The paper deals with the development of a nonlinear one-dimensional modular dynamic model for the simulation of transient behavior of compression systems. The model is based on balance equations of mass, momentum, and energy, which are derived through a general approach and are written by using the finite difference method. The model also takes rotating mass dynamics into account through a lumped parameter approach. Moreover, it reproduces the behavior of the system in the presence of the surge phenomenon through steady-state performance maps, which represent the compressor operation in the inverse flow region by means of a third degree polynomial curve. The model is implemented through the Matlab Simulink tool, where the system of ordinary differential equations is solved by using a fourth- and fifth-order Runge–Kutta method. A sensitivity analysis is carried out to evaluate the influence on compressor outlet pressure oscillations of the model parameters, of the supplied torque, of ambient conditions and of the shape of the compressor characteristic curves. The results show that the model proves effective in capturing the physical essence of surge phenomenon without being computationally too heavy.

1.
Greitzer
,
E. M.
, 1976, “
Surge and Rotating Stall in Axial Flow Compressor: Part 1, Theoretical Compression System Model
ASME J. Eng. Power
0022-0825,
98
, pp.
190
198
.
2.
Moore
,
F. K.
, and
Greitzer
,
E. M.
, 1986, “
A Theory of Post-Stall Transients in Axial Compression Systems: Part I-Development of Equations
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
108
, pp.
68
76
.
3.
Fink
,
D. A.
,
Cumpsty
,
N. A.
, and
Greitzer
,
E. M.
, 1992, “
Surge Dynamics in a Free-Spool Centrifugal Compressor System
,”
ASME J. Turbomach.
0889-504X,
114
, pp.
321
332
.
4.
Mansoux
,
C. A.
,
Gysling
,
D. L.
,
Setiawan
,
J. D.
, and
Paduano
,
J. D.
, 1994, “
Distributed Nonlinear Modeling and Stability Analysis of Axial Compressor Stall And Surge
,”
Proceedings of American Control Conference
, Baltimore, MD, June 29–July 1, pp.
2305
2316
.
5.
McCaughan
,
F. E.
, 1989, “
Application of Bifurcation Theory to Axial Flow Compressor Instability
,”
ASME J. Turbomach.
0889-504X,
111
, pp.
426
433
.
6.
McCaughan
,
F. E.
, 1990, “
Bifurcational Analysis of Axial Flow Compressor Stability
,”
SIAM J. Appl. Math.
0036-1399,
50
(
5
), pp.
1232
1253
.
7.
Hös
,
C.
,
Champneys
,
A.
, and
Kullmann
,
L.
, 2003, “
Bifurcational Analysis of Surge and Rotating Stall in the Moore-Greitzer Compression System
,”
IMA J. Appl. Math.
0272-4960,
68
(
2
), pp.
205
228
.
8.
Vaidya
,
U.
,
Ananthkrishnan
,
N.
, and
Walimbe
,
V.
, 2000, “
Nonlinear Control of Surge and Stall in Axial Flow Compressor
,”
Proceedings of the 5th National Conference on Airbreathing Engines and Aerospace Propulsion (NCABE 2000)
, Hyderabad, India, December 21–23, pp.
102
110
.
9.
Humbert
,
J. S.
, and
Krener
,
A. J.
, 1998, “
Dynamics and Control of Entrained Greitzer Compressor Models
,”
Int. J. Control
0020-7179,
71
(
5
), pp.
807
821
.
10.
D’Andrea
,
R.
,
Behnken
,
R. L.
, and
Murray
,
R. M.
, 1997, “
Rotating Stall Control of an Axial Flow Compressor using Pulsed Air Injection
,”
ASME J. Turbomach.
0889-504X,
119
(
4
), pp.
742
752
.
11.
Protz
,
M.
, and
Paduano
,
J. D.
, 1997, “
Rotating Stall and Surge: Alternate Modeling and Control Concepts
,”
Proceedings of the 1997 International Conference on Control Application
, Hartford, CN, October 5–7, pp.
866
873
.
12.
Gravdahl
,
J. T.
, 1998, “
Modeling and Control of Surge and Rotating Stall in Compressors
,” Ph.D. thesis, Norwegian University of Science and Technology, Trondheim, Norway.
13.
Arnulfi
,
G. L.
,
Giannattasio
,
P.
,
Giusto
,
C.
,
Massardo
,
A. F.
,
Micheli
,
D.
, and
Pinamonti
,
P.
, 1998, “
Multistage Centrifugal Compressor Surge Analysis: Part II–Numerical Simulation and Dynamic Control Parameters Evaluation
,”
ASME J. Turbomach.
0889-504X,
121
, pp.
312
320
.
14.
Arnulfi
,
G. L.
,
Giannattasio
,
P.
,
Micheli
,
D.
, and
Pinamonti
,
P.
, 2001, “
An Innovative Device for Passive Control of Surge in Industrial Compression Systems
,”
ASME J. Turbomach.
0889-504X,
123
, pp.
473
482
.
15.
Li
,
M.
, and
Zheng
,
Q.
, 2004, “
Wet Compression System Stability Analysis. Part I–Wet Compression Moore Greitzer Transient Model
,” ASME Paper No. GT 2004-54018.
16.
Hale
,
A. A.
, and
Davis
,
M. W.
, 1992, “
DYNamic Turbine Engine Compressor Code DYNTECC–Theory and Capabilities
,” AIAA-92-3190,
Proceedings of 28th AIAA/SAE/ASME/ASEE Joint Propulsion Conference and Exhibit
, Nashville, TN, July 6–8.
17.
Owen
,
A. K.
,
Daugherty
,
A.
,
Garrard
,
D.
,
Reynolds
,
H. C.
, and
Wright
,
R. D.
, 1999, “
A Parametric Starting Study of an Axial-Centrifugal Gas Turbine Engine Using a One-Dimensional Dynamic Engine Model and Comparisons to Experimental Results: Part I–Model Development and Facility Description
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
121
, pp.
377
383
.
18.
Owen
,
A. K.
,
Daugherty
,
A.
,
Garrard
,
D.
,
Reynolds
,
H. C.
, and
Wright
,
R. D.
, 1999, “
A Parametric Starting Study of an Axial-Centrifugal Gas Turbine Engine Using a One-Dimensional Dynamic Engine Model and Comparisons to Experimental Results: Part II–Simulation Calibration and Trade-Off Study
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
121
, pp.
384
393
.
19.
Owen
,
A. K.
, and
Davis
,
M. W.
, Jr.
, 1994, “
Modeling The Dynamic Behavior of an Axial-Centrifugal Compression System
,” AIAA-94-2802,
Proceedings of 30th AIAA/ASME/SAE/ASEE Joint Propulsion Conference
, Indianapolis, IN, June 27–29.
20.
Cousins
,
W. T.
, 1996, “
The Dynamics of Stall and Surge Behavior in Axialcentrifugal Compressors
,” Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
21.
Theotokatos
,
G.
, and
Kyrtatos
,
N. P.
, 2003, “
Investigation of a Large High-Speed Diesel Engine Transient Behavior Including Compressor Surging and Emergency Shutdown
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
125
, pp.
580
589
.
22.
Theotokatos
,
G.
, and
Kyrtatos
,
N. P.
, 2001, “
Diesel Engine Transient Operation with Turbocharger Compressor Surging
,” SAE Paper No. 2001-01-1241.
23.
Schmitz
,
M. B.
, and
Fitzky
,
G.
, 2004, “
Surge Cycle of Turbochargers: Simulation and Comparison to Experiments
,” ASME Paper No. GT 2004-53036.
24.
Botha
,
B. W.
,
du Toit
,
B.
, and
Rousseau
,
P. G.
, 2003, “
Development of a Mathematical Compressor Model to Predict Surge in a Closed Loop Brayton Cycle
,” ASME Paper No. GT 2003-38795.
25.
Hahn
,
A.
, 2000, “
Modeling and control of Solid Oxide Fuel Cell–Gas Turbine Power Plant Systems
,” Ph.D. thesis, University of Pittsburgh, Pittsburgh, PA.
26.
Hildebrandt
,
A.
,
Genrup
,
M.
, and
Assadi
,
M.
, 2004, “
Steady-State and Transient Compressor Surge Behaviour Within a SOFC-GT-Hybrid System
,” ASME Paper No. GT 2004-53892.
27.
Botros
,
K. K.
,
Campbell
,
P. J.
, and
Mah
,
D. B.
, 1991, “
Dynamic Simulation of Compressor Station Operation Including Centrifugal Compressor and Gas Turbine
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
113
, pp.
300
311
.
28.
Botros
,
K. K.
, 1994, “
Transient Phenomena in Compressor Stations During Surge
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
116
, pp.
133
142
.
29.
Botros
,
K. K.
,
Jungowski
,
W. M.
, and
Richards
,
D. J.
, 1996, “
Compressor Station Recycle System Dynamics During Emergency Shutdown
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
118
, pp.
641
653
.
30.
Bakken
,
L. E.
,
Bjørge
,
T.
,
Bradley
,
T. M.
, and
Smith
,
N.
, 2002, “
Validation of Compressor Transient Behaviour
,” ASME Paper No. GT-2002-30279.
31.
Tveit
,
G. B.
,
Bjørge
,
T.
, and
Bakken
,
L. E.
, 2005, “
Impact of Compressor Protection System on Rundown Characteristics
,” ASME Paper No. GT 2005-68436.
32.
Ohanian
,
S.
, and
Kurz
,
R.
, 2001, “
Series or Parallel Arrangement in a Two-Unit Compression Station
,” ASME Paper No. 2001-GT-0230.
33.
Gravdahl
,
J. T.
, and
Egeland
,
O.
, 1997, “
A Moore-Greitzer Axial Compressor Model with Spool Dynamics
,”
Proceedings of the 36th IEEE Conference on Decision and Control
San Diego, CA, December 10–12, pp.
4714
4719
.
34.
Emmons
,
H. W.
,
Pearson
,
C. E.
, and
Grant
,
H. P.
, 1955, “
Compressor Surge and Stall Propagation
,”
Trans. ASME
0097-6822,
77
, pp.
455
469
.
35.
Koff
,
S. G.
, and
Greitzer
,
E. M.
, 1984, “
Stalled Flow Performance for Axial Compressors–I: Axisymmetric Characteristics
,” ASME Paper No. 84-GT-93.
36.
Greitzer
,
E. M.
, 1976, “
Surge and Rotating Stall in Axial Flow Compressor: Part 2, Experimental Results and Comparison with Theory
,”
ASME J. Eng. Power
0022-0825,
98
, pp.
199
211
.
37.
Toyama
,
K.
,
Runstadler
,
P. W.
, Jr.
, and
Dean
,
R. C.
, Jr.
, 1976, “
An Experimental Study of Surge in Centrifugal Compressors
,”
ASME J. Fluids Eng.
0098-2202,
99
, pp.
115
131
.
38.
Lawless
,
P. B.
,
Frey
,
K. K.
, and
Fleeter
,
S.
, 1997, “
Rotating Stall Spatial Domain Characterization in Axial and Centrifugal Compressors
,”
Turbomachinery Fluid Dynamics and Heat Transfer
,
Marcel Dekker
, New York, pp.
367
382
.
39.
Arnulfi
,
G. L.
,
Giannattasio
,
P.
,
Giusto
,
C.
,
Massardo
,
A. F.
,
Micheli
,
D.
, and
Pinamonti
,
P.
, 1998, “
Multistage Centrifugal Compressor Surge Analysis: Part I–Experimental Investigation
,”
ASME J. Turbomach.
0889-504X,
121
, pp.
305
311
.
40.
Hoss
,
B.
,
Leinhos
,
D.
, and
Fottner
,
L.
, 1998, “
Stall Inception in the Compressor System of a Turbofan Engine
,” ASME Paper No. 98-GT-475.
41.
Nurzia
,
F.
,
Palomba
,
C.
, and
Puddu
,
P.
, 2000, “
Experimental Investigation of Stall in a Two Stage Compressor
,” ASME Paper No. 2000-GT-0571.
42.
Skoch
,
G. J.
, 2003, “
Experimental Investigation of Centrifugal Compressor Stabilization Techniques
,”
J. Turbomach.
0889-504X
125
,
704
713
.
43.
Horodko
,
L.
, 2005, “
Investigation of Centrifugal Compressor Surge with Wavelet Methods
,”
Proceedings of 6th Conference on TURBOMACHINERY Fluid Dynamics and Thermodynamics
,
Lille
, France, March 7–11.
44.
Gravdahl
,
J. T.
, and
Egeland
,
O.
, 1999,
Compressor Surge and Rotating Stall Modeling and Control
,
Springer
, London.
45.
Tavakoli
,
S.
,
Griffin
,
I.
, and
Fleming
,
P.
, 2004, “
An Overview of Compressor Instabilities: Basic Concepts and Control
,”
Proceedings of the 16th IFAC International Symposium on Automatic Control in Aerospace
,
St. Petersburg
, Russia, June 14–18.
46.
Vachtsevanos
,
G.
,
Kang
,
H.
,
Cheng
,
J.
, and
Kim
,
I.
, 1992, “
Detection and Identification of Axial Flow Compressor Instabilities
,”
J. Guid. Control Dyn.
0731-5090,
15
, pp.
1216
1223
.
47.
Kurz
,
R.
, and
White
,
R. C.
, 2004, “
Surge avoidance in gas compression systems
,”
ASME J. Turbomach.
0889-504X,
126
, pp.
501
506
.
48.
Hansen
,
K. E.
,
Jorgensen
,
P.
, and
Larsen
,
P. S.
, 1981, “
Experimental and Theoretical Study of Surge in a Small Centrifugal Compressor
,”
ASME J. Fluids Eng.
0098-2202,
103
, pp.
391
394
.
49.
Niazi
,
S.
, 2000, “
Numerical Simulation of Rotating Stall and Surge Alleviation in Axial Compressors
,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
50.
Venturini
,
M.
, 2005, “
Development and Experimental Validation of a Compressor Dynamic Model
,”
ASME J. Turbomach.
0889-504X,
127
(
3
), pp.
599
608
.
51.
Batchelor
,
G. K.
, 1973,
An Introduction to Fluid Dynamics
,
Cambridge University Press
, Cambridge, UK.
52.
Backus
,
G.
, 1997,
Continuum Mechanics
,
Samizdat Press
, USA.
53.
Gong
,
Y.
, 1999, “
A Computational Model for Rotating Stall and Inlet Distortion in Multistage Compressors
,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
54.
Bettocchi
,
R.
,
Pinelli
,
M.
, and
Spina
,
P. R.
, 2005, “
A MultiStage Compressor Test Facility: Uncertainty Analysis and Preliminary Test Results
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
127
(
1
), pp.
170
177
.
55.
Fink
,
D. A.
, 1988, “
Surge Dynamics and Unsteady Flow Phenomena
,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
56.
Van Essen
,
H. A.
, and
de Lange
,
H. C.
, 2001, “
Nonlinear Model Predictive Control Experiments on a Laboratory Gas Turbine Installation
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
123
, pp.
347
352
.
57.
Šilhavý
,
M.
, 1997,
The Mechanics and Thermodynamics of Continuous Media
,
Springer
, Berlin, Germany.
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