Use of Fin Equation to Calculate Nusselt Numbers for Rotating Discs
Use of Fin Equation to Calculate Nusselt Numbers for Rotating Discs
复制标题
利用鳍方程计算旋转圆盘的努塞尔数
DOI：
10.1115/gt2015-42029
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发表时间：
2015
影响因子：
2.6
通讯作者：
J. Owen
中科院分区：
文献类型：
--
作者：
Hui Tang;T. Shardlow;J. Owen
薄圆盘中的传导可以用翅片方程来模拟，对于具有恒定传热系数的圆盘，该方程有解析解。然而，对流（特别是自由对流）在圆盘系统是一个共轭问题：在流体和固体中的热传递是耦合的，和传导和对流的相对效果与毕奥数，Bi，这反过来又是相关的努塞尔数。原则上，如果圆盘温度的径向分布是已知的，那么Bi可以用数值确定。但是，从温度测量确定热通量是一个反问题的例子，其中温度的小不确定性可能会在计算的热通量中产生大的不确定性。本文将贝叶斯统计应用于圆肋方程的逆解，以产生旋转圆盘的Bi的可靠估计，并使用模拟噪声温度测量的数值实验来证明贝叶斯方法的有效性。利用已发表的实验温度测量结果，该方法还可应用于同向旋转压缩机盘之间空腔中浮力诱导流动的共轭问题。Copyright © 2015 by ASME
Conduction in thin discs can be modelled using the fin equation, and there are analytical solutions of this equation for a circular disc with a constant heat-transfer coefficient. However, convection (particularly free convection) in rotating-disc systems is a conjugate problem: the heat transfer in the fluid and the solid are coupled, and the relative effects of conduction and convection are related to the Biot number, Bi, which in turn is related to the Nusselt number. In principle, if the radial distribution of the disc temperature is known then Bi can be determined numerically. But the determination of heat flux from temperature measurements is an example of an inverse problem where small uncertainties in the temperatures can create large uncertainties in the computed heat flux. In this paper, Bayesian statistics are applied to the inverse solution of the circular fin equation to produce reliable estimates of Bi for rotating discs, and numerical experiments using simulated noisy temperature measurements are used to demonstrate the effectiveness of the Bayesian method. Using published experimental temperature measurements, the method is also applied to the conjugate problem of buoyancy-induced flow in the cavity between corotating compressor discs.Copyright © 2015 by ASME