To rapidly and accurately identify the characteristics of the distributed force and reconstruct the force field on tube bundles in a cross flow, modal decomposition methods for a three-dimensional turbulent flow are studied. This is done with proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and the regularization method for DMD. A 3-D turbulent cross flow computational fluid dynamics model is simulated to obtain the temporal–spatial force field acting on the tubes. Applying direct Fourier transformation to the data yields the frequency contents of the field as a reference for other analyses. POD provides high-accuracy reconstruction of the force field with 43 modes, and each mode contains multiple frequency contents of the Fourier transformation. In comparison, DMD successfully demonstrates the relation between single frequencies and the spatial distribution on the tube surface. To solve the ill-posedness of singular value decomposition (SVD), the key mathematical processing of both decomposition methods, the Tikhonov regularization method is introduced into field reconstruction. The regularization operator and parameter determined by solving a functional extremum problem yield a criterion that can be applied to the SVD of the DMD, which effectively reduces the number of DMD modes required to reconstruct the field to 16 with the same level of norm error.

为了快速准确地识别分布力的特性并在横流中重建管束上的力场，研究了三维湍流的模态分解方法。这可以通过适当的正交分解（POD），动态模式分解（DMD）和DMD的正则化方法来完成。对3-D湍流错流计算流体动力学模型进行了仿真，以获得作用在管道上的时空力场。将直接傅立叶变换应用于数据会产生该字段的频率内容，以作为其他分析的参考。POD提供了43种模式的力场高精度重建，每个模式都包含傅里叶变换的多个频率内容。相比下，DMD成功地证明了单频与管表面空间分布之间的关系。为了解决奇异值分解（SVD）的不适定性，这两种分解方法的关键数学处理，将Tikhonov正则化方法引入场重构。通过求解功能极值问题确定的正则化运算符和参数会产生可应用于DMD的SVD的准则，从而有效地将重构场所需的DMD模式数量减少到16个，且范数误差相同。将Tikhonov正则化方法引入现场重建。通过求解函数极值问题确定的正则化运算符和参数会产生可应用于DMD的SVD的准则，从而有效地将重构场所需的DMD模式数量减少到16个，且范数误差相同。将Tikhonov正则化方法引入现场重建。通过求解函数极值问题确定的正则化运算符和参数会产生可应用于DMD的SVD的准则，从而有效地将重构场所需的DMD模式数量减少到16个，且范数误差相同。