineplain fin surface which increases with a increase inReynolds number at a given α . VGs induce strongervortical fluid flow due to which heat transfer coefficientbecomes higher, thereby, augments the heat transferbetween the fluid and surface. It is observed that Nusseltnumber increases as α varies from 0◦ to −20◦, however,the increment becomes insignificant as α goes higherthan 0◦.

To make a rational comparison between the heattransfer performance at different α , Colburn-j factornormalized with the baseline plain fin value is plotted inFig.5b. It can be seen that adding RWVG can enhance theheat transfer by up to 55% at a given Reynolds number.Moreover, it is interesting to note that Colburn-j factorratio of fins with RWVG at α = −10◦ and α = −20◦

decreases as the Reynolds number increases whileremains more or less constant at α = 0◦ over theReynolds number range. The results indicate thatRWVGs in double fin and tube heat exchanger tend toloose their advantage relative to baseline plain fin athigher Reynolds number.

4.2 Induced Flow LossEnhancement in heat transfer in most of the applicationsis accompanied with a penalty of pressure loss. Toaccount for this penalty, the Euler number with a differentangle of attack is plotted against Reynolds number in Fig.6a. The figure shows that Euler number increases as α

vary from 0◦ to −20◦. At α =−20◦, Euler number is thehighest which is due to the increased fluid velocity andconsequently large pressure loss. The RWVG withα = 0◦ performs nearly similar to the baseline plain findesign.

Another factor called friction factor (f ) is evaluatedusing Eq.15. Figure 6b compares the normalized frictionfactor at different angles of attack to the baseline plain findesign. It can be seen that friction factor ratio remainsnearly constant over the entire range of Reynolds number,however, fins with RWVGs have higher friction factorthan baseline plain fin and the highest at α = −20◦. Atα = −20◦ and Re = 11000, friction factor is 20% higherthan that of baseline plain fin design. It is demonstratedby the results that adding RWVG to the fin surfaceincreases the pressure loss which certainly is adisadvantage to the overall performance.

It is clear from the results that the angle of attack ofRWVG has a significant impact on thermal and pressureloss characteristics of a fin and tube heat exchanger. It is,therefore, essential to analyze both characteristicstogether. In the present study, the overall performance isevaluated using Volume goodness factor from Eq.16.

0

10

20

30

40

50

60

70

4000 6000 8000 10000 12000

Nusse

lt n

um

be

r [-

]

Reynolds number [-]

α = -20º

α = -10º

α = 0º

Without VG

(a) Nusselt number

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

4000 6000 8000 10000 12000

j/j o

[-]

Reynolds number [-]

α = -20º

α = -10º

α = 0º

Without VG

(b) Colburn j factor

Figure 5. Heat transfer characteristics with RWVG at differentangle of attack

Figure 7 compares the factor with the plain fin factor as areference. it is found that RWVG at α =−10◦ has highervolume goodness factor followed by α = −20◦ over theentire range of Reynolds number in this study whichindicates that α =−10◦ performs better in comparison toRWVG at other angles of attack when both heat transferand pressure losses are considered together. The RWVGat α = −10◦ and Re = 5000 has 32% higher volumegoodness factor than that of conventional plain finsurface.

It is important to emphasize that the overallperformance of the heat exchanger with RWVG atα = −20◦ and α = −10◦ decreases as the Reynoldsnumber increases which indicate that the advantage of

DOI: 10.3384/ecp1713813 Proceedings of the 58th SIMS September 25th - 27th, Reykjavik, Iceland

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0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

4000 6000 8000 10000 12000

Eule

r n

um

be

r [-

]

Reynolds number [-]

α = -20º

α = -10º

α = 0º

Without VG

(a) Euler number

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

2

4000 6000 8000 10000 12000

f/f o

[-]

Reynolds number [-]

α = -20º

α = -10º

α = 0º

Without VG

(b) Friction factor

Figure 6. Pressure loss evaluation with RWVG at different angleof attack

using RWVG at these angles of attack becomes lessuseful for higher Reynolds number. This is due torelatively lower heat transfer and higher pressure loss athigher Reynolds number (Figs.5b and 6b). On the otherhand, performance improvement by RWVG at α = 0◦ isnoticed insignificant and nearly constant at all Reynoldsnumbers.

A larger value of Volume goodness factor leads toreduced heat exchanger volume and weight which isdesirable in most of the practical applications. AddingRWVG at α = −10◦ in the double fin and tube heatexchanger can not only increase the overall performancebut also fulfills the light weight heat exchanger demandsin a number of applications.

0

0,4

0,8

1,2

1,6

4000 6000 8000 10000 12000

(j/f

1/3)/

(jo/f

o1

/3)

[-]

Reynolds number [-]

α = -20º

α = -10º

α = 0º

Without VG

Figure 7. Overall performance comparision RWVG at differentangle of attack

5 ConclusionPerformance enhancement using RWVGs in the doublefin and tube heat exchanger is investigated numerically inthe present study. The influence of different angles ofattack of RWVG on heat transfer and pressure losscharacteristics in relation to baseline plain fin design isdemonstrated and discussed. The study can be concludedwith following outcomes:

• The RWVGs significantly influence the thermalperformance over the investigated range ofReynolds number i.e.5000 ≤ Re ≤ 11000. Inreference to the reference design with plain fin,thermal performance is enhanced by up to 55% byRWVG with an angle of attack at α =−20◦.

• It is interesting to note that beyond α = −10◦, theangle of attack does not show significantimprovement in thermal performance and performssimilarly to α =−10◦.

• As the angle of attack of RWVG varies from 0◦ to−20◦, the pressure loss also increases. However, thetrend remains more or less same over the entire rangeof Reynolds number studied.

• The overall performance enhancement is evaluatedby comparing the volume goodness factor. Underthe given operating conditions, the vortex generatorat an angle of attack −10◦ is found to enhance theoverall performance by up to 32%, thus furnishesthe best performed double fin and tube heatexchanger design.

• The present investigation is useful not only inenhancing the overall performance of a double fin

DOI: 10.3384/ecp1713813 Proceedings of the 58th SIMS September 25th - 27th, Reykjavik, Iceland

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and tube heat exchanger but also directs the futurestudies to limit the range of angle of attack of VGswhile focusing on the VG location and other designparameters.

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