Article 正式发布 Versions 1 Vol 28 (6) : 1176-1185 2019
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Thermal Analysis of a Volumetric Solar Receiver;太阳能容积式吸热器热分析
: 2019 - 11 - 05
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Abstract & Keywords
Abstract: The volumetric receiver has received wide attention due to its high thermal efficiency. This paper studied a new type of a solid-liquid composite volumetric receiver. The heat transfer in a solid-liquid composite volumetric solar receiver was analyzed using a one-dimensional unsteady simulation model of the solid-liquid receiver. The model included absorption of the incident solar radiation by the glass window, the silicon carbide porous ceramic heat absorber panel and the water. The results were verified against experimental data for a volumetric receiver and the error did not exceed 10%. It can be used to predict the heat transfer in solid-liquid composite volumetric receivers. 对固液复合式容积式吸热器传热过程展开分析,建立了固液复合式容积式吸热器一维非稳态仿真模型。仿真模型中分别考虑了容积式吸热器采光窗、碳化硅多孔陶瓷吸热板和传热流体对入射太阳辐射的吸收作用。该模型仿真结果得到容积式吸热器实验平台的实测验证,可用于固液复合式容积式吸热器的动态性能预测。
Keywords: solar receiver, solid-liquid composite absorber, silicon carbide porous ceramic, volumetric solar collector
1. Introduction
A solar collector absorbs solar radiation and transmits the thermal energy to a heat transfer fluid which in this study is water. Solar collectors can be divided into non-concentrating collectors and concentrating collectors. The non-concentrating collectors do not change the direction of solar radiation entering the collector's aperture and do not concentrate the solar radiation onto the collector absorber. Concentrating collectors generally consist of a concentrator and a receiver. The concentrator redirects the solar radiation onto the receiver. The receiver absorbs the solar radiation and transmits the thermal energy to the working fluid [1]. Most receivers today use absorbing surfaces to convert the solar energy from radiation to internal thermal energy. Although surface-based receivers can efficiently transform the solar radiation into thermal energy in the surface, they are not well suited for then transferring the heat to the water. In particular, absorbers with high solar concentration ratios often have a large temperature difference between the absorber and the water. This temperature difference leads to significant heat losses that lower the overall solar energy conversion efficiency. In a volumetric receiver, the concentrated solar radiation is absorbed by an absorber that has excellent heat transfer characteristics with the working fluid which reduces the temperature difference between the absorber and the fluid [2,3].
 
Nomenclature
Aarea/m2γabsorber panel inclination/°
athermal diffusivity/m2∙s-1εporosity
cspecific heat/J∙kg-1∙°C-1ηefficiency
dpequivalent particle diameter/mθzzenith angle/°
enatural logarithmλthermal conductivity/W∙m-1∙°C-1
Gtotal solar irradiance on a horizontal
plane/W∙m-2
νkinematic viscosity/m2∙s-1
Gdhorizontal diffuse solar irradiance/W∙m-2ρdensity/kg∙m-3
ggravitational acceleration/m∙s-2τtime/s
hconvective heat transfer coefficient
/W∙m-2∙°C-1
Dimensionless numbers
hvvolumetric heat transfer coefficient
/W∙m-3∙°C-1
GrGrashof number
Ithermal flux/W∙m-2NuNusselt number
L1receiver height/mRaRayleigh number
L2receiver width/mReReynolds number
L3receiver length/mPrPrandtl number
mass flow rate/kg∙s-1Subscripts
qthermal energy/Waair
heat source/Waveaverage
rthickness/mabporous ceramic absorber panel
ttemperature/°Cgglazed window
uinternal energy/Jininlet
Vvolume/m3wheat transfer fluid
vvelocity/m·s-1nanatural convection
yaxial coordinate/mpforced convection
Greek charactersHmixed convection
αabsorptivityAbbreviations
αsfsurface area density/m-1DNIdirect normal irradiance/W∙m-2
βthermal expansion coefficient/k-1
A volumetric receiver can use a gas or a liquid for the working fluid. Liquid volumetric receivers using a liquid such as water normally have fine particles added to the working fluid as the absorber. Andrej et al. [4] studied the effects of solar irradiance, working fluid height, and the optical thickness of the working fluid on the internal temperature distribution in a liquid volumetric receiver using a one-dimensional model of the liquid volumetric receiver. Seung-Hyun et al.[5] compared the thermal efficiencies of surface and volumetric solar receivers. Ruomei et al.[6] experimentally studied the heat transfer characteristics of a volumetric receiver using CuO-H2O nanofluids. Volumetric receivers have higher receiver efficiencies than absorbing surfaces based receivers, but have problems such as particle losses in practical applications. Wang et al. studied a solid-liquid composite volumetric receiver having a glazed window, a porous ceramic absorber panel, a supporting structure and an insulating layer. The porous ceramic absorber panel did not move with the water so the absorber did not deteriorate over time as particles can.
There are few research tools for analyzing volumetric receivers. For this reason, a one-dimensional unsteady volumetric receiver model was developed to predict the heat transfer in a solid-liquid volumetric receiver. The incident solar radiation is assumed to be absorbed by the glass window, the water and the absorber matrix. The heat transfer between the water and the absorber was modeled by a volumetric heat transfer coefficient. The one-dimensional, unsteady model of the solid-liquid composite volumetric receiver was then verified against experimental data. A photograph of the solid-liquid composite volumetric receiver experimental platform is shown in Fig. 1.


 
Fig. 1 Photograph of the experimental system
2. Modelling
2.1   Volumetric receiver heat transfer mechanisms
The physical structure of the volumetric receiver studied in this paper is shown in Fig. 2(a). When the volumetric receiver is working, the solar radiation concentrated by the concentrator first reaches the glass window. Part of the incident solar radiation is absorbed by the glass window and converted into thermal energy which is then transferred to the water and the external environment by convection heat transfer. Part of the solar radiation passing through the glass window is directly absorbed by the water as internal energy of the water with the rest absorbed by the porous ceramic absorber panel and converted into internal energy in the solid which is then transferred to the water by convective heat transfer.
The volumetric receiver can be divided into two stages during operation. When the receiver circulation pump is in operation, cold water continuously enters the volumetric receiver from the bottom and hot water continuously flows from the top. During this stage, the main thermal processes are the absorption of the solar radiation by the glass window, the porous ceramic absorber panel and the water and the convective heat transfer between the glass window, the porous ceramic absorber panel, the environment and the water along with the internal heat conduction in the glass window, the porous ceramic absorber panel and the water. This stage includes both natural convection and forced convection and the influence of natural convection needs to be considered.
When the receiver circulation pump stops working, water no longer flows in or out of the volumetric. During this stage, the main differences between these thermal processes and those during steady state operation are the absence of water flow in or out of the volumetric receiver and the lack of forced convective heat transfer between the water and the window with only natural convection heat transfer present.
The model assumes that the insulation is very good, so the convective heat loss between the insulation layer and the environment can be neglected.
The volumetric receiver studied in this paper is mainly used in solar heating systems, and the interior of the volumetric receiver is directly connected to the environment. So, the model also assumes that the fluid temperature in the volumetric receiver does not exceed 100°C and the radiant heat loss between the volumetric receiver and the surrounding environment can be neglected.
Qiang [7], Li [8] and Jiang [9]numerically analyzed the energy flows on a receiver surface with their results verified against experimental data. Their results indicated that the absorption of the solar insolation incident on the volumetric receiver surface can be modeled by a one- dimensional model along the y direction.


 
Fig. 2 (a) Physical structure of a volumetric receiver and (b) Energy balance in a volumetric receiver
2.2   Governing equations
A reduced-order unsteady model of a volumetric receiver was developed by simplifying the three- dimensional volumetric receiver design based on the following assumptions:
(1) The absorption of the solar insolation incident on the volumetric receiver can be described by a one- dimensional normal distribution in the y direction shown in Fig. 2.
(2) The temperatures of the porous ceramic absorber panel, the glass window and the water are uniform in the x direction shown in Fig. 2.
(3) When the receiver circulation pump is in operation, the water flow inside the receiver can be modeled as plug flow.
(4) The surfaces are all adiabatic.
With these assumptions, energy conversation analysis was conducted for a microelement dy, as shown in Fig. 2(b). The energy equations for the glass window, the porous ceramic absorber panel and the water can be given as:
For the glass window:
where the term on the left side is the internal energy change in the glass window. The first term on the right side is the heat conduction in the glass window in the y direction; The second term on the right side is the convective heat transfer between the window and the environment. The third term on the right side is the convective heat transfer between the glass window and the water. Since the glass absorbs incident solar radiation, it has a large influence on the heat transfer of the glass window. Therefore, the fourth term on the right side is the solar insolation absorbed by the glass.
For the porous ceramic absorber panel:
where the term on the left side is the internal energy change in the porous ceramic absorber panel. The first term on the right side is the heat conduction in the porous ceramic absorber panel in the y direction. The second term on the right side is the convective heat transfer between the porous ceramic absorber panel and the water. The third term on the right side is the solar insolation absorbed by the porous ceramic material.
For the water:
where the term on the left side is the internal energy change in the water. The first term on the right side is the heat conduction in the water in the y direction. The second term on the right side is the convective heat transfer between the porous ceramic absorber panel and the water. The third term on the right side is the convective heat transfer between the glass window and the water. The fourth term on the right side is the solar insolation absorbed by the water.
2.3   Model solution
The volumetric receiver model is first divided into several elements along the y direction as shown in Fig. 2(a) with the control equations discretized using the finite volume method [10]. The discretized governing equations are:
At the inlet, the discrete forms of the glazed window, porous ceramic absorber panel and water energy balance equations are (i=1):
Glass window:
Porous ceramic absorber panel:
Water:
The discrete forms of the energy balance equations in the interiors of each section are ():
Glass window:
Porous ceramic absorber panel:
Water:
At the outlet boundary (i=n), the discrete forms of the energy balance equations are:
Glass window:
Porous ceramic absorber panel:
Water:
where △y is the element height; △y=L1 /n; τ is the time step; Aga =Agw =L3 ∙∆y; Vw =∆yL2L3 ‒(1‒ε)Vab ; Vg = ∆yrgL3 ; Vab =∆yrabL3 ; Awd =L2L3 ; Agd =rgL3 and Aabd = rabL3. Subscript i indicates the i-th area, superscript (0) indicates the previous time step and superscript (1) indicates the current time step.
2.4   Constitutive equations
(1) Incident solar insolation distribution
The solar insolation distribution incident on the target (target structure size 3 m × 3 m) was measured using an indirect method based on a CCD camera and a target. Fig. 3 shows the measured insolation flux distribution along the y direction of the target and a Gaussian curve at 11:30 am on September 28, 2018. According to experimental test results, the solar insolation distribution incident on the surface of the volumetric receiver is as follows [11,12]:
where, Ahel is concentrator field aperture area, and ηhel is efficiency of the concentrator field.
The solar insolation distribution incident on the water is:


 
Fig. 3 Measured solar insolation distribution incident on the target
The solar insolation distribution finally incident on the porous ceramic absorber panel is [13]:
(2) Surface convective heat transfer coefficient on the glass window
The surface convective heat transfer coefficient between the glass window and the water can be cal- culated from the appropriate Nusselt number relation as:
The glass window is assumed to be a vertical flat plate. When the pump is not running, the natural convection heat transfer coefficient between the glass window and the water is calculated using the equation recommended by Churchill and Chu [14] which is applicable for all Rayleigh numbers:
The Rayleigh number is:
When the pump is running, the forced convection heat transfer coefficient between the window and the water can be calculated using [15]:
The Reynolds number is defined as:
In Section 2.2 we assume that the water flow inside the receiver can be modeled as plug flow. According to this assumption, the speed of the water inside the receiver be calculated as:
When the receiver circulation pump is running, natural convection can still affect the heat transfer which can be evaluated based on the ratio of the Grashof and Reynolds numbers. When Grw /Rew2 <0.1, the effect of natural convection can be ignored. When 0.1≤Grw /Rew2 ≤10, the flow is in the mixed convection regime. When Grw /Rew2 >10, the effect of forced convection can be neglected.
The Grashof number is defined as:
In the mixed convection condition, the Nusselt number can be calculated as [16]:
The surface convective heat transfer coefficient between the window and the environment can also be calculated using Eqs. (28–34).
(3) Volumetric heat transfer coefficient
The volumetric heat transfer coefficients can be calculated by:
Since the volumetric heat transfer coefficient is generally quite large, the temperature difference between the silicon carbide porous ceramic heat absorbing plate and the water can be assumed to be quite small. Thus, when the receiver circulation pump is running, the effect of natural convection on the convective heat transfer between the porous ceramic absorber panel and the water can be neglected. The volumetric heat transfer coefficient can then be calculated as [17,18]:
when 75<Red <350, hsf is obtained by linear interpolation of Eqs. (28) and (29). Red is defined as:
When the receiver circulation pump stops working, the volumetric convective heat transfer coefficient between the porous ceramic absorber panel and the water can be calculated as [19]:
Where Rad is defined as:
(4) Water thermophysical properties
The water properties, including the density, specific heat, thermal conductivity, and viscosity, were fit as continuous curves as functions of temperature (0–100°C) from the data in Ref. [15]:
3. Experimental Platform


 
Fig. 4 Solid-liquid composite volumetric receiver


 
Fig. 5 Schematic of the experimental system
Table 1 Borosilicate glass properties
 
parametervalueparametervalue
Thermal conductivity/
W∙(m∙°C)-1
1.2extinction coefficient/m-110.4
heat capacity/J∙(kg∙°C)-1980density/kg·m-32230
Table 2 Silicon carbide ceramic properties
 
parametervalueparametervalue
Thermal conductivity/
W∙(m∙°C)-1
3average pore
size/m
5
porosity0.85heat capacity
/J∙(kg∙°C)-1
1010
equivalent particle diameter/m1density/kg∙m-32700


 
Fig. 6 Installation positions of the temperature sensors (a) front view and (b) top view
Fig. 7 compares the measured DNI with calculated values at the Badaling Solar Thermal Power Experimental Site in China on May 6, 2018.


 
Fig. 7 Comparison of measured and calculated DNI
4. Experimental Results and Model Validation


 


 


 
Fig. 8 (a) Measured receiver circulation pump outlet flow rate and volumetric receiver inlet temperature on August 1, 2018 from 10:30 to 14:30; (b) Measured DNI on August 1, 2018 from 10:30 to 14:30; (c) Comparison of the simulation results with measurements for August 1, 2018 from 10:30 to 14:30


 


 


 
Fig. 9 (a) Measured receiver circulation pump outlet flow rate and volumetric receiver inlet temperature on August 2, 2018 from 13:00 to 17:30; (b) Measured DNI on August 2, 2018 from 13:00 to 17:30; (c) Comparison of the simulation results with measurements for August 2, 2018 from 13:00 to 17:30
5. Conclusions
The heat transfer in a solid-liquid composite volumetric receiver was analyzed using a one- dimensional unsteady model of the volumetric receiver. An experimental platform was built using the Huangdicheng 3000 m3 seasonal storage and heating system in China to verify the model. Various predicted temperatures in the volumetric receiver compared well the measured temperatures for two different operating conditions. Thus, the model can be used to predict the performance characteristics and to design solid-liquid composite volumetric receivers.
Acknowledgments
This work was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDA21050200) and the National Natural Science Foundation of China Project (No. 61671429). This work was also supported by the Guangdong Innovative and Entrepreneurial Research Team Program (No. 2013N070).
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Article and author information
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CHEN Longfei1,2,3,5,7
YANG Ming2,3,4,5,6,7
LI Jinping1
BAI Yakai2,3,4,5,6,7
LI Xiaoxia1,2,3,5,7
TANG Wenxue7,8
YANG Nancong7,8
WANG Zhifeng1,2,3,5,7,*
zhifeng@vip.sina.com
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Published: Nov. 5, 2019 (Versions1
References
Journal of Thermal Science