A numerical investigation of the geometric effects on the performance of plate finned-tube heat exchanger

A numerical investigation of the geometric effects on the performance of plate

finned-tube heat exchanger

Chi-Wen Lu

a

_{, Jeng-Min Huang}

a

_{, W.C. Nien}

a

_{, Chi-Chuan Wang}

b,⇑

a

Department of Refrigeration, Air Conditioning and Energy Engineering, National Chin-Yi University of Technology, No. 35, Lane 215, Chung-Shan Rd., Sec. 1, Taiping City, Taichung County 411, Taiwan

b

Department of Mechanical Engineering, National Chiao Tung University, 1001 University Road, 300 Hsinchu, Taiwan

a r t i c l e

i n f o

Article history: Received 10 June 2009

Received in revised form 8 February 2010 Accepted 15 October 2010

Available online 20 November 2010 Keywords:

Fin-and-tube heat exchanger Axial fan

CFD

a b s t r a c t

This study numerically examines the geometric parameters on the performance of a two-row fin-and-tube heat exchanger. Effects of fin pitch, fin-and-tube pitch, fin thickness, and fin-and-tube diameter are termed with. The simulation indicates that the performance, in terms of Q/DP and COP, increases with longitudinal tube pitch or with transverse tube pitch, and it decreases with larger tube diameter or fin thickness. An optimum value for Q/DP occurs at a 6–8 fpi at a fixed flow rate condition. There is not much difference in choosing the index of Q/DP or COP under fixed flow rate condition. However, when the simulation are performed with the actual axial fan whose P–Q curve being implemented. It is found that Q/DP peaks at 12 fpi while COP peaks at 16 fpi.

Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Finned-tube heat exchangers are frequently used in HVAC&R applications. Its easier manufacturing, simpler construction, lower cost, and relatively easy in maintenance make it one of the most commonly used heat exchangers. The performance of fin-and-tube heat exchangers are related to many geometric parameters such as fin pitch, tube pitch, tube size, and fin thickness. It is quite difficult to achieve the best performance subject to these parameters in the early days. This is because results normally relied on experimenta-tion and it is very unlikely to examine all kind of geometric influ-ences from the manufacturing fin-and-tube heat exchangers. Hence, early experimental studies conducted by Rich [1,2], who investigated a total of fourteen coils, in which the tube size were 13.34 mm. The corresponding longitudinal and transverse tube pitches were 27.5 and 31.75 mm, respectively. He examined the effect of fin spacing and the number of tube row, and concluded that the heat transfer coefficient was essentially independent of the fin spacings and the pressure drops per row is independent of the number of tube rows.

McQuiston[3] provided test results for five heat exchangers ([3], Fp = 1.81–6.35 mm, Do= 9.96 mm, Pl= 22 mm, Pt= 25.4 mm,

and Row = 4), and he later[4]proposed the first popular correla-tion by employed a ‘‘finning factor’’, defined as Ao/Ato, to correlate

his data along with those by Rich[1,2]. A strong dependence of heat transfer performance with the finning factor was observed. McQuiston[4]showed an (Ao/Ato)0.15dependence in his

correla-tion. The friction factor correlation proposed by McQuiston [4]

claimed to have ±35% accuracy. Based on the previously published data, Gray and Webb[5]developed a correlation to correlate the existing experimental data. The root-mean-square error of the resulting correlation was 7.3% for heat transfer coefficients, and 7.8% for friction factors. Seshimo and Fujii[6]had provided test re-sults for a total of 35 samples. Unfortunately, their test range was limited to 0.5 m s1_{< V}

fr< 2.5 m s1. Wang et al.[7]had presented

fifteen samples of plain fin-and-tube heat exchangers to examine the effect of several geometrical parameters, including the number of tube rows, fin spacing, and fin thickness but their test samples were limited to one configuration. Rosman et al.[8]conducted heat transfer experiments on a two-row exchanger, and compared his test results with some previous studies with good accuracy. How-ever, the foregoing results were limited to certain configuration and results were based on the tested samples.

A more comprehensive experimental study concerning para-metric influences and its correlation on the air side performance having plain fin configuration had been carried out by Wang and Chi[9]and Wang et al.[10]. Some influences such as the number of tube row, fin pitch and tube size on the air side performance had been reported. Madi et al.[11]also examined the relevant geo-metric influences (fin pitch, fin thickness and tube pitch) for 28 samples, including 7 plain fins and 21 wavy fins. Their test results indicated smaller fin thickness result in higher heat transfer 0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.enconman.2010.10.026

⇑Corresponding author.

E-mail address:ccwang@mail.nctu.edu.tw(C.-C. Wang).

Contents lists available atScienceDirect

Energy Conversion and Management

coefficient. Wongwises and Chokeman[12]investigated the effects of a fin pitch and number of tube rows on the air side performance of fin-and-tube heat exchangers having herringbone wavy fin con-figuration at various fin thicknesses. The experimental results revealed that the fin pitch has an insignificant effect on the heat transfer characteristic. The friction factor increases with increasing fin pitch when ReDc> 2500. Ma et al.[13]studied the air side heat

transfer and friction characteristics of wavy fin-and-tube heat exchangers with and without hydrophilic coating, their results indicated that the influence of the hydrophilic coating on heat transfer performance is mainly related to the flow conditions of condensation water on the fin surface without hydrophilic coating. The aforementioned study was mainly based on experimental test results. Despite numerous experimental data were reported, the optimum performance of the associated heat exchangers are still unavailable due to limitation of practical manufacturing. With the advent of high performance computational power, researchers like Fiebig et al.[14]or Jang et al.[15]exploitation of numerical tools to study the complex interactions amid geometric parameters of fin-and-tube heat exchangers are therefore feasible. Hence it is the objective of this study to examine the optimization of fin-and-tube heat exchangers through numerical calculations. The simulations are first conducted at a fixed flow rate to examine the best performance and then further calculations are performed with practical fan/exchanger combinations.

2. Physical model, governing equations and numerical method In this study, simulations are made with staggered fin-and-tube heat exchangers having plain fin configuration. Influences of fron-tal velocity, tube pitch, tube size, and fin thickness on the air side performance are examined in this study. A schematic of the heat exchanger is depicted inFig. 1a while the associated computa-tional domain is shown in Fig. 1b. Some detailed geometric parameters for conducting the simulations are tabulated in

Table 1and the physical properties of air and aluminum are tab-ulated in Table 2. As the airflow flows across the fin-and-tube heat exchanger is actually a quite complex one involving complex interactions amid flow field and obstacles (tube and fins). Hence some assumptions are made in the following to simplify the calculation:

(1) Steady state prevails. (2) Buoyancy force is neglected.

(3) The heat transfer is via sensible heat only, no mass transfer is being taken place.

(4) Incompressible flow, constant properties.

(5) Effects of heat dissipation and thermal radiation are negligible.

(6) Smooth surface conditions for the fin-and-tube.

The corresponding boundary conditions used for simulations are:

(1) No slip conditions at the solid surfaces.

(2) Conjugate heat transfer prevails amid fin and airflow. Nomenclature

Ao total surface area, m2

Ato outside surface area of tube

Cp specific heat of constant pressure, J kg1K1

COP performance index, COP = Q/ðDP  _VÞ, coefficient of performance

dc fin collar outside diameter, mm

Dh hydraulic diameter, m

Fp fin pitch, mm

h heat transfer coefficient, W m2_K1

L depth of the heat exchanger, m

N the number of tube row Pl longitudinal tube pitch, mm

Pt transverse tube pitch, mm

Pr Prandtl number

DP pressure drop, Pa Q heat transfer rate, W

ReDh Reynolds number based on hydraulic diameter

Vfr frontal velocity, m s1

_

V volume flow rate, m3_s1

x+ _{reciprocal of the inverse Graetz number}

Fig. 1. Schematic of the computational domain for (a) the heat exchanger; (b) actual computational domain (including prior and posterior extension).

Table 1

Geometric details of the simulated heat exchanger (unit: mm). Depth Additional extension section at the entrance Additional extension section at the outlet Fp Pt Pl Vfr dc df 6.350 20.0 1.2 4.235 15 6 0.080 25.4 1.4 3.175 19.05 8 0.115 38.1 19.05 95.25 30.0 1.6 2.115 23 10 0.160 35.0 1.8 1.590 27 12 0.200 40.0 2.0 1.265

(3) The tube wall temperature is fixed at 328 K. This is typically applicable for a condenser situation.

(4) Additional extension sections prior to and posterior to the heat exchanger are included in the simulation, and their cor-responding length are given inTable 1. The uniform velocity assumption is given at the entrance of the extension section. A free-gradient outlet boundary condition is set at the exit of downstream extension.

(5) The ‘‘symmetry’’ boundary is set at the two symmetrical planes.

A commercial CFD code Star-CD is used in this study to calculate the flow and temperature fields of the fin-and-tube heat exchang-ers. Except Leu et al.[16]using standard K–

e

turbulent model, most previous researches like Jang et al.[15]and Mendez et al.[17]used laminar flow equations in the simulation of fin-and-tube heat ex-changer. In this study, the wake flow at the exit of heat exchanger might be in transition or in turbulent flow region. Therefore simu-lation may not converge by the laminar flow model. In this regard, low-Reynolds number K–

e

model is applied in this study in order to calculate a mixed flow fields (combined laminar, transition and turbulent flow types) as suggested by Huang et al.[18]. A test of low-Reynolds model is performed to examine the applicability of this model in the mixed flow field. Firstly, low-Reynolds model is used to calculate a fully laminar flow field (a heat exchanger with 0.2 m s1_{inlet air velocity). The solution is almost the same}

as that of calculation from the laminar equations. The eddy viscos-ities are very small compared with molecular viscosviscos-ities. This indi-cates that the low-Reynolds number turbulent model can be directly applied even at the laminar flow region. Then the inlet air velocity is increased to 2 m s1_{, calculated results of the flow}

field shows that the eddy viscosities of the flow between fins are near zero, suggesting a laminar flow region prevails. However, the eddy viscosity increases rapidly as the flow leaving the fins. In fact, the highest eddy viscosity in the wake is about 70 times higher than molecular viscosity (1.5  105_m2_s1_{). Hence the flow}

is no longer laminar.

The following equations are used in this study:

– Low-Reynolds number K–

e

turbulence model momentum equa-tion (air side).

– Low-Reynolds number K–

e

turbulence model energy equation (air side).

– Heat conduction equation (fins).

Detailed description of the turbulent model can be found in the Star-CD user’s manuals. The mesh used in the study is shown in

Fig. 2. Due to the complexity of fin–tube geometry, an unstructured Table 2

Properties of the fin material and air. Density (kg m3 ) Specific heat (J kg1 k1 ) Thermal conductivity (W m1_K1₎ Dynamic viscosity (kg m1 s1 ) Fin 2702 903 237 Air 1.205 1006 0.02637 1.81  105

Fig. 2. Schematic of the computational grid structure (a) for the whole heat exchanger; (b) adjacent to the round tube; and (c) nearby the fin. Table 3

Results of grid dependence check.

Cell Heat transfer rate (W) Relative error (%)

39,200 0.4381609

0.6113 106,500 0.4354986

0.3078 203,400 0.4341621

Sample heat exchanger with Pt= 25.4 mm, Pl= 19.05 mm, dc= 10 mm, Fp= 1.59 mm,

df= 0.115 mm, Vfr= 1.6 m s1.

Table 4

Comparison between experimental heat transfer coefficients (h, W m2

K1

)[8]and the present simulation.

Vfr(m s1) Computational results Experimental results [8] Deviation (%) 1.20 51.44 47 8.64 1.34 53.17 50 5.96 2.35 64.26 63.5 1.19 6.20 100.68 101 0.31

grid system is generated by ‘‘Auto Mesh’’ function of Star-CD for the airflow channel and the structured grid is used in the solid part. Star-CD is a finite-volume based CFD package. The central differ-ence method is used to discretize the diffusion term and the

con-vection term is discretized by upwind difference method. Simple scheme is applied on the iteration procedure. Numerical conver-gence is accepted only when the residuals of velocities, pressure, temperature and turbulent kinetic energy are smaller than 105_.

Fin per inch

Q

(W)/

Δ

P

(Pa)

Pl= 19.05mm Pt/2 = 12.7mm = 0.115mm dc = 10mm Vfr= 1.6m/s 4 8 12 16 20 20 24 28 32

(a) effect of fin pitch

Fin thickness (mm)

Q

(W)/

Δ

P

(Pa)

_P l= 19.05mm Pt/2 = 12.7mm fpi = 16 dc = 10mm Vfr= 1.6m/s 0.08 0.12 0.16 0.2 20 22 24 26 28

(b)

effect of fin thickness

P

l

(mm)

Q

(W)/

Δ

P

(Pa)

Pt/2 = 12.7mm = 0.115mm dc = 10mm Vfr= 1.6m/s fpi = 16 12 16 20 24 28 20 22 24 26 28 30

(c) effect of longitudinal tube pitch

P

t

/2 (mm)

Q

(W)/

Δ

P

(Pa)

Pl= 19.05mm = 0.115mm dc = 10mm Vfr= 1.6m/s fpi = 16 12 16 20 20 24 28 32 36

(d) effect of transverse tube pitch

Tube diameter (mm)

Q

(W)/

Δ

P

(Pa)

Pl= 19.05mm Pt/2 = 12.7mm = 0.115mm Vfr= 1.6m/s fpi = 16 6 8 10 12 16 20 24 28 32 36 40

(e) effect of tube diameter

Fig. 3. Influence of geometric parameters for (a) fin pitch; (b) fin thickness; (c) longitudinal tube pitch; (d) transverse tube pitch and (e) tube diameter on the performance index Q/DP at a fixed frontal velocity of 1.6 m s1_.

Grid dependence check is carried out and results are tabulated in

Table 3. Typical grid sizes are from 106,500 and 203,400. To avoid the run-off error resulting from numerical instability, double preci-sion is used throughout the computation.

3. Results and discussion

In order to validate the accuracy of the simulation, calculations are compared with the experimental work from Wang and Chi[9], and the comparisons are tabulated inTable 4. As seen in the table, the deviation between numerical and experimental results is less than 10%, which is within the typical experimental uncertainty (3%–15%). From the above validation, it is concluded that the sim-ulation software is capable of solving the heat exchanger problem with reasonable accuracy.

The following calculations are then carried out for a two-row fin-and-tube heat exchanger with its characteristic dimension being 145 mm (W)  127 mm (H)  38.1 mm (L). The effects of fin number, fin thickness, transverse tube pitch, and longitudinal tube pitch on overall performance of the heat exchanger is then investigated. For a better characterization of the relevant effects, the performance of heat exchanger is termed Q/DP and Q =ðDP  _VÞ as the evaluation index. Where Q is the heat exchange rate,DP is the pressure drop across the heat exchanger, and _V is the volumetric flow rate. In the subsequent discussion, Q =ðDP  _VÞ is designated as COP for it represents the ratio amid actual heat transfer rate and the provided pumping work.

The effect of individual parameters, such as fin pitch, fin thick-ness, longitudinal tube pitch, and transverse tube pitch on overall

performance is respectively depicted inFig. 3. Most of the geomet-ric parametgeomet-ric influence, except fin pitch, shows an asymptotic trend. For instance, Q/DP dwindles with the rise of tube diameter and of fin thickness. In the meantime, Q/DP steadily increases with the rise of longitudinal tube pitch and of transverse tube pitch. These results are expected the associated reduction of pressure drops outperforms heat transfer rate in the former and is opposite in the latter. However, an unusual optimal phenomenon is encoun-tered concerning the influence of fin pitch. It is interesting to know that Q/DP peaks at a fin pitch around 6–8 fpi. Apparently one can expect a rise of heat transfer rate and pressure drop by adding sur-faces. In general the pressure drop outlasts heat transfer and exhib-its a decreasing trend of Q/DP when the fin pitch is reduced. The heat transfer performance of a fin-and-tube heat exchanger is actu-ally associated with the interactions of airflow with tubes and fins. For a plain channel without tube interruption, its performance is strongly related to simultaneous developments of flow and tem-perature field, yet the influence of the entrance development is re-lated to the reciprocal of the inverse Graetz number x+_{, which is}

defined as

HX resistance curve

and A fan P-Q

curve intersection

HX resistance curve

A fan P-Q

HX heat transfer curve

Air velocity at HX resistance

curve and A fan P-Q curve

intersection

Heat transfer

corrspond to

intersection

0.4 0.8 1.2 1.6 2.0 2.4 2.8 0 70 80 60 50 40 30 20 10 V(m/s)

P

(Pa) A01-20fpi-ΔP 309.9725 0.9732 350 400 300 250 200 150 100 50 0 450 500 550 600 A01-20fpi-Q

Q

(W)

650

Fig. 4. Actual performance subject to the flow resistance and P–Q fan curve of a axial fan. 4 8 12 16 20 20 24 28 32 36 A-Fan B-Fan C-Fan D-Fan E-Fan F-Fan G-Fan

Fig. 5. Influence of fin pitch subject to actual fan curve on the performance index Q/DP at a fixed frontal velocity of 1.6 m s1

. 4 8 12 16 20 800 1200 1600 2000 2400 A-Fan B-Fan C-Fan D-Fan E-Fan F-Fan G-Fan

Fig. 6. Influence of fin pitch subject to actual fan curve on the performance index COP at a fixed frontal velocity of 1.6 m s1_.

xþ_¼ L=Dh ReDhPr

ð1Þ

where L is the streamwise duct length and Pr is the Prandtl number. The flow may be considered to be fully developed when x+_{> 0.04} [19]. The developing length for a very low fin pitch such as 20 fpi is only as low as 3–4 mm, indicating the major portion of fin-and-tube heat exchangers fall into the fully developed category thereby giving rise to a lower performance as the fin pitch is reduced. In the meantime, the presence of tube row provides an augmentation to heat transfer by generating longitudinal vortices and unstable de-fected swing flow (Coanda effect). These two augmented effects are more conspicuous when fewer fin surfaces is present and an op-posed influence is imop-posed on these two heat transfer augmenta-tion mechanisms when fin surface is increased. This is because adding fin surface inevitably stabilizes the flow field and lessens the contributions of vortices and unstable flow field. As a conse-quence, one can see a maximum value of Q/DP occurring adjacent to a fin pitch of 6–8 fpi. Notice that other geometric effects such as fin thickness, longitudinal tube pitch, and transverse tube pitch do not processes such unusual characteristic.

The foregoing results are conducted at a fixed flow rate (frontal velocity). Normally heat exchangers are accompanied with fans to fulfill the heat transfer duty. The actual performance of the heat exchangers depends on the interactions amid fan and heat exchangers. Therefore, the present study had investigated the asso-ciated influences of fans on the overall performances. This is made by selecting some commercially available axial fans whose perfor-mances are available in terms of P–Q curves. Implementing the ac-tual P–Q curves subject to the simulated pressure drop of the heat exchanger, one can therefore obtain the actual flow rate and its heat transfer rate at a specific fin pitch. As a result, we can obtain a sim-ilar Q/DP vs. fpi subject to actual fan performance as shown inFig. 5. Analogously, the graph of Q/DP vs. fin pitch also exhibits a bulge phenomenon, yet the maximum value is quite independent of fans occurring at a fin pitch of 12 fpi as compared to 6–8 fpi at a fixed flow rate. The shift of the optimum fin pitch toward to a higher va-lue is actually in connected with the fan P–Q curve itself. As can be seen from a typical P–Q curve of an axial fan inFig. 4, moderate or large flow rate are encountered at a lower pressure drop region while significant static pressure rise occurs only when the flow rate is less than half of the maximum flow rate. This phenomenon is in conjunction with the characteristics of axial flow fan and is applica-ble to all the axial fans tested in this study. As a result, despite lower flow resistance occurs at a low flow rate for a very low fin pitch, the amount of surface area could not fulfill a larger heat duty, leading to a lower Q/DP. In the meantime, surplus surface area not only pro-vides a higher flow resistance but also decrease the heat transfer performance (as aforementioned in foregoing section), hence con-siderable decline of Q/DP is seen for larger fin pitch. Summation of these two extremes and the maximum occurs at a fin pitch of 12 fpi which is much higher than simulation at a fixed flow rate. Interestingly, the locus of all the tested fans is quite similar and they all peak at 12 fpi. This is again due to the similar P–Q curve of the axial fans. Correspondingly, COP vs. fpi also reveals similar trend but its peak value had been shifted to about 16 fpi, as shown in

Fig. 6. Notice that the disparity between COP and Q/DP comes from the effect of flow rate. Yet a larger fin surface limits the airflow rate, thus a higher value of COP moves toward a larger fin pitch. 4. Conclusion

This study numerically examines the geometric parameters on the air side performance of a two-row fin-and-tube heat exchan-ger. Effects of fin pitch, tube pitch, fin thickness, and tube diameter on the performance of heat exchanger is investigated. The

perfor-mance is termed with are termed with Q/DP and COP. Major con-clusions from the simulations are given as follows:

(1) The performance of fin-and-tube heat exchanger, Q/DP, dwindles with the rise of tube diameter and of fin thickness. In the meantime, Q/DP steadily increases with the rise of longitudinal tube pitch and of transverse tube pitch. (2) A optimum value for Q/DP vs. fin pitch is encountered and it

occurs at a 6–8 fpi at a fixed flow rate condition. This is because higher fin pitch may result in fully developed flow and deteriorate the overall performance, yet a substantial rise of heat transfer caused by vortex and unstable is observed when fin surfaces are considerably removed. (3) There is not much difference in choosing the index of Q/DP

or COP under fixed flow rate condition. However, when the simulation are performed with the actual axial fan whose P–Q curve being implemented. It is found that Q/DP peaks at 12 fpi while COP peaks at 16 fpi.

Acknowledgement

The authors would like to thank some financial support from the National Science Council (99-2218-E-009-012-MY2) of Taiwan. References

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