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管内单相流强迫对流湍流传热关联式研究

2019-09-10王莉张立圣方贤德黄永宽庄凤婷

航空科学技术 2019年3期
关键词:管内湍流

王莉 张立圣 方贤德 黄永宽 庄凤婷

摘要:管内单相流强迫对流湍流传热广泛应用于各个工业领域。目前有很多管内单相流强迫对流湍流传热关联式,需要对其计算精度进行评价分析,便于选用。本文通过试验,获得了46组R134a在水平圆铜管内的单相流强迫对流湍流传热数据,从23篇文献中收集了1220组试验数据,建立了一个含有1266组数据的管内单相流强迫对流湍流传热试验数据库。用这个数据库对14个现有管内单相流强迫对流湍流传热关联式进行了评价分析,鉴别出了预测精度高的关联式,为管内单相流强迫对流湍流传热关联式的选用提供了依据。

关键词:强迫对流;管内;传热;关联式;湍流;单相流

中图分类号:TK124    文献标识码:A     DOI:10.19452/j.issn1007-5453.2019.03.009

管内单相流强迫对流(简称管内强迫对流)湍流传热广泛应用于航空航天、能源建筑、石油化工等各个工业领域,如航空领域的飞机环境控制系统、动力系统、燃油系统等。相关设备和系统的研发设计离不开管内强迫对流湍流传热的计算,因此许多研究者提出了管内强迫对流湍流传热关联式。

随着航空航天技术和微电子技术的发展,大功率高密度电子设备的冷却提出了两相流传热技术的需求。研究发现,大多数两相流传热模型是在单相流传热模型的基础上发展而来的,最常见的是基于Dittus-Boelter公式的传热模型,其次是基于Gnielinski公式的传热模型。因此,单相流传热关联式的准确性也直接影响两相流传热计算的准确度。

目前公开报道的管内强迫对流湍流传热关联式很多,这一方面给工程应用带来了方便,另一方面也给关联式的选用带来了困惑。使用者往往不知道该选用哪个关联式。为此,本文一方面广泛收集整理管内强迫对流湍流试验数据,并通过试验获得部分数据,建立试验数据库;另一方面收集现有传热关联式。在此基础上,利用试验数据对关联式进行评价分析,获得各关联式对数据库的预测精度,为管内强迫对流湍流传热关联式的选用提供依据。

1管内强迫对流湍流传热的试验研究

1.1试验装置

试验装置如图1所示,主要由试验段、冷凝器、储液罐、过冷器、齿轮栗、流量计以及预热段组成。试验段为光滑圆铜管,内径分别为1.002mm和2.168mm,长200mm,水平放置。

工质为R134a制冷剂。制冷剂由储液罐被齿轮泵抽出,经过涡轮流量计,进入预热段。预热后经过长100mm的发展段,进入试验段。制冷剂在试验段中再次被加热,经过冷凝器,回到储液罐。如此循环。预热段和试验段有均匀缠绕的铜丝,用于通电加热R134a制冷剂。发展段的管径与试验段的管径一致。温度用T型热电偶测量。

1.2试验结果和不确定度分析

本试验共获得46组R134a在水平圆管中的强迫对流湍流传热试验数据。限于篇幅,数据整理过程不予详述。试验参数范围见表1。试验的不确定度根据Kline和McClintock提出的方法确定,见表2。

2从现有文献中获得的管内强迫对流湍流传热试验数据

除了通过试验获得的46组R134a管内强迫对流湍流传热试验数据外,从23篇已经发表的文献中收集了1220组试验数据,见表3。表中的试验数据参数范围为:雷诺数Re=3040〜651357,普朗特数Pr=0.9〜7.3,热流密度q=2〜34468kW/m,质量流速G=139〜39832kg/(m·s),水力直径D=0.25〜17.68mm,包含了水、氮、二氧化碳、氩、R134a、RC318和R113等7种工质。

3管内强迫对流湍流传热关联式

研究者提出了很多管内强迫对流湍流传热关联式,本文收集整理了14个,分别是Dittus-Boelter,Gnielinski,Sieder-Tate,Petukhov-Kirillov,Adams,Heta,Kakac,Ghajar-Tam,Hausen,Choi,Yu,Wang-Peng,Debray和Wu-Little等。由于篇幅限制,這里只列出对于本文数据库预测精度较高的前5个关系式,见表4。表中,f为Moody摩擦因数;D为管内径或水力直径,单位为m;L为换热有效长度与热入口段长度的和,单位为m;μ为[动力]黏度,单位为Pa·s;下标w表示定性温度为壁面温度,其他参数的定性温度为流体平均温度。

4管内强迫对流湍流传热关联式的评价

本文采用平均绝对误差(MAD)作为评价管内强迫对流湍流传热关联式预测精度的标准。MAD越小,预测精度越高。

此外,采用平均相对误差反映关联式在总体上是高估(MRD>0%)还是低估(MRD<0%)了数据库。

利用上述试验获得的46组和从文献中收集到的1220组管内强迫对流湍流试验数据组成的数据库,对14个管内强迫对流湍流传热关联式进行评价分析。表5中列出了预测精度最高的前5个关联式的评价结果。从表中可以看出,预测精度最高的是Gnielinski关联式,MAD=19.5%。Gnielinski、Sieder-Tate和Ghajar-Tam关联式对壁温的影响进行了修正。这种修正有助于提高公式的预测精度,但同时也增加了公式使用的困难。另外,在实际应用中,由于壁温一般是未知条件,含有与壁温有关的参数会增加公式预测的不确定性。综合分析可知,管内强迫对流湍流传热关联式还需进一步深入研究。

图2和图3分别是Gnielinski公式和Dittus-Boelter公式传热系数计算值与试验值的比较。可以看出,在传热系数大于60kW/(m·K)时,Gnielinski公式的計算精度显著高于Dittus-Boeltert1]公式的计算精度。

图4和图5分别是Gnielinski公式和Dittus-Boelter公式努塞尔数计算值与试验值的比较。可以看出,当努塞尔数Nu=150〜250时,Dittus-Boelter公式预测精度较高,其他情况下,Gnielinski公式预测精度较高。

5结论

本文建立了一个由1266组试验数据组成的管内强迫对流湍流传热试验数据库,包括作者试验获得的46组和从现有文献中获取的1220组。用该数据库对14个管内强迫对流湍流传热关联式进行了评价分析,可以得出以下结论:

(1)基于本文数据库,预测准确度最好的前5个关联式依次为Gnielinski,Dittus-Boelter,Sieder-Tate、Petukhov-Kirillov和Ghajar-Tam关联式,其MAD分别为19.5%、21.4%、23.3%、23.4%和24.2%。

(2)在本文数据范围内,在传热系数大于60 kW/(m2·K)时,Gnielinski公式的计算精度显著高于Dittus-Boelter公式的计算精度;当Nu=150〜250时,Dittus-Boelter公式预测精度较高,其他情况下,Gnielinski公式预测精度较高。

(3)Gnielinski、Sieder-Tate和Ghajar-Tam关联式引入了壁温影响的修正,实际应用中含有与壁温有关的参数会增加公式预测的不确定性,当壁温和流体温度相差不是很大时,可舍去壁温修正项。

(4)管内强迫对流湍流传热关联式的预测精度仍有待提高。

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