Thermal analysis of solar central receiver tube with porous inserts and non-uniform heat flux

Applied Energy xxx (2015) xxx–xxx

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Thermal analysis of solar central receiver tube with porous inserts and non-uniform heat flux q Zhang-Jing Zheng, Ming-Jia Li, Ya-Ling He ⇑ Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


A solar central receiver tube with

non-uniform heat flux is numerically studied.
A new method is suggested to determine the configurations of porous inserts.
Effects of porous insert layouts on the performance of receiver tube are analyzed.
Some optimal porous insert configurations are proposed for different purposes.

a r t i c l e

i n f o

Article history: Received 11 August 2015 Received in revised form 16 November 2015 Accepted 29 November 2015 Available online xxxx Keywords: Solar energy utilization Central receiver tube Heat transfer enhancement Porous medium Numerical simulation Optimization

a b s t r a c t In this paper, enhancement for convection heat transfer of turbulent flow in a solar central receiver tube with porous medium and non-uniform circumferential heat flux was numerically investigated. A new method was introduced to build different porous medium configurations in a unified grid system. Four kinds of enhanced receiver tubes (ERTs) with different porous insert configurations were modeled to optimize the performance of ERT. Furthermore, parameters including filling ratio of porous medium, thermal conductivity ratio (thermal conductivity of porous medium versus that of working fluid), porosity and Reynolds number were analyzed. The results showed that ERT partially filled with porous medium has better heat transfer performance than that fully filled with porous medium. The configuration of porous insert for optimal thermal or thermo-hydraulic performance is interactively affected by all the parameters discussed in this paper. The thermal conductivity ratio is the most crucial parameter to the thermal or thermo-hydraulic performance of ERT. The value of thermal conductivity ratio should be greater than 100 to obtain a good thermo-hydraulic performance. The ERTs with horizontal cylindrical segment shaped porous inserts and hollow cylinder shaped porous inserts are proposed because they can obtain optimal thermal or thermo-hydraulic performance. Ó 2015 Elsevier Ltd. All rights reserved.

q This paper was presented at the 7th International Conference on Applied Energy (ICAE2015), March 28–31, 2015, Abu Dhabi, UAE (Original paper title: ‘‘Optimization of Porous Insert Configuration in a central Receiver Tube for Heat Transfer Enhancement” and Paper No.: 514). ⇑ Corresponding author. E-mail address: [email protected] (Y.-L. He).

1. Introduction Solar power tower (SPT), as a primal concentrating solar power (CSP) technology, has numerous remarkable advantages including low average cost and large-scale power generation [1,2]. In SPT

http://dx.doi.org/10.1016/j.apenergy.2015.11.039 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

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Nomenclature A cp Di f F h h0 H K L La Nu p q q0 Re T u, v, w U x, y, z

flow area (m2) specific heat (J kg1 K1) inner diameter of receiver tube (m) friction factor inertia coefficient heat transfer coefficient (W m2 K1) height of catalyst (m) dimensionless height of porous medium permeability (m2) length of ERT (m) length of auxiliary segment (m) Nusselt number pressure (Pa) heat transfer rate per unit area (W m2) heat flux at tube crown (W m2) Reynolds number temperature (K) superficial velocity at x, y, z direction respectively (m s1) dimensionless x velocity component Cartesian coordinates (m)

system, the receiver is a key component because it converts the solar radiation concentrated by heliostat field into thermal energy. Nevertheless, the typical optical concentration factor of SPT can reach as high as 1000 and the corresponding solar flux impinging on the receiver can reach up to 1.0 MW m2 [3]. Meanwhile, the distribution of solar flux on the receiver is significant nonuniform. These extreme working conditions make the most uncertain lifetime of receiver [4]. Therefore, many studies have focused on predicting and improving the performance of receiver for SPT [5,6]. Being a typical receiver for SPT, tubular receiver is applicable to various heat transfer fluid (HTF), such as supercritical carbon dioxide, synthetic oils, liquid sodium, water/steam and molten salt [7,8]. The tubular receiver consists of many paralleled tubes. The high flux density and non-uniform flux distributing on each receiver tube can cause high temperature gradients within receiver tube wall and flow region, which has been proven by theoretical, numerical and experimental methods [9–17]. The uneven temperature field may result in many problems [18–22] such as aggravating the plastic deformation of receiver tube, facilitating degradation of the selective absorptive coating and the heat transfer fluid (e.g. thermal oil and molten salt) and decreasing the allowable solar flux density of system. Heat transfer enhancement can be employed to solve these problems due to its ability to decrease the irreversibility of heat convection [23,24]. Some methods of heat transfer enhancement have been put forward for the solar receiver tube with non-uniform heat flux. He et al. [25] proposed unilateral longitudinal vortex generators to enhance heat transfer in a parabolic trough receiver tube. The longitudinal vortex generators were only stamped on the side of the receiver tube with high heat flux. The results showed that the comprehensive heat transfer performance is improved. Muñoz et al. [26] numerically analyzed the thermal, mechanical and hydrodynamic performance of internal helically finned tube for parabolic trough, and found that using the enhanced tube can reduce the temperature gradients within the tube wall and increase the efficiency of solar plant. However, it is difficult to manufacture the special receiver tube mentioned above. Inserting porous medium

Greek symbols binary flag turbulent energy dissipation rate (m2 s3) h circle angle (deg) k thermal conductivity (W m1 K1) l kinetic viscosity (Pa s) lt turbulent viscosity (Pa s) q density (kg m3) r turbulent Prandtl number u porosity

a e

subscripts c clear receiver tube e effective f fluid in inlet m mean out outlet por porous medium s solid w wall

is another effective way to enhance convection heat transfer in the receiver tube by rebuilding the velocity field and increasing the effective thermal conductivity of fluid. More importantly, the porous can be easily inserted into the receiver tube by gluing with thermal epoxy, soldering, joining, etc. [27,28]. Therefore, the applications of porous inserts to enhance heat transfer of the receiver tube were extremely extensive. Reddy et al. [29–31] numerically investigated the heat transfer enhancement of parabolic trough receiver tubes with porous disc and porous block. The effects of porous disc/block configurations on the heat transfer performance of receiver tube with non-uniform heat flux were studied. Ghasemi et al. [32,33] proposed porous segmental rings for heat transfer enhancement of parabolic trough receiver tube. The effects of segmental rings layouts on the heat transfer and system performance for non-uniform heat flux were discussed. Mwesigye et al. [34] studied the thermal and thermodynamic performance of a parabolic trough receiver tube with porous inserts. The porous medium was centrally placed in the receiver tube to avoid any possible hotspots caused by non-uniform heat flux distribution. Wang et al. [28] numerically analyzed the enhancement of forced convective heat transfer in a parabolic trough receiver tube with metal foams and non-uniform heat flux. Horizontal cylindrical segment shaped porous inserts were proposed to obtain the optimal thermal or thermo-hydraulic performance. Based on the studies above, it can be found that the non-uniform heat flux is an important factor when the heat transfer enhancement for the receiver tube is studied. However, most heat transfer enhancement methods of receiver tube with non-uniform heat flux were proposed for solar parabolic trough system. For central receiver tube, more studies are needed to find out the appropriate heat transfer enhancement, since the heat flux distribution of central receiver tube is different from that of parabolic trough receiver tube. In this paper, the heat transfer enhancement in a solar central receiver tube with porous medium and non-uniform heat flux was numerically investigated. A new method was adopted to determine the different porous medium configurations in a unified grid system. Based on this new method, the porous insert configurations were optimized for improving thermal or thermo-hydraulic

Please cite this article in press as: Zheng Z-J et al. Thermal analysis of solar central receiver tube with porous inserts and non-uniform heat flux. Appl Energy (2015), http://dx.doi.org/10.1016/j.apenergy.2015.11.039

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performance of central receiver tube with non-uniform heat flux. This numerical optimization method can be further extended to other analysis of flow and heat transfer in porous medium.

Table 1 Parameters of the Solar Two receiver [35].

2. Model

Value

Receiver thermal rating Heat transfer fluid

42.2 MW Mixed nitrate molten salt (60 wt.% NaNO3 and 40 wt.% KNO3) 0.8 MW m2 558 K 838 K Alloy 800H 18.41 W m1 K1 6.2 m 21 mm 18.6 mm

Peak flux Inlet temperature of receiver Outlet temperature of receiver Receiver tube material Thermal conductivity of receiver tube Receiver height Outside diameter of receiver tube Inside diameter of receiver tube

2.1. Physical model The schematic diagram of a typical external tubular receiver designed for Solar Two project is shown in Fig. 1a. It can be seen that the tubular receiver is formed by a number of vertical blocks of panels. Each panel includes an inlet header/nozzle, an outlet header/nozzle and some tubes. The detailed parameters of this tubular receiver are listed in Table 1 [35]. The heat transfer enhancement of fully developed region in a single enhanced receiver tube (ERT) is numerically investigated in this paper (see Fig. 1b). The length of ERT is 0.5 m, and an auxiliary segment with a length of 1.5 m is placed before the inlet of ERT to make sure that the fluid is fully developed in the ERT. Fig. 1c presents the circumferential heat flux distribution on the outside surface of a single receiver tube. It can be seen that only the sunward section (90° 6 h 6 90°) of the receiver tube absorbs the sunlight, so the circumferential heat flux distribution of receiver tube is nonuniform. Porous medium is filled in the ERT to enhance the convective heat transfer between the HTF and the receiver tube. The porous insert is made of metal foam and can be processed into the desired shape by wire cut electrical discharge machining (WEDM) [28]. Four kinds of ERTs with different porous insert configurations are modeled to optimize the performance of ERT (see Fig. 2) [36]: (a) cylinder shaped porous insert filled in the core of receiver tube (ERT-I); (b) hollow cylinder shaped porous insert attached to the inner surface of receiver tube (ERT-II); (c) horizontal cylindrical segment shaped porous insert filled in the lower part of receiver tube (ERT-III); (d) horizontal cylindrical segment shaped porous insert filled in the upper part of receiver tube (ERT-IV). The porous inserts keep the same axial length as the ERT and the mass of porous inserts can be determined by a dimensionless parameter ´ /Di. Four typical metal foams with different parameters are H=h selected based on the experiment data of Calmidi et al. [37], which are shown in Table 2.

Parameters

2.2. Governing equations During the considered range of Reynolds numbers, the flow in the ERT is in the fully developed turbulent regime. Therefore, the governing equations are the continuity, momentum, standard k–e model, and energy equations which can be expressed as Eqs. (1)– (11). Some assumptions in the simulation are listed as follows: (1) the flow in the receiver tube is in a steady state; (2) the porous medium is regarded as homogeneous and isotropic; (3) the fluid phase and the solid phase in porous medium exist in a state of local thermal equilibrium; (4) the Forcheimer–Brinkman model is adopted to describe the flow in the porous region; (5) the heat loss at the outer wall of receiver tube is not taken into account since this paper only focuses on the heat transfer enhancement between the HTF and the receiver tube; (6) the connection between the inner wall and porous insert is so tightly that the contact thermal resistant is ignored. Continuity equation:

@ ðqui Þ ¼ 0 @xi

ð1Þ

Momentum equation:


 @ @p 1 @ @ui @uj ð q u u Þ ¼  þ ð l þ l Þ þ i j t @xi u @xj u2 @xi @xj @xi 
 2 @ul l þ lt qF ujui dij  a ui þ pffiffiffiffi j~  ðlt þ lÞ 3 @xl K K 1

ð2Þ

Fig. 1. (a) Schematic of external tubular receiver, (b) schematic of single receiver tube and (c) cross-section of single receiver tube filled with porous medium.

Please cite this article in press as: Zheng Z-J et al. Thermal analysis of solar central receiver tube with porous inserts and non-uniform heat flux. Appl Energy (2015), http://dx.doi.org/10.1016/j.apenergy.2015.11.039

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0.5h´

h´

z

h´ h´

x

y

Di

(a)

(b)

(c)

(d)

Porous

Fig. 2. ERT configurations [36]: (a) ERT-I, (b) ERT-II, (c) ERT-III, (d) ERT-IV.

2.3. Boundary conditions

Table 2 Properties of metal foams [37]. # Case1 Case2 Case3 Case4

K (m2)

PPI

u 0.9726 0.9546 0.9486 0.9272

F 7

2.7  10 1.3  107 1.2  107 0.61  107

5 20 10 40

0.097 0.093 0.097 0.089

where the binary flag a is used to determine the momentum equation suits the fluid region or porous region, and can be expressed as follows:



a¼

0;

fluid region

1;

porous region

k equation:

@ @ ðqui kÞ ¼ @xi @xi

e equation: @ @ ðqui eÞ ¼ @xi @xi




ð3Þ





lþ

lt @k þ Gk  qe rk @xi

lþ

lt @k e þ ðc G  c qeÞ re @xi k 1 k 2






ð4Þ



ð5Þ

where the turbulent viscosity lt and the production of turbulent viscosity Gk are given as:

lt ¼ c l q

k


 @ui @ui @uj þ @xj @xj @xi

2

e

;

G k ¼ lt

ð6Þ

The standard constants of k equation and e equation are employed: cl = 0.09, c1 = 1.44, c2 = 1.92, rk = 1.0, re = 1.3, rT = 0.85. Energy equation: Fluid region:

@ @ ðqcp ui TÞ ¼ @xi @xi














lt @ k e T Pr rT @xi qcp l

(1) For the fluid domain, the inlet and outlet boundary are defined as: Inlet: constant velocity and temperature condition, u = uin, v = w = 0, T = Tin = 673 K. Outlet: fully-developed condition, ou/ox = ov/ox = ow/ox = op/ox = oT/ox = 0. (2) The symmetrical boundary is defined as: Fluid domain: ou/oy = ov/oy = ow/oy = op/ox = oT/oy = 0. Solid domain: u = v = w = 0, oT/oy = 0. (3) The ends of receiver tube are defined as adiabatic walls: u = v = w = 0, oT/ox = 0. (4) The inner surface of the receiver tube is defined as velocity no-slip and temperature coupled interface: u = v = w = 0, Tf = Tw. (5) In order to analyze the performance of ERT under real nonuniform solar heat flux boundary condition, a cosine distribution of heat flux is assumed in this paper [38]. The local heat flux is calculated by Eq. (12) and shown in Fig. 4. q0 is the heat flux at tube crown and equal to 0.8 MW m2 [39].

 q¼

q0 cos h 0 6 h 6 90 0 90 < h 6 180

ð12Þ



ð7Þ

þ

Porous region:

@ @ ðqcp ui TÞ ¼ @xi @xi




lt @ kf T Pr rT @xi qcp l

As shown in Fig. 1c, the heat flux distribution on the outer surface of the receiver tube is symmetric. Therefore, half of the receiver tube (0° 6 h 6 180°) including the region in the receiver tube and the tube wall are considered as the simulation domain (see Fig. 3). More details are expressed as follows:



þ

ð8Þ

Solid region: 2

@ T @ 2 xi

¼0

ð9Þ

where the effective thermal conductivity (ke) is calculated by the mathematical model of Calmidi et al. [37] #1 pffiffi pffiffiffi "   3 0:09 bL 0:91 bL  bL 3 2   þ ke ¼ þ  pffiffi b ðks  kf Þ 2 kf þ 1 þ b ðks kf Þ kf þ 23 bL ðks  kf Þ kf þ 0:12 3 L L

3

ð10Þ

b 0:09 þ ¼ L

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi 20:09ð1þp4ffi Þ 3 0:0081 þ 2 3ð1  uÞ 3 h

i 2 2  0:09 1 þ p4ffiffi 3 3

ð11Þ Fig. 3. Computation domain and meshes generation of receiver tube.

Please cite this article in press as: Zheng Z-J et al. Thermal analysis of solar central receiver tube with porous inserts and non-uniform heat flux. Appl Energy (2015), http://dx.doi.org/10.1016/j.apenergy.2015.11.039

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2.5. Parameter definitions

1.0 0.9

In order to analyze the thermal and thermal-hydraulic characteristics of ERT, some parameters are defined as follows: The filling ratio of porous medium is calculated as:

q0

0.8

0º

0.7 0.6

q/q0

5

FRP ¼

©

0.5

90º

O

0.4 ± 180º

0.1 0.0 0

20

40

60

80

100

120

140

ð13Þ

where mpor is the actual mass of porous medium in the ERT, mpor,full is the theoretically maximum mass of porous medium fully filled in the ERT. Based on Fig. 2, the mass of four kinds of porous inserts can be calculated as:

0.3 0.2

mpor mpor;full

160

180

θ / deg Fig. 4. Distribution of non-uniform solar heat flux boundary condition.

2.4. Numerical methods

mpor;I ¼ mpor;II ¼

p

qpor H2 D2i L

4

p 4

qpor ð1  HÞ2 D2i L


 1 2 0:5Di  HDi Di arccos 4 0:5Di qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð0:5Di  HDi Þ ð0:5Di Þ  ð0:5Di  HDi Þ2

ð14Þ ð15Þ

mpor;III ¼ mpor;IV ¼ qpor L

The geometric model is created and meshed using the CFD preprocessing software GAMBIT 2.2. A new method is employed to build different porous medium configurations in a unified grid system [40]. Based on this new method, the performance of ERT with different porous insert configurations can be rapidly predicted and the impact of grid division on the simulation results can be eliminated. The flowchart of this new method is shown in Fig. 5. It can be seen that the construction of porous insert is finished before solving governing equations in the process of numerical simulation. The CFD commercial code FLUENT 6.3 is used to simulate the flow and heat transfer processes in the receiver tube [41]. The governing equations are discretized by the finite volume method (FVM) [42]. The convective terms in energy and momentum equations are discretized with the second upwind scheme. The coupling between velocity and pressure is based on SIMPLE algorithm [43]. The convergence criterions for the normalized residuals of all solved variables are restricted to be less than 106. During computation, the thermo-physical properties of molten salt under a temperature of 673 K are selected [44]: q = 1835.6 kg m3, cp = 1511.8 J kg1 K1, k = 0.519 W m1 K1, l = 1.7764  103 kg m1 s1.

The formula of mpor,full is given as:

mpor;full ¼

Criterion for the construction of four kinds of porous inserts

p 4

qpor D2i L

ð17Þ

The Reynolds number and average Nusselt number can be calculated as [45]:

Re ¼

quDi hDi ; Nu ¼ l kf

ð18Þ

where h is the average heat transfer coefficient of ERT. The pump power and friction factor are given as [46]:

Pp ¼ uDpA;

f ¼

Dp Di L ð1=2Þqu2

ð19Þ

where Dp is the differential pressure between the inlet and outlet of ERT, A is the flow area of ERT. The performance evaluation criterion (PEC) of heat transfer enhancement under constant pumping power is defined as [47]:

PEC ¼ Start FVM

ð16Þ

Nu=Nuc ðf =f c Þ

1=3

ð20Þ

where the subscript ‘‘c” represents clear receiver tube without porous medium.

Import mesh

Get the coordinate geometry of each cell in mesh system Determine if the i cell is in the porous region ? Yes

φi≠1, αi=1

No

φi=1, αi=0

Finish the configuration design of porous insert

Porous insert-Ι: ≤ xi/L≤ 1.0, 0.75≤ (yi2+zi2)0.5/Di≤ H Porous insert-ΙΙ: ≤ xi/L≤ 1.0, 0.75≤ (yi2+zi2)0.5/Di≥ (1-H) Porous insert-ΙΙΙ: ≤ xi/L≤ 1.0, 0.75≤ (zi/Di+0.5)≤ ≤ H Porous insert-ΙV: 0.75≤ ≤ xi/L≤ 1.0, ≥ H (zi/Di+0.5)≥

Solve the governing equations

Fig. 5. Flowchart of a new method used for the construction of porous inserts.

3. Code checking and models validation 3.1. Code checking Since the unified grid solution is used for all ERTs with different porous insert configurations, it is just needed to investigate the grid independence test for a steady state turbulent flow in the clear receiver tube without porous insert. A constant heat flux condition (q = 750,000 W m2) is applied to the outer surface of receiver tube. Four different grid systems are tested: 20 (radial)  24 (circumferential)  333 (axial), 31  41  571, 41  58  800 and 50  73  1000. The predicted results of four different grid systems are listed in Table 3. The difference of Nu and f between the third and fourth grid system are less than 0.6% and 0.15%, respectively. So the third grid system is chosen by making a trade-off between the CPU time and the accuracy.

Please cite this article in press as: Zheng Z-J et al. Thermal analysis of solar central receiver tube with porous inserts and non-uniform heat flux. Appl Energy (2015), http://dx.doi.org/10.1016/j.apenergy.2015.11.039

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Table 3 Predicted results of different grid systems.

4. Results and discussion 4.1. Effects of filling ratio of porous medium

Grid systems

Tout (K)

Tw,m (K)

Nu

f

20  24  333 31  41  571 41  58  800 50  73  1000

705.91 703.65 702.80 702.24

751.71 752.03 752.11 752.21

487.12 476.28 472.57 469.79

0.01848 0.01838 0.01835 0.01833

The effects of FRP and configuration of porous insert on the performance of ERT are studied in the first place since the filling ratio of porous medium (FRP) is related to the mass and material cost of porous medium. The values of ks/kf, u and Re are set to 1.0, 0.9726 and 90,000, respectively. Fig. 8 shows Nu/Nuc, Pp/Pp,c and PEC for different FRP.

3.2. Models validation 4.0 ERT-I ERT-II ERT-III ERT-IV

3.5 3.0

Nu/Nuc

Fig. 6 shows Nu and f for a turbulent flow in a clear receiver tube without porous medium under uniform heat flux boundary condition. It can be seen that Nu predicted by this paper is between the two values calculated by Sieder-Tate correlation and Gnielinski correlation [48]. Also the maximum error of f between the predicted data by this paper and the value calculated by Filonenko correlation [48] is less than 0.9%. Fig. 7 shows that Nu and f for a turbulent flow in a circular tube partially filled with porous medium are validated with the experiment data of Huang et al. [49,50]. The porous medium made of copper is placed at the core of the tube in cylindrical shape. The maximum errors of Nu and f between the predicted data by this study and the experimental data of Huang et al. are less than 6.1% and 12.5%, respectively.

2.5 2.0 1.5 1.0 0.5 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

FRP

(a) 600

0.028 Nu-This paper Nu-Gnielinski correlation Nu-Sieder-Tate correlation f-This paper f-Filonenko correlation

500

10

3

10

2

10

1

10

0

0.026

0.024

300

0.022

200

0.020

100 0.0

4

4

2.0x10

4

4.0x10

ERT-I ERT-II ERT-III ERT-IV

0.018 5 1.0x10

4

6.0x10

Pp/Pp,c

f

Nu

400

8.0x10

Re

0.0

0.1

0.2

0.3

0.4

Fig. 6. Simulation result compared with experimental correlations for receiver tube without porous medium.

0.5

0.6

0.7

0.8

0.6

0.7

0.8

0.9

1.0

FRP

(b) 1.0 0.9

270

1.4

240

1.2

210

1.0

0.6

0.8

0.5

0.8

150

Nu- this paper Nu- experiment of Huang et al. f- this paper f- experiment of Huang et al.

0.6 0.4

90

0.2

4

1.2x10

4

4

1.4x10

1.6x10

0.4

ERT-I ERT-II ERT-III ERT-IV

0.3

120

60 4 1.0x10

PEC

180

f

Nu

0.7

4

1.8x10

0.0 4 2.0x10

Re Fig. 7. Simulation result compared with experimental results for tube partially filled with porous medium.

0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.9

1.0

FRP

(c) Fig. 8. Effects of FRP on the performance of ERTs: (a) Nu/Nuc, (b) Pp/Pp,c, (c) PEC.

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It can be seen from Fig. 8a that the values of Nu/Nuc of four kinds of ERTs increase and then decrease with the increase of FRP. Therefore, ERT partially filled with porous medium has better heat transfer performance than ERT fully filled with porous medium (FRP = 1.0). The values of FRP for four kinds of ERTs to obtain the optimal Nu/Nuc are 0.81, 0.51, 0.75 and 0.25, respectively. It also can be seen that ERT-I has better Nu/Nuc than ERT-II and ERT-IV for all FRP. ERT-III and ERT-I can obtain approximate peak values of Nu/Nuc when FRP is about 0.8. The maximum Nu of ERT-I and ERT-III are nearly 4 times as much as that of clear receiver tube. It can be seen from Fig. 8b that Pp/Pp,c of four kinds of ERTs sharply increase with the increase of FRP. This is because that the flow resistance is significantly high in the porous medium. It also can be seen that the Pp/Pp,c of ERT-I and ERT-II is larger than that of ERT-III and ERT-IV. This is because that inserting the porous medium at core of ERT or attaching the porous medium to the tube wall is more likely to increase the fluid velocity gradient and momentum dissipation in the boundary layer, which will greatly increase the flow resistance [36]. From Fig. 8a and b, it can be found that porous insert can enhance the convection heat transfer, but increases the pump power. Therefore, it is necessary to discuss heat transfer enhancement and hydraulic performance integrally. Fig. 8c shows that the values of PEC of all ERTs are lower than 1.0, which means the thermo-hydraulic performance of ERT with porous insert is poor when ks/kf = 1.0. Porous insert enhances the convection heat transfer in receiver tube mainly through rebuilding the velocity field in receiver tube when ks/kf = 1.0. Therefore, the velocity fields in four kinds of ERTs are discussed. Fig. 9 shows the dimensionless axial velocity fields at the cross section in fully developed region of receiver tube. It is clear that the velocity field in the receiver tube can be significantly rebuilt by using porous inserts. Compared to the clear receiver tube, ERT fully filled with porous medium has more uniform velocity field and larger fluid velocity near tube wall, so the convective heat transfer can be enhanced by ERT fully filled with porous medium. However, it is not efficient to increase the fluid

velocity in the lower part of the receiver tube since the heat flux only exists on the upper wall of receiver tube. ERT-I and ERT-III can make the fluid flow through the gap between porous insert and the upper wall of ERT. Therefore, the heat can be effectively taken away by the HTF in ERT-I and ERT-III. Fig. 10 shows the temperature distributions on the outer surface of receiver tube. It can be seen that the temperature distribution on the outer surface of the ERT with porous inserts is more uniform than that of clear receiver tube. The hotspot caused by non-uniform heat flux distribution can be avoided by using the ERT with porous inserts, especially by using the ERT-I and ERTIII. This is because that ERT-I and ERT-III have best heat transfer performance when ks/kf = 1.0. 4.2. Effects of thermal conductivity ratio Considering the high operating temperature of receiver, corrosion of molten salt and material cost, three kinds of potential engineering materials, including steel, silicon carbide and copper, are chosen to manufacture porous inserts. Thermal conductivity of these materials is listed in Table 4. It can be seen from Table 4 that the maximum thermal conductivity ratio approaches 1.0  103. Therefore, the thermal conductivity ratio concerned in this study ranges from 1 to 1.0  103. In order to study the effects of thermal conductivity ratio (ks/kf) on the performance of ERT, the values of u and Re are set to 0.9726 and 90,000, respectively. Each kind of ERT is given a constant H to obtain good Nu/Nuc or PEC when ks/kf > 1.0. Fig. 11 shows Nu/Nuc and PEC of four kinds of ERTs for different ks/kf. The Nu/Nuc and PEC of ERT fully filled with porous medium is also displayed in Fig. 11 for comparison. It can be seen that ERT fully filled with porous medium has weaker thermal and Table 4 Thermal conductivity of three engineering materials. Materials

ks

ks/kf

Steel (Fe) Silicon carbide (SiC) Copper (Cu)

18.4 118 [51] 387.6 [50]

38.5 227.4 746.8

Fig. 9. Dimensionless axial velocity distributions in the fully developed region of ERTs with or without porous inserts.

Fig. 10. Temperature distributions on the outer surface of ERTs with or without porous inserts.

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Z.-J. Zheng et al. / Applied Energy xxx (2015) xxx–xxx

8

6 ERT-I (FRP=0.81) ERT-II (FRP=0.51) ERT-III (FRP=0.86) ERT-IV (FRP=0.37) ERT-Fully filled

Fe

6

Nu/Nuc

4

3

5 4 3

2

2 0.92

1 10 0

10 1

10 2

/

s

0.93

0.94

0.95

3

ERT-I (FRP=0.01) ERT-II (FRP=0.19) ERT-III (FRP=0.75) ERT-IV (FRP=0.05) ERT-Fully filled

ERT-III (FRP=0.75) ERT-IV (FRP=0.05)

2

10

Pp /Pp,c

1.2

0.98

10

ERT-I (FRP=0.01) ERT-II (FRP=0.19)

1.4

0.97

(a)

f

1.8 1.6

0.96

10 3

(a)

1.0

PEC

ERT-I (FRP=0.81) ERT-II (FRP=0.51) ERT-III (FRP=0.86) ERT-IV (FRP=0.37)

7

Cu

Nu/Nuc

5

SiC

1

10

0.8 0.6 SiC

Fe

Cu

0.4

0

10 0.92

0.2 0.0 10

0

10

1

10

/ s

2

10

0.93

0.94

0.95

0.96

0.97

0.98

0.97

0.98

(b)

3

f

2.0

(b)

ERT-I (FRP=0.01) ERT-II (FRP=0.19) ERT-III (FRP=0.75) ERT-IV (FRP=0.05)

1.8 Fig. 11. Effects of ks/kf on the performance of ERTs: (a) Nu/Nuc, (b) PEC.

4.3. Effects of porosity ERT partially filled with porous medium can obtain better thermal and hydraulic performance than ERT fully filled porous

1.6

PEC

thermo-hydraulic performance than ERT partially filled with porous medium even though the value of ks/kf is high. Therefore, increasing the thermal conductivity of porous medium in the lower part of receiver tube does not have significant effects on enhancing the thermal performance of receiver tube. It can be seen from Fig. 11a that Nu/Nuc of all kinds of ERTs except ERT-I increase with the increase of ks/kf. The change of ks/kf has no effects on Nu/Nuc of ERT-I, which is because increasing the value of ks/kf cannot increase the effective thermal conductivity of HTF near the wall of ERT-I. It also can be seen that ERT-III has highest Nu/Nuc for a large range of ks/kf, and ERT-II can obtain higher Nu/Nuc than ERT-I when the value of ks/kf is high. Therefore, ks/kf affects the configuration of porous insert for optimal thermal performance of ERT. It can be seen from Fig. 11b that the variation tendency of PEC of all ERTs keeps the same with Nu/Nuc, because the ks/kf has no influence on pump power. It also can be seen that the ERT-IV has the highest PEC, and the PEC of ERT-II and ERT-IV can be greater than 1.0 only when ks/kf > 100. Therefore, ks/kf is a crucial parameter for optimal thermo-hydraulic performance of ERT. From the point of view of practical application, Sic and Cu whose ks/kf can be larger than 100 are recommended as materials of porous medium for heat transfer enhancement of molten salt receiver.

1.4 1.2 1.0 0.8 0.6 0.92

0.93

0.94

0.95

0.96

(c) Fig. 12. Effects of u on the performance of ERTs: (a) Nu/Nuc, (b) Pp/Pp,c, (c) PEC.

medium under non-uniform heat flux condition. Therefore, only the performance of ERT partially filled with porous medium is discussed in this section. The FRP of four kinds of ERTs are the same as those in Section 4.2. In order to study the effects of porosity (u) on the performance of ERT, the values of ks/kf and Re are set to 1000 and 90,000, respectively. Fig. 12 shows Nu/Nuc and PEC of four kinds of ERTs for different u. It can be obtained from Fig. 12a that Nu/Nuc of all ERTs decrease with the increase of u. This is because the ability of rebuilding velocity field and the effective thermal conductivity both decrease with the increase of u. Fig. 12b indicates that Pp/Pp,c of all ERTs decrease with the increase of u. The reason is that the flow resistance decreases with the increase of u. Fig. 12c indicates that

Please cite this article in press as: Zheng Z-J et al. Thermal analysis of solar central receiver tube with porous inserts and non-uniform heat flux. Appl Energy (2015), http://dx.doi.org/10.1016/j.apenergy.2015.11.039

Z.-J. Zheng et al. / Applied Energy xxx (2015) xxx–xxx

6.0 ERT-I (FRP=0.81) ERT-II (FRP=0.51) ERT-III (FRP=0.86) ERT-IV (FRP=0.37)

5.5

Nu/Nuc

5.0

9

It also can be found from Fig. 12 that ERT-III has the highest Nu/ Nuc and ERT-II has the highest PEC. However, PEC of ERT-IV is higher than that of ERT-II when u > 0.97. Therefore, u affects the configuration of porous insert for optimal thermo-hydraulic performance.

4.5

4.4. Effects of Reynolds number 4.0 3.5 3.0 2.5 4 4 4 4 4 4 4 4 5 2x10 3x10 4x10 5x10 6x10 7x10 8x10 9x10 1x10

Re

(a) 3

10

ERT-III (FRP=0.75) ERT-IV (FRP=0.05)

ERT-I (FRP=0.01) ERT-II (FRP=0.19) 2

Pp /Pp,c

10

1

10

The effects of Reynolds number (Re) on the performance of four kinds of ERTs are studied in this section. The values of u and ks/kf are set to 0.9726 and 1000, respectively. The values of FRP are the same as those of Section 4.2. Fig. 13 shows Nu/Nuc, Pp/Pp,c and PEC of four kinds of ERTs for different Re. It can be seen from Fig. 13a that Nu/Nuc of ERT-II, ERT-III and ERT-IV decrease with the increase of Re, while Nu/Nuc of ERT-I increases with the increase of Re. The thermal performance enhancement of ERT-I is attributed to the rebuilding of velocity field by porous insert, so it can be concluded that the ability of porous insert to rebuild velocity field increases with increasing Re. It also can be seen from Fig. 13a that Nu/Nuc of ERT-II is the largest when Re is lower than 50,000, while Nu/Nuc of ERT-III is the largest when Re exceeds 50,000. Therefore, Re affects the configuration of porous insert for optimal thermal performance. It can be seen from Fig. 13b and c that Pp/Pp,c of four kinds of ERTs increase with the increase of Re, which results in the decreasing of PEC with the increase of Re. It also can be seen from Fig. 13c that PEC of ERT-II and ERT-IV can be larger than 1.0. ERT-II has larger PEC when Re is lower than 80,000, while ERT-IV has larger PEC when Re exceeds 80,000. Therefore, Re affects the configuration of porous insert for optimal thermo-hydraulic performance.

0

10 4 4 4 4 4 4 4 4 5 2x10 3x10 4x10 5x10 6x10 7x10 8x10 9x10 1x10

Re

(b) 2.0 1.8

PEC

1.6

ERT-I (FRP=0.01) ERT-II (FRP=0.19) ERT-III (FRP=0.75) ERT-IV (FRP=0.05)

1.4 1.2 1.0 0.8 0.6 4 4 4 4 4 4 4 4 5 2x10 3x10 4x10 5x10 6x10 7x10 8x10 9x10 1x10

Re

(c) Fig. 13. Effects of Re on the performance of ERTs: (a) Nu/Nuc, (b) Pp/Pp,c, (c) PEC.

PEC of ERT-II, ERT-III and ERT-IV decrease with the increase of u, but PEC of ERT-I increases with increasing u. The reason is that decreasing u can effectively enhance the thermal performance of ERT-II, ERT-III and ERT-IV by increasing the effective thermal conductivity of HTF especially when the value of ks/kf exceeds a certain value, although the pump power increases with the decrease of u. However, the change of effective thermal conductivity has no effect on the thermal performance of ERT-I. So, the thermohydraulic performance of ERT-I increases with the increase of u.

5. Conclusions In this paper, a new method for the construction of porous inserts was coupled with CFD code to optimize the heat transfer enhancement in a solar central receiver tube with different porous insert configurations and non-uniform circumferential heat flux. The effects of some parameters (FRP, ks/kf, u and Re) on the thermal and thermo-hydraulic performance of ERT were discussed. The conclusions could be drawn as follows: (1) The ERT with porous insert can be used to avoid the hotspot caused by non-uniform heat flux due to its ability of heat transfer enhancement. The ERT partially filled with porous medium can obtain better heat transfer performance than that fully filled with porous medium. (2) The performance enhancement of ERT is interactively affected by all the parameters (FRP, ks/kf, u and Re). Among these parameters, ks/kf is the most crucial one. The value of ks/kf should be greater than 100 to obtain a good thermohydraulic performance. (3) ERT-III can obtain best thermal performance for a wide range of parameters, while ERT-II can obtain better Nu than ERT-III with low Re. (4) ERT-II and ERT-IV are recommended to obtain good thermalhydraulic performance with a relatively high value of ks/kf. ERT-II can obtain best PEC for low Re and u, while ERT-IV can obtain best PEC for high Re and u.

Acknowledgements This work is supported by the Key Project of National Natural Science Foundation of China (No. 51436007) and the National Natural Science Foundation of China (No. 51176155).

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References [1] Behar O, Khellaf A, Mohammedi K. A review of studies on central receiver solar thermal power plants. Renew Sust Energ Rev 2013;23:12–39. [2] Zheng ZJ, He YL, Li YS. An entransy dissipation-based optimization principle for solar power tower plants. Sci China Technol Sci 2014;57:773–83. [3] Romero M, Buck R, Pacheco JE. An update on solar central receiver systems, projects, and technologies. J Sol Energy Eng 2002;124:98–108. [4] Rodríguez-Sánchez MR, Soria-Verdugo A, Almendros-Ibáñez JA, Acosta-Iborra A, Santana D. Thermal design guidelines of solar power towers. Appl Therm Eng 2014;63:428–38. [5] Ho CK, Iverson BD. Review of high-temperature central receiver designs for concentrating solar power. Renew Sust Energ Rev 2014;29:835–46. [6] He YL, Cheng ZD, Cui FQ, Li ZY, Li D. Numerical investigations on a pressurized volumetric receiver: Solar concentrating and collecting modelling. Renew Energy 2012;44:368–79. [7] Tian Y, Zhao CY. A review of solar collectors and thermal energy storage in solar thermal applications. Appl Energy 2013;104:538–53. [8] Vignaroobana K, Xu XH, Arvay A, Hsu K, Kannan AM. Heat transfer fluids for concentrating solar power systems – a review. Appl Energy 2015;146:383–96. [9] Lu JF, Ding J, Yang JP. Heat transfer performance of an external receiver pipe under unilateral concentrated solar radiation. Sol Energy 2010;84:1879–87. [10] He YL, Xiao J, Cheng ZD, Tao YB. A MCRT and FVM coupled simulation method for energy conversion process in parabolic trough solar collector. Renew Energy 2011;36:976–85. [11] Cheng ZD, He YL, Cui FQ. A new modelling method and unified code with MCRT for concentrating solar collectors and its applications. Appl Energy 2013;101:686–98. [12] Cheng ZD, He YL, Cui FQ, Du BC, Zheng ZJ, Xu Y. Comparative and sensitive analysis for parabolic trough solar collectors with a detailed Monte Carlo raytracing optical model. Appl Energy 2014;115:559–72. [13] Chang C, Li X, Zhang QQ. Experimental and numerical study of the heat transfer characteristics in solar thermal absorber tubes with circumferentially non-uniform heat flux. Energy Proc 2014;49:305–13. [14] Roldán MI, Monterreal R. Heat flux and temperature prediction on a volumetric receiver installed in a solar furnace. Appl Energy 2014;120:65–74. [15] Wu ZY, Li SD, Yuan GF, Lei DQ, Wang ZF. Three-dimensional numerical study of heat transfer characteristics of parabolic trough receiver. Appl Energy 2014;113:902–11. [16] Qiu Y, He YL, Cheng ZD, Wang K. Study on optical and thermal performance of a linear Fresnel solar reflector using molten salt as HTF with MCRT and FVM methods. Appl Energy 2015;146:162–73. [17] Cheng ZD, He YL, Du BC, Wang K, Liang Q. Geometric optimization on optical performance of parabolic trough solar collector systems using particle swarm optimization algorithm. Appl Energy 2015;148:282–93. [18] Lata JM, Rodriguez M, de Lara MA. High flux central receivers of molten salts for the new generation of commercial stand-alone solar power plants. J Sol Energy Eng 2008;130:1–5. [19] Flores O, Marugán-Cruz C, Santana D, García-Villalba M. Thermal stresses analysis of a circular tube in a central receiver. Energy Proc 2014;49:354–62. [20] Wang K, He YL, Cheng ZD. A design method and numerical study for a new type parabolic trough solar collector with uniform solar flux distribution. Sci China Technol Sci 2014;57:531–40. [21] Wu ZY, Lei DQ, Yuan GF, Shao JJ, Zhang YT, Wang ZF. Structural reliability analysis of parabolic trough receivers. Appl Energy 2014;123:232–41. [22] Yu Q, Wang ZF, Xu ES. Analysis and improvement of solar flux distribution inside a cavity receiver based on multi-focal points of heliostat field. Appl Energy 2014;136:417–30. [23] Yang ML, Yang XX, Yang XP, Ding J. Heat transfer enhancement and performance of the molten salt receiver of a solar power tower. Appl Energy 2010;87:2808–11. [24] Mwesigye A, Huan ZJ, Meyer JP. Thermodynamic optimisation of the performance of a parabolic trough receiver using synthetic oil–Al2O3 nanofluid. Appl Energy 2015;156:398–412.

[25] Cheng ZD, He YL, Cui FC. Numerical study of heat transfer enhancement by unilateral longitudinal vortex generators inside parabolic trough solar receivers. Int J Heat Mass Transfer 2012;55:5631–41. [26] Muñoz J, Abánades A. Analysis of internal helically finned tubes for parabolic trough design by CFD tools. Appl Energy 2011;88:4139–49. [27] Ravi Kumar K, Reddy K. Thermal analysis of solar parabolic trough with porous disc receiver. Appl Energy 2009;86:1804–12. [28] Wang P, Liu DY, Xu C. Numerical study of heat transfer enhancement in the receiver tube of direct steam generation with parabolic trough by inserting metal foams. Appl Energy 2012;102:449–60. [29] Ravi Kumar K, Reddy K. Effect of porous disc receiver configurations on performance of solar parabolic trough concentrator. Heat Mass Transfer 2012;48:555–71. [30] Reddy K, Satyanarayana G. Numerical study of porous finned receiver for solar parabolic trough concentrator. Eng Appl Comp Fluid 2008;2:172–84. [31] Reddy K, Kumar KR, Satyanarayana G. Numerical investigation of energyefficient receiver for solar parabolic trough concentrator. Heat Transfer Eng 2008;29:961–72. [32] Ghasemi SE, Ranjbar AA, Ramiar A. Three-dimensional numerical analysis of heat transfer characteristics of solar parabolic collector with two segmental rings. J Math Comput Sci 2013;7:89–100. [33] Ghasemi SE, Ranjbar AA, Ramiar A. Numerical study on thermal performance of solar parabolic trough collector. J Math Comput Sci 2013;7:1–12. [34] Mwesigye A, Bello-Ochende T, Meyer JP. Heat transfer and thermodynamic performance of a parabolic trough receiver with centrally placed perforated plate inserts. Appl Energy 2014;136:989–1003. [35] Pacheco JE. Final test and evaluation results from the Solar Two project. Sandia National Laboratories report SAND; 2002. [36] Zheng ZJ, He Y, He YL, Wang K. Numerical optimization of catalyst configurations in a solar parabolic trough receiver–reactor with non-uniform heat flux. Sol Energy 2015;122:113–25. [37] Calmidi VV, Mahajan RL. Forced convection in high porosity metal foams. J Heat Transfer 2000;122:557–65. [38] Kolb GJ. An evaluation of possible next-generation high temperature moltensalt power towers. Sandia National Laboratories; 2011. [39] Liao ZR, Li X, Xu C, Chang C, Wang ZF. Allowable flux density on a solar central receiver. Renew Energy 2014;62:747–53. [40] Zheng ZJ, Li MJ, He YL. Optimization of porous insert configurations for heat transfer enhancement in tubes based on genetic algorithm and CFD. Int J Heat Mass Transfer 2015;87:376–9. [41] Fluent Inc. FLUENT 6.3 user’s guide. Fluent Publishing Company, Lebanon; 2007. [42] He YL, Tao WQ. Multiscale simulations of heat transfer and fluid flow problems. ASME J Heat Transfer 2012;134:1–13. [43] Tao WQ. Numerical heat transfer. Xi’an: Xi’an Jiaotong University Press; 2001. [44] Zavoico AB. Solar power tower design basis document. Sandia National Laboratories report SAND; 2001. [45] Wu M, Li MJ, Xu C, He YL, Tao WQ. The impact of concrete structure on the thermal performance of the dual-media thermocline thermal storage tank using concrete as the solid medium. Appl Energy 2014;113:1363–71. [46] He YL, Tao WQ. Convective heat transfer enhancement: mechanism, techniques and performance evaluation. Adv Heat Transfer 2014;46:87–186. [47] He YL, Zhang YW. Advances and outlooks of heat transfer enhancement by longitudinal vortex generators. Adv Heat Transfer 2012;44:119–85. [48] Yang SM, Tao WQ. Heat transfer. Beijing: Higher Education Press; 2006. [49] Huang ZF. Experimental and numerical studies of enhancing heat transfer in a tube by inserting porous media at the core. Ph.D. dissertation, Huazhong University of Science and Technology; 2004. [50] Huang ZF, Nakayama A, Yang K, Yang C, Liu W. Enhancing heat transfer in the core flow by using porous medium insert in a tube. Int J Heat Mass Transfer 2010;53:1164–74. [51] Xu C, Song Z, Chen L, Zhen Y. Numerical investigation on porous media heat transfer in a solar tower receiver. Renew Energy 2011;36:1138–44.

Please cite this article in press as: Zheng Z-J et al. Thermal analysis of solar central receiver tube with porous inserts and non-uniform heat flux. Appl Energy (2015), http://dx.doi.org/10.1016/j.apenergy.2015.11.039