Use of fin equation to calculate Nusselt numbers for rotating disks
Use of fin equation to calculate Nusselt numbers for rotating disks
复制标题
使用 fin 方程计算旋转圆盘的努塞尔数
DOI：
10.1115/1.4031355
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发表时间：
2015
影响因子：
1.7
通讯作者：
J. Owen
中科院分区：
文献类型：
--
作者：
Hui Tang;T. Shardlow;J. Owen
薄盘中的传导可以用有限元方程来模拟，对于具有恒定换热系数的圆盘，该方程有其解析解。然而，旋转圆盘系统中的对流(特别是自由对流)是一个魔术门问题：流体和固体中的换热是耦合的，导热和对流的相对效应与Biot数有关，而Biot数又与Nusselt数有关。原则上，如果圆盘温度的径向分布是已知的，那么可以用数值方法来确定。但根据温度测量确定热通量是一个逆问题的例子，其中温度的小不确定性可能会在计算的热通量中产生很大的不确定性。本文将贝叶斯统计方法应用到圆周翅片方程的逆解中，得到了可靠的旋转圆盘B_i的估计值，并用模拟噪声温度测量的数值实验验证了贝叶斯方法的有效性。利用已发表的实验温度测量，该方法也被应用于同向旋转压气机盘间空腔内浮力诱导流动的共轭问题。
Conduction in thin discs can be modelled using the finequation, 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 conju gate 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 determina tion 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 pa per, Bayesian statistics are applied to the inverse solution of the cir cular fin equation to produce reliable estimates of Bi for rotating discs, and numerical experiments using simulated noisy tempera ture 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 com pressor discs.