Mode analysis for multiple parameter conditions of nozzle internal unsteady flow using Parametric Global Proper Orthogonal Decomposition

Abstract

Analysis methods based on mode decomposition have been proposed to describe the characteristics of flow phenomena. Among them, proper orthogonal decomposition (POD), which decomposes modes into eigenvalues and basis vectors, has long been used. Many studies have shown that POD is a useful method for capturing the characteristics of unsteady flow. In particular, Snapshot POD has attracted much recent attention and has been used to solve unsteady flow problems. However, the basis vectors of the mode obtained by conventional POD is different for each condition. Therefore, whether the basis vectors of each mode are switching in the direction of parameters (e.g. different shapes or different Reynolds numbers) or whether they develop or decay is difficult to discuss. As a result, discussions on conventional POD tend to be qualitative. To address this issue, the present study uses Parametric Global POD, a method that perfectly matches basis vectors in results with different parameters (in this study, different Reynolds numbers). Parametric Global POD method was applied to the analysis of the flow field in a curved pipe and found to capture the development or decay of modes with major basis vectors in the direction of parameters, which is difficult to achieve with conventional POD methods.