夏熱冬暖地區(qū)陽臺壁掛式平板型太陽能熱水器水量配比優(yōu)化

魏生賢，胡粉娥，楊慧敏

夏熱冬暖地區(qū)陽臺壁掛式平板型太陽能熱水器水量配比優(yōu)化

魏生賢1，胡粉娥2，楊慧敏3

（1. 曲靖師范學(xué)院磁性材料及器件研究中心，曲靖 655011；2. 曲靖師范學(xué)院化學(xué)與環(huán)境科學(xué)學(xué)院，曲靖 655011；3. 曲靖師范學(xué)院物理與電子工程學(xué)院，曲靖 655011）

基于中國夏熱冬暖地區(qū)13城市的典型氣象數(shù)據(jù)，利用所建數(shù)學(xué)模型對陽臺壁掛式平板型太陽能熱水器的水量配比、方位角因子和太陽能保證率進行了計算。結(jié)果顯示，南向陽臺壁掛式太陽能熱水器春、夏、秋、冬4季和全年水量配比分別位于21.1～50.3、22.9～55.7、33.8～57.9、25.0～54.6和28.3～49.3 kg/m2之間。為便于應(yīng)用，該文分別給出了南向陽臺壁掛式太陽能熱水器水量配比與水平面日均總太陽輻射量、溫升-輻射量比值、傾角間的線性關(guān)系式。對于非南向陽臺壁掛式太陽能熱水器，季均和年均方位角因子隨方位角的增大而逐漸減小。傾角為60°～90°、方位角為10°～90°時，季均和年均方位角因子分別位于0.67～0.99和0.74～0.99之間。當方位角小于20°、30°、40°、50°時，方位角對水量配比的影響分別約為3%、7%、10%和15%。方位角位于60°～90°時，方位角對水量配比存在20%～33%左右的影響。進一步分析發(fā)現(xiàn)，夏熱冬暖地區(qū)南向陽臺壁掛式太陽能熱水器的年均太陽能保證率位于0.41～0.56之間，推廣應(yīng)用潛力較大。

太陽能；熱水器；優(yōu)化；夏熱冬暖地區(qū)；水量配比；方位角；方位角因子；太陽能保證率

0 引 言

太陽能熱水器的大規(guī)模應(yīng)用，對中國節(jié)能減排、改善生態(tài)環(huán)境、實現(xiàn)“2020年非化石能源的份額達到15%”的綠色發(fā)展目標具有積極作用[1-2]。為提升平板型太陽能熱水器的經(jīng)濟性能和熱性能，國內(nèi)學(xué)者對微熱管陣列平板型太陽能熱水器[3-5]、立面陽臺式太陽能熱水器[6]的熱性能進行了研究。此外，國外學(xué)者對平板型集熱器的傳熱機制與能效、熱水器的總體性能等進行了更深入的研究[7-15]。

此外，為保證平板型太陽能熱水器的高效運行和用戶對水箱終溫的需求，世界各國因氣候不同對平板型太陽能熱水器水箱容水量與集熱面積配比Vt/Ac（tankvolume-to-collector-area ratio，水量配比）給出了不同的推薦值[16-23]。中國氣候復(fù)雜，不同氣候條件下陽臺壁掛式太陽能熱水器的水量配比勢必存在差異。本課題組建立了平板型太陽能熱水器的水量配比模型，模型計算值與試驗值的相對誤差小于10%[24]。并利用所建模型分析了中國溫和地區(qū)陽臺壁掛式平板型太陽能熱水器的水量配比，給出了部分有意義的結(jié)果[25]。為完善中國不同氣候條件下陽臺壁掛式太陽能熱水器的水量配比，本文以中國夏熱冬暖地區(qū)13個城市為例，利用前期所建模型對陽臺壁掛式平板型太陽能熱水器的水量配比、方位角因子和太陽能保證率進行了計算與分析。研究結(jié)果對陽臺壁掛式平板型太陽能熱水器的優(yōu)化、應(yīng)用和相關(guān)國標的制定具有較好的指導(dǎo)意義。

1 模型描述

1.1 水量配比模型

在滿足一定熱負荷條件下，水箱容水量與集熱面積比Vt/Ac為[25]

式中Vt為水箱容水量，kg；Ac為集熱器采光面積，m2；t1、t2分別為日出和日落時刻，s；(τα)為透射-吸收積；Iβ為單位傾斜面上時均接收的太陽總輻射強度[26]，W/m2；ULf為平板集熱器熱損失系數(shù)，W/(m2·℃)；包含頂部熱損[27-28]、底部與邊緣熱損[13,29]。Tabs與Tair為吸熱板與環(huán)境溫度，℃；Cp為水的比熱，kJ/(kg·℃)；Thot為水箱終溫，℃；Tw為自來水溫度，℃。此模型已通過試驗驗證，計算值與試驗值的相對百分誤差小于10%[24-25]。模型的適用范圍為：Iβ≥300 W/m2，Tair≥5 ℃，Tw≥5 ℃，Thot≥Tw，Tabs≥Tair[24-25]。

1.2 太陽能保證率

太陽能保證率定義為太陽能供熱系統(tǒng)提供的熱量與總熱負荷的比例，用f表示，即

式中Qaux為月平均日的輔助加熱量，J。Q Load為用戶水熱負荷，J；Qu為集熱器輸出能量，J。

1.3 方位角因子

此因子定義為相同傾角下不同方位角安裝集熱器時的水量配比(Vt/Ac)與正南向安裝集熱器時的水量配比(Vt/Ac)n的比值，記為kγ，即

2 數(shù)據(jù)來源

計算過程中，東方、瓊海、?？凇㈦姲?、汕尾、廣州、河源、福州、欽州、南寧、勐臘、瀾滄、元江13個城市典型氣象數(shù)據(jù)均取自文獻[30]。日均太陽輻射、環(huán)境溫度和風速的分布分別如圖1所示。圖1顯示，1）日均太陽輻射位于14.0～16.0 MJ/m2的天數(shù)最多，占22.4%；日均太陽輻射位于12.0～20.0 MJ/m2的天數(shù)占總天數(shù)的62.2%，此地區(qū)的太陽能利用前景較好。2）日均環(huán)境溫度位于25.0～30.0 ℃的天數(shù)最多，占41.7%；日均環(huán)境溫度位于20.0～35.0 ℃的天數(shù)占總天數(shù)的68.6%。3）日均風速位于0～0.5 m/s的天數(shù)最多，占51.9%；日均風速位于0～3.0 m/s的天數(shù)占總天數(shù)的87.2%。由于陽臺朝向并非均為正南向，且同一傾角斜面上接受的太陽輻射基本上以正南向?qū)ΨQ分布，故計算中集熱器方位角取值為0～90°。其他主要參數(shù)：Thot=60 ℃，(τα)=0.81，Cp= 4.187 kJ/(kg·℃)，β=60°～90°。

圖1 典型氣象數(shù)據(jù)的分布情況Fig.1 Typical meteorological data distribution

3 結(jié)果與分析

3.1 正南向陽臺壁掛式太陽能熱水器的水量配比

利用MATLAB軟件對夏熱冬暖地區(qū)13個城市正南向安裝使用的陽臺壁掛式平板型太陽能熱水器的水量配比進行了計算，結(jié)果如表1所示。表1的數(shù)據(jù)顯示隨著傾角的增大，各城市季均和年均水量配比逐漸減小。集熱器傾角為60°、70°、80°、90°時，夏熱冬暖地區(qū)春、夏、秋、冬4季和年均水量配比的取值范圍分別為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）夏熱冬暖地區(qū)春、夏、秋、冬4季和年均水量配比分別位于21.1～50.3、22.9～55.7、33.8～57.9、25.0～54.6、28.3～49.3 kg/m2之間。

表1的數(shù)據(jù)和各城市典型氣象數(shù)據(jù)的分析表明，年均水量配比(Vt/Ac)n與水平面上月平均日太陽總輻射量Hh具有較好的正相關(guān)性，線性擬合關(guān)系如圖2所示。水平面上的太陽能輻射越強，單位集熱面上接收到的太陽能越多，單位集熱面積可配置的水量就越大，故(Vt/Ac)n與Hh具有正相關(guān)性。圖2顯示，隨著傾角的增大，擬合線的截距和斜率逐漸減小。各傾角下的擬合關(guān)系如下：

式中Hh為水平面上日均太陽總輻射量，MJ/m2；R為線性相關(guān)系數(shù)。由式（6）至式（9）可知，(Vt/Ac)n與Hh間的線性相關(guān)系數(shù)r位于0.82與0.84之間。

年均水量配比(Vt/Ac)n與溫升–輻射量比值(Thot–Tw)/Hh具有較好的負相關(guān)性，結(jié)果如圖3所示。實現(xiàn)溫升–輻射量的比值增大的方法有：保持輻射量不變時增大溫升或保持溫升不變減小輻射量。因此，輻射量不變又希望增大溫升時必須減小集熱器單位面積的水量配比；減少輻射量又希望溫升不變時必須相應(yīng)地減少集熱器單位面積的水量配比。故(Vt/Ac)n與(Thot–Tw)/Hh具有負相關(guān)性。圖3顯示，隨著傾角的增大，(Vt/Ac)n與(Thot–Tw)/Hh擬合線的截距和斜率逐漸減小。各傾角下的擬合關(guān)系如下：

表1 正南向陽臺壁掛式太陽能熱水器的水量配比Table1 Values of (Vt/Ac)nfor balcony wall-mounted solar water heater with south-facing collector kg·m–2

圖2 南向年均水量配比與日均太陽輻射量的關(guān)系Fig.2 Variations of (Vt/Ac)nwith Hhfor south facing collector

由式（10）至式（13）可知，(Vt/Ac)n與(Thot–Tw)/Hh間的線性相關(guān)系數(shù)r位于?0.84與?0.96之間。

為便于確定不同傾角下陽臺壁掛式太陽能熱水器的水量配比，本文利用公式（14）對表1的數(shù)值進行了線性擬合，擬合系數(shù)如表2所示。(Vt/Ac)n與β的相關(guān)性較好，相關(guān)系數(shù)r絕對值均大于0.99。

依據(jù)不同季節(jié)的供熱目的，可利用公式（14）和表2的數(shù)據(jù)快速有效地確定夏熱冬暖地區(qū)南向陽臺壁掛式平板型太陽能熱水器的水量配比。

圖3 南向年均水量配比與(Thot–Tw)/Hh的關(guān)系Fig.3 Variations of (Vt/Ac)nwith (Thot–Tw)/Hhfor south facing collector

3.2 非正南向陽臺壁掛式太陽能熱水器的水量配比

圖4給出了夏熱冬暖地區(qū)陽臺壁掛式太陽能熱水器水量配比的方位角因子與方位角的變化關(guān)系。由圖4可知：1）季均和年均水量配比的方位角因子隨方位角的增大而逐漸減小。2）同一傾角下，冬季的方位角因子隨方位角的增大而減少的幅度最大。3）傾角為60°～90°、方位角為10°～90°時，春、夏、秋、冬4季和年均方位角因子分別位于0.80～0.99、0.72～0.99、0.79～1.00、0.67～0.99和0.74～0.99之間。4）傾角為60°～90°、方位角小于20°、30°、40°、50°時，季均和年均方位角因子分別位于0.97～0.99、0.93～0.99、0.89～0.99和0.85～0.99之間；方位角對水量配比的影響分別為3%、7%、10%和 15%左右。5）當傾角和方位角均位于60°～90°時，方位角對水量配比存在20%～33%左右的影響。

表2 (Vt/Ac)n與β的線性擬合系數(shù)Table2 Linear fitting coefficients between (Vt/Ac)nand β

圖4 方位角因子與方位角的關(guān)系Fig.4 Relationships between azimuth factor and azimuth angle

3.3 南向陽臺壁掛式太陽能熱水器的太陽能保證率

圖5為南向陽臺壁掛式太陽能熱水器的年均太陽能保證率。由圖5可知：1）傾角為60°、70°、80°、90°時，夏熱冬暖地區(qū)13城市的年均太陽能保證率分別位于0.44～0.52、0.41～0.53、0.41～0.54和0.42～0.56之間。由此可知，各傾角下的太陽能保證率波動范圍基本一致，即傾角對年均太陽能保證率的影響較小。2）因不同傾角下單位集熱面積上接收到的太陽輻射存在差異，因此同一城市，不同傾角下的年均太陽能保證率存在一定的差異。但差異較小，差異最大的是瓊海、?？凇㈦姲?，相差為0.04左右。3）年均太陽能保證率較小的是電白、廣州、河源，太陽能保證率位于0.41～0.46之間；年均太陽能保證率較大的是瓊海、海口、勐臘、元江，太陽能保證率位于0.50～0.56之間。

圖5 各城市的年均太陽能保證率Fig.5 Yearly average solar fraction for different cities

4 結(jié) 論

1）夏熱冬暖地區(qū)，南向陽臺壁掛式太陽能熱水器的季均和年均水量配比隨傾角的增大而逐漸減小。

2）南向陽臺壁掛式太陽能熱水器春、夏、秋、冬4季和年均水量配比分別位于21.1～50.3、22.9～55.7、33.8～57.9、25.0～54.6、28.3～49.3 kg/m2之間。

3）南向陽臺壁掛式太陽能熱水器年均水量配比與水平面上月平均日太陽總輻射量成正相關(guān)性，與溫升–輻射量比值成負相關(guān)性，不同傾角下相關(guān)系數(shù)的絕對值分別大于0.82與0.84。

4）夏熱冬暖地區(qū)各城市季均和年均水量配比與傾角間存在較強的線性相關(guān)性，本文給出了各城市相關(guān)系數(shù)絕對值大于0.99的線性關(guān)系式。

5）季均和年均水量配比的方位角因子隨方位角的增大而逐漸減小。傾角為60°～90°、方位角為10°～90°時，春、夏、秋、冬4季和年均水量配比的方位角因子分別位于0.80～0.99、0.72～0.99、0.79～1.00、0.67～0.99和0.74～0.99之間。

6）當方位角小于20°、30°、40°、50°時，方位角對水量配比的影響分別為3%、7%、10%和15%左右。方位角位于60°～90°時，方位角對水量配比存在20%～33%左右的影響。

7）傾角為60°、70°、80°、90°時，夏熱冬暖地區(qū)13城市的年均太陽能保證率分別位于0.44～0.52、0.41～0.53、0.41～0.54和0.42～0.56之間。

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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

魏生賢，胡粉娥，楊慧敏. 夏熱冬暖地區(qū)陽臺壁掛式平板型太陽能熱水器水量配比優(yōu)化[J]. 農(nóng)業(yè)工程學(xué)報，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-云南聯(lián)合基金重點項目（U1137605）；云南省科技廳面上項目(2013FZ111)；曲靖師范學(xué)院科技創(chuàng)新團隊項目（TD201301）

魏生賢，男，云南省梁河縣人，教授，博士，從事太陽能熱利用的研究工作。曲靖 曲靖師范學(xué)院磁性材料及器件研究中心，655011。

Email：wsx_8600@163.com