Data-Driven Modal Decomposition Analysis of Unsteady Flow in a Multi-Stage Turbine

TL;DR

This study compares POD and DMD modal analysis methods applied to unsteady flow in a turbine, highlighting their effectiveness in reconstructing flow features and capturing dynamic behavior.

Contribution

It introduces and evaluates multiple DMD variants against POD for analyzing turbine flow, revealing their relative accuracy and dynamic insights.

Findings

DMD variants achieve reconstruction accuracy comparable to POD.

Neutral DMD modes dominate the unsteady flow dynamics.

Higher adiabatic efficiency correlates with larger mode components.

Abstract

Two data-driven modal analysis approaches, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are applied to analyze the unsteady flow obtained by solving the Reynolds-averaged Navier-Stokes (RANS) equations in a 1.5-stage axial turbine. The reduced-order reconstructed pressure, dominant mode shapes, and dynamic features of these dominant modes in the downstream stator of the turbine are compared between POD and four DMD variants. It is found that the DMD methods based on the amplitude criterion, the Tissot criterion, and the sparsity-promoting DMD (SP-DMD) achieve reconstruction accuracy comparable to that of POD, while the frequency criterion proves unsuitable for the present problem. The second and third POD and DMD modes capture the dominant pressure fluctuation structures within the stator, and there is similarity between the corresponding POD and DMD spatial modes. The unsteady flow is primarily governed by neutral DMD modes characterized by high amplitudes and low frequencies corresponding to the basic and harmonic frequencies driven by the rotor passing frequency. While the POD analysis provides accurate reconstruction for the original snapshots, the time evolution of each POD mode does not reflect the true dynamic feature of the system. In particular, they misrepresent the fundamental frequencies of the problem. In addition, the correlations between the dominant modes in the downstream stator and the turbine adiabatic efficiency are explored across different stator clocking configurations. It is found that a clocking configuration with higher adiabatic efficiency at 50% span corresponds to a larger spatial and time component of the second and third DMD mode pair, and similarly a larger second POD mode.