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Heat transfer and friction of molten salt and supercritical CO2 flowing in an airfoil channel of a printed circuit heat exchanger
International Journal of Heat and Mass Transfer 150 (2020) 119006
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Heat transfer and friction of molten salt and supercritical CO2 flowing in an airfoil channel of a printed circuit heat exchanger Hong-Yuan Shi, Ming-Jia Li ⇑, Wen-Qi Wang, Yu Qiu, Wen-Quan Tao 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
a r t i c l e
i n f o
Article history: Received 4 July 2019 Received in revised form 20 October 2019 Accepted 5 November 2019
Keywords: Airfoil fin Printed circuit heat exchanger Molten salt Supercritical carbon dioxide Concentrating solar power
a b s t r a c t Airfoil printed circuit heat exchanger (PCHE) is considered as one of the competitive candidates in the 3rd generation of concentrating solar power (CSP) plant, where the molten salt and supercritical carbon dioxide (S-CO2) are adopted as the heat transfer fluids (HTFs). To study the flow features and heat transfer performance of the two HTFs in the airfoil channel of PCHE, a three-dimensional numerical model was firstly developed and validated by experiment. Then, the friction features and heat transfer of the two HTFs under different mass flow rate and inlet temperature conditions were numerically investigated. Then, the performance of distributed airfoil channels was compared with that of straight channels and zigzag channels. Finally, the heat transfer and friction factor correlations were fitted for the two HTFs in the airfoil channel of PCHE, which can be used in relatively wide ranges of Reynolds number and temperature. The results show that the larger inlet temperature leads to higher heat transfer performance for molten salt, but causes lower heat transfer performance for S-CO2. The airfoil channels have the best comprehensive heat transfer performance among these three channels at the given pumping power. Moreover, the maximum deviations between the simulation results and the proposed heat transfer correlations are within ±6% for both the molten salt and S-CO2. Finally, the maximum deviations between the proposed friction correlations and the calculated results are within ±4% and ±8% for the salt and S-CO2, respectively. The correlations and results given in current study can contribute to the design and application of airfoil PCHEs in the 3rd generation of CSP plant. Ó 2020 Elsevier Ltd. All rights reserved.
1. Introduction The high-efficiency utilization of solar energy is a potential way to relieve serious environmental issues induced by the overexploitation of fossil fuels [1–3]. In order to utilize solar energy, concentrating solar power (CSP) technique, including parabolic trough collector [4,5], solar power tower (SPT) [6,7], linear Fresnel reflector [8,9], and parabolic dish collector [10], has developed rapidly in recent years. Among these technologies, molten-salt SPT integrated with supercritical carbon dioxide (S-CO2) Brayton power cycle is considered as one of the major pathways in the 3rd generation of CSP plant [11–13], as shown in Fig. 1. As a crucial component of SPT plant, heat exchanger in transferring thermal energy from molten salt to S-CO2, is of great importance to the efficiency of the whole plant [14,15]. Printed circuit heat exchanger (PCHE) is compact and capable of withstanding high temperature and pressure [16]. Therefore, it is promising for the heat exchange between
⇑ Corresponding author. E-mail address: [email protected] (M.-J. Li). https://doi.org/10.1016/j.ijheatmasstransfer.2019.119006 0017-9310/Ó 2020 Elsevier Ltd. All rights reserved.
molten salt and S-CO2, and has attracted much interest in recent years. In recent years, different types of PCHEs have been widely investigated. Caccia et al. [17] fabricated a straight channel PCHE, which was made of a robust composite of ceramic and metal tungsten. They analyzed the thermal-hydraulic performance of this PCHE using molten salt and S-CO2 for a 10-MW-electric CSP plant. To enhance the heat transfer futures of the straight fins, the PCHE with zigzag fins, which can intensify flow disturbance, was developed and studied. For example, Saeed et al. [18] numerically studied the heat transfer and flow friction of S-CO2 in a zigzag channel PCHE with different fin arrangement for Reynolds number in the range of 2,500–60,000. However, the zigzag-fin PCHE causes a significant pressure drop [19]. To solve this problem, PCHE with distributed fins was developed and widely investigated. Ngo et al. [20] evaluated the pressure drop and heat transfer of a PCHE with distributed S-shaped fins by experiment using S-CO2 as the HTF, which had a temperature range of 308 K-553 K and a pressure range of 2.2 MPa-12.0 MPa. The results show that S-shaped PCHE exhibits lower pressure drop in comparison with that of zigzag PCHE. Kim et al. [21] numerically studied a PCHE with distributed
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Nomenclature Ac cross section area of channel (m2) A heat transfer area (m2) Cl, C1e, C2e, C3e, go, bR constants in numerical model cp specific heat capacity at constant pressure, (Jkg1K1) Dh hydraulic diameter (m) f Darcy friction factor g gravity (ms2) H height of simulation domain (m) h specific enthalpy (Jkg1), convective heat transfer coefficient (Wm2K1) height of bottom wall (m) Hb He height of element channel (m) Hf height of airfoil fin (m) Hs height of straight fin (m) height of top wall (m) Ht k turbulent kinetic energy of flow (m2s2) K overall heat transfer coefficient of PCHE (Wm2K1) L length of simulation domain (m), distance between inlet and outlet (m) La transverse pitch (m) Lb longitudinal pitch (m) length of element channel (m) Le Lf length of airfoil fin (m) Lst staggered pitch (m) Nu dimensionless Nusselt number p pressure (Pa) Pe,a perimeter of airfoil fin (m2) Pr dimensionless Prantal number Prt turbulent Prandtl number of energy Q heat transfer rate (W) qm mass flow rate (kgs1) Re dimensionless Reynolds number Se lateral area of the element channel in hot side (m2) Se,a top surface area of airfoil fin (m2) T temperature (K) tw height of middle wall (m) temperature of heat transfer surface (K) Tw
airfoil fins using S-CO2 with a temperature range of 380.9–552.9 K and a pressure range of 2.52–8.28 MPa. The results indicate that the pressure drop of airfoil PCHE is merely one-twentieth of that of zigzag PCHE, but the heat transfer is nearly the same as that of zigzag PCHE. Wang and He et al. [22] developed and tested a airfoil PCHE using molten salt with a temperature range of 470.8–527.4 K. Their results present that airfoil fins have better heat transfer performance compared with published correlations of straight fins and zigzag fins for Reynolds number in the range of 500–1600. Pidaparti et al. [23] studied the friction features and heat transfer of airfoil PCHE using S-CO2 by experiment with a temperature range of 293–473 K and a pressure range of 7.5–10.2 MPa. The results show that the airfoil PCHE exhibits lower friction factor compared with zigzag-fin PCHE. Yoon et al. [24] made a comparison of the PCHEs with straight fins, zigzag fins, S-shaped fins, and airfoil fins. Their study shows that heat transfer performance of airfoil PCHE is the highest among these four PCHEs. Review of the literature, it can be summarized that airfoil PCHE is a potential heat exchanger for the 3rd generation of CSP plant that employs molten salt and S-CO2 due to its low pressure drop and excellent heat transfer performance. To enable the design and application of the airfoil PCHE in the CSP, heat transfer and friction correlations are essential. However, only one heat transfer
u v Ve W Wc We Wf x, y, z
component of velocity (ms1) velocity (ms1) volume of the element channel in hot side (m3) width of simulation domain (m) width of cold channel (m) width of element channel (m) width of airfoil fin (m) Cartesian axes of PCHE system (m)
Abbreviations CSP concentrating solar power HTF heat transfer fluid PCHE printed circuit heat exchanger S-CO2 supercritical carbon dioxide Greek symbols ak inverse effective Prandtl number for k ae inverse effective Prandtl number for e dij unit tensor Dp pressure drop (Pa) DTm logarithm mean temperature difference (K) e turbulent dissipation rate of flow (m2s3) k thermal conductivity (Wm2K1) l dynamic viscosity (kgm1s1) lt turbulent viscosity of flow (kgm1s1) q density (kgm3) Subscription Ave average cold cold side of the PCHE f airfoil fin, fluid hot hot side of the PCHE in inlet out outlet salt molten salt w wall s standard structure
correlation for molten salt flowing in the airfoil PCHE has been obtained when temperature is less than 530 K [22]. Moreover, only one heat transfer correlation for S-CO2 in the airfoil PCHE has been obtained when temperature is less than 473 K and pressure is less than 10.2 MPa [23]. It is found that current experimental temperature is far lower than the realistic temperature in the 3rd generation of CSP. It is known that the friction features and heat transfer of S-CO2 and molten salt are directly influenced by the thermophysical properties that vary with the temperature significantly [25,36]. Thus, it is necessary to further investigate on the heat transfer and friction of molten salt and S-CO2 under the realistic operation condition (973 K, 20 MPa) in the 3rd generation of CSP [13]. Besides, all of the computational models used to evaluate the airfoil PCHE in pervious researches are not validated by experimental results of airfoil PCHE. Therefore, it is also necessary to develop a numerical model validated by experiment. To study on this topic, a three-dimensional numerical model is developed to evaluate friction features and heat transfer of airfoil PCHE. The calculated results are compared with experimental data procured in the airfoil PCHE to validate the model. Then, based on the model, the friction features and heat transfer of the two HTFs under different mass flow rate and inlet temperature conditions are analyzed. Moreover, the performance of airfoil channels is
H.-Y. Shi et al. / International Journal of Heat and Mass Transfer 150 (2020) 119006
3
Fig. 1. Schematic diagram of typical CSP plant.
compared with that of straight channels and zigzag channels. Finally, heat transfer and flow friction correlations are developed for the two HTFs in the airfoil channel of PCHE, which can be used in relatively wide ranges of Reynolds numbers and temperature. The main contributions of current work are summarized as: (1) A three-dimensional numerical model is developed to investigate heat transfer and friction of molten salt and S-CO2 in the airfoil channel of PCHE. The simulation results are compared with experimental data procured in the airfoil PCHE to validate the model. (2) The new heat transfer and flow friction correlations of molten salt and S-CO2 in the airfoil channel of PCHE are fitted. The ranges of correlations cover the typical working conditions in the 3rd generation of CSP, which can provide help to design the airfoil PCHE. (3) The friction features and heat transfer of the two HTFs flowing in the airfoil channel of PCHE are studied detailedly under different mass flow rate and inlet temperature conditions, and the performance of airfoil channels is compared with that of straight channels and zigzag channels. 2. Methodology 2.1. Physical model The airfoil PCHE designed in our previous study is chosen as the physical model [22] and demonstrated in Fig. 2. It has a length of 400 mm, a width of 130 mm, and a height of 70.5 mm. The PCHE consists of 12 hot-side plates with airfoil channels and 13 coldside plates with straight rectangular channels, which are made of 316L stainless steel and processed by photochemical method. Each hot-side plate and cold-side plate have 40 airfoil channels and 40 rectangular channels, respectively. Moreover, the hot-side plates and cold-side plates are stacked one by one, as shown in Fig. 3. More details about the PCHE can be found in our previous research [22].
Fig. 2. Photo of PCHE.
2.2. Heat transfer fluid Molten salt and S-CO2 are adopted as the HTFs in the airfoil channel. This is because in the 3rd generation of CSP technique, molten salt is considered as a promising HTF for its high working temperature, relatively mature technology, and low price. Moreover, S-CO2 Brayton power cycle is integrated in the 3rd generation of CSP technique. The molten salt used in the study is a MgCl2-KCl binary eutectic salt (43.4 wt% MgCl2, 56.6 wt% KCl), which can work at a temperature higher than 973 K with a melting point of 697.4 K. The thermophysical properties of the molten salt are obtained from Ref. [26]. For the S-CO2, its thermophysical properties under pressure condition of 20 MPa are firstly obtained from NIST data [27]. The pressure change of S-CO2 in the channel is much smaller than the operating pressure (less than 0.8%), so the effects of the pressure change on the properties is insignificant. Besides, S-CO2 is also adopted as the HTF in the straight rectangular channel. Both the thermophysical properties of the molten salt and S-CO2 change with temperature, which should be considered in the simulation for a typical temperature range, as shown in Fig. 4. The thermophysical properties are fitted in a form of piecewise functions and given in Table. A1 in Appendix A.
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Fig. 3. Stacked plates.
Fig. 4. Thermophysical properties of MgCl2-KCl and S-CO2.
Fig. 5. Cross section of micro-channels.
2.3. Numerical model There are many micro-channels in the PCHE, which consume large computing resources and time when all the channels are modeled and computed, as shown in Fig. 5. Therefore, a single
airfoil channel and a straight rectangular channel are selected as the simulation domain because of the symmetrical and periodic characteristics of the flow, as shown in Fig. 6. The geometry of airfoil fins is obtained from our previous work in Ref. [38]. The airfoil channel contains 50 rows of staggered NACA 0025 airfoil fins. The
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Fig. 6. Schematic diagram of simulation domain.
detailed geometrical parameters of simulation domain are summarized in Table 1. From the studies of Kim et al. [21] and Tsuzuki et al. [28], it is found that the renormalization group (RNG) k-e turbulence model can evaluate the flow friction and heat transfer performance of HTFs in the PCHE with distributed fins suitably, because the model takes into consideration the effects of swirl on turbulence. The comparison between three different turbulence models is carried out, as shown in Table 2. It can be seen that the deviation of calculated results for RNG k-e model is 1.23% comparing with experiment results [22]. For Standard k-e model and SST k-x model, the deviations are 38.57% and 46.92%, respectively. The results show that RNG model can achieve the most accurate prediction comparing with standard k-e model and SST k-x model. Therefore, RNG k-e turbulence model with the enhanced wall functions is used in the present model. The y+ of the near-wall node is maintained less than 5 by altering the grid case by case to guarantee that the wall functions are valid [36]. The governing equations adopted in the study include continuity equation, momentum equation, energy equation, and RNG k-e equations with enhanced wall functions [29]. The steady-state equations are shown in Eqs. (1)–(7). Continuity equation:
@ ðqui Þ ¼ 0 @xi
ð1Þ
Momentum equation:
@ui @uj 2 @ul @ @p @ þ qg i qui uj ¼ þ l þ lt þ dij @xi @xi @xj @xj @xi 3 @xl ð2Þ Energy equation:
@ @ l lt @T ðqui hÞ ¼ cp þ @xi @xi Pr Prt @xi
ð3Þ
k equation:
@ @ @k þ Gk þ Gb qe ðqkui Þ ¼ ak leff @xi @xi @xi
ð4Þ
e equation:
@ @xi
2 @e ðqeui Þ ¼ @x@ ae leff @x þ C 1e ke ðGk þ C 3e Gb Þ C 2e q ek Re i
Gk ¼ qu0i u0j
ð5Þ
i
@uj l @T 1 @q ; Gb ¼ bg i t ; b¼ ; @xi Pr t @xi q @T p
lt ¼ qC l
k
2
e ð6Þ
Re ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffi k C l qg3 ð1 g=go Þ e2 1 @ui @uj þ ; g ¼ 2Eij Eij ; Eij ¼ 3 2 @xj @xi 1 þ bR g k e
ð7Þ
Table 1 Geometrical parameters of simulation domain. Parameters
Value
Parameters
Value
length of simulation domain L width of simulation domain W height of simulation domain H length of airfoil fin Lf width of airfoil fin Wf height of airfoil fin Hf longitudinal pitch Lb
400.0 mm 3.0 mm 5.0 mm 4.0 mm 1.0 mm 1.5 mm 8.0 mm
transverse pitch La staggered pitch Lst height of straight fin Hs width of cold channel Wc height of top wall Ht height of middle wall tw height of bottom wall Hb
3.0 4.0 1.5 2.0 0.5 1.0 0.5
mm mm mm mm mm mm mm
Table 2 Turbulence model comparison. Results for Hitec
Experiment [22]
RNG k-e with enhanced wall function
Standard k-e with enhanced wall function
SST k-x
Nu/[Pr1/3(lf/lw)0.14] Error (%)
26.11 –
25.79 1.23
16.04 38.57
13.86 46.92
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where Cl = 0.0845, C1e = 1.42, C2e = 1.68, Prt = 0.85, bR = 0.012, go = 4.38. C3e = tanh|v2/v1|, v2 and v1 are the velocity components parallel and perpendicular to the gravitational vector, respectively. Fig. 6 shows the simulation domain and contains the main boundary conditions The details are summarized as follows: (1) Inlet of the fluid region: mass-inlet boundary. (2) Outlet of the fluid region: pressure outlet boundary. (3) Interface between fluid region and solid region: coupled boundary and no-slip boundary. (4) Periodic boundary conditions for the top and bottom surfaces. (5) Symmetry boundary conditions for left and right surfaces. (6) Adiabatic boundary conditions for other surfaces.
Z T hot;in ¼ AZc
Ac
3. Parameter definitions and model validation 3.1. Parameter definitions
Dh ¼ 4V e =Se
ð8Þ
V e ¼ ðLe W e Se;a ÞHe
ð9Þ
Se ¼ 2ðPe;a He =2Þ þ 2ðLe Lfin Þt þ 2ðW e Le Se;a Þ
ð10Þ
where Ve and Se represent the volume and the lateral area of the element channel, respectively; Le, We, and He are the length, width, and height of the element channel, respectively; Se,a and Pe,a represent the top surface area and perimeter of airfoil fin, respectively. The overall heat transfer coefficient (K) of PCHE is shown in Eq. (11).
K¼
Q ave ; Q ave ¼ ðQ hot þ Q cold Þ=2 DT m Ahot
DT m ¼
T T cold;out T hot;out T cold;in hot;in ln T hot;in T cold;out = T hot;out T cold;in
ð11Þ
T cp qv dA
Ac
cp qv dA
ð13Þ
ð14Þ
Then, the convective heat transfer coefficient (hhot) in the hot side can be calculated by Eq. (15).
1 1 Ahot t w Ahot K hcold Acold kw Aw
ð15Þ
where tw represents wall thickness; Aw represents the total wall surface area of the PCHE; kw represents the thermal conduction of wall, which is 16.3 Wm1K1. Based on the above parametrical definitions, the Reynolds number (Re), Nusselt number (Nu), Prandtl number (Pr), and friction factor (f) can be calculated by Eq. (16) and Eq. (17).
qm Dh hDh ; Nu ¼ ; Pr ¼ lAc k
f ¼ Dp
Dh 1 ; L ð1=2Þqv 2
v¼
lc p k
qm
qAc
ð16Þ
ð17Þ
where qm, represents the mass flow rate; l represents the dynamic viscosity; k represents the thermal conduction; cp represents the specific heat capacity; L represents the distance between inlet and outlet; Dp represents the pressure drop. The performance evaluation criteria (PEC) of heat transfer enhancement of PCHE at given pumping power is shown in Eq. (18) [32].
PEC ¼
Nu Nus
, 1=3 f fs
ð18Þ
where Nu, f, Nus, and fs are calculated by Eq. (16) and Eq. (17), and the subscript ‘‘s” indicates the standard structure. When the value of PEC is larger than one, it shows the PCHE has a better comprehensive heat transfer performance than that of standard structure at the identical pumping power.
ð12Þ
where Thot,in and Thot,out are the inlet and outlet temperature of the hot side, which are shown in Eq. (13). Tcold,in and Tcold,out are the inlet and outlet temperature of the cold side, which are calculated in the same way.
Fig. 7. Element channel.
; T hot;out ¼ AZc
Q ave T cold; out þ T cold; in Acold T w 2
hcold ¼
Re ¼
A method which defines Dh with considering both the size and configuration of airfoil fins is adopted in present research [31]. Fig. 7 presents a periodic element channel chose in current study. Then, Dh can be calculated by Eqs. (8)–(10).
cp qv dA
Z
The convective heat transfer coefficient (hcold) in the cold side is shown in Eq. (14).
hhot ¼ The entire governing equations are solved by FLUENT 18.0 commercial software with double precision. The pressure and convection terms are implemented by the PRESTO! scheme and a second-order scheme, respectively. The coupling pressure and velocity are solved by SIMPLE algorithm. The convergence criteria for each governing equation is that all residual targets are set to 10-6.
T cp qv dA
3.2. Mesh independence check and model validation Hexahedral meshes were generated in the fluid region and solid region. The mesh in the adjacent zone of fin wall should be fine enough to meet the requirements of wall function. Therefore, the first layer of grid near the fin wall in the fluid domain is hold with the initial height of 0.01 mm and the ratio of increment is 1.2, as shown in Fig. 8. To eliminate the conceivable influence of grid number on simulation, grid independence check should be examined for each case. An example was shown as follows, which conducted with a ternary molten salt in the hot side and a synthetic oil in the cold side. The HTFs were used in our previous experimental study. Fig. 9 gives the results of the grid independence check, and shows that the outlet temperature of the cold side and hot side have only little change when the mesh number is larger than 11,432,432. Taking into consideration the time and computational accuracy, the mesh number of 11,432,432 is adequate for current simulation. The grid independence check is also conducted for other cases.
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Fig. 10. Simulation results versus the experimental results.
Fig. 8. Schematic diagram of grid.
Th, out Tc, out
493
417
492
416
491
415
490
414
489 400
600
800
1000
1200
Grid number / × 10
1400
Table 3 The ranges of velocity and temperature for HTFs.
418
Outlet Temperature Tcold, out / K
Outlet Temperature Thot, out / K
494
413 1600
HTFs
Inlet velocity/ms1
Inlet temperature/K
Fluid temperature/K
MgCl2-KCl salt S-CO2
0.71–7.57 2.01–25.19
873–1073 873–1073
807–1073 779–1073
Firstly, the influences of mass flow rate and inlet temperature on the heat transfer and friction features are investigated. Then, the performance of straight channels and zigzag channels are compared with that of airfoil channels. Finally, new correlations of these two HTFs in the airfoil channel of PCHE are fitted, respectively. The examined ranges of the velocity and temperature for the two HTFs are given in Table 3, which cover the typical working conditions in the 3rd generation of CSP.
4
4.1. Heat transfer and flow friction of HTFs in airfoil channel
Fig. 9. Grid independence.
Comparison with our previous experiment for airfoil PCHE [22] is used to validate the numerical model adopted in current study. The experiment was conducted on a molten salt testing platform, which was designed and built in Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, China [33–35]. The geometrical parameters of the airfoil PCHE used in the experimental study are the same with what have mentioned in Section 2.1 of this paper. In the experiment, a ternary salt called Hitec was used in the hot side, and a synthetic oil called YD-325 was employed in the cold side. The operating temperature and volume flow rate of the salt ranged from 470.8 K to 527.4 K and 6.25 m3h1 to 15.88 m3h1, respectively. The thermophysical properties of Hitec and YD-325 are given in Table A2 in Appendix A. Fig. 10 illustrates the comparison between the modeling data and the testing results. It is observed that the simulation results are in good agreement with experimental results, and the maximum deviation is within ±12%, which indicates that the numerical model is reliable. 4. Results and discussions In this section, molten salt and S-CO2 are adopted to study the heat transfer and friction features of the airfoil channel of PCHE.
Molten salt and S-CO2 are used to study the heat transfer and friction features in the airfoil channel under different mass flow rate (qm) and inlet temperature (Tin), as shown in Fig. 11. For the molten salt, Nu/Pr0.4 increases with the increment of qm when Tin is fixed, while the friction factor (f) decreases as shown in Fig. 11 (a). This is because the larger qm leads to more intense turbulence, which enhances the heat transfer performance. The increment of the square of velocity is larger than pressure drop, which causes the decrement of friction factor. Meanwhile, it can also be observed that Nu/Pr0.4 increases with the increment of Tin at a constant qm, while the friction factor decreases. This is due to higher temperature leading to lower dynamic viscosity and density, as shown in Fig. 4(a), which cause higher Re number and velocity at a constant qm, respectively. Fig. 11(b) shows the effect of qm and Tin on S-CO2. It is seen that Nu/Pr0.4 increases with ascending qm when Tin is fixed, while the friction factor decreases. The phenomenon is caused by the similar reason for the salt. Moreover, it can be also found that both Nu/Pr0.4 and the friction factor decrease with the increment of Tin at a constant of qm. The effect of Tin on heat transfer performance of S-CO2 is quite different from that of salt. This is because the change of the dynamic viscosity of S-CO2 with temperature is opposite to that of the molten salt, as can be seen from Fig. 4. The larger Tin leads to larger dynamic viscosity, which causes lower Re number at a constant qm.
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Fig. 11. Influences of mass flow rate and inlet temperature on heat transfer and friction features in airfoil channel.
Fig. 12. Effects of buoyancy on heat transfer and friction of S-CO2 at different inlet temperature.
The buoyancy has some unexpected influence on performance of S-CO2. Therefore, the effects of buoyancy on S-CO2 are estimated and the results are shown in Fig. 12. It can be seen that the buoyancy nearly has no effects on the heat transfer and friction of S-CO2 in current range of working temperature. This is because present temperature and pressure conditions are far away from the pseudo-critical region, which will not cause dramatic change of thermophysical properties. It is convenient to see how much heat is transferred directly between the fluids and how much goes through the wall by numerical method. Hence, the calculated results of the heat
transferred directly between the fluids and going through the wall are shown in Table 4. It can be seen that the heat transferred directly between the fluids are almost equivalent to that going through the wall. This is because the heat transferred directly between the fluids and going through the wall are mandatorily equal in numerical model due to the energy conservation [29,30]. Furthermore, molten salt is taken as an example to investigate the local flow field and temperature field in the airfoil channel. The molten salt has a mass flow rate of 0.0295 kgs1 and an inlet temperature of 973 K. Fig. 13 depicts the flow and temperature field at the middle cross section (z = 3.75 mm) of salt zone for the first three rows of the airfoil fins. It can be seen from Fig. 13 (a) that there exists local high pressure in the head region of fins because of the stagnation of salt. The pressure gradually decreases along the flow direction but low-pressure regions exist near the position where the airfoil fins has the highest thickness. This is because the highest fin thickness causes minimum flow cross section area and highest velocity. Fig. 13(b) illustrates that the thermal boundary layer becomes thicker along the fin edge. The temperature of HTF in the main flow region is higher than that of HTF in the tail region of fins. Fig. 13(c) shows that the velocity has a periodic variation in the flow direction. This is because the staggered fin arrays cause periodic change of the flow cross section area along the flow direction. It is also observed that the velocity of HTF in the main flow region is higher than that of HTF in the tail region of fins. However, the turbulent kinetic energy in the tail region is higher than that in the main flow region, as shown in Fig. 13(d). This is because the airfoil fins intensify the mixture of the HTFs from two adjacent channels in the tail region of fins, which increases the turbulent kinetic energy behind the fins.
Table 4 Comparison between the heat transferred directly between the fluids and going through the wall (ms-co2 = 0.009834 kgs1, Ts-co2 = 773 K). Case
Heat going through salt wall/W
Heat carried by salt/W
Error/%
Heat going through S-CO2 wall /W
Heat carried by S-CO2/W
Error/%
msalt = 0.022 kgs1 Tsalt,in = 973 K msalt = 0.022 kgs1 Tsalt,in = 873 K msalt = 0.0445 kgs1 Tsalt,in = 973 K msalt = 0.0445 kgs1 Tsalt,in = 1073 K
1179.11
1177.21
0.16%
1179.11
1179.36
0.02%
582.38
581.38
0.17%
582.39
582.62
0.04%
1365.99
1364.45
0.11%
1365.99
1366.06
0.01%
2066.97
2064.79
0.11%
2066.96
2067.00
0.01%
H.-Y. Shi et al. / International Journal of Heat and Mass Transfer 150 (2020) 119006
(a) Pressure
9
(b) Temperature
(c) Velocity
(d) Turbulent kinetic energy
Fig. 13. Flow field and temperature field of molten salt in airfoil channel (z = 3.75 mm).
Fig. 14. Comparison with straight channels.
4.2. Comparison between airfoil channels and two typical channels In this part, molten salt is taken as the HTF to compare the heat transfer performance and friction features of the airfoil channels with those of straight channels and zigzag channels.
4.2.1. Airfoil channels versus straight channels Qiu et al. [36] found that Gnielinski’s correlation (see Eq. (19)) and Filonenko’s correlation (see Eq. (20)) can be used to predict the heat transfer and friction features of salts in the smooth channel with the maximum deviations of ±15% and ±2%, respectively.
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Hence, these correlations are adopted to predict the heat transfer and friction of salts in the straight channel of PCHE. Fig. 14 illustrates the comparison of heat transfer and friction factor between airfoil channels and straight channels. It can be found in Fig. 14(a) that the heat transfer of the airfoil channels is almost 2 times that of the straight channels. Meanwhile, Fig. 14 (b) shows that the value of friction factor of the airfoil channels is also higher than that of the straight channels. Besides, Fig. 14 (c) indicates that the PEC of the airfoil channels is larger than that of the straight channels, when the straight channels are adopted as the standard structure. The results indicate that the distributed airfoil channels can enhance heat transfer performance when compared with straight channels. In the meantime, airfoil channels also increase the flow friction. The airfoil channels have the better comprehensive heat transfer performance comparing with straight channels at the same pumping power.
h i 0:11 Nu ¼ 0:012 Re0:87 280 Pr0:4 1 þ ðDh =LÞ2=3 Pr f =Prw Re ¼ 2300 106 ; Pr ¼ 0:6 105 2
f ¼ ð1:82lgðReÞ 1:64Þ ; Re ¼ 2300 106 ; Pr ¼ 0:6 105
ð19Þ
ð20Þ
4.2.2. Airfoil channels versus zigzag channels The experimental results of the heat transfer and friction factor (f) in zigzag channel are compared with present simulation data of airfoil fins, as shown in Fig. 15. In Fig. 15(a), it can be found that the value of (Nu-4.089)/Pr0.58 of the airfoil channels is higher than that of the zigzag channels [37]. However, Fig. 15(b) shows that the value of friction factor (f) of the airfoil channels is almost the same as that of the zigzag channels. Fig. 15(c) indicates that the PEC of airfoil channels is larger than that of zigzag channels, when the zigzag channels are adopted as the standard structure. The results indicate that airfoil channels exhibit better heat transfer features than that of zigzag channels under the same pumping power. The above results indicate that the airfoil channels have the best comprehensive heat transfer performance at the given pumping power among these three structures. This is because the distributed airfoil fins bring about alternant enlargement and shrinkage in the cross section of channel, which enhance the heat transfer. Meanwhile, the airfoil fins have a streamlined shape, which can avoid overlarge flow friction. Therefore, the airfoil PCHE is an excellent choice for the 3rd generation of CSP plant.
Fig. 15. Comparison with zigzag channels.
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4.3. New heat transfer and friction factor correlations for HTFs in airfoil channel Considering the lack of reliable heat transfer and friction factor correlations of salt and S-CO2 in the airfoil channel of PCHE, the corresponding correlations are fitted with relatively wide ranges of Re number and temperature. The expression of heat transfer correlations in form of Ref.[36] is adopted. Meanwhile, the Darcy friction law is used for friction correlations. 4.3.1. Correlations for molten salt in airfoil channel To better predict the heat transfer and friction features of salt in airfoil channel, the calculated data under a wide range of Re number and temperature are employed to develop two correlations, which are given in Eq. (21) and Eq. (22). Fig. 16 depicts the comparison between the heat transfer correlation and the calculated results. It is seen that the calculated results fit well with the heat transfer correlation, with a maximum deviation of ±6%. Fig. 17 illustrates the comparison between the friction correlation and the calculated results. The friction correlation is commendably coincident with calculated results, with a maximum deviation of ±4%.
1=3 Nusalt ¼ 0:063Re0:755 salt Pr salt
where Resalt = 509–6,773, Prsalt = 7.5–9.5, lsalt/lw = 0.84–0.93. 4.3.2. Correlations for S-CO2 in airfoil channel For S-CO2, the heat transfer and friction correlations are also fitted and given in Eq. (23) and Eq. (24), respectively. A comparison between the simulation results and the heat transfer correlation is illustrated in Fig. 18. The heat transfer correlation agrees well with the simulation results, with a maximum deviation of ±6%. Fig. 19 illustrates the comparison between the friction correlation and the calculated results. It can be observed that the calculated results are in good agreement with fitted friction correlation. The largest deviation of calculated results and developed correlation is smaller than ±8%. In present study, the working temperature of S-CO2 ranges from 779 K to 1073 K, which is far away from the pseudo-critical region. It can be seen that variations of properties of S-CO2 have less effects on heat transfer and friction under above temperature conditions. 0:4 NuSCO2 ¼ 0:0986Re0:687 SCO2 Pr SCO2
+6%
w
T in=973K
lSCO2 =lw
0:14
ð23Þ
S-CO2
-6%
salt
30 20
Nusalt=0.063Re0.755 Pr1/3 ( salt salt
10
S-CO2
350
T in=873K
salt
/
w
)0.14
+6%
T in=973K
300
T in=1073K
/
T in=1073K
40
)0.14]
T in=873K
50
·( NuS-CO2/[Pr0.4 S-CO2
)0.14]
ð21Þ
400
/
w
0:14
ð22Þ
MgCl2-KCl
Nusalt/[Pr1/3 ·( salt
lsalt =lw
f salt ¼ 3:07Re0:462 salt
60
-6%
250 200 150 100
Pr0.4 ( NuS-CO2=0.0986Re0.687 S-CO2 S-CO2
50
S-CO2
/
w
)0.14
0
0 0
0
1000 2000 3000 4000 5000 6000 7000 8000
Resalt
2
4
6
8
10
12
14
16
12
14
ReS-CO2 / × 104
Fig. 16. Heat transfer correlation for molten salt.
Fig. 18. Heat transfer correlation for S-CO2.
0.20
0.050 MgCl2-KCl
0.18
T in=873K
S-CO2
0.045
T in=973K
0.16
T in=873K T in=973K
0.040
T in=1073K
0.14
T in=1073K
0.035
0.12
fS-CO2
fsalt
+4%
0.10
+8%
0.030 0.025
-4%
0.08
fsalt=3.07Re-0.462 salt
0.06
-8%
0.020
fS-CO2=0.513Re-0.667 S-CO2
0.015 0.010
0.04 0
1000 2000 3000 4000 5000 6000 7000 8000
Resalt
Fig. 17. Friction factor correlation for molten salt.
0
2
4
6
8
10
ReS-CO2 / × 104 Fig. 19. Friction factor correlation for S-CO2.
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H.-Y. Shi et al. / International Journal of Heat and Mass Transfer 150 (2020) 119006
Table A1 Thermophysical properties of MgCl2-KCl [26] and S-CO2 [27]. HTFs
Temperature range/K
Piecewise functions of the properties
MgCl2-KCl
723.15–1073.15 723.15–1073.15 723.15–1073.15 723.15–1073.15 673–1173 673–973 973–1173 673–1173 673–1173
q = 0.552(T 273.15) + 1903.7, kgm3 cp = 0.1046(T 703.15) + 989.6, Jkg1K1 k = 1.0E 4(T 273.15) + 0.5047, Wm1K1 l = 1.784E 8(T 273.15)2 –2.91E 5(T 273.15) + 1.4965E 2, kgm1s1 q = 1.7502E 4 T2 4.5727E 1 T + 382.91, kgm3 cp = 1.1368E 6 T3 + 3.0368E 3 T2 2.5183 T + 1890, Jkg1K1 cp = 1.6692E 1 T + 1105.9, Jkg1K1 k = 4.2972E 9 T2 + 7.3888E 5 T + 4.6548E-3, Wm1K1 l = 3.4566E 12 T2 + 3.3913E 8 T + 1.2126E 5, kgm1s1
S-CO2
Table A2 Thermophysical properties of Hitec [35] and YD-325 [35]. HTFs
Temperature range/K
Piecewise functions of the properties
Hitec
420–800 420–800 420–536 536–800 420–440 440–500 500–800 300–573 300–573 300–573 323–423 423–523
q = 0.733 T + 2280.22, kgm3
YD-325
f SCO2 ¼ 0:513Re0:667 SCO2
cp = 1560, Jkg1K1 k = 1.863E 8 T3 + 2.551E 5 T2 0.01176 T + 2.2627, Wm1K1 k = 6.47E 4 T + 0.7663, Wm1K1 l = 1.742173E 6 T3 + 2.27615E 3 T2 0.99143 T + 143.9826, kgm1s1 l = 7.2058E 9 T3 + 1.08225E 5 T2 5.4754E-3 T + 0.93845, kgm1s1 l = 8.507E 13 T4 2.4331E 9 T3 + 2.6275E-6 T2 1.2768E 3 T + 0.23846, kgm1s1 q = 0.6311 T + 1199.13, kgm3 cp = 3.40 T + 776.0, Jkg1K1 k = 6.68E 5 T + 0.1416, Wm1K1 l = 4.066E 9 T3 + 5.2746E 6 T2 2.283E 3 T + 0.33065, kgm1s1 l = 4.413E 10 T3 + 6.735E 7 T2 3.452E-4 T + 0.05989, kgm1s1
ð24Þ
where ReS-CO2 = 11,671–123,483, PrS-CO2 = 0.73–0.75, lS-CO2/
lw = 1.03–1.09. The above results indicate that the developed correlations can evaluate the heat transfer and friction features well for salt and S-CO2 in the airfoil channel of PCHE, which can contribute to the design and application of PCHE in the 3rd generation of CSP plants. 5. Conclusions
(4) For the salt, the heat transfer and friction factor correlations are proposed, where Resalt = 509–6,773, Prsalt = 7.5–9.5, lsalt/ lw = 0.84–0.93. The heat transfer and friction factor correlations are also developed for the S-CO2, where ReS-CO2 = 11, 671–123,483, PrS-CO2 = 0.73–0.75, lS-CO2/lw = 1.03–1.09. All the deviations between the fitted heat transfer correlations and the simulation data are within ± 6% for the two HTFs. The entire deviations between the friction correlations and the simulation data are within ±4% and ±8% for the salt and S-CO2, respectively.
In this paper, the heat transfer and flow friction performance of molten salt and S-CO2 in the airfoil channel of PCHE was investigated with relatively wide ranges of Re number and temperature, which cover typical working conditions in the 3rd generation of CSP. The conclusions are obtained as follows.
In conclusion, these new heat transfer and friction factor correlations and beneficial results can be used for the design of airfoil PCHE in the 3rd generation of CSP plant.
(1) A three-dimensional numerical model was developed to simulate heat transfer and friction features of the two heat transfer fluids, and then validated by comparing the calculated results with our pervious experimental results procured in the airfoil PCHE. The maximum deviation is within ±12%, which demonstrates that the computational model adopted in current study is credible. (2) The influences of mass flow rate and inlet temperature on the performance of the two heat transfer fluids were studied. The larger inlet temperature leads to higher heat transfer performance for molten salt, but causes lower heat transfer performance for S-CO2. For both the two heat transfer fluids, the friction factor decreases with the increment of inlet temperature. (3) The heat transfer and friction features of the straight channels and zigzag channels were compared with that of the airfoil channels. The distributed airfoil fins can enhance the disturbance and achieve better heat transfer performance without exceeding increment of flow friction. Besides, airfoil channels have the best comprehensive heat transfer performance at given pumping power.
The study is supported by the National Key R&D Program of China (2017YFB0601801) and the National Natural Science Foundation of China (No. 51806165).
Acknowledgements
Appendix A See Table A1 and Table A2. References [1] D.V. Spracklen, Global warming: China’s contribution to climate change, Nature 531 (7594) (2016) 310. [2] M.J. Li, Y.L. He, W.Q. Tao, Modeling a hybrid methodology for evaluating and forecasting regional energy efficiency in China, Appl. Energy 185 (2017) 1769– 1777. [3] Y.L. He, K. Wang, Y. Qiu, B.C. Du, Q. Liang, S. Du, Review of the solar flux distribution in concentrated solar power: non-uniform features, challenges, and solutions, Appl. Therm. Eng. 149 (2019) 448–474. [4] Y.L. He, J. Xiao, Z.D. Cheng, Y.B. Tao, A MCRT and FVM coupled simulation method for energy conversion process in parabolic trough solar collector, Renew. Energy 36 (3) (2011) 976–985. [5] Y.L. He, D.H. Mei, W.Q. Tao, W.W. Yang, H.L. Liu, Simulation of the parabolic trough solar energy generation system with organic Rankine cycle, Appl. Energy 97 (2012) 630–641.
H.-Y. Shi et al. / International Journal of Heat and Mass Transfer 150 (2020) 119006 [6] W.Q. Wang, Y. Qiu, M.J. Li, F. Cao, Z.B. Liu, Optical efficiency improvement of solar power tower by employing and optimizing novel fin-like receivers, Energy Convers. Manage. 184 (2019) 219–234. [7] B.C. Du, Y.L. He, Z.J. Zheng, Z.D. Cheng, Analysis of thermal stress and fatigue fracture for the solar tower molten salt receiver, Appl. Therm. Eng. 99 (2016) 741–750. [8] Y. Qiu, Y.L. He, Z.D. Cheng, K. Wang, Study on optical and thermal performance of a linear Fresnel solar reflector using molten salt as HTF with MCRT and FVM methods, Appl. Energy 146 (2015) 162–173. [9] Y. Qiu, Y.L. He, M. Wu, Z.J. Zheng, A comprehensive model for optical and thermal characterization of a linear Fresnel solar reflector with a trapezoidal cavity receiver, Renew. Energ. 97 (2016) 129–144. [10] F.Q. Cui, Y.L. He, Z.D. Cheng, Y.S. Li, Study on combined heat loss of a dish receiver with quartz glass cover, Appl. Energy 112 (2013) 690–696. [11] T.O. Dunlop, D.J. Jarvis, W.E. Voice, J.H. Sullivan, Stabilization of molten salt materials using metal chlorides for solar thermal storage, Sci. Rep. 8 (1) (2018) 8190. [12] K. Wang, Y.L. He, H.H. Zhu, Integration between supercritical CO2 Brayton cycles and molten salt solar power towers: A review and a comprehensive comparison of different cycle layouts, Appl. Energy 195 (2017) 819–836. [13] M. Mehos, C. Turchi, J. Vidal, M. Wagner, Z.W. Ma, C. Ho, et al., Concentrating solar power Gen3 demonstration roadmap[R], National Renewable Energy Lab. (NREL), Golden, CO (United States), 2017. [14] M.J. Li, J.L. Xu, F. Cao, J.Q. Guo, Z.X. Tong, H.H. Zhu, The investigation of thermoeconomic performance and conceptual design for the miniaturized leadcooled fast reactor composing supercritical CO2 power cycle, Energy 173 (2019) 174–195. [15] K. Wang, Y.L. He, Thermodynamic analysis and optimization of a molten salt solar power tower integrated with a recompression supercritical CO2 Brayton cycle based on integrated modeling, Energy Convers. Manage. 135 (2017) 336– 350. [16] P. Sabharwall, D. Clark, M. Glazoff, G.Q. Zheng, K. Sridharan, M. Anderson, Advanced heat exchanger development for molten salts, Nucl. Eng. Des. 280 (2014) 42–56. [17] M. Caccia, M. Tabandeh-Khorshid, G. Itskos, A.R. Strayer, A.S. Caldwell, S. Pidaparti, et al., Ceramic–metal composites for heat exchangers in concentrated solar power plants, Nature 562 (7727) (2018) 406. [18] M. Saeed, M.H. Kim, Thermal and hydraulic performance of SCO2 PCHE with different fin configurations, Appl. Therm. Eng. 127 (2017) 975–985. [19] N. Bartel, M. Chen, V.P. Utgikar, X. Sun, I.H. Kim, R. Christensen, et al., Comparative analysis of compact heat exchangers for application as the intermediate heat exchanger for advanced nuclear reactors, Ann. Nucl. Energy 81 (2015) 143–149. [20] T.L. Ngo, Y. Kato, K. Nikitin, T. Ishizuka, Heat transfer and pressure drop correlations of microchannel heat exchangers with S-shaped and zigzag fins for carbon dioxide cycles, Exp. Therm Fluid Sci. 32 (2) (2007) 560–570. [21] D.E. Kim, M.H. Kim, J.E. Cha, S.O. Kim, Numerical investigation on thermal– hydraulic performance of new printed circuit heat exchanger model, Nucl. Eng. Des. 238 (12) (2008) 3269–3276.
13
[22] W.Q. Wang, Y. Qiu, Y.L. He, H.Y. Shi, Experimental study on the heat transfer performance of a molten-salt printed circuit heat exchanger with airfoil fins for concentrating solar power, Int. J. Heat Mass Transf. 135 (2019) 837–846. [23] S.R. Pidaparti, M.H. Anderson, D. Ranjan, Experimental investigation of thermal-hydraulic performance of discontinuous fin printed circuit heat exchangers for supercritical CO2 power cycles, Exp. Therm Fluid Sci. 106 (2019) 119–129. [24] S.H. Yoon, H.C. No, G.B. Kang, Assessment of straight, zigzag, S-shape, and airfoil PCHEs for intermediate heat exchangers of HTGRs and SFRs, Nucl. Eng. Des. 270 (2014) 334–343. [25] C. Dang, E. Hihara, In-tube cooling heat transfer of supercritical carbon dioxide. Part 1. Experimental measurement, Int. J. Refrig 27 (7) (2004) 736–747. [26] X.K. Xu, X.X. Wang, P.W. Li, Y.Y. Li, Q. Hao, B. Xiao, et al., Experimental test of properties of KCl–MgCl2 eutectic molten salt for heat transfer and thermal storage fluid in concentrated solar power systems, J. Sol. Energy Eng. 140 (5) (2018) 051011. [27] Linstrom P J, Mallard W G. National Institute of Standards and Technology: Gaithersburg, MD, 2005. 2011. [28] N. Tsuzuki, Y. Kato, T. Ishiduka, High performance printed circuit heat exchanger, Appl. Therm. Eng. 27 (10) (2007) 1702–1707. [29] W.Q. Tao, Numerical Heat Transfer, second ed., Xi’an Jiaotong University Press, Xi’an, 2001. [30] H.K. Versteeg, W. Malalasekera, An introduction to computational fluid dynamics: the finite volume method, second ed., Pearson Education, London, 2007. [31] T.H. Kim, J.G. Kwon, S.H. Yoon, H.S. Park, M.H. Kim, J.E. Cha, Numerical analysis of air-foil shaped fin performance in printed circuit heat exchanger in a supercritical carbon dioxide power cycle, Nucl. Eng. Des. 288 (2015) 110–118. [32] Z.D. Cheng, Y.L. He, F.Q. Cui, Numerical study of heat transfer enhancement by unilateral longitudinal vortex generators inside parabolic trough solar receivers, Int. J. Heat Mass Transf. 55 (21–22) (2012) 5631–5641. [33] Y.L. He, Z.J. Zheng, B.C. Du, K. Wang, Y. Qiu, Experimental investigation on turbulent heat transfer characteristics of molten salt in a shell-and-tube heat exchanger, Appl. Therm. Eng. 108 (2016) 1206–1213. [34] B.C. Du, Y.L. He, K. Wang, H.H. Zhu, Convective heat transfer of molten salt in the shell-and-tube heat exchanger with segmental baffles, Int. J. Heat Mass Transf. 113 (2017) 456–465. [35] Y. Qiu, M.J. Li, W.Q. Wang, B.C. Du, K. Wang, An experimental study on the heat transfer performance of a prototype molten-salt rod baffle heat exchanger for concentrated solar power, Energy 156 (2018) 63–72. [36] Y. Qiu, M.J. Li, M.J. Li, H.H. Zhang, B. Ning, Numerical and experimental study on heat transfer and flow features of representative molten salts for energy applications in turbulent tube flow, Int. J. Heat Mass Transf. 135 (2019) 732– 745. [37] I.H. Kim, H.C. No, Thermal hydraulic performance analysis of a printed circuit heat exchanger using a helium–water test loop and numerical simulations, Appl. Therm. Eng. 31 (17–18) (2011) 4064–4073. [38] H.Y. Shi, H. Liu, J.G. Xiong, Y. Qiu, Y.L. He, Study on flow and heat transfer characteristics of an airfoil printed circuit heat exchanger with dimples, J. Eng. Thermophys. 40 (2019) 857–862.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer and friction of molten salt and supercritical CO2 flowing in an airfoil channel of a printed circuit heat exchanger Hong-Yuan Shi, Ming-Jia Li ⇑, Wen-Qi Wang, Yu Qiu, Wen-Quan Tao 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
a r t i c l e
i n f o
Article history: Received 4 July 2019 Received in revised form 20 October 2019 Accepted 5 November 2019
Keywords: Airfoil fin Printed circuit heat exchanger Molten salt Supercritical carbon dioxide Concentrating solar power
a b s t r a c t Airfoil printed circuit heat exchanger (PCHE) is considered as one of the competitive candidates in the 3rd generation of concentrating solar power (CSP) plant, where the molten salt and supercritical carbon dioxide (S-CO2) are adopted as the heat transfer fluids (HTFs). To study the flow features and heat transfer performance of the two HTFs in the airfoil channel of PCHE, a three-dimensional numerical model was firstly developed and validated by experiment. Then, the friction features and heat transfer of the two HTFs under different mass flow rate and inlet temperature conditions were numerically investigated. Then, the performance of distributed airfoil channels was compared with that of straight channels and zigzag channels. Finally, the heat transfer and friction factor correlations were fitted for the two HTFs in the airfoil channel of PCHE, which can be used in relatively wide ranges of Reynolds number and temperature. The results show that the larger inlet temperature leads to higher heat transfer performance for molten salt, but causes lower heat transfer performance for S-CO2. The airfoil channels have the best comprehensive heat transfer performance among these three channels at the given pumping power. Moreover, the maximum deviations between the simulation results and the proposed heat transfer correlations are within ±6% for both the molten salt and S-CO2. Finally, the maximum deviations between the proposed friction correlations and the calculated results are within ±4% and ±8% for the salt and S-CO2, respectively. The correlations and results given in current study can contribute to the design and application of airfoil PCHEs in the 3rd generation of CSP plant. Ó 2020 Elsevier Ltd. All rights reserved.
1. Introduction The high-efficiency utilization of solar energy is a potential way to relieve serious environmental issues induced by the overexploitation of fossil fuels [1–3]. In order to utilize solar energy, concentrating solar power (CSP) technique, including parabolic trough collector [4,5], solar power tower (SPT) [6,7], linear Fresnel reflector [8,9], and parabolic dish collector [10], has developed rapidly in recent years. Among these technologies, molten-salt SPT integrated with supercritical carbon dioxide (S-CO2) Brayton power cycle is considered as one of the major pathways in the 3rd generation of CSP plant [11–13], as shown in Fig. 1. As a crucial component of SPT plant, heat exchanger in transferring thermal energy from molten salt to S-CO2, is of great importance to the efficiency of the whole plant [14,15]. Printed circuit heat exchanger (PCHE) is compact and capable of withstanding high temperature and pressure [16]. Therefore, it is promising for the heat exchange between
⇑ Corresponding author. E-mail address: [email protected] (M.-J. Li). https://doi.org/10.1016/j.ijheatmasstransfer.2019.119006 0017-9310/Ó 2020 Elsevier Ltd. All rights reserved.
molten salt and S-CO2, and has attracted much interest in recent years. In recent years, different types of PCHEs have been widely investigated. Caccia et al. [17] fabricated a straight channel PCHE, which was made of a robust composite of ceramic and metal tungsten. They analyzed the thermal-hydraulic performance of this PCHE using molten salt and S-CO2 for a 10-MW-electric CSP plant. To enhance the heat transfer futures of the straight fins, the PCHE with zigzag fins, which can intensify flow disturbance, was developed and studied. For example, Saeed et al. [18] numerically studied the heat transfer and flow friction of S-CO2 in a zigzag channel PCHE with different fin arrangement for Reynolds number in the range of 2,500–60,000. However, the zigzag-fin PCHE causes a significant pressure drop [19]. To solve this problem, PCHE with distributed fins was developed and widely investigated. Ngo et al. [20] evaluated the pressure drop and heat transfer of a PCHE with distributed S-shaped fins by experiment using S-CO2 as the HTF, which had a temperature range of 308 K-553 K and a pressure range of 2.2 MPa-12.0 MPa. The results show that S-shaped PCHE exhibits lower pressure drop in comparison with that of zigzag PCHE. Kim et al. [21] numerically studied a PCHE with distributed
2
H.-Y. Shi et al. / International Journal of Heat and Mass Transfer 150 (2020) 119006
Nomenclature Ac cross section area of channel (m2) A heat transfer area (m2) Cl, C1e, C2e, C3e, go, bR constants in numerical model cp specific heat capacity at constant pressure, (Jkg1K1) Dh hydraulic diameter (m) f Darcy friction factor g gravity (ms2) H height of simulation domain (m) h specific enthalpy (Jkg1), convective heat transfer coefficient (Wm2K1) height of bottom wall (m) Hb He height of element channel (m) Hf height of airfoil fin (m) Hs height of straight fin (m) height of top wall (m) Ht k turbulent kinetic energy of flow (m2s2) K overall heat transfer coefficient of PCHE (Wm2K1) L length of simulation domain (m), distance between inlet and outlet (m) La transverse pitch (m) Lb longitudinal pitch (m) length of element channel (m) Le Lf length of airfoil fin (m) Lst staggered pitch (m) Nu dimensionless Nusselt number p pressure (Pa) Pe,a perimeter of airfoil fin (m2) Pr dimensionless Prantal number Prt turbulent Prandtl number of energy Q heat transfer rate (W) qm mass flow rate (kgs1) Re dimensionless Reynolds number Se lateral area of the element channel in hot side (m2) Se,a top surface area of airfoil fin (m2) T temperature (K) tw height of middle wall (m) temperature of heat transfer surface (K) Tw
airfoil fins using S-CO2 with a temperature range of 380.9–552.9 K and a pressure range of 2.52–8.28 MPa. The results indicate that the pressure drop of airfoil PCHE is merely one-twentieth of that of zigzag PCHE, but the heat transfer is nearly the same as that of zigzag PCHE. Wang and He et al. [22] developed and tested a airfoil PCHE using molten salt with a temperature range of 470.8–527.4 K. Their results present that airfoil fins have better heat transfer performance compared with published correlations of straight fins and zigzag fins for Reynolds number in the range of 500–1600. Pidaparti et al. [23] studied the friction features and heat transfer of airfoil PCHE using S-CO2 by experiment with a temperature range of 293–473 K and a pressure range of 7.5–10.2 MPa. The results show that the airfoil PCHE exhibits lower friction factor compared with zigzag-fin PCHE. Yoon et al. [24] made a comparison of the PCHEs with straight fins, zigzag fins, S-shaped fins, and airfoil fins. Their study shows that heat transfer performance of airfoil PCHE is the highest among these four PCHEs. Review of the literature, it can be summarized that airfoil PCHE is a potential heat exchanger for the 3rd generation of CSP plant that employs molten salt and S-CO2 due to its low pressure drop and excellent heat transfer performance. To enable the design and application of the airfoil PCHE in the CSP, heat transfer and friction correlations are essential. However, only one heat transfer
u v Ve W Wc We Wf x, y, z
component of velocity (ms1) velocity (ms1) volume of the element channel in hot side (m3) width of simulation domain (m) width of cold channel (m) width of element channel (m) width of airfoil fin (m) Cartesian axes of PCHE system (m)
Abbreviations CSP concentrating solar power HTF heat transfer fluid PCHE printed circuit heat exchanger S-CO2 supercritical carbon dioxide Greek symbols ak inverse effective Prandtl number for k ae inverse effective Prandtl number for e dij unit tensor Dp pressure drop (Pa) DTm logarithm mean temperature difference (K) e turbulent dissipation rate of flow (m2s3) k thermal conductivity (Wm2K1) l dynamic viscosity (kgm1s1) lt turbulent viscosity of flow (kgm1s1) q density (kgm3) Subscription Ave average cold cold side of the PCHE f airfoil fin, fluid hot hot side of the PCHE in inlet out outlet salt molten salt w wall s standard structure
correlation for molten salt flowing in the airfoil PCHE has been obtained when temperature is less than 530 K [22]. Moreover, only one heat transfer correlation for S-CO2 in the airfoil PCHE has been obtained when temperature is less than 473 K and pressure is less than 10.2 MPa [23]. It is found that current experimental temperature is far lower than the realistic temperature in the 3rd generation of CSP. It is known that the friction features and heat transfer of S-CO2 and molten salt are directly influenced by the thermophysical properties that vary with the temperature significantly [25,36]. Thus, it is necessary to further investigate on the heat transfer and friction of molten salt and S-CO2 under the realistic operation condition (973 K, 20 MPa) in the 3rd generation of CSP [13]. Besides, all of the computational models used to evaluate the airfoil PCHE in pervious researches are not validated by experimental results of airfoil PCHE. Therefore, it is also necessary to develop a numerical model validated by experiment. To study on this topic, a three-dimensional numerical model is developed to evaluate friction features and heat transfer of airfoil PCHE. The calculated results are compared with experimental data procured in the airfoil PCHE to validate the model. Then, based on the model, the friction features and heat transfer of the two HTFs under different mass flow rate and inlet temperature conditions are analyzed. Moreover, the performance of airfoil channels is
H.-Y. Shi et al. / International Journal of Heat and Mass Transfer 150 (2020) 119006
3
Fig. 1. Schematic diagram of typical CSP plant.
compared with that of straight channels and zigzag channels. Finally, heat transfer and flow friction correlations are developed for the two HTFs in the airfoil channel of PCHE, which can be used in relatively wide ranges of Reynolds numbers and temperature. The main contributions of current work are summarized as: (1) A three-dimensional numerical model is developed to investigate heat transfer and friction of molten salt and S-CO2 in the airfoil channel of PCHE. The simulation results are compared with experimental data procured in the airfoil PCHE to validate the model. (2) The new heat transfer and flow friction correlations of molten salt and S-CO2 in the airfoil channel of PCHE are fitted. The ranges of correlations cover the typical working conditions in the 3rd generation of CSP, which can provide help to design the airfoil PCHE. (3) The friction features and heat transfer of the two HTFs flowing in the airfoil channel of PCHE are studied detailedly under different mass flow rate and inlet temperature conditions, and the performance of airfoil channels is compared with that of straight channels and zigzag channels. 2. Methodology 2.1. Physical model The airfoil PCHE designed in our previous study is chosen as the physical model [22] and demonstrated in Fig. 2. It has a length of 400 mm, a width of 130 mm, and a height of 70.5 mm. The PCHE consists of 12 hot-side plates with airfoil channels and 13 coldside plates with straight rectangular channels, which are made of 316L stainless steel and processed by photochemical method. Each hot-side plate and cold-side plate have 40 airfoil channels and 40 rectangular channels, respectively. Moreover, the hot-side plates and cold-side plates are stacked one by one, as shown in Fig. 3. More details about the PCHE can be found in our previous research [22].
Fig. 2. Photo of PCHE.
2.2. Heat transfer fluid Molten salt and S-CO2 are adopted as the HTFs in the airfoil channel. This is because in the 3rd generation of CSP technique, molten salt is considered as a promising HTF for its high working temperature, relatively mature technology, and low price. Moreover, S-CO2 Brayton power cycle is integrated in the 3rd generation of CSP technique. The molten salt used in the study is a MgCl2-KCl binary eutectic salt (43.4 wt% MgCl2, 56.6 wt% KCl), which can work at a temperature higher than 973 K with a melting point of 697.4 K. The thermophysical properties of the molten salt are obtained from Ref. [26]. For the S-CO2, its thermophysical properties under pressure condition of 20 MPa are firstly obtained from NIST data [27]. The pressure change of S-CO2 in the channel is much smaller than the operating pressure (less than 0.8%), so the effects of the pressure change on the properties is insignificant. Besides, S-CO2 is also adopted as the HTF in the straight rectangular channel. Both the thermophysical properties of the molten salt and S-CO2 change with temperature, which should be considered in the simulation for a typical temperature range, as shown in Fig. 4. The thermophysical properties are fitted in a form of piecewise functions and given in Table. A1 in Appendix A.
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Fig. 3. Stacked plates.
Fig. 4. Thermophysical properties of MgCl2-KCl and S-CO2.
Fig. 5. Cross section of micro-channels.
2.3. Numerical model There are many micro-channels in the PCHE, which consume large computing resources and time when all the channels are modeled and computed, as shown in Fig. 5. Therefore, a single
airfoil channel and a straight rectangular channel are selected as the simulation domain because of the symmetrical and periodic characteristics of the flow, as shown in Fig. 6. The geometry of airfoil fins is obtained from our previous work in Ref. [38]. The airfoil channel contains 50 rows of staggered NACA 0025 airfoil fins. The
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H.-Y. Shi et al. / International Journal of Heat and Mass Transfer 150 (2020) 119006
Fig. 6. Schematic diagram of simulation domain.
detailed geometrical parameters of simulation domain are summarized in Table 1. From the studies of Kim et al. [21] and Tsuzuki et al. [28], it is found that the renormalization group (RNG) k-e turbulence model can evaluate the flow friction and heat transfer performance of HTFs in the PCHE with distributed fins suitably, because the model takes into consideration the effects of swirl on turbulence. The comparison between three different turbulence models is carried out, as shown in Table 2. It can be seen that the deviation of calculated results for RNG k-e model is 1.23% comparing with experiment results [22]. For Standard k-e model and SST k-x model, the deviations are 38.57% and 46.92%, respectively. The results show that RNG model can achieve the most accurate prediction comparing with standard k-e model and SST k-x model. Therefore, RNG k-e turbulence model with the enhanced wall functions is used in the present model. The y+ of the near-wall node is maintained less than 5 by altering the grid case by case to guarantee that the wall functions are valid [36]. The governing equations adopted in the study include continuity equation, momentum equation, energy equation, and RNG k-e equations with enhanced wall functions [29]. The steady-state equations are shown in Eqs. (1)–(7). Continuity equation:
@ ðqui Þ ¼ 0 @xi
ð1Þ
Momentum equation:
@ui @uj 2 @ul @ @p @ þ qg i qui uj ¼ þ l þ lt þ dij @xi @xi @xj @xj @xi 3 @xl ð2Þ Energy equation:
@ @ l lt @T ðqui hÞ ¼ cp þ @xi @xi Pr Prt @xi
ð3Þ
k equation:
@ @ @k þ Gk þ Gb qe ðqkui Þ ¼ ak leff @xi @xi @xi
ð4Þ
e equation:
@ @xi
2 @e ðqeui Þ ¼ @x@ ae leff @x þ C 1e ke ðGk þ C 3e Gb Þ C 2e q ek Re i
Gk ¼ qu0i u0j
ð5Þ
i
@uj l @T 1 @q ; Gb ¼ bg i t ; b¼ ; @xi Pr t @xi q @T p
lt ¼ qC l
k
2
e ð6Þ
Re ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffi k C l qg3 ð1 g=go Þ e2 1 @ui @uj þ ; g ¼ 2Eij Eij ; Eij ¼ 3 2 @xj @xi 1 þ bR g k e
ð7Þ
Table 1 Geometrical parameters of simulation domain. Parameters
Value
Parameters
Value
length of simulation domain L width of simulation domain W height of simulation domain H length of airfoil fin Lf width of airfoil fin Wf height of airfoil fin Hf longitudinal pitch Lb
400.0 mm 3.0 mm 5.0 mm 4.0 mm 1.0 mm 1.5 mm 8.0 mm
transverse pitch La staggered pitch Lst height of straight fin Hs width of cold channel Wc height of top wall Ht height of middle wall tw height of bottom wall Hb
3.0 4.0 1.5 2.0 0.5 1.0 0.5
mm mm mm mm mm mm mm
Table 2 Turbulence model comparison. Results for Hitec
Experiment [22]
RNG k-e with enhanced wall function
Standard k-e with enhanced wall function
SST k-x
Nu/[Pr1/3(lf/lw)0.14] Error (%)
26.11 –
25.79 1.23
16.04 38.57
13.86 46.92
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where Cl = 0.0845, C1e = 1.42, C2e = 1.68, Prt = 0.85, bR = 0.012, go = 4.38. C3e = tanh|v2/v1|, v2 and v1 are the velocity components parallel and perpendicular to the gravitational vector, respectively. Fig. 6 shows the simulation domain and contains the main boundary conditions The details are summarized as follows: (1) Inlet of the fluid region: mass-inlet boundary. (2) Outlet of the fluid region: pressure outlet boundary. (3) Interface between fluid region and solid region: coupled boundary and no-slip boundary. (4) Periodic boundary conditions for the top and bottom surfaces. (5) Symmetry boundary conditions for left and right surfaces. (6) Adiabatic boundary conditions for other surfaces.
Z T hot;in ¼ AZc
Ac
3. Parameter definitions and model validation 3.1. Parameter definitions
Dh ¼ 4V e =Se
ð8Þ
V e ¼ ðLe W e Se;a ÞHe
ð9Þ
Se ¼ 2ðPe;a He =2Þ þ 2ðLe Lfin Þt þ 2ðW e Le Se;a Þ
ð10Þ
where Ve and Se represent the volume and the lateral area of the element channel, respectively; Le, We, and He are the length, width, and height of the element channel, respectively; Se,a and Pe,a represent the top surface area and perimeter of airfoil fin, respectively. The overall heat transfer coefficient (K) of PCHE is shown in Eq. (11).
K¼
Q ave ; Q ave ¼ ðQ hot þ Q cold Þ=2 DT m Ahot
DT m ¼
T T cold;out T hot;out T cold;in hot;in ln T hot;in T cold;out = T hot;out T cold;in
ð11Þ
T cp qv dA
Ac
cp qv dA
ð13Þ
ð14Þ
Then, the convective heat transfer coefficient (hhot) in the hot side can be calculated by Eq. (15).
1 1 Ahot t w Ahot K hcold Acold kw Aw
ð15Þ
where tw represents wall thickness; Aw represents the total wall surface area of the PCHE; kw represents the thermal conduction of wall, which is 16.3 Wm1K1. Based on the above parametrical definitions, the Reynolds number (Re), Nusselt number (Nu), Prandtl number (Pr), and friction factor (f) can be calculated by Eq. (16) and Eq. (17).
qm Dh hDh ; Nu ¼ ; Pr ¼ lAc k
f ¼ Dp
Dh 1 ; L ð1=2Þqv 2
v¼
lc p k
qm
qAc
ð16Þ
ð17Þ
where qm, represents the mass flow rate; l represents the dynamic viscosity; k represents the thermal conduction; cp represents the specific heat capacity; L represents the distance between inlet and outlet; Dp represents the pressure drop. The performance evaluation criteria (PEC) of heat transfer enhancement of PCHE at given pumping power is shown in Eq. (18) [32].
PEC ¼
Nu Nus
, 1=3 f fs
ð18Þ
where Nu, f, Nus, and fs are calculated by Eq. (16) and Eq. (17), and the subscript ‘‘s” indicates the standard structure. When the value of PEC is larger than one, it shows the PCHE has a better comprehensive heat transfer performance than that of standard structure at the identical pumping power.
ð12Þ
where Thot,in and Thot,out are the inlet and outlet temperature of the hot side, which are shown in Eq. (13). Tcold,in and Tcold,out are the inlet and outlet temperature of the cold side, which are calculated in the same way.
Fig. 7. Element channel.
; T hot;out ¼ AZc
Q ave T cold; out þ T cold; in Acold T w 2
hcold ¼
Re ¼
A method which defines Dh with considering both the size and configuration of airfoil fins is adopted in present research [31]. Fig. 7 presents a periodic element channel chose in current study. Then, Dh can be calculated by Eqs. (8)–(10).
cp qv dA
Z
The convective heat transfer coefficient (hcold) in the cold side is shown in Eq. (14).
hhot ¼ The entire governing equations are solved by FLUENT 18.0 commercial software with double precision. The pressure and convection terms are implemented by the PRESTO! scheme and a second-order scheme, respectively. The coupling pressure and velocity are solved by SIMPLE algorithm. The convergence criteria for each governing equation is that all residual targets are set to 10-6.
T cp qv dA
3.2. Mesh independence check and model validation Hexahedral meshes were generated in the fluid region and solid region. The mesh in the adjacent zone of fin wall should be fine enough to meet the requirements of wall function. Therefore, the first layer of grid near the fin wall in the fluid domain is hold with the initial height of 0.01 mm and the ratio of increment is 1.2, as shown in Fig. 8. To eliminate the conceivable influence of grid number on simulation, grid independence check should be examined for each case. An example was shown as follows, which conducted with a ternary molten salt in the hot side and a synthetic oil in the cold side. The HTFs were used in our previous experimental study. Fig. 9 gives the results of the grid independence check, and shows that the outlet temperature of the cold side and hot side have only little change when the mesh number is larger than 11,432,432. Taking into consideration the time and computational accuracy, the mesh number of 11,432,432 is adequate for current simulation. The grid independence check is also conducted for other cases.
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Fig. 10. Simulation results versus the experimental results.
Fig. 8. Schematic diagram of grid.
Th, out Tc, out
493
417
492
416
491
415
490
414
489 400
600
800
1000
1200
Grid number / × 10
1400
Table 3 The ranges of velocity and temperature for HTFs.
418
Outlet Temperature Tcold, out / K
Outlet Temperature Thot, out / K
494
413 1600
HTFs
Inlet velocity/ms1
Inlet temperature/K
Fluid temperature/K
MgCl2-KCl salt S-CO2
0.71–7.57 2.01–25.19
873–1073 873–1073
807–1073 779–1073
Firstly, the influences of mass flow rate and inlet temperature on the heat transfer and friction features are investigated. Then, the performance of straight channels and zigzag channels are compared with that of airfoil channels. Finally, new correlations of these two HTFs in the airfoil channel of PCHE are fitted, respectively. The examined ranges of the velocity and temperature for the two HTFs are given in Table 3, which cover the typical working conditions in the 3rd generation of CSP.
4
4.1. Heat transfer and flow friction of HTFs in airfoil channel
Fig. 9. Grid independence.
Comparison with our previous experiment for airfoil PCHE [22] is used to validate the numerical model adopted in current study. The experiment was conducted on a molten salt testing platform, which was designed and built in Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, China [33–35]. The geometrical parameters of the airfoil PCHE used in the experimental study are the same with what have mentioned in Section 2.1 of this paper. In the experiment, a ternary salt called Hitec was used in the hot side, and a synthetic oil called YD-325 was employed in the cold side. The operating temperature and volume flow rate of the salt ranged from 470.8 K to 527.4 K and 6.25 m3h1 to 15.88 m3h1, respectively. The thermophysical properties of Hitec and YD-325 are given in Table A2 in Appendix A. Fig. 10 illustrates the comparison between the modeling data and the testing results. It is observed that the simulation results are in good agreement with experimental results, and the maximum deviation is within ±12%, which indicates that the numerical model is reliable. 4. Results and discussions In this section, molten salt and S-CO2 are adopted to study the heat transfer and friction features of the airfoil channel of PCHE.
Molten salt and S-CO2 are used to study the heat transfer and friction features in the airfoil channel under different mass flow rate (qm) and inlet temperature (Tin), as shown in Fig. 11. For the molten salt, Nu/Pr0.4 increases with the increment of qm when Tin is fixed, while the friction factor (f) decreases as shown in Fig. 11 (a). This is because the larger qm leads to more intense turbulence, which enhances the heat transfer performance. The increment of the square of velocity is larger than pressure drop, which causes the decrement of friction factor. Meanwhile, it can also be observed that Nu/Pr0.4 increases with the increment of Tin at a constant qm, while the friction factor decreases. This is due to higher temperature leading to lower dynamic viscosity and density, as shown in Fig. 4(a), which cause higher Re number and velocity at a constant qm, respectively. Fig. 11(b) shows the effect of qm and Tin on S-CO2. It is seen that Nu/Pr0.4 increases with ascending qm when Tin is fixed, while the friction factor decreases. The phenomenon is caused by the similar reason for the salt. Moreover, it can be also found that both Nu/Pr0.4 and the friction factor decrease with the increment of Tin at a constant of qm. The effect of Tin on heat transfer performance of S-CO2 is quite different from that of salt. This is because the change of the dynamic viscosity of S-CO2 with temperature is opposite to that of the molten salt, as can be seen from Fig. 4. The larger Tin leads to larger dynamic viscosity, which causes lower Re number at a constant qm.
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Fig. 11. Influences of mass flow rate and inlet temperature on heat transfer and friction features in airfoil channel.
Fig. 12. Effects of buoyancy on heat transfer and friction of S-CO2 at different inlet temperature.
The buoyancy has some unexpected influence on performance of S-CO2. Therefore, the effects of buoyancy on S-CO2 are estimated and the results are shown in Fig. 12. It can be seen that the buoyancy nearly has no effects on the heat transfer and friction of S-CO2 in current range of working temperature. This is because present temperature and pressure conditions are far away from the pseudo-critical region, which will not cause dramatic change of thermophysical properties. It is convenient to see how much heat is transferred directly between the fluids and how much goes through the wall by numerical method. Hence, the calculated results of the heat
transferred directly between the fluids and going through the wall are shown in Table 4. It can be seen that the heat transferred directly between the fluids are almost equivalent to that going through the wall. This is because the heat transferred directly between the fluids and going through the wall are mandatorily equal in numerical model due to the energy conservation [29,30]. Furthermore, molten salt is taken as an example to investigate the local flow field and temperature field in the airfoil channel. The molten salt has a mass flow rate of 0.0295 kgs1 and an inlet temperature of 973 K. Fig. 13 depicts the flow and temperature field at the middle cross section (z = 3.75 mm) of salt zone for the first three rows of the airfoil fins. It can be seen from Fig. 13 (a) that there exists local high pressure in the head region of fins because of the stagnation of salt. The pressure gradually decreases along the flow direction but low-pressure regions exist near the position where the airfoil fins has the highest thickness. This is because the highest fin thickness causes minimum flow cross section area and highest velocity. Fig. 13(b) illustrates that the thermal boundary layer becomes thicker along the fin edge. The temperature of HTF in the main flow region is higher than that of HTF in the tail region of fins. Fig. 13(c) shows that the velocity has a periodic variation in the flow direction. This is because the staggered fin arrays cause periodic change of the flow cross section area along the flow direction. It is also observed that the velocity of HTF in the main flow region is higher than that of HTF in the tail region of fins. However, the turbulent kinetic energy in the tail region is higher than that in the main flow region, as shown in Fig. 13(d). This is because the airfoil fins intensify the mixture of the HTFs from two adjacent channels in the tail region of fins, which increases the turbulent kinetic energy behind the fins.
Table 4 Comparison between the heat transferred directly between the fluids and going through the wall (ms-co2 = 0.009834 kgs1, Ts-co2 = 773 K). Case
Heat going through salt wall/W
Heat carried by salt/W
Error/%
Heat going through S-CO2 wall /W
Heat carried by S-CO2/W
Error/%
msalt = 0.022 kgs1 Tsalt,in = 973 K msalt = 0.022 kgs1 Tsalt,in = 873 K msalt = 0.0445 kgs1 Tsalt,in = 973 K msalt = 0.0445 kgs1 Tsalt,in = 1073 K
1179.11
1177.21
0.16%
1179.11
1179.36
0.02%
582.38
581.38
0.17%
582.39
582.62
0.04%
1365.99
1364.45
0.11%
1365.99
1366.06
0.01%
2066.97
2064.79
0.11%
2066.96
2067.00
0.01%
H.-Y. Shi et al. / International Journal of Heat and Mass Transfer 150 (2020) 119006
(a) Pressure
9
(b) Temperature
(c) Velocity
(d) Turbulent kinetic energy
Fig. 13. Flow field and temperature field of molten salt in airfoil channel (z = 3.75 mm).
Fig. 14. Comparison with straight channels.
4.2. Comparison between airfoil channels and two typical channels In this part, molten salt is taken as the HTF to compare the heat transfer performance and friction features of the airfoil channels with those of straight channels and zigzag channels.
4.2.1. Airfoil channels versus straight channels Qiu et al. [36] found that Gnielinski’s correlation (see Eq. (19)) and Filonenko’s correlation (see Eq. (20)) can be used to predict the heat transfer and friction features of salts in the smooth channel with the maximum deviations of ±15% and ±2%, respectively.
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Hence, these correlations are adopted to predict the heat transfer and friction of salts in the straight channel of PCHE. Fig. 14 illustrates the comparison of heat transfer and friction factor between airfoil channels and straight channels. It can be found in Fig. 14(a) that the heat transfer of the airfoil channels is almost 2 times that of the straight channels. Meanwhile, Fig. 14 (b) shows that the value of friction factor of the airfoil channels is also higher than that of the straight channels. Besides, Fig. 14 (c) indicates that the PEC of the airfoil channels is larger than that of the straight channels, when the straight channels are adopted as the standard structure. The results indicate that the distributed airfoil channels can enhance heat transfer performance when compared with straight channels. In the meantime, airfoil channels also increase the flow friction. The airfoil channels have the better comprehensive heat transfer performance comparing with straight channels at the same pumping power.
h i 0:11 Nu ¼ 0:012 Re0:87 280 Pr0:4 1 þ ðDh =LÞ2=3 Pr f =Prw Re ¼ 2300 106 ; Pr ¼ 0:6 105 2
f ¼ ð1:82lgðReÞ 1:64Þ ; Re ¼ 2300 106 ; Pr ¼ 0:6 105
ð19Þ
ð20Þ
4.2.2. Airfoil channels versus zigzag channels The experimental results of the heat transfer and friction factor (f) in zigzag channel are compared with present simulation data of airfoil fins, as shown in Fig. 15. In Fig. 15(a), it can be found that the value of (Nu-4.089)/Pr0.58 of the airfoil channels is higher than that of the zigzag channels [37]. However, Fig. 15(b) shows that the value of friction factor (f) of the airfoil channels is almost the same as that of the zigzag channels. Fig. 15(c) indicates that the PEC of airfoil channels is larger than that of zigzag channels, when the zigzag channels are adopted as the standard structure. The results indicate that airfoil channels exhibit better heat transfer features than that of zigzag channels under the same pumping power. The above results indicate that the airfoil channels have the best comprehensive heat transfer performance at the given pumping power among these three structures. This is because the distributed airfoil fins bring about alternant enlargement and shrinkage in the cross section of channel, which enhance the heat transfer. Meanwhile, the airfoil fins have a streamlined shape, which can avoid overlarge flow friction. Therefore, the airfoil PCHE is an excellent choice for the 3rd generation of CSP plant.
Fig. 15. Comparison with zigzag channels.
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4.3. New heat transfer and friction factor correlations for HTFs in airfoil channel Considering the lack of reliable heat transfer and friction factor correlations of salt and S-CO2 in the airfoil channel of PCHE, the corresponding correlations are fitted with relatively wide ranges of Re number and temperature. The expression of heat transfer correlations in form of Ref.[36] is adopted. Meanwhile, the Darcy friction law is used for friction correlations. 4.3.1. Correlations for molten salt in airfoil channel To better predict the heat transfer and friction features of salt in airfoil channel, the calculated data under a wide range of Re number and temperature are employed to develop two correlations, which are given in Eq. (21) and Eq. (22). Fig. 16 depicts the comparison between the heat transfer correlation and the calculated results. It is seen that the calculated results fit well with the heat transfer correlation, with a maximum deviation of ±6%. Fig. 17 illustrates the comparison between the friction correlation and the calculated results. The friction correlation is commendably coincident with calculated results, with a maximum deviation of ±4%.
1=3 Nusalt ¼ 0:063Re0:755 salt Pr salt
where Resalt = 509–6,773, Prsalt = 7.5–9.5, lsalt/lw = 0.84–0.93. 4.3.2. Correlations for S-CO2 in airfoil channel For S-CO2, the heat transfer and friction correlations are also fitted and given in Eq. (23) and Eq. (24), respectively. A comparison between the simulation results and the heat transfer correlation is illustrated in Fig. 18. The heat transfer correlation agrees well with the simulation results, with a maximum deviation of ±6%. Fig. 19 illustrates the comparison between the friction correlation and the calculated results. It can be observed that the calculated results are in good agreement with fitted friction correlation. The largest deviation of calculated results and developed correlation is smaller than ±8%. In present study, the working temperature of S-CO2 ranges from 779 K to 1073 K, which is far away from the pseudo-critical region. It can be seen that variations of properties of S-CO2 have less effects on heat transfer and friction under above temperature conditions. 0:4 NuSCO2 ¼ 0:0986Re0:687 SCO2 Pr SCO2
+6%
w
T in=973K
lSCO2 =lw
0:14
ð23Þ
S-CO2
-6%
salt
30 20
Nusalt=0.063Re0.755 Pr1/3 ( salt salt
10
S-CO2
350
T in=873K
salt
/
w
)0.14
+6%
T in=973K
300
T in=1073K
/
T in=1073K
40
)0.14]
T in=873K
50
·( NuS-CO2/[Pr0.4 S-CO2
)0.14]
ð21Þ
400
/
w
0:14
ð22Þ
MgCl2-KCl
Nusalt/[Pr1/3 ·( salt
lsalt =lw
f salt ¼ 3:07Re0:462 salt
60
-6%
250 200 150 100
Pr0.4 ( NuS-CO2=0.0986Re0.687 S-CO2 S-CO2
50
S-CO2
/
w
)0.14
0
0 0
0
1000 2000 3000 4000 5000 6000 7000 8000
Resalt
2
4
6
8
10
12
14
16
12
14
ReS-CO2 / × 104
Fig. 16. Heat transfer correlation for molten salt.
Fig. 18. Heat transfer correlation for S-CO2.
0.20
0.050 MgCl2-KCl
0.18
T in=873K
S-CO2
0.045
T in=973K
0.16
T in=873K T in=973K
0.040
T in=1073K
0.14
T in=1073K
0.035
0.12
fS-CO2
fsalt
+4%
0.10
+8%
0.030 0.025
-4%
0.08
fsalt=3.07Re-0.462 salt
0.06
-8%
0.020
fS-CO2=0.513Re-0.667 S-CO2
0.015 0.010
0.04 0
1000 2000 3000 4000 5000 6000 7000 8000
Resalt
Fig. 17. Friction factor correlation for molten salt.
0
2
4
6
8
10
ReS-CO2 / × 104 Fig. 19. Friction factor correlation for S-CO2.
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H.-Y. Shi et al. / International Journal of Heat and Mass Transfer 150 (2020) 119006
Table A1 Thermophysical properties of MgCl2-KCl [26] and S-CO2 [27]. HTFs
Temperature range/K
Piecewise functions of the properties
MgCl2-KCl
723.15–1073.15 723.15–1073.15 723.15–1073.15 723.15–1073.15 673–1173 673–973 973–1173 673–1173 673–1173
q = 0.552(T 273.15) + 1903.7, kgm3 cp = 0.1046(T 703.15) + 989.6, Jkg1K1 k = 1.0E 4(T 273.15) + 0.5047, Wm1K1 l = 1.784E 8(T 273.15)2 –2.91E 5(T 273.15) + 1.4965E 2, kgm1s1 q = 1.7502E 4 T2 4.5727E 1 T + 382.91, kgm3 cp = 1.1368E 6 T3 + 3.0368E 3 T2 2.5183 T + 1890, Jkg1K1 cp = 1.6692E 1 T + 1105.9, Jkg1K1 k = 4.2972E 9 T2 + 7.3888E 5 T + 4.6548E-3, Wm1K1 l = 3.4566E 12 T2 + 3.3913E 8 T + 1.2126E 5, kgm1s1
S-CO2
Table A2 Thermophysical properties of Hitec [35] and YD-325 [35]. HTFs
Temperature range/K
Piecewise functions of the properties
Hitec
420–800 420–800 420–536 536–800 420–440 440–500 500–800 300–573 300–573 300–573 323–423 423–523
q = 0.733 T + 2280.22, kgm3
YD-325
f SCO2 ¼ 0:513Re0:667 SCO2
cp = 1560, Jkg1K1 k = 1.863E 8 T3 + 2.551E 5 T2 0.01176 T + 2.2627, Wm1K1 k = 6.47E 4 T + 0.7663, Wm1K1 l = 1.742173E 6 T3 + 2.27615E 3 T2 0.99143 T + 143.9826, kgm1s1 l = 7.2058E 9 T3 + 1.08225E 5 T2 5.4754E-3 T + 0.93845, kgm1s1 l = 8.507E 13 T4 2.4331E 9 T3 + 2.6275E-6 T2 1.2768E 3 T + 0.23846, kgm1s1 q = 0.6311 T + 1199.13, kgm3 cp = 3.40 T + 776.0, Jkg1K1 k = 6.68E 5 T + 0.1416, Wm1K1 l = 4.066E 9 T3 + 5.2746E 6 T2 2.283E 3 T + 0.33065, kgm1s1 l = 4.413E 10 T3 + 6.735E 7 T2 3.452E-4 T + 0.05989, kgm1s1
ð24Þ
where ReS-CO2 = 11,671–123,483, PrS-CO2 = 0.73–0.75, lS-CO2/
lw = 1.03–1.09. The above results indicate that the developed correlations can evaluate the heat transfer and friction features well for salt and S-CO2 in the airfoil channel of PCHE, which can contribute to the design and application of PCHE in the 3rd generation of CSP plants. 5. Conclusions
(4) For the salt, the heat transfer and friction factor correlations are proposed, where Resalt = 509–6,773, Prsalt = 7.5–9.5, lsalt/ lw = 0.84–0.93. The heat transfer and friction factor correlations are also developed for the S-CO2, where ReS-CO2 = 11, 671–123,483, PrS-CO2 = 0.73–0.75, lS-CO2/lw = 1.03–1.09. All the deviations between the fitted heat transfer correlations and the simulation data are within ± 6% for the two HTFs. The entire deviations between the friction correlations and the simulation data are within ±4% and ±8% for the salt and S-CO2, respectively.
In this paper, the heat transfer and flow friction performance of molten salt and S-CO2 in the airfoil channel of PCHE was investigated with relatively wide ranges of Re number and temperature, which cover typical working conditions in the 3rd generation of CSP. The conclusions are obtained as follows.
In conclusion, these new heat transfer and friction factor correlations and beneficial results can be used for the design of airfoil PCHE in the 3rd generation of CSP plant.
(1) A three-dimensional numerical model was developed to simulate heat transfer and friction features of the two heat transfer fluids, and then validated by comparing the calculated results with our pervious experimental results procured in the airfoil PCHE. The maximum deviation is within ±12%, which demonstrates that the computational model adopted in current study is credible. (2) The influences of mass flow rate and inlet temperature on the performance of the two heat transfer fluids were studied. The larger inlet temperature leads to higher heat transfer performance for molten salt, but causes lower heat transfer performance for S-CO2. For both the two heat transfer fluids, the friction factor decreases with the increment of inlet temperature. (3) The heat transfer and friction features of the straight channels and zigzag channels were compared with that of the airfoil channels. The distributed airfoil fins can enhance the disturbance and achieve better heat transfer performance without exceeding increment of flow friction. Besides, airfoil channels have the best comprehensive heat transfer performance at given pumping power.
The study is supported by the National Key R&D Program of China (2017YFB0601801) and the National Natural Science Foundation of China (No. 51806165).
Acknowledgements
Appendix A See Table A1 and Table A2. References [1] D.V. Spracklen, Global warming: China’s contribution to climate change, Nature 531 (7594) (2016) 310. [2] M.J. Li, Y.L. He, W.Q. Tao, Modeling a hybrid methodology for evaluating and forecasting regional energy efficiency in China, Appl. Energy 185 (2017) 1769– 1777. [3] Y.L. He, K. Wang, Y. Qiu, B.C. Du, Q. Liang, S. Du, Review of the solar flux distribution in concentrated solar power: non-uniform features, challenges, and solutions, Appl. Therm. Eng. 149 (2019) 448–474. [4] Y.L. He, J. Xiao, Z.D. Cheng, Y.B. Tao, A MCRT and FVM coupled simulation method for energy conversion process in parabolic trough solar collector, Renew. Energy 36 (3) (2011) 976–985. [5] Y.L. He, D.H. Mei, W.Q. Tao, W.W. Yang, H.L. Liu, Simulation of the parabolic trough solar energy generation system with organic Rankine cycle, Appl. Energy 97 (2012) 630–641.
H.-Y. Shi et al. / International Journal of Heat and Mass Transfer 150 (2020) 119006 [6] W.Q. Wang, Y. Qiu, M.J. Li, F. Cao, Z.B. Liu, Optical efficiency improvement of solar power tower by employing and optimizing novel fin-like receivers, Energy Convers. Manage. 184 (2019) 219–234. [7] B.C. Du, Y.L. He, Z.J. Zheng, Z.D. Cheng, Analysis of thermal stress and fatigue fracture for the solar tower molten salt receiver, Appl. Therm. Eng. 99 (2016) 741–750. [8] Y. Qiu, Y.L. He, Z.D. Cheng, K. Wang, Study on optical and thermal performance of a linear Fresnel solar reflector using molten salt as HTF with MCRT and FVM methods, Appl. Energy 146 (2015) 162–173. [9] Y. Qiu, Y.L. He, M. Wu, Z.J. Zheng, A comprehensive model for optical and thermal characterization of a linear Fresnel solar reflector with a trapezoidal cavity receiver, Renew. Energ. 97 (2016) 129–144. [10] F.Q. Cui, Y.L. He, Z.D. Cheng, Y.S. Li, Study on combined heat loss of a dish receiver with quartz glass cover, Appl. Energy 112 (2013) 690–696. [11] T.O. Dunlop, D.J. Jarvis, W.E. Voice, J.H. Sullivan, Stabilization of molten salt materials using metal chlorides for solar thermal storage, Sci. Rep. 8 (1) (2018) 8190. [12] K. Wang, Y.L. He, H.H. Zhu, Integration between supercritical CO2 Brayton cycles and molten salt solar power towers: A review and a comprehensive comparison of different cycle layouts, Appl. Energy 195 (2017) 819–836. [13] M. Mehos, C. Turchi, J. Vidal, M. Wagner, Z.W. Ma, C. Ho, et al., Concentrating solar power Gen3 demonstration roadmap[R], National Renewable Energy Lab. (NREL), Golden, CO (United States), 2017. [14] M.J. Li, J.L. Xu, F. Cao, J.Q. Guo, Z.X. Tong, H.H. Zhu, The investigation of thermoeconomic performance and conceptual design for the miniaturized leadcooled fast reactor composing supercritical CO2 power cycle, Energy 173 (2019) 174–195. [15] K. Wang, Y.L. He, Thermodynamic analysis and optimization of a molten salt solar power tower integrated with a recompression supercritical CO2 Brayton cycle based on integrated modeling, Energy Convers. Manage. 135 (2017) 336– 350. [16] P. Sabharwall, D. Clark, M. Glazoff, G.Q. Zheng, K. Sridharan, M. Anderson, Advanced heat exchanger development for molten salts, Nucl. Eng. Des. 280 (2014) 42–56. [17] M. Caccia, M. Tabandeh-Khorshid, G. Itskos, A.R. Strayer, A.S. Caldwell, S. Pidaparti, et al., Ceramic–metal composites for heat exchangers in concentrated solar power plants, Nature 562 (7727) (2018) 406. [18] M. Saeed, M.H. Kim, Thermal and hydraulic performance of SCO2 PCHE with different fin configurations, Appl. Therm. Eng. 127 (2017) 975–985. [19] N. Bartel, M. Chen, V.P. Utgikar, X. Sun, I.H. Kim, R. Christensen, et al., Comparative analysis of compact heat exchangers for application as the intermediate heat exchanger for advanced nuclear reactors, Ann. Nucl. Energy 81 (2015) 143–149. [20] T.L. Ngo, Y. Kato, K. Nikitin, T. Ishizuka, Heat transfer and pressure drop correlations of microchannel heat exchangers with S-shaped and zigzag fins for carbon dioxide cycles, Exp. Therm Fluid Sci. 32 (2) (2007) 560–570. [21] D.E. Kim, M.H. Kim, J.E. Cha, S.O. Kim, Numerical investigation on thermal– hydraulic performance of new printed circuit heat exchanger model, Nucl. Eng. Des. 238 (12) (2008) 3269–3276.
13
[22] W.Q. Wang, Y. Qiu, Y.L. He, H.Y. Shi, Experimental study on the heat transfer performance of a molten-salt printed circuit heat exchanger with airfoil fins for concentrating solar power, Int. J. Heat Mass Transf. 135 (2019) 837–846. [23] S.R. Pidaparti, M.H. Anderson, D. Ranjan, Experimental investigation of thermal-hydraulic performance of discontinuous fin printed circuit heat exchangers for supercritical CO2 power cycles, Exp. Therm Fluid Sci. 106 (2019) 119–129. [24] S.H. Yoon, H.C. No, G.B. Kang, Assessment of straight, zigzag, S-shape, and airfoil PCHEs for intermediate heat exchangers of HTGRs and SFRs, Nucl. Eng. Des. 270 (2014) 334–343. [25] C. Dang, E. Hihara, In-tube cooling heat transfer of supercritical carbon dioxide. Part 1. Experimental measurement, Int. J. Refrig 27 (7) (2004) 736–747. [26] X.K. Xu, X.X. Wang, P.W. Li, Y.Y. Li, Q. Hao, B. Xiao, et al., Experimental test of properties of KCl–MgCl2 eutectic molten salt for heat transfer and thermal storage fluid in concentrated solar power systems, J. Sol. Energy Eng. 140 (5) (2018) 051011. [27] Linstrom P J, Mallard W G. National Institute of Standards and Technology: Gaithersburg, MD, 2005. 2011. [28] N. Tsuzuki, Y. Kato, T. Ishiduka, High performance printed circuit heat exchanger, Appl. Therm. Eng. 27 (10) (2007) 1702–1707. [29] W.Q. Tao, Numerical Heat Transfer, second ed., Xi’an Jiaotong University Press, Xi’an, 2001. [30] H.K. Versteeg, W. Malalasekera, An introduction to computational fluid dynamics: the finite volume method, second ed., Pearson Education, London, 2007. [31] T.H. Kim, J.G. Kwon, S.H. Yoon, H.S. Park, M.H. Kim, J.E. Cha, Numerical analysis of air-foil shaped fin performance in printed circuit heat exchanger in a supercritical carbon dioxide power cycle, Nucl. Eng. Des. 288 (2015) 110–118. [32] Z.D. Cheng, Y.L. He, F.Q. Cui, Numerical study of heat transfer enhancement by unilateral longitudinal vortex generators inside parabolic trough solar receivers, Int. J. Heat Mass Transf. 55 (21–22) (2012) 5631–5641. [33] Y.L. He, Z.J. Zheng, B.C. Du, K. Wang, Y. Qiu, Experimental investigation on turbulent heat transfer characteristics of molten salt in a shell-and-tube heat exchanger, Appl. Therm. Eng. 108 (2016) 1206–1213. [34] B.C. Du, Y.L. He, K. Wang, H.H. Zhu, Convective heat transfer of molten salt in the shell-and-tube heat exchanger with segmental baffles, Int. J. Heat Mass Transf. 113 (2017) 456–465. [35] Y. Qiu, M.J. Li, W.Q. Wang, B.C. Du, K. Wang, An experimental study on the heat transfer performance of a prototype molten-salt rod baffle heat exchanger for concentrated solar power, Energy 156 (2018) 63–72. [36] Y. Qiu, M.J. Li, M.J. Li, H.H. Zhang, B. Ning, Numerical and experimental study on heat transfer and flow features of representative molten salts for energy applications in turbulent tube flow, Int. J. Heat Mass Transf. 135 (2019) 732– 745. [37] I.H. Kim, H.C. No, Thermal hydraulic performance analysis of a printed circuit heat exchanger using a helium–water test loop and numerical simulations, Appl. Therm. Eng. 31 (17–18) (2011) 4064–4073. [38] H.Y. Shi, H. Liu, J.G. Xiong, Y. Qiu, Y.L. He, Study on flow and heat transfer characteristics of an airfoil printed circuit heat exchanger with dimples, J. Eng. Thermophys. 40 (2019) 857–862.