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Journal of Vibration and Acoustics | Volume 133 | Issue 5 | Research Paper
Research Papers

An Enhanced Greitzer Compressor Model Including Pipeline Dynamics and Surge

[+] Author and Article Information
Se Young Yoon

Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904-4743

Zongli Lin1

Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904-4743zl5y@virginia.edu

Christopher Goyne, Paul E. Allaire

Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904-4746

1

Corresponding author.

J. Vib. Acoust 133(5), 051005 (Jul 26, 2011) (14 pages) doi:10.1115/1.4003937 History: Received May 05, 2010; Revised December 24, 2010; Published July 26, 2011; Online July 26, 2011
Article
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The modeling of a centrifugal compressor system with exhaust and plenum piping acoustics is presented in this paper. For an experimental centrifugal compressor test rig with modular inlet and exhaust piping, a mathematical model of the system dynamics is derived based on the Greitzer compression system model. In order to include the dynamics of the piping acoustics, a transmission line model is added to the original compressor equations and different compressor-piping configurations were tested. The resulting mathematical representations of the compression system dynamics are compared with the measured response of the experimental setup. Employing active magnetic bearings to perturb the axial impeller tip clearance of the compressor, the compression system is excited over a wide frequency range and the input-output response from the impeller tip clearance to the plenum pressure rise is analyzed. Additionally, the simulated surge oscillations are compared with the measured response in the surge condition. A good agreement is observed between the experimental and theoretical frequency responses of from the tip clearance to the output pressure, both in stable operation and during surge.
Copyright © 2011 by American Society of Mechanical Engineers
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References

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Gravdahl, J. T., and Egeland, O., 1999, "Compressor Surge and Rotating Stall: Modeling and Control", Springer-Verlag, London, UK.
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4
Emmons, H. W., Pearson, C. E., and Grant, H. P., 1955, “Compressor Surge and Stall Propagation,” Trans. ASME, 77 , pp. 455–469.
5
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Moore, F. K., and Greitzer, E. M., 1986, “A Theory of Post-Stall Transients in Axial Compressor Systems: Part I—Development of Equations,” ASME J. Eng. Gas Turbines Power, 108 (1), pp. 68–76.  [CrossRef]
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van Helvoirt, J., and d. Jager, B., 2007, “Dynamic Model Including Piping Acoustics of a Centrifugal Compression System,” J. Sound Vib., 302 , pp. 361–378.  [CrossRef]
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Jungowski, W. M., M. H, W., and Price, G. R., 1996, “Pressure Oscillations Occurring in a Centrifugal Compressor System With and Without Passive and Active Surge Control,” ASME J. Turbomach., 118 , pp. 29–40.
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Krus, P., Weddfelt, K., and Palmberg, J., 1994, “Fast Pipeline Models for Simulation of Hydraulic Systems,” ASME J. Dyn. Syst., Meas., Control, 116 , pp. 132–136.  [CrossRef]
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Yoon, S. Y., Lin, Z., Lim, K. T., Goyne, C., and Allaire, P. E., 2010, “Model Validation for an Active Magnetic Bearing Based Compressor Surge Control Test Rig,” ASME J. Vibr. Acoust., 132 , p. 061005.  [CrossRef]
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Senoo, Y., 1987, “Pressure Losses and Flow Field Distortion Induced by Tip Clearance of Centrifugal and Axial Compressors,” JSME Int. J., 30 , pp. 375–385.
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v. Helvoirt, J., d. Jager, B., Steinbuch, M., and Smeulers, J., 2004, “Stability Parameter Identification for a Centrifugal Compression System,” 43rd IEEE Conference on Decision and Control .
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Figures

Grahic Jump Location
+Photograph of the experimental setup, including the direction of the inlet and the outlet air flow
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Photograph of the experimental setup, including the direction of the inlet and the outlet air flow
Figure 1

Photograph of the experimental setup, including the direction of the inlet and the outlet air flow

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+Layout of the experimental setup, including the compressor, instrumentations, and the movable throttle valve. Possible throttle valve locations are at 2.2 m, 7.1 m, and 15.2 m along the exhaust piping measured from the compressor.
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Layout of the experimental setup, including the compressor, instrumentations, and the movable throttle valve. Possible throttle valve locations are at 2.2 m, 7.1 m, and 15.2 m along the exhaust piping measured from the compressor.
Figure 2

Layout of the experimental setup, including the compressor, instrumentations, and the movable throttle valve. Possible throttle valve locations are at 2.2 m, 7.1 m, and 15.2 m along the exhaust piping measured from the compressor.

Grahic Jump Location
+The single-stage centrifugal compressor in the experimental setup operates with an unshrouded impeller and a vaneless diffuser. The rotor is radially supported by two radial AMBs, and a single thrust AMB provides the axial support.
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The single-stage centrifugal compressor in the experimental setup operates with an unshrouded impeller and a vaneless diffuser. The rotor is radially supported by two radial AMBs, and a single thrust AMB provides the axial support.
Figure 3

The single-stage centrifugal compressor in the experimental setup operates with an unshrouded impeller and a vaneless diffuser. The rotor is radially supported by two radial AMBs, and a single thrust AMB provides the axial support.

Grahic Jump Location
+Compressor characteristic curve for the experimental setup measured at various operating speeds
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Compressor characteristic curve for the experimental setup measured at various operating speeds
Figure 4

Compressor characteristic curve for the experimental setup measured at various operating speeds

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+Schematic drawing of a compression system described by the Greitzer model
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Schematic drawing of a compression system described by the Greitzer model
Figure 5

Schematic drawing of a compression system described by the Greitzer model

Grahic Jump Location
+Characteristic curve of the compressor fitted to experimental data
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Characteristic curve of the compressor fitted to experimental data
Figure 6

Characteristic curve of the compressor fitted to experimental data

Grahic Jump Location
+Block diagram of the Greitzer compression system model. The compression system consists of the compressor, the plenum volume, and the throttle valve.
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Block diagram of the Greitzer compression system model. The compression system consists of the compressor, the plenum volume, and the throttle valve.
Figure 7

Block diagram of the Greitzer compression system model. The compression system consists of the compressor, the plenum volume, and the throttle valve.

Grahic Jump Location
+Measured characteristic curves at δcl of 0 mils, +6 mils (0.1524 mm) and −6 mils (−0.1524 mm). The predicted curves from Eq. 7 are also plotted at the nominal clearance (solid line), and δcl of +6 mils (0.1524 mm) (dash-dotted line) and −6 mils (−0.1524 mm) (dashed line), respectively.
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Measured characteristic curves at δcl of 0 mils, +6 mils (0.1524 mm) and −6 mils (−0.1524 mm). The predicted curves from Eq. 7 are also plotted at the nominal clearance (solid line), and δcl of +6 mils (0.1524 mm) (dash-dotted line) and −6 mils (−0.1524 mm) (dashed line), respectively.
Figure 8

Measured characteristic curves at δcl of 0 mils, +6 mils (0.1524 mm) and −6 mils (−0.1524 mm). The predicted curves from Eq. 7 are also plotted at the nominal clearance (solid line), and δcl of +6 mils (0.1524 mm) (dash-dotted line) and −6 mils (−0.1524 mm) (dashed line), respectively.

Grahic Jump Location
+Experimental Bodes plot from disturbances in the impeller tip clearance (m) to the plenum pressure rise Ψp at 35%, 32%, and 30% throttle valve openings
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Experimental Bodes plot from disturbances in the impeller tip clearance (m) to the plenum pressure rise Ψp at 35%, 32%, and 30% throttle valve openings
Figure 9

Experimental Bodes plot from disturbances in the impeller tip clearance (m) to the plenum pressure rise Ψp at 35%, 32%, and 30% throttle valve openings

Grahic Jump Location
+Comparison between simulated frequency response of the Greitzer model versus experimental Bode plots from tip clearance (m) to plenum pressure rise Ψp. Throttle valve at 32% open.
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Comparison between simulated frequency response of the Greitzer model versus experimental Bode plots from tip clearance (m) to plenum pressure rise Ψp. Throttle valve at 32% open.
Figure 10

Comparison between simulated frequency response of the Greitzer model versus experimental Bode plots from tip clearance (m) to plenum pressure rise Ψp. Throttle valve at 32% open.

Grahic Jump Location
+Block diagram of the pipeline model, modified from Refs. 16,20. The inputs are the pressure and volume flow rate at the pipe boundaries and the outputs are the upstream and downstream characteristics Cu(s) and Cd(s).
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Block diagram of the pipeline model, modified from Refs. 16,20. The inputs are the pressure and volume flow rate at the pipe boundaries and the outputs are the upstream and downstream characteristics Cu(s) and Cd(s).
Figure 11

Block diagram of the pipeline model, modified from Refs. 16,20. The inputs are the pressure and volume flow rate at the pipe boundaries and the outputs are the upstream and downstream characteristics Cu(s) and Cd(s).

Grahic Jump Location
+Block diagram of the compression system model with pipeline dynamics at the compressor exhaust
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Block diagram of the compression system model with pipeline dynamics at the compressor exhaust
Figure 12

Block diagram of the compression system model with pipeline dynamics at the compressor exhaust

Grahic Jump Location
+Comparison between simulated the Bode plots from tip clearance (m) to plenum pressure rise Ψp for the model with piping acoustics at compressor exhaust versus the experimental measurement. Throttle valve at 32% open.
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Comparison between simulated the Bode plots from tip clearance (m) to plenum pressure rise Ψp for the model with piping acoustics at compressor exhaust versus the experimental measurement. Throttle valve at 32% open.
Figure 13

Comparison between simulated the Bode plots from tip clearance (m) to plenum pressure rise Ψp for the model with piping acoustics at compressor exhaust versus the experimental measurement. Throttle valve at 32% open.

Grahic Jump Location
+Block diagram of the compression system model with the pipeline dynamics at the plenum output
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Block diagram of the compression system model with the pipeline dynamics at the plenum output
Figure 14

Block diagram of the compression system model with the pipeline dynamics at the plenum output

Grahic Jump Location
+Comparison between simulated the Bode plots from tip clearance (m) to plenum pressure rise Ψp for the compression system with piping acoustics at plenum output versus experimental measurement. Throttle valve at 32% open.
View Large  |  Save Figure  |  Download Slide (.ppt)
Comparison between simulated the Bode plots from tip clearance (m) to plenum pressure rise Ψp for the compression system with piping acoustics at plenum output versus experimental measurement. Throttle valve at 32% open.
Figure 15

Comparison between simulated the Bode plots from tip clearance (m) to plenum pressure rise Ψp for the compression system with piping acoustics at plenum output versus experimental measurement. Throttle valve at 32% open.

Grahic Jump Location
+Comparison between simulated the Bode plots from tip clearance (m) to plenum pressure rise Ψp for the compression system with piping acoustics at plenum output versus experimental measurement. Throttle valve at 34% open.
View Large  |  Save Figure  |  Download Slide (.ppt)
Comparison between simulated the Bode plots from tip clearance (m) to plenum pressure rise Ψp for the compression system with piping acoustics at plenum output versus experimental measurement. Throttle valve at 34% open.
Figure 16

Comparison between simulated the Bode plots from tip clearance (m) to plenum pressure rise Ψp for the compression system with piping acoustics at plenum output versus experimental measurement. Throttle valve at 34% open.

Grahic Jump Location
+Bode plots from simulation of the compression system with pipeline dynamics at the plenum output, from the impeller tip clearance disturbance (m) to the plenum pressure rise Ψp at 32%, 34%, and 36% throttle valve openings
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Bode plots from simulation of the compression system with pipeline dynamics at the plenum output, from the impeller tip clearance disturbance (m) to the plenum pressure rise Ψp at 32%, 34%, and 36% throttle valve openings
Figure 17

Bode plots from simulation of the compression system with pipeline dynamics at the plenum output, from the impeller tip clearance disturbance (m) to the plenum pressure rise Ψp at 32%, 34%, and 36% throttle valve openings

Grahic Jump Location
+Comparison between the measured and the simulated plenum pressure rise Ψp during compressor surge
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Comparison between the measured and the simulated plenum pressure rise Ψp during compressor surge
Figure 18

Comparison between the measured and the simulated plenum pressure rise Ψp during compressor surge

Grahic Jump Location
+Comparison between the frequency components of the measured and the simulated plenum pressure rise Ψp during compressor surge
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Comparison between the frequency components of the measured and the simulated plenum pressure rise Ψp during compressor surge
Figure 19

Comparison between the frequency components of the measured and the simulated plenum pressure rise Ψp during compressor surge

Grahic Jump Location
+Comparison between simulated the Bode plots from the tip clearance (m) to plenum pressure rise Ψp for the compression system with the modal approximation of the piping acoustics at plenum output versus experimental measurement. Throttle valve at 32% open.
View Large  |  Save Figure  |  Download Slide (.ppt)
Comparison between simulated the Bode plots from the tip clearance (m) to plenum pressure rise Ψp for the compression system with the modal approximation of the piping acoustics at plenum output versus experimental measurement. Throttle valve at 32% open.
Figure 20

Comparison between simulated the Bode plots from the tip clearance (m) to plenum pressure rise Ψp for the compression system with the modal approximation of the piping acoustics at plenum output versus experimental measurement. Throttle valve at 32% open.

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