Modal decomposition methods for distributed excitation force field on tube bundle in cross flow

Abstract

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.