二维两层介质界面接触热阻的反辨识研究
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摘要
接触热阻是研究工程传热问题的重要参数,很多工程领域都需要有效辨识出接触热阻。针对目前接触热阻辨识方法局限于一维两层介质传热,只能求出一个接触热阻单值,以及温度测点必须布置在介质温度梯度方向上等问题,采用边界元法与共轭梯度法相结合的方法,对二维两层介质界面接触热阻进行反辨识研究。该方法可以求解出随界面接触线位置变化的接触热阻,并且边界元算法只需离散边界,不需要对内部区域进行离散,因此温度测点位置可以任意选取。建立二维两层介质传热模型作为算例并进行分析:该方法可以有效求解接触热阻,但作为反辨识方法的一种同样存在不适定性,并且温度测点距离接触界面越远误差越大,采用最小二乘法对求解结果进行优化处理可以有效提高辨识精度和稳定性。
Thermal contact resistance(TCR) is one of the important parameters in heat transfer problems of engineering,and it is necessary to estimate the value of TCR effectively in many engineering fields. Considering the limitation of current estimation methods of TCR such as only focusing on one-dimensional thermal conduction,getting a single value of TCR merely,and the temperature measuring points only being placed in temperature gradient direction of mediums,boundary element method(BEM) and conjugate gradient method are combined to estimate the TCR in planar mediums. The value of TCR in relation to the position of contact interface line is estimated with this method,and the positions of temperature measuring points can be selected randomly because of the characteristic of BEM that there is no necessity to discrete the inner area and it is sufficient to discrete the boundary. The analysis of calculation examples base on heat transfer model of planar medium demonstrates that: this method can estimate the TCR effectively,but the ill-posedness is also existed in this method which is one of the inverse problems,and the calculation error of TCR is increased with the distance from temperature measuring points to contact interface,the estimation precision and stability can be improved after optimization with least square method.
Thermal contact resistance(TCR) is one of the important parameters in heat transfer problems of engineering,and it is necessary to estimate the value of TCR effectively in many engineering fields. Considering the limitation of current estimation methods of TCR such as only focusing on one-dimensional thermal conduction,getting a single value of TCR merely,and the temperature measuring points only being placed in temperature gradient direction of mediums,boundary element method(BEM) and conjugate gradient method are combined to estimate the TCR in planar mediums. The value of TCR in relation to the position of contact interface line is estimated with this method,and the positions of temperature measuring points can be selected randomly because of the characteristic of BEM that there is no necessity to discrete the inner area and it is sufficient to discrete the boundary. The analysis of calculation examples base on heat transfer model of planar medium demonstrates that: this method can estimate the TCR effectively,but the ill-posedness is also existed in this method which is one of the inverse problems,and the calculation error of TCR is increased with the distance from temperature measuring points to contact interface,the estimation precision and stability can be improved after optimization with least square method.
引文
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[3]Ramamurthi K,Kumar S S,Abilash P M.Thermal Contact Conductance of Molybdenum-Sulphide-Coated Joints at Low Temperature[J].Thermophys Heat Transf,2007,21(4):811-813
[4]Bahrami M,Yovanovich M M,Culham J R.Thermal Contact Resistance at Low Contact Pressure:Effect of Elastic Deformation[J].International Journal of Heat and Mass Transfer,2005,48(16):3284-3293
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[6]李磊涛,郑晓亚.一种瞬态接触热导数值模拟方法[J].机械工程学报,2016,52(6):174-180Li Leitao,Zheng Xiaoya.A Numerical Simulation Method of Transient Thermal Contact Conductance[J].Journal of Mechanical Engineering,2016,52(6):174-180(in Chinese)
[7]李建平,刘涛,王伯长,等.铝卷径向接触热阻的仿真研究[J].金属热处理,2009,34(4):91-95Li Jianping,Liu Tao,Wang Bochang,et al.Simulation of the Radial Contact Thermal Resistance for the Aluminum Coil[J].Heat Treatment of Metals,2009,34(4):91-95(in Chinese)
[8]刘冬欢,郑小平,黄拳章,等.C/C复合材料与高温合金GH600之间高温接触热阻的试验研究[J].航空学报,2010,31(11):2189-2194Liu Donghuan,Zheng Xiaoping,Huang Quanzhang,et al.Experimental Investigation of High-Temperature Thermal Contact Resistance between C/C Composite Material and Superalloy GH600[J].ACTA Aeronautica et Astronautica Sinica,2010,31(11):2189-2194(in Chinese)
[9]石友安,桂业伟,杜雁霞,等.相变材料热控系统内部接触热阻的辨识方法研究[J].实验流体力学,2012,26(4):54-58Shi You'an,Gui Yewei,Du Yanxia,et al.Study on Thermal Contact Resistance Estimation in the Phase-Change Material Thermal Control Device[J].Journal of Experiments in Fluid Mechanics,2012,26(4):54-58(in Chinese)
[10]El-Sabbagh A M,Fieberg C,El-Marg E,et al.Modeling of Transient Thermal Contact Resistance out of Conjugate Gradient Method[J].Materialwissenschaft und Werkstofftechnik,2007,38(4):288-293
[11]Gill J,Divo E,Kassab A J.Estimating Thermal Contact Resistance Using Sensitivity Analysis and Regularization[J].Engineering Analysis with Boundary Elements,2009,33(1):54-62
[12]王超.高强钢热成形接触导热和零件力学性能及工艺优化研究[D].武汉:华中科技大学,2014Wang Chao.Investigation on Thermal Contact Behavior and Prediction of Mechanical Properties and Process Optimization in HotStamping[D].Wuhan,Huazhong University of Science and Technology,2014(in Chinese)
[13]张平,宣益民,李强.界面接触热阻的研究进展[J].化工学报,2012,63(2):335-349Zhang Ping,Xuan Yimin,Li Qiang.Development on Thermal Contact Resistance[J].CIESC Journal,2012,63(2):335-349(in Chinese)
[14]Alifanov O M.Solution of an Inverse Problem of Heat Conduction by Iteration Methods[J].Journal of Engineering Physics and Thermophysics,1974,26(4):471-476(in Chinese)
[2]王安良,赵剑锋.接触热阻预测的研究综述[J].中国科学:技术科学,2011,41(5):545-556Wang Anliang,Zhao Jianfeng.The Research Overview of Prediction of Thermal Contact Resistance[J].Scientia Sinica Techologica,2011,41(5):545-556(in Chinese)
[3]Ramamurthi K,Kumar S S,Abilash P M.Thermal Contact Conductance of Molybdenum-Sulphide-Coated Joints at Low Temperature[J].Thermophys Heat Transf,2007,21(4):811-813
[4]Bahrami M,Yovanovich M M,Culham J R.Thermal Contact Resistance at Low Contact Pressure:Effect of Elastic Deformation[J].International Journal of Heat and Mass Transfer,2005,48(16):3284-3293
[5]刘冬欢,王飞,曾凡文,等.高温接触热阻的有限元模拟方法[J].工程力学,2012,29(9):375-379Liu Donghuan,Wang Fei,Zeng Fanwen,et al.Finite Element Simulation Method of High Temperature Thermal Contact Resistance[J].Engineering Mechanics,2012,29(9):375-379(in Chinese)
[6]李磊涛,郑晓亚.一种瞬态接触热导数值模拟方法[J].机械工程学报,2016,52(6):174-180Li Leitao,Zheng Xiaoya.A Numerical Simulation Method of Transient Thermal Contact Conductance[J].Journal of Mechanical Engineering,2016,52(6):174-180(in Chinese)
[7]李建平,刘涛,王伯长,等.铝卷径向接触热阻的仿真研究[J].金属热处理,2009,34(4):91-95Li Jianping,Liu Tao,Wang Bochang,et al.Simulation of the Radial Contact Thermal Resistance for the Aluminum Coil[J].Heat Treatment of Metals,2009,34(4):91-95(in Chinese)
[8]刘冬欢,郑小平,黄拳章,等.C/C复合材料与高温合金GH600之间高温接触热阻的试验研究[J].航空学报,2010,31(11):2189-2194Liu Donghuan,Zheng Xiaoping,Huang Quanzhang,et al.Experimental Investigation of High-Temperature Thermal Contact Resistance between C/C Composite Material and Superalloy GH600[J].ACTA Aeronautica et Astronautica Sinica,2010,31(11):2189-2194(in Chinese)
[9]石友安,桂业伟,杜雁霞,等.相变材料热控系统内部接触热阻的辨识方法研究[J].实验流体力学,2012,26(4):54-58Shi You'an,Gui Yewei,Du Yanxia,et al.Study on Thermal Contact Resistance Estimation in the Phase-Change Material Thermal Control Device[J].Journal of Experiments in Fluid Mechanics,2012,26(4):54-58(in Chinese)
[10]El-Sabbagh A M,Fieberg C,El-Marg E,et al.Modeling of Transient Thermal Contact Resistance out of Conjugate Gradient Method[J].Materialwissenschaft und Werkstofftechnik,2007,38(4):288-293
[11]Gill J,Divo E,Kassab A J.Estimating Thermal Contact Resistance Using Sensitivity Analysis and Regularization[J].Engineering Analysis with Boundary Elements,2009,33(1):54-62
[12]王超.高强钢热成形接触导热和零件力学性能及工艺优化研究[D].武汉:华中科技大学,2014Wang Chao.Investigation on Thermal Contact Behavior and Prediction of Mechanical Properties and Process Optimization in HotStamping[D].Wuhan,Huazhong University of Science and Technology,2014(in Chinese)
[13]张平,宣益民,李强.界面接触热阻的研究进展[J].化工学报,2012,63(2):335-349Zhang Ping,Xuan Yimin,Li Qiang.Development on Thermal Contact Resistance[J].CIESC Journal,2012,63(2):335-349(in Chinese)
[14]Alifanov O M.Solution of an Inverse Problem of Heat Conduction by Iteration Methods[J].Journal of Engineering Physics and Thermophysics,1974,26(4):471-476(in Chinese)