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

Yalu Zhu, Feng Liu

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.

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

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.

Paper Structure

This paper contains 13 sections, 13 equations, 20 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Data-Driven Modal Decomposition Methods
  3. Proper Orthogonal Decomposition
  4. Dynamic Mode Decomposition
  5. Mode Selection Criteria in DMD
  6. Code Implementation
  7. Flow Field Generation
  8. Results and Discussions
  9. Reduced-Order Reconstruction
  10. Mode Shapes
  11. Mode Dynamics
  12. Influence of Stator Clocking
  13. Conclusions

Figures (20)

  • Figure 1: Grids over blade surfaces and hub of the turbine.
  • Figure 2: History of static pressure at the outlet of each blade row.
  • Figure 3: Variation of reconstruction residual with number of retained modes.
  • Figure 4: Variation of mode growth rate of DMD with mode index.
  • Figure 5: Contours of relative error of reconstructed pressure by the first seven modes. DMD is based on the Tissot criterion.
  • ...and 15 more figures