Cincinnati OH, Ohio, USA b Korea Heat Exchanger Co. Ltd, Gunsan, Jeonbuk, Korea. Philadelphia, Pennsylvania, USA. Available online: 18 May 2012

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1 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: Registered office: Mortimer House, 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: 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, To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: 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,

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3 Numerical Heat Transfer, Part A, 61: , 2012 Copyright # Taylor & Francis Group, LLC ISSN: print= online DOI: / EVALUATION OF ENHANCED HEAT TRANSFER WITHIN A FOUR ROW FINNED TUBE ARRAY OF AN AIR COOLED STEAM CONDENSER Rupak K. Banerjee 1, Madhura Karve 1, Jong Ho Ha 2, Dong Hwan lee 3, and Young I. Cho 4 1 Department of Mechanical Engineering, University of Cincinnati, Cincinnati OH, Ohio, USA 2 Korea Heat Exchanger Co. Ltd, Gunsan, Jeonbuk, Korea 3 Chonbuk National University, Jeonju, Joenbuk, Korea 4 Department 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 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 1 m=s 5 m=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%) ofdp performance ratio. Perforations in the downstream region at 120, 150, Received 18 February 2011; accepted 3 February 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. Rupak.Banerjee@uc.edu 735

4 736 R. K. BANERJEE ET AL. NOMENCLATURE A total surface area, m 2 A c frontal area, m 2 C p specific heat at constant pressure, J=kg-K D outer tube diameter, m E total internal energy, m 2 =s 2 f friction factor h heat transfer coefficient, W=m 2 -K j thermal conductivity, W=m-K k turbulent kinetic energy, m 2 =s 2 l fin length, m n number of tube rows p static pressure of air, Pa q heat flux (q ¼ h DT), W=m 2 s fin pitch, m T temperature, K t fin thickness, m v velocity of air, m=s Nu Nusselt number ¼ h D=j Pr Prandtl number ¼ m C P =j Re in Reynolds number ¼ q V D=m S L longitudinal pitch of tubes, m S T transverse pitch of tubes, m a thermal diffusivity, m 2 =s e turbulent energy dissipation, m 2 =s 3 t specific volume, m 3 =kg q density of air, kg=m 3 m viscosity of air, kg=m-s h angular location, degrees DP differential pressure, Pa r ¼ d dx i þ d dy j þ d dz k Subscripts eff effective max maximum t turbulent 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 condensers (ACSC) in power plants or as radiators in automobiles. The design of such an array has been investigated by previous researchers due to the complexities involved in the cross flow of air over the tube bundles. The efficiency of finned-tubes depends 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 structure. High pressure and high temperature steam is let into these finned-tubes, which are cooled by a large fan at the base of the A-frame structure. It is a relatively inexpensive alternative to the water cooled condensers. ACSCs have gained more importance recently as a water conservation measure in regions with limited water resources. However, under extreme climatic conditions ACSCs are faced with problems such as inefficient performance in high temperature regions, such as the desert, and freezing and choking of finned-tubes in low temperature regions. Enhancing the heat transfer coefficient (h) of the fins can help in minimizing the problems associated with extreme climatic conditions. Researchers have explored several approaches of reducing air side resistance in order to increase heat transfer from finned-tube surfaces.

5 ENHANCED HEAT TRANSFER WITHIN A CONDENSER 737 Heat transfer enhancement techniques, such as surface vibration and magnetic field, are classified as active techniques based on the use of external power [5]. In contrast, passive techniques included: treated or rough surfaces, and an extended surface with alterations such as wavy fins, slotted fins, and perforated fins. Webb [1] surveyed developments in plate-fin and circular-fin heat exchangers and suggested the use of slotted and punched fins for increasing the heat transfer. Webb [1] recommended the use of the correlation for heat transfer presented by Briggs and Young [2], and correlation for pressure drop presented by Robinson and Briggs [3]. Žukauskas [4] introduced correlations for Nusselt number (Nu) and pressure drop (DP) for an inline as well as a staggered arrangement of finned-tube bundles. Flow through the tube bundles was reported to have three circumferential regions: laminar, turbulent, and separated flows. Žukauskas [4] also mentioned the need to artificially disrupt the boundary layer to attain better performance of the heat exchanger. Wang et al. [6] studied wavy fins and presented an empirical correlation for herringbone plate-fin-tube heat exchangers. Tao et al. [7] studied plate fins with a slotted X arrangement of strips commonly used in air conditioning. This arrangement resulted in a 97% increase in h and a 63% increase in DP. Cheng et al. [8] studied three different configurations of X protruding strips, positioned along the flow direction according to the rule of front coarse and rear dense. Recent studies of pin fins by Sahin et al. [9] and of rectangular fins by Shaeri et al. [10] increased the surface contact area of fluids by perforations. This assisted in improving turbulence and mixing, and in reducing the friction factor. Jang et al. [11] was the first to study annular finned-tubes numerically. Simulations of a staggered arrangement of annular finned-tubes under dry and wet operating conditions were conducted and validated experimentally. They showed that isothermal fin approximation overestimates the heat transfer coefficient by 5 35%. Mon et al. [12] performed numerical calculations of annular finned-tubes to investigate 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 applied constant temperature to tube walls. They reported that the boundary layer development 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 of perforated annular fins has not been studied in detail. Perforations disrupt the boundary layer and enhance mixing of the flow. This motivated the authors to evaluate performance of the annular finned-tubes with perforations. The main objective of the 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 steam inside, were cooled with forced air flow. This research employed three-dimensional numerical calculations of four row finned-tubes. Comparison of both the heat transfer 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 were evaluated for various combinations of perforations Losses in ACSC Different types of losses such as pressure drop (primary loss) across the tube bundle and secondary losses such as inlet loss, fan loss, and jetting loss were reported

6 738 R. K. BANERJEE ET AL. by the researchers in the A-frame structures. Kroger [13] studied various secondary losses in A-frame structures and reported that secondary losses were of the same order 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 secondary losses, such as by geometric modifications of the fin spacing within the fin-tube bundles. Meyer et al. [14] investigated plenum losses and found that heat exchanger inlet geometry has an influence on plenum losses. Further, Meyer et al. [15] conducted experiments with four types of eight blade axial flow fans. They used both elliptical and rectangular cross-sections of tubes and fins to study inlet losses. The cross-sectional profile of finned-tubes was found to be one of the important factors influencing inlet pressure drop. Also, losses were observed to increase with a decrease in angle of incidence of inlet air. However, to the authors knowledge, heat exchanger loss due to the changed spacing of fins within the finned-tube bundle has not been reported in the existing literature. This study altered the spacing of the fins along the arms 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 air flow and heat transfer over solid and perforated finned-tube configurations Computational domain. The domain with four finned-tubes in staggered arrangement and symmetric boundaries was developed, as shown in Figure 1a. This type of arrangement is typical for ACSCs. Geometrical dimensions were similar to those by Jang et al. [11], as shown in Table 1. Thickness of the tubes was considered with the inner diameter of the tube as the boundary of the domain. Circular perforations, 4 mm 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 domain showed geometrical symmetry, only the top part from 0 to 180 of the finned-tube was developed. Thus, a perforated finned-tube with a symmetric surface had four perforations at 60,90, 120, and 150 and a half perforation at 180. Domain boundaries were extended to minimize the effect of the uniform flow boundary condition at the inlet on the flow velocity near the finned-tube walls. The inlet plane of the flow domain was located 1.5 fin diameters upstream from the first finned-tube, while the outlet plane was 5 fin diameters downstream from the last finned-tube Governing equations. Conjugate fluid flow and heat transfer calculations were carried out to solve conduction in the tube and fin walls and forced convection over the finned-tubes. Continuity and momentum equations for the air side flow were solved as follows. rðq vþ ¼0 rðq vvþ¼ rp þrmðrvþ ð1þ ð2þ

7 ENHANCED HEAT TRANSFER WITHIN A CONDENSER 739 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. Table 1. Dimensions of finned-tube array for computational and analytical calculations Geometrical parameter Dimensions in mm Inside tube diameter (D i ) 23.2 Outside tube diameter (D) 27 Fin outer diameter (D f ) 41 Fin thickness (t) 0.5 Fin spacing (s) 3.5 Transverse tube pitch (S T ) 21.5 Longitudinal tube pitch 73 Tube material Steel Fin material Aluminum

8 740 R. K. BANERJEE ET AL. Energy equation [16] for the convection over the finned-tubes was solved as follows. r½vðqe þ pþš ¼ r ðj eff rtþ ð3þ In the above equation the effective conductivity is as follows. j eff ¼ða c P Þ=m eff ð4þ Here, the effective viscosity is as follows. m eff ¼ m þ m t The Reynolds number (Re) was calculated using the maximum velocity in the domain and the outer diameter of the tube as the length parameter (Re ¼ q D v max =m). Re was found to be in the lower turbulent scale within the range of 4,000 to 24,000. Steady state numerical calculations were carried out using the RNG k e turbulent model to account for small scale vortices and the effects of swirl on turbulence. Standard equations were solved for the RNG k e model [16]: rðq kvþ¼rða k m eff rkþ qe þ G k h e rðqevþ¼rða e m eff reþþc 1e ig k C 2e q e2 R e k k where a k ¼ a e ¼ are the inverse effective Prandtl numbers for k and e, respectively. The model constants C 1e (¼ 1.42) and C 2e (¼ 1.68) are derived analytically by the RNG theory [16]. The term G k represents the generation of turbulence kinetic energy due to the mean velocity gradients and is calculated as follows. qv j G k ¼ qv i v j ð8þ qx i m t is turbulent viscosity and is defined based on the turbulence model being used. For the RNG k e turbulence model [16], ð5þ ð6þ ð7þ m t ¼ q c m k 2 =e; where c m ¼ 0:0845 c m qg 3 1 g g 0 e 2 R e ¼ 1 þ b g 3 k ð9þ ð10þ where b ¼ 0.012, g ¼ Sk e, and g 0 ¼ 4.38; here, S is strain rate magnitude. Energy equation [16] for the convection over the finned-tubes was solved using the following equation.

9 where E is defined as ENHANCED HEAT TRANSFER WITHIN A CONDENSER 741 E ¼ H þ p q þ v2 2 ð11þ and H ¼ specific enthalpy, defined as Z H ¼ c p qt ð12þ T ref In solid, the energy equation that was solved has the following form [20]. rðvqhþ¼rðjrtþ Boundary conditions. Solid (no perforations) and perforated (perforations at 60 to 180 with 30 interval) cases were simulated for inlet free stream air velocities of 1, 3, and 5 m=s at 300 K for validation of Nusselt number (Nu) and friction factor (f). Other combinations of perforated cases were simulated for free stream velocity of 3 m=s. Density of the inlet air is calculated during numerical calculations based on incompressible ideal gas law [16], where density is dependent only on the operating pressure and local temperature. No slip condition was applied to the outer tube and the fin walls. The inner tube wall was assumed to have a constant temperature of the condensing steam (350 K). This model considered conduction within the fin and the tube thickness. Symmetric planes, as shown in Figure 1a, were assumed to have zero diffusive flux. All the normal gradients of flow variables were set to zero at the plane of symmetry. Free stream air properties were specified as viscosity (m) ¼ kg=m-s, specific heat (C p ) ¼ J=kg-K, and thermal conductivity (j) ¼ W=m-K. Hexahedral elements, as shown in Figure 2, were used to mesh the flow domain. Total element count in the domain was 426,500 and the maximum skewness was Mesh with finer element size was used near the fins and outer tube walls to ð13þ 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.

10 742 R. K. BANERJEE ET AL. Table 2. Heat transfer coefficient and Nusselt number results for grid independence study Cases Heat transfer coefficient Nusselt number Fine case ,994.9 Present case ,001.8 Coarse case ,782.4 capture the sharp velocity gradient accurately. The size of mesh elements increased and became coarser away from the walls. Two additional cases of solid fins, coarser mesh with 15% less mesh count, and finer mesh with 15% more mesh count were assessed. Nu and h values of all three cases (fine, coarse, and present) were compared. Nu and h values (Table 2) for the present solid fin case were within 0.2% of the finer mesh case A-Frame Structure Analysis A-frame structure of the ACSC was simulated to reduce the overall pressure drop in the structure by altering the fin spacing across the tube Computational domain. A two-dimensional geometry of the right symmetric half side of the A-frame was developed, as shown in Figure 3a. Fins representing four row finned-tube arrays along the arms of the A-frame were created. Perforations 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.

11 ENHANCED HEAT TRANSFER WITHIN A CONDENSER 743 Outlet boundary of the domain was located at a distance of 25 times fin length. Four cases, with change in spacing of the fins over the entire arms of the A-frame, were simulated to assess the reduction in DP, as described in Figure 3b. Total number of 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 the system was calculated at three locations, marked as 1, 2 and 3 in Figure 3a. Steady state lower turbulent scale (Re ranges from 4,000 to 24,000) simulations were performed using k x shear stress transport model (SST) equations, as shown below. rðq kvþ¼rðc k rkþþg k Y k ð14þ 1 qk qx rðqxvþ¼rðc x rxþþg x Y x þ 2ð1 F 1 Þqr x;2 ð15þ x qx j qx j where r k and r w are the turbulent Prandtl numbers of k and x, respectively [16]. The Y k and Y w represent the effective dissipation of k and x, respectively [16]. Similarly, G k and G x are generation of k and x, respectively [16]. Turbulent viscosity required to calculate, C k (effective diffusivity of k) and C w (effective diffusivity of x) is defined as follows. m t ¼ qk x 1 ð16þ max 1 a ; SF 2 a 1 x where a is the turbulent viscosity damping factor for low-reynolds-number correction, S is the strain rate magnitude, and F 1, F 2 are the blending function for modeling near-wall and far-field zones in the k x SST turbulence model. Other constants that are used in the calculation for the turbulence model [16] are a k;1 ¼ 1:176; a k;2 ¼ 1:0; r x;1 ¼ 2:0; r x;2 ¼ 1:168; a 1 ¼ 0:38; b i;1 ¼ 0:075; and b i;2 ¼ 0: Boundary conditions. An inlet boundary represented forced air velocity of 3 m=s from the fan. A pressure outlet boundary condition was used at the outlet boundary of the domain. A no slip wall boundary condition was applied on the fin array. A wall boundary condition was also specified at boundaries, representing the steam duct and other walls of the A-frame. A symmetry condition was imposed on the left side boundary by specifying all normal gradients as zero. Geometry was meshed with finer quadrilateral elements between the fins and with relatively coarser triangular elements in the remaining domain. The interface type of boundary was used to account for the transition from quadrilateral to triangular mesh elements. Total element count was about 100,000 and had maximum skewness of 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 and Briggs correlation [3], as mentioned in Eqs. (17) and (18), respectively.

12 744 R. K. BANERJEE ET AL. hi Nu ¼ 0:134 Re 0:681 Pr ð13 = Þ s 0:2 s l t hi 0:1134 ð17þ f ¼ 18:93 Re 0:361 S T D 0:927 S 0:515 T ð18þ S L The Reynolds number (Re) in Eqs. (17) and (18) were calculated at the minimum cross section area, perpendicular to the flow. According to the continuity equation, the area of minimum cross section has maximum flow velocity. For finned-tube configurations, the area of minimum cross section is the thin space between the two fins. Hence, Eq. (19), reported by Zukauskas [4], was used to calculate the maximum velocity. v max ¼ S Tv S T D Friction factor (f) for the numerical simulations was calculated as f ¼ DP nqv 2 ð19þ ð20þ Figure 4. Comparison of computational and analytical results for the solid case. (a) Comparison of Nusselt number with Briggs and Young correlation, and (b) comparison of friction factor with Robinson and Briggs correlation.

13 ENHANCED HEAT TRANSFER WITHIN A CONDENSER 745 Table 3. Fin performance ratios and angular location (theta in degrees) of perforations along the fin surface for various perforation cases Cases Perforation location Heat flux, q (Q=m 2 ) Fin q performance ratio (%) (A) Pressure drop, DP (Pa) Fin DP performance ratio (%) (B) Relative q-dp factor (A=B) Solid 3, Perforated 60 to 180 3, Case , Case , Case , Case , Case , Case 6 120, 150 3, Case 7 120, 180 3, Case 8 120, 150, 180 3, Indicates favorable fin performance values. Values of DP in Eq. (20) and Nu values are obtained from a post processing step in Fluent. A reference temperature of 300 K was used for calculating Nu. Comparison of analytical and computational results of Nu and f is shown in Figure 4. Computational results for Nu number were within 15.7% of the analytical correlation (Figure 4a). From Figure 4b, it is observed that velocity changes do not alter the general decreasing trend of the friction factor, and the difference between analytical and numerical results remained nearly the same for all velocity values. A 43.7% difference for a velocity of 5 m=s was observed between numerical and analytical results. Though the results for f are not close to the analytical results, they are consistent with the data reported by Mon et al. [12]. They showed that the numerical results for Nu and f were within 25% and 40%, respectively, with those obtained by analytical results. Other perforation combinations, as shown in Table 3, were also simulated 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) to assess the variation of velocity and temperature distributions across the domain. The velocity and temperature distribution on the surface of solid fins were then compared with those of perforated fins (perforations at 60 to 180 with 30 interval). Other cases with single, double, and triple perforations, as described in Table 3, were simulated to assess the effect of perforation location on velocity and temperature profiles. Percentage reductions in perforated fin surface area for heat transfer calculation for various perforation combinations are shown in Table 4. The case of solid fins was used as the baseline case to compare subsequent cases involving various combinations of perforations Comparison of solid and perforated cases. Velocity vectors and temperature of the solid finned-tubes for the free stream velocity of 3 m=s are shown

14 746 R. K. BANERJEE ET AL. Table 4. Fin h performance ratios for various perforation cases Cases Perforation location Reduction in area of fins (%) Heat transfer coefficient, h (W=m 2 -K) Fin heat transfer performance ratio (%) Solid 76.4 Perforated 60 to Case Case Case Case Case Case 6 120, Case 7 120, Case 8 120, 150, Indicates favorable fin performance values. in Figure 5. It was observed that free stream air flow approaching the finned-tube array 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, being inversely proportional to velocity, was the maximum in the domain. Pressure started decreasing as the flow advanced, creating favorable flow conditions [dp=dx < 0] in the upstream region of all fins. Maximum velocity was observed at about h ¼ 90. Thereafter, velocity started decreasing and pressure started increasing, creating a positive pressure gradient [dp=dx > 0]. This resulted in flow separation from the fin wall, creating wake areas. Formation of a recirculation zone was observed in the downstream regions of the first, second, and third finned-tube rows followed by a large wake area at the downstream region of the fourth finned-tube row. Fluid particles in this region lost energy in overcoming the shear forces in the boundary layer. The remaining energy was insufficient to resist increasing pressure forces, resulting in a reversal of fluid particles. Because of the slower air flow, high temperatures persisted in wake areas. Thus, the upstream half of the region experienced higher heat removal than the downstream region. Subsequent to the solid fins, perforations were introduced in the downstream region with an attempt to improve the flow characteristics and increase the heat transfer efficiency. Four and one-half perforations were created on a symmetric model 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 free stream velocity of 3 m=s, using velocity vectors (Figure 5a for solid fin and Figure 5b for perforated fins) and temperature contours. Temperature contours of solid fins (Figure 5c) and perforated fins (Figure 5d) showed a reduction in size of the high temperature zones in the downstream region of the tubes. The average temperature of the fins and tube walls in the perforated case was 4 K less than the solid case. In general, a significant reduction in temperature was observed in the downstream region of the fourth row of finned-tubes. Comparison of velocity contours showed that perforations altered the velocity gradients in the domain. Recirculation zones in the downstream region of the first and subsequent finned-tubes were disrupted by the perforations. As a result, these recirculation zones shrank in size.

15 ENHANCED HEAT TRANSFER WITHIN A CONDENSER 747 Figure 5. Comparison of solid and perforated fins for free stream velocity of 3 m=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). 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 h ranging from 0 to 180 is plotted in Figure 6 for solid and perforated fins. As shown in Figure 6a, the first row of finned-tubes was directly exposed to free stream air flow and was generally unaffected by perforations. However, the value of Nu number for the perforated finned-tubes was observed to increase gradually as the flow advanced from fin-1 to fin-4. As discussed earlier, the flow over the solid fin was detached from the wall at about 90, resulting in a recirculation zone in the downstream region. Nu number at h ¼ 90 (near the point of detachment) was observed to have almost the same value for perforated and solid fins (Figures 6a and 6b). As angular locations from 120 to 180 were in the recirculation areas, perforations at these locations improved mixing due to enhanced turbulence. Thus, Nu numbers were observed to increase 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 influenced by the increased mixing and turbulence of air in the upstream region. Hence,

16 748 R. K. BANERJEE ET AL. 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 3 m=s; (b) fin-2; (c) fin-3; and (d) fin-4, the last finned-tube in the direction of free stream. 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 downstream finned-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-tube was 6.7% and 9.5%, respectively. The percentage increase of Nu number for perforated fins was defined with respect to the solid fins as [(Nu perforated Nu solid ) 100=Nu solid ]. An increase in Nu for the entire array of finned-tubes was observed to be 7.07%. Žukauskas [4] reported that hydrodynamic forces arising due to the turbulent fluctuations 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 the design of finned-tubes. Perforations, which increased h and the Nu number, also increased the pressure drop by about 11.87% [(DP perforated DP solid ) 100=DP solid ]. Thus, for better optimization perforations should be placed only at the locations which result in a minimum increase in DP and the maximum Nu (or h) Performance ratios. Symmetric fin combinations were assessed to find the location of perforation that result in higher h and q, but lower the increase in 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 geometric symmetry, half perforation was created at h ¼ 180 (case 5). Based on the results of the best single perforation location, additional cases with multiple perforations,

17 ENHANCED HEAT TRANSFER WITHIN A CONDENSER (case 6), (case 7) and (case 8), were assessed to obtain a combination that has a better balance between enhanced q and minimal increase in DP. Three fin performance ratios were introduced to calculate a percentage increase in DP, q, and h values for perforated fin cases in relation to the solid fin. Fin DP performance ratio ¼ DP perfo DP solid DP solid 100 ð21aþ Fin q performance ratio ¼ q perfo q solid q solid 100 ð21bþ Fin h performance ratio ¼ h perfo h solid 100 ð21cþ h solid Fin q and DP performance ratios for single and half perforation cases in the semi-circular fin domain with reference to the solid case are shown in Figure 7. It was observed that case 3 (h ¼ 120 ) resulted in the least increase in DP and maximum increase in q values. The results for case 4 (h ¼ 150 )and5(h¼180 ) showed a somewhat lower increase in q when compared to the increase in DP. However, cases 1 (h ¼ 60 ) and 2 (h ¼ 90 ) showed a reverse trend with a maximum increase in DP and the least increase in q values. Thus, perforation at h ¼ 60 and 90 were not beneficial and were of little practical use Relative q-dp factor. The efficiency of perforations was determined to find the optimum case having the least increase in DP with the maximum increase in q. Calculations, as shown in the last column of Table 3, were conducted to find the relative q-dp factor, a dimensionless quantity defined as the ratio between fin q performance ratio and fin DP performance ratio. Figure 7. Plot of fin q- and h- performance ratios for single perforation configurations (cases 1 5).

18 750 R. K. BANERJEE ET AL. fin q performance ratio Relative q DP factor ¼ fin Dp performance ratio ¼ ð½q perfo q solid Š=q solid Þ ð½dp perfo DP solid Š=DP solid Þ ð22þ A higher value of relative q-dp factor implies a combination of maximum increase in q values in conjunction with a minimum increase in DP values. Thus, a relative q-dp factor value greater than unity indicates a better performing fin configuration. Amongst the single perforated cases, perforation at h ¼ 120 (case 3) provided the best result with a 1.70%increase in fin q performance ratio, while an increase in fin DP performance ratio was only 1.39%. Thus, the relative q-dp factor of 1.23 for case 3 was better as compared to cases 4 (0.97) and 5 (0.85). Relative q-dp factor was even lower (0.21) for the perforations at h ¼ 60 (case 1) and h ¼ 90 (case 2). These combinations resulted in a significant increase in DP causing a lower relative q-dp factor. It was evident that perforations placed in the downstream half portion (between h ¼ 90 to 180 ) were more advantageous than in the upstream half portion (between h ¼ 0 to 90 ). Hence, for better relative q-dp factor, it was recommended to have perforations only in the downstream region beyond the point of detachment (h ¼ 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 was less than 1. Results of fin h performance ratio, tabulated in Table 4, also confirm that perforations in the downstream region result in better heat transfer. An increase in all three fin performance ratios (q, h, and DP) and relative q-dp factor for multiple perforation cases are also shown in Tables 3 and 4. Case 8 showed a maximum increase in q (3.99%) performance ratio coupled with a relatively lower increase in DP (3.81%) performance ratio among all the combinations. Since the relative q-dp factor was greater than 1 for case 8 (1.05), it was considered more favorable than the other multiple perforation cases. Cases 6 (relative q-dp factor ¼ 0.78) and 7 (relative q-dp factor ¼ 0.87) can be incorporated if higher heat transfer rates are desired, while an increase in pressure drop is allowable for the structure. However, it must be noted that from the perspective of relative q-dp factor, case 3 (perforation at h ¼ 120 ; relative q-dp factor ¼ 1.23) is better than case 8 (perforations at h ¼ 120, 150, and 180 ; relative q-dp factor ¼ 1.05) Fin Spacing in an A-Frame Structure Four cases of fin spacing were configured, as shown in Figure 3b. Analysis was initiated with case A, the base line case, with evenly spaced fins at a pitch of 3.5 mm. Velocity vectors and pressure contours were plotted to study the flow field in the domain. Pressure drop was measured across all three locations and tabulated in Table 5. It was observed that velocity at the upstream side of the fins increased from the inlet end towards the top end. Cases B and C were configured such that fins were clustered 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 C showed a favorable change with a decrease in DP by 1% (location 2). Case C showed

19 ENHANCED HEAT TRANSFER WITHIN A CONDENSER 751 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 DP A B C D indicates favorable change in DP. that more air flow occurred through the central region of the fin array. Based on this observation, case D with clustered fins at both inlet and top ends and sparsely spaced fins 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 air resistance. Pressure magnitude (Figure 8b) was observed to be reduced on the upstream side of the fin array. Thus, DP across the fins was decreased by 1.9% Figure 8. Comparison of velocity vectors for cases A and D. (a) Velocity vectors and (b) contours of pressure (color figure available online).

20 752 R. K. BANERJEE ET AL. (location 2). This additional reduction in DP, provided by the use of unequal fin spacing along the arms of the A-frame, can facilitate the use of multiple perforations for yielding higher heat transfer. 4. DISCUSSION The h and DP are important parameters in the design of an annular finned-tube array. Heat transfer enhancement with perforations on the annular fin surface was studied numerically using various combinations of perforations. These arrays, commonly used in air cooled steam condensers (ACSC), are known for high pressure losses. The fin spacing along the arms of the A-frame was changed to reduce the DP across the fin bundle. Fin spacing is one of the important geometric factors influencing fluid flow and heat transfer. Unequal spacing reduced the pressure loss in the A-frame structure, but its effects on heat transfer in a perforated annular finned-tube array are unknown. Perforated finned-tube array with unequal fin spacing needs to be 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 provide more aerodynamic properties than the circular fins. Perforated finned-tube array with an elliptical cross section can be studied in the future to evaluate h and DP characteristics. Heat transfer and pressure drop in a three-dimensional A-frame structure can be evaluated using the optimum number of perforations on annular fins and fin spacing along the arms of the A-frame. 5. CONCLUSION An annular finned-tube array with perforations was studied numerically for assessing the enhancement of heat transfer while minimizing an increase in pressure drop across the domain. To calculate the efficiency of the location of a perforation, a relative q-dp factor was defined as the ratio of increase in fin q performance ratio and 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, particularly for perforation at h ¼ 120. Multiple perforations at h ¼ 120, 150, and 180 also showed a favorable relative q-dp factor. The number of perforations was limited by the allowable DP in the system. Unequal spacing along the A-frame structure of ACSCs could decrease the pressure drop across the finned-tube bundle. Clustered spacing at the inlet and top ends and large spacing at the center assisted in reducing the upstream pressure of the air and DP in the system. Thus, penalty in DP for a perforated fin can possibly be 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 Transfer Eng., vol. 1, pp , D. E. Briggs and E. H. Young, Convection Heat Transfer and Pressure Drop of Air Flowing across Triangular Pitch Banks of Finned Tubes, Chem. Eng. Prog. Symp. Ser., vol. 59, pp. 1 10, 1963.

21 ENHANCED HEAT TRANSFER WITHIN A CONDENSER K. K. Robinson and D. E. Briggs, Pressure Drop of Air Flowing across Triangular Pitch Banks of Finned Tubes, Chem. Eng. Prog. Symp. Ser., vol. 62, pp , A. Zhukauskas, High-Performance Single-Phase Heat Exchangers, chaps , pp , Hemisphere Publishing, New York, A. E. Bergles, R. L. Webb, and G. H. Junkan, Energy Conservation via Heat Transfer Enhancement, Midwest Energy Conf., vol. 4, pp , 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 , W. Q. Tao, Z. G. Qu, and Y. L. He, Experimental and 3-D Numerical Study of Air Side Heat Transfer and Pressure Drop of Slotted Fin Surface, Int. Conf. on Enhanced, Compact and Ultra-Compact Heat Exchangers: Sci. Eng. and Tech., Whistler, British Columbia, Canada, paper 15, Y. P. Cheng, Z. G. Qu, and W. Q. Tao, Y. L. He, Numerical Design of Efficient Slotted Fin Surface based on the Field Synergy Principle, Numer. Heat Transfer A, vol. 45, pp , B. Sahin and A. Demir, Thermal Performance Analysis and Optimum Design Parameters of Heat Exchanger Having Perforated Pin Fins, Energy Conversion and Management, vol. 49, pp , M. R. Shaeri and M. Yaghoubi, Numerical Analysis of Turbulent Convection Heat Transfer from an Array of Perforated Fins, Int. J. of Heat and Fluid Flow, vol. 30, pp , 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 , M. S. Mon, and U. Gross, Numerical Study of Fin-Spacing Effects in Annular-Finned Tube Heat Exchangers, Int. J. of Heat and Mass Transfer, vol. 47, pp , D. G. Kroger, Fan Performance in Air-Cooled Steam Condensers, Heat Recovery Systems and CHP, vol. 14, pp , C. J. Meyer and D. G. Kroeger, Plenum Chamber Flow Losses in Forced Draught Air-Cooled Heat Exchangers, Appl. Therm. Eng., vol. 18, pp , C. J. Meyer and D. G. Kroeger, Air Cooled Heat Exchanger Inlet Flow Losses, Appl. Therm. Eng., vol. 21, pp , FLUENT Incorporated, FLUENT 6.3 User s Guide, Fluent Inc., Lebanon, NH, USA, L. A. O. Rocha, F. E. M. Saboya, and J. V. C. Vargas, A Comparative Study of Elliptical and Circular Sections in One- and Two-Row Tubes and Plate Fin Heat Exchangers, Int. J. Heat and Fluid Flow, vol. 18, pp , 1997.