(a)
(b)
Fig.1 Physical and mathematical models for solar collectors. (a) Natural convection heat transfer; (b) Forced convection heat transfer
Abstract：The experimental study of natural convection in all-glass evacuated tube solar collectors is performed through the experimental platform of the solar-assisted fuel cell system. The experimental facility includes solar collectors with different length and diameter tubes, different coating materials, and with/without guide plates, respectively. Three-dimensional mathematical models on natural and forced convections in the solar collectors are established and the experimental data is validated by field synergy and entransy principles. The results of natural convection show that the water temperature increases and thermal efficiency decreases gradually with the evacuated tube length. The thermal efficiency increases when absorption rates increase from 0.95 to 1.0 and emission rates decrease from 0.16 to 0.06. The thermal efficiency of solar collectors is increased after being equipped with the guide plate, which is attributed to the disappearance of the mixed flow and the enhancement of the heat transfer at the bottom of the evacuated tube. The results of forced convertion indicate that the Reynolds, Nusselt and entransy increments of the horizontal double collectors are higher than those of the vertical single collector while the entransy dissipation is lower than that of the vertical single collector. It is concluded that the solar collectors with guide plates are suitable for natural convection while the double horizontal collectors are suitable for forced convection in the thermal field of solar-assisted fuel cell systems with low and medium temperatures.
Key words：all-glass evacuated tube solar collectors; the solar-assisted fuel cells; field synergy principle; entransy dissipation
Solar energy is a type of renewable energy and it plays a significant role in saving conventional energy and protecting the environment. Fuel cells are the most efficient means to directly convert the chemical energy stored in fuels to electrical energy through an electrochemical reaction in an isothermal process. As a result, the solar energy coupled with fuel cell technology will be one of the most promising options for the future green energy solutions due to its high efficiency and environmental friendliness[1-2]. PV panels and batteries along with an electrolyser/hydrogen tank and the fuel cell can form a hybrid power generation system called the solar-assisted fuel cell system (SAFCS)[3]. In order to improve the entire energy efficiency of the SAFCS, it is crucially important to enhance the thermal performance of the all-glass evacuated tube solar system. The simulation results of a single tube water heater indicate that there is a stagnation zone at the bottom of the evacuated tube and a random vortex at the junction of the water tank, thus reducing the heat transfer efficiency of the evacuated tube. However, when the vortex disappears and the flow becomes stable, the heat transfer efficiency increases while the evacuated tube is equipped with guide plates[4-7]. Therefore, it is an effective way to use the guide plate to enhance the heat transfer in the solar water heater. The experimental results show that when the water temperature exceeds 45 ℃, the system efficiency will be 0.49 to 0.57 if the evacuated tube length, water tank volume and insulation thickness are reasonably allocated[8-9].
On the basis of the above-mentioned research, in order to develop the SAFCS, the solar water heaters of different tube lengths, diameters, coating materials and guide plates are studied by using the FLUENT and the experimental platform of the SAFCS. The simulation results are compared with the experimental data in detail. The effects of tube lengths, diameters, coating materials and guide plates on the heat transfer performance of all-glass evacuated tube solar water heaters are further analyzed by using field synergy and entransy methods.
1.1 Mathematical models
The all-glass evacuated tube solar collector is mainly composed of a water tank, insulation layer, inner glass tube, cover glass tube, support pieces, getter, reflector and guide plate. In the simulation process, the initial conditions for velocities are set to be u=0, v=0 and w=0 with all solid walls having no slip boundary while the PISO operator and DO radiation model are adopted. The outer wall temperature is regarded as a constant temperature, T0=293 K. The evacuated tubes are regarded as overall being cylinder heated. Coating is seen as an internal heating source. The half ball at the end of the glass tube is processed into a flat shape. The Laminar model is adopted for natural convection while the k-epsilon turbulence model is used for forced convection. The water heater with reflectors is described as being double heated while the other is single heated, as shown in Fig.1.
(a)
(b)
Fig.1 Physical and mathematical models for solar collectors. (a) Natural convection heat transfer; (b) Forced convection heat transfer
1.2 Governing equations
The general variable equation is
·gradφ)+Sφ
(1)
where ρ is the fluid density, kg/m3; t is the time, s; φ is the general variable; div is the vector divergence; Γ is the diffusion coefficient; grad is the general variable gradient; Sφ is the general variable source term; u=ui+vj+wz, u, v, w are the velocity components in the x, y, z coordinates.
The radiative transfer equation is
(α+σc)I(r,s)= 
φ(s,s′)dΩ′
(2)
where r is the position vector; s is the direction vector; s′ is the scattering direction;l is the one-way length (stroke length);α is the absorption coefficient; n is the refractive index; σc is the scattering coefficient; σ is the Stephen-Boltzmann number, W/(m2·K4); I is the radiation intensity depending on position vector r and direction vector s; T is the local temperature, K; φ is the phase function; Ω′ is the space solid angle; and α+σc is the medium optical depth.
The standard k-ε equation is
ρε-YM+Sk
(3)
(4)
where Gk generated by the mean velocity gradient is a turbulent kinetic energy term;Gb caused by buoyancy is a turbulent kinetic energy term; YM is the pulse expansion coefficient in the compressible turbulent flow;C1ε, C2ε, C3ε are the empirical constants; αε is the Prandtl number corresponding to dissipation rate ε and αk is the Prandtl number corresponding to turbulent kinetic energy k; Sk and Sε are the custom source terms.
1.3 Performance indicators
The collector thermal efficiency η is defined as
(5)
where ρw is the water density, kg/m3; cpw is the water specific heat, J/(kg·℃); vs is the fluid volume in the water tank, m3; te is the end temperature,℃; tb is the initial temperature, ℃;Ac is the contour aperture area, m2; G is the irradiation, W/m2.
The Reynolds number Re is defined as
(6)
where u is the average velocity of the evacuated tube outlet, m/s; d is the internal diameter of the evacuated tube, m; and γ is the fluid viscosity, m2/s.
The Prandtl number Pr is expressed as
(7)
where cp is the fluid constant pressure specific heat, kJ/(kg·℃); μ is the fluid dynamic viscosity, kg/(m·s); λf is the thermal conductivity, W/(m·℃).
The Nusselt number Nu is given as
Nu=0.023Re0.8Pr0.4
(8)
The entransy variable is written as
(9)
where ΔEh is the entransy variable, J·K; M is the object quality, kg; cv is the constant volume specific heat, J/(kg·K).
The entransy dissipation Eφ is defined as
Eφ=-q·
T=λf(T)2
(10)
where T is the temperature gradient.
2.1 Experimental devices
The test setup of influence factors for the solar water heater is shown in Fig.2. The thermal performance tests of solar water heaters are conducted on two types of evacuated tubes in φ47×1 500 mm and φ58×1 800 mm with different absorptivities, emissivities and photovoltaic parameters, and with/without guide plates. Two methods of stagnation and change water are adopted in the test process. The instruments for measuring temperature, humidity, radiation intensity, and wind speed and direction are equipped in the test system and a data acquisition system based on PC is used to collect and process the test data.
Fig.2 Experimental platform of natural convection for comprehensive utilization of solar energy
2.2 Tube length and diameter
The test setup is constructed to test the thermal performance of evacuated tube water heaters. The central water temperature is recorded every 10 min with the PT100 thermal resistances installed at the bottom of the water tank. As shown in Fig.3(a), the central point temperature of two single tube water heaters gradually increases with the radiant duration of time. Although the central point water temperature of the water tank with a tube of φ58×1 800 mm is higher than that of the water tank of φ47×1 500 mm during stagnation and change water processes, the thermal efficiency of water heater of φ47×1 500 mm is better than that of φ58×1 800 mm. The influence of irradiance variation and the tube length with a single or double heated water heater on thermal efficiency are simulated by using the above-developed mathematical model for the evacuated tube. As shown in Fig.3(b), the central point temperature of two single tube water heaters gradually rises with irradiation and heated time, but the water temperature of φ58×1 800 mm is higher than that of φ47×1 500 mm. The entransy increment of two single tube water heaters gradually increases with the tube length, but the entransy increment of φ58 mm is higher than that of φ47 mm in the same tube length. The entransy increment for water in the tank with the tube of φ58 mm heated on double surfaces is higher than that of the single surface. There is a fluctuation at 1 800 mm, but the entransy increment of water in the tank with the tube of φ47 mm heated on a single surface is higher than that of the double surface.
(a)
(b)
Fig.3 Simulation analysis of tube diameters and lengths. (a) Thermal efficiency verification; (b) Evacuated tube length
2.3 Absorptivity and emissivity
The solar water heater with the evacuated tube of φ58×1 800 mm in different absorptivities and emissivities is used to evaluate the thermal performance. The test results demonstrate that the temperature rise indicates negative growth at the beginning of the stagnation test due to the overnight heat loss, but the temperature rise becomes positive. The heater thermal performance with the tube of high absorptivity is superior to that of low absorptivity. The influences of absorptivity and emissivity on the thermal efficiency of heaters are simulated with the absorptivity ranging from 0.8 to 1.0 and the emissivity from 0.06 to 0.36. As shown in Fig.4, both entransy increment and thermal efficiency decrease with the increase in absorptivity from 0.85 to 0.95, but increase sharply with the increase in absorptivity from 0.95 to 1.0.
2.4 Guide plate
The solar water heater equipped with guide plates in φ58×1 800 mm evacuated tube of high absorptivity is tested and simulated to determine the effect of guide plates on the water heaters. As shown in Fig.5, although the water heating rate of the tank with guide plates equipped in the tube is lower than that of the water heater without guide plates at the test beginning with stagnation and change in water, the average water temperature of a heater with guide plates is higher by a value ranging from 0.1 to 0.5 ℃ than that of the heater without guide plates with the increase in the irradiation time. The influence of length,thickness and position of the guide plates on the thermal efficiency is simulated by using the above-developed mathematical model. As shown in Tab.1, the reasonable guide plate length of the tube heated on a single surface is 50 to 100 mm from the bottom of the evacuated tube, but that of the tube heated on the double surface is 1 000 to 1 600 mm from the mouth of the evacuated tube. The water temperature decreases at first and then increases gradually with the guide plates extending toward the evacuated tube bottom. The reasonable plate length for the tube heated on the single surface is 1 740 mm while the reasonable one for the tube heated on the double surface is 1 500 mm. The reasonable position of the guide plates for both tubes is 15 to 20 mm above the tube central axis when the guide plates move along the radial direction.
(a)
(b)
Fig.4 Simulation analysis for absorptivity and emissivity.(a) Absorptivity; (b) Emissivity
Fig.5 The experimental data for guide plate
Tab.1 The reasonable length and position of guide plates
Specifications/mmSingleheatedlength/mmSingleheatedposition/mmDoubleheatedlength/mmDoubleheatedposition/mmϕ47×12001100Above161070Centralϕ47×15001440Above161070Above4ϕ47×18001710Above161480Centralϕ58×15001440Above201200Above20ϕ58×18001740Above201500Above20ϕ58×21002030Above201600Above20
The field synergy principle theoretically describes the synergy degree of flow and heat transfer, which employs the β angle to define the synergy degree of velocity vector and the temperature gradient vector. The field synergy principle is used to analyze the field synergy in the water heater with guide plates and that in the water heater with horizontal double collectors, as shown in Figs.6 and 7.
3.1 Natural convective heat transfer
In Fig.6(a), it is observed that the temperature layering is obvious in the water tank and it is more obvious at the bottom of the water tank. The β-angle values are 90° on the bottom of the water tank. Vertical flows and horizontal flows in the water tank are due to jet disturbance. Thermal fluid flows into the water tank along the evacuated tube wall. The β-angle values are 0° because the velocity vectors are consistent with the temperature gradient vectors. The cyclotron flow is formed in the evacuated tube by a natural convective heat transfer. The temperature at the bottom of the evacuated tube is higher than other areas because the stagnation zone reduces heat transfer. The temperature layering in the water tank is of uniform distribution and the temperature gradient vectors decrease after being equipped with guide plates. The flow in the evacuated tube is more uniform because the cyclotron flow disappears when the guide plate separates the cold and hot fluid, thus decreasing the stagnation area at the bottom of evacuated tubes.
(a)
(b)Fig.6 Field synergy analysis. (a) For guide plate; (b) For horizontal double collector
3.2 Forced convective heat transfer
In Fig.6(b), the β-angle values are 0° or 180° because the collector overall temperatures gradually decrease from the evacuated tube bottom to the manifold, which causes more fluid to absorb bottom heat, the internal flow of evacuated tube is smooth and the mixed flow in the evacuated tube disappears. The manifold velocity gradually decreases because there is backflow in the internal. The fluid temperature along the flow direction increases because fluid absorbs solar radiation. The field synergy in the collector outlet is greater than others because the temperature field is consistent with the velocity field according to the numerical simulation values.
The entransy principle and entransy dissipation extreme principle are applied to analyze the enhancement of heat transfer in the water heaters according to Eqs.(9) and (10)[10-11]. The obtained results for the entransy dissipation for natural and forced convection heat transfers are shown in Fig.7.
4.1 Natural convective heat transfer
As shown in Fig.7(a), the entransy increment gradually rises with heating time. The entransy increment with double heated surfaces is larger than others. The entransy increment with the guide plate for the initial period is lower than that of the single heated surface, indicating that the guide plate improves the field synergy in the evacuated tube and reduces entransy dissipation. Entransy dissipation increases at first and then decreases because many backflows are formed in the evacuated tube by the double surfaces being heated. Entransy dissipation along the evacuated tube gradually increases and it is higher than others because the stagnation zone at the bottom of the evacuated tube is formed by the single surface being heated.
(a)
(b)
Fig.7 Entransy dissipation.(a) For natural convection;(b) For forced convection
4.2 Forced convective heat transfer
Although entransy increments of vertical single and horizontal double collectors are negative values in the initial period, their entransy increments gradually increase with heating time. As shown in Fig.7(b), the entransy dissipations of the vertical single collector and horizontal double collectors gradually decrease along the evacuated tube axial. The enhancement heat transfer effect of the horizontal double collectors is greater than that of the single vertical collector. The entransy increment of the horizontal double collectors is higher than that of single vertical collectors, but the entransy dissipation of the horizontal double collectors is lower than that of the single vertical collector.
The experiment and simulation of all-glass evacuated tube solar water heaters are conducted in the solar-assisted fuel cell system. The results show that the thermal performance of the water heater with a reflector is better than that of the ordinary water heater. The average temperature of the water tank gradually increases and the thermal efficiency decreases with tube diameter and length. The performance of the water heater is improved by increasing the absorptivity from 0.95 to 1.0 and decreasing the emissivity from 0.16 to 0.06. The entransy increment of horizontal double collectors is higher than that of the vertical single collector while the entransy dissipation is lower than that of the vertical single collector. It is concluded that the solar collectors with guide plates are suitable for natural convection while the double horizontal collectors are suitable for forced convection in the thermal field of solar-assisted fuel cell systems at low and medium temperatures.
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摘要：以太阳能与燃料电池耦合系统为应用背景,对不同管长和管径、不同吸收率和发射率和有/无内置导流板3种不同情况下的太阳能集热器进行试验研究．建立太阳能集热器自然对流和强迫对流数值计算模型,并应用场协同和火积理论分析模拟计算数据．自然对流研究表明,随着真空管长度的增加,水箱温度逐渐升高,但集热效率逐渐下降;当吸收率在0.95～1.0范围内升高,发射率在0.16～0.06范围内降低时,集热效率逐渐上升;全玻璃真空管加装导流板后,由于真空管中混流消失和真空管底部强化传热作用而提高了太阳能集热器的热效率．强迫对流研究表明,横双排太阳能集热器的雷诺数、努赛尔数和火积增量均高于竖直单排太阳能集热器;横双排太阳能集热器的火积耗散低于竖直单排太阳能集热器．研究结果表明,在中低温太阳能耦合燃料电池集热场,自然对流宜采用内置导流板太阳能集热器,强迫对流宜采用横双排太阳能集热器．
关键词：全玻璃真空管太阳能集热器; 太阳能耦合燃料电池; 场协同; 火积耗散
中图分类号：TK515
Foundation items：The National Natural Science Foundation of China (No.51376110, 51541604), the Major International (Regional) Joint Research Project of the National Natural Science Foundation of China (No. 61320106011).
Citation：：Zhang Tao, Han Jitian, Chen Changnian, et al．Experiment and numerical simulation on flow and heat transfer in all-glass evacuated tube solar collectors[J]．Journal of Southeast University (English Edition),2016,32(4):489-495．
DOI：10.3969/j.issn.1003-7985.2016.04.016.
DOI：10.3969/j.issn.1003-7985.2016.04.016
Received 2016-05-18.
Biographies：Zhang Tao(1974—),male,doctor; Han Jitian(corresponding author), male, doctor, professor, jthan@sdu.edu.cn.