基于本征正交分解的环境温度分布快速预测模型研究
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摘要
本文基于Karhunen-Loeve分解的原理,使用本征正交分解方法(Proper Orthogonal Decomposition,POD)对高维非线性的流动及传热过程进行降阶,获得研究对象所处流场的各阶模态以用于温度场的重构预测。将本征正交分解模型预测温度分布的准确度及响应速度和通过流动及传热控制方程的离散求解获取温度分布的过程进行对比,对比结果显示本征正交分解具有较高的准确度和更加敏捷的温度预测响应速度,并且其预测过程占用更少的计算资源。结果显示,每次离散求解流动及传热控制方程约耗时93 s,而使用本征正交分解模型获取热环境所需的时间约为6 ms,并且后者的平均泛化误差小于5%。
Based on the principle of Karhunen-Loeve decomposition, the proper orthogonal decomposition method is used to simplify the high-dimensional and nonlinear coupled flow and heat transfer process, and the various modes of the flow field in which the research object located are obtained and used for reconstruction of temperature distribution. The prediction accuracy of temperature distribution and response speed of the proper orthogonal decomposition model are compared with the process of obtaining the temperature distribution by the numerical solution derived from corresponding flow and heat transfer control equations. The comparison results show that the proper orthogonal decomposition presents reasonable accuracy and has a more agile temperature prediction speed. Moreover, the prediction process of proper orthogonal decomposition occupies less computing resources. The results show that each numerical solution of the flow and heat transfer control equation takes about 93 seconds, and the time required to obtain the thermal environment using the proper orthogonal decomposition method is about 6 milliseconds and its average generalization error is less than 5%.
Based on the principle of Karhunen-Loeve decomposition, the proper orthogonal decomposition method is used to simplify the high-dimensional and nonlinear coupled flow and heat transfer process, and the various modes of the flow field in which the research object located are obtained and used for reconstruction of temperature distribution. The prediction accuracy of temperature distribution and response speed of the proper orthogonal decomposition model are compared with the process of obtaining the temperature distribution by the numerical solution derived from corresponding flow and heat transfer control equations. The comparison results show that the proper orthogonal decomposition presents reasonable accuracy and has a more agile temperature prediction speed. Moreover, the prediction process of proper orthogonal decomposition occupies less computing resources. The results show that each numerical solution of the flow and heat transfer control equation takes about 93 seconds, and the time required to obtain the thermal environment using the proper orthogonal decomposition method is about 6 milliseconds and its average generalization error is less than 5%.
引文
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[3]住房和城乡建设部科技发展促进中心.中国建筑节能发展报告[M].北京:中国建筑工业出版社,2011.
[4]方兴,晋欣桥,杜志敏.基于数据包络分析的空调系统控制策略评估[J].暖通空调,2018(3):21-28.
[5]DURAND-ESTEBE B,CéDRIC L B,MANCOS J N,et al.Simulation of a temperature adaptive control strategy for an IWSE economizer in a data center[J].Applied Energy,2014,134:45-56.
[6]GIRAULT V,RAVIART P A.Finite element methods for Navier-Stokes equations:theory and algorithms[M].Berlin:Springer Science and Business Media,2012.
[7]马相雪,李灿.焊接厂房置换通风气流组织试验研究[J].制冷技术,2010,30(4):33-37.
[8]潘乐燕.汽车前端冷却模块流场模拟与试验研究[J].制冷技术,2011,31(2):19-22.
[9]王亮,谭洪卫,周志仁.世博会大空间空调气流组织优化设计--挪威馆,主题馆[J].制冷技术,2010,30(S1):61-65.
[10]刘显晨,徐玉党,陈龙,等.火车站候车厅热舒适性模拟研究[J].制冷技术,2011,31(1):18-21.
[11]刘巧玲,杜志敏,晋欣桥.VAV空调系统室内温度传感器位置的影响研究[J].建筑热能通风空调,2013,32(1):11-14.
[12]徐培璠,杜志敏,晋欣桥.DOAS+CRCP空调系统的TRNSYS-CFD混合仿真研究[J].建筑热能通风空调,2015,34(6):49-53.
[13]聂春生,黄建栋,王迅,等.基于POD方法的复杂外形飞行器热环境快速预测方法[J].空气动力学学报,2015,35(6):760-765.
[14]吴学红,陶文铨,吕彦力,等.不可压缩流动问题快速计算的降阶模型[J].中国电机工程学报,2010,30(26):69-74.
[15]SAMADIANI E,JOSHI Y,HAMANN H,et al.Reduced Order Thermal Modeling of Data Centers via Distributed Sensor Data[J].Journal of Heat Transfer,2012,134(4):041401-1-041401-8.
[16]陆亚俊,马最良,邹平华,等.暖通空调[M].北京:中国建筑工业出版社,2007.
[17]CURRIE I G,CURRIE I G.Fundamental mechanics of fluids[M].Boca Raton:CRC Press,2002.
[18]PATANKAR S.Numerical heat transfer and fluid flow[M].Washington:CRC press,1980.
[19]戴锅生.传热学[M].北京:高等教育出版社,1999:110.
[20]SAMADIANI E,JOSHI Y.Proper orthogonal decomposition for reduced order thermal modeling of air cooled data centers[J].Journal of Heat Transfer,2010,132(7):071402.
[21]BERKOOZ G,HOLMES P,LUMLEY J L.The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows[J].Annual Review of Fluid Mechanics,1993,25(1):539-575.