0
Research Papers: Gas Turbines: Structures and Dynamics

Developing a Reduced-Order Model of Nonsynchronous Vibration in Turbomachinery Using Proper-Orthogonal Decomposition Methods

[+] Author and Article Information
Stephen T. Clark

Department of Mechanical Engineering,
Duke University,
Durham, NC 27708
e-mail: stc@duke.edu

Fanny M. Besem

Department of Mechanical Engineering,
Duke University,
Durham, NC 27708
e-mail: fb46@duke.edu

Robert E. Kielb

Department of Mechanical Engineering,
Duke University,
Durham, NC 27708
e-mail: rkielb@duke.edu

Jeffrey P. Thomas

Department of Mechanical Engineering,
Duke University,
Durham, NC 27708
e-mail: jthomas@duke.edu

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 15, 2014; final manuscript received August 30, 2014; published online November 18, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(5), 052501 (May 01, 2015) (11 pages) Paper No: GTP-14-1400; doi: 10.1115/1.4028675 History: Received July 15, 2014; Revised August 30, 2014; Online November 18, 2014

The paper develops a reduced-order model of nonsynchronous vibration (NSV) using proper orthogonal decomposition (POD) methods. The approach was successfully developed and implemented, requiring between two and six POD modes to accurately predict computational fluid dynamics (CFD) solutions that are experiencing NSV. This POD method was first developed and demonstrated for a transversely moving, two-dimensional cylinder in cross-flow. Later, the method was used for the prediction of CFD solutions for a two-dimensional compressor blade. This research is the first to offer a POD approach to the reduced-order modeling of NSV in turbomachinery. Modeling NSV is especially challenging because NSV is caused by complicated, unsteady flow dynamics; this initial study helps researchers understand the causes of NSV, and aids in the future development of predictive tools for aeromechanical design engineers.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Thomassin, J., Vo, H. D., and Mureithi, N. W., 2011. “The Tip Clearance Flow Resonance Behind Axial Compressor Nonsynchronous Vibration,” ASME J. Turbomach., 133(4), p. 041030. [CrossRef]
Drolet, M., Vo, H. D., and Mureithi, N. W., 2013, “Effect of Tip Clearance on the Prediction of Nonsynchronous Vibrations in Axial Compressors,” ASME J. Turbomach., 135(1), p. 011023. [CrossRef]
Im, H. S., and Zha, G. C., 2012, “Simulation of Non-Synchronous Blade Vibration of an Axial Compressor Using a Fully-Coupled Fluid/Structure Interaction,” ASME Paper No. GT2012-68150. [CrossRef]
Spiker, M. A., 2008, “Development of an Efficient Design Method for Non-Synchronous Vibration,” Ph.D. thesis, Duke University, Department of Mechanical Engineering and Materials Science, Durham, NC.
Mailach, R., Lehmann, I., and Vogeler, K., 2001, “Rotating Instabilities in an Axial Compressor Originating From the Fluctuating Blade Tip Vortex,” ASME J. Turbomach., 123(3), pp. 453–463. [CrossRef]
Sanders, A., 2005, “Nonsynchronous Vibration (NSV) Due to a Flow-Induced Aerodynamic Instability in a Composite Fan Stator,” ASME J. Turbomach., 127(2), pp. 412–421. [CrossRef]
Thomassin, J., Vo, H. D., and Mureithi, N. W., 2009, “Blade Tip Clearance Flow and Compressor Nonsynchronous Vibrations: The Jet Core Feedback Theory as the Coupling Mechanism,” ASME J. Turbomach., 131(1), p. 011013. [CrossRef]
Marz, J., Hah, C., and Neise, W., 2002, “An Experimental and Numerical Investigation Into the Mechanisms of Rotating Instability,” ASME J. Turbomach., 124(3), pp. 367–375. [CrossRef]
Hall, K. C., Thomas, J. P., and Dowell, E. H., 2002, “Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique,” AIAA J., 40(5) pp. 879–886. [CrossRef]
Hall, K. C., 1994, “Eigenanalysis of Unsteady Flows About Airfoils, Cascades, and Wings,” AIAA J., 32(12), pp. 2426–2432. [CrossRef]
Hall, K. C., Thomas, J. P., and Dowell, E. H., 1999, “Reduced-Order Modeling of Unsteady Small-Disturbance Flows Using a Frequency-Domain Proper Orthogonal Decomposition Technique,” AIAA 37th Aerospace Sciences Meeting and Exhibition Reno, NV, Jan. 11–14, AIAA Paper No. 99-0655. [CrossRef]
Willcox, K., and Peraire, J., 2002, “Balanced Model Reduction Via the Proper Orthogonal Decomposition,” AIAA J., 40(11), pp. 801–819. [CrossRef]
Spiker, M., Kielb, R., Thomas, J., and Hall, K. C., 2009, “Application of Enforced Motion to Study 2-D Cascade Lock-In Effect,” 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forums and Aerospace Exposition, Orlando, FL, Jan. 5–8, AIAA Paper No. 2009-892. [CrossRef]
Dowell, E. H., Hall, K. C., Thomas, J. P., Kielb, R. E., Spiker, M. A., and Denegri, C. M., Jr., 2008, “A New Solution Method for Unsteady Flows Around Oscillating Bluff Bodies,” IUTAM Symposium on Fluid-Structure Interaction in Ocean Engineering, Hamburg, Germany, July 23–26, p. 37.
Jones, G. W., and Walker, R. C., 1969, “Aerodynamic Forces on a Stationary and Oscillating Circular Cylinder at High Reynolds Numbers,” NASA Langley Research Center, Hampton, VA, Technical Report No. NASA TR R-300.
Allemang, R. J., 2003, “The Modal Assurance Criterion—Twenty Years of Use and Abuse,” Sound Vib., 37(8), pp. 14–21, available at: http://www.sandv.com/downloads/0308alle.pdf
Clark, S. T., 2013, “Design for Coupled-Mode Flutter and Non-Synchronous Vibration in Turbomachinery,” Ph.D. thesis, Duke University, Department of Mechanical Engineering and Materials Science, Durham, NC.

Figures

Grahic Jump Location
Fig. 1

Unsteady pressure contours at an instant in time. (a) First harmonic of the first POD mode. (b) Second harmonic of the first POD mode. (c) Third harmonic of the first POD mode.

Grahic Jump Location
Fig. 2

Unsteady pressure contours at an instant in time. Subfigures (a)–(f) show the first harmonic of the first six POD modes. Each POD mode shows a decreasing contribution to the instability in the flow field around the cylinder.

Grahic Jump Location
Fig. 3

CFD lock-in region for Re = 120 cylinder

Grahic Jump Location
Fig. 4

CFD snapshots chosen for POD analysis for Re = 120. The CFD snapshots span both Strouhal number and enforced-motion amplitude. The circles are the CFD snapshots; the squares are the CFD solutions to be reconstructed.

Grahic Jump Location
Fig. 5

MAC values for each reconstructed CFD solution using two (left) and six (right) POD modes

Grahic Jump Location
Fig. 6

Comparison of the unsteady surface pressure at the bottom surface of the cylinder between the original CFD solution and the reconstructions with two, four, and six POD modes. All solutions are for St = 0.16 and are reconstructions of Re = 120 solutions; h/D = 0.10. The magnitude of the unsteady pressure is nondimensionalized by its maximum value.

Grahic Jump Location
Fig. 7

Unsteady pressure contours at an instant in time for a Strouhal number St = 0.16, and an amplitude of oscillation h/D = 0.05. (a) Original CFD solution. (b) Reconstructed flow field using two POD modes. (c) Reconstructed flow field using six POD modes.

Grahic Jump Location
Fig. 8

Each αph coefficient is fit using a high-order surface polynomial. This figure shows a linear interpolation between each data point to create a surface. Least square methods will be used to fit the data set, allowing the calculation of the αph coefficients. This figure shows the surface of the real part of α11.

Grahic Jump Location
Fig. 9

Each αph coefficient is fit using a high-order surface polynomial. This figure shows a fifth-order polynomial in Strouhal number and amplitude created to fit the real part of α11.

Grahic Jump Location
Fig. 10

A distorted view of the two-dimensional CI grid used in CFD studies. The HO – H grid has dimensions of 17 × 33 × 5, 193 × 33 × 5, and 17 × 33 × 5 in each block, respectively. The grid has been distorted for proprietary reasons.

Grahic Jump Location
Fig. 11

Lock-in region of the CI for IBPA = −60 deg. The CFD solutions used to form the POD modes are identified with red squares. The blue circles represent the CFD solutions predicted using the complex αph coefficient method.

Grahic Jump Location
Fig. 12

Harmonic visualization of the unsteady pressure of the first POD mode. The color contours represent low (blue) to high (red) unsteady pressure values.

Grahic Jump Location
Fig. 13

The MAC value for each of the predicted C1 CFD solutions, compared with the full CFD solution. The left subfigure uses two POD modes while the right subfigure uses six POD modes.

Grahic Jump Location
Fig. 14

Two 2D C1 predicted solutions (left figures) compared with their CFD solutions (right figures). The first row is for a frequency of 1414 Hz at an amplitude of 1 deg. The second row is for a frequency of 1200 Hz, and an amplitude of 1 deg.

Grahic Jump Location
Fig. 15

The magnitude of the generalized force for an IBPA = −60 deg

Grahic Jump Location
Fig. 16

MAC value for each of the predicted C1 CFD solutions. The lock-in region was split into two subregions at a frequency of 1415 Hz, as shown by the dashed black line. The left subfigure uses two POD modes while the right subfigure uses six POD modes.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In