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Optical and thermal performance of a high-temperature spiral solar particle receiver
Available online at www.sciencedirect.com
ScienceDirect Solar Energy 109 (2014) 200–213 www.elsevier.com/locate/solener
Optical and thermal performance of a high-temperature spiral solar particle receiver Gang Xiao, Kaikai Guo, Mingjiang Ni ⇑, Zhongyang Luo, Kefa Cen State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China Received 24 May 2014; received in revised form 25 August 2014; accepted 28 August 2014 Available online 19 September 2014 Communicated by: Associate Editor Robert Pitz-Paal
Abstract A spiral solar particle receiver (SSPR) with a conical cover was proposed, and the performance was experimentally and numerically investigated. The SSPR was heated by a concentrated radiant flux of 5 kW over a 10 cm-diameter aperture with a maximum irradiance of over 700 kW/m2. The experimental results indicated the particle temperature increase reached over 625 °C in a single pass with an optical and a thermal efficiency of 87% and 60%, respectively, when the mass flow rate was 0.21 kg/min. The optical performances of the solar simulator and the receiver were combined and simulated by the Monte-Carlo ray-tracing method. Based on the optical model, a dynamic thermal conversion model was built, which indicated the particle temperature and the overall efficiency of SSPR would reach 628–673 °C and 58.9–63.7%, respectively, when the SSPR was coupled with a 3 m two-stage dish concentrator with a solar inclination angle ranging from 60° to 120°. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Spiral solar particle receiver; High temperature; Dynamic thermal conversion model, Monte-Carlo ray-tracing method
1. Introduction An efficient and reliable receiver is crucial for solar energy thermal utilization (Kim et al., 2010; Prakash et al., 2009). Particle receivers are promising, especially for high-temperature systems (>700 °C). High-temperature particles can be used as mediums for concentrating solar powers (CSP) applications (Giuliano et al., 2011; Kitzmiller and Miller, 2010), thermochemical reactions (Chueh et al., 2010; Steinfeld, 2005) and thermal storage (Ho et al., 2009). Sandia National Laboratories (SNL) has investigated the falling particle receivers for dozens of years (Chen and Tan, 2010) and recently developed a new generation ⇑ Corresponding author. Tel.: +86 571 87953290; fax: +86 571 87951616. E-mail address: [email protected] (M. Ni).
http://dx.doi.org/10.1016/j.solener.2014.08.037 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
recently (Ho, 2013), which is expected to be used in a solar tower system. Siegel and Kolb (2009) paid a lot of work on on-sun tests of receiver prototypes. The experimental results showed the particle temperature increased more than 200 °C in a single pass, and their models indicated the outlet temperature of particles could increase from 600 °C to 900 °C with an efficiency of 70% when the average irradiance was 80 W/cm2 (Siegel et al., 2010). Chen et al. (2009) built a receiver model and analyzed the influences of particle size, wind and the bottom opening on the falling particle receiver. Based on the falling particle receivers, Roeger et al. (2011) proposed a face-down receiver using recirculation of particles to get a better efficiency, especially under part-load operation. Their results showed a highly total annual solar-to-electric efficiency of 24% by using a surround field. Wu et al. (2014) recently proposed a novel
G. Xiao et al. / Solar Energy 109 (2014) 200–213
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Nomenclature Isimulator Ta Tps
current of simulator (A) atmospheric reference temperature (°C) reference temperatures of particle-steel surface (°C) Tg reference temperature of glass (°C) Tcov reference temperature of cover (°C) Tcav reference temperature of air inside the cavity (°C) Tw temperature of cooling water (°C) Tpo temperature of particles at the outlet (°C) Tpi temperature of particles at the inlet (°C) Tpc temperature of particles in the insulation cup (°C) Tot reference wall temperature of outlet tube (°C) Qape,incident incident radiant power at the aperture of SSPR (W) Qp,absorb radiant power absorbed by particles (W) Qiw,absorb radiant power absorbed by inner wall surface (W) Qcov,absorb radiant power absorbed by cover (W) Qabsorb radiant power absorbed by SSPR (W) Qsolar solar radiant power (W) Qr,ps, Qr,g, Qr,cov radiation heat transfer between particle-steel surface, glass and cover (W) Qc,pscav, Qc,gcav, Qc,covcav convection heat transfer between particle-steel surface, glass, cover and air inside this SSPR (W) Qr,ga radiation heat transfer between glass and atmosphere (W) Qc,ga convection heat transfer between glass and atmosphere (W) Qd,ps conduction heat transfer between particlesteel surface and atmosphere (W) Qd,cov conduction heat transfer between cover and atmosphere (W) Qw heat loss of cooling unit (W) Qp net heat gained by particles (W)
centrifugal particle receiver and carried out experiments under a high-flux solar simulator, where a thin particle film was formed on the inner surface of a rotating cylindrical receiver. The experimental results demonstrated that the particle outlet temperature was up to 900 °C. A moving bed heat exchanger was investigated by Baumann et al. (2014), where stored heat of particles was used for a steam turbine. Their results suggested that small particles, high inlet velocities and narrowed tube arrangement were helpful to improve heat transfer. A small-particle receiver was proposed by Hunt (1978) and developed by Miller (1988). Their model indicated the temperature can be increased up to 1100 °C with an
Qps Qg Qcov Qcav gconcentrator goptical gthermal goverall cp cps
net heat gained by particle-steel surface (W) net heat gained by glass (W) net heat gained by cover (W) net heat gained by air inside cavity (W) concentration efficiency of concentrator (/) optical efficiency (/) thermal efficiency (/) overall efficiency (/) specific heat capacity of particles (J/(kg °C)) specific heat capacity of particle-steel surface (J/(kg °C)) cg specific heat capacity of glass (J/(kg °C)) ccov specific heat capacity of cover (J/(kg °C)) ccav specific heat capacity of air inside cavity (J/ (kg °C)) cot specific heat capacity of outlet tube (J/ (kg °C)) Fpsg, Fpscov, Fgcov angle factor between particle-steel surface, glass and cover (/) Eps, Eg, Ecov emissive power of particle-steel surface, glass, cover (W) Jps, Jg, Jcov radiosity of particle-steel surface, glass, cover (W) Aps, Ag, Acov area of particle-steel surface, glass, cover (m2) eps, eg, ecov emissivity of particle-steel surface, glass, cover (/) m0p mass flow rate of particles (kg/s) mps mass of particle-steel surface (kg) mg mass of glass (kg) mot mass of outlet tube (kg) mcov mass of cover (kg) mcav mass of air inside cavity (kg) hpscav, hgcavhcovcav convection heat transfer coefficients between particle-steel surface, glass, cover and air inside this SSPR (W/(m2 K)) L characteristic length (m) k heat conductivity coefficient (W/(m K))
efficiency of 80%. However, it was hard to find practical materials working at 1100 °C, especially to seal highpressure air in the window, and it was also noticed that windows were probably contaminated by particles. Flamant (1982) firstly brought out a fluidized bed particle receiver based on his theoretical and experimental study. Later, Kodama et al. (2008) proposed an internally circulating fluidized bed, which was used to convert concentrated radiant power into chemical energy. The coal cokes can be converted into CO by reacting with CO2 under the radiant power, and the peak efficiencies of energy conversion and carbon conversion were 12% and 73%, respectively, when the input radiant power was 3 kW (Gokon et al., 2012).
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A spiral solar particle receiver (SSPR) coupled with a twostage dish concentrator was proposed by Xiao et al. (2014a,b). Particles were driven along a spiral path, where particles absorbed concentrated solar radiant power, and the particle temperature increase of a single pass exceeded 350 °C when the average irradiance was 19 kW/m2. In this paper, experiments were performed by using an improved SSPR with a conical cover. A dynamic numerical model was built, coupling with an optical model and a thermal conversion model. According to this model, the performance of a solar thermal utilization system, combining a 3 m two-stage concentrator and this spiral particle receiver, was forecasted. 2. Experimental setup and methods Fig. 2. Focus points of five solar simulators converge at the aperture of SSP.
2.1. Solar simulator system and irradiance measurement method
value was gained by the CCD-camera Lambertian method, and the absolute value was measured by a power sensor, provided by Ophir Company, Israel. Then, the absolute irradiance distribution could be calculated (Xiao et al., 2014a,b). The absolute irradiance distribution of a single solar simulator is displayed in Fig. 3, and most radiant power focused within a 10-cm-diameter spot, which reached over 1 kW, and the maximum irradiance reached 150 kW/m2.
A solar simulator system was built to provide a stable solar radiant power source. A single solar simulator was composed of a 4 m-focal-length ellipsoidal reflector and a 7-kWe Xenon-lamp, as shown in Fig. 1. Five single simulators and controllers made up the solar simulator system. The focuses of the five solar simulators were on the same position, passing the SSPR aperture, as shown in Fig. 2. The relative irradiance distribution was measured by a CCD-camera Lambertian method (Ballestrin et al., 2006; Ulmer et al., 2002), as shown in Fig. 1. The lamp and the Lambertian target were respectively located at the two focuses of an ellipsoidal reflector. The CCD-camera was provided by the ORCA, Japan. The Lambertian target was produced by the Ocean Optics, USA. A calibration factor was calculated through comparing the relative and the absolute irradiance values of a certain spot. The relative
2.2. Spiral solar particle receiver Table 1 shows the particle physical properties. The size range is 300–900 nm, tested by a Malvern laser diffraction apparatus (Mastersizer 2000), provided by Malvern Instruments Ltd. of UK, and the average of absorptivity is 90%, tested by U-4100 spectrophotometer, as shown in
Protective shell Xe-lamp
110 142
73
408 Electrode
Ellipsoidal reflector
440
CCD-camera
Lambertian target
Fig. 1. Configuration of a single solar simulator and CCD-camera Lambertian measurement method.
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Fig. 5. Particle absorptivity vs. wavelength.
Fig. 3. Absolute irradiance distribution of a single solar simulator (kW/m2).
Particle-steel surface
Glass
Insulation
Outlet tube Controller
Spring
Table 1 Particle physical properties.
Electromagnet
Physical properties
Item
Composition
83% Al2O3, 5% SiO2, 6% Fe2O3 and others 90% roundness, 300–900 nm diameter 90% 1275 (700 °C) 1.8 2.0 (700 °C)
Size Absorptivity Heat capacity (J kg3 k1) Bulk density (g cm3) Thermal conductivity (W/(m K))
Cover
Fig. 4. Particle size distribution.
Figs. 4 and 5, respectively. Besides, the particles are commercially available at a low price. The schematic of the spiral solar particle receiver system is shown in Fig. 6. In this system, the configuration of particle surface is shown in Fig. 7. An insulation cover is fixed on the particle surface to reduce the heat loss, which is shown in Fig. 8. The cold particles were added into the feed hopper and flowed into the SSPR center from the inlet. An electromagnet made the spiral surface vibrate under certain frequency to drive particles to move along the spiral path,
Water tank Cooling unit
Fig. 6. Spiral solar particle receiver (SSPR) system.
where the power of driving system was less than 50 W. The particle moving trail is shown in Fig. 7. A cooling unit was around the electromagnet to avoid over-heating. Ten Ktype thermocouples were positioned at 18 cm intervals along the spiral path, which was made of 310S (ASTM) steel. The cover and spiral surface were wrapped by heat insulation cotton. The high temperature particles flowed into an insulation cup through an outlet tube. The particle mass flow rate depended on the particle layer thickness and the particle moving velocity. The thickness of the particle layer depended on the open of inlet and the particle moving velocity depended on the electromagnet power. In this experiment, the particle layer thickness was set at 5 and 15 mm. As shown in Fig. 8, the basal side of the receiver was called “spiral surface”, and the upright side of the receiver was called “inner wall surface”. The spiral surface was totally covered by particles, and the particle layer was thick enough to prevent the spiral steel surface from being directly irradiated. It was noticed that the inner wall surface was directly irradiated. The particle force evaluation is shown in Fig. 9, where N was the elastic force which was imposed on particle with S direction, Nx and Ny were the decomposition of N on x and y direction, and the G was the gravity of particle. The x and y direction were perpendicular and opposite to the gravity, respectively, and the S direction was along the elastic force of the spring, which are also shown in Fig. 8. The particle
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Particle moving trail
Inlet Feed hopper
Thermocouples
S
Ny
N
Nx
G
mm Outlet tube Spiral surface
Fig. 9. Particle force evaluation.
Vibration measurement point
Fig. 7. Configuration of particle-steel surface.
would move with simple harmonic vibration when the Ny was bigger than G. The vibration frequency and accelerated speed with Ny direction of spiral surface was measured by PLUSE, provided by B& K, Denmark. From the center to the edge of spiral surface, the vibration frequency was the same, and the vibration acceleration increased. In this paper, a point near the outlet was defined as the reference point of the vibration measurement. The measurement results of the reference point are shown in Fig. 10. When the working voltage was 220 V, the frequency, f, and the maximum accelerated speed of reference point with Ny direction, N 00y max , were 100 Hz and 27.5 m/s2, respectively. According to Tse et al. (1966), the particle moving velocity is obtained by, V cp
Fig. 10. Results of vibration measurement of reference point.
Outlet tube Tot
Thermocouple
φ 30
SSPR 200
g n2p ¼g cot b 2p f
ð1Þ Insulation cup
where g is the gravitational acceleration. b is the vibration angular, which is 25°. g is the correction factor, which depends on particle property. p is the ratio of vibration frequency of spiral surface to particles. np is the jump factor, which is calculated by the relation equation between the jump factor and the throw index. The throw index depended on the ratio of N 00y max and g. When the working voltage is 220 V, np is approximately 0.83, which implies the residence time of particles in the air is less than the period of spiral surface. Therefore, p is 1. The particle mass flow rate can be controlled by adjusting the power
φ 37 0
φ1
17
Tpc
Fig. 11. Particle temperature measurement device (mm).
of electromagnet, which decides N 00y max . The mass flow rate of particles ranged from 0.09 to 0.39 kg/min. The particle temperature was measured after collecting enough particles in a high-temperature insulation cup, as shown in Fig. 11. The particles continuously flowed into the insulation cup through the outlet tube. Tpc was the temperature of particles in the insulation cup, and Tot was the wall temperature of the outlet tube. It took about one Inner wall surface
Y
S
X
140
Spiral surface
10
Fig. 8. Configuration of SSPR.
G. Xiao et al. / Solar Energy 109 (2014) 200–213
205
minutes until Tpc reached steady-state. Then the particles were put into a container and the insulation cup was used for the next measurement. The thermocouple was placed at the center of cross section, closed to the bottom of the insulation cup. The particles falling process from the outlet tube into the insulation cup was assumed to be similar to the freely falling particle curtain reported by Chen et al. (2007). The particle temperature was A1 T pc when the particles left the outlet tube, where A was the normalized particle temperature as the fall height in the freely falling particle curtain. The depth of the insulation cup was 200 mm, therefore, A was 0.92, according to the report of Chen et al. (2007). The particle temperature, Tpo when the particles flowed into the outlet tube, is obtained by, 1 dT ot 0 cp mp T po T pc ¼ cot mot ð2Þ A dt where cp ; m0p ; cot and mot are the specific heat capacity, the mass flow rate of particles, the specific heat capacity and the mass of the outlet tube, respectively. Fig. 12 displays the receiver under an operating condition.
Fig. 13. Optical simulation result of a single solar simulator.
3. Simulation 3.1. Optical simulation All rays were emitted from a 5-mm-major-axis and 2-mm-minor-axis ellipsoid (Petrasch et al., 2007), which was located at the focus of the ellipsoidal reflector. There were 1 million rays for each solar simulator in the optical simulation model. The optical simulation was carried out by Monte-Carlo ray-tracing method, and the results are shown in Fig. 13. Fig. 14 shows the simulation results matched well with the experimental results of the irradiance distribution of a single solar simulator. The source model
Fig. 14. Simulation and experimental results of irradiance distributions of a single solar simulator.
Fig. 12. SSPR under an operating condition.
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of solar simulator system contained five single solar simulators, and the structure is shown in Fig. 2. The absorptance of glass for solar simulator radiant flux was ignored in the optical simulation model. The particle flow is assumed to be on a continuous surface with an absorptivity of 90%. Optical simulation results of the receiver are listed in Table 2. Isimulator is the current of simulator. Qape,incident is the incident radiant power at the aperture of SSPR. Qp,absorb, Qiw,absorb and Qcov,absorb are the radiant powers absorbed by the particles on the spiral surface, the inner wall surface and the cover, respectively. Qabsorb is the total radiant power absorbed by SSPR. The maximum incident radiant power at the aperture is 5079.4 W. The optical efficiency, goptical, is defined by goptical ¼
Qabsorb Qape;incident
ð3Þ
The optical efficiency was kept at 87.1% and most of radiant power was absorbed by the particles. The flux distributions on the particle surface under different radiant powers are shown in Fig. 15. The blackish green surface was the particle surface. There were five spots on the particle surface from the five solar simulators respectively. The peak irradiance at the particle surface were 204 and 232 kW/m2 for the radiant powers of 4469.0 W and 5079.4 W, respectively. 3.2. Thermal model 3.2.1. Assumptions The cooling water temperature, Tw, and the atmosphere temperature, Ta, were both set at 25 °C. The outer walls of cover and the particle-steel surfaces were assumed to be the atmosphere temperature. There was no air leaking from the SSPR, and the air did not absorb radiant power. The two sides of glass were isothermal. The steel surface, including particles on it, was regarded as one control volume in the thermal model, called particle-steel surface. 3.2.2. Thermal model Fig. 16 shows the schematic of the receiver heat transfer model. Tps, Tg, Tcov and Tcav are the reference temperatures of the particle-steel surface, glass, cover and air inside the receiver, respectively. Qr,ps, Qr,g and Qr,cov are the radiation heat transfers of the particle-steel surface, glass and cover, respectively. Qc,pscav, Qc,gcav and Qc,covcav are the convection heat transfers between the particle-steel surface,
Fig. 15. Irradiance distributions on particle surface on radiant powers of 4469.0 W (a) and 5079.4 W (b) at the aperture (Unit: kW/m2).
glass, cover and air inside the SSPR, respectively. Qr,ga and Qc,ga are the radiation and the convection heat transfers, respectively, between the glass and the atmosphere. Qw is the heat loss of the cooling unit. Energy equations for the particle-steel surface, glass and cover are respectively presented as follows, Qp þ Qps ¼ Qp;absorb þ Qiw;absorb Qr;p Qc;pcav Qw Qd;p
ð4Þ
Table 2 Optical simulation results of SSPR at different radiant powers of the solar simulators. Isimulator (A)
Qape,incident (W)
Qp,absorb (W)
Qiw,absorb (W)
Qcov,absorb (W)
Qabsorb (W)
80 100 120 140 160
1802.0 2455.5 3139.1 4469.0 5079.4
1175.7 1601.9 2047.9 2915.7 3313.9
324 441.4 564.4 803.4 913.1
70.6 96.1 123.1 175.1 198.9
1570.3 2139.4 2735.4 3894.2 4425.9
G. Xiao et al. / Solar Energy 109 (2014) 200–213
Eps ¼ rAps T 4ps
Qr , g − a Qc , g − a
Ta
Tg Qr , g
Qd ,cov Qr ,cov
Qc ,cov −cav Qcov,absorb Q p ,absorb
Qd , ps
Tw
Eg ¼
Qc , g −cav
Tcav
Qst ,absorb
Qr , ps
Tps
Qw
Eps J ps Qg ¼ 0 Qr;g Qr;ga Qc;gcav Qc;ga
ð5Þ
Qcov ¼ Qcov;absorb Qr;cov Qc;covcav Qd;cov
ð6Þ
where Qp was the net heat gained by the flow-out particle, which is given by, ð7Þ
Tpo is the outlet temperature of particle flow, and Tpi is the inlet temperature of particle flow, where Tpi is 25 °C. Qps is the net heat gained by the particle-steel surface, which is expressed by, Qps ¼ cps mps
dT ps dt
ð8Þ
cps is the specific heat capacity of the particle-steel surface, mps is the mass of the particle-steel surface. t is the time. Qg is the net heat gained by the glass, which is given by, Q g ¼ cg m g
dT g dt
ð9Þ
dT cov dt
ð10Þ
where ccov and mcov are the specific heat capacity and the mass of the cover, respectively. Qr,ps, Qr,g and Qr,cov are respectively given by Yang and Tao (2006), Qr;ps ¼
Qr;g ¼
Eps J ps 1eps ep Aps
Eg J g
Qr;cov ¼
ð16Þ
1eps eps Aps
Eg J g
þ
1 Aps F psg
Ecov J cov 1ecov ecov Acov
1 Aps F psg
J ps J g
þ
1eg eg A g
J g J ps
þ
þ
þ
1 Aps F pscov
J cov J g
J ps J cov 1
J cov J ps
J g J cov
Aps F pscov
ð17Þ
¼0
1 Ag F gcov
þ
¼0
1 Ag F gcov
ð18Þ ¼0
ð19Þ
where Fpsg, Fpscov, Fgcov are the view factor. According to Yang and Tao (2006), Fpsg, Fpscov, Fgcov are 0.0672, 0.9382, 0.4125, respectively. As to the convection heat transfer, Qc,pscav, Qc,gcav and Qc,covcav are respectively given by, Qc;pscav ¼ hpscav Ap ðT ps T cav Þ
ð20Þ
Qc;gcav ¼ hgcav Ag ðT g T cav Þ
ð21Þ
Qc;covcav ¼ hcovcav Acov ðT cov T cav Þ
ð22Þ
where hpscav, hgcav, hcovcav are the convection heat transfer coefficients, which are respectively given by Frank and David (1981) and Weng and Cheng (1987), 1
where cg and mg are the specific heat capacity and the mass of the glass, respectively. Qcov is the net heat gained by the cover, which is given by, Qcov ¼ ccov mcov
ð15Þ
rAcov T 4cov
r is the Stefan–Boltzmann constant. As to the particle-steel surface, glass, cover, Jps, Jg and Jcov are the radiosities, eps, eg and ecov are the emissivities, and Aps, Ag and Acov are the areas, respectively. Assuming that the particle-steel surface, glass, cover were one enclosed space, the radiation heat transfer between them is given by,
Fig. 16. Schematic of heat transfer model.
Qp ¼ cp m0p ðT po T pi Þ
ð14Þ
rAg T 4g
Ecov ¼
Tcov
Qc , ps −cav
207
1eg eg Ag
Ecov J cov 1ecov ecov Acov
ð11Þ
ð12Þ
hps;cav ¼
0:54kps;cav ðGrps;cav Prps;cav Þ4 Lps:cav
hg;cav ¼
0:27kg;cav ðGrg;cav Prg;cav Þ4 Lg;cav
1
ð24Þ 1
hcov;cav
0:59kcov;cav ðGrcov;cav Prcov;cav Þ4 ¼ Lcov;cav
ð25Þ
Gr, Pr, k are the Grashof number, the Prandtl number and the heat conductivity coefficient, respectively, which depend on the each reference temperature, i.e. Tps, Tg, Tcov, and Tcav. In this model, L is the characteristic length, which is the ratio of the area and the perimeter. Qd,p and Qd,cov are the heat conduction losses through the insulation for the particle-steel surface and the cover, respectively. To simplify the model, the heat conduction is considered to be steady, which is given by Yang and Tao (2006),
ð13Þ
where Eps, Eg and Ecov are the emissive powers of the particle-steel surface, glass, cover, respectively, which are presented as,
ð23Þ
Qd;p ¼ Aps
kinsul ðT ps T a Þ linsul
Qd;cov ¼ 2pkinsul ðT cov T a Þ
ð26Þ Z
h¼H h¼0
ln
1 rþl
insul
r
dh
ð27Þ
208
G. Xiao et al. / Solar Energy 109 (2014) 200–213
where kinsul, linsul are the heat conductivity and thickness of insulation. r and h are the inner wall radius and height of cover. The inner wall radius is the function of the height of cover. For the air inside the receiver, the energy equation is given by, Qcav ¼ hp;cav Ap ðT cav T p Þ þ hg;cav Ag ðT cav T g Þ þ hcov;cav Acov ðT cav T cov Þ
ð28Þ
where Qcav is the net heat gained by the air, which is expressed by Qcav ¼ ccav mcav
dT cav dt
ð29Þ
ccav, mcav and Tcav are the specific heat capacity, the mass and the reference temperature of the air, respectively. Qr,ga and Qc,ga are the radiation and the convection heat transfers between the glass and the atmosphere, respectively, and are expressed by, Qr;ga ¼ eg rAg T 4g T 4a ð30Þ Qc;ga ¼ hga Ag ðT g T a Þ
ð31Þ
where hga is given by Frank and David (1981) 1
hg;a ¼
0:54kg;a ðGrg;a Prg;a Þ4 Lg;a
ð32Þ
The convection heat transfer was ignored because the gap between the steel surface and the cooling unit was narrow enough. The heat loss of the cooling unit is given by, Qw ¼ eps rAw T 4ps T 4w ð33Þ
Fig. 17. Experimental results on radiant power of 4469.0 W (a) and 5079.4 W (b) at the aperture when the mass flow was 0.21 kg/min.
4. Experimental results and discussions By considering Eqs. (7)–(33), (4)–(6) and (28) are written as, cp m0p ðT po T pi Þ þ cps mps þ Qiw;incident
dT ps ¼ Qp;incident dt
Eps J ps 1eps eps Aps
hpscav Aps ðT ps T cav Þ
kinsul eps rAw T 4ps T 4w Aps ðT ps T a Þ linsul dT g Eg J g ¼ 0 1eg eg rAg T 4g T 4a cg m g dt
ð34Þ
eg Ag
hgcav Ag ðT g T cav Þ hga Ag ðT g T a Þ dT cov Ecov J cov ¼ Qcov;incident 1ecov ccov mcov dt e A
ð35Þ
cov cov
hcovcav Acov ðT cov T cav Þ Z h¼H 2pkinsul ðT cov T a Þ h¼0
1 dh lnðrþlrinsul Þ
dT cav ¼ hps;cav Aps ðT cav T ps Þ dt þ hg;cav Ag ðT cav T g Þ þ hcov;cav Acov ðT cav T cov Þ
ð36Þ
ccav mcav
ð37Þ
4.1. Experimental results Fig. 17 shows the experimental results when the particle mass flow rate was 0.21 kg/min and the radiant powers were 4469.0 W or 5079.4 W at the aperture. The experimental particle temperature at the outlet, where the particles left the SSPR and flowed into the outlet tube, Tpo, was obtained by Eq. (2). The heating process was divided into three phases. At Phase I (0–6 min), the particle temperature reached 250–350 °C, which was a little faster than that of the particle-steel surface. It was because the heat capacity of particle flow is much less than that of particle-steel surface. The particles absorbed directly the radiant flux and flowed out of SSPR. For Phase II (6–35 min), the particle-steel surface temperature became higher than the particle temperature. It was because that the cold particles from the inlet were continuously added and mixed into the hot particle flow. The cold particles were heated by the radiant flux and the steel surface. For Phase III (>35 min), the temperature of particles and steel surface reached steady-state. Because the particles had not enough time to be heated by the radiant flux and steel surface, the
G. Xiao et al. / Solar Energy 109 (2014) 200–213
temperature of particles was little lower than that of the steel surface. The thermal efficiency of SSPR is defined as gthermal ¼
Qp
ð38Þ
Qabsorb
The particle temperatures stabilized at 590 °C and 650 °C after 30 min and the thermal efficiencies were 61.7% and 60.5% with radiant powers of 4469.0 W and 5079.4 W, respectively. It was noticed that the fluctuations of temperatures may be caused by the weight changing of particles in the feed hopper, which affected the maximum accelerated speed of spiral surface under a certain electromagnetic force. Therefore, there was a little fluctuation for particle moving velocity and the particle mass flow rate, leading a temperature fluctuation. The relative errors in our experiment are listed in Table 3. The relative error of absolute irradiance measurement is given by, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eabrd ¼ E2rerd þ E2ps ð39Þ where Ererd is the relative error of relative irradiance distribution measurement, including the relative errors caused by camera, filter set, Lambertian target and image correction (Xiao et al., 2014a,b), and Eps is the relative error of power sensor to measure absolute irradiance value. As the simulator system was composed of five simulators, the experimental relative error of optical efficiency is given by, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Egoptical ¼ 5 E2abrd þ E2simulator þ E2reflectivity ð40Þ where the Esimulator is the relative error caused by simulator optical model, which is obtained by comparing Figs. 3 and 13. Ereflectivity is reflectivity relative error caused by receiver optical model. Considering the thermocouple relative error and particle mass flow rate relative error are 1% and 2%, respectively, the experimental relative error of thermal efficiency is given by,
Egthermal ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E2goptical þ E2thermocouple þ E2m0p
Relative error estimate (%)
Relative irradiance distribution measurement, Ererd Power sensor, Eps Absolute irradiance distribution measurement, Eabrd Simulator optical model, Esimulator Reflectivity in optical simulation, Ereflectivity Experimental relative error of optical efficiency, Egoptical Temperature measurement, Ethermocouple Mass flow rate measurement, Emp Experimental relative error of thermal efficiency, Egthermal
±2.05–2.82
ð41Þ
where Ethermocouple and Emp are the thermocouple relative error and particle mass flow rate relative error, respectively. 4.2. Discussion on experimental and simulated results Particles were driven along the spiral path and some of them fell from the upper path into the lower path, extending the total heating time. Meanwhile, the particle moving trail became very complicated for simulation. In order to simplify the process, a relationship of Tp and Tpo was built and obtained by experimental results with the inlet temperature of particle of 25 °C, as shown in Fig. 18. The relationship between Tps and Tpo can be written as T ps ¼ 1:24 T po 61:02
ð42Þ
The simulation results could be obtained by combining Eqs. (34)–(37) and (42), as shown in Fig. 19, which demonstrated that the simulation results had a good agreement with experimental ones. The simulated temperatures rose a little faster and higher than the experiments’ at the heating process, probably because there was some leakage of hot air at the outlet. The glass temperatures reached equilibrium quickly at 491 °C and 536 °C, respectively. The cover temperatures reached 671 °C and 723 °C on radiant powers of 4469.0 W and 5079.4 W, respectively. The temperature of glass and cover increased more slowly than that of particle-steel surface. Fig. 20 displays the equilibrium temperatures of the particles, glass and cover, and the thermal efficiency at different particle mass flow rates when the radiant power was 5079.4 W. The particle temperature declined from 650 °C to 500 °C and the thermal efficiency rose up from 60% to 80% when the particle mass flow rate increased from 0.21 kg/min to 0.39 kg/min. Fig. 21 shows the comparisons of the heat losses and thermal efficiency between the study of Xiao et al. (2014a,b) and this paper, when the mass flow rate was 0.21 kg/min. The radiation loss and the convection loss
Table 3 The estimated relative errors in our experiment. Error sources
209
±3 ±3.63–4.12 ±0.78 ±3 ±8.83–9.84 ±1 ±2 ±9.11–10.1 Fig. 18. Relationship of Tps and Tpo.
210
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Fig. 21. Heat losses and thermal efficiency when the mass flow was 0.21 kg/min.
(a) Fig. 19. Simulation and experimental results on radiant power of 4469.0 W (a) and 5079.4 W (b).
Sample rays Second-stage concentrator
First-stage concentrator SSPR
(b)
Fig. 20. Equilibrium temperatures of components of SSPR and thermal efficiency vs. particle mass flow.
were greatly reduced to 240 W and 46 W in this paper, respectively, while in the previous study they were 880 W and 590 W, respectively (Xiao et al., 2014a,b) when the radiant power was 5079.4 W. The thermal efficiency did not improve greatly, because the heat loss of cooling unit was very remarkable, reaching 1360 W. The cooling unit could be improved by filling insulation material into the gap between the steel surface and the
(c) Fig. 22. Sample rays on a 3 m two-stage dish concentrator for three solar inclination angles, including 60° (a), 90° (b) and 120° (c).
cooling unit. Moreover, the electromagnet will be replaced by a more powerful one in further works. The heat loss of the cooling unit would be reduced by 80%, considering the junction between the springs and the steel surface.
G. Xiao et al. / Solar Energy 109 (2014) 200–213
The thermal efficiency of SSPR with an improved cooling unit would be 71–87% on the 3 m two-stage dish concentrator. Spiral surface
Focal spot
Inner wall surface
(a)
5. Forecast based on a 3 m two-stage dish concentrator Based on the optical and thermal models presented, the performance of SSPR with an improved cooling unit was investigated on a 3 m two-stage dish concentrator. The aperture center of SSPR was fixed at the focus of a twostage dish concentrator. The rays inside the receiver were varying as the solar inclination angle because the two-stage dish concentrator tracked the sun and the receiver was immovable. Three solar inclination angles, including 60°, 90° and 120°, were investigated in this paper, as shown in Fig. 22. The solar flux was set to 800 W/m2. The diameters of first and second concentrator were 3000 mm and 600 mm, respectively (Zhang et al., 2014). The ray number was over 1.8 million. The flux distributions for three solar inclination angles are shown in Fig. 23. The pink surface was the inner wall surface and the green surface was the spiral surface. The spiral surface is totally covered by the particles and the inner wall surface is directed irradiated. The diameter of the focal spot was about 150 mm. The focal spot was moving and the flux distribution was changed. The most of solar radiant power was absorbed by the spiral surface. The inner wall surface would absorb more solar radiant power as the solar inclination angle was away from 90°. The simulation results for three inclination angles are shown in Table 4. The incident radiant power at the aperture was 4306.5 W for three inclination angles, which indicated the concentration efficiency was the same, 76.2%, and the aperture was big enough for rays coming in. The concentration efficiency of two-stage dish concentrator is defined by, gconcentrator ¼
(b)
211
Qape;incident Qsolar
ð43Þ
where Qsolar is the solar radiant power input at the dish concentrator. The optical efficiencies of SSPR were 84.1%, 84.8%, 76.6% for 60°, 90° and 120°, respectively. The spiral receiver was unsymmetrical, and the absorptivities of particles and steel surface were different. The particle temperature and the SSPR efficiency changed when the solar inclination angle ranged from 60° to 120°. As for 60°, more irradiance reached the spiral surface, while as for 120° more irradiance reached the steel surface. The particle mass flow rate was set to 0.21 kg/min. The thermal simulated results were obtained by the thermal model, as shown in Fig. 24 and Table 4. The particle temTable 4 The simulation results of SSPR on a 3 m two-stage dish concentrator.
(c) Fig. 23. Irradiance distributions on a 3 m two-stage dish concentrator for three solar inclination angles, including 60° (a), 90° (b) and 120° (c) (Unit: kW/m2).
Inclination angles (°)
Qapt,incident (W)
Qabsorb (W)
goptical (%)
Qp (W)
gthermal (%)
goverall (%)
60 90 120
4306.5 4306.5 4306.5
3620.9 3650.2 3298.2
84.1 84.8 76.6
2725.4 2741.3 2537.6
75.3 75.1 76.9
63.3 63.7 58.9
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References
Fig. 24. Particle-steel surface temperature and particle temperature on a 3 m two-stage dish concentrator for three solar inclination angles.
perature was 628–673 °C at the outlet, and the particle-steel surface temperature was 718–773 °C. The thermal efficiency of SSPR was 75.3–76.9%. The overall efficiency of SSPR is defined by, goverall ¼ goptical gthermal
ð44Þ
The maximum overall efficiency of SSPR was 63.7% when the solar inclination angle was 90°. 6. Conclusion The SSPR with a conical cover was performed under the solar simulator. A dynamic thermal model was coupled with an optical model based on the Monte-Carlo method, which was validated through experimental results. The experimental results showed that a stable high-temperature particle flow was produced. The particle temperature reached 650 °C at the outlet after 30 min on a radiant power of 5 kW at the aperture, and the thermal efficiency was 60%. The heat loss analysis indicated the radiation loss and convection loss were effectively reduced. The performance of SSPR with an improved cooling unit was forecasted on a 3 m two-stage dish concentrator, where the particle temperature reached 673 °C with an overall efficiency of 63.7%. Acknowledgements The authors gratefully acknowledge the support from the National Natural Science Foundation of China (No. 51476140), the Important Science & Technology Specific Projects of Zhejiang Province (No. 2012C01022-1) and the program of Introducing Talents of Discipline to University (No. B08026). The authors thank Mr. Pietro Campana of Ma¨lardalen University, Sweden, for his advice on experimental methods and language.
Ballestrin, J., Estrada, C.A., Rodriguez-Alonso, M., Perez-Rabago, C., Langley, L.W., Barnes, A., 2006. Heat flux sensors: calorimeters or radiometers?. Sol. Energy 80 1314–1320. Baumann, T., Zunft, S., Tamme, R., 2014. Moving bed heat exchangers for use with heat storage in concentrating solar plants: a multiphase model. Heat Transfer Eng. 35, 224–231. Chen, H.J., Chen, Y.T., Hsieh, H.T., Kolb, G., Siegel, N., 2007. Numerical investigation on optimal design of solid particle solar receiver. In: Proceedings of the Energy Sustainability Conference 2007, pp. 971–979. Chen, Y.T., Tan, T.D., 2010. Review of study on solid particle solar receivers. Renew. Sust. Energy Rev. 14, 265–276. Chen, Y.T., Tan, T.D., Chen, Z.Q., Siegel, N., Kolb, G.J., 2009. Wind effect on the performance of solid particle solar receivers with and without the protection of an aerowindow. Sol. Energy 83, 1815–1827. Chueh, W.C., Falter, C., Abbott, M., Scipio, D., Furler, P., Haile, S.M., Steinfeld, A., 2010. High-flux solar-driven thermochemical dissociation of CO2 and H2O using nonstoichiometric ceria. Science 330, 1797– 1801. Flamant, G., 1982. Theoretical and experimental-study of radiant-heat transfer in a solar fluidized-bed receiver. Aiche. J. 28, 529–535. Frank, P.I., David, P.D., 1981. Fundamentals of Heat Transfer. John Wiley & Sons, Inc., Canada. Giuliano, S., Buck, R., Eguiguren, S., 2011. Analysis of solar-thermal power plants with thermal energy storage and solar-hybrid operation strategy. J. Sol. Energy-T ASME 133. Gokon, N., Ono, R., Hatamachi, T., Li, L.Y., Kim, H.J., Kodama, T., 2012. CO2 gasification of coal cokes using internally circulating fluidized bed reactor by concentrated Xe-light irradiation for solar gasification. Int. J. Hydrogen. Energy 37, 12128–12137. Ho, C.K., 2013. Technology advancements for next generation falling particle receiver, in: SolarPACES 2013, Las Vegas. Ho, C.K., Khalsa, S.S., Siegel, N.P., 2009. Modeling on-sun tests of a prototype solid particle receiver for concentrating solar power processes and storage. In: Es2009: Proceedings of the Asme 3rd International Conference on Energy Sustainability, vol 2, pp. 543–550. Hunt, A.J., 1978. Small particle heat exchange. In: Lawrence Berkeley Laboratory. Kim, K., Moujaes, S.F., Kolb, G.J., 2010. Experimental and simulation study on wind affecting particle flow in a solar receiver. Sol. Energy 84, 263–270. Kitzmiller, K., Miller, F., 2010. Thermodynamic cycles for a small particle heat exchange receiver used in concentrating solar power plants. In: Es2010: Proceedings of Asme 4th International Conference on Energy Sustainability, vol 2, pp. 553–563. Kodama, T., Enomoto, S.I., Hatamachi, T., Gokon, N., 2008. Application of an internally circulating fluidized bed for windowed solar chemical reactor with direct irradiation of reacting particles. J. Sol. Energy-T ASME 130. Miller, F., 1988. Radiative heat transfer in a flowing gas-particle mixture [dissertation]. In: Univ. of California at Berkeley, Univ. of California at Berkeley, 1988. Petrasch, J., Coray, P., Meier, A., Brack, M., Haberling, P., Wuillemin, D., Steinfeld, A., 2007. A novel 50 kW 11,000 suns high-flux solar simulator based on an array of xenon arc lamps. J. Sol. Energy-T ASME, 129 405–411. Prakash, M., Kedare, S.B., Nayak, J.K., 2009. Investigations on heat losses from a solar cavity receiver. Sol. Energy 83, 157–170. Roeger, M., Amsbeck, L., Gobereit, B., Buck, R., 2011. Face-down solid particle receiver using recirculation. J. Sol. Energy-T ASME 133. Siegel, N., Kolb, G., 2009. Design and on-sun testing of a solid particle receiver prototype. In: Es2008: Proceedings of the 2nd International Conference on Energy Sustainability, vol 2, pp. 329–334.
G. Xiao et al. / Solar Energy 109 (2014) 200–213 Siegel, N.P., Ho, C.K., Khalsa, S.S., Kolb, G.J., 2010. Development and evaluation of a prototype solid particle receiver: on-sun testing and model validation. J. Sol. Energy-T ASME 132. Steinfeld, A., 2005. Solar thermochemical production of hydrogen – a review. Sol. Energy 78, 603–615. Tse, F.S., Morse, I.E., Hinkle, R.T., 1966. Mechanical Vibrations. Allyn and Bacon. Ulmer, S., Reinalter, W., Heller, P., Lupfert, E., Martinez, D., 2002. Beam characterization and improvement with a flux mapping system for dish concentrators. J. Sol. Energy-T ASME 124, 182–188. Weng, Z.J., Cheng, H., 1987. Heat Transfer. Shanghai Jiaotong University. Wu, W., Amsbeck, L., Buck, R., Uhlig, R., Ritz-Paal, R., 2014. Proof of concept test of a centrifugal particle receiver. Energy Procedia 49, 560– 568.
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ScienceDirect Solar Energy 109 (2014) 200–213 www.elsevier.com/locate/solener
Optical and thermal performance of a high-temperature spiral solar particle receiver Gang Xiao, Kaikai Guo, Mingjiang Ni ⇑, Zhongyang Luo, Kefa Cen State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China Received 24 May 2014; received in revised form 25 August 2014; accepted 28 August 2014 Available online 19 September 2014 Communicated by: Associate Editor Robert Pitz-Paal
Abstract A spiral solar particle receiver (SSPR) with a conical cover was proposed, and the performance was experimentally and numerically investigated. The SSPR was heated by a concentrated radiant flux of 5 kW over a 10 cm-diameter aperture with a maximum irradiance of over 700 kW/m2. The experimental results indicated the particle temperature increase reached over 625 °C in a single pass with an optical and a thermal efficiency of 87% and 60%, respectively, when the mass flow rate was 0.21 kg/min. The optical performances of the solar simulator and the receiver were combined and simulated by the Monte-Carlo ray-tracing method. Based on the optical model, a dynamic thermal conversion model was built, which indicated the particle temperature and the overall efficiency of SSPR would reach 628–673 °C and 58.9–63.7%, respectively, when the SSPR was coupled with a 3 m two-stage dish concentrator with a solar inclination angle ranging from 60° to 120°. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Spiral solar particle receiver; High temperature; Dynamic thermal conversion model, Monte-Carlo ray-tracing method
1. Introduction An efficient and reliable receiver is crucial for solar energy thermal utilization (Kim et al., 2010; Prakash et al., 2009). Particle receivers are promising, especially for high-temperature systems (>700 °C). High-temperature particles can be used as mediums for concentrating solar powers (CSP) applications (Giuliano et al., 2011; Kitzmiller and Miller, 2010), thermochemical reactions (Chueh et al., 2010; Steinfeld, 2005) and thermal storage (Ho et al., 2009). Sandia National Laboratories (SNL) has investigated the falling particle receivers for dozens of years (Chen and Tan, 2010) and recently developed a new generation ⇑ Corresponding author. Tel.: +86 571 87953290; fax: +86 571 87951616. E-mail address: [email protected] (M. Ni).
http://dx.doi.org/10.1016/j.solener.2014.08.037 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.
recently (Ho, 2013), which is expected to be used in a solar tower system. Siegel and Kolb (2009) paid a lot of work on on-sun tests of receiver prototypes. The experimental results showed the particle temperature increased more than 200 °C in a single pass, and their models indicated the outlet temperature of particles could increase from 600 °C to 900 °C with an efficiency of 70% when the average irradiance was 80 W/cm2 (Siegel et al., 2010). Chen et al. (2009) built a receiver model and analyzed the influences of particle size, wind and the bottom opening on the falling particle receiver. Based on the falling particle receivers, Roeger et al. (2011) proposed a face-down receiver using recirculation of particles to get a better efficiency, especially under part-load operation. Their results showed a highly total annual solar-to-electric efficiency of 24% by using a surround field. Wu et al. (2014) recently proposed a novel
G. Xiao et al. / Solar Energy 109 (2014) 200–213
201
Nomenclature Isimulator Ta Tps
current of simulator (A) atmospheric reference temperature (°C) reference temperatures of particle-steel surface (°C) Tg reference temperature of glass (°C) Tcov reference temperature of cover (°C) Tcav reference temperature of air inside the cavity (°C) Tw temperature of cooling water (°C) Tpo temperature of particles at the outlet (°C) Tpi temperature of particles at the inlet (°C) Tpc temperature of particles in the insulation cup (°C) Tot reference wall temperature of outlet tube (°C) Qape,incident incident radiant power at the aperture of SSPR (W) Qp,absorb radiant power absorbed by particles (W) Qiw,absorb radiant power absorbed by inner wall surface (W) Qcov,absorb radiant power absorbed by cover (W) Qabsorb radiant power absorbed by SSPR (W) Qsolar solar radiant power (W) Qr,ps, Qr,g, Qr,cov radiation heat transfer between particle-steel surface, glass and cover (W) Qc,pscav, Qc,gcav, Qc,covcav convection heat transfer between particle-steel surface, glass, cover and air inside this SSPR (W) Qr,ga radiation heat transfer between glass and atmosphere (W) Qc,ga convection heat transfer between glass and atmosphere (W) Qd,ps conduction heat transfer between particlesteel surface and atmosphere (W) Qd,cov conduction heat transfer between cover and atmosphere (W) Qw heat loss of cooling unit (W) Qp net heat gained by particles (W)
centrifugal particle receiver and carried out experiments under a high-flux solar simulator, where a thin particle film was formed on the inner surface of a rotating cylindrical receiver. The experimental results demonstrated that the particle outlet temperature was up to 900 °C. A moving bed heat exchanger was investigated by Baumann et al. (2014), where stored heat of particles was used for a steam turbine. Their results suggested that small particles, high inlet velocities and narrowed tube arrangement were helpful to improve heat transfer. A small-particle receiver was proposed by Hunt (1978) and developed by Miller (1988). Their model indicated the temperature can be increased up to 1100 °C with an
Qps Qg Qcov Qcav gconcentrator goptical gthermal goverall cp cps
net heat gained by particle-steel surface (W) net heat gained by glass (W) net heat gained by cover (W) net heat gained by air inside cavity (W) concentration efficiency of concentrator (/) optical efficiency (/) thermal efficiency (/) overall efficiency (/) specific heat capacity of particles (J/(kg °C)) specific heat capacity of particle-steel surface (J/(kg °C)) cg specific heat capacity of glass (J/(kg °C)) ccov specific heat capacity of cover (J/(kg °C)) ccav specific heat capacity of air inside cavity (J/ (kg °C)) cot specific heat capacity of outlet tube (J/ (kg °C)) Fpsg, Fpscov, Fgcov angle factor between particle-steel surface, glass and cover (/) Eps, Eg, Ecov emissive power of particle-steel surface, glass, cover (W) Jps, Jg, Jcov radiosity of particle-steel surface, glass, cover (W) Aps, Ag, Acov area of particle-steel surface, glass, cover (m2) eps, eg, ecov emissivity of particle-steel surface, glass, cover (/) m0p mass flow rate of particles (kg/s) mps mass of particle-steel surface (kg) mg mass of glass (kg) mot mass of outlet tube (kg) mcov mass of cover (kg) mcav mass of air inside cavity (kg) hpscav, hgcavhcovcav convection heat transfer coefficients between particle-steel surface, glass, cover and air inside this SSPR (W/(m2 K)) L characteristic length (m) k heat conductivity coefficient (W/(m K))
efficiency of 80%. However, it was hard to find practical materials working at 1100 °C, especially to seal highpressure air in the window, and it was also noticed that windows were probably contaminated by particles. Flamant (1982) firstly brought out a fluidized bed particle receiver based on his theoretical and experimental study. Later, Kodama et al. (2008) proposed an internally circulating fluidized bed, which was used to convert concentrated radiant power into chemical energy. The coal cokes can be converted into CO by reacting with CO2 under the radiant power, and the peak efficiencies of energy conversion and carbon conversion were 12% and 73%, respectively, when the input radiant power was 3 kW (Gokon et al., 2012).
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A spiral solar particle receiver (SSPR) coupled with a twostage dish concentrator was proposed by Xiao et al. (2014a,b). Particles were driven along a spiral path, where particles absorbed concentrated solar radiant power, and the particle temperature increase of a single pass exceeded 350 °C when the average irradiance was 19 kW/m2. In this paper, experiments were performed by using an improved SSPR with a conical cover. A dynamic numerical model was built, coupling with an optical model and a thermal conversion model. According to this model, the performance of a solar thermal utilization system, combining a 3 m two-stage concentrator and this spiral particle receiver, was forecasted. 2. Experimental setup and methods Fig. 2. Focus points of five solar simulators converge at the aperture of SSP.
2.1. Solar simulator system and irradiance measurement method
value was gained by the CCD-camera Lambertian method, and the absolute value was measured by a power sensor, provided by Ophir Company, Israel. Then, the absolute irradiance distribution could be calculated (Xiao et al., 2014a,b). The absolute irradiance distribution of a single solar simulator is displayed in Fig. 3, and most radiant power focused within a 10-cm-diameter spot, which reached over 1 kW, and the maximum irradiance reached 150 kW/m2.
A solar simulator system was built to provide a stable solar radiant power source. A single solar simulator was composed of a 4 m-focal-length ellipsoidal reflector and a 7-kWe Xenon-lamp, as shown in Fig. 1. Five single simulators and controllers made up the solar simulator system. The focuses of the five solar simulators were on the same position, passing the SSPR aperture, as shown in Fig. 2. The relative irradiance distribution was measured by a CCD-camera Lambertian method (Ballestrin et al., 2006; Ulmer et al., 2002), as shown in Fig. 1. The lamp and the Lambertian target were respectively located at the two focuses of an ellipsoidal reflector. The CCD-camera was provided by the ORCA, Japan. The Lambertian target was produced by the Ocean Optics, USA. A calibration factor was calculated through comparing the relative and the absolute irradiance values of a certain spot. The relative
2.2. Spiral solar particle receiver Table 1 shows the particle physical properties. The size range is 300–900 nm, tested by a Malvern laser diffraction apparatus (Mastersizer 2000), provided by Malvern Instruments Ltd. of UK, and the average of absorptivity is 90%, tested by U-4100 spectrophotometer, as shown in
Protective shell Xe-lamp
110 142
73
408 Electrode
Ellipsoidal reflector
440
CCD-camera
Lambertian target
Fig. 1. Configuration of a single solar simulator and CCD-camera Lambertian measurement method.
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Fig. 5. Particle absorptivity vs. wavelength.
Fig. 3. Absolute irradiance distribution of a single solar simulator (kW/m2).
Particle-steel surface
Glass
Insulation
Outlet tube Controller
Spring
Table 1 Particle physical properties.
Electromagnet
Physical properties
Item
Composition
83% Al2O3, 5% SiO2, 6% Fe2O3 and others 90% roundness, 300–900 nm diameter 90% 1275 (700 °C) 1.8 2.0 (700 °C)
Size Absorptivity Heat capacity (J kg3 k1) Bulk density (g cm3) Thermal conductivity (W/(m K))
Cover
Fig. 4. Particle size distribution.
Figs. 4 and 5, respectively. Besides, the particles are commercially available at a low price. The schematic of the spiral solar particle receiver system is shown in Fig. 6. In this system, the configuration of particle surface is shown in Fig. 7. An insulation cover is fixed on the particle surface to reduce the heat loss, which is shown in Fig. 8. The cold particles were added into the feed hopper and flowed into the SSPR center from the inlet. An electromagnet made the spiral surface vibrate under certain frequency to drive particles to move along the spiral path,
Water tank Cooling unit
Fig. 6. Spiral solar particle receiver (SSPR) system.
where the power of driving system was less than 50 W. The particle moving trail is shown in Fig. 7. A cooling unit was around the electromagnet to avoid over-heating. Ten Ktype thermocouples were positioned at 18 cm intervals along the spiral path, which was made of 310S (ASTM) steel. The cover and spiral surface were wrapped by heat insulation cotton. The high temperature particles flowed into an insulation cup through an outlet tube. The particle mass flow rate depended on the particle layer thickness and the particle moving velocity. The thickness of the particle layer depended on the open of inlet and the particle moving velocity depended on the electromagnet power. In this experiment, the particle layer thickness was set at 5 and 15 mm. As shown in Fig. 8, the basal side of the receiver was called “spiral surface”, and the upright side of the receiver was called “inner wall surface”. The spiral surface was totally covered by particles, and the particle layer was thick enough to prevent the spiral steel surface from being directly irradiated. It was noticed that the inner wall surface was directly irradiated. The particle force evaluation is shown in Fig. 9, where N was the elastic force which was imposed on particle with S direction, Nx and Ny were the decomposition of N on x and y direction, and the G was the gravity of particle. The x and y direction were perpendicular and opposite to the gravity, respectively, and the S direction was along the elastic force of the spring, which are also shown in Fig. 8. The particle
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Particle moving trail
Inlet Feed hopper
Thermocouples
S
Ny
N
Nx
G
mm Outlet tube Spiral surface
Fig. 9. Particle force evaluation.
Vibration measurement point
Fig. 7. Configuration of particle-steel surface.
would move with simple harmonic vibration when the Ny was bigger than G. The vibration frequency and accelerated speed with Ny direction of spiral surface was measured by PLUSE, provided by B& K, Denmark. From the center to the edge of spiral surface, the vibration frequency was the same, and the vibration acceleration increased. In this paper, a point near the outlet was defined as the reference point of the vibration measurement. The measurement results of the reference point are shown in Fig. 10. When the working voltage was 220 V, the frequency, f, and the maximum accelerated speed of reference point with Ny direction, N 00y max , were 100 Hz and 27.5 m/s2, respectively. According to Tse et al. (1966), the particle moving velocity is obtained by, V cp
Fig. 10. Results of vibration measurement of reference point.
Outlet tube Tot
Thermocouple
φ 30
SSPR 200
g n2p ¼g cot b 2p f
ð1Þ Insulation cup
where g is the gravitational acceleration. b is the vibration angular, which is 25°. g is the correction factor, which depends on particle property. p is the ratio of vibration frequency of spiral surface to particles. np is the jump factor, which is calculated by the relation equation between the jump factor and the throw index. The throw index depended on the ratio of N 00y max and g. When the working voltage is 220 V, np is approximately 0.83, which implies the residence time of particles in the air is less than the period of spiral surface. Therefore, p is 1. The particle mass flow rate can be controlled by adjusting the power
φ 37 0
φ1
17
Tpc
Fig. 11. Particle temperature measurement device (mm).
of electromagnet, which decides N 00y max . The mass flow rate of particles ranged from 0.09 to 0.39 kg/min. The particle temperature was measured after collecting enough particles in a high-temperature insulation cup, as shown in Fig. 11. The particles continuously flowed into the insulation cup through the outlet tube. Tpc was the temperature of particles in the insulation cup, and Tot was the wall temperature of the outlet tube. It took about one Inner wall surface
Y
S
X
140
Spiral surface
10
Fig. 8. Configuration of SSPR.
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minutes until Tpc reached steady-state. Then the particles were put into a container and the insulation cup was used for the next measurement. The thermocouple was placed at the center of cross section, closed to the bottom of the insulation cup. The particles falling process from the outlet tube into the insulation cup was assumed to be similar to the freely falling particle curtain reported by Chen et al. (2007). The particle temperature was A1 T pc when the particles left the outlet tube, where A was the normalized particle temperature as the fall height in the freely falling particle curtain. The depth of the insulation cup was 200 mm, therefore, A was 0.92, according to the report of Chen et al. (2007). The particle temperature, Tpo when the particles flowed into the outlet tube, is obtained by, 1 dT ot 0 cp mp T po T pc ¼ cot mot ð2Þ A dt where cp ; m0p ; cot and mot are the specific heat capacity, the mass flow rate of particles, the specific heat capacity and the mass of the outlet tube, respectively. Fig. 12 displays the receiver under an operating condition.
Fig. 13. Optical simulation result of a single solar simulator.
3. Simulation 3.1. Optical simulation All rays were emitted from a 5-mm-major-axis and 2-mm-minor-axis ellipsoid (Petrasch et al., 2007), which was located at the focus of the ellipsoidal reflector. There were 1 million rays for each solar simulator in the optical simulation model. The optical simulation was carried out by Monte-Carlo ray-tracing method, and the results are shown in Fig. 13. Fig. 14 shows the simulation results matched well with the experimental results of the irradiance distribution of a single solar simulator. The source model
Fig. 14. Simulation and experimental results of irradiance distributions of a single solar simulator.
Fig. 12. SSPR under an operating condition.
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G. Xiao et al. / Solar Energy 109 (2014) 200–213
of solar simulator system contained five single solar simulators, and the structure is shown in Fig. 2. The absorptance of glass for solar simulator radiant flux was ignored in the optical simulation model. The particle flow is assumed to be on a continuous surface with an absorptivity of 90%. Optical simulation results of the receiver are listed in Table 2. Isimulator is the current of simulator. Qape,incident is the incident radiant power at the aperture of SSPR. Qp,absorb, Qiw,absorb and Qcov,absorb are the radiant powers absorbed by the particles on the spiral surface, the inner wall surface and the cover, respectively. Qabsorb is the total radiant power absorbed by SSPR. The maximum incident radiant power at the aperture is 5079.4 W. The optical efficiency, goptical, is defined by goptical ¼
Qabsorb Qape;incident
ð3Þ
The optical efficiency was kept at 87.1% and most of radiant power was absorbed by the particles. The flux distributions on the particle surface under different radiant powers are shown in Fig. 15. The blackish green surface was the particle surface. There were five spots on the particle surface from the five solar simulators respectively. The peak irradiance at the particle surface were 204 and 232 kW/m2 for the radiant powers of 4469.0 W and 5079.4 W, respectively. 3.2. Thermal model 3.2.1. Assumptions The cooling water temperature, Tw, and the atmosphere temperature, Ta, were both set at 25 °C. The outer walls of cover and the particle-steel surfaces were assumed to be the atmosphere temperature. There was no air leaking from the SSPR, and the air did not absorb radiant power. The two sides of glass were isothermal. The steel surface, including particles on it, was regarded as one control volume in the thermal model, called particle-steel surface. 3.2.2. Thermal model Fig. 16 shows the schematic of the receiver heat transfer model. Tps, Tg, Tcov and Tcav are the reference temperatures of the particle-steel surface, glass, cover and air inside the receiver, respectively. Qr,ps, Qr,g and Qr,cov are the radiation heat transfers of the particle-steel surface, glass and cover, respectively. Qc,pscav, Qc,gcav and Qc,covcav are the convection heat transfers between the particle-steel surface,
Fig. 15. Irradiance distributions on particle surface on radiant powers of 4469.0 W (a) and 5079.4 W (b) at the aperture (Unit: kW/m2).
glass, cover and air inside the SSPR, respectively. Qr,ga and Qc,ga are the radiation and the convection heat transfers, respectively, between the glass and the atmosphere. Qw is the heat loss of the cooling unit. Energy equations for the particle-steel surface, glass and cover are respectively presented as follows, Qp þ Qps ¼ Qp;absorb þ Qiw;absorb Qr;p Qc;pcav Qw Qd;p
ð4Þ
Table 2 Optical simulation results of SSPR at different radiant powers of the solar simulators. Isimulator (A)
Qape,incident (W)
Qp,absorb (W)
Qiw,absorb (W)
Qcov,absorb (W)
Qabsorb (W)
80 100 120 140 160
1802.0 2455.5 3139.1 4469.0 5079.4
1175.7 1601.9 2047.9 2915.7 3313.9
324 441.4 564.4 803.4 913.1
70.6 96.1 123.1 175.1 198.9
1570.3 2139.4 2735.4 3894.2 4425.9
G. Xiao et al. / Solar Energy 109 (2014) 200–213
Eps ¼ rAps T 4ps
Qr , g − a Qc , g − a
Ta
Tg Qr , g
Qd ,cov Qr ,cov
Qc ,cov −cav Qcov,absorb Q p ,absorb
Qd , ps
Tw
Eg ¼
Qc , g −cav
Tcav
Qst ,absorb
Qr , ps
Tps
Qw
Eps J ps Qg ¼ 0 Qr;g Qr;ga Qc;gcav Qc;ga
ð5Þ
Qcov ¼ Qcov;absorb Qr;cov Qc;covcav Qd;cov
ð6Þ
where Qp was the net heat gained by the flow-out particle, which is given by, ð7Þ
Tpo is the outlet temperature of particle flow, and Tpi is the inlet temperature of particle flow, where Tpi is 25 °C. Qps is the net heat gained by the particle-steel surface, which is expressed by, Qps ¼ cps mps
dT ps dt
ð8Þ
cps is the specific heat capacity of the particle-steel surface, mps is the mass of the particle-steel surface. t is the time. Qg is the net heat gained by the glass, which is given by, Q g ¼ cg m g
dT g dt
ð9Þ
dT cov dt
ð10Þ
where ccov and mcov are the specific heat capacity and the mass of the cover, respectively. Qr,ps, Qr,g and Qr,cov are respectively given by Yang and Tao (2006), Qr;ps ¼
Qr;g ¼
Eps J ps 1eps ep Aps
Eg J g
Qr;cov ¼
ð16Þ
1eps eps Aps
Eg J g
þ
1 Aps F psg
Ecov J cov 1ecov ecov Acov
1 Aps F psg
J ps J g
þ
1eg eg A g
J g J ps
þ
þ
þ
1 Aps F pscov
J cov J g
J ps J cov 1
J cov J ps
J g J cov
Aps F pscov
ð17Þ
¼0
1 Ag F gcov
þ
¼0
1 Ag F gcov
ð18Þ ¼0
ð19Þ
where Fpsg, Fpscov, Fgcov are the view factor. According to Yang and Tao (2006), Fpsg, Fpscov, Fgcov are 0.0672, 0.9382, 0.4125, respectively. As to the convection heat transfer, Qc,pscav, Qc,gcav and Qc,covcav are respectively given by, Qc;pscav ¼ hpscav Ap ðT ps T cav Þ
ð20Þ
Qc;gcav ¼ hgcav Ag ðT g T cav Þ
ð21Þ
Qc;covcav ¼ hcovcav Acov ðT cov T cav Þ
ð22Þ
where hpscav, hgcav, hcovcav are the convection heat transfer coefficients, which are respectively given by Frank and David (1981) and Weng and Cheng (1987), 1
where cg and mg are the specific heat capacity and the mass of the glass, respectively. Qcov is the net heat gained by the cover, which is given by, Qcov ¼ ccov mcov
ð15Þ
rAcov T 4cov
r is the Stefan–Boltzmann constant. As to the particle-steel surface, glass, cover, Jps, Jg and Jcov are the radiosities, eps, eg and ecov are the emissivities, and Aps, Ag and Acov are the areas, respectively. Assuming that the particle-steel surface, glass, cover were one enclosed space, the radiation heat transfer between them is given by,
Fig. 16. Schematic of heat transfer model.
Qp ¼ cp m0p ðT po T pi Þ
ð14Þ
rAg T 4g
Ecov ¼
Tcov
Qc , ps −cav
207
1eg eg Ag
Ecov J cov 1ecov ecov Acov
ð11Þ
ð12Þ
hps;cav ¼
0:54kps;cav ðGrps;cav Prps;cav Þ4 Lps:cav
hg;cav ¼
0:27kg;cav ðGrg;cav Prg;cav Þ4 Lg;cav
1
ð24Þ 1
hcov;cav
0:59kcov;cav ðGrcov;cav Prcov;cav Þ4 ¼ Lcov;cav
ð25Þ
Gr, Pr, k are the Grashof number, the Prandtl number and the heat conductivity coefficient, respectively, which depend on the each reference temperature, i.e. Tps, Tg, Tcov, and Tcav. In this model, L is the characteristic length, which is the ratio of the area and the perimeter. Qd,p and Qd,cov are the heat conduction losses through the insulation for the particle-steel surface and the cover, respectively. To simplify the model, the heat conduction is considered to be steady, which is given by Yang and Tao (2006),
ð13Þ
where Eps, Eg and Ecov are the emissive powers of the particle-steel surface, glass, cover, respectively, which are presented as,
ð23Þ
Qd;p ¼ Aps
kinsul ðT ps T a Þ linsul
Qd;cov ¼ 2pkinsul ðT cov T a Þ
ð26Þ Z
h¼H h¼0
ln
1 rþl
insul
r
dh
ð27Þ
208
G. Xiao et al. / Solar Energy 109 (2014) 200–213
where kinsul, linsul are the heat conductivity and thickness of insulation. r and h are the inner wall radius and height of cover. The inner wall radius is the function of the height of cover. For the air inside the receiver, the energy equation is given by, Qcav ¼ hp;cav Ap ðT cav T p Þ þ hg;cav Ag ðT cav T g Þ þ hcov;cav Acov ðT cav T cov Þ
ð28Þ
where Qcav is the net heat gained by the air, which is expressed by Qcav ¼ ccav mcav
dT cav dt
ð29Þ
ccav, mcav and Tcav are the specific heat capacity, the mass and the reference temperature of the air, respectively. Qr,ga and Qc,ga are the radiation and the convection heat transfers between the glass and the atmosphere, respectively, and are expressed by, Qr;ga ¼ eg rAg T 4g T 4a ð30Þ Qc;ga ¼ hga Ag ðT g T a Þ
ð31Þ
where hga is given by Frank and David (1981) 1
hg;a ¼
0:54kg;a ðGrg;a Prg;a Þ4 Lg;a
ð32Þ
The convection heat transfer was ignored because the gap between the steel surface and the cooling unit was narrow enough. The heat loss of the cooling unit is given by, Qw ¼ eps rAw T 4ps T 4w ð33Þ
Fig. 17. Experimental results on radiant power of 4469.0 W (a) and 5079.4 W (b) at the aperture when the mass flow was 0.21 kg/min.
4. Experimental results and discussions By considering Eqs. (7)–(33), (4)–(6) and (28) are written as, cp m0p ðT po T pi Þ þ cps mps þ Qiw;incident
dT ps ¼ Qp;incident dt
Eps J ps 1eps eps Aps
hpscav Aps ðT ps T cav Þ
kinsul eps rAw T 4ps T 4w Aps ðT ps T a Þ linsul dT g Eg J g ¼ 0 1eg eg rAg T 4g T 4a cg m g dt
ð34Þ
eg Ag
hgcav Ag ðT g T cav Þ hga Ag ðT g T a Þ dT cov Ecov J cov ¼ Qcov;incident 1ecov ccov mcov dt e A
ð35Þ
cov cov
hcovcav Acov ðT cov T cav Þ Z h¼H 2pkinsul ðT cov T a Þ h¼0
1 dh lnðrþlrinsul Þ
dT cav ¼ hps;cav Aps ðT cav T ps Þ dt þ hg;cav Ag ðT cav T g Þ þ hcov;cav Acov ðT cav T cov Þ
ð36Þ
ccav mcav
ð37Þ
4.1. Experimental results Fig. 17 shows the experimental results when the particle mass flow rate was 0.21 kg/min and the radiant powers were 4469.0 W or 5079.4 W at the aperture. The experimental particle temperature at the outlet, where the particles left the SSPR and flowed into the outlet tube, Tpo, was obtained by Eq. (2). The heating process was divided into three phases. At Phase I (0–6 min), the particle temperature reached 250–350 °C, which was a little faster than that of the particle-steel surface. It was because the heat capacity of particle flow is much less than that of particle-steel surface. The particles absorbed directly the radiant flux and flowed out of SSPR. For Phase II (6–35 min), the particle-steel surface temperature became higher than the particle temperature. It was because that the cold particles from the inlet were continuously added and mixed into the hot particle flow. The cold particles were heated by the radiant flux and the steel surface. For Phase III (>35 min), the temperature of particles and steel surface reached steady-state. Because the particles had not enough time to be heated by the radiant flux and steel surface, the
G. Xiao et al. / Solar Energy 109 (2014) 200–213
temperature of particles was little lower than that of the steel surface. The thermal efficiency of SSPR is defined as gthermal ¼
Qp
ð38Þ
Qabsorb
The particle temperatures stabilized at 590 °C and 650 °C after 30 min and the thermal efficiencies were 61.7% and 60.5% with radiant powers of 4469.0 W and 5079.4 W, respectively. It was noticed that the fluctuations of temperatures may be caused by the weight changing of particles in the feed hopper, which affected the maximum accelerated speed of spiral surface under a certain electromagnetic force. Therefore, there was a little fluctuation for particle moving velocity and the particle mass flow rate, leading a temperature fluctuation. The relative errors in our experiment are listed in Table 3. The relative error of absolute irradiance measurement is given by, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Eabrd ¼ E2rerd þ E2ps ð39Þ where Ererd is the relative error of relative irradiance distribution measurement, including the relative errors caused by camera, filter set, Lambertian target and image correction (Xiao et al., 2014a,b), and Eps is the relative error of power sensor to measure absolute irradiance value. As the simulator system was composed of five simulators, the experimental relative error of optical efficiency is given by, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Egoptical ¼ 5 E2abrd þ E2simulator þ E2reflectivity ð40Þ where the Esimulator is the relative error caused by simulator optical model, which is obtained by comparing Figs. 3 and 13. Ereflectivity is reflectivity relative error caused by receiver optical model. Considering the thermocouple relative error and particle mass flow rate relative error are 1% and 2%, respectively, the experimental relative error of thermal efficiency is given by,
Egthermal ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E2goptical þ E2thermocouple þ E2m0p
Relative error estimate (%)
Relative irradiance distribution measurement, Ererd Power sensor, Eps Absolute irradiance distribution measurement, Eabrd Simulator optical model, Esimulator Reflectivity in optical simulation, Ereflectivity Experimental relative error of optical efficiency, Egoptical Temperature measurement, Ethermocouple Mass flow rate measurement, Emp Experimental relative error of thermal efficiency, Egthermal
±2.05–2.82
ð41Þ
where Ethermocouple and Emp are the thermocouple relative error and particle mass flow rate relative error, respectively. 4.2. Discussion on experimental and simulated results Particles were driven along the spiral path and some of them fell from the upper path into the lower path, extending the total heating time. Meanwhile, the particle moving trail became very complicated for simulation. In order to simplify the process, a relationship of Tp and Tpo was built and obtained by experimental results with the inlet temperature of particle of 25 °C, as shown in Fig. 18. The relationship between Tps and Tpo can be written as T ps ¼ 1:24 T po 61:02
ð42Þ
The simulation results could be obtained by combining Eqs. (34)–(37) and (42), as shown in Fig. 19, which demonstrated that the simulation results had a good agreement with experimental ones. The simulated temperatures rose a little faster and higher than the experiments’ at the heating process, probably because there was some leakage of hot air at the outlet. The glass temperatures reached equilibrium quickly at 491 °C and 536 °C, respectively. The cover temperatures reached 671 °C and 723 °C on radiant powers of 4469.0 W and 5079.4 W, respectively. The temperature of glass and cover increased more slowly than that of particle-steel surface. Fig. 20 displays the equilibrium temperatures of the particles, glass and cover, and the thermal efficiency at different particle mass flow rates when the radiant power was 5079.4 W. The particle temperature declined from 650 °C to 500 °C and the thermal efficiency rose up from 60% to 80% when the particle mass flow rate increased from 0.21 kg/min to 0.39 kg/min. Fig. 21 shows the comparisons of the heat losses and thermal efficiency between the study of Xiao et al. (2014a,b) and this paper, when the mass flow rate was 0.21 kg/min. The radiation loss and the convection loss
Table 3 The estimated relative errors in our experiment. Error sources
209
±3 ±3.63–4.12 ±0.78 ±3 ±8.83–9.84 ±1 ±2 ±9.11–10.1 Fig. 18. Relationship of Tps and Tpo.
210
G. Xiao et al. / Solar Energy 109 (2014) 200–213
Fig. 21. Heat losses and thermal efficiency when the mass flow was 0.21 kg/min.
(a) Fig. 19. Simulation and experimental results on radiant power of 4469.0 W (a) and 5079.4 W (b).
Sample rays Second-stage concentrator
First-stage concentrator SSPR
(b)
Fig. 20. Equilibrium temperatures of components of SSPR and thermal efficiency vs. particle mass flow.
were greatly reduced to 240 W and 46 W in this paper, respectively, while in the previous study they were 880 W and 590 W, respectively (Xiao et al., 2014a,b) when the radiant power was 5079.4 W. The thermal efficiency did not improve greatly, because the heat loss of cooling unit was very remarkable, reaching 1360 W. The cooling unit could be improved by filling insulation material into the gap between the steel surface and the
(c) Fig. 22. Sample rays on a 3 m two-stage dish concentrator for three solar inclination angles, including 60° (a), 90° (b) and 120° (c).
cooling unit. Moreover, the electromagnet will be replaced by a more powerful one in further works. The heat loss of the cooling unit would be reduced by 80%, considering the junction between the springs and the steel surface.
G. Xiao et al. / Solar Energy 109 (2014) 200–213
The thermal efficiency of SSPR with an improved cooling unit would be 71–87% on the 3 m two-stage dish concentrator. Spiral surface
Focal spot
Inner wall surface
(a)
5. Forecast based on a 3 m two-stage dish concentrator Based on the optical and thermal models presented, the performance of SSPR with an improved cooling unit was investigated on a 3 m two-stage dish concentrator. The aperture center of SSPR was fixed at the focus of a twostage dish concentrator. The rays inside the receiver were varying as the solar inclination angle because the two-stage dish concentrator tracked the sun and the receiver was immovable. Three solar inclination angles, including 60°, 90° and 120°, were investigated in this paper, as shown in Fig. 22. The solar flux was set to 800 W/m2. The diameters of first and second concentrator were 3000 mm and 600 mm, respectively (Zhang et al., 2014). The ray number was over 1.8 million. The flux distributions for three solar inclination angles are shown in Fig. 23. The pink surface was the inner wall surface and the green surface was the spiral surface. The spiral surface is totally covered by the particles and the inner wall surface is directed irradiated. The diameter of the focal spot was about 150 mm. The focal spot was moving and the flux distribution was changed. The most of solar radiant power was absorbed by the spiral surface. The inner wall surface would absorb more solar radiant power as the solar inclination angle was away from 90°. The simulation results for three inclination angles are shown in Table 4. The incident radiant power at the aperture was 4306.5 W for three inclination angles, which indicated the concentration efficiency was the same, 76.2%, and the aperture was big enough for rays coming in. The concentration efficiency of two-stage dish concentrator is defined by, gconcentrator ¼
(b)
211
Qape;incident Qsolar
ð43Þ
where Qsolar is the solar radiant power input at the dish concentrator. The optical efficiencies of SSPR were 84.1%, 84.8%, 76.6% for 60°, 90° and 120°, respectively. The spiral receiver was unsymmetrical, and the absorptivities of particles and steel surface were different. The particle temperature and the SSPR efficiency changed when the solar inclination angle ranged from 60° to 120°. As for 60°, more irradiance reached the spiral surface, while as for 120° more irradiance reached the steel surface. The particle mass flow rate was set to 0.21 kg/min. The thermal simulated results were obtained by the thermal model, as shown in Fig. 24 and Table 4. The particle temTable 4 The simulation results of SSPR on a 3 m two-stage dish concentrator.
(c) Fig. 23. Irradiance distributions on a 3 m two-stage dish concentrator for three solar inclination angles, including 60° (a), 90° (b) and 120° (c) (Unit: kW/m2).
Inclination angles (°)
Qapt,incident (W)
Qabsorb (W)
goptical (%)
Qp (W)
gthermal (%)
goverall (%)
60 90 120
4306.5 4306.5 4306.5
3620.9 3650.2 3298.2
84.1 84.8 76.6
2725.4 2741.3 2537.6
75.3 75.1 76.9
63.3 63.7 58.9
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G. Xiao et al. / Solar Energy 109 (2014) 200–213
References
Fig. 24. Particle-steel surface temperature and particle temperature on a 3 m two-stage dish concentrator for three solar inclination angles.
perature was 628–673 °C at the outlet, and the particle-steel surface temperature was 718–773 °C. The thermal efficiency of SSPR was 75.3–76.9%. The overall efficiency of SSPR is defined by, goverall ¼ goptical gthermal
ð44Þ
The maximum overall efficiency of SSPR was 63.7% when the solar inclination angle was 90°. 6. Conclusion The SSPR with a conical cover was performed under the solar simulator. A dynamic thermal model was coupled with an optical model based on the Monte-Carlo method, which was validated through experimental results. The experimental results showed that a stable high-temperature particle flow was produced. The particle temperature reached 650 °C at the outlet after 30 min on a radiant power of 5 kW at the aperture, and the thermal efficiency was 60%. The heat loss analysis indicated the radiation loss and convection loss were effectively reduced. The performance of SSPR with an improved cooling unit was forecasted on a 3 m two-stage dish concentrator, where the particle temperature reached 673 °C with an overall efficiency of 63.7%. Acknowledgements The authors gratefully acknowledge the support from the National Natural Science Foundation of China (No. 51476140), the Important Science & Technology Specific Projects of Zhejiang Province (No. 2012C01022-1) and the program of Introducing Talents of Discipline to University (No. B08026). The authors thank Mr. Pietro Campana of Ma¨lardalen University, Sweden, for his advice on experimental methods and language.
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