This article was downloaded by: [University of Cincinnati Libraries] On: 20 May 2012, At: 12:10 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/unht20 Evaluation of Enhanced Heat Transfer Within a Four Row Finned Tube Array of an Air Cooled Steam Condenser Rupak K. Banerjee a , Madhura Karve a , Jong Ho Ha b , Dong Hwan lee c & Young I. Cho d a Department of Mechanical Engineering, University of Cincinnati, Cincinnati OH, Ohio, USA b Korea Heat Exchanger Co. Ltd, Gunsan, Jeonbuk, Korea c Chonbuk National University, Jeonju, Joenbuk, Korea d Department of Mechanical Engineering, Drexel University, Philadelphia, Pennsylvania, USA Available online: 18 May 2012 To cite this article: Rupak K. Banerjee, Madhura Karve, Jong Ho Ha, Dong Hwan lee & Young I. Cho (2012): Evaluation of Enhanced Heat Transfer Within a Four Row Finned Tube Array of an Air Cooled Steam Condenser, Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology, 61:10, 735-753 To link to this article: http://dx.doi.org/10.1080/10407782.2012.667649 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings,
Transcript
This article was downloaded by: [University of Cincinnati Libraries]On: 20 May 2012, At: 12:10Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Numerical Heat Transfer, Part A:Applications: An International Journal ofComputation and MethodologyPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/unht20
Evaluation of Enhanced Heat TransferWithin a Four Row Finned Tube Array ofan Air Cooled Steam CondenserRupak K. Banerjee a , Madhura Karve a , Jong Ho Ha b , Dong Hwanlee c & Young I. Cho da Department of Mechanical Engineering, University of Cincinnati,Cincinnati OH, Ohio, USAb Korea Heat Exchanger Co. Ltd, Gunsan, Jeonbuk, Koreac Chonbuk National University, Jeonju, Joenbuk, Koread Department of Mechanical Engineering, Drexel University,Philadelphia, Pennsylvania, USA
Available online: 18 May 2012
To cite this article: Rupak K. Banerjee, Madhura Karve, Jong Ho Ha, Dong Hwan lee & Young I.Cho (2012): Evaluation of Enhanced Heat Transfer Within a Four Row Finned Tube Array of an AirCooled Steam Condenser, Numerical Heat Transfer, Part A: Applications: An International Journal ofComputation and Methodology, 61:10, 735-753
To link to this article: http://dx.doi.org/10.1080/10407782.2012.667649
PLEASE SCROLL DOWN FOR ARTICLE
Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden.
The publisher does not give any warranty express or implied or make any representationthat the contents will be complete or accurate or up to date. The accuracy of anyinstructions, formulae, and drug doses should be independently verified with primarysources. The publisher shall not be liable for any loss, actions, claims, proceedings,
demand, or costs or damages whatsoever or howsoever caused arising directly orindirectly in connection with or arising out of the use of this material.
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EVALUATION OF ENHANCED HEAT TRANSFERWITHIN A FOUR ROW FINNED TUBE ARRAYOF AN AIR COOLED STEAM CONDENSER
Rupak K. Banerjee1, Madhura Karve1, Jong Ho Ha2,Dong Hwan lee3, and Young I. Cho41Department of Mechanical Engineering, University of Cincinnati,Cincinnati OH, Ohio, USA2Korea Heat Exchanger Co. Ltd, Gunsan, Jeonbuk, Korea3Chonbuk National University, Jeonju, Joenbuk, Korea4Department of Mechanical Engineering, Drexel University, Philadelphia,Pennsylvania, USA
Air cooled steam condensers (ACSC) consist of finned-tube arrays bundled in an A-frame
structure. Inefficient performance under extreme temperature operating conditions is a
common problem in ACSCs. The purpose of this study was to improve the heat transfer
characteristics of an annular finned-tube system for better performance in extreme climatic
conditions. Perforations were created on the surface of the annular fins to increase heat
transfer coefficient (h). Mesh generation and finite volume analyses were performed using
Gambit 2.4.6 and Fluent 6.3 with an RNG k–e turbulent model to calculate pressure drop
(DP), heat flux (q), and heat transfer coefficient (h). Solid (no perforations) finned-tubes
were simulated with free stream velocity ranging between 1m=s–5m=s and validated with
the published data. Computations were performed for perforations at 30� interval starting
at �60�, �90�, �120�, �150�, and �180� from the stagnation point. Five cases with single
perforation and three cases with multiple perforations were evaluated for determining the
maximum q and h, as well as minimum DP. For the perforated case (perforations starting
from 60� at interval of 30�), the fin q and h performance ratios increased by 5.96% and
7.07%, respectively. Consequently, the fin DP performance ratio increased by 11.87%.
Thus, increased q and h is accompanied with a penalty of higher DP. In contrast, a single
perforation location at 120� provided favorable results with a 1.70% and 2.23% increase in
q and h performance ratios, respectively, while there was a relatively smaller increase (only
1.39%) of DP performance ratio. Perforations in the downstream region at �120�, �150�,
Received 18 February 2011; accepted 3 February 2012.
Rupak K Banerjee and Madhura Karve have contributed equally to this article. Madhura Karve
implemented the mathematical analyses, numerical calculations, and drafted initial versions of the
article under the supervision of Rupak K: Banerjee. Dong Lee, Jong Ha, and Young Cho provided
technical insights into this research during model design and numerical data analysis. Madhura Karve
could not effectively complete the rebuttal and implement the modifications based on the reviewer’s
comments within the stipulated time because of her commitment with her new employer. In light of
this, Rupak K. Banerjee, with the assistance of Marwan Al-Rjoub, Anup Paul and Kranthi Kolli,
completed the rebuttal that was acceptable to the other co-authors.
Address correspondence to Rupak K. Banerjee, Mechanical Engineering Program, School of
Dynamic Systems, 593, Rhodes Hall, ML 0072, University of Cincinnati, Cincinnati, OH 45220, USA.
Numerical Heat Transfer, Part A, 61: 735–753, 2012
Copyright # Taylor & Francis Group, LLC
ISSN: 1040-7782 print=1521-0634 online
DOI: 10.1080/10407782.2012.667649
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and �180� also resulted in a similar favorable outcome. Furthermore, the spacing of the fins
along the arms of an A-frame ACSC was altered to decrease DP across the finned-tube
array. Fin spacing in the A-frame structure with sparsely spaced fins in the center resulted
in a 1.80% reduction in DP. Thus, penalty in DP for a perforated fin can possibly be offset
by changing the fin spacing along the arms of an A-frame structure.
1. INTRODUCTION
Finned-tube heat exchangers are commonly employed as air cooled steam con-densers (ACSC) in power plants or as radiators in automobiles. The design of suchan array has been investigated by previous researchers due to the complexitiesinvolved in the cross flow of air over the tube bundles. The efficiency of finned-tubesdepends on geometric parameters such as fin and tube spacing, operating conditions,and material properties. Efficient fins help to reduce the number of tube rows,resulting in compactness of design as well as saving energy.
A typical ACSC has four row finned-tube arrays stacked in an A-frame struc-ture. High pressure and high temperature steam is let into these finned-tubes, whichare cooled by a large fan at the base of the A-frame structure. It is a relatively inex-pensive alternative to the water cooled condensers. ACSCs have gained more impor-tance recently as a water conservation measure in regions with limited waterresources. However, under extreme climatic conditions ACSCs are faced with prob-lems such as inefficient performance in high temperature regions, such as the desert,and freezing and choking of finned-tubes in low temperature regions. Enhancing theheat transfer coefficient (h) of the fins can help in minimizing the problems associatedwith extreme climatic conditions. Researchers have explored several approaches ofreducing air side resistance in order to increase heat transfer from finned-tubesurfaces.
NOMENCLATURE
A total surface area, m2
Ac frontal area, m2
Cp specific heat at constant pressure,
J=kg-K
D outer tube diameter, m
E total internal energy, m2=s2
f friction factor
h heat transfer coefficient, W=m2-K
j thermal conductivity, W=m-K
k turbulent kinetic energy, m2=s2
l fin length, m
n number of tube rows
p static pressure of air, Pa
q heat flux (q¼ hDT), W=m2
s fin pitch, m
T temperature, K
t fin thickness, m
v velocity of air, m=s
Nu Nusselt number¼ h�D=jPr Prandtl number¼m�CP=jRein Reynolds number¼q�V�D=mSL longitudinal pitch of tubes, m
ST transverse pitch of tubes, m
a thermal diffusivity, m2=s
e turbulent energy dissipation, m2=s3
t specific volume, m3=kg
q density of air, kg=m3
m viscosity of air, kg=m-s
h angular location, degrees
DP differential pressure, Pa
r ¼ ddx i þ d
dy j þ ddz k
Subscripts
eff effective
max maximum
t turbulent
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Heat transfer enhancement techniques, such as surface vibration and magneticfield, are classified as active techniques based on the use of external power [5]. In con-trast, passive techniques included: treated or rough surfaces, and an extended surfacewith alterations such as wavy fins, slotted fins, and perforated fins. Webb [1] surveyeddevelopments in plate-fin and circular-fin heat exchangers and suggested the use ofslotted and punched fins for increasing the heat transfer. Webb [1] recommendedthe use of the correlation for heat transfer presented by Briggs and Young [2], andcorrelation for pressure drop presented by Robinson and Briggs [3]. Zukauskas [4]introduced correlations for Nusselt number (Nu) and pressure drop (DP) for an inlineas well as a staggered arrangement of finned-tube bundles. Flow through the tubebundles was reported to have three circumferential regions: laminar, turbulent, andseparated flows. Zukauskas [4] also mentioned the need to artificially disrupt theboundary layer to attain better performance of the heat exchanger.
Wang et al. [6] studied wavy fins and presented an empirical correlation forherringbone plate-fin-tube heat exchangers. Tao et al. [7] studied plate fins with aslotted X arrangement of strips commonly used in air conditioning. This arrange-ment resulted in a 97% increase in h and a 63% increase in DP. Cheng et al. [8] stud-ied three different configurations of X protruding strips, positioned along the flowdirection according to the rule of ‘‘front coarse and rear dense.’’ Recent studies ofpin fins by Sahin et al. [9] and of rectangular fins by Shaeri et al. [10] increasedthe surface contact area of fluids by perforations. This assisted in improving turbu-lence and mixing, and in reducing the friction factor.
Jang et al. [11] was the first to study annular finned-tubes numerically. Simula-tions of a staggered arrangement of annular finned-tubes under dry and wet operat-ing conditions were conducted and validated experimentally. They showed thatisothermal fin approximation overestimates the heat transfer coefficient by 5–35%.Mon et al. [12] performed numerical calculations of annular finned-tubes to investi-gate the effect of variation of fin spacing on the rate of heat transfer. Mon et al. [12]accounted for heat conduction and convection through fin thickness and appliedconstant temperature to tube walls. They reported that the boundary layer develop-ment on fin and tube surfaces mainly depends on the ratio of fin spacing to fin height.
Abundant literature regarding annular fins has been published, but the idea ofperforated annular fins has not been studied in detail. Perforations disrupt theboundary layer and enhance mixing of the flow. This motivated the authors to evalu-ate performance of the annular finned-tubes with perforations. The main objective ofthe present study was to assess the increase in heat transfer and pressure drop (DP)due to the circular perforations. Annular finned-tubes, which typically carry steaminside, were cooled with forced air flow. This research employed three-dimensionalnumerical calculations of four row finned-tubes. Comparison of both the heat trans-fer rates and changes in DP was performed for solid (no perforations) and perforated(perforations at �60� to �180�, with 30� interval) fins. Variations in DP wereevaluated for various combinations of perforations.
1.1. Losses in ACSC
Different types of losses such as pressure drop (primary loss) across the tubebundle and secondary losses such as inlet loss, fan loss, and jetting loss were reported
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by the researchers in the A-frame structures. Kroger [13] studied various secondarylosses in A-frame structures and reported that secondary losses were of the sameorder as primary pressure losses. Since perforations in a fin increase pressure drop[7, 12], it is important to assess if such losses could be offset by reducing secondarylosses, such as by geometric modifications of the fin spacing within the fin-tube bun-dles. Meyer et al. [14] investigated plenum losses and found that heat exchanger inletgeometry has an influence on plenum losses. Further, Meyer et al. [15] conductedexperiments with four types of eight blade axial flow fans. They used both ellipticaland rectangular cross-sections of tubes and fins to study inlet losses. Thecross-sectional profile of finned-tubes was found to be one of the important factorsinfluencing inlet pressure drop. Also, losses were observed to increase with a decreasein angle of incidence of inlet air. However, to the authors’ knowledge, heat exchan-ger loss due to the changed spacing of fins within the finned-tube bundle has not beenreported in the existing literature. This study altered the spacing of the fins along thearms of an A-frame structure to assess reduction in pressure drop, which, in turn,may off-set the increased pressure losses due to perforations.
2. Methodology
2.1. Finned-Tube Analysis
Numerical calculations were conducted by simulating three-dimensional airflow and heat transfer over solid and perforated finned-tube configurations.
2.1.1. Computational domain. The domain with four finned-tubes in stag-gered arrangement and symmetric boundaries was developed, as shown in Figure 1a.This type of arrangement is typical for ACSCs. Geometrical dimensions were similarto those by Jang et al. [11], as shown in Table 1. Thickness of the tubes was consideredwith the inner diameter of the tube as the boundary of the domain. Circular perfora-tions, 4mm in diameter, were located at a pitch interval of 30� around the annular fin,starting at 60� (Figure 1b), to �60� in the clockwise direction. Since the domainshowed geometrical symmetry, only the top part from 0� to 180� of the finned-tubewas developed. Thus, a perforated finned-tube with a symmetric surface had four per-forations at 60�, 90�, 120�, and 150� and a half perforation at 180�. Domain bound-aries were extended to minimize the effect of the uniform flow boundary conditionat the inlet on the flow velocity near the finned-tube walls. The inlet plane of the flowdomain was located 1.5 fin diameters upstream from the first finned-tube, while theoutlet plane was 5 fin diameters downstream from the last finned-tube.
2.1.2. Governing equations. Conjugate fluid flow and heat transfer calcula-tions were carried out to solve conduction in the tube and fin walls and forcedconvection over the finned-tubes.
Continuity and momentum equations for the air side flow were solved asfollows.
r � ðq vÞ ¼ 0 ð1Þ
r � ðq v vÞ ¼ �rpþr � mðrvÞ ð2Þ
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Table 1. Dimensions of finned-tube array for computational and analytical calculations
Geometrical parameter Dimensions in mm
Inside tube diameter (Di) 23.2
Outside tube diameter (D) 27
Fin outer diameter (Df) 41
Fin thickness (t) 0.5
Fin spacing (s) 3.5
Transverse tube pitch (ST) 21.5
Longitudinal tube pitch 73
Tube material Steel
Fin material Aluminum
Figure 1. Geometry of finned-tube array. (a) Staggered arrangement of fins labeled fin-1–fin-4 from left to
right and with a perforated finned surface; (b) angular locations of perforations on any fin surface; and (c)
3-D view of finned-tube array.
ENHANCED HEAT TRANSFER WITHIN A CONDENSER 739
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Energy equation [16] for the convection over the finned-tubes was solved as fol-lows.
r � ½vðqE þ pÞ� ¼ �r � ðjeffrTÞ ð3Þ
In the above equation the effective conductivity is as follows.
jeff ¼ ða� cPÞ=meff ð4Þ
Here, the effective viscosity is as follows.
meff ¼ mþ mt ð5Þ
The Reynolds number (Re) was calculated using the maximum velocity in thedomain and the outer diameter of the tube as the length parameter(Re ¼ q�D� vmax=m). Re was found to be in the lower turbulent scale within therange of 4,000 to 24,000. Steady state numerical calculations were carried out usingthe RNG k–e turbulent model to account for small scale vortices and the effects ofswirl on turbulence. Standard equations were solved for the RNG k–e model [16]:
r � ðq k vÞ ¼ rðak meffr � kÞ � qeþ Gk ð6Þ
r � ðq e vÞ ¼ r � ðaemeff r � eÞ þ C1eek
h iGk � C2eq
e2
k
� �� Re ð7Þ
where ak¼ ae¼ 1.393 are the inverse effective Prandtl numbers for k and e, respect-ively. The model constants C1e (¼ 1.42) and C2e(¼ 1.68) are derived analytically bythe RNG theory [16]. The term Gk represents the generation of turbulence kineticenergy due to the mean velocity gradients and is calculated as follows.
Gk ¼ �qvivjqvjqxi
ð8Þ
mt is turbulent viscosity and is defined based on the turbulence model beingused. For the RNG k–e turbulence model [16],
mt ¼ q� cm � k2=e; where cm ¼ 0:0845 ð9Þ
Re ¼cmqg3 1� g
g0
� �1þ bg3
e2
k
� �ð10Þ
where b¼ 0.012, g ¼ S ke , and g0¼ 4.38; here, S is strain rate magnitude.
Energy equation [16] for the convection over the finned-tubes was solved usingthe following equation.
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where E is defined as
E ¼ H þ p
qþ v2
2ð11Þ
and H¼ specific enthalpy, defined as
H ¼ZTref
cpqT ð12Þ
In solid, the energy equation that was solved has the following form [20].
r � ðvqhÞ ¼ r � ðjrTÞ ð13Þ
2.1.3. Boundary conditions. Solid (no perforations) and perforated(perforations at �60� to �180� with 30� interval) cases were simulated for inlet freestream air velocities of 1, 3, and 5m=s at 300K for validation of Nusselt number(Nu) and friction factor (f). Other combinations of perforated cases were simulatedfor free stream velocity of 3m=s. Density of the inlet air is calculated duringnumerical calculations based on incompressible ideal gas law [16], where density isdependent only on the operating pressure and local temperature. No slip conditionwas applied to the outer tube and the fin walls. The inner tube wall was assumed tohave a constant temperature of the condensing steam (350K). This model consideredconduction within the fin and the tube thickness. Symmetric planes, as shown inFigure 1a, were assumed to have zero diffusive flux. All the normal gradients of flowvariables were set to zero at the plane of symmetry. Free stream air properties werespecified as viscosity (m)¼ 1.798� 10�5 kg=m-s, specific heat (Cp)¼ 1006.43 J=kg-K,and thermal conductivity (j)¼ 0.0242W=m-K.
Hexahedral elements, as shown in Figure 2, were used to mesh the flowdomain. Total element count in the domain was 426,500 and the maximum skewnesswas 0.76. Mesh with finer element size was used near the fins and outer tube walls to
Figure 2. Hexagonal mesh. (a) Mesh across the domain with fine mesh elements near the finned-tube walls
and relatively coarser mesh elements away from the walls; and (b) mesh over the fin and tube surfaces.
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capture the sharp velocity gradient accurately. The size of mesh elements increasedand became coarser away from the walls. Two additional cases of solid fins, coarsermesh with 15% less mesh count, and finer mesh with 15% more mesh count wereassessed. Nu and h values of all three cases (fine, coarse, and present) were com-pared. Nu and h values (Table 2) for the present solid fin case were within 0.2%of the finer mesh case.
2.2. A-Frame Structure Analysis
A-frame structure of the ACSC was simulated to reduce the overall pressuredrop in the structure by altering the fin spacing across the tube.
2.2.1. Computational domain. A two-dimensional geometry of the rightsymmetric half side of the A-frame was developed, as shown in Figure 3a. Fins repre-senting four row finned-tube arrays along the arms of the A-frame were created. Per-forations on the finned-tubes were not considered in this representative fin array.
Figure 3. Uneven distribution of fins along the arms of the A-frame. (a) Computational domain and
boundary conditions, and (b) uneven fin distribution cases.
Table 2. Heat transfer coefficient and Nusselt number results for grid independence study
Cases Heat transfer coefficient Nusselt number
Fine case 72.5 2,994.9
Present case 72.6 3,001.8
Coarse case 67.3 2,782.4
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Outlet boundary of the domain was located at a distance of 25 times fin length. Fourcases, with change in spacing of the fins over the entire arms of the A-frame, weresimulated to assess the reduction in DP, as described in Figure 3b. Total numberof fins in each of the cases was the same.
Continuity and momentum equations were solved, as described in Eqs. (1) and(2), respectively, to calculate the pressure drop (DP) across the fins. The DP in thesystem was calculated at three locations, marked as 1, 2 and 3 in Figure 3a. Steadystate lower turbulent scale (Re ranges from 4,000 to 24,000) simulations were per-formed using k–x shear stress transport model (SST) equations, as shown below.
r � ðq k vÞ ¼ r � ðCkr � kÞ þ Gk � Yk ð14Þ
r � ðqx vÞ ¼ r � ðCxr � xÞ þ Gx � Yx þ 2ð1� F1Þqrx;21
xqkqxj
qxqxj
ð15Þ
where rk and rw are the turbulent Prandtl numbers of k and x, respectively[16]. The Yk and Yw represent the effective dissipation of k and x, respectively[16]. Similarly, Gk and Gx are generation of k and x, respectively [16]. Turbulent vis-cosity required to calculate, Ck (effective diffusivity of k) and Cw (effective diffusivityof x) is defined as follows.
mt ¼qkx
1
max 1a� ;
SF2
a1x
� � ð16Þ
where a� is the turbulent viscosity damping factor for low-Reynolds-numbercorrection, S is the strain rate magnitude, and F1, F2 are the blending function formodeling near-wall and far-field zones in the k–x SST turbulence model. Other con-stants that are used in the calculation for the turbulence model [16] are ak;1 ¼1:176; ak;2 ¼ 1:0;rx;1 ¼ 2:0;rx;2 ¼ 1:168; a1 ¼ 0:38; bi;1 ¼ 0:075; and bi;2 ¼ 0:0828.
2.2.2. Boundary conditions. An inlet boundary represented forced air velo-city of 3m=s from the fan. A pressure outlet boundary condition was used at the out-let boundary of the domain. A no slip wall boundary condition was applied on thefin array. A wall boundary condition was also specified at boundaries, representingthe steam duct and other walls of the A-frame. A symmetry condition was imposedon the left side boundary by specifying all normal gradients as zero. Geometry wasmeshed with finer quadrilateral elements between the fins and with relatively coarsertriangular elements in the remaining domain. The interface type of boundary wasused to account for the transition from quadrilateral to triangular mesh elements.Total element count was about 100,000 and had maximum skewness of 0.75.
2.3. Validation with Analytical Results
Computational results of solid fins were validated for the Nusselt number (Nu)with Briggs and Young correlation [2], and for friction factor (f) with Robinson andBriggs correlation [3], as mentioned in Eqs. (17) and (18), respectively.
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Nu ¼ 0:134�Re0:681 � Pr 1 3=ð Þ � s
l
h i0:2� s
t
h i0:1134ð17Þ
f ¼ 18:93�Re�0:361 � ST
D
� ��0:927
� ST
SL
� �0:515ð18Þ
The Reynolds number (Re) in Eqs. (17) and (18) were calculated at the mini-mum cross section area, perpendicular to the flow. According to the continuity equa-tion, the area of minimum cross section has maximum flow velocity. For finned-tubeconfigurations, the area of minimum cross section is the thin space between the twofins. Hence, Eq. (19), reported by Zukauskas [4], was used to calculate the maximumvelocity.
vmax ¼STv
ST �Dð19Þ
Friction factor (f) for the numerical simulations was calculated as
f ¼ DPnqv2
ð20Þ
Figure 4. Comparison of computational and analytical results for the solid case. (a) Comparison of Nus-
selt number with Briggs and Young correlation, and (b) comparison of friction factor with Robinson and
Briggs correlation.
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Values of DP in Eq. (20) and Nu values are obtained from a post processingstep in Fluent. A reference temperature of 300K was used for calculating Nu.
Comparison of analytical and computational results of Nu and f is shown inFigure 4. Computational results for Nu number were within 15.7% of the analyticalcorrelation (Figure 4a). From Figure 4b, it is observed that velocity changes do notalter the general decreasing trend of the friction factor, and the difference betweenanalytical and numerical results remained nearly the same for all velocity values.A 43.7% difference for a velocity of 5m=s was observed between numerical and ana-lytical results. Though the results for f are not close to the analytical results, they areconsistent with the data reported by Mon et al. [12]. They showed that the numericalresults for Nu and f were within �25% and �40%, respectively, with those obtainedby analytical results. Other perforation combinations, as shown in Table 3, were alsosimulated in order to evaluate the variation of DP with the location of perforation.
3. RESULTS
3.1. Solid and Perforated Finned-Tubes
Numerical calculations were conducted for the solid fins (no perforations) toassess the variation of velocity and temperature distributions across the domain.The velocity and temperature distribution on the surface of solid fins were thencompared with those of perforated fins (perforations at �60� to �180� with 30�
interval). Other cases with single, double, and triple perforations, as described inTable 3, were simulated to assess the effect of perforation location on velocity andtemperature profiles. Percentage reductions in perforated fin surface area for heattransfer calculation for various perforation combinations are shown in Table 4.The case of solid fins was used as the baseline case to compare subsequent casesinvolving various combinations of perforations.
3.1.1. Comparison of solid and perforated cases. Velocity vectors andtemperature of the solid finned-tubes for the free stream velocity of 3m=s are shown
Table 3. Fin performance ratios and angular location (theta in degrees) of perforations along the fin sur-
face for various perforation cases
Cases
Perforation
location
Heat flux,
q (Q=m2)
Fin q
performance
ratio (%) (A)
Pressure
drop,
DP (Pa)
Fin DPperformance
ratio (%) (B)
Relative
q-DP factor
(A=B)
Solid — 3,136.11 — 115.4 — —
Perforated 60� to 180� 3,323.05 5.96 129.1 11.87 0.50
Case 8 120�, 150�, 180� 3,261.08 �3.99 119.8 �3.81 �1.05
�Indicates favorable fin performance values.
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in Figure 5. It was observed that free stream air flow approaching the finned-tubearray encountered stagnation at the angular location (h) of 0� at the first row(Figure 1b). At this point, flow velocity reduced to zero and total pressure, beinginversely proportional to velocity, was the maximum in the domain. Pressure starteddecreasing as the flow advanced, creating favorable flow conditions [dp=dx< 0] in theupstream region of all fins. Maximum velocity was observed at about h¼ 90�. There-after, velocity started decreasing and pressure started increasing, creating a positivepressure gradient [dp=dx> 0]. This resulted in flow separation from the fin wall, cre-ating wake areas. Formation of a recirculation zone was observed in the downstreamregions of the first, second, and third finned-tube rows followed by a large wake areaat the downstream region of the fourth finned-tube row. Fluid particles in this regionlost energy in overcoming the shear forces in the boundary layer. The remainingenergy was insufficient to resist increasing pressure forces, resulting in a reversalof fluid particles. Because of the slower air flow, high temperatures persisted in wakeareas. Thus, the upstream half of the region experienced higher heat removal thanthe downstream region.
Subsequent to the solid fins, perforations were introduced in the downstreamregion with an attempt to improve the flow characteristics and increase the heattransfer efficiency. Four and one-half perforations were created on a symmetricmodel of the fin surface (equivalent to nine perforations on a complete fin surface),as discussed earlier (Figure 1b). Solid and perforated fins were compared at a freestream velocity of 3m=s, using velocity vectors (Figure 5a for solid fin andFigure 5b for perforated fins) and temperature contours. Temperature contours ofsolid fins (Figure 5c) and perforated fins (Figure 5d) showed a reduction in size ofthe high temperature zones in the downstream region of the tubes. The average tem-perature of the fins and tube walls in the perforated case was 4K less than the solidcase. In general, a significant reduction in temperature was observed in the down-stream region of the fourth row of finned-tubes. Comparison of velocity contoursshowed that perforations altered the velocity gradients in the domain. Recirculationzones in the downstream region of the first and subsequent finned-tubes were dis-rupted by the perforations. As a result, these recirculation zones shrank in size.
Table 4. Fin h performance ratios for various perforation cases
Perforations in this region also increased the mixing of air in the downstream areas.An overall enhancement in the values of heat flux (q) and heat transfer coefficient (h)were observed for the perforated fins as compared to the solid fins.
A comparison of the Nusselt number (Nu) number along the fin surface for hranging from 0� to 180� is plotted in Figure 6 for solid and perforated fins. As shownin Figure 6a, the first row of finned-tubes was directly exposed to free stream air flowand was generally unaffected by perforations. However, the value of Nu number forthe perforated finned-tubes was observed to increase gradually as the flow advancedfrom fin-1 to fin-4. As discussed earlier, the flow over the solid fin was detached fromthe wall at about 90�, resulting in a recirculation zone in the downstream region. Nunumber at h¼ 90� (near the point of detachment) was observed to have almost thesame value for perforated and solid fins (Figures 6a and 6b). As angular locationsfrom 120� to 180� were in the recirculation areas, perforations at these locationsimproved mixing due to enhanced turbulence. Thus, Nu numbers were observed toincrease for every perforated finned-tube for h values starting from 90� to 180�.The flow in the upstream region of the inner finned-tubes (rows 2 and 3) was influ-enced by the increased mixing and turbulence of air in the upstream region. Hence,
Figure 5. Comparison of solid and perforated fins for free stream velocity of 3m=s. (a) Velocity vectors for
the solid fin case; (b) velocity vectors for the perforated fin case; (c) temperature contours for solid fins; and
(d) temperature contours for perforated fins (color figure available online).
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a considerable rise in Nu was observed at the upstream locations for the third(Figure 6c) and fourth (Figure 6d) finned-tubes. It was evident that downstreamfinned-tubes benefited from the perforations of upstream fins. The increase in the area
averaged Nusselt number (Nu) for the third and the fourth perforated finned-tubewas 6.7% and 9.5%, respectively. The percentage increase of Nu number for perfor-ated fins was defined with respect to the solid fins as [(Nuperforated�Nusolid)�100=Nusolid]. An increase in Nu for the entire array of finned-tubes was observed tobe 7.07%.
Zukauskas [4] reported that hydrodynamic forces arising due to the turbulentfluctuations of the flow and pressure was one of the causes of flow-induced vibrations.Thus, limiting the pressure drop (DP) becomes one of the primary challenges in thedesign of finned-tubes. Perforations, which increased h and the Nu number, alsoincreased the pressure drop by about 11.87% [(DPperforated�DPsolid)� 100=DPsolid].Thus, for better optimization perforations should be placed only at the locationswhich result in a minimum increase in DP and the maximum Nu (or h).
3.1.2. Performance ratios. Symmetric fin combinations were assessed tofind the location of perforation that result in higher h and q, but lower the increasein DP, as shown in Table 3. Four combinations of single perforation at 60� (case 1),90� (case 2), 120� (case 3), and 150� (case 4) were evaluated. Due to the geometricsymmetry, half perforation was created at h¼ 180� (case 5). Based on the resultsof the best single perforation location, additional cases with multiple perforations,
Figure 6. Plot of Nusselt number versus h (theta in degrees) along the fin surface shows enhanced heat
transfer. (a) Fin 1, first finned-tube facing the free stream air flow at 3m=s; (b) fin-2; (c) fin-3; and (d)
fin-4, the last finned-tube in the direction of free stream.
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120�–150� (case 6), 120�–180� (case 7) and 120�–150�–180� (case 8), were assessed toobtain a combination that has a better balance between enhanced q and minimalincrease in DP. Three fin performance ratios were introduced to calculate a percent-age increase in DP, q, and h values for perforated fin cases in relation to the solid fin.
Fin DP performance ratio ¼ DPperfo � DPsolid
DPsolid� 100 ð21aÞ
Fin q performance ratio ¼ qperfo � qsolidqsolid
� 100 ð21bÞ
Fin h performance ratio ¼ hperfo � hsolidhsolid
� 100 ð21cÞ
Fin q and DP performance ratios for single and half perforation cases in thesemi-circular fin domain with reference to the solid case are shown in Figure 7. Itwas observed that case 3 (h¼ 120�) resulted in the least increase in DP and maximumincrease in q values. The results for case 4 (h¼ 150�) and 5 (h¼ 180�) showed a some-what lower increase in q when compared to the increase in DP. However, cases 1(h¼ 60�) and 2 (h¼ 90�) showed a reverse trend with a maximum increase in DPand the least increase in q values. Thus, perforation at h¼ 60� and 90� were not ben-eficial and were of little practical use.
3.1.3. Relative q-DP factor. The efficiency of perforations was determined tofind the optimum case having the least increase in DP with the maximum increase inq. Calculations, as shown in the last column of Table 3, were conducted to find therelative q-DP factor, a dimensionless quantity defined as the ratio between fin q per-formance ratio and fin DP performance ratio.
Figure 7. Plot of fin q- and h- performance ratios for single perforation configurations (cases 1–5).
A higher value of relative q-DP factor implies a combination of maximumincrease in q values in conjunction with a minimum increase in DP values. Thus, arelative q-DP factor value greater than unity indicates a better performing fin con-figuration.
Amongst the single perforated cases, perforation at h¼ 120� (case 3) providedthe best result with a 1.70%increase in fin q performance ratio, while an increase infin DP performance ratio was only 1.39%. Thus, the relative q-DP factor of 1.23 forcase 3 was better as compared to cases 4 (0.97) and 5 (0.85). Relative q-DP factor waseven lower (0.21) for the perforations at h¼ 60� (case 1) and h¼ 90� (case 2). Thesecombinations resulted in a significant increase in DP causing a lower relative q-DPfactor. It was evident that perforations placed in the downstream half portion(between h¼ 90� to 180�) were more advantageous than in the upstream half portion(between h¼ 0� to 90�). Hence, for better relative q-DP factor, it was recommendedto have perforations only in the downstream region beyond the point of detachment(h¼ 90�). As discussed earlier, the perforated case (perforations at �60� to �180�
with 30� interval) had high pressure drop and, hence, the relative q-DP factor wasless than 1. Results of fin h performance ratio, tabulated in Table 4, also confirm thatperforations in the downstream region result in better heat transfer.
An increase in all three fin performance ratios (q, h, and DP) and relative q-DPfactor for multiple perforation cases are also shown in Tables 3 and 4. Case 8 showeda maximum increase in q (3.99%) performance ratio coupled with a relatively lowerincrease in DP (3.81%) performance ratio among all the combinations. Since the rela-tive q-DP factor was greater than 1 for case 8 (1.05), it was considered more favor-able than the other multiple perforation cases. Cases 6 (relative q-DP factor¼ 0.78)and 7 (relative q-DP factor¼ 0.87) can be incorporated if higher heat transfer ratesare desired, while an increase in pressure drop is allowable for the structure. How-ever, it must be noted that from the perspective of relative q-DP factor, case 3 (per-foration at h¼ 120�; relative q-DP factor¼ 1.23) is better than case 8 (perforations ath¼ 120�, 150�, and 180�; relative q-DP factor¼ 1.05).
3.2. Fin Spacing in an A-Frame Structure
Four cases of fin spacing were configured, as shown in Figure 3b. Analysis wasinitiated with case A, the base line case, with evenly spaced fins at a pitch of 3.5mm.Velocity vectors and pressure contours were plotted to study the flow field in thedomain. Pressure drop was measured across all three locations and tabulated inTable 5. It was observed that velocity at the upstream side of the fins increased fromthe inlet end towards the top end. Cases B and C were configured such that fins wereclustered at the inlet end and the fin spacing was increased towards the top end.However, DP across the fins for case B increased by 2.1% (location 2). Case Cshowed a favorable change with a decrease in DP by 1% (location 2). Case C showed
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that more air flow occurred through the central region of the fin array. Based on thisobservation, case D with clustered fins at both inlet and top ends and sparsely spacedfins at the center was developed.
A comparison of velocity vectors between cases A and D is shown in Figure 8a.The sparsely placed fins at the center facilitated greater air flow with reduced airresistance. Pressure magnitude (Figure 8b) was observed to be reduced on theupstream side of the fin array. Thus, DP across the fins was decreased by 1.9%
Table 5. Pressure drop (DP) characteristics for combinations of fin spacing
Case Location 1 Location 2 Location 3
DP (Pa) % change in DP DP (Pa) % change in DP DP (Pa) % change in DPA 2.85 – 2.87 – 1.19 –
B 2.91 2.11 2.93 2.1 1.26 5.88
C 2.82 �1.16 2.84 �1.03� 1.18 �0.88
D 2.80 �1.75 2.82 �1.86� 1.18 �1.28
�indicates favorable change in DP.
Figure 8. Comparison of velocity vectors for cases A and D. (a) Velocity vectors and (b) contours of press-
ure (color figure available online).
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(location 2). This additional reduction in DP, provided by the use of unequal fin spa-cing along the arms of the A-frame, can facilitate the use of multiple perforations foryielding higher heat transfer.
4. DISCUSSION
The h and DP are important parameters in the design of an annular finned-tubearray. Heat transfer enhancement with perforations on the annular fin surface wasstudied numerically using various combinations of perforations. These arrays, com-monly used in air cooled steam condensers (ACSC), are known for high pressurelosses. The fin spacing along the arms of the A-frame was changed to reduce theDP across the fin bundle. Fin spacing is one of the important geometric factors influ-encing fluid flow and heat transfer. Unequal spacing reduced the pressure loss in theA-frame structure, but its effects on heat transfer in a perforated annular finned-tubearray are unknown. Perforated finned-tube array with unequal fin spacing needs tobe studied together to assess the change in heat transfer and DP characteristics.
Elliptical shaped finned-tubes, such as studies by Rocha et al. [17], will providemore aerodynamic properties than the circular fins. Perforated finned-tube arraywith an elliptical cross section can be studied in the future to evaluate h and DP char-acteristics. Heat transfer and pressure drop in a three-dimensional A-frame structurecan be evaluated using the optimum number of perforations on annular fins and finspacing along the arms of the A-frame.
5. CONCLUSION
An annular finned-tube array with perforations was studied numerically forassessing the enhancement of heat transfer while minimizing an increase in pressuredrop across the domain. To calculate the efficiency of the location of a perforation, arelative q-DP factor was defined as the ratio of increase in fin q performance ratioand increase in fin DP performance ratio. A perforation in the wake area (120�,150�, or 180�) beyond the point of detachment was found to be more efficient, parti-cularly for perforation at h¼ 120�. Multiple perforations at h¼ 120�, 150�, and 180�
also showed a favorable relative q-DP factor. The number of perforations was lim-ited by the allowable DP in the system.
Unequal spacing along the A-frame structure of ACSCs could decrease thepressure drop across the finned-tube bundle. Clustered spacing at the inlet and topends and large spacing at the center assisted in reducing the upstream pressure ofthe air and DP in the system. Thus, penalty in DP for a perforated fin can possiblybe offset by changing the fin spacing along the arms of the A-frame structure.
REFERENCES
1. R. L. Webb, Air Side Heat Transfer in Finned Tube Heat Exchangers, Heat TransferEng., vol. 1, pp. 33–89, 1980.
2. D. E. Briggs and E. H. Young, Convection Heat Transfer and Pressure Drop of Air Flow-ing across Triangular Pitch Banks of Finned Tubes, Chem. Eng. Prog. Symp. Ser., vol. 59,pp. 1–10, 1963.
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3. K. K. Robinson and D. E. Briggs, Pressure Drop of Air Flowing across Triangular PitchBanks of Finned Tubes, Chem. Eng. Prog. Symp. Ser., vol. 62, pp. 177–184, 1966.
4. A. Zhukauskas, High-Performance Single-Phase Heat Exchangers, chaps. 14–15, pp. 291–346, Hemisphere Publishing, New York, 1989.
5. A. E. Bergles, R. L. Webb, and G. H. Junkan, Energy Conservation via Heat TransferEnhancement, Midwest Energy Conf., vol. 4, pp. 193–200, 1979.
6. C. C. Wang and K. Y. Chi, Heat Transfer, and Friction Characteristics of Plain Fin-and-Tube Heat Exchangers, Part I: New Experimental Data, Int. J. Heat and Mass Transfer,vol. 43, pp. 2681–2691, 2000.
7. W. Q. Tao, Z. G. Qu, and Y. L. He, Experimental and 3-D Numerical Study of Air SideHeat Transfer and Pressure Drop of Slotted Fin Surface, Int. Conf. on Enhanced, Compactand Ultra-Compact Heat Exchangers: Sci. Eng. and Tech., Whistler, British Columbia,Canada, paper 15, 2005.
8. Y. P. Cheng, Z. G. Qu, and W. Q. Tao, Y. L. He, Numerical Design of Efficient SlottedFin Surface based on the Field Synergy Principle, Numer. Heat Transfer A, vol. 45, pp.517–538, 2004.
9. B. Sahin and A. Demir, Thermal Performance Analysis and Optimum Design Parametersof Heat Exchanger Having Perforated Pin Fins, Energy Conversion and Management, vol.49, pp. 1684–1695, 2008.
10. M. R. Shaeri and M. Yaghoubi, Numerical Analysis of Turbulent Convection HeatTransfer from an Array of Perforated Fins, Int. J. of Heat and Fluid Flow, vol. 30,
pp. 218–228, 2009.11. J. Y. Jang, J. T. Lai, and L. C. Liu, The Thermal-Hydraulic Characteristics of Staggered
Circular Finned-Tube Heat Exchangers under Dry and Dehumidifying Conditions, Int.J. of Heat and Mass Transfer, vol. 41, pp. 3321–3337, 1998.
12. M. S. Mon, and U. Gross, Numerical Study of Fin-Spacing Effects in Annular-FinnedTube Heat Exchangers, Int. J. of Heat and Mass Transfer, vol. 47, pp. 1953–1964, 2004 .
13. D. G. Kroger, Fan Performance in Air-Cooled Steam Condensers,Heat Recovery Systemsand CHP, vol. 14, pp. 391–399, 1994.
14. C. J. Meyer and D. G. Kroeger, Plenum Chamber Flow Losses in Forced DraughtAir-Cooled Heat Exchangers, Appl. Therm. Eng., vol. 18, pp. 875–893, 1998.
15. C. J. Meyer and D. G. Kroeger, Air Cooled Heat Exchanger Inlet Flow Losses, Appl.Therm. Eng., vol. 21, pp. 771–786, 2000.
