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Heat transfer performance and entropy generation of helical square tubes with various curvature radiuses
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ScienceDirect
Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Available Energy Energy Procedia Procedia 00 00 (2017) (2017) 000–000 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
– (2017) 000–000 Energy Procedia 00 www.elsevier.com/locate/procedia
9th 9th International International Conference Conference on on Applied Applied Energy, Energy, ICAE2017, ICAE2017, 21-24 21-24 August August 2017, 2017, Cardiff, Cardiff, UK UK
Heat transfer performance and entropy generation of helical square The 15th International Symposium on District Heating and Cooling tubes with various curvature radiuses bb Assessing the Jundika feasibility of a,a,using heat demand-outdoor Jundika C Kurnia Kurnia *, Agus Agusthe P Sasmito Sasmito C *, P temperature function forTechnologi a long-term district heat demand forecast Department PETRONAS, Department of of Mechanical Mechanical Engineering, Engineering, Universiti Universiti Technologi PETRONAS, 32610 32610 Bandar Bandar Seri Seri Iskandar, Iskandar, Perak Perak Darul Darul Ridzuan, Ridzuan, Malaysia Malaysia a a
b bDepartment
Department of of Mining Mining and and Materials Materials Engineering, Engineering, McGill McGill University, University, 3450 3450 University, University, Montreal, Montreal, QC, QC, H3A2A7 H3A2A7 Canada Canada
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc a Abstract IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b
Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France
c Département Énergétiques Environnement - IMT Atlantique, rue Alfred 44300 Nantes, in France Having of higher transfer compact helical tubes been commonly adopted major Having key key advantages advantages ofSystèmes higher heat heat transferetand and compact size, size, helical tubes4have have been Kastler, commonly adopted in major industry industry applications especially heat exchangers and chemical reactors. On top of their encouraging industrial adoption, helical applications especially heat exchangers and chemical reactors. On top of their encouraging industrial adoption, helical tubes tubes have have attracted significant significant attention attention from from researchers researchers worldwide worldwide due due to to its its complex complex flow flow behavior. behavior. This This study study addresses addresses the the flow flow attracted characteristic characteristic and and heat heat transfer transfer performance performance of of aa laminar laminar flow flow inside inside helical helical tubes tubes with with various various curvature curvature diameters. diameters. The The laminar laminar Abstract flow flow of of aa Newtonian Newtonian fluid fluid inside inside helical helical tubes tubes is is investigated investigated by by utilizing utilizing aa computational computational fluid fluid dynamics dynamics approach. approach. Both Both constant constant wall temperature and constant wall heat flux conditions are examined. Their heat transfer performance is numerically wall temperature and constant wall heat flux conditions are examined. Their heat transfer performance is numerically evaluated evaluated District heating areconcept commonly addressed in the literature as one the of the most effective forisdecreasing the and compared by networks utilizing the the of Figure Figure of Merit Merit (FoM). In addition, addition, inefficiency of the the solutions helical tube tube analyzed by by and compared by utilizing concept of of (FoM). In the inefficiency of helical is analyzed greenhouse gas emissions from the building sector.indicate These systems require highperformance investments which are as returned through the heat utilizing entropy generation analysis. The results that heat transfer increases the curvature radius utilizing entropy generation analysis. The results indicate that heat transfer performance increases as the curvature radius sales. Due to the changed climate conditions and building renovationthan policies, heat demand in the future could decrease, decreases. decreases. Albeit Albeit higher higher pressure pressure drop, drop, helical helical coil coil generate generate lower lower entropy entropy than straight straight tube. tube. prolonging the investment return period. © 2017 The Authors. Published Elsevier Ltd. © 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. ©The 2017 main scope ofresponsibility this paper isby to assess the feasibility of using the heat demand – outdoor temperature function for heat demand Peer-review under of the scientific committee of the 9th International on Applied Energy. Peer-review under responsibility of the scientific committee of of the the 9th 9th International International Conference Conference on on Applied Applied Energy. Energy. Peer-review under responsibility of thelocated scientific forecast. The district of Alvalade, in committee Lisbon (Portugal), was used as aConference case study. The district is consisted of 665 buildings thatentropy vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Keywords: Keywords: coil; coil; entropy generation; generation; helical; helical; heat heat transfer transfer performance performance renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications 1. Introduction 1.(the Introduction error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). Helical tube has been known for its heat transfer rate and smaller footprints. As aa result, it Helical has coefficient been widely widely known on foraverage its higher higher heatthe transfer and up smaller Asthat result, it has has been been The value tube of slope increased within range rate of 3.8% to 8%footprints. per decade, corresponds to the widely adopted in various industrial applications, especially heat exchanger and chemical reactor. The higher widely adopted in various industrial especially heat exchanger and chemical reactor. Theofhigher heat decrease in the number of heating hoursapplications, of 22-139h during the heating season (depending on the combination weatherheat and transfer rate of tube from the of secondary flow, which only transfer ratescenarios of helical helical tube is is originated originated fromhand, the presence presence of the the curvature-induced curvature-induced secondary flow,(depending which not not on only renovation considered). On the other function intercept increased for 7.8-12.7% per decade the induce heat but also complex phenomena helical tube. helical tube coupledhigher scenarios). The values could be usedtransport to modify the functioninside parameters the Thus, scenarios considered, and induce higher heat transfer transfer butsuggested also creates creates complex transport phenomena inside helicalfor tube. Thus, helical tube does does improve the accuracy of heat demand estimations.
© 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * * Corresponding Corresponding author. author. Tel.: Tel.: +605 +605 368 368 7157; 7157; fax: fax: +605 +605 365 365 6461. 6461. Cooling.
E-mail E-mail address: address: [email protected] [email protected] (J.C. (J.C. Kurnia), Kurnia), [email protected] [email protected] (A.P. (A.P. Sasmito). Sasmito). Keywords: Heat demand; Forecast; Climate change 1876-6102 1876-6102 © © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. Peer-review Peer-review under under responsibility responsibility of of the the scientific scientific committee committee of of the the 9th 9th International International Conference Conference on on Applied Applied Energy. Energy.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
© 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy.
2
et al. / – Author name / Energy Procedia 00 (2017) 000–000
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not only gain popularity in industrial applications, it also attracts considerable attention from researcher worldwide. Accordingly, large number of studies on helical tube have been conducted and reported. Table 1. Geometrical parameters of studied straight and helical tubes. Parameters
Value
Unit
w
0.01
m
s
0.01
m
L
1.2
m
Rh1
0.03
m
Rh2
0.04
m
Rh3
0.05
m
Fig. 1. Schematics representations of a) straight tube and helical tube with helical radius of: b) 3 cm; c) 4 cm; and d) 5 cm.
Early studies were conducted to investigate the mechanism of secondary flow and its associated heat transfer [12]. Recent studies examine various key parameters affecting heat transfer and propose numerous methods to enhance the heat transfer further [3-11]. However, most of these studies focused on the heat transfer performance of helical tube according to the first law of thermodynamics. Recently, second law thermodynamics is increasingly utilized to evaluate heat transfer performance as it allows for identification on the cause of inefficiency in the system [12]. In our previous study [13], we investigated heat transfer performance and entropy generation of laminar flow in helical tubes with various cross-sections. The results suggested that helical coil offers higher heat transfer and lower entropy generation albeit higher pressure drops. In this study, we extend our investigation by evaluating the heat transfer performance and entropy generation helical non-circular tube with different helical curvature. The evaluation is conducted by utilizing computational fluid dynamics (CFD) approach which is coupled with entropy generation analysis. Potential advantages and limitations of the designs will be discussed in light of the numerical results. 2. Mathematical model The flow characteristic and heat transfer performance in a square straight and helical tube is evaluated by utilizing a three dimensional CFD model for an incompressible laminar Newtonian fluid. The schematic diagram of the model and its physical characteristics are presented in Fig. 1 and Table 1, respectively. It should be noted that the total length of all tubes are similar to ensure fair heat transfer comparison. The mass, momentum and energy conservation theories are applied in our model and defined as the equations shown below,
u 0
(1)
( u u) P u (u) T ,
(2)
c p u T k 2T
(3)
where ρ is the fluid density, u is the velocity, P is the pressure, μ is the dynamic viscosity, cp is the specific heat, k represents thermal conductivity and variable T as the temperature.
et al. / – Author name / Energy Procedia 00 (2017) 000–000
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3
Similar to our previous study [13], entropy balanced equation for open system is adopted to investigate the entropy generation in the studied geometries. The second law thermodynamic for continuum frame work is given by
σ s g 0
(4)
where and sg are the entropy flux and the entropy generation rate per unit volume, respectively. Temperaturedependent air is chosen as the heat transfer fluid. The entropy generation rate per unit volume (s g) is considered to consist of 2 component, i.e. heat transfer component (sh) and viscous dissipation component (s) [12,13] The boundary conditions are illustrated in Fig. 1. A fine structured mesh was implemented on the near wall region to resolve boundary layer while an increasingly coarser mesh is applied towards the middle tube to optimize the computational resources and time. The model was solved with Semi-Implicit Pressure-Linked Equation (SIMPLE) algorithm, second order upwind discretization and Algebric Multi-grid (AMG) method. A convergence criterion of 10-4 was set for conservation of mass and 10-6 for other parameters. 3. Results and discussion Numerical simulations for straight and helical coiled tubes with square cross-section were conducted with both constant wall heat flux and constant wall temperature. In the previous study [13], the mathematical model has been validated by comparing its prediction against the experimental results for both straight and coiled tube. Good agreement is achieved between model prediction and experimental measured counterparts. For the sake of brevity, details model validation is not re-presented in here. Instead readers are encouraged to refer our previous study [13].
Fig. 2. Axial velocity profile (a) and temperature (b) of airflow in a straight and helical tubes with constant wall temperature at L=25 cm.
3.1. Effect of geometry and curvature diameter It is of interest to investigate the effect of helical curvature on the velocity profile inside the tubes. Fig. 2a presents the axial velocity profile of airflow inside the tubes at a constant wall temperature of 323.15 K. Here, it can be clearly observed the presence of secondary flow inside helical tube which does not present in straight tube. This secondary flow is the result of centrifugal force due to curvature which leads to significant radial pressure gradient in the flow core region [13]. In addition, closer inspection reveals that higher and more uniform velocity is observed at the area near the outer wall as the curvature diameter decrease. As expected velocity profile inside the tubes will directly affect the heat transfer performance, as can be inferred from Fig. 2b which shows the axial temperature distribution for the straight and helical tubes at constant wall temperature. For helical tubes, a higher temperature gradient is observed at the area near the outer wall, indicating a higher heat transfer. Moreover, it can be seen that at the same length from the inlet, the average fluid temperature inside the helical tubes is higher as compared to that inside the straight tube. This is further indication that higher heat transfer indeed occurs in the helical tubes. Looking
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into the effect of curvature diameter, it is revealed that higher and more uniform temperature distribution is observed for helical tube with smaller curvature diameter. This is attributed by the stronger secondary flow in a helical tube with smaller curvature which enhance mixing and heat transfer inside the tubes.
Fig. 3. Mixed mean temperature along the tube length for: a) constant wall temperature and b) constant wall heat flux.
Fig. 4. Contour of entropy generation due to heat transfer, viscous dissipation and total entropy in a straight and helical tubes with constant wall temperature at L=25 cm.
Looking further into the mixed mean temperature along the tube length for both constant wall temperature and constant wall heat flux, as presented in Fig. 3, it is found that for both cases, helical tubes with smaller curvature diameter offers the highest heat transfer performance, indicated by a higher mixed mean temperature. It is also noted that for the constant wall temperature case, helical tube requires much shorter length to reach the wall temperature while straight tube cannot reach the wall temperature for the given tube length. This highlights the potential of helical tube for heat exchanger application. In addition, helical coils offer reduction in capital cost since shorter pipe is required to achieve the desired temperature. Fig. 4 presents distribution of heat transfer component and viscous dissipation component of entropy generation inside the tube, respectively. Here, it appears that helical tubes generate lower entropy as compared to the straight counterpart. In addition, it can be seen that for helical tubes, maximum entropy generation due to heat transfer occurs near the outer wall area. This is attributed to the fact that maximum heat transfer takes place at the outer wall, mirrored by high temperature gradient, as presented in Fig. 2. For the straight tube, on the other hand, entropy generation due to heat transfer is generated equally on all walls with the maximum generation occurs at the center of the wall. In contrast to heat transfer contributions, for entropy generation due to viscous dissipation, helical tubes generate more entropy than straight tube. The viscous dissipation contribution is, however, significantly smaller than heat transfer contribution. Hence, on total, helical tube generate lower entropy than straight tube, as presented in Fig. 4. Similar trend is observed in Fig. 5 which presents entropy generation along the tube. The entropy generation for all helical tubes is significantly lower than straight tube. Among the helical tubes, it is found that larger helical
et al. / – Author name / Energy Procedia 00 (2017) 000–000
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5
curvature radius results in higher entropy generation. Interestingly, the trend of entropy generation for constant wall temperature and constant wall heat flux is distinctly different, i.e. asymptotic for constant wall temperature and relatively constant for constant wall heat flux. This is can be conveniently explained by the fact that for constant wall temperature, temperature different between bulk fluid and wall in the entrance region is large, inducing large entropy generation. In contrast, for constant wall heat flux, both wall and bulk fluid temperature increase gradually, creating relatively constant temperature gradient between both.
Fig. 5. Local entropy generation (sg) along the tube length for: a) constant wall temperature and b) constant wall heat flux.
3.2. Overall heat transfer performance The overall heat transfer performance for parameters investigated in this study is summarized in Table 2. Here, several features are apparent: 1) for both constant wall temperature and constant wall heat flux, the total heat transfer rate for helical tube is higher as compared to that of straight tube which is attributed to the presence of secondary flow in helical tubes, 2) helical tubes with smaller curvature radius offer higher heat transfer rate due to stronger secondary flow which enhance mixing. Table 2. Total heat transfer rate, pressure drop, FoM and global entropy generation* inside the tubes. Geometry
Constant Twall
Constant qwall
Q (W)
P (Pa)
FoM
sh
s
sg
Q (W)
P (Pa)
FoM
sh
s
sg
Helical 3 cm
4.52
40.89
496.98
4.07
0.14
4.21
5.03
39.35
574.74
0.78
0.13
0.91
Helical 4 cm
4.49
38.24
528.17
4.12
0.13
4.25
4.97
36.78
607.94
0.81
0.13
0.93
Helical 5 cm
4.46
35.41
567.03
4.22
0.13
4.35
4.86
34.22
638.88
0.85
0.12
0.97
Straight
4.02
13.35
1354.63
5.42
0.06
5.48
4.22
13.10
1450.78
3.85
0.06
3.90
*entropy generation (sh, s , sg ) is presented in 10-4 W K-1
A further point of interest in the current study is to evaluate the pumping power required to drive the flow through the tubes. As presented in Table 2, the heat transfer enhancement in helical tubes has to be paid pay an increase in pumping power. Smaller curvature radius results in higher pressure drop along the tubes and in turn higher pumping power requirement. As compared to straight tubes which has the identical total length, helical tubes require more than double pumping power. This may hinder the feasibility of helical tubes for heat exchanger application of space is not a major issue. In order to have a fair and comprehensive comparison on the heat transfer performances of the studied geometries, the concept of figure of merit (FoM) is introduced and utilized. As explained in earlier section, this is defined as the ratio of output (heat transfer rate) to input (pumping power). The results are summarized in Table 2. It was found that even though straight tube offers the smallest heat transfer rate, surprisingly it provides the highest figure of merit. This can be traced back to the fact that straight tube posses the smallest pressure drop, as shown in Table 2. Therefore, smaller heat transfer is compensated with even smaller pumping power requirement. On the
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other hand, while smaller radius helical tubes has the highest heat transfer rate, due to its triple pumping power requirement, it has the smallest figure of merit. Another key interest is entropy generation within the tube, as presented in Table 2. Notably, the difference between entropy generation in helical and straight tube for constant wall temperature is not as large as those for constant wall heat flux. Furthermore, it is found that helical coil generate lower entropy, highlighting the potential of helical tube in practical application despite higher pumping power requirement. 4. Conclusions Flow characteristic, heat transfer performance and entropy generation of a laminar flow inside helical tubes with various curvature diameters have been numerically investigated by utilizing a computational fluid dynamic (CFD) approach. Three curvature radiuses - 3 cm, 4 cm and 5 cm - were evaluated and compared with straight tube with identical cross-section. The result indicates the superior performance of helical tube heat transfer as compared to that of straight tube. In addition, smaller curvature radius was found to offers higher heat transfer performance at cost of higher pumping power requirement. Overall, despite their higher heat transfer rate, helical tubes scores low figure of merit due to its high pumping power requirement. However, from the second thermodynamics law view, helical tube generates lower entropy, indicating potential application for system with low inefficiency. Smaller curvature radius generates lower entropy despite inducing higher pressure drop. As a continuation, study on the heat transfer performance of helically coiled square double pipe heat exchanger is underway. The performance will be compared to that of circular cross-section. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Dravid AN, Smith KA, Merril EW, Brian PLT. Effect of secondary fluid motion on laminar flow heat transfer in helically coiled tubes. AIChE J 1971;17:1114-22. Akiyama M, Cheng KC. Graetz problem in curved pipes with uniform wall heat flux. Appl Sci Res 1974;29:401-18. Sasmito AP, Kurnia JC, Wang W, Jangam SV, Mujumdar AS. Numerical analysis of laminar heat transfer performance of in-plane spiral ducts with various cross-sections at fixed cross-section area. Int J Heat Mass Transf 2012;55:5882-90. Wu Z, Wang L, Sundén B. Pressure drop and convective heat transfer of water and nanofluids in a double-pipe helical heat exchanger. Appl Therm Eng 2013;60:266-74. Kurnia JC, Sasmito AP. Mujumdar AS. Laminar heat transfer performance of power law fluids in coiled square tube with various configurations. Int Commun Heat Mass Transf 2014;57:100-8. Mirfendereski S, Abbassi A, Saffar-awal M. Experimental and numerical investigation of nanofluid heat transfer in helically coiled tubes at constant wall heat flux. Adv Powder Technol 2015;26:1483-94. Kong M, Alvarado JL, Terrell Jr W, Thies C. Performance characteristics of microencapsulated phase change material slurry in a helically coiled tube. Int J Heat Mass Transf 2016;101:901-14. Kurnia JC, Sasmito AP. Mujumdar AS. Thermal performance of coiled square tubes at large temperature differences for heat exchanger application. Heat Transfer Eng 2016;37:1341-56. Aly WIA. Thermal and hydrodynamic performance of aqueou CuO and Al2O3 nanofluids in an annular coiled tube under constant wall temperature and laminar flow conditions. J Heat Transfer 2016;138:102401. Alimoradi A, Veysi F. Predition of heat transfer coefficients of shell and coiled tube heat exchangers using numerical method and experimental validation. Int J Therm Sci 2016;107:196-208. Zachar A. Analysis of coiled-tube heat exchangers to improve heat transfer rate with spirally corrugated wall. Int J Heat Mass Transf 2010;53:3928-39. Sciacovelli A, Verda V, Sciubba E, Entropy generation analysis as a design tool-a review, Renew Susatin Energy Rev 2015;43:1167-1181. Kurnia JC, Sasmito AP, Shamim T, Mujumdar AS. Numerical investigation of heat transfer and entropy generation of laminar flow in helical tubes with various cross sections. Appl Therm Eng 2016;102:849-60.
ScienceDirect
Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Available Energy Energy Procedia Procedia 00 00 (2017) (2017) 000–000 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
– (2017) 000–000 Energy Procedia 00 www.elsevier.com/locate/procedia
9th 9th International International Conference Conference on on Applied Applied Energy, Energy, ICAE2017, ICAE2017, 21-24 21-24 August August 2017, 2017, Cardiff, Cardiff, UK UK
Heat transfer performance and entropy generation of helical square The 15th International Symposium on District Heating and Cooling tubes with various curvature radiuses bb Assessing the Jundika feasibility of a,a,using heat demand-outdoor Jundika C Kurnia Kurnia *, Agus Agusthe P Sasmito Sasmito C *, P temperature function forTechnologi a long-term district heat demand forecast Department PETRONAS, Department of of Mechanical Mechanical Engineering, Engineering, Universiti Universiti Technologi PETRONAS, 32610 32610 Bandar Bandar Seri Seri Iskandar, Iskandar, Perak Perak Darul Darul Ridzuan, Ridzuan, Malaysia Malaysia a a
b bDepartment
Department of of Mining Mining and and Materials Materials Engineering, Engineering, McGill McGill University, University, 3450 3450 University, University, Montreal, Montreal, QC, QC, H3A2A7 H3A2A7 Canada Canada
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc a Abstract IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b
Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France
c Département Énergétiques Environnement - IMT Atlantique, rue Alfred 44300 Nantes, in France Having of higher transfer compact helical tubes been commonly adopted major Having key key advantages advantages ofSystèmes higher heat heat transferetand and compact size, size, helical tubes4have have been Kastler, commonly adopted in major industry industry applications especially heat exchangers and chemical reactors. On top of their encouraging industrial adoption, helical applications especially heat exchangers and chemical reactors. On top of their encouraging industrial adoption, helical tubes tubes have have attracted significant significant attention attention from from researchers researchers worldwide worldwide due due to to its its complex complex flow flow behavior. behavior. This This study study addresses addresses the the flow flow attracted characteristic characteristic and and heat heat transfer transfer performance performance of of aa laminar laminar flow flow inside inside helical helical tubes tubes with with various various curvature curvature diameters. diameters. The The laminar laminar Abstract flow flow of of aa Newtonian Newtonian fluid fluid inside inside helical helical tubes tubes is is investigated investigated by by utilizing utilizing aa computational computational fluid fluid dynamics dynamics approach. approach. Both Both constant constant wall temperature and constant wall heat flux conditions are examined. Their heat transfer performance is numerically wall temperature and constant wall heat flux conditions are examined. Their heat transfer performance is numerically evaluated evaluated District heating areconcept commonly addressed in the literature as one the of the most effective forisdecreasing the and compared by networks utilizing the the of Figure Figure of Merit Merit (FoM). In addition, addition, inefficiency of the the solutions helical tube tube analyzed by by and compared by utilizing concept of of (FoM). In the inefficiency of helical is analyzed greenhouse gas emissions from the building sector.indicate These systems require highperformance investments which are as returned through the heat utilizing entropy generation analysis. The results that heat transfer increases the curvature radius utilizing entropy generation analysis. The results indicate that heat transfer performance increases as the curvature radius sales. Due to the changed climate conditions and building renovationthan policies, heat demand in the future could decrease, decreases. decreases. Albeit Albeit higher higher pressure pressure drop, drop, helical helical coil coil generate generate lower lower entropy entropy than straight straight tube. tube. prolonging the investment return period. © 2017 The Authors. Published Elsevier Ltd. © 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. ©The 2017 main scope ofresponsibility this paper isby to assess the feasibility of using the heat demand – outdoor temperature function for heat demand Peer-review under of the scientific committee of the 9th International on Applied Energy. Peer-review under responsibility of the scientific committee of of the the 9th 9th International International Conference Conference on on Applied Applied Energy. Energy. Peer-review under responsibility of thelocated scientific forecast. The district of Alvalade, in committee Lisbon (Portugal), was used as aConference case study. The district is consisted of 665 buildings thatentropy vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Keywords: Keywords: coil; coil; entropy generation; generation; helical; helical; heat heat transfer transfer performance performance renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications 1. Introduction 1.(the Introduction error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). Helical tube has been known for its heat transfer rate and smaller footprints. As aa result, it Helical has coefficient been widely widely known on foraverage its higher higher heatthe transfer and up smaller Asthat result, it has has been been The value tube of slope increased within range rate of 3.8% to 8%footprints. per decade, corresponds to the widely adopted in various industrial applications, especially heat exchanger and chemical reactor. The higher widely adopted in various industrial especially heat exchanger and chemical reactor. Theofhigher heat decrease in the number of heating hoursapplications, of 22-139h during the heating season (depending on the combination weatherheat and transfer rate of tube from the of secondary flow, which only transfer ratescenarios of helical helical tube is is originated originated fromhand, the presence presence of the the curvature-induced curvature-induced secondary flow,(depending which not not on only renovation considered). On the other function intercept increased for 7.8-12.7% per decade the induce heat but also complex phenomena helical tube. helical tube coupledhigher scenarios). The values could be usedtransport to modify the functioninside parameters the Thus, scenarios considered, and induce higher heat transfer transfer butsuggested also creates creates complex transport phenomena inside helicalfor tube. Thus, helical tube does does improve the accuracy of heat demand estimations.
© 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * * Corresponding Corresponding author. author. Tel.: Tel.: +605 +605 368 368 7157; 7157; fax: fax: +605 +605 365 365 6461. 6461. Cooling.
E-mail E-mail address: address: [email protected] [email protected] (J.C. (J.C. Kurnia), Kurnia), [email protected] [email protected] (A.P. (A.P. Sasmito). Sasmito). Keywords: Heat demand; Forecast; Climate change 1876-6102 1876-6102 © © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. Peer-review Peer-review under under responsibility responsibility of of the the scientific scientific committee committee of of the the 9th 9th International International Conference Conference on on Applied Applied Energy. Energy.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
© 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy.
2
et al. / – Author name / Energy Procedia 00 (2017) 000–000
4065
not only gain popularity in industrial applications, it also attracts considerable attention from researcher worldwide. Accordingly, large number of studies on helical tube have been conducted and reported. Table 1. Geometrical parameters of studied straight and helical tubes. Parameters
Value
Unit
w
0.01
m
s
0.01
m
L
1.2
m
Rh1
0.03
m
Rh2
0.04
m
Rh3
0.05
m
Fig. 1. Schematics representations of a) straight tube and helical tube with helical radius of: b) 3 cm; c) 4 cm; and d) 5 cm.
Early studies were conducted to investigate the mechanism of secondary flow and its associated heat transfer [12]. Recent studies examine various key parameters affecting heat transfer and propose numerous methods to enhance the heat transfer further [3-11]. However, most of these studies focused on the heat transfer performance of helical tube according to the first law of thermodynamics. Recently, second law thermodynamics is increasingly utilized to evaluate heat transfer performance as it allows for identification on the cause of inefficiency in the system [12]. In our previous study [13], we investigated heat transfer performance and entropy generation of laminar flow in helical tubes with various cross-sections. The results suggested that helical coil offers higher heat transfer and lower entropy generation albeit higher pressure drops. In this study, we extend our investigation by evaluating the heat transfer performance and entropy generation helical non-circular tube with different helical curvature. The evaluation is conducted by utilizing computational fluid dynamics (CFD) approach which is coupled with entropy generation analysis. Potential advantages and limitations of the designs will be discussed in light of the numerical results. 2. Mathematical model The flow characteristic and heat transfer performance in a square straight and helical tube is evaluated by utilizing a three dimensional CFD model for an incompressible laminar Newtonian fluid. The schematic diagram of the model and its physical characteristics are presented in Fig. 1 and Table 1, respectively. It should be noted that the total length of all tubes are similar to ensure fair heat transfer comparison. The mass, momentum and energy conservation theories are applied in our model and defined as the equations shown below,
u 0
(1)
( u u) P u (u) T ,
(2)
c p u T k 2T
(3)
where ρ is the fluid density, u is the velocity, P is the pressure, μ is the dynamic viscosity, cp is the specific heat, k represents thermal conductivity and variable T as the temperature.
et al. / – Author name / Energy Procedia 00 (2017) 000–000
4066
3
Similar to our previous study [13], entropy balanced equation for open system is adopted to investigate the entropy generation in the studied geometries. The second law thermodynamic for continuum frame work is given by
σ s g 0
(4)
where and sg are the entropy flux and the entropy generation rate per unit volume, respectively. Temperaturedependent air is chosen as the heat transfer fluid. The entropy generation rate per unit volume (s g) is considered to consist of 2 component, i.e. heat transfer component (sh) and viscous dissipation component (s) [12,13] The boundary conditions are illustrated in Fig. 1. A fine structured mesh was implemented on the near wall region to resolve boundary layer while an increasingly coarser mesh is applied towards the middle tube to optimize the computational resources and time. The model was solved with Semi-Implicit Pressure-Linked Equation (SIMPLE) algorithm, second order upwind discretization and Algebric Multi-grid (AMG) method. A convergence criterion of 10-4 was set for conservation of mass and 10-6 for other parameters. 3. Results and discussion Numerical simulations for straight and helical coiled tubes with square cross-section were conducted with both constant wall heat flux and constant wall temperature. In the previous study [13], the mathematical model has been validated by comparing its prediction against the experimental results for both straight and coiled tube. Good agreement is achieved between model prediction and experimental measured counterparts. For the sake of brevity, details model validation is not re-presented in here. Instead readers are encouraged to refer our previous study [13].
Fig. 2. Axial velocity profile (a) and temperature (b) of airflow in a straight and helical tubes with constant wall temperature at L=25 cm.
3.1. Effect of geometry and curvature diameter It is of interest to investigate the effect of helical curvature on the velocity profile inside the tubes. Fig. 2a presents the axial velocity profile of airflow inside the tubes at a constant wall temperature of 323.15 K. Here, it can be clearly observed the presence of secondary flow inside helical tube which does not present in straight tube. This secondary flow is the result of centrifugal force due to curvature which leads to significant radial pressure gradient in the flow core region [13]. In addition, closer inspection reveals that higher and more uniform velocity is observed at the area near the outer wall as the curvature diameter decrease. As expected velocity profile inside the tubes will directly affect the heat transfer performance, as can be inferred from Fig. 2b which shows the axial temperature distribution for the straight and helical tubes at constant wall temperature. For helical tubes, a higher temperature gradient is observed at the area near the outer wall, indicating a higher heat transfer. Moreover, it can be seen that at the same length from the inlet, the average fluid temperature inside the helical tubes is higher as compared to that inside the straight tube. This is further indication that higher heat transfer indeed occurs in the helical tubes. Looking
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into the effect of curvature diameter, it is revealed that higher and more uniform temperature distribution is observed for helical tube with smaller curvature diameter. This is attributed by the stronger secondary flow in a helical tube with smaller curvature which enhance mixing and heat transfer inside the tubes.
Fig. 3. Mixed mean temperature along the tube length for: a) constant wall temperature and b) constant wall heat flux.
Fig. 4. Contour of entropy generation due to heat transfer, viscous dissipation and total entropy in a straight and helical tubes with constant wall temperature at L=25 cm.
Looking further into the mixed mean temperature along the tube length for both constant wall temperature and constant wall heat flux, as presented in Fig. 3, it is found that for both cases, helical tubes with smaller curvature diameter offers the highest heat transfer performance, indicated by a higher mixed mean temperature. It is also noted that for the constant wall temperature case, helical tube requires much shorter length to reach the wall temperature while straight tube cannot reach the wall temperature for the given tube length. This highlights the potential of helical tube for heat exchanger application. In addition, helical coils offer reduction in capital cost since shorter pipe is required to achieve the desired temperature. Fig. 4 presents distribution of heat transfer component and viscous dissipation component of entropy generation inside the tube, respectively. Here, it appears that helical tubes generate lower entropy as compared to the straight counterpart. In addition, it can be seen that for helical tubes, maximum entropy generation due to heat transfer occurs near the outer wall area. This is attributed to the fact that maximum heat transfer takes place at the outer wall, mirrored by high temperature gradient, as presented in Fig. 2. For the straight tube, on the other hand, entropy generation due to heat transfer is generated equally on all walls with the maximum generation occurs at the center of the wall. In contrast to heat transfer contributions, for entropy generation due to viscous dissipation, helical tubes generate more entropy than straight tube. The viscous dissipation contribution is, however, significantly smaller than heat transfer contribution. Hence, on total, helical tube generate lower entropy than straight tube, as presented in Fig. 4. Similar trend is observed in Fig. 5 which presents entropy generation along the tube. The entropy generation for all helical tubes is significantly lower than straight tube. Among the helical tubes, it is found that larger helical
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curvature radius results in higher entropy generation. Interestingly, the trend of entropy generation for constant wall temperature and constant wall heat flux is distinctly different, i.e. asymptotic for constant wall temperature and relatively constant for constant wall heat flux. This is can be conveniently explained by the fact that for constant wall temperature, temperature different between bulk fluid and wall in the entrance region is large, inducing large entropy generation. In contrast, for constant wall heat flux, both wall and bulk fluid temperature increase gradually, creating relatively constant temperature gradient between both.
Fig. 5. Local entropy generation (sg) along the tube length for: a) constant wall temperature and b) constant wall heat flux.
3.2. Overall heat transfer performance The overall heat transfer performance for parameters investigated in this study is summarized in Table 2. Here, several features are apparent: 1) for both constant wall temperature and constant wall heat flux, the total heat transfer rate for helical tube is higher as compared to that of straight tube which is attributed to the presence of secondary flow in helical tubes, 2) helical tubes with smaller curvature radius offer higher heat transfer rate due to stronger secondary flow which enhance mixing. Table 2. Total heat transfer rate, pressure drop, FoM and global entropy generation* inside the tubes. Geometry
Constant Twall
Constant qwall
Q (W)
P (Pa)
FoM
sh
s
sg
Q (W)
P (Pa)
FoM
sh
s
sg
Helical 3 cm
4.52
40.89
496.98
4.07
0.14
4.21
5.03
39.35
574.74
0.78
0.13
0.91
Helical 4 cm
4.49
38.24
528.17
4.12
0.13
4.25
4.97
36.78
607.94
0.81
0.13
0.93
Helical 5 cm
4.46
35.41
567.03
4.22
0.13
4.35
4.86
34.22
638.88
0.85
0.12
0.97
Straight
4.02
13.35
1354.63
5.42
0.06
5.48
4.22
13.10
1450.78
3.85
0.06
3.90
*entropy generation (sh, s , sg ) is presented in 10-4 W K-1
A further point of interest in the current study is to evaluate the pumping power required to drive the flow through the tubes. As presented in Table 2, the heat transfer enhancement in helical tubes has to be paid pay an increase in pumping power. Smaller curvature radius results in higher pressure drop along the tubes and in turn higher pumping power requirement. As compared to straight tubes which has the identical total length, helical tubes require more than double pumping power. This may hinder the feasibility of helical tubes for heat exchanger application of space is not a major issue. In order to have a fair and comprehensive comparison on the heat transfer performances of the studied geometries, the concept of figure of merit (FoM) is introduced and utilized. As explained in earlier section, this is defined as the ratio of output (heat transfer rate) to input (pumping power). The results are summarized in Table 2. It was found that even though straight tube offers the smallest heat transfer rate, surprisingly it provides the highest figure of merit. This can be traced back to the fact that straight tube posses the smallest pressure drop, as shown in Table 2. Therefore, smaller heat transfer is compensated with even smaller pumping power requirement. On the
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other hand, while smaller radius helical tubes has the highest heat transfer rate, due to its triple pumping power requirement, it has the smallest figure of merit. Another key interest is entropy generation within the tube, as presented in Table 2. Notably, the difference between entropy generation in helical and straight tube for constant wall temperature is not as large as those for constant wall heat flux. Furthermore, it is found that helical coil generate lower entropy, highlighting the potential of helical tube in practical application despite higher pumping power requirement. 4. Conclusions Flow characteristic, heat transfer performance and entropy generation of a laminar flow inside helical tubes with various curvature diameters have been numerically investigated by utilizing a computational fluid dynamic (CFD) approach. Three curvature radiuses - 3 cm, 4 cm and 5 cm - were evaluated and compared with straight tube with identical cross-section. The result indicates the superior performance of helical tube heat transfer as compared to that of straight tube. In addition, smaller curvature radius was found to offers higher heat transfer performance at cost of higher pumping power requirement. Overall, despite their higher heat transfer rate, helical tubes scores low figure of merit due to its high pumping power requirement. However, from the second thermodynamics law view, helical tube generates lower entropy, indicating potential application for system with low inefficiency. Smaller curvature radius generates lower entropy despite inducing higher pressure drop. As a continuation, study on the heat transfer performance of helically coiled square double pipe heat exchanger is underway. The performance will be compared to that of circular cross-section. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
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