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Effect of geometric factors on performance of a sodium to air heat exchanger in a fast breeder reactor
Annals of Nuclear Energy 75 (2015) 428–437
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Effect of geometric factors on performance of a sodium to air heat exchanger in a fast breeder reactor K. Kannan a,⇑, V. Vinod b, G. Padmakumar b, R. Rudramoorthy a, K.K. Rajan b a b
Department of Production Engineering, PSG College of Technology, Coimbatore 641 004, India Fast Reactor Technology Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India
a r t i c l e
i n f o
Article history: Received 21 April 2014 Received in revised form 14 August 2014 Accepted 14 August 2014
Keywords: Sodium to air heat exchanger Decay heat removal Sodium cooled fast breeder reactor Finned tube cross flow heat exchanger Geometric factors Numerical simulation
a b s t r a c t Prototype fast breeder reactor (PFBR) has a safety grade decay heat removal system whose performance depends on the effective functioning of natural convection heat exchangers called sodium to air heat exchangers. The development of Representative Elementary Volume (REV) model for the sodium to air heat exchanger is necessary to envisage its design and to study the effect of various factors for continuous improvement in design. With a Representative Elementary Volume, the hydrodynamic and heat transfer characteristics of the heat exchanger was studied and the results agree well with experimental data. The effect of longitudinal pitch and transverse pitch on the heat exchanger performance has been studied and an improvement of 22% in heat transfer is predicted. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction A sodium cooled, pool type, prototype fast breeder reactor (PFBR) has a safety grade decay heat removal (SGDHR) system, which is a passive circuit and is used to remove the decay heat from the reactor core after its shutdown. SGDHR system is a completely passive system except dampers on the airside. SGDHR system of a 500 MWe PFBR consists of 4 independent loops of each 8 MW heat removal capacity. Each SGDHR loop consists of sodium-sodium heat exchanger (DHX) dipped in hot pool, sodium to air heat exchanger placed outside the reactor containment building at an higher elevation, an expansion tank, associated piping, air dampers and a stack. Sodium air heat exchanger placed outside the reactor containment, is a natural convection type heat exchanger. The current interest is to enhance its performance by improving its effectiveness by which a reduction in heat transfer area can be achieved. The complexity of cross flow heat exchangers stems from their geometrical configuration, the physical phenomena present in the transfer of heat, and the large number of variables involved in their operation. As a consequence of such complexity, no analytical solutions entirely based on first-principles approach are available; ⇑ Corresponding author. Tel.: +91 94433 75460. E-mail addresses: [email protected] (K. Kannan), [email protected] (V. Vinod), [email protected] (G. Padmakumar), [email protected] (R. Rudramoorthy), [email protected] (K.K. Rajan). http://dx.doi.org/10.1016/j.anucene.2014.08.029 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.
most calculations are based on empirical information from the manufacturers of these equipments and, presently, the vast majority of the analyses for predicting their behavior include assumptions and conditions that are not consistent with the phenomena occurring in them under actual states of operation. The shortcomings in the current approach thus lead, in many cases, to unsatisfactory predictions of the heat transfer with errors that can be sometimes of the order of 25–30% or even higher. Since the heat exchanger performance is very often a key factor in the overall thermal system design, constant improvements in their modeling and simulation are definitely needed to increase the accuracy of their predictions and, consequently, to improve the reliability and efficiency of thermal systems for the specific application. Yang et al. (2014) reviewed the CFD’s effectiveness in prediction of heat transfer in a shell and tube heat exchanger when the four different modeling methods called unit model, periodic model, porous model and whole model are applied. Mahmood et al. (2012) reviewed CFD applications in various heat exchangers design with the collection of journals published from year 1986 to 2011. The most of the studies are related to plate heat exchangers and new types of heat exchangers. The available literatures have been categorized into four namely (i) flow maldistribution analysis (ii) pressure drop analysis (iii) Thermal analysis (iv) design optimization studies. Authors have concluded that easily accessible general purpose CFD commercial software can fulfill the requirements of CFD analysis of various heat exchangers with
429
K. Kannan et al. / Annals of Nuclear Energy 75 (2015) 428–437 Table 2 Sodium temperature in different pipes.
Fig. 1. Skeleton model of sodium to air heat exchanger.
Fig. 2. One tube bundle with REV.
deviation up to 36% in some exceptional cases when compared to the experimental studies. Yongqing et al. (2011) modeled half of the shell side of a new type of shell and tube heat exchanger for analyzing the effect of tube support structure over shell side flow characteristics and heat transfer characteristics. Velocity distribution in shell side along with convection heat transfer coefficient values for 5 flow fluxes where equivalent Reynolds number was less than 15,000 in shell-side of H-shape heat exchanger has been reported. Mochizuki and Takano (2009) derived the empirical correlations applicable to the design of commercial scale sodium air heat exchangers from the experiments conducted in three facilities. Authors have compared the heat transfer coefficients with earlier correlations and found that the agreement was good.
Pipes
Temperature (K)
Pipes
Temperature (K)
1 2 3 4 5 6
603.7 597.5 594.9 646.4 648.0 648.9
7 8 9 10 11 12
699.2 697.7 695.8 742.8 745.0 747.1
Mohammadi et al. (2009) divided the shell side of E type shell and tube heat exchanger into 6 zones for the analysis of the effect of baffle orientation over flow and heat transfer characteristics. A shell side gain factor and performance factor has been introduced to analyze and compare the different cases when the shell side fluids were changed. Zhang et al. (2009a,b) has reported the shortcomings of modeling and analyzing shell side flow and heat transfer characteristics with porous medium and distributed resistance concept with a detailed literature survey support. Sunden (2007) reviewed CFD’s effectiveness for analysis of single phase flows. The review starts with generalized form of governing equations, the basics of finite volume method, procedure for solution of the momentum equations, available turbulence models and continues with useful notes about CFD’s effectiveness like Nusselt number predictions in turbulence region were 50% more than experimental one in certain cases which demands the careful application of CFD in a given application for reduced error percentage. Sahin et al. (2007) considered two fins with half fin thickness including flow path for analysis of fin inclination angle (0–30°) influence over a commercial fin and tube heat exchanger performance in laminar region. When the inclination was increased from 0° to 30°, it was found out that the increase in inclination angle decreased the fin spacing which has resulted in increase in velocity and the rate of heat transfer. The net increase in total heat transfer was 105% maximum, at 30° inclination. Dirkse et al. (2006) created CFD model for a natural convection shell and tube heat exchanger with baffles. The feature of complex geometry had been simplified considerably resulting in an almost two dimensional mesh with only 30,000 quadrilateral mesh cells. Mon and Gross (2004) modeled a flow domain with half fin and half air path having three and five row of tubes and analyzed the effect of fin spacing on hydrodynamic and thermal characteristics of annular finned tube heat exchangers with the aid of FLUENT. The authors found good agreement in heat transfer results whereas the pressure drop results were found to exceed by more than 50%. It is evident from the literature that the hydrodynamic and heat transfer characteristics are expected to change whenever a change in pitch, fin spacing, etc. is implemented. It necessitates the numerical flow visualization in conjugate heat transfer condition of each configuration of heat exchanger which helps to further improve its design. Most of the work reported is in the field of new types of heat exchangers with simplified flow domain reasonably. It is also clear that the domain with more number of fins and bundles in a
Table 1 Geometric dimensions of REV. Sl. No.
Geometry of Representative Elementary Volume
Dimensions (mm)
Sl. No.
Geometry of Representative Elementary Volume
Dimensions (mm)
1 2 3 4 5 6
Length of shell side Breadth of the shell side Height of the shell side Tube diameter Thickness of each fin Diameter of the fin
159 15.24 2384.5 38.1 1.22 63.1
7 8 9 10
Fin pitch Height of the fin Number of fins per tube Number of rows
5.08 12.5 3 12 (each row having one and half pipes)
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K. Kannan et al. / Annals of Nuclear Energy 75 (2015) 428–437
(a)
(b)
Fig. 3. REV indicating (a) boundary conditions (b) longitudinal and transverse pitch.
Table 3 Mesh independence data. Case
Mesh size
Temperature rise error %
1 2
76,65,569 1,03,01,348 (34%) 1,78,68,875 (133.10%)
+10.6 +9.6
2.2 2.4
37 55
+10.5
2.2
100
3
Total heat flux error %
Computational time in hours
Fig. 5. Density contour.
Fig. 4. The tubes numbered from bottom of air entry.
heat exchanger will represent the actual conditions in a better manner. Hence, the objective of this study is that (i) visualize hydrodynamic characteristics of shell side air in a Representative Elementary Volume (REV) with four bundles of staggered tubes with three fins (ii) study the thermal characteristics of a shell and tube heat exchanger when longitudinal pitch and transverse pitch values are changed numerically.
2. Numerical simulation The sodium air heat exchanger of current interest is as shown in Fig. 1. The domain is with overall size of 1.09 m 1.72 m 3.38 m
and includes number of tube supports, longitudinal baffles and transverse baffles. The analysis of the entire domain with both side fluids is numerically expensive. Hence a Representative Elementary Volume (in rectangle shape) as shown in Fig. 2 is selected for the study purpose. The data about geometry of REV is as given in Table 1.
2.1. Governing equations The numerical simulations have been conducted with ANSYS FLUENT research version. Three dimensional Navier Stokes equations along with Energy equation and RNG k-e turbulence model without any source terms have been solved in the flow domain. The sodium flow and the air flow through sodium to air heat exchanger are generated by buoyancy driven forces. Since full system is not in the consideration of this study, the mass flow rate of air at the inlet to REV has been calculated by dividing ratio of the whole heat exchanger fins to REV fins from the air mass flow rate at full load condition. The fluid domain for analysis is REV from the heat exchanger.
K. Kannan et al. / Annals of Nuclear Energy 75 (2015) 428–437
431
Fig. 6. Pressure contour. Fig. 8. Temperature contour.
zero, i.e., no convective heat flux across the symmetry plane occurs and buoyancy and radiation effects have been neglected. Pressure velocity coupling was by SIMPLE algorithm. The iterations were initiated with 1st order discretisation schemes and after 500 iterations; the scheme was upgraded for 2nd order schemes. The domain has been discretised with 100,00,000 tetrahedral control volumes approximately. Sufficient care has been taken to retain fine mesh around each tube where the steep gradient is anticipated. The Reynolds number based on minimum flow area is in the range of 1880 to 5200. Pipes are named from bottom to top in each row as in Fig. 4. 2.2. Mesh independence
Fig. 7. Velocity contour.
The fins have been modeled as solid in flow domain along with tube outer surface. The non dimensional distance between first cell and wall, y+ has been maintained at 2.26 on an average. The boundary condition at the fin-tube surface is no slip for fluid flow and constant wall temperature for tube inner surface. In heat exchanger, the fluid has to travel along inlet nozzle, transition duct in the inlet side and between the tubes before it reaches REV. When the air enters, it enters with a velocity pattern, not with uniform velocity. It results in turbulence intensity variation from 0% to 6.3%. Hence, the average 3% turbulence intensity is specified. Outlet boundary condition is set as pressure outlet condition with atmospheric pressure value. During air travel from the inlet to outlet, significant change in density is experienced. That is implemented through ideal gas law for density calculation. The tube side fluid effect is implemented through experimental temperatures measured, assigned to tube inner walls as given in Table 2 (Vinod et al. (2013)). The tube material is stainless steel 316 type. At the symmetry planes as shown in Fig. 3, heat flux is assumed zero. The normal velocity component at the symmetry plane is
The Table 3 indicates the results of mesh independence study. The bench mark is experimental data on heat exchanger heat flux and the temperature rise of air across the heat exchanger. When finer mesh is implemented,(The number of control volumes in the flow domain were increased from 1,03,01,348 to 1,78,68,875), appreciable change in heat transfer characteristics is not experienced but computational time is doubled approximately. Hence, it is decided to continue with 1 crore mesh for the parametric study.
Fig. 9. How the velocity vectors figures are extracted.
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K. Kannan et al. / Annals of Nuclear Energy 75 (2015) 428–437
Fig. 10. Velocity vector in tube back side.
K. Kannan et al. / Annals of Nuclear Energy 75 (2015) 428–437
Fig. 11. Position angle around a tube fin.
3. Results of Representative Elementary Volume analysis 3.1. Flow characteristics The global pattern of flow variable changes in the flow domain in a z plane is as shown in Figs. 5–8. The air behavior in shell side is
433
important to maximize the effectiveness of the heat exchanger. As per design, every tube has to receive air uniformly which is difficult to achieve in practical. It is evident from Figs. 5–8. Moreover the global pattern of flow variables helps to understand the local behavior of air in a better way. For example, when the air crosses the first bundle and enters the second bundle, the air velocity is expected to reach uniform at every point but the jet effect between tubes is experienced. That causes similar pattern of air recirculation behind the tubes in successive bundles, which is not favorable from heat transfer perspective. Careful analysis of air in the domain reveals that the adverse phenomena are major in back side of tubes whereas in the remaining zones, the air flows without major change in its variables. Fig. 9 shows how the velocity contours are extracted from the backside of each tube which is useful to explore further about the adverse phenomena like horse shoe vortex formation behind the tube, jet formation in between tubes, etc. The existence of adverse phenomena is evident from Fig. 10. The tubes 1, 2, 4, 5, 7, 8, 10, 11 are directly exposed to fluid whereas the remaining tubes are in the shadow region of 1, 4, 7, 10 irrespective of gap between tube bundles of 345 mm. The velocity of the air has varied from 0.065 m/s in tube back side to 7.16 m/s in space between tubes. The maximum velocity of air is experienced in passage
Fig. 12. Heat transfer coefficient vs. points at angle around a tube.
Fig. 13. Average heat transfer coefficient vs. No. of tube.
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K. Kannan et al. / Annals of Nuclear Energy 75 (2015) 428–437
Fig. 14. Average Nusselt number vs. Number of tube.
between adjacent tubes. In overall, double horse vortices with different magnitudes are present behind directly exposed tubes (first two tubes in every bundle) whereas the remaining tubes are experiencing reverse flow alone.
Table 4 Longitudinal and transverse pitch variation data.
3.2. Thermal characteristics
Cases
Longitudinal and transverse pitch, SL and ST
Cases
Longitudinal and transverse pitch, SL and ST
1 2 3 4
50 mm 50 mm 65 mm 70 mm
5 6 7 8
70 mm 75 mm 80 mm 75 mm
41 mm 53 mm 55 mm 41 mm
55 mm 53 mm 41 mm 55 mm
The local convection heat transfer coefficient, h of the air at various locations around a tube fin as shown in Fig. 11 is collected. The h data is collected from control volumes on middle fin outer surface (tip area) over each tube. In each tube, the front stagnation point is shown as zero degree in flow path. The location for study is selected at every 45 degree in clock wise direction. The lower heat transfer coefficient values at 180 degree angle confirm the ill effect of horse vortex formation behind the tubes. The tube location in tube bundle dictates maximum heat transfer coefficient value position which is evident from Fig. 12. The position at which maximum heat transfer coefficient value is experienced changes from tube to tube due to associated flow physics complexity. It ensures that the pattern of boundary layer
Fig. 15. Variation in temperature rise and total heat transfer.
K. Kannan et al. / Annals of Nuclear Energy 75 (2015) 428–437
435
Fig. 16. H vs. longitudinal pitch for representative tubes.
Fig. 17. F vs. longitudinal pitch for representative tubes.
formation and separation around each tube is entirely different from each other. Representative Elementary Volume has four bundles. Each bundle has 3 full tubes and 2 half tubes. In air flow path, the bundles and full tubes are numbered in ascending order. Figs. 13 and 14 shows average local convection heat transfer coefficient and average local Nusselt number variation along the air flow path. As maximum temperature difference between fluids exist in the air entrance area, maximum values of average local convection heat transfer coefficient and average local Nusselt number are experienced in first bundle tubes. That is compared to the remaining bundles; higher amount of heat transfer is in first bundle. In first and fourth bundle, the maximum local heat transfer coefficient value is associated with 2nd tube followed by 1st and 3rd tube whereas in the remaining bundles the local heat transfer coefficient values descend from tube 1 to 3.
3.3. Effect of longitudinal pitch and transverse pitch on thermal characteristics The effect of longitudinal and transverse pitch variation on the heat exchanger performance is studied. The variation in pitch is done as given in Table 4. Longitudinal pitch is 70 mm and transverse pitch is 53 mm in original design. The mass flow rate of air at full load condition is the inlet boundary condition for the entire study. The pressure loss when both pitches are reduced increases approximately 4 times whereas when both the pitches are increased decreases approximately half and according to the case, the pressure variation is experienced. When the pitch value is increased, the total heat transfer across the REV with respect to original has reduced. When the pitch value is reduced both in longitudinal as well as in transverse direction, the REV performance with respect to original has started to increase as shown in
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K. Kannan et al. / Annals of Nuclear Energy 75 (2015) 428–437
Fig. 18. H vs. transverse pitch for representative tubes.
Fig. 19. F vs. transverse pitch for representative tubes.
Fig. 15 but at the same time the pressure drop across the heat exchanger also increases. When the longitudinal pitch is varied, the details of local average convection heat transfer coefficient and local average skin friction coefficient along the flow path is plotted for better understanding as shown in Figs. 16 and 17. When longitudinal pitch, SL is increased, the decrease in local maximum velocity is experienced from 7.16 m/s to 6.84 m/s. When longitudinal pitch, SL is decreased, the increase in local maximum velocity from 7.16 m/s to 8.51 m/s is experienced. It reflects correspondingly in the overall heat transfer coefficient. When the transverse pitch is controlled, the details of local average convection heat transfer coefficient and local average skin friction coefficient along the flow path is plotted for better
understanding as shown in Figs. 18 and 19. When transverse pitch, ST is increased, the decrease in local maximum velocity from 7.16 m/s to 7.1 m/s is experienced. When transverse pitch, ST is decreased, the increase in local maximum velocity from 7.16 m/s to 11.08 m/s is experienced. It reflects correspondingly in the overall heat transfer coefficient. When both longitudinal pitch, SL and transverse pitch, ST are increased, the decrease in local maximum velocity from 7.16 m/s to 6.84 m/s is experienced. When both longitudinal pitch, SL and transverse pitch, ST are decreased, the increase in local maximum velocity from 7.16 m/ s to 12.84 m/s is experienced. When both pitches are varied, the mixed effect is experienced as shown in Fig. 20. Still the transverse pitch effect is dominant compared to longitudinal pitch effect.
K. Kannan et al. / Annals of Nuclear Energy 75 (2015) 428–437
437
Fig. 20. Effect of longitudinal pitch and transverse pitch on local heat transfer coefficient.
4. Conclusions
References
The sodium to air heat exchanger performance is a key factor in decay heat disposal of prototype fast breeder reactors. The constant improvements in their modeling and simulation are necessary to improve the reliability and efficiency of it at different conditions due to the limitations in experiments. As the analysis of a heat exchanger in actual size with both side fluid flow is numerically expensive, a Representative Elementary Volume (REV) from 2 MW sodium to air heat exchanger has been extracted and the shell side flow in REV with heat transfer has been simulated successfully. The difference in temperature rise of air across the heat exchanger between experimental and numerical is within 5%. The air velocity around the tubes has varied from 0.065 m/s to 7.16 m/s. The velocity change depends on tube location in particular bundle and bundle location. The velocity contours from different planes of REV confirm the basics. The negative velocity is experienced behind the tubes whereas the maximum velocity is experienced in tube sides. The local heat transfer coefficient around the tubes changes from 0.689 W/m2 K to 91.01 W/m2 K but the change in the local heat transfer coefficient is based on the flow physics complexity, fluid temperature, tube location in particular bundle and bundle location. The temperature contour from different planes of REV confirms the same. The study has also predicted similar pattern of air recirculation behind the tubes in successive bundles, which is not favorable from heat transfer perspective. The decrease in longitudinal pitch and transverse pitch has resulted in an increase of 22% maximum in heat transfer, at the cost of increased pressure drop in shell side. With REV model, further the study can be extended with parameters like gap between bundles, fin pitch, etc.
Dirkse, H.M., Wilko, K.P.V.L., Walle, T.V.D., Sebastian, L.S., Bot, B.P.A.G., 2006. A computational fluid dynamics model for designing heat exchangers based on natural convection. Bio Syst. Eng. 94, 443–452. Mahmood, M., Bhutta, A., Hayat, N., Bashir, M.H., Khan, A.R., Ahmad, K.N., Khan, S., 2012. CFD applications in various heat exchangers design: A review. Appl. Therm. Eng. 32, 1–12. Mochizuki, H., Takano, M., 2009. Heat transfer in heat exchangers of sodium cooled fast reactor systems. Nucl. Eng. Des. 239, 295–307. Mohammadi, K., Heidemann, W., Steinhagen, H.M., 2009. Numerical investigation of the effect of baffle orientation on heat transfer and pressure drop in a shell and tube heat exchanger with leakage flows. Heat Transfer Eng. 30, 1123–1135. Mon, M.S., Gross, U., 2004. Numerical study of fin-spacing effects in annular-finned tube heat exchangers. Int. J. Heat Mass Transf. 47, 1953–1964. Sahin, H.M., Dal, A.R., Baysal, E., 2007. 3-D Numerical study on the correlation between variable inclined fin angles and thermal behavior in plate fin-tube heat exchanger. Appl. Therm. Eng. 27, 1806–1816. Sunden, B., 2007. Computational fluid dynamics in research and design of heat exchangers. Heat Transfer Eng. 28, 898–910. Vinod, V., Pathak, S.P., Paunikar, V.D., Suresh Kumar, V.A., Noushad, I.B., Rajan, K.K., 2013. Experimental evaluation of sodium to air heat exchanger performance. Ann. Nucl. Energy 58, 6–11. Yang, J., Maa, L., Bock, J., Jacobi, A.M., Liu, W., 2014. A comparison of four numerical modeling approaches for enhanced shell-and-tube heat exchangers with experimental validation. Appl. Therm. Eng. 65, 369–383. Yongqing, W., Xin, G., Ke, W., Qiwu, D., 2011. Numerical investigation of shell-side characteristics of H-shape baffle heat exchanger. Procedia Eng. 18, 53–58. Zhang, J.F., He, Y.L., Tao, W.Q., 2009a. 3D numerical simulation on shell-and-tube heat exchangers with middle-overlapped helical baffles and continuous baffles – Part I: Numerical model and results of whole heat exchanger with middleoverlapped helical baffles. Int. J. Heat Mass Transf. 52, 5371–5380. Zhang, J.F., He, Y.L., Tao, W.Q., 2009b. 3D numerical simulation on shell-and-tube heat exchangers with middle-overlapped helical baffles and continuous baffles – Part II: Simulation results of periodic model and comparison between continuous and non continuous helical baffles. Int. J. Heat Mass Transf. 52, 5381–5389.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Effect of geometric factors on performance of a sodium to air heat exchanger in a fast breeder reactor K. Kannan a,⇑, V. Vinod b, G. Padmakumar b, R. Rudramoorthy a, K.K. Rajan b a b
Department of Production Engineering, PSG College of Technology, Coimbatore 641 004, India Fast Reactor Technology Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India
a r t i c l e
i n f o
Article history: Received 21 April 2014 Received in revised form 14 August 2014 Accepted 14 August 2014
Keywords: Sodium to air heat exchanger Decay heat removal Sodium cooled fast breeder reactor Finned tube cross flow heat exchanger Geometric factors Numerical simulation
a b s t r a c t Prototype fast breeder reactor (PFBR) has a safety grade decay heat removal system whose performance depends on the effective functioning of natural convection heat exchangers called sodium to air heat exchangers. The development of Representative Elementary Volume (REV) model for the sodium to air heat exchanger is necessary to envisage its design and to study the effect of various factors for continuous improvement in design. With a Representative Elementary Volume, the hydrodynamic and heat transfer characteristics of the heat exchanger was studied and the results agree well with experimental data. The effect of longitudinal pitch and transverse pitch on the heat exchanger performance has been studied and an improvement of 22% in heat transfer is predicted. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction A sodium cooled, pool type, prototype fast breeder reactor (PFBR) has a safety grade decay heat removal (SGDHR) system, which is a passive circuit and is used to remove the decay heat from the reactor core after its shutdown. SGDHR system is a completely passive system except dampers on the airside. SGDHR system of a 500 MWe PFBR consists of 4 independent loops of each 8 MW heat removal capacity. Each SGDHR loop consists of sodium-sodium heat exchanger (DHX) dipped in hot pool, sodium to air heat exchanger placed outside the reactor containment building at an higher elevation, an expansion tank, associated piping, air dampers and a stack. Sodium air heat exchanger placed outside the reactor containment, is a natural convection type heat exchanger. The current interest is to enhance its performance by improving its effectiveness by which a reduction in heat transfer area can be achieved. The complexity of cross flow heat exchangers stems from their geometrical configuration, the physical phenomena present in the transfer of heat, and the large number of variables involved in their operation. As a consequence of such complexity, no analytical solutions entirely based on first-principles approach are available; ⇑ Corresponding author. Tel.: +91 94433 75460. E-mail addresses: [email protected] (K. Kannan), [email protected] (V. Vinod), [email protected] (G. Padmakumar), [email protected] (R. Rudramoorthy), [email protected] (K.K. Rajan). http://dx.doi.org/10.1016/j.anucene.2014.08.029 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.
most calculations are based on empirical information from the manufacturers of these equipments and, presently, the vast majority of the analyses for predicting their behavior include assumptions and conditions that are not consistent with the phenomena occurring in them under actual states of operation. The shortcomings in the current approach thus lead, in many cases, to unsatisfactory predictions of the heat transfer with errors that can be sometimes of the order of 25–30% or even higher. Since the heat exchanger performance is very often a key factor in the overall thermal system design, constant improvements in their modeling and simulation are definitely needed to increase the accuracy of their predictions and, consequently, to improve the reliability and efficiency of thermal systems for the specific application. Yang et al. (2014) reviewed the CFD’s effectiveness in prediction of heat transfer in a shell and tube heat exchanger when the four different modeling methods called unit model, periodic model, porous model and whole model are applied. Mahmood et al. (2012) reviewed CFD applications in various heat exchangers design with the collection of journals published from year 1986 to 2011. The most of the studies are related to plate heat exchangers and new types of heat exchangers. The available literatures have been categorized into four namely (i) flow maldistribution analysis (ii) pressure drop analysis (iii) Thermal analysis (iv) design optimization studies. Authors have concluded that easily accessible general purpose CFD commercial software can fulfill the requirements of CFD analysis of various heat exchangers with
429
K. Kannan et al. / Annals of Nuclear Energy 75 (2015) 428–437 Table 2 Sodium temperature in different pipes.
Fig. 1. Skeleton model of sodium to air heat exchanger.
Fig. 2. One tube bundle with REV.
deviation up to 36% in some exceptional cases when compared to the experimental studies. Yongqing et al. (2011) modeled half of the shell side of a new type of shell and tube heat exchanger for analyzing the effect of tube support structure over shell side flow characteristics and heat transfer characteristics. Velocity distribution in shell side along with convection heat transfer coefficient values for 5 flow fluxes where equivalent Reynolds number was less than 15,000 in shell-side of H-shape heat exchanger has been reported. Mochizuki and Takano (2009) derived the empirical correlations applicable to the design of commercial scale sodium air heat exchangers from the experiments conducted in three facilities. Authors have compared the heat transfer coefficients with earlier correlations and found that the agreement was good.
Pipes
Temperature (K)
Pipes
Temperature (K)
1 2 3 4 5 6
603.7 597.5 594.9 646.4 648.0 648.9
7 8 9 10 11 12
699.2 697.7 695.8 742.8 745.0 747.1
Mohammadi et al. (2009) divided the shell side of E type shell and tube heat exchanger into 6 zones for the analysis of the effect of baffle orientation over flow and heat transfer characteristics. A shell side gain factor and performance factor has been introduced to analyze and compare the different cases when the shell side fluids were changed. Zhang et al. (2009a,b) has reported the shortcomings of modeling and analyzing shell side flow and heat transfer characteristics with porous medium and distributed resistance concept with a detailed literature survey support. Sunden (2007) reviewed CFD’s effectiveness for analysis of single phase flows. The review starts with generalized form of governing equations, the basics of finite volume method, procedure for solution of the momentum equations, available turbulence models and continues with useful notes about CFD’s effectiveness like Nusselt number predictions in turbulence region were 50% more than experimental one in certain cases which demands the careful application of CFD in a given application for reduced error percentage. Sahin et al. (2007) considered two fins with half fin thickness including flow path for analysis of fin inclination angle (0–30°) influence over a commercial fin and tube heat exchanger performance in laminar region. When the inclination was increased from 0° to 30°, it was found out that the increase in inclination angle decreased the fin spacing which has resulted in increase in velocity and the rate of heat transfer. The net increase in total heat transfer was 105% maximum, at 30° inclination. Dirkse et al. (2006) created CFD model for a natural convection shell and tube heat exchanger with baffles. The feature of complex geometry had been simplified considerably resulting in an almost two dimensional mesh with only 30,000 quadrilateral mesh cells. Mon and Gross (2004) modeled a flow domain with half fin and half air path having three and five row of tubes and analyzed the effect of fin spacing on hydrodynamic and thermal characteristics of annular finned tube heat exchangers with the aid of FLUENT. The authors found good agreement in heat transfer results whereas the pressure drop results were found to exceed by more than 50%. It is evident from the literature that the hydrodynamic and heat transfer characteristics are expected to change whenever a change in pitch, fin spacing, etc. is implemented. It necessitates the numerical flow visualization in conjugate heat transfer condition of each configuration of heat exchanger which helps to further improve its design. Most of the work reported is in the field of new types of heat exchangers with simplified flow domain reasonably. It is also clear that the domain with more number of fins and bundles in a
Table 1 Geometric dimensions of REV. Sl. No.
Geometry of Representative Elementary Volume
Dimensions (mm)
Sl. No.
Geometry of Representative Elementary Volume
Dimensions (mm)
1 2 3 4 5 6
Length of shell side Breadth of the shell side Height of the shell side Tube diameter Thickness of each fin Diameter of the fin
159 15.24 2384.5 38.1 1.22 63.1
7 8 9 10
Fin pitch Height of the fin Number of fins per tube Number of rows
5.08 12.5 3 12 (each row having one and half pipes)
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K. Kannan et al. / Annals of Nuclear Energy 75 (2015) 428–437
(a)
(b)
Fig. 3. REV indicating (a) boundary conditions (b) longitudinal and transverse pitch.
Table 3 Mesh independence data. Case
Mesh size
Temperature rise error %
1 2
76,65,569 1,03,01,348 (34%) 1,78,68,875 (133.10%)
+10.6 +9.6
2.2 2.4
37 55
+10.5
2.2
100
3
Total heat flux error %
Computational time in hours
Fig. 5. Density contour.
Fig. 4. The tubes numbered from bottom of air entry.
heat exchanger will represent the actual conditions in a better manner. Hence, the objective of this study is that (i) visualize hydrodynamic characteristics of shell side air in a Representative Elementary Volume (REV) with four bundles of staggered tubes with three fins (ii) study the thermal characteristics of a shell and tube heat exchanger when longitudinal pitch and transverse pitch values are changed numerically.
2. Numerical simulation The sodium air heat exchanger of current interest is as shown in Fig. 1. The domain is with overall size of 1.09 m 1.72 m 3.38 m
and includes number of tube supports, longitudinal baffles and transverse baffles. The analysis of the entire domain with both side fluids is numerically expensive. Hence a Representative Elementary Volume (in rectangle shape) as shown in Fig. 2 is selected for the study purpose. The data about geometry of REV is as given in Table 1.
2.1. Governing equations The numerical simulations have been conducted with ANSYS FLUENT research version. Three dimensional Navier Stokes equations along with Energy equation and RNG k-e turbulence model without any source terms have been solved in the flow domain. The sodium flow and the air flow through sodium to air heat exchanger are generated by buoyancy driven forces. Since full system is not in the consideration of this study, the mass flow rate of air at the inlet to REV has been calculated by dividing ratio of the whole heat exchanger fins to REV fins from the air mass flow rate at full load condition. The fluid domain for analysis is REV from the heat exchanger.
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Fig. 6. Pressure contour. Fig. 8. Temperature contour.
zero, i.e., no convective heat flux across the symmetry plane occurs and buoyancy and radiation effects have been neglected. Pressure velocity coupling was by SIMPLE algorithm. The iterations were initiated with 1st order discretisation schemes and after 500 iterations; the scheme was upgraded for 2nd order schemes. The domain has been discretised with 100,00,000 tetrahedral control volumes approximately. Sufficient care has been taken to retain fine mesh around each tube where the steep gradient is anticipated. The Reynolds number based on minimum flow area is in the range of 1880 to 5200. Pipes are named from bottom to top in each row as in Fig. 4. 2.2. Mesh independence
Fig. 7. Velocity contour.
The fins have been modeled as solid in flow domain along with tube outer surface. The non dimensional distance between first cell and wall, y+ has been maintained at 2.26 on an average. The boundary condition at the fin-tube surface is no slip for fluid flow and constant wall temperature for tube inner surface. In heat exchanger, the fluid has to travel along inlet nozzle, transition duct in the inlet side and between the tubes before it reaches REV. When the air enters, it enters with a velocity pattern, not with uniform velocity. It results in turbulence intensity variation from 0% to 6.3%. Hence, the average 3% turbulence intensity is specified. Outlet boundary condition is set as pressure outlet condition with atmospheric pressure value. During air travel from the inlet to outlet, significant change in density is experienced. That is implemented through ideal gas law for density calculation. The tube side fluid effect is implemented through experimental temperatures measured, assigned to tube inner walls as given in Table 2 (Vinod et al. (2013)). The tube material is stainless steel 316 type. At the symmetry planes as shown in Fig. 3, heat flux is assumed zero. The normal velocity component at the symmetry plane is
The Table 3 indicates the results of mesh independence study. The bench mark is experimental data on heat exchanger heat flux and the temperature rise of air across the heat exchanger. When finer mesh is implemented,(The number of control volumes in the flow domain were increased from 1,03,01,348 to 1,78,68,875), appreciable change in heat transfer characteristics is not experienced but computational time is doubled approximately. Hence, it is decided to continue with 1 crore mesh for the parametric study.
Fig. 9. How the velocity vectors figures are extracted.
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Fig. 10. Velocity vector in tube back side.
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Fig. 11. Position angle around a tube fin.
3. Results of Representative Elementary Volume analysis 3.1. Flow characteristics The global pattern of flow variable changes in the flow domain in a z plane is as shown in Figs. 5–8. The air behavior in shell side is
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important to maximize the effectiveness of the heat exchanger. As per design, every tube has to receive air uniformly which is difficult to achieve in practical. It is evident from Figs. 5–8. Moreover the global pattern of flow variables helps to understand the local behavior of air in a better way. For example, when the air crosses the first bundle and enters the second bundle, the air velocity is expected to reach uniform at every point but the jet effect between tubes is experienced. That causes similar pattern of air recirculation behind the tubes in successive bundles, which is not favorable from heat transfer perspective. Careful analysis of air in the domain reveals that the adverse phenomena are major in back side of tubes whereas in the remaining zones, the air flows without major change in its variables. Fig. 9 shows how the velocity contours are extracted from the backside of each tube which is useful to explore further about the adverse phenomena like horse shoe vortex formation behind the tube, jet formation in between tubes, etc. The existence of adverse phenomena is evident from Fig. 10. The tubes 1, 2, 4, 5, 7, 8, 10, 11 are directly exposed to fluid whereas the remaining tubes are in the shadow region of 1, 4, 7, 10 irrespective of gap between tube bundles of 345 mm. The velocity of the air has varied from 0.065 m/s in tube back side to 7.16 m/s in space between tubes. The maximum velocity of air is experienced in passage
Fig. 12. Heat transfer coefficient vs. points at angle around a tube.
Fig. 13. Average heat transfer coefficient vs. No. of tube.
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Fig. 14. Average Nusselt number vs. Number of tube.
between adjacent tubes. In overall, double horse vortices with different magnitudes are present behind directly exposed tubes (first two tubes in every bundle) whereas the remaining tubes are experiencing reverse flow alone.
Table 4 Longitudinal and transverse pitch variation data.
3.2. Thermal characteristics
Cases
Longitudinal and transverse pitch, SL and ST
Cases
Longitudinal and transverse pitch, SL and ST
1 2 3 4
50 mm 50 mm 65 mm 70 mm
5 6 7 8
70 mm 75 mm 80 mm 75 mm
41 mm 53 mm 55 mm 41 mm
55 mm 53 mm 41 mm 55 mm
The local convection heat transfer coefficient, h of the air at various locations around a tube fin as shown in Fig. 11 is collected. The h data is collected from control volumes on middle fin outer surface (tip area) over each tube. In each tube, the front stagnation point is shown as zero degree in flow path. The location for study is selected at every 45 degree in clock wise direction. The lower heat transfer coefficient values at 180 degree angle confirm the ill effect of horse vortex formation behind the tubes. The tube location in tube bundle dictates maximum heat transfer coefficient value position which is evident from Fig. 12. The position at which maximum heat transfer coefficient value is experienced changes from tube to tube due to associated flow physics complexity. It ensures that the pattern of boundary layer
Fig. 15. Variation in temperature rise and total heat transfer.
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Fig. 16. H vs. longitudinal pitch for representative tubes.
Fig. 17. F vs. longitudinal pitch for representative tubes.
formation and separation around each tube is entirely different from each other. Representative Elementary Volume has four bundles. Each bundle has 3 full tubes and 2 half tubes. In air flow path, the bundles and full tubes are numbered in ascending order. Figs. 13 and 14 shows average local convection heat transfer coefficient and average local Nusselt number variation along the air flow path. As maximum temperature difference between fluids exist in the air entrance area, maximum values of average local convection heat transfer coefficient and average local Nusselt number are experienced in first bundle tubes. That is compared to the remaining bundles; higher amount of heat transfer is in first bundle. In first and fourth bundle, the maximum local heat transfer coefficient value is associated with 2nd tube followed by 1st and 3rd tube whereas in the remaining bundles the local heat transfer coefficient values descend from tube 1 to 3.
3.3. Effect of longitudinal pitch and transverse pitch on thermal characteristics The effect of longitudinal and transverse pitch variation on the heat exchanger performance is studied. The variation in pitch is done as given in Table 4. Longitudinal pitch is 70 mm and transverse pitch is 53 mm in original design. The mass flow rate of air at full load condition is the inlet boundary condition for the entire study. The pressure loss when both pitches are reduced increases approximately 4 times whereas when both the pitches are increased decreases approximately half and according to the case, the pressure variation is experienced. When the pitch value is increased, the total heat transfer across the REV with respect to original has reduced. When the pitch value is reduced both in longitudinal as well as in transverse direction, the REV performance with respect to original has started to increase as shown in
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Fig. 18. H vs. transverse pitch for representative tubes.
Fig. 19. F vs. transverse pitch for representative tubes.
Fig. 15 but at the same time the pressure drop across the heat exchanger also increases. When the longitudinal pitch is varied, the details of local average convection heat transfer coefficient and local average skin friction coefficient along the flow path is plotted for better understanding as shown in Figs. 16 and 17. When longitudinal pitch, SL is increased, the decrease in local maximum velocity is experienced from 7.16 m/s to 6.84 m/s. When longitudinal pitch, SL is decreased, the increase in local maximum velocity from 7.16 m/s to 8.51 m/s is experienced. It reflects correspondingly in the overall heat transfer coefficient. When the transverse pitch is controlled, the details of local average convection heat transfer coefficient and local average skin friction coefficient along the flow path is plotted for better
understanding as shown in Figs. 18 and 19. When transverse pitch, ST is increased, the decrease in local maximum velocity from 7.16 m/s to 7.1 m/s is experienced. When transverse pitch, ST is decreased, the increase in local maximum velocity from 7.16 m/s to 11.08 m/s is experienced. It reflects correspondingly in the overall heat transfer coefficient. When both longitudinal pitch, SL and transverse pitch, ST are increased, the decrease in local maximum velocity from 7.16 m/s to 6.84 m/s is experienced. When both longitudinal pitch, SL and transverse pitch, ST are decreased, the increase in local maximum velocity from 7.16 m/ s to 12.84 m/s is experienced. When both pitches are varied, the mixed effect is experienced as shown in Fig. 20. Still the transverse pitch effect is dominant compared to longitudinal pitch effect.
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Fig. 20. Effect of longitudinal pitch and transverse pitch on local heat transfer coefficient.
4. Conclusions
References
The sodium to air heat exchanger performance is a key factor in decay heat disposal of prototype fast breeder reactors. The constant improvements in their modeling and simulation are necessary to improve the reliability and efficiency of it at different conditions due to the limitations in experiments. As the analysis of a heat exchanger in actual size with both side fluid flow is numerically expensive, a Representative Elementary Volume (REV) from 2 MW sodium to air heat exchanger has been extracted and the shell side flow in REV with heat transfer has been simulated successfully. The difference in temperature rise of air across the heat exchanger between experimental and numerical is within 5%. The air velocity around the tubes has varied from 0.065 m/s to 7.16 m/s. The velocity change depends on tube location in particular bundle and bundle location. The velocity contours from different planes of REV confirm the basics. The negative velocity is experienced behind the tubes whereas the maximum velocity is experienced in tube sides. The local heat transfer coefficient around the tubes changes from 0.689 W/m2 K to 91.01 W/m2 K but the change in the local heat transfer coefficient is based on the flow physics complexity, fluid temperature, tube location in particular bundle and bundle location. The temperature contour from different planes of REV confirms the same. The study has also predicted similar pattern of air recirculation behind the tubes in successive bundles, which is not favorable from heat transfer perspective. The decrease in longitudinal pitch and transverse pitch has resulted in an increase of 22% maximum in heat transfer, at the cost of increased pressure drop in shell side. With REV model, further the study can be extended with parameters like gap between bundles, fin pitch, etc.
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