Enhanced heat transfer in a parabolic trough solar receiver by inserting rods and using molten salt as heat transfer fluid

Applied Energy 220 (2018) 337–350

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Enhanced heat transfer in a parabolic trough solar receiver by inserting rods and using molten salt as heat transfer fluid☆

T

⁎

Chun Changa,b, Adriano Sciacovellib, Zhiyong Wua, , Xin Lia, Yongliang Lib, Mingzhi Zhaoc, Jie Denga, Zhifeng Wanga, Yulong Dingb a

Key Laboratory of Solar Thermal Energy and Photovoltaic System, Institute of Electrical Engineering, Chinese Academy of Sciences, Haidian District, Beijing 100190, China Birmingham Centre for Energy Storage, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom c College of Energy and Power Engineering, Inner Mongolia University of Technology, Hohhot 010051, China b

H I GH L IG H T S

three-dimensional model for • Aparabolic trough receiver with rod

G R A P H I C A L A B S T R A C T

a

A typical parabolic trough solar collector system with damaged receiver tubes, the calculated non-uniform heat flux distribution, and the schematic structure of a parabolic trough receiver.

insert is developed.

of the rod insert key para• Effects meters are investigated. comprehensive integrated perfor• Amance factor is introduced and examined.

mechanism of molten salt heat • The transfer enhancement is revealed. rod parameters are re• Optimum commended.

A R T I C LE I N FO

A B S T R A C T

Keywords: Non-uniform heat flux Parabolic trough receiver Concentric rod and eccentric rod inserts Performance evaluation criteria Integrated performance factor Molten salt

With the aim to enhance the reliability and overall heat transfer performance of a parabolic trough receiver, concentric rod and eccentric rod are introduced as turbulators, and the flow and convective heat transfer characteristics of molten salt in a parabolic trough receiver are analyzed. A three-dimensional model was developed and has been validated with experimental results and empirical equations. Highly non-uniform heat flux was provided by a novel parabolic trough collector. The result shows that both concentric rod insert and eccentric rod insert can enhance the heat transfer performance effectively. For a parabolic trough receiver with a concentric rod insert, with the increasing of dimensionless diameter B, the normalized Nusselt number is about 1.10 to 7.42 times over a plain parabolic trough receiver. The performance evaluation criteria can't reasonably evaluate the effect of B growth on the comprehensive heat transfer performance. By introducing integrated performance factor, it can give a reasonable solution, and it shows that the integrated performance factor has a significance decreases with the increase of Reynolds number when B is larger than 0.8. With B increasing, the integrated performance factor of parabolic trough receiver with concentric rod insert decreasing under a certain Reynolds number. For an eccentric rod insert, the performance evaluation criteria and the integrated performance factor decrease with the increasing of Reynolds number under a certain dimensionless eccentricity H. The

☆ ⁎

The short version of the paper was presented at ICAE2017, Aug 21–24, Cardiff, UK. This paper is a substantial extension of the short version of the conference paper. Corresponding author.

https://doi.org/10.1016/j.apenergy.2018.03.091 Received 10 December 2017; Received in revised form 8 March 2018; Accepted 25 March 2018 0306-2619/ © 2018 Elsevier Ltd. All rights reserved.

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performance evaluation criteria decreases from about 1.84 to 1.68 times over a plain parabolic trough receiver when H is 0.8. Moreover, the temperature distribution can be uniformed and the maximum temperature on the absorber tube also can be remarkably reduced with the increasing of B and H under a certain Reynolds number, which helps to reduce the thermal deflection and increase the reliability for a parabolic trough receiver.

1. Introduction

of the DNI. However, the absorber tube in these approaches is ideal smooth plain tube and cannot be used effectively to resolve the issues of overheating and structure rupture in a PTR working with high temperature MS. To enhance the convective heat transfer in PTR, much research focuses on various techniques for the heat transfer enhancement in PTR with wavy or rough surfaces, usage of molten salt or nanofluids and installation of turbulator or swirl flow device inside the absorber tube [34,35]. Waghole et al. [36] made an investigation on the heat transfer and friction factor of silver nanofluid in PTR with twisted tape inserts by the experimental method. The experiments show that friction factor, Nusselt number, and enhancement efficiency of enhanced PTR are found to be 1.0–1.75 times, 1.25–2.10 times and 135–205%, respectively, over plain PTR. Reddy et al. [37,38] presented the experimental investigation of heat transfer of a PTR with porous disc enhanced according to ASHRAE 93-1986 test procedure. Six different receiver configurations are investigated. The results show that the porous disc enhanced receiver improves the performance of the PTR significantly. Xiao et al. [39] developed a novel double tube helical heat exchanger using MS as HTF and the heat transfer enhancement in a helical annular duct was achieved. The heat transfer enhancement ratio was found to be enlarged by smaller inner-outer-pipe diameter ratio and lower molten salt temperature. Wang et al. [40] numerically studied the effect of inserting metal foams in PTR on heat transfer. The result shows that for constant layout and porosity, the geometrical parameter affects on the thermal performance greatly. While for constant layout and geometrical parameter, the porosity affects on the thermal performance slightly. Wang et al. [41] numerically investigated heat transfer enhancement of PTR with a symmetric outward corrugated tube. The effective heat transfer coefficient can be enhanced up to 8.4% and maximum thermal strain can be decreased up to 13.1%. Huang et al. [42] numerically studied the fully developed turbulent convective heat transfer in dimpled tubes of PTR. The results indicate that Nusselt number and the average friction factor in dimpled receiver tubes under non-uniform heat flux are larger than those under uniform heat flux and the deep dimples are far superior to the shallow dimples for the same Grashof number. Lu et al. [43–45] experimentally investigated the convective heat transfer of ternary nitrate salt in a transversely grooved tube and spirally grooved tube with uniform heat flux. Results show that Nusselt number of transversely grooved and spirally grooved tube is remarkably higher than that of the plain tube, and molten salt should avoid worsening phenomena for high-temperature difference and low heat transfer coefficient. Chen et al. [46] experimentally investigated the enhanced heat transfer of mixed MS in a transversally corrugated tube with three different sets of parameters and found the drag coefficient for transversally corrugated tubes is larger than that of a smooth tube. In these studies, although the enhanced heat transfer methods such as metal foam and porous disc can achieve higher heat transfer intensification, they all cannot meet the operation of MS draining when MS is used as HTF, MS will freeze in PTR if it is not completely drained. Moreover, due to the limitation of industrial processing and manufacturing costs, the structure and the processing technology of the PTR should not be too complex. Therefore, there is little possibility that the enhanced heat transfer methods such as a corrugated tube, a spiral tube or an internal finned tube can be easily used in a PTR. To make matters worse, the corrugated tube, spiral tube will aggravate the thermal bending deformation damage of the PTR with extreme non-uniform heat flux. The concentric rod and eccentric rod inserts are simple and feasible

Energy utilization and ecological environment are the hot issues in the current global social development [1–3], and almost 90% of the global energy budget centering around thermal energy conversion and storage [4–6]. Solar energy has been regarded as a promising inexhaustible source of clean energy due to its abundance and easy accessibility [7,8]. As a kind of sustainable and compatible electric generating technology, concentrated solar power (CSP) can solve the mismatch between energy generating supplies and user demand [9–12]. The International Energy Agency (IEA) predicts that CSP could meet up to 12% of the global electricity demand by 2050 [13]. Among the various CSP collection technologies, parabolic trough collector (PTC) is the most mature and widely used technology in the past decades [14–19]. However, due to the maximum operating temperature of heat transfer oil is less than 666 K, the further improvement of power generation efficiency has encountered bottlenecks. Increasing the concentration ratio (more than 100) and operating temperature (more than 700 K) are the key approaches to further improve the efficiency of PTC system. Heat transfer oil cannot work safely over 673 K to avoid decomposition [20]. Molten salt (MS) [21] has gained a lot of research and application due to its advantages of high working temperature (higher than 830 K), large specific heat, high thermal stability, low vapor pressure and low cost, etc. PTC with MS technology received special attention in recent years for its high performance and low-cost aspects [22]. A typical PTC system consists of an array of parabolic shaped mirrors to track the sun and concentrate the direct normal irradiance (DNI) onto parabolic trough receiver (PTR) tubes which are fixed at the PTC’s focal line, as shown in Fig. 1a. The heat flux distributed on the PTR surface is extremely high and non-uniform, as presented in Fig. 1b. The PTR plays a vital role in absorbing solar energy and convert it into high-temperature heat, the principle structure of a PTR is illustrated in Fig. 1c. The overheating of the receiver tube and heat transfer fluid (HTF) and the induce structure rupture due to excessive thermal deformation are most likely to happen when the system works at high-temperature [23–25]. PRT typically account for 30% of the cost of a solar field. In order to avoid these damages, the issues of convective heat transfer and fluid flow of MS in PTR with extremely high and non-uniform heat flux are widely concerned [26,27]. Liu et al. [28] and Wu et al. [29] experimentally studied the MS convective heat transfer in a circular tube and obtained serval heat transfer correlations with circumferentially uniform heat flux. However, the non-uniform heat flux thermal boundary of the PTR was neglect in these studies. Wu et al. [30] also experimentally investigated the heat loss of a PTC with a new developed low-melting-point MS. The convective heat transfer correlations were calculated with Reynolds number between 10,000 and 21,000, and Prandtl number between 9.5 and 12.2. Results show that the heat transfer coefficients with low melting point MS demonstrate good agreement with Gnielinski equation and Sieder-Tate equation. Xiong et al. [31] numerically investigated the thermal performance of heat loss of a PTR under steady state. The results show that annular pressure and selective coatings make greater influence to heat loss than wind speed. Cheng et al. [32] developed a 3D optical model to study the thermal performance of a PTC, the results show that the method and model are reliable to simulate PTC concentrating solar collectors. Wang et al. [33] numerically investigated the performance of a PTR using molten salt as HTF by a coupled three-dimensional simulation and found that the circumferential temperature difference (CTD) of the PTR increases with the rising 338

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Nomenclature B cp D DNI e f F Gk Gr h H I L m Nu P Pr q Q r R Re S St T u W

y+ z

dimensionless diameter specific heat, J kg−1 K−1 hydraulic diameter, m direct normal irradiance, W m−2 eccentricity, m friction factor focal length, m production of turbulent viscosity Grashof number, Gr = g·β ·ΔT ·D3 ·ν−2 convective heat transfer coefficient, W m−2 K−1 dimensionless eccentricity turbulence intensity length, m mass flow rate, kg s−1 Nusselt number, Nu = h·D·λ−1 pressure, Pa Prandtl number, Pr = ν ·α −1 heat flux, W m−2 thermal power, W radius, m thermal resistance, K W−1 Reynolds number, Re = ρ ·u·D ·μ −3 source term Stanton number, St = Nu·Re−1 ·Pr −1 temperature, K velocity, m s−1 aperture width, m

dimensionless wall distance axial coordinates, m

Greek symbols thermal diffusivity of the fluid, m2 s−1 fluid thermal expansion coefficient, K−1 density, kg m−3 dynamic viscosity of the fluid thickness, m kinematic viscosity, m2 s−1 turbulent dissipation rate kinetic energy central angle, · heat conductivity, W m−1 K−1 turbulent Prandtl number

α β ρ μ δ ν ε κ θ λ σ Subscripts a Bl cond conv g in out p rad rod

absorber tube Blasius conduction convection Glass tube inlet outlet plain tube radiation rod

Usually, the conduction and convection heat transfer in the vacuum gap can be ignored to a qualified PTR. The non-uniform heat flux distribution of the axial direction of a PTR can be ignored, the heat flux distribution contours by the normal 5.77 m PTC is shown in Fig. 2(c). Fig. 2(d) shows the non-uniform heat flux on the cross-section of a PTR from a novel 6.77 m PTC and a normal 5.77 m PTC. It can be seen that the extreme heat flux of the 6.77 m PTC is significantly higher than that of the 5.77 m. Fig. 3 is the geometry of a plain PTR, and the enhanced PTR with concentric rod and eccentric rod inserts. The characteristics of the PTC, PTR in this study are presented in Table 1. The characteristics of the enhanced PTR with a concentric rod are listed in Table 2, and specifications of the studied eccentric rod inserts are shown in Table 3.where dimensionless diameter B = rrod/(ra−δa) .where dimensionless eccentricity H = e /(ra−δa−rrod ) . The composition of MS is sodium nitrate (NaNO3, 60 wt%) and potassium nitrate (KNO3, 40 wt%). The physical properties of it are listed in Table 4 (300–600 °C, t is in °C):

choices for heat transfer enhancement in this situation [47,48], this kind of structure will not cause MS discharge problems while enhancing heat transfer. It can also help to improve the thermal bending resistance of a PTR. While in the previous studies of this topic, MS only flows in the inner tube and does not take into account the influence of nonuniform heat flux. In the present paper, three-dimensional investigations on the PTR by inserting a concentric rod and an eccentric rod is performed. MS flows between the PTR absorber tube and the rod insert. The effect of the heat flux, diameter ration and eccentricity ratio on convective heat transfer and fluid flow are analyzed. A comparative analysis of comprehensive heat transfer enhancement is also carried out. The results of this study are essential for the design improvement of a PTR with MS technology as it can increase the efficiency and reliability at the same time. 2. Physical models Fig. 1(c) shows the schematic structure of a PTR made of a metal absorber tube covered with a selective coating, bellows at two ends, and a glass envelope, respectively. There is a vacuum gap between the glass envelope and absorber tube. The absorber tube absorbs solar energy and transforms it into thermal energy and the selective coating enhances this conversion. Bellows connects the absorber tube and the glass envelope to an enclosed vacuum space to reduce conduction and convection heat loss. Fig. 2(a) and (b) present the energy balance model and the thermal resistance model on the PTR cross-section. The concentrated solar flux Qsol travels through the glass envelope and distributes on the absorber tube surface. A small part of the solar energy is absorbed by the glass as Qabs, some parts of the solar energy are released to the environment through conduction, convection, and radiation as Qloss. Most of the solar energy is absorbed by the selective coating and converts it into high-temperature heat, then be conducted through the absorber tube and eventually taken away by HTF through convection as Qobtain.

3. Numerical approach 3.1. Mathematical model and boundary conditions Based on the assumption that the fluid flow and heat transfer are fully turbulent (Reynolds number is greater than 1 × 10 4 ) and steadystate, the coupled heat transfer within the PTR is calculated by finite volume method (FVM). The three-dimensional Reynolds average Navier-Stokes (RANS) governing equations can be presented as follows [49]: Continuity equation

∂ (ρui ) = 0 ∂x i Momentum equation 339

(1)

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Fig. 1. (a) Parabolic trough collector with receiver tube; (b) Calculated spot distribution of a normal 5.77 m aperture width PTC;(c) Schematic structure of a PTR.

Fig. 2. (a) Energy balance model on the cross-section of a PTR; (b) thermal resistance network; (c) heat flux on the outer wall of a PTR; (d) heat flux on the crosssection of a PTR.

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Fig. 3. Geometry and grid of the plain parabolic trough receiver, with concentric rod and eccentric rod inserts. Table 1 Specifications of the studied PTC and PTR.

Table 3 Specifications of the studied PTR enhanced by an eccentric rod with different H under B = 0.6.

Symbol

W

F

L

rg

ra

δg

δa

Value (m)

6.77

1.71

4.060

0.12

0.035

0.003

0.003

∂uj ⎞ 2 ∂ ∂P ∂ ⎡ ∂u ∂u ⎤ + (ρui uj ) = − (μ + μt ) ⎜⎛ i + (μ + μt ) i δij⎥ + ρgi ⎟− ∂x i ∂x i ∂x j ⎢ ∂ ∂ ∂x i x x 3 j i ⎝ ⎠ ⎣ ⎦ (2)

Symbol

H1

H2

H3

H4

H5

H6

H e (m)

0.4 0.00512

0.6 0.00768

0.8 0.01024

−0.4 −0.00512

−0.6 −0.00768

−0.8 −0.01024

Table 4 Properties of MS. Property

Value

Unit

ρ cP λ μ

2090−0.636t 1443 + 0.172 t

22.714−0.120 t+ 2.281 × 10−4t 2−1.474 × 10−7t 3

kg/m3 J/kg·K W/m ·K mPa · s

Pr

69.07219−0.36515 t+ 6.9 × 10−4t 2−4.461 × 10−7t 3

—

Energy equation

μ ∂T ⎤ ∂ ∂ ⎡⎛ μ (ρui T ) = + t⎞ + Sh ⎥ ∂x i ∂x i ⎢ Pr σ T ⎠ ∂x i ⎦ ⎣⎝ ⎜

⎟

(3)

The turbulent kinetic energy k and its rate of dissipation ε are obtained from these equations:

μ ∂k ⎤ ∂ ∂ ⎡⎛ (ρui k ) = μ + t⎞ + Gk−ρε ⎥ σ ∂x i ∂x i ⎢ k ⎠ ∂x i ⎦ ⎣⎝

(4)

μ ∂ε ⎤ ∂ ∂ ⎡⎛ ε (ρui ε) = μ + t⎞ + (c1 Gk−c2 ρε) ⎥ ∂x i ∂x i ⎢ σ k ε ⎠ ∂x i ⎦ ⎣⎝

(5)

⎜

⎜

⎟

Sh is heat source. The other standard constants σT = 0.85, c1 = 1.44 , c2 = 1.92 , σk = 1.0 , and σε = 1.3. Standard wall functions are used as the near wall treatment, and y+ is controlled between 16.38 and 148.55. Boundary conditions are as follows:

⎟

(1) Inlet: u = vin , T = Tin = 623.15 K , I = 0.16Re−0.125 , kin = 1.5(uin I )2 , εin = cμ0.75 kin1.5/[0.14(ra−δa)]. (2) Outlet: fully developed condition. (3) No slip boundary near the wall. (4) The non-uniform heat flux computed by MCRT is applied on the absorber tube outer wall surface as a heat source with user-defined functions (UDF) profile. The DNI is 1000 W/m2. (5) The adiabatic boundary condition is applied to the two ends of the PTR except for the HTF region.

In these equations, turbulent viscosity μt can be computed by

μt = cμ ρ

k2 ε

(6)

where cμ is a constant and equal to 0.09. And Gk represents the generation of turbulent kinetic energy as

Gk = μt

∂uj ⎞ ∂ui ⎛ ∂ui 2 ∂u ρkδij i + ⎜ ⎟ + ∂x j ⎝ ∂x j ∂x i ⎠ 3 ∂x j

0.443 + 1.9 × 10−4t

(7)

Table 2 Specifications of the studied PTR enhanced by a concentric rod with different B. Symbol

B1

B2

B3

B4

B5

B6

B7

B8

B9

B rrod (m)

0.1 0.0032

0.2 0.0064

0.3 0.0096

0.4 0.0128

0.5 0.016

0.6 0.0192

0.7 0.0224

0.8 0.0256

0.9 0.0288

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4. Results and discussions

The non-dimensional Nusselt number, Reynolds number and Grashof number can be defined as [49]:

4.1. Effects of dimensionless diameter with concentric rod insert

Nu =

hD λ

(8)

Re =

ρuD μ

(9)

Gr =

gβ ΔTD3 ν2

In this section, the relationship of dimensionless diameter B to the heat transfer enhancement of PTR with concentric rod are numerically investigated. The heat flux is provided by the novel PTC with 6.77 m aperture width. Under the condition of DNI is 1000 W/m2 and the MS inlet temperature is 623.15 K. The general criterion Gr / Re 2 is used for determining the effects of free convection, and it is within the range of 1.1 × 10−5 to 0.072 for B from 0.1 to 0.9 and Re from 1 × 104 to 3 × 104, all less than 0.1. Combined with Re is larger than 1 × 104 and the flow is fully developed turbulence, it can be confirmed that the natural convection can be ignored in these cases. Fig. 4 shows the variations of temperature distributions with dimensionless diameter B on different cross sections along the flow direction of the absorber tube, the mass flow rate in these cases is 1.1762 kg/s. It can be found that the temperature distributions of the MS and absorber tube become dramatically non-uniform along the flow direction with same B. While the temperature distributions of the MS and absorber tube at the same cross section become slightly uniform with B increasing, and the maximum temperature of each section at the same position also decreases with the increase of B. A possible reason is that when B increases, more cold MS was pushed to the inner surface of the absorber tube, owing to the fact that the local heat transfer coefficient is much higher than that of the plain tube and the absorber tube with smaller B, which indicates that more heat flux is absorbed by MS with the increase of B. Fig. 5 presents the temperature distributions and velocity distributions in the cross-section of z = 2 m for different B when the mass flow of MS is 1.1762 kg/s. It can be seen that because the heat flux is nonuniform, the temperature field presents a non-uniform profile along the circumferential direction consistent with heat flux distribution. The temperature at the downside is higher than that at the upside. Because the flow is fully turbulent, natural convection by the buoyancy-driven flow can be neglected and the influence of the non-uniform heat flux on the flow field can be ignored, and the velocity field presents a concentric distribution due to the influence of flow boundary layer. With the increase of B, the maximum temperature and the non-uniformity of temperature distribution decreases significantly in solid region and fluid region. It is because when B increases, this means that the diameter of the inserting rod is gradually increased, and the main stream with the highest flow velocity in the tube is gradually approaching the inner wall surface of the absorber tube through extrusion effect of the inserted rod, which enhances the heat transfer in the tube. Especially when B = 0.9, the non-uniform distribution of temperature in the solid region and liquid region is reduced to a minimum. It can be concluded that the heat transfer of MS can be enhanced by inserting concentric rods. The temperature distribution can be uniformed and the maximum temperature on the absorber tube also can be significantly reduced with B increasing. Fig. 6 shows the variations of normalized Nusselt number (NuB∗ = NuB / Nup ) and normalized friction factor ( f B∗ = fB / fp ) over dimensionless diameter B at Re = 1 × 104 and Re = 3 × 104,

(10)

where D is hydraulic diameter of the absorber tube it is the inner diameter of plain absorber tube, and it equals to 2 D= 4π [(ra−δa)2−rrod ]/2π [(ra−δa) + rrod] = 2(ra−δa−rrod ) for enhanced heat transfer PTR. u is the cross-section mean velocity of the fluid. β is the fluid thermal expansion coefficient.

3.2. Methodology The governing equations above were solved by using the FVM code FLUENT6.3. SIMPLE scheme was used to deal with the pressure-velocity coupling. And the spatial discretization of pressure is second order, the discretization of momentum, turbulent kinetic energy, turbulent dissipation rate and energy equation are all second order upwind. The convergence criterions for continuity, velocity, k, and ε are all 10−5 , and for energy is 10−6 . To make sure the simulation results reliable and accurate, a grid independence study was considered, see Table 5. Comparisons for MS heat transfer and flow in a plain PTR at Re = 2 × 104 and Re = 4 × 104 are performed under three different grid systems. The relative deviation among the grid number of 36(θ) × 20(r) × 100(z), 36(θ) × 30(r) × 200(z), and 36(θ) × 40(r) × 400(z) are all within 0.22%. The simulation results are also compared with Nusselt number from experimental results and friction factor from empirical equations. Wu et al. [30] have obtained a correlation from an experiment on MS turbulent convective heat transfer in a plain PTR, which is presented as:

Nu p = 0.0239Re 0.804 Pr 0.33

(11)

The comparative results show that the Nusselt numbers from simulation are good accordant with Wu’s experimental values, and the maximum difference between the simulations (Nu p ) and the experimental results (NuWu ) is less than 8.95%. The maximum difference of friction factor between simulation ( fp ) and Blasius equation [50] results ( fBl ) is less than −3.67%. Blasius equation is recommended as:

fp = 0.046Rep−0.2

(12)

The good agreements show that the simulation model is reliable and in the present research, the grid number of 36(θ) × 20(r) × 100(z) is adopted. Y+ is between 11.4 and 212.1 in these simulations. Table 5 Validation results for grid independency.

36(θ)×20(r) 36(θ)×30(r) 36(θ)×40(r) 36(θ)×20(r) 36(θ)×30(r) 36(θ)×40(r)

×100(z) ×200(z) ×400(z) ×100(z) ×200(z) ×400(z)

Re 2 × 104 2 × 104 2 × 104 4 × 104 4 × 104 4 × 104

y+ 20.29 21.33 21.54 36.99 37.99 38.14

Simulation

Experimental

Nup 118.23 118.46 118.73 216.86 216.89 216.99

Nuwu 129.85 129.85 129.85 226.71 226.71 226.71

342

Error (%) −8.95 −8.77 −8.57 −4.35 −4.33 −4.29

Simulation

Blasius

fp 0.006311 0.006315 0.006316 0.005322 0.005323 0.005324

f Bl 0.006347 0.006347 0.006347 0.005525 0.005525 0.005525

Error (%) −0.56 −0.50 −0.49 −3.68 −3.65 −3.64

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Fig. 4. Variations of temperature distributions in the absorber tube with dimensionless diameter (ṁ = 1.1762 kg/s).

respectively. From the figure, it can be observed that with B increasing, NuB∗ is remarkably rising from 1.10 to 7.42 times over a plain PTR. And the growth rate of NuB∗ increases with B increasing. Other clear trend is that the growth rate of NuB∗ is also increases with the increasing of Re.

The similar trends exist in the variations of f B∗ effected by B and Re. The friction factor in the enhanced heat transfer PTR is calculated by Fanning equation [50]:

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Fig. 5. Effects of B on temperature and flow field distributions in the cross-section of z = 2 m (ṁ = 1.1762 kg/s).

fB =

Δp ·Di 2ρu2L

normalized friction factor to change over B and Re is similar. For the heat transfer enhancement, both heat transfer and flow resistance should be considered simultaneously. The performance evaluation criteria (PEC) [50] is employed to assess the comprehensive enhancement

(13)

Since the tendency of the normalized Nusselt number and 344

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St =

Nu RePr

(16)

Fig. 8 presents the effects of B on IPF and temperature drop, when the Re is in the range of 1 × 104 to 3 × 104, respectively. The temperature drop refers to the temperature difference between the maximum tube temperature of an enhanced PTR to a plain PTR. It shows that IPF decreases with the increasing of Re under a certain B. And with B increasing, the IPF of PTR with concentric rod insert decreases under a certain Re. This tendency is more obvious as B is larger than 0.8. It means that with the increasing of B, the influence of flow resistance increases rapidly, and gradually plays a leading role in IPF and cause the rapid reduction of overall heat transfer performance. The temperature difference ΔTtube between the maximum tube temperature of enhancing heat transfer PTR and plain PTR increases with the increasing of Re and B, and it reaches more than 100 K when B is 0.9 and Re is larger than 1 × 104. The diameter of the concentric rod insert has an optimized value, and B6, B7 and B8 have better overall performance in terms of IPF and material temperature reduction.

Fig. 6. Effects of B on the normalized Nusselt number and normalized friction factor at different Re.

4.2. Effects of dimensionless eccentricity with eccentric rod insert In this section, the relationship of the dimensionless eccentricity H to the heat transfer enhancement of PTR with an eccentric rod is numerically investigated. The value of B in these simulations is 0.6, the heat flux is provided by the novel PTC with 6.77 m aperture width. The DNI is 1000 W/m2 and the inlet temperature of the molten salt is 623.15 K. The general criterion Gr / Re 2 is used for determining the effects of free convection, and it is within the range of 1.8 × 10−4 to 6.3 × 10−3, for the absolute value of H is taken from 0.4 to 0.8 and Re from 1 × 104 to 6 × 104, all less than 0.1. Combined with Re is larger than 1 × 104 and the flow is fully developed turbulence, it can be confirmed that the natural convection can be ignored in these cases. Fig. 9 shows the variations of temperature distributions with dimensionless eccentricity H on different cross sections along the flow direction of the absorber tube, the mass flow rate in these cases is 1.1762 kg/s. It can be found that the temperature distributions of the MS and absorber tube become dramatically non-uniform along the flow direction with same H. The temperature distributions of the MS and absorber tube at the same cross section become slightly uniform when H increases from 0.4 to 0.8, and the maximum temperature of each section at the same position also decreases with the increase of H. While when H changes from −0.4 to −0.8, the change of temperature distributions is different. A possible reason is that when H increases from 0.4 to 0.8, more cold MS was pushed to the inner surface of the absorber tube, which indicates that more heat flux is absorbed by MS with the increase of H. However, when H changes from −0.4 to −0.8, more cold

Fig. 7. Effects of B on performance evaluation criteria and pressure drop at different Re.

of heat transfer.

PEC =

NuB / Nup Nu∗ Nu∗ = ∗B = f∗ fB (fB / fp )1/3

(14)

Fig. 7 presents the effects of B on PEC and pressure drop, when Re is in the range of 1 × 104 to 3 × 104, respectively. It can be seen that PEC slightly decreases with the increase of Re under a certain B, but has a significant increase with the increasing of B at a certain Re. PEC is about 1.12 to 3.38 times compared to the plain PTR when B grows from 0.1 to 0.9. The pressure drop increases with the increasing of B and Re, and there is a sharp increase when B is larger than 0.8. It shows that the concentric rod insert has a dramatically enhancing effect on the MS heat transfer in the PTR. And the greater the diameter of the concentric rod insert, the better the effect of heat transfer. It should be noted that as the diameter increases, a particular situation occurs. When the diameter of the rod is equal to the inner diameter of the absorber tube, the effect of heat transfer enhancement should be reduced to zero. However, by the analysis of PEC, this tendency cannot be indicated. Therefore, it is necessary to find a comprehensive heat transfer performance evaluation index which can reflect the effect of heat transfer enhancement. Therefore, a comprehensive integrated performance factor (IPF) is introduced.

IPF =

StB / Stp St∗ St∗ = ∗B = ∗ f fB fB / fp

(15)

Fig. 8. Effects of B on integrated performance factor and temperature drop at different Re.

St is the Stanton number, equals to [51] 345

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Fig. 9. Variations of temperature distributions in the absorber tube with dimensionless eccentricity (B = 0.6, ṁ = 1.1762 kg/s).

velocity distributions in the cross-section of z = 2 m when B equals 0.6 and the MS mass flow is 1.1762 kg/s. It can be seen that because the heat flux is non-uniform, the temperature field presents a non-uniform profile along the circumferential direction consistent with heat flux

MS was pushed to the inner surface of the absorber tube, but away from the heat flux side, which weakens the reduction of the maximum tube wall temperature. Fig. 10 presents effects of H on temperature distributions and 346

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Fig. 10. Effects of H on temperature and flow field distributions in the cross-section of z = 2 m (B = 0.6, ṁ = 1.1762 kg/s).

influence of the non-uniform heat flux on the flow field can be ignored, and the velocity filed presents an eccentric distribution due to the influence of flow boundary layer. As seen from this figure, compared with

distribution. The temperature at the downside is higher than that at the upside. For the cause of the flow is fully developed turbulence, natural convection by the buoyancy-driven flow can be neglected and the 347

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plain PTR and enhanced PTR with concentric rod inserts, the enhanced PTR with eccentric rod inserts show different heat transfer enhancement effects with the increasing of H. When the eccentric setting is away from the heating side, more and more MS with lower temperature is pushed to the heating side with the increasing of H, and the main stream with the highest flow velocity is gradually approaching the downside inner wall surface of the absorber tube. The thickness of velocity boundary layer and thermal boundary layer decrease as the Reynolds number increases. It enhances the heat transfer in the absorber tube. The non-uniformity of temperature distribution decreases significantly in solid region and fluid region with H increasing. But when the eccentric setting close to the heating side, more and more MS with lower temperature are pushed to the unheated side, and the main stream with the highest flow velocity is gradually departing the downside inner wall surface of the absorber tube. It weakens the heat transfer in the absorber tube. Coupled with the influence of the boundary layer, the fluid velocity near the inner wall surface of the directed heating side is relatively low, which results in a rise in the fluid temperature in this region, which is significantly showed in temperature and velocity distribution contours for H6 when H is −0.8. Fig. 11 illustrates the effects of dimensionless eccentricity H on PEC and normalized friction factor f∗ ( f B∗ = fB / fp , f H∗ = fH / fp ). B6 is the case of a concentric rod with B equal to 0.6. The value of H in the cases takes from Table 3, with B equal to 0.6 all the time. It is clear in Fig. 9 that PEC increases with the growth of H, but decreases with the increasing of Re. The PEC of B6 is about 1.73 times over a plain PTR at Re = 2 × 104, while the PEC of H3 is about 1.81 times over a plain PTR at the same Re, it means that by the eccentricity setting, there is a further 4.43% improvement on heat transfer performance. In the case of the same eccentric distance, the eccentric setting far away from the heating side is more conducive to the enhancement of heat transfer than the eccentric setting close to the heating side. It is because the main stream with the highest flow velocity in the tube is gradually approaching the heated side of the absorber tube through extrusion effect of the inserted rod, which enhances the heat transfer in the tube. The PEC of H6 is about 1.79 times over a plain PTR at Re = 2 × 104, about 1.05% less than that of H3 at the same Re. The normalized friction factor f∗ decreases the with the growth of H, but increases with the increasing of Re. The f B∗ of B6 is about 2.59 times over a plain PTR at Re = 2×104, while the f H∗ of H3 is about 2.04 times over a plain PTR at the same Re, it means that by the eccentricity setting, there is a further 21.38% improvement on reducing the flow resistance. As expected, the normalized friction factor f∗ is the same for the cases with same eccentricity either far away or toward the heating side. The effects of H on IPF and temperature drop are compared in

Fig. 12. Effects of H on integrated performance factor and temperature drop at different Re.

Fig. 12. IPF increases with the growth of H but decreases with the increasing of Re. The IPF of B6 is about 0.92 times over a plain PTR at Re = 2 × 104, while the IPF of H3 is about 1.13 times over a plain PTR at the same Re, it means that by the eccentricity setting, there is a further 22.60% improvement on heat transfer performance. In the case of the same eccentric distance, the eccentric setting far away from the heating side is more conducive to the enhancement of heat transfer than the eccentric setting close to the heating side. The IPF of H6 is about 1.12 times over a plain PTR at Re = 2 × 104, about 1.05% less than that of H3 at the same Re. The temperature drop refers to the temperature difference between the maximum tube temperature of an enhanced PTR to a plain PTR. The temperature drop decreases the with the growth of H and the increasing of Re. The maximum tube temperature of B6, H3, and H6 is about 56.7 K, 57.0 K, and 43.8 K less than a plain PTR at Re = 1 × 104, respectively. It means that by the eccentricity setting, there is a further improvement in reducing the maximum tube wall temperature. But only the eccentric setting far away from the heating side can help to reduce the tube wall temperature. The eccentric setting close to the heating side weakens the reduction of the maximum tube wall temperature. 5. Conclusions This study investigates the effect of enhanced molten salt heat transfer in a parabolic trough receiver by introducing concentric and eccentric rod inserts, and the comprehensive performance of the heat transfer enhancement is analyzed. The non-uniform heat flux of a novel parabolic trough collector and the varying properties of molten salt have been considered. The following conclusions have been derived. (1) The usage of a concentric rod insert for a parabolic trough receiver can enhance the heat transfer performance effectively. With the increasing of B, NuB∗ is about 1.10 to 7.42 times over a plain parabolic trough receiver. f B∗ increases with the increasing of Re and the increasing of B. The temperature distribution can be uniformed. The maximum temperature on the absorber tube also can be remarkably reduced with B increasing, the temperature drop can reaches 107.5 K when B equals 0.9 at Re = 3 × 104. (2) For a concentric rod insert, when B increases from 0.1 to 0.9, the performance evaluation criteria is about 1.12 to 3.38 times than for the plain parabolic trough receiver at Re = 1 × 104. By introducing integrated performance factor, it can give a reasonable solution, and it shows that the integrated performance factor has a significance decreases with the increase of Re under a certain B. But with B increasing, the integrated performance factor of parabolic trough receiver with concentric rod inserts decreasing under a

Fig. 11. Effects of H on performance evaluation criteria and normalized friction factor at different Re. 348

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certain Re. This tendency is more obvious when B is larger than 0.8. (3) Compared with the concentric rod insert case, an eccentric rod insert for parabolic trough receiver can further improve the heat transfer performance. Both the performance evaluation criteria and the integrated performance factor decrease with the increase of Re. In the case of the same eccentric distance, the eccentric setting away from the heating side is more effective in the enhancement of heat transfer and the reducing of the maximum tube wall temperature than the eccentric setting close to the heating side. While they are almost the same for reducing the flow resistance. The nonuniformity of the temperature distribution decreases significantly in solid region and fluid region with H increasing. But only the eccentric setting away from the heating side helps to reduce the tube wall temperature. The eccentric setting close to the heating side weakens the reduction of the maximum tube wall temperature.

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