夏热冬暖地区阳台壁挂式平板型太阳能热水器水量配比优化

魏生贤，胡粉娥，杨慧敏

夏热冬暖地区阳台壁挂式平板型太阳能热水器水量配比优化

魏生贤1，胡粉娥2，杨慧敏3

（1. 曲靖师范学院磁性材料及器件研究中心，曲靖 655011；2. 曲靖师范学院化学与环境科学学院，曲靖 655011；3. 曲靖师范学院物理与电子工程学院，曲靖 655011）

基于中国夏热冬暖地区13城市的典型气象数据，利用所建数学模型对阳台壁挂式平板型太阳能热水器的水量配比、方位角因子和太阳能保证率进行了计算。结果显示，南向阳台壁挂式太阳能热水器春、夏、秋、冬4季和全年水量配比分别位于21.1～50.3、22.9～55.7、33.8～57.9、25.0～54.6和28.3～49.3 kg/m2之间。为便于应用，该文分别给出了南向阳台壁挂式太阳能热水器水量配比与水平面日均总太阳辐射量、温升-辐射量比值、倾角间的线性关系式。对于非南向阳台壁挂式太阳能热水器，季均和年均方位角因子随方位角的增大而逐渐减小。倾角为60°～90°、方位角为10°～90°时，季均和年均方位角因子分别位于0.67～0.99和0.74～0.99之间。当方位角小于20°、30°、40°、50°时，方位角对水量配比的影响分别约为3%、7%、10%和15%。方位角位于60°～90°时，方位角对水量配比存在20%～33%左右的影响。进一步分析发现，夏热冬暖地区南向阳台壁挂式太阳能热水器的年均太阳能保证率位于0.41～0.56之间，推广应用潜力较大。

太阳能；热水器；优化；夏热冬暖地区；水量配比；方位角；方位角因子；太阳能保证率

0 引 言

太阳能热水器的大规模应用，对中国节能减排、改善生态环境、实现“2020年非化石能源的份额达到15%”的绿色发展目标具有积极作用[1-2]。为提升平板型太阳能热水器的经济性能和热性能，国内学者对微热管阵列平板型太阳能热水器[3-5]、立面阳台式太阳能热水器[6]的热性能进行了研究。此外，国外学者对平板型集热器的传热机制与能效、热水器的总体性能等进行了更深入的研究[7-15]。

此外，为保证平板型太阳能热水器的高效运行和用户对水箱终温的需求，世界各国因气候不同对平板型太阳能热水器水箱容水量与集热面积配比Vt/Ac（tankvolume-to-collector-area ratio，水量配比）给出了不同的推荐值[16-23]。中国气候复杂，不同气候条件下阳台壁挂式太阳能热水器的水量配比势必存在差异。本课题组建立了平板型太阳能热水器的水量配比模型，模型计算值与试验值的相对误差小于10%[24]。并利用所建模型分析了中国温和地区阳台壁挂式平板型太阳能热水器的水量配比，给出了部分有意义的结果[25]。为完善中国不同气候条件下阳台壁挂式太阳能热水器的水量配比，本文以中国夏热冬暖地区13个城市为例，利用前期所建模型对阳台壁挂式平板型太阳能热水器的水量配比、方位角因子和太阳能保证率进行了计算与分析。研究结果对阳台壁挂式平板型太阳能热水器的优化、应用和相关国标的制定具有较好的指导意义。

1 模型描述

1.1 水量配比模型

在满足一定热负荷条件下，水箱容水量与集热面积比Vt/Ac为[25]

式中Vt为水箱容水量，kg；Ac为集热器采光面积，m2；t1、t2分别为日出和日落时刻，s；(τα)为透射-吸收积；Iβ为单位倾斜面上时均接收的太阳总辐射强度[26]，W/m2；ULf为平板集热器热损失系数，W/(m2·℃)；包含顶部热损[27-28]、底部与边缘热损[13,29]。Tabs与Tair为吸热板与环境温度，℃；Cp为水的比热，kJ/(kg·℃)；Thot为水箱终温，℃；Tw为自来水温度，℃。此模型已通过试验验证，计算值与试验值的相对百分误差小于10%[24-25]。模型的适用范围为：Iβ≥300 W/m2，Tair≥5 ℃，Tw≥5 ℃，Thot≥Tw，Tabs≥Tair[24-25]。

1.2 太阳能保证率

太阳能保证率定义为太阳能供热系统提供的热量与总热负荷的比例，用f表示，即

式中Qaux为月平均日的辅助加热量，J。Q Load为用户水热负荷，J；Qu为集热器输出能量，J。

1.3 方位角因子

此因子定义为相同倾角下不同方位角安装集热器时的水量配比(Vt/Ac)与正南向安装集热器时的水量配比(Vt/Ac)n的比值，记为kγ，即

2 数据来源

计算过程中，东方、琼海、海口、电白、汕尾、广州、河源、福州、钦州、南宁、勐腊、澜沧、元江13个城市典型气象数据均取自文献[30]。日均太阳辐射、环境温度和风速的分布分别如图1所示。图1显示，1）日均太阳辐射位于14.0～16.0 MJ/m2的天数最多，占22.4%；日均太阳辐射位于12.0～20.0 MJ/m2的天数占总天数的62.2%，此地区的太阳能利用前景较好。2）日均环境温度位于25.0～30.0 ℃的天数最多，占41.7%；日均环境温度位于20.0～35.0 ℃的天数占总天数的68.6%。3）日均风速位于0～0.5 m/s的天数最多，占51.9%；日均风速位于0～3.0 m/s的天数占总天数的87.2%。由于阳台朝向并非均为正南向，且同一倾角斜面上接受的太阳辐射基本上以正南向对称分布，故计算中集热器方位角取值为0～90°。其他主要参数：Thot=60 ℃，(τα)=0.81，Cp= 4.187 kJ/(kg·℃)，β=60°～90°。

图1 典型气象数据的分布情况Fig.1 Typical meteorological data distribution

3 结果与分析

3.1 正南向阳台壁挂式太阳能热水器的水量配比

利用MATLAB软件对夏热冬暖地区13个城市正南向安装使用的阳台壁挂式平板型太阳能热水器的水量配比进行了计算，结果如表1所示。表1的数据显示随着倾角的增大，各城市季均和年均水量配比逐渐减小。集热器倾角为60°、70°、80°、90°时，夏热冬暖地区春、夏、秋、冬4季和年均水量配比的取值范围分别为29.8～50.3、37.5～55.7、44.3～57.9、30.1～54.6、39.5～ 49.3 kg/m2；27.2～44.8、32.8～47.8、41.5～53.9、29.0～52.1、36.2～44.7 kg/m2；24.2～38.7、27.9～39.4、37.9～49.0、27.2～48.4、32.4～39.8 kg/m2；21.1～32.4、22.9～30.9、33.8～43.3、25.0～43.7、28.3～34.4 kg/m2。2）夏热冬暖地区春、夏、秋、冬4季和年均水量配比分别位于21.1～50.3、22.9～55.7、33.8～57.9、25.0～54.6、28.3～49.3 kg/m2之间。

表1的数据和各城市典型气象数据的分析表明，年均水量配比(Vt/Ac)n与水平面上月平均日太阳总辐射量Hh具有较好的正相关性，线性拟合关系如图2所示。水平面上的太阳能辐射越强，单位集热面上接收到的太阳能越多，单位集热面积可配置的水量就越大，故(Vt/Ac)n与Hh具有正相关性。图2显示，随着倾角的增大，拟合线的截距和斜率逐渐减小。各倾角下的拟合关系如下：

式中Hh为水平面上日均太阳总辐射量，MJ/m2；R为线性相关系数。由式（6）至式（9）可知，(Vt/Ac)n与Hh间的线性相关系数r位于0.82与0.84之间。

年均水量配比(Vt/Ac)n与温升–辐射量比值(Thot–Tw)/Hh具有较好的负相关性，结果如图3所示。实现温升–辐射量的比值增大的方法有：保持辐射量不变时增大温升或保持温升不变减小辐射量。因此，辐射量不变又希望增大温升时必须减小集热器单位面积的水量配比；减少辐射量又希望温升不变时必须相应地减少集热器单位面积的水量配比。故(Vt/Ac)n与(Thot–Tw)/Hh具有负相关性。图3显示，随着倾角的增大，(Vt/Ac)n与(Thot–Tw)/Hh拟合线的截距和斜率逐渐减小。各倾角下的拟合关系如下：

表1 正南向阳台壁挂式太阳能热水器的水量配比Table1 Values of (Vt/Ac)nfor balcony wall-mounted solar water heater with south-facing collector kg·m–2

图2 南向年均水量配比与日均太阳辐射量的关系Fig.2 Variations of (Vt/Ac)nwith Hhfor south facing collector

由式（10）至式（13）可知，(Vt/Ac)n与(Thot–Tw)/Hh间的线性相关系数r位于−0.84与−0.96之间。

为便于确定不同倾角下阳台壁挂式太阳能热水器的水量配比，本文利用公式（14）对表1的数值进行了线性拟合，拟合系数如表2所示。(Vt/Ac)n与β的相关性较好，相关系数r绝对值均大于0.99。

依据不同季节的供热目的，可利用公式（14）和表2的数据快速有效地确定夏热冬暖地区南向阳台壁挂式平板型太阳能热水器的水量配比。

图3 南向年均水量配比与(Thot–Tw)/Hh的关系Fig.3 Variations of (Vt/Ac)nwith (Thot–Tw)/Hhfor south facing collector

3.2 非正南向阳台壁挂式太阳能热水器的水量配比

图4给出了夏热冬暖地区阳台壁挂式太阳能热水器水量配比的方位角因子与方位角的变化关系。由图4可知：1）季均和年均水量配比的方位角因子随方位角的增大而逐渐减小。2）同一倾角下，冬季的方位角因子随方位角的增大而减少的幅度最大。3）倾角为60°～90°、方位角为10°～90°时，春、夏、秋、冬4季和年均方位角因子分别位于0.80～0.99、0.72～0.99、0.79～1.00、0.67～0.99和0.74～0.99之间。4）倾角为60°～90°、方位角小于20°、30°、40°、50°时，季均和年均方位角因子分别位于0.97～0.99、0.93～0.99、0.89～0.99和0.85～0.99之间；方位角对水量配比的影响分别为3%、7%、10%和 15%左右。5）当倾角和方位角均位于60°～90°时，方位角对水量配比存在20%～33%左右的影响。

表2 (Vt/Ac)n与β的线性拟合系数Table2 Linear fitting coefficients between (Vt/Ac)nand β

图4 方位角因子与方位角的关系Fig.4 Relationships between azimuth factor and azimuth angle

3.3 南向阳台壁挂式太阳能热水器的太阳能保证率

图5为南向阳台壁挂式太阳能热水器的年均太阳能保证率。由图5可知：1）倾角为60°、70°、80°、90°时，夏热冬暖地区13城市的年均太阳能保证率分别位于0.44～0.52、0.41～0.53、0.41～0.54和0.42～0.56之间。由此可知，各倾角下的太阳能保证率波动范围基本一致，即倾角对年均太阳能保证率的影响较小。2）因不同倾角下单位集热面积上接收到的太阳辐射存在差异，因此同一城市，不同倾角下的年均太阳能保证率存在一定的差异。但差异较小，差异最大的是琼海、海口、电白，相差为0.04左右。3）年均太阳能保证率较小的是电白、广州、河源，太阳能保证率位于0.41～0.46之间；年均太阳能保证率较大的是琼海、海口、勐腊、元江，太阳能保证率位于0.50～0.56之间。

图5 各城市的年均太阳能保证率Fig.5 Yearly average solar fraction for different cities

4 结 论

1）夏热冬暖地区，南向阳台壁挂式太阳能热水器的季均和年均水量配比随倾角的增大而逐渐减小。

2）南向阳台壁挂式太阳能热水器春、夏、秋、冬4季和年均水量配比分别位于21.1～50.3、22.9～55.7、33.8～57.9、25.0～54.6、28.3～49.3 kg/m2之间。

3）南向阳台壁挂式太阳能热水器年均水量配比与水平面上月平均日太阳总辐射量成正相关性，与温升–辐射量比值成负相关性，不同倾角下相关系数的绝对值分别大于0.82与0.84。

4）夏热冬暖地区各城市季均和年均水量配比与倾角间存在较强的线性相关性，本文给出了各城市相关系数绝对值大于0.99的线性关系式。

5）季均和年均水量配比的方位角因子随方位角的增大而逐渐减小。倾角为60°～90°、方位角为10°～90°时，春、夏、秋、冬4季和年均水量配比的方位角因子分别位于0.80～0.99、0.72～0.99、0.79～1.00、0.67～0.99和0.74～0.99之间。

6）当方位角小于20°、30°、40°、50°时，方位角对水量配比的影响分别为3%、7%、10%和15%左右。方位角位于60°～90°时，方位角对水量配比存在20%～33%左右的影响。

7）倾角为60°、70°、80°、90°时，夏热冬暖地区13城市的年均太阳能保证率分别位于0.44～0.52、0.41～0.53、0.41～0.54和0.42～0.56之间。

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Optimization of tank-volume-to-collector-area ratio for balcony wall-mounted flat-plate solar water heater in hot summer and warm winter region of China

Wei Shengxian1, Hu Fene2, Yang Huimin3
(1. Center for Magnetic Materials and Devices, Qujing Normal University, Qujing 655011, China; 2. College of Chemistry and Environmental Science, Qujing Normal University, Qujing 655011, China; 3. College of Physics and Electronic Engineering, Qujing Normal University, Qujing 655011, China)

The thermal performance and economical efficiency of the flat-plate type solar water heater has been studied by researchers at home and abroad. In order to ensure the efficient operation of the solar water heater and user's demand to the terminal temperature of tank, the countries all over the world with different climates have given different recommended value for tank-volume-to-collector-area ratio (the ratio was abbreviated as Vt/Ac) of the flat-plate solar water heater. However, the value range of recommended value from literatures was too big for the practical application due to the complex climates. In addition, the main residential buildings in large and medium-sized cities in China were mostly high-rise buildings. The solar water heater installed on roof could only meet hot water use for the top six to eight floors. The application of the balcony wall-mounted solar water heater was the one of the effective ways to solve hot water needs for the rest of users in high-rise buildings. Based on the typical meteorological data of 13 cities in hot summer and warm winter region of China, the values of Vt/Ac, azimuth factor and solar reliability fraction of the balcony wall-mounted flat-plate solar water heater have been calculated by using the established mathematical model. The water tank terminal temperature of 60 ℃, the collector angle of 60°-90° and the azimuth angle of 0-90° were used in theoretical calculation. The results showed that, for south-facing balcony wall-mounted solar water heater in hot summer and warm winter region, the ranges of (Vt/Ac)nin spring, summer, autumn, winter and the whole year were 21.1-50.3, 22.9-55.7, 33.8-57.9, 25.0-54.6 and 28.3-49.3 kg/m2, respectively. For convenience of the practical application, the linear regression relations between the annual average (Vt/Ac)nand the tilt angle, daily total solar radiation on the horizontal and the ratio of temperature to daily total solar radiation were given for south-facing balcony wall-mounted solar water heater. For the non-south-facing balcony wall-mounted solar water heater, the seasonal and annual average azimuth factors decreased with the increase of the azimuth angle. The seasonal and annual average azimuth factors ranged from 0.67 to 0.99 and 0.74 to 0.99 when the tilt angle and azimuth angle were respectively at 60°-90° and 10°-90°. The azimuth angle had about 3%, 7%, 10% and 15% effect on Vt/Acfor winter and spring, summer, autumn and the whole year when the azimuth angles were less than or equal to 20°, 30°, 40° and 50°. The azimuth angle had about 20%-33% effect on the above-mentioned Vt/Acwhen the azimuth angle increased form 60° to 90°. Further discussion found that the annual average solar fraction ranged from 0.41 to 0.56 for the south-facing balcony wall-mounted flat-plate solar water heater used in hot summer and warm winter region of China.

solar energy; water heaters; optimization; hot summer and warm winter region; tank-volume-to-collector-area ratio; azimuth angle; azimuth factor; solar fraction

10.11975/j.issn.1002-6819.2017.05.029

TK519

A

1002-6819(2017)-05-0199-06

魏生贤，胡粉娥，杨慧敏. 夏热冬暖地区阳台壁挂式平板型太阳能热水器水量配比优化[J]. 农业工程学报，2017，33(5)：199－204.

10.11975/j.issn.1002-6819.2017.05.029 http://www.tcsae.org

Wei Shengxian, Hu Fene, Yang Huimin. Optimization of tank-volume-to-collector-area ratio for balcony wall-mounted flat-plate solar water heater in hot summer and warm winter region of China[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2017, 33(5): 199－204. (in Chinese with English abstract)

doi：10.11975/j.issn.1002-6819.2017.05.029 http://www.tcsae.org

2016-04-30

2016-12-28

NSFC-云南联合基金重点项目（U1137605）；云南省科技厅面上项目(2013FZ111)；曲靖师范学院科技创新团队项目（TD201301）

魏生贤，男，云南省梁河县人，教授，博士，从事太阳能热利用的研究工作。曲靖 曲靖师范学院磁性材料及器件研究中心，655011。

Email：wsx_8600@163.com