Science in China Series E: Technological Sciences © 2008
SCIENCE IN CHINA PRESS
Springer
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Investigation on performance of a solar thermophotovoltaic system CHEN Xue, XUAN YiMin† & HAN YuGe School of Power Engineering, Nanjing University of Science & Technology, Nanjing 210094, China
In the light of the thermo-electric conversion principle, a model for predicting the performance of a solar thermophotovoltaic system is presented. The temperature distributions of the emitter for different concentrator ratios are numerically computed and the influence of the concentrator ratio on the system performance is analyzed. Numerical results show that the emitter temperature and the system efficiency increase with increase of the concentrator ratio. The effects of some other factors such as the spectral filter, cell temperature, and the reflectivity of the top and bottom surfaces of the emitter on the conversion performance of the STPV system are discussed. STPV, emitter, temperature, system efficiency
1
Introduction
Solar thermophotovoltaic (STPV) is a new type of photo-electric conversion system developed from the thermophotovoltaic (TPV) by using the solar energy as the heat source. The basic feature of an STPV is in the use of high temperature emitter as an intermediate element which absorbs the solar concentrated light and emits the photonic energy to PV cells that convert the thermal radiation energy into electricity. The potential advantages of such a system are the use of clean and sustainable energy source. At the present time, several institutes in the world have shown great interests in development of the STPV system, such as EDTEK[1] in USA, Ioffe Physical-Technical Institute in Russia[2] and NASA institute[3]. Some types of the prototypes have been fabricated and tested and they have great potentials for both civil and military applications. However, little research work on the STPV has been done in China. The two basic elements of an STPV system are the solar concentrator and a thermo-electric conversion unit. The power conversion unit is composed of thermal radiator, filter, PV cells, waste heat management system and some subassemblies. By following the solar energy collector and the thermo-electric conversion unit, the numerical
Received May 15, 2008; accepted August 29, 2008 doi: 10.1007/s11431-008-0302-7 † Corresponding author (email:
[email protected]) Supported by the Natural Science Foundation of Jiangsu Province of China (Grant No. BK2007726)
Sci China Ser E-Tech Sci | Dec. 2008 | vol. 51 | no. 12 | 2295-2304
model of predicting the performance of a solar thermophotovoltaic system and the heat conduction in the emitter is constructed. The temperature distributions of the emitter for different concentrator ratios are numerically computed and the effects of some important factors on the conversion performance of the STPV system are discussed. The results may be useful in optimizing the system performance.
2
System modeling
A schematic drawing of the STPV system is shown in Figure 1, which consists of a sunlight concentrator, absorber-emitter, filter, PV arrays, reflectors, etc. The emitter is made of gray body material and the Si/SiO2 photonic crystal filter[4] is employed, while the PV cells are the low bandgap GaSb cells, the top and bottom surfaces reflect the radiation totally to ensure the radiation to be absorbed by the cells completely[1]. The emitter and the cell array are assembled on two coaxial columns, and the emitter inlet aperture depends on the concentration ratio, correspondingly, on the size of facula. The thickness of the emitter is 2 mm and the height is 3 cm. The diameter of the outer column is 4 cm, and the cell is as large as 2 cm×1 cm.
Figure 1 Scheme of STPV system.
2.1 Solar concentrator The cassegrainian type solar concentrator[1] used here consists of a parabolic solar concentrator dish and a secondary reflector. An accurate cassegrainian concentrator could focus the incident sunlight to a point since the primary reflector is a parabolic dish with “fast” optics and the second reflector may intercept and redirect the energy to a new focal point without any error[5]. But due to inevitable problems in production, it is assumed that facula will form after the sunlight concentration. The range of the concentrator ratio is set to be 2000―8000, and the diameter of the primary concentrator is 60 cm, then the diameter of the facula is changed between 6 mm and 13 mm. The concentrator is defined as CR = (a / a′) 2 ,
(1)
where a is the aperture of the primary reflector, and a′ is the diameter of the facula. Sunrays are considered to be parallel and the peak solar intensity is assumed to be 850 W/m2[6].
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The reflectance of the reflector is 0.92[1], some solar energy is lost during the concentrated process. 2.2 Energy balance equation of the emitter The incident solar radiation is focused on the absorber, and the temperature of the emitter rises. Infrared energy radiated from the emitter is converted to electricity by the cells. At high temperature, radiation between the emitter, the cells and the reflecting surfaces is considered to be the most important and to take place in a sealed chamber, whereas a part of the radiation may leak out through the inlet aperture to environment. The following idealities have been introduced in the modeling: (1) all the sunrays concentrated by the reflectors enter the absorber chamber to heat it; (2) emitter is a gray body with emissivity equal to 0.85 and is resistant to high temperature; (3) all the surfaces are considered to be diffused; (4) since the temperature of the other surfaces is lower than that of the emitter, according to T4 relation, only the radiation of the emitter is taken into account. 2.2.1 Energy balance equation of the interior nodes. According to the energy conservation , the balance equation of the unit (i, j, k) inside the emitter is expressed as
Q1 + Q2 + Q3 − ρ CpΔv
dT = 0, dt
(2)
where ρ and Cp are the density and the specific heat of the emitter, respectively, and Q1 is the rate of heat transfer by conduction from the surrounding nodes to (i, j, k ): Q1 = λΔr Δz
Ti n+1,+1j ,k − Ti ,nj+,1k r ( k ) Δθ
+ λΔr Δz
Ti n−1,+1j ,k − Ti ,nj+,1k r (k )Δθ
,
(3)
where Ti n, j+,k1 is the temperature of node (i, j, k) at (n+1) time. Q2 is the rate of heat transfer by conduction from the lengthways nodes to (i, j, k): Q2 = λ r (k )ΔθΔr
Ti ,nj++11,k − Ti ,nj+,1k
+ λ r (k )ΔθΔr
Ti ,nj+−11,k − Ti ,nj+,1k
. (4) Δz Δz And Q3 is the rate of heat transfer by conduction from the neighboring nodes to (i, j, k) in the thickness direction, i.e. Ti ,nj+,1k +1 − Ti ,nj+,1k Ti ,nj+,1k −1 − Ti ,nj+,1k Δr ⎤ Δr ⎤ ⎡ ⎡ . Q3 = λ ⎢ r (k ) + ⎥ ΔθΔz + λ ⎢ r (k ) − ⎥ ΔθΔz 2⎦ 2⎦ Δr Δr ⎣ ⎣
(5)
2.2.2 Energy balance equation of the nodes on the inner surface. The heat exchange between node (i, j, k) (k=1) on the inner surface with the outside is expressed by Q4 + Q5 + Q6 − Q7 − ρ CpΔv
dT = 0, dt
(6)
where Q4 is the concentrated solar radiation received by unit (i, j, k). The routes of the sunrays in the absorber chamber are tracked by the ray tracing method. The number of the beams that the unit (i, j, k) absorbed is calculated as Ni , j , k , then the total solar energy it absorbed is obtained as Q4 = Qsun ×
Ni , j ,k N
.
(7)
Q5 is the radiation from other units to (i, j, k) (all grids include itself): CHEN Xue et al. Sci China Ser E-Tech Sci | Dec. 2008 | vol. 51 | no. 12 | 2295-2304
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Q5 =
∑
h,l ,m
Fh,l ,m −i , j , k εσ Th4,l ,m Sunit ,
(8)
where Fh,l ,m −i , j , k is the view factor of unit (h, l, m) to unit (i, j, k ), and S unit is the area of the unit. The view factor is computed by the Monte Carlo method[7]. By tracing the radiation beams emitted by the unit (i, j, k), the number of the beams received by (i, j, k) is summed up, then the view factor could be obtained as
Fh,l ,m −i , j ,k =
Ni , j ,k N
.
(9)
Q6 is the heat conduction rate transferred to (i, j, k), and Q7 is the radiation from the unit (i, j, k) to environment: Q7 = ε iσ Ti ,4j ,k S unit .
(10)
2.2.3 Energy balance equation of the nodes on the outer surface. The heat exchange between node (i, j, k) on the outer surface and the outside (k=M, M is the total number of the nodes in the thickness direction) is expressed as
Q8 + Q9 − Q10 − ρ CpΔv
dT = 0. dt
(11)
(1) Q8 is the radiation returned to emitter after reflecting from the filter. 100
Q8 = ∑
∑ Fh,l ,m−i, j ,k
λ = 0 h ,l , m
ε c1 ⎡ ⎛ c ⎞ ⎤ λ ⎢exp ⎜ 2n +1 ⎟ − 1⎥ ⎜ λT ⎟ ⎥ ⎢ ⎝ h ,l ,m ⎠ ⎦ ⎣
Sunit ,
(12)
5
where c1 = 3.742 × 108 W · μm 4 · m −2 , and c2 = 1.439 × 104 μm ⋅ K . The view factor is still calculated by the Monte Carlo method. The transmissivity of the filter changes with the wavelength, also the view factor. So it is necessary to trace the energy bundles in every wavelength unit (0.02 μm). A random number is produced to compare with the transmissivity of the filter, if R ≤ τ λ [4], the bundle could transmit to the cells (it is assumed that the bundles that pass the filter could be received by cells), otherwise it is reflected. According to the number of bundles received by the unit, the view factor in every wavelength unit could be obtained. (2) Q9 is the heat conduction rate transferred to (i, j, k). (3) Q10 is the radiation from the unit (i, j, k) to environment. Since the energy balance equation has the item of radiation, linearization must be taken to solve the problem: Ti (, nj ,+k1)4 ≈ 4Ti ,nj ,k Ti ,nj+,1k − 3Ti ,nj4, k ,
(13)
where Ti ,nj ,k is the temperature of node (i, j, k) at the previous time. If, together with the constant item, it is regarded as a coefficient, then eq. (13) will be a linear expression about the Ti ,nj+,1k . In this way, the original nonlinear problem would be translated to a linear one[8]. The relaxation iteration method is adopted in calculation. The iteration procedure is continued by calculating new values Ti ,nj+,1k from the Ti ,nj ,k values of the previous iteration until the difference of the average tempera2298
CHEN Xue et al. Sci China Ser E-Tech Sci | Dec. 2008 | vol. 51 | no. 12 | 2295-2304
ture of the two iterations
