Analysis of Unsteady Flow Structures in a Radial Turbomachine by Using Proper Orthogonal Decomposition

Abstract

Tonalities in hydro and airborne noise emission are a known problem of turbomachines, wherein the tonalities in the noise spectrum are associated with the different orders of the blade passing frequency (BPF). The proper orthogonal decomposition (POD) method was utilized to find the relationship between the fluctuations in the pressure field at the BPF orders which are the origin of the noise emission and the correlated fluctuations in the turbulent velocity field in terms of coherent, periodic flow structures. In order the provide the input data for the POD analysis, a URANS k-ω-SST scale adaptive simulation (SAS) of the turbulent flow field in a single stage radial pump under part load conditions was performed. Compared to traditional two equation turbulence models this approach is less dissipative and allows the development of small scale turbulence structures and is therefore an appropriate method for this study. In order to compute the POD correlation matrix Sirovich’s “Methods of Snapshots” was applied to the unsteady pressure and velocity fields from the CFD simulation. The discrimination of coherent, periodic flow structures and the incoherent, chaotic turbulence was carried out by analyzing the POD eigenvalue distributions, the POD mode shapes and the spectral properties of the POD time coefficients. Five coupled POD mode pairs were identified in total, which were strictly correlated with the 1st, 2nd, 3rd, 4th and 5th order of the BPF and therefore responsible for the noise emission at these discrete frequencies. The coherent structures were explored on the basis of the spatial POD velocity und pressure mode shapes and in terms of vortical structures after an additional phase averaging. The scope of this study is to introduce an enhanced collection of post processing techniques which are capable of analyzing highly unsteady flow fields from numerical simulations in a better way than is possible by just using traditional techniques like the evaluation of integral or time averaged quantities. The identified coherent flow structures and their associated pressure fluctuations are key elements for a proper comprehension of the internal dynamics of the turbulent flow field in a turbomachine and therefore essential for the understanding of the noise generation processes and the optimization of such machines.