Scholarly article on topic 'Heat Transfer Enhancement and Performance of Solar Thermal Absorber Tubes with Circumferentially Non-uniform Heat Flux'

Heat Transfer Enhancement and Performance of Solar Thermal Absorber Tubes with Circumferentially Non-uniform Heat Flux Academic research paper on "Materials engineering"

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{"Heat transfer enhancement" / "Twisted tapes" / "Molten salt" / "Solar receiver tube"}

Abstract of research paper on Materials engineering, author of scientific article — C. Chang, C. Xu, Z.Y. Wu, X. Li, Q.Q. Zhang, et al.

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 (γ=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 γ 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.

Academic research paper on topic "Heat Transfer Enhancement and Performance of Solar Thermal Absorber Tubes with Circumferentially Non-uniform Heat Flux"

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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

aKey Laboratory of Solar Thermal Energy and Photovoltaic System, Institute of Electrical Engineering, Chinese Academy of Sciences, 6

Beiertiao,Zhongguancun, Beijing, 100190, China bNorth China Electric Power University, 2 BeinongRoad,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 (y=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 y 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 (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of 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: chang21st@mail.iee.ac.cn

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

Nomenclature

C clearance ratios

c width of the twisted tape [mm]

S specific heat at constant pressure [ kJ/ (kg ■ K) ]

P density [ kgfm ]

L length of the solar receiver tube [mm]

D diameter of the outer tube [mm]

d diameter of the inner tube [mm]

H intercept of twisted tape [mm]

rs,i radius of the outer tube [mm]

rs,o radius of the inner tube [mm]

A thermal conductivity [ W/(m ■ K) ]

M dynamic viscosity [ mPa ■ s ]

Re Reynolds number [ UD!J v ]

Pr Prandtl number [ pvcp/ X ]

m mass flow rate [ kg/s ]

Nu Nusselt number at inside surface [ hDtJXf ]

T temperature [k]

f friction factor

q the heat flux on tube surface [W/tf ]

u the radial velocity [m/s]

v the circumferential velocity [m/s]

w the axial velocity [m/s]

e circular angle of cross-section [degree]

r diffusion coefficient

S source term

general variable

r 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 auto-tracking 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 °C 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

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.l.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 c>,the width of the twisted tape is c. Intercept H is the 180° twist length. The numerical analysis is made for twisted tape at six different twist ratios y ( y= 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.

So far receiver tuhc

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.

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 (KN0340% wt+ NaN0360%wt) will vary with temperature[25], this study considers the effects of the variable properties of molten salt.

> = 2090 - 0.636T Cp = 1443 + 0.172T

<2 = 0.443 +1.9 x 10~4 T (1)

H = 22.714 - 0.12T + 2.28 x 10~4T2 -1.474 x 10"7 T3 Pr = 69.072 19 - 0.365 15T + 6.9 x 10"4T2 - 4.461x 107T3

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/m3, the thermal conductivity 16.3 W/(m• K) ,and specific heat capacity 0.505 kJI (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 1093 °C.

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) S (mm) 7 C

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

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.

— (p<t>) + div • (pu$) = div ■ (rgrad </>) + S (2)

The boundary conditions are list as:

À8T dr

= 0, d e (0, -) u (— ,2m)

2 2 (3)

T (r, 9,0) = To

u(r,0,0) = v(r ,6>,0) = 0 w(r,6,0) = 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) k-s 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 than10~6. 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<y+<106.7. Different mass flow rate are calculated and the range of Reynolds number 7485-30,553.

3. Analysis of the results and discussion

3.1. Effect of the clearance ratio C

The results when H is the same, the heat transfer and flow in solar receiver tube with five different twisted tapes : Tube#1 is smooth tube with C=1, Tube#2 with C=0.7, Tube#3 with C=0.5, Tube#4 with C=0.2, Tube#5 is tight-fit with C=0 are studied. Heat flux q is 600kW/tf, 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. 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 950

Tube#1

Tube#2

♦ Tube#3

■ xXA ■ Tube#4

♦ . X ♦ XA " X A ♦ #X ♦ Tube#5 ■ X A ■

0 5000 10000 15000 20000 25000 30000 35000 40000 Re

>1000 950

XX* ♦

AX X A ■ aX X A w ♦X

Tube#1 Tube#2 Tube#3 Tube#4 ♦ Tube#5

5000 10000 15000 20000 25000 30000 35000 40000 Re

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.

Tube#2 Tube#3 Tube#4 Tube#5

Xw y y y A A A A

X X X X X A A A A A

10000 20000 30000 40000

Tube#2

Tube#3

Tube#4

Tube#5

X ♦ ♦ A X X x ♦x ♦x

A X X X x

■ * A A ▲

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 y

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 y=12.5, Tube#6 with twisted ratio y=5, Tube#7 with twisted ratio y=2.5 are studied. Heat flux q is 600kW/m2, 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 y to maximum tube wall temperature, maximum molten salt film temperature, Nusselt number Nu and friction factor f are analyzed.

Fig.6 shows when twisted ratio y 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.

Tube#5 Tube#6 □ Tube#7

10000 15000

fe 800

Tube#5 Tube#6 □ Tube#7

10000 15000

Fig.6. Effects of twisted ratio y to the maximum temperature of (a) tube wall; (b) molten salt

Fig.7a shows that with twisted ratio y decrease, heat transfer in the receiver tube is significantly enhanced, when twisted ratio y=2.5, Nusselt number can be nearly 2.9 times than smooth tube. Fig.7b shows the friction factor increase significantly with twisted ratio y decrease, especially when twisted ratio y=2.5 the friction factor jumped increase to around 2.5 times than smooth tube, that means the pump power consumption will increase significantly.

♦ Tube#5

• Tube#6 □ Tube#7

10000 15000 Re

Fig. 7. Effects of twisted ratio y to (a) Nusselt number; (b) friction factor

Tube#5 • Tube#6 □ Tube#7

10000 15000 Re

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 y decrease, especially when y=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 y slow down with Reynolds number increase. (4) The friction factor increase with the decrease of clearance ratios C and twisted ratio y. That means more pump consumption will need with heat transfer enhancement. Optimization of the clearance ratios C and twisted ratio y is needed to obtain a good effect of heat transfer enhancement.

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.

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