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Frontiers in Energy

Front. Energy    2019, Vol. 13 Issue (2) : 284-295     https://doi.org/10.1007/s11708-019-0613-3
RESEARCH ARTICLE
Geometric optimization model for the solar cavity receiver with helical pipe at different solar radiation
Chongzhe ZOU1, Huayi FENG2, Yanping ZHANG3(), Quentin FALCOZ4, Cheng ZHANG2, Wei GAO2
1. School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2. China-EU Institute for Clean and Renewable Energy, Huazhong University of Science and Technology, Wuhan 430074, China
3. School of Energy and Power Engineering; China-EU Institute for Clean and Renewable Energy, Huazhong University of Science and Technology, Wuhan 430074, China
4. China-EU Institute for Clean and Renewable Energy, Huazhong University of Science and Technology, Wuhan 430074, China; PROMES-CNRS Laboratory, 7 rue du Four Solaire, 66120 Font-Romeu-Odeillo-via, France
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Abstract

In consideration of geometric parameters, several researches have already optimized the thermal efficiency of the cylindrical cavity receiver. However, most of the optimal results have been achieved at a fixed solar radiation. At different direct normal irradiance (DNI), any single optimal result may not be suitable enough for different regions over the world. This study constructed a 3-D numerical model of cylindrical cavity receiver with DNI variation. In the model of a cylindrical cavity receiver containing a helical pipe, the heat losses of the cavity and heat transfer of working medium were also taken into account. The simulation results show that for a particular DNI in the range of 400 W/m2 to 800 W/m2, there exists a best design for achieving a highest thermal efficiency of the cavity receiver. Besides, for a receiver in constant geometric parameters, the total heat losses increases dramatically with the DNI increasing in that range, as well as the temperature of the working medium. The thermal efficiency presented a different variation tendency with the heat losses, which is 2.45% as a minimum decline. In summary, this paper proposed an optimization method in the form of a bunch of fitting curves which could be applied to receiver design in different DNI regions, with comparatively appropriate thermal performances.

Keywords cylindrical cavity receiver      3-D numerical simulation      geometric optimization      direct normal irradiation     
Corresponding Authors: Yanping ZHANG   
Online First Date: 16 April 2019    Issue Date: 04 July 2019
 Cite this article:   
Chongzhe ZOU,Huayi FENG,Yanping ZHANG, et al. Geometric optimization model for the solar cavity receiver with helical pipe at different solar radiation[J]. Front. Energy, 2019, 13(2): 284-295.
 URL:  
http://journal.hep.com.cn/fie/EN/10.1007/s11708-019-0613-3
http://journal.hep.com.cn/fie/EN/Y2019/V13/I2/284
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Chongzhe ZOU
Huayi FENG
Yanping ZHANG
Quentin FALCOZ
Cheng ZHANG
Wei GAO
Fig.1  Schematic diagram of the solar cavity receiver
Fig.2  Cross-section of the cavity receiver
Parameters Value
Ambient temperature/K 300
Inlet temperature of the working fluid/K 623
Inlet pressure of the working fluid/MPa 0.45
Mass flow of working fluid/(kg?s–1) 0.05
Allowed pressure drop/Pa 1000
Thermal conductivity of insulating layer/(W?m–1?K–1) 0.06
Thermal conductivity of SiC pipe/(W?m–1?K–1) 8
Insulating layer thickness/mm 75
Helical pipe thickness/mm 5
Inclination angle of aperture/(° ) 45
Absorptivity of SiC pipe 0.86
Emissivity of ceramic fiber insulation 0.9
Stefan-Boltzmann constant/(J? m–2?K–4) 5.67 × 10-8
Tab.1  Basic parameters of the cavity receiver
Parameter Value
Surface area of dish mirror Am/m2 55
Interception factor τi 0.94
Shading factor τs 0.99
Reflectivity of the parabolic dish ρr 1
Focal length f/m 5
Tab.2  Parameters of the dish
Fig.3  Model for pipe boundary settings
Fig.4  Cavity receiver and computational domain grid generation
Case
1 1_repeat 2 3
Grid number 1033274 1033274 1694251 2193964
Thermal efficiency (η)/% 77.79 77.54 77.90 77.95
Relative deviation of η% - 0.32 0.14 0.21
Total energy losses Qloss/W 7402 7470 7389 7369
Relative deviation of Qloss/% - 0.92 0.18 0.45
Tab.3  Grid independency test results
Aperture diameter/mm Nu in present study Nu of Wu’s model Deviation/% Nu of Zou’s model Deviation%
184 6.66 6.99 5.00 6.87 3.20
220 10.39 9.91 4.57 10.99 5.80
250 12.50 12.73 1.80 12.9 3.17
280 17.08 15.82 7.37 17.31 1.33
300 19.22 18.08 5.91 19.72 2.62
Tab.4  Nusselt numbers of convection loss
Aperture diameter dap/mm Surface temperature Tcav/K
DNI= 400 DNI= 500 DNI= 600 DNI= 700 DNI= 800
184 929.1 1004 1077 1148 1216
220 920.7 993.3 1063 1131 1196
250 913.4 983.7 1051 1116 1178
280 905.7 973.7 1039 1101 1160
300 900.3 966.8 1030 1090 1148
Tab.5  Surface temperatures of the helical pipe at different DNI values (W/m2)
Fig.5  Temperature contours of the receiver at an aperture diameter of 184 mm
Fig.6  Variation of heat loss with DNI at an aperture diameter of 184 mm
Fig.7  Variation of cavity thermal efficiency with DNI
DNI/(W?m–2) Thermal efficiency h/% Outlet temperature Tout/K Heat losses Qloss/W
400 90.70 917 1631
600 89.84 1062 2718
800 88.52 1197 4130
Tab.6  Cavity thermal efficiency, outlet temperature, and heat losses at different DNI values
Fig.8  Three-dimensional plot of effect of aperture diameter and cavity length on thermal efficiency at a DNI of 400 W/m2
Fig.9  Three-dimensional plot of effect of DNI and aperture diameter on thermal efficiency at a cavity length of 560 mm
Fig.10  Three-dimensional plot of effect of DNI and cavity length on thermal efficiency at an aperture diameter of 184 mm
Fig.11  Fitting curves of optimum geometric design at different DNI values
DNI/(W?m–2) R2 a1/mm a2 a3/mm-1 a4/mm-2
400 0.999 499.2 1.60 -0.0028 1.78 × 10-6
600 0.994 368.1 1.32 -0.0044 3.31 × 10-6
800 0.999 407.0 1.54 -0.0045 2.97
Tab.7  Parameters of fitting curves
Region Frequent DNI/(W?m–2) Fitting equation
Wuhan 400 l=(499.2 1.60dap)/(1 0.0028dap 1.78× 106 dap2)
Beijing 600 l=(386.1 1.32dap)/(1 0.0044dap+3.31× 106 dap2)
Lhasa 800 l=(407.0 1.54dap)/(1 0.0045dap+2.97× 106 dap2)
Tab.8  Fitting equations of different regions
Am Dish area/m2
Acav Area of cavity inner wall/m2
Cp Special heat capacity/(J?kg–1?K–1)
CSP Concentrated solar power
dap Aperture diameter/mm
dcav Cavity inner diameter/mm
DNI Direct normal irradiance/(W?m–2)
f Focal length/m
hconv Heat transfer coefficient/(W? m–2?K–4)
l Cavity length/mm
Nuconv Nusselt number
Qconv Convection heat loss/W
Qin Energy entering the receiver/W
Quse Energy absorbed by the working fluid/W
Qloss Energy loss/W
Qrad Radiation heat loss/W
S2S Surface-to-surface
Tamb Ambient temperature/K
Tcav Temperature of cavity inner wall/K
Toutlet Pipe outlet temperature/K
Tpipe Temperature of pipe/K
  
η Cavity thermal efficiency
λ Thermal conductivity/(W? m–1?K–1)
μ Dynamic viscosity/(N?s? m–2)
θ Cavity inclination angle/(° )
ρr Reflectivity of the parabolic dish
τi Interception factor
τs Shading factor
  
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