- Email: [email protected]
Heat Transfer Enhancement and Performance of Solar Thermal Absorber Tubes with Circumferentially Non-uniform Heat Flux
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 69 (2015) 320 – 327
International Conference on Concentrating Solar Power and Chemical Energy Systems, SolarPACES 2014
Heat transfer enhancement and performance of solar thermal absorber tubes with circumferentially non-uniform heat flux C.Changa*, C.Xub, Z.Y.Wua, X.Lia, Q.Q.Zhanga, Z.F.Wanga a
Key Laboratory of Solar Thermal Energy and Photovoltaic System, Institute of Electrical Engineering, Chinese Academy of Sciences, 6 Beiertiao,Zhongguancun, Beijing, 100190, China b North China Electric Power University, 2 Beinong Road,Changping District,Beijing, 102206,China
Abstract A numerical study was undertaken for investigating the heat transfer enhancement in a molten salt solar receiver tube with the twisted tapes. Various parameters of twisted tapes are studied in this paper. Comparisons of the Nusselt number and friction factor of twisted tape with previous correlation are made to evaluate the turbulence models used. Effects of the clearance ratios (C=0 (tight fit), 0.2, 0.5, 0.7 and 1) and twist ratios (Ȗ=2.5, 5.0, 12.5, 15.6, 25, 41.7) on heat transfer rate (Nu), friction factor (f) are examined under non-uniform heat flux using molten salt as the testing fluid. Furthermore, the influence of grid generation on prediction results is also reported. Numerical calculations were performed with FLUENT 6.3.2 code, in the range of Reynolds number 7485-30553. The results show that the insert twisted tape can significantly improve the uniformity of temperature distribution of tube wall and molten salt. The decreases of clearance rate C and twisted rate Ȗ can enhance the heat transfer effectively. Especially when clearance rate C=0, that is the heat transfer enhancement effect with tight-fit twisted tape is the most significant. But at the same time, the decreases of clearance rate and twisted rate also lead to increase the friction factor. These methods and results can be extended to the heat transfer enhancement of all the solar concentrated receivers. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
© 2015 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer reviewbybythe thescientific scientific conference committee of SolarPACES 2014responsibility under responsibility Peer review conference committee of SolarPACES 2014 under of PSE AGof PSE AG. Keywords: Heat transfer enhancement; Twisted tapes; Molten salt; Solar receiver tube
* Corresponding author. Tel.: +86-10-82671373; fax: +.86-10-62587946. E-mail address: [email protected]
1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of PSE AG doi:10.1016/j.egypro.2015.03.036
C. Chang et al. / Energy Procedia 69 (2015) 320 – 327
321
Nomenclature C c
clearance ratios width of the twisted tape [mm]
cp
specific heat at constant pressure [ kJ kg K ]
H rs ,i
density [ kg m3 ] length of the solar receiver tube [mm] diameter of the outer tube [mm] diameter of the inner tube [mm] intercept of twisted tape [mm] radius of the outer tube [mm]
rs ,o
radius of the inner tube [mm]
O
thermal conductivity [ W m K ] dynamic viscosity [ mPa s ] Reynolds number [ UDs ,i Q ] Prandtl number [ UQ c p O f ]
U L D d
P Re Pr
m Nu
T
f q u v w T * S
I
¤
mass flow rate [ kg s ] Nusselt number at inside surface [ hDs ,i O f ] temperature [K] friction factor the heat flux on tube surface [W/] the radial velocity [m/s] the circumferential velocity [m/s] the axial velocity [m/s] circular angle of cross-section [degree] diffusion coefficient source term general variable twist ratios
1. Introduction Solar thermal power technology is one of the promising approaches to providing the world with clean, renewable and cost-competitive power on a large scale. In a solar thermal power plant, solar energy is collected by autotracking reflectors like dishes, parabolic-troughs or heliostats, and then transferred to thermal energy by a receiver, then delivered by a heat transfer fluid (HTF) into a steam generator to generate steam for producing electricity in a turbine[1-7]. Molten salt have recently been used as one of the most promising heat transfer and storage fluid at high temperature range of 450-565 ć with very low pressures[8-9]. The two-tank or thermocline heat storage characteristics of molten salt have been widely studied [10-13], while the convective heat transfer performances of molten salt as heat transfer fluid in solar receiver tubes with circumferentially non-uniform heat flux were investigated in very few literature. Wu et al.[14-15] investigated turbulent and transition region convective heat transfer with molten salt in a circular pipe, and found good agreement between the experimental data and the correlations by Hausen and Gnielinski. Lu et al.[16] studied the transition and turbulent convective heat transfer performances of molten salt in spirally grooved tube with experimental method, and found that Nusselt number of molten salt flow in spirally grooved tube was higher than that of smooth tube, and the groove height increment can remarkable enhance heat transfer. However, the heat transfer performance with non-uniform heat flux was not analyzed. Chang et al[17] and Yang et al[18] used the computational fluid dynamics method to reveal the turbulent
322
C. Chang et al. / Energy Procedia 69 (2015) 320 – 327
convective heat transfer performance of a solar receiver tube with circumferentially non-uniform heat flux, and the temperature distribution of the tube wall and molten salt is very non-uniform, and the formula of Dittus-Boelter and Sieder–Tate are not suitable for the heat transfer performance computation of a solar tube receiver. In actual solar thermal power plant, because the concentrated solar radiation distribution on the outside wall of the solar receiver tube is very high and circumferentially non-uniform, the failure of thermal stress and thermal distortion of receiver should be evaluated, and the overheating of tube materials and heat transfer fluid materials should be considered to avoid. There exist numerous studies on heat transfer enhancement by inserting fins, twisted tapes baffles and coil wires[19-24].The thermal boundary are all uniform heat flux around circumference. The outer surface of the solar receiver tube is generally circular tube, the insert twisted tapes method has a good application prospect for it can enhanced heat transfer without change the appearance of the solar receiver tube. In present paper, numerical analyses were conducted to investigate the heat transfer enhancement performances of molten salt in a twisted tape inserted tube with circumferentially non-uniform heat flux. Effects of the clearance ratio and twist rate were analysis in this research. 2. Physical model and mathematical foundation 2.1. Model and parameters The physical model of a single solar receiver tube with twisted tape insert is shown in Fig.1.The length between the tube inlet and outlet is L, the tube’s outer diameter is D, the tube’s inner diameter is d. The thickness of the twisted tape is Gthe width of the twisted tape is c. Intercept H is the 180etwist length. The numerical analysis is made for twisted tape at six different twist ratios ¤ (¤= H/c = 2.5, 5.0, 12.5, 15.6, 25, 41.7) and clearance ratios C (C=(d-c)/d=0 (tight fit), 0.2, 0.5, 0.7 and 1). The molten salt flows into the inlet, absorbs heat to increase the temperature and then flows out of the outlet.
Fig. 1. Geometry of a solar receiver tube with twisted tape inserts.
One side of tube called the heating surface receives heat flux from the solar radiation, and the other side is call adiabatic surface covered with heat insulator.Fig.2 shows the non-uniform heat flux on the heating surface.
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C. Chang et al. / Energy Procedia 69 (2015) 320 – 327
Fig. 2. Heat flux distribution scheme along the circumference direction.
Some assumptions are required for applying of the conventional flow equations and energy equations to model the heat transfer process in the receiver tube with twisted tape. The major assumptions are :(1) the flow through the twisted tape is turbulent and steady state,(2)natural convection and thermal radiation are neglected. Since the physical properties of Solar Salt (KNO340% wt+ NaNO360%wt) will vary with temperature[25], this study considers the effects of the variable properties of molten salt.
U 2090 0.636T ° °C p 1443 0.172T °° 4 ®O 0.443 1.9 u 10 T ° 4 2 7 3 ° P 22.714 0.12T 2.28 u 10 T 1.474 u 10 T ° °¯ Pr 69.072 19 0.365 15T 6.9 u 104 T 2 4.461 u 107 T 3
(1)
This study considers the impact of wall heat conduction on heat transfer. Alloy 625 is selected as the material of the receiver tube, with the density 8440 kg/mϢˈthe thermal conductivity 16.3 W m K , and specific heat capacity 0.505 kJ kg K . Alloy 625 is a Nickel-Chromium alloy used for its high strength, excellent fabricability and outstanding corrosion resistance during the temperature range from cryogenic to 1093ć. The geometry parameters of the receiver tube are shown in table1, tube diameter and thickness are close to Solar Two molten salt receiver. Table 1. Geometry parameters of the receiver tube. D (mm)
d (mm)
L(mm)
24
20
1000
Various parameters of twisted tapes are studied in this paper, as listed in tabe2. Table 2. Summary of the receiver tube with different twisted taps insert. Receiver tubes
c(mm)
H(mm)
G (mm)
Ȗ
Tube#1
0
0
0
-
1
Tube#2
6
250
1
41.7
0.7
Tube#3
10
250
1
25
0.5
Tube#4
16
250
1
15.6
0.2
Tube#5
20
250
1
12.5
0
Tube#6
20
100
1
5
0
Tube#7
20
50
1
2.5
0
C
324
C. Chang et al. / Energy Procedia 69 (2015) 320 – 327
2.2. Governing equations Based on the approximations, the governing differential equations used to describe the fluid flow and heat transfer in round tubes with twisted tape inserts are established. w (2) ( UI ) div ( U uI ) div (*grad I ) S wt The boundary conditions are list as: wT S 3S qmax , T [ , ] °O wr 2 2 r rs ,o ° ° wT S 3S °°O 0, T (0, ) ( , 2S) w r 2 2 (3) ® r rs ,o ° °T (r ,T ,0) T0 °u (r ,T ,0) v(r ,T , 0) 0 ° °¯ w(r ,T ,0) w0 2.3. Grids and solution The commercial CFD software Fluent6.3 is used to simulate the heat transfer process. Grid structure and density has an important influence on the calculation results and convergence rate. The grid generation is shown in Fig.3.
Fig. 3. Tube with twisted tape and grid generation (a) cross section; (b) axial direction.
To evaluate the pressure field, the pressure-velocity coupling algorithm SIMPLE is selected. Different turbulence models were considered and the Renormalized Group (RNG) N-H model has a better results. Second-order upwind format for the pressure and momentum, the solution convergence is met when the difference between normalized residual of the algebraic equation and the prescribed value is less than106. Grid independent solution is obtained by comparing the solution for different levels. The total numbers of elements used are approximately 100,000, 150,000, 200,000 and 250,000. Relatively stable results can be obtained when grids around 200,000(grids and elements number in Fig.3 case is 196,064 and 166,200 respectively). In all cases 49.7
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C. Chang et al. / Energy Procedia 69 (2015) 320 – 327
of five different cases for all tubes are 596g/s, 894g/s, 1193g/s, 1491g/s,1789g/s respectively. All flow are fully developed turbulent flow.The effects of clearance ratio C to maximum tube wall temperature, maximum molten salt film temperature, Nusselt number Nu and friction factor f are analyzed. Fig.4 shows when clearance ratios C decrease both the maximum temperature of tube wall and molten salt are decreased significantly. This means the insert twisted tape can dramatically enhance the heat transfer and improve the uniformity of the temperature field. 1000
1000 Tube#1
950
950 Tube#1
Tube#2
900
Tube#3
Tube#2
900
850
Tube#3 850
Tube#4
800
Tube#5
750
800
Tube#4 Tube#5
700 750
650 600
700 0
0
5000 10000 15000 20000 25000 30000 35000 40000
5000 10000 15000 20000 25000 30000 35000 40000
Fig. 4. Effects of clearance ratio C to the maximum temperature of (a) tube wall; (b) molten salt.
Fig.5a shows that with clearance ratios C decrease, heat transfer in the receiver tube is significantly enhanced, and tight-fit twisted tape(when C=0) can obtain the best enhancement results, Nusselt number can be 2.5 times than smooth tube. Fig.5b shows the fiction factor increase with clearance ratios decrease, the range changed less than 1.2 times to smooth tube.
4
1.2
Tube#2
Tube#2
Tube#3
Tube#3 Tube#4
Tube#4
3
Tube#5
Tube#5 1.1
2
1
1 0
10000
20000
30000
40000
0
10000
20000
30000
40000
Fig. 5. Effects of clearance ratio C to (a) Nusselt number; (b) friction factor.
3.2. Effect of the twisted ratio Ȗ The results when tight-fit C=0, the heat transfer and flow in solar receiver tube with three different twisted tapes : Tube#5 with twisted ratio Ȗ=12.5, Tube#6 with twisted ratio Ȗ=5, Tube#7 with twisted ratio Ȗ=2.5 are studied. Heat flux q is 600kW/, inlet temperature of molten salt T is 573K, and the mass flow rates of five different cases for all tubes are 596g/s, 894g/s, 1193g/s, 1491g/s,1789g/s respectively. The effects of twisted ratio Ȗ to maximum tube wall temperature, maximum molten salt film temperature, Nusselt number Nu and friction factor f are analyzed.
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C. Chang et al. / Energy Procedia 69 (2015) 320 – 327
Fig.6 shows when twisted ratio Ȗ decrease both the maximum temperature of tube wall and molten salt are decreased too. This means the heavy twisted tape can obtain a better enhancement result and can better improve the uniformity of the temperature field. 900
950 Tube#5
Tube#5
Tube#6
Tube#6
Tube#7
850
Tube#7
800
700
750
650
600 0
5000
10000
15000
20000
25000
0
5000
10000
15000
20000
25000
Fig.6. Effects of twisted ratio Ȗ to the maximum temperature of (a) tube wall; (b) molten salt
Fig.7a shows that with twisted ratio Ȗ decrease, heat transfer in the receiver tube is significantly enhanced, when twisted ratio Ȗ=2.5, Nusselt number can be nearly 2.9 times than smooth tube. Fig.7b shows the friction factor increase significantly with twisted ratio Ȗ decrease, especially when twisted ratio Ȗ=2.5 the friction factor jumped increase to around 2.5 times than smooth tube, that means the pump power consumption will increase significantly. 4
4
Tube#5
Tube#5
Tube#6
Tube#6 Tube#7
3
Tube#7
3
2
2
1
1 0
5000
10000
15000
20000
25000
0
5000
10000
15000
20000
25000
Fig. 7. Effects of twisted ratio Ȗ to (a) Nusselt number; (b) friction factor
4. Conclusions (1) The heat transfer in the receiver tube can be significantly enhanced with the clearance ratios C decrease, especially when C=0, the tight-fit twisted tape can obtain the best enhancement result. (2) The heat transfer in the receiver tube can be significantly enhanced with the twisted ratio Ȗ decrease, especially when Ȗ=2.5, the Nusselt number can be about 2.9 times than smooth tube. (3) Then enhancement effect of clearance ratios C and twisted ratio Ȗ slow down with Reynolds number increase. (4) The friction factor increase with the decrease of clearance ratios C and twisted ratio Ȗ. That means more pump consumption will need with heat transfer enhancement. Optimization of the clearance ratios C and twisted ratio Ȗ is needed to obtain a good effect of heat transfer enhancement.
C. Chang et al. / Energy Procedia 69 (2015) 320 – 327
Acknowledgements This work was supported by National Natural Science Foundation of China (51006096), National Basic Research Program of China (2010CB227104) and the Research Program of Beijing Municipal Science & Technology Commission (D121100001012001). Finally, the authors thank the reviewers for their helpful comments and suggestions. References [1] Sukhatme SP. Solar thermal power generation[C]. Proceedings of the Indian Academy of Sciences-Chemical Sciences.1997,109(6): 521-531. [2] Tsoutsos T, Gekas V, et al. Technical and economical evaluation of solar thermal power generation[J]. Renewable Energy.2003,28(6): 873886. [3] Behar O, et al.. A review of studies on central receiver solar thermal power plants[J]. Renewable and Sustainable Energy Reviews. 2013 ˄23˅: 12-39. [4] Romero M, Steinfeld A. Concentrating solar thermal power and thermochemical fuels[J]. Energy & Environmental Science. 2012.5(11) : 9234-9245. [5] Price H, Lüpfert E, Kearney D, et al..Advances in parabolic trough solar power technology[J]. Journal of Solar Energy Engineering. 2002,124 :109-125. [6] Concentrating solar power: its potential contribution to a sustainable energy future. The European Academies Science Advisory Council (EASAC) policy report 16, November; 2011. [7] Romero M, Buck R, Pacheco J E. An update on solar central receiver systems, projects and technologies[J]. Journal of Solar Energy Engineering. 2002,124:98–108. [8] Keamey D, Kelly B. Engineering Aspects of a molten salt heat transfer fluid in a trough solar field [J]ˊEnergy.2004˄29˅:861-870. [9] Pacheco JE, Dunkin SR. Assessment of molten salt solar central receiver freeze-up and recovery events. Solar Engineering.1996:85-90. [10] Herrmann U, Kelly B,Price H,et al. Two-tank molten salt storage for parabolic trough solar power plants[J].Energy.2004,29(6):883-893. [11] Jams EP, Steven KS, Kolb WJ, et al. Development of a molten salt thermocline thermal storage system for parabolic trough plants [J]. Journal of Solar Energy Engineering, 2002,124:153-159. [12] Yang Z, Garimella SV. Thermal analysis of solar thermal energy storage in a molten-salt thermocline[J].Solar Energy.2010(84):974-985. [13] Pacheco JE, Showalter SK,Kolb WJ. Thermocline thermal storage system for parabolic trough plants[J]. Journal of Solar Energy Engineering. 2002,124 :153-159. [14] Liu B, Wu YT, Ma CF, Ye M, Guo H. Turbulent convective heat transfer with molten salt in a circular pipe [J].International Communications in Heat and Mass Transfer. 2009(36):912-916. [15] Wu YT, Liu B, Ma CF, Guo H. Convective heat transfer in the laminar-turbulent transition region with molten salt in a circular tube[J]. Experimental Thermal and Fluid Science.2009(33):1128-1132. [16] Lu JF, Sheng XY, Ding J, Yang JP. Transition and turbulent convective heat transfer of molten salt in spirally grooved tube[J]. Experimental Thermal and Fluid Science.2013(47):180-185. [17] Chang C, Li X, Zhang QQ. Experimental and numerical study of the heat transfer characteristics in solar thermal absorber tubes with circumfenentially non-uniform heat flux[J]. Eenergy Procedia.2014(49):305-313. [18] Yang XP, Yang XX, Ding J, Shao YY, Fan HB. Numerical simulation study on the heat transfer characteristics of the tube receiver of the solar thermal power tower[J]. Applied Energy.2012(90):142-147. [19]Bharadwaj P., Khondge AD., Date AW. Heat transfer and pressure drop in a spirally grooved tube with twisted tape insert. International Journal of Heat and Mass Transfer, Volume 52, Issues 7–8, March 2009, Pages 1938-1944. [20] Yakut K, Alemdaroglu N, Sahin B, Celik C. Optimum design-parameters of a heat exchanger having hexagonal fins[J]. Applied Energy.2006;83:82–98. [21] Zhang Z, Yu Z, Fang X. An experimental heat transfer study for helically flowing outside petal-shaped finned tubes with different geometrical parameters[J]. Applied Thermal Engineering 2007;27:268–72. [22] Tijing LD, Pak BC, Baek BJ, Lee DH. A study on heat transfer enhancement using straight and twisted internal fins[J]. International Communication Heat Mass Transfer 2006;33:719–26. [23] Eimsa-ard S, Thianpong C, Promvonge P. Experimental investigation of heat transfer and flow friction in a circular tube fitted with regularly spaced twisted tape elements[J]. International Communication Heat Mass Transfer 2006;33:1225–33. [24] Chang SW, Jan YJ, Liou JS. Turbulent heat transfer and pressure drop in tube fitted with serrated twisted tape[J]. International Journal Thermal Science 2007;46:506–18. [25] Pacheco J E,Ralph M E,Chavez J M,et al. Results of molten salt panel and component experiments for solar central receivers:cold fill,freeze/thaw,thermal cycling and shock,and instrumentation tests,SAND94-2525 [R].New Mexico and Livermore,California:Sandia National Laboratories,1995.
327
ScienceDirect Energy Procedia 69 (2015) 320 – 327
International Conference on Concentrating Solar Power and Chemical Energy Systems, SolarPACES 2014
Heat transfer enhancement and performance of solar thermal absorber tubes with circumferentially non-uniform heat flux C.Changa*, C.Xub, Z.Y.Wua, X.Lia, Q.Q.Zhanga, Z.F.Wanga a
Key Laboratory of Solar Thermal Energy and Photovoltaic System, Institute of Electrical Engineering, Chinese Academy of Sciences, 6 Beiertiao,Zhongguancun, Beijing, 100190, China b North China Electric Power University, 2 Beinong Road,Changping District,Beijing, 102206,China
Abstract A numerical study was undertaken for investigating the heat transfer enhancement in a molten salt solar receiver tube with the twisted tapes. Various parameters of twisted tapes are studied in this paper. Comparisons of the Nusselt number and friction factor of twisted tape with previous correlation are made to evaluate the turbulence models used. Effects of the clearance ratios (C=0 (tight fit), 0.2, 0.5, 0.7 and 1) and twist ratios (Ȗ=2.5, 5.0, 12.5, 15.6, 25, 41.7) on heat transfer rate (Nu), friction factor (f) are examined under non-uniform heat flux using molten salt as the testing fluid. Furthermore, the influence of grid generation on prediction results is also reported. Numerical calculations were performed with FLUENT 6.3.2 code, in the range of Reynolds number 7485-30553. The results show that the insert twisted tape can significantly improve the uniformity of temperature distribution of tube wall and molten salt. The decreases of clearance rate C and twisted rate Ȗ can enhance the heat transfer effectively. Especially when clearance rate C=0, that is the heat transfer enhancement effect with tight-fit twisted tape is the most significant. But at the same time, the decreases of clearance rate and twisted rate also lead to increase the friction factor. These methods and results can be extended to the heat transfer enhancement of all the solar concentrated receivers. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
© 2015 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer reviewbybythe thescientific scientific conference committee of SolarPACES 2014responsibility under responsibility Peer review conference committee of SolarPACES 2014 under of PSE AGof PSE AG. Keywords: Heat transfer enhancement; Twisted tapes; Molten salt; Solar receiver tube
* Corresponding author. Tel.: +86-10-82671373; fax: +.86-10-62587946. E-mail address: [email protected]
1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of PSE AG doi:10.1016/j.egypro.2015.03.036
C. Chang et al. / Energy Procedia 69 (2015) 320 – 327
321
Nomenclature C c
clearance ratios width of the twisted tape [mm]
cp
specific heat at constant pressure [ kJ kg K ]
H rs ,i
density [ kg m3 ] length of the solar receiver tube [mm] diameter of the outer tube [mm] diameter of the inner tube [mm] intercept of twisted tape [mm] radius of the outer tube [mm]
rs ,o
radius of the inner tube [mm]
O
thermal conductivity [ W m K ] dynamic viscosity [ mPa s ] Reynolds number [ UDs ,i Q ] Prandtl number [ UQ c p O f ]
U L D d
P Re Pr
m Nu
T
f q u v w T * S
I
¤
mass flow rate [ kg s ] Nusselt number at inside surface [ hDs ,i O f ] temperature [K] friction factor the heat flux on tube surface [W/] the radial velocity [m/s] the circumferential velocity [m/s] the axial velocity [m/s] circular angle of cross-section [degree] diffusion coefficient source term general variable twist ratios
1. Introduction Solar thermal power technology is one of the promising approaches to providing the world with clean, renewable and cost-competitive power on a large scale. In a solar thermal power plant, solar energy is collected by autotracking reflectors like dishes, parabolic-troughs or heliostats, and then transferred to thermal energy by a receiver, then delivered by a heat transfer fluid (HTF) into a steam generator to generate steam for producing electricity in a turbine[1-7]. Molten salt have recently been used as one of the most promising heat transfer and storage fluid at high temperature range of 450-565 ć with very low pressures[8-9]. The two-tank or thermocline heat storage characteristics of molten salt have been widely studied [10-13], while the convective heat transfer performances of molten salt as heat transfer fluid in solar receiver tubes with circumferentially non-uniform heat flux were investigated in very few literature. Wu et al.[14-15] investigated turbulent and transition region convective heat transfer with molten salt in a circular pipe, and found good agreement between the experimental data and the correlations by Hausen and Gnielinski. Lu et al.[16] studied the transition and turbulent convective heat transfer performances of molten salt in spirally grooved tube with experimental method, and found that Nusselt number of molten salt flow in spirally grooved tube was higher than that of smooth tube, and the groove height increment can remarkable enhance heat transfer. However, the heat transfer performance with non-uniform heat flux was not analyzed. Chang et al[17] and Yang et al[18] used the computational fluid dynamics method to reveal the turbulent
322
C. Chang et al. / Energy Procedia 69 (2015) 320 – 327
convective heat transfer performance of a solar receiver tube with circumferentially non-uniform heat flux, and the temperature distribution of the tube wall and molten salt is very non-uniform, and the formula of Dittus-Boelter and Sieder–Tate are not suitable for the heat transfer performance computation of a solar tube receiver. In actual solar thermal power plant, because the concentrated solar radiation distribution on the outside wall of the solar receiver tube is very high and circumferentially non-uniform, the failure of thermal stress and thermal distortion of receiver should be evaluated, and the overheating of tube materials and heat transfer fluid materials should be considered to avoid. There exist numerous studies on heat transfer enhancement by inserting fins, twisted tapes baffles and coil wires[19-24].The thermal boundary are all uniform heat flux around circumference. The outer surface of the solar receiver tube is generally circular tube, the insert twisted tapes method has a good application prospect for it can enhanced heat transfer without change the appearance of the solar receiver tube. In present paper, numerical analyses were conducted to investigate the heat transfer enhancement performances of molten salt in a twisted tape inserted tube with circumferentially non-uniform heat flux. Effects of the clearance ratio and twist rate were analysis in this research. 2. Physical model and mathematical foundation 2.1. Model and parameters The physical model of a single solar receiver tube with twisted tape insert is shown in Fig.1.The length between the tube inlet and outlet is L, the tube’s outer diameter is D, the tube’s inner diameter is d. The thickness of the twisted tape is Gthe width of the twisted tape is c. Intercept H is the 180etwist length. The numerical analysis is made for twisted tape at six different twist ratios ¤ (¤= H/c = 2.5, 5.0, 12.5, 15.6, 25, 41.7) and clearance ratios C (C=(d-c)/d=0 (tight fit), 0.2, 0.5, 0.7 and 1). The molten salt flows into the inlet, absorbs heat to increase the temperature and then flows out of the outlet.
Fig. 1. Geometry of a solar receiver tube with twisted tape inserts.
One side of tube called the heating surface receives heat flux from the solar radiation, and the other side is call adiabatic surface covered with heat insulator.Fig.2 shows the non-uniform heat flux on the heating surface.
323
C. Chang et al. / Energy Procedia 69 (2015) 320 – 327
Fig. 2. Heat flux distribution scheme along the circumference direction.
Some assumptions are required for applying of the conventional flow equations and energy equations to model the heat transfer process in the receiver tube with twisted tape. The major assumptions are :(1) the flow through the twisted tape is turbulent and steady state,(2)natural convection and thermal radiation are neglected. Since the physical properties of Solar Salt (KNO340% wt+ NaNO360%wt) will vary with temperature[25], this study considers the effects of the variable properties of molten salt.
U 2090 0.636T ° °C p 1443 0.172T °° 4 ®O 0.443 1.9 u 10 T ° 4 2 7 3 ° P 22.714 0.12T 2.28 u 10 T 1.474 u 10 T ° °¯ Pr 69.072 19 0.365 15T 6.9 u 104 T 2 4.461 u 107 T 3
(1)
This study considers the impact of wall heat conduction on heat transfer. Alloy 625 is selected as the material of the receiver tube, with the density 8440 kg/mϢˈthe thermal conductivity 16.3 W m K , and specific heat capacity 0.505 kJ kg K . Alloy 625 is a Nickel-Chromium alloy used for its high strength, excellent fabricability and outstanding corrosion resistance during the temperature range from cryogenic to 1093ć. The geometry parameters of the receiver tube are shown in table1, tube diameter and thickness are close to Solar Two molten salt receiver. Table 1. Geometry parameters of the receiver tube. D (mm)
d (mm)
L(mm)
24
20
1000
Various parameters of twisted tapes are studied in this paper, as listed in tabe2. Table 2. Summary of the receiver tube with different twisted taps insert. Receiver tubes
c(mm)
H(mm)
G (mm)
Ȗ
Tube#1
0
0
0
-
1
Tube#2
6
250
1
41.7
0.7
Tube#3
10
250
1
25
0.5
Tube#4
16
250
1
15.6
0.2
Tube#5
20
250
1
12.5
0
Tube#6
20
100
1
5
0
Tube#7
20
50
1
2.5
0
C
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2.2. Governing equations Based on the approximations, the governing differential equations used to describe the fluid flow and heat transfer in round tubes with twisted tape inserts are established. w (2) ( UI ) div ( U uI ) div (*grad I ) S wt The boundary conditions are list as: wT S 3S qmax , T [ , ] °O wr 2 2 r rs ,o ° ° wT S 3S °°O 0, T (0, ) ( , 2S) w r 2 2 (3) ® r rs ,o ° °T (r ,T ,0) T0 °u (r ,T ,0) v(r ,T , 0) 0 ° °¯ w(r ,T ,0) w0 2.3. Grids and solution The commercial CFD software Fluent6.3 is used to simulate the heat transfer process. Grid structure and density has an important influence on the calculation results and convergence rate. The grid generation is shown in Fig.3.
Fig. 3. Tube with twisted tape and grid generation (a) cross section; (b) axial direction.
To evaluate the pressure field, the pressure-velocity coupling algorithm SIMPLE is selected. Different turbulence models were considered and the Renormalized Group (RNG) N-H model has a better results. Second-order upwind format for the pressure and momentum, the solution convergence is met when the difference between normalized residual of the algebraic equation and the prescribed value is less than106. Grid independent solution is obtained by comparing the solution for different levels. The total numbers of elements used are approximately 100,000, 150,000, 200,000 and 250,000. Relatively stable results can be obtained when grids around 200,000(grids and elements number in Fig.3 case is 196,064 and 166,200 respectively). In all cases 49.7
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of five different cases for all tubes are 596g/s, 894g/s, 1193g/s, 1491g/s,1789g/s respectively. All flow are fully developed turbulent flow.The effects of clearance ratio C to maximum tube wall temperature, maximum molten salt film temperature, Nusselt number Nu and friction factor f are analyzed. Fig.4 shows when clearance ratios C decrease both the maximum temperature of tube wall and molten salt are decreased significantly. This means the insert twisted tape can dramatically enhance the heat transfer and improve the uniformity of the temperature field. 1000
1000 Tube#1
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Fig. 4. Effects of clearance ratio C to the maximum temperature of (a) tube wall; (b) molten salt.
Fig.5a shows that with clearance ratios C decrease, heat transfer in the receiver tube is significantly enhanced, and tight-fit twisted tape(when C=0) can obtain the best enhancement results, Nusselt number can be 2.5 times than smooth tube. Fig.5b shows the fiction factor increase with clearance ratios decrease, the range changed less than 1.2 times to smooth tube.
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Fig. 5. Effects of clearance ratio C to (a) Nusselt number; (b) friction factor.
3.2. Effect of the twisted ratio Ȗ The results when tight-fit C=0, the heat transfer and flow in solar receiver tube with three different twisted tapes : Tube#5 with twisted ratio Ȗ=12.5, Tube#6 with twisted ratio Ȗ=5, Tube#7 with twisted ratio Ȗ=2.5 are studied. Heat flux q is 600kW/, inlet temperature of molten salt T is 573K, and the mass flow rates of five different cases for all tubes are 596g/s, 894g/s, 1193g/s, 1491g/s,1789g/s respectively. The effects of twisted ratio Ȗ to maximum tube wall temperature, maximum molten salt film temperature, Nusselt number Nu and friction factor f are analyzed.
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Fig.6 shows when twisted ratio Ȗ decrease both the maximum temperature of tube wall and molten salt are decreased too. This means the heavy twisted tape can obtain a better enhancement result and can better improve the uniformity of the temperature field. 900
950 Tube#5
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Fig.6. Effects of twisted ratio Ȗ to the maximum temperature of (a) tube wall; (b) molten salt
Fig.7a shows that with twisted ratio Ȗ decrease, heat transfer in the receiver tube is significantly enhanced, when twisted ratio Ȗ=2.5, Nusselt number can be nearly 2.9 times than smooth tube. Fig.7b shows the friction factor increase significantly with twisted ratio Ȗ decrease, especially when twisted ratio Ȗ=2.5 the friction factor jumped increase to around 2.5 times than smooth tube, that means the pump power consumption will increase significantly. 4
4
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Fig. 7. Effects of twisted ratio Ȗ to (a) Nusselt number; (b) friction factor
4. Conclusions (1) The heat transfer in the receiver tube can be significantly enhanced with the clearance ratios C decrease, especially when C=0, the tight-fit twisted tape can obtain the best enhancement result. (2) The heat transfer in the receiver tube can be significantly enhanced with the twisted ratio Ȗ decrease, especially when Ȗ=2.5, the Nusselt number can be about 2.9 times than smooth tube. (3) Then enhancement effect of clearance ratios C and twisted ratio Ȗ slow down with Reynolds number increase. (4) The friction factor increase with the decrease of clearance ratios C and twisted ratio Ȗ. That means more pump consumption will need with heat transfer enhancement. Optimization of the clearance ratios C and twisted ratio Ȗ is needed to obtain a good effect of heat transfer enhancement.
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Acknowledgements This work was supported by National Natural Science Foundation of China (51006096), National Basic Research Program of China (2010CB227104) and the Research Program of Beijing Municipal Science & Technology Commission (D121100001012001). Finally, the authors thank the reviewers for their helpful comments and suggestions. References [1] Sukhatme SP. Solar thermal power generation[C]. Proceedings of the Indian Academy of Sciences-Chemical Sciences.1997,109(6): 521-531. [2] Tsoutsos T, Gekas V, et al. Technical and economical evaluation of solar thermal power generation[J]. Renewable Energy.2003,28(6): 873886. [3] Behar O, et al.. A review of studies on central receiver solar thermal power plants[J]. Renewable and Sustainable Energy Reviews. 2013 ˄23˅: 12-39. [4] Romero M, Steinfeld A. Concentrating solar thermal power and thermochemical fuels[J]. Energy & Environmental Science. 2012.5(11) : 9234-9245. [5] Price H, Lüpfert E, Kearney D, et al..Advances in parabolic trough solar power technology[J]. Journal of Solar Energy Engineering. 2002,124 :109-125. [6] Concentrating solar power: its potential contribution to a sustainable energy future. The European Academies Science Advisory Council (EASAC) policy report 16, November; 2011. [7] Romero M, Buck R, Pacheco J E. An update on solar central receiver systems, projects and technologies[J]. Journal of Solar Energy Engineering. 2002,124:98–108. [8] Keamey D, Kelly B. Engineering Aspects of a molten salt heat transfer fluid in a trough solar field [J]ˊEnergy.2004˄29˅:861-870. [9] Pacheco JE, Dunkin SR. Assessment of molten salt solar central receiver freeze-up and recovery events. Solar Engineering.1996:85-90. [10] Herrmann U, Kelly B,Price H,et al. Two-tank molten salt storage for parabolic trough solar power plants[J].Energy.2004,29(6):883-893. [11] Jams EP, Steven KS, Kolb WJ, et al. Development of a molten salt thermocline thermal storage system for parabolic trough plants [J]. Journal of Solar Energy Engineering, 2002,124:153-159. [12] Yang Z, Garimella SV. Thermal analysis of solar thermal energy storage in a molten-salt thermocline[J].Solar Energy.2010(84):974-985. [13] Pacheco JE, Showalter SK,Kolb WJ. Thermocline thermal storage system for parabolic trough plants[J]. Journal of Solar Energy Engineering. 2002,124 :153-159. [14] Liu B, Wu YT, Ma CF, Ye M, Guo H. Turbulent convective heat transfer with molten salt in a circular pipe [J].International Communications in Heat and Mass Transfer. 2009(36):912-916. [15] Wu YT, Liu B, Ma CF, Guo H. Convective heat transfer in the laminar-turbulent transition region with molten salt in a circular tube[J]. Experimental Thermal and Fluid Science.2009(33):1128-1132. [16] Lu JF, Sheng XY, Ding J, Yang JP. Transition and turbulent convective heat transfer of molten salt in spirally grooved tube[J]. Experimental Thermal and Fluid Science.2013(47):180-185. [17] Chang C, Li X, Zhang QQ. Experimental and numerical study of the heat transfer characteristics in solar thermal absorber tubes with circumfenentially non-uniform heat flux[J]. Eenergy Procedia.2014(49):305-313. [18] Yang XP, Yang XX, Ding J, Shao YY, Fan HB. Numerical simulation study on the heat transfer characteristics of the tube receiver of the solar thermal power tower[J]. Applied Energy.2012(90):142-147. [19]Bharadwaj P., Khondge AD., Date AW. Heat transfer and pressure drop in a spirally grooved tube with twisted tape insert. International Journal of Heat and Mass Transfer, Volume 52, Issues 7–8, March 2009, Pages 1938-1944. [20] Yakut K, Alemdaroglu N, Sahin B, Celik C. Optimum design-parameters of a heat exchanger having hexagonal fins[J]. Applied Energy.2006;83:82–98. [21] Zhang Z, Yu Z, Fang X. An experimental heat transfer study for helically flowing outside petal-shaped finned tubes with different geometrical parameters[J]. Applied Thermal Engineering 2007;27:268–72. [22] Tijing LD, Pak BC, Baek BJ, Lee DH. A study on heat transfer enhancement using straight and twisted internal fins[J]. International Communication Heat Mass Transfer 2006;33:719–26. [23] Eimsa-ard S, Thianpong C, Promvonge P. Experimental investigation of heat transfer and flow friction in a circular tube fitted with regularly spaced twisted tape elements[J]. International Communication Heat Mass Transfer 2006;33:1225–33. [24] Chang SW, Jan YJ, Liou JS. Turbulent heat transfer and pressure drop in tube fitted with serrated twisted tape[J]. International Journal Thermal Science 2007;46:506–18. [25] Pacheco J E,Ralph M E,Chavez J M,et al. Results of molten salt panel and component experiments for solar central receivers:cold fill,freeze/thaw,thermal cycling and shock,and instrumentation tests,SAND94-2525 [R].New Mexico and Livermore,California:Sandia National Laboratories,1995.
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