A complete and compact control-oriented compressor model consisting of a mass flow submodel and an efficiency submodel is described. The final application of the model is a complete two-stroke mean value engine model (MVEM) which requires simulating the compressor operating at the low-flow and low-pressure ratio area. The model is based on previous research done for automotive-size compressors, and it is shown to be general enough to adapt well to the characteristics of the marine-size compressors. A physics-based efficiency model allows, together with the mass flow model, extrapolating to low-pressure ratios. The complexity of the model makes its parameterization a difficult task; hence, a method to efficiently estimate the 19 model parameters is proposed. The method computes analytic model gradients and uses them to minimize the orthogonal distances between the modeled speed lines (SpLs) and the measured points. The results of the parameter estimation are tested against nine different standard marine-size maps showing good agreement with the measured data. Furthermore, the results also show the importance of estimating the parameters of the mass flow and efficiency submodels at the same time to obtain an accurate model. The extrapolation capabilities to low-load regions are also tested using low-load measurements from an automotive-size compressor. It is shown that the model follows the measured efficiency trend down to low loads.

References

References
1.
IMO
,
2013
,
MARPOL: Annex VI and NTC 2008 With Guidelines for Implementation
,
International Maritime Organization
, London, UK.
2.
Hendricks
,
E.
,
1986
, “
A Compact, Comprehensive Model of Large Turbocharged, Two-Stroke Diesel Engines
,”
SAE
Technical Paper No. 861190.
3.
Jensen
,
J.-P.
,
Kristensen
,
A. F.
,
Sorenson
,
S. C.
,
Houbak
,
N.
, and
Hendricks
,
E.
,
1991
, “
Mean Value Modeling of a Small Turbocharged Diesel Engine
,”
SAE
Technical Paper No. 910070.
4.
Jung
,
M.
,
2003
, “
Mean-Value Modelling and Robust Control of the Airpath of a Turbocharged Diesel Engine
,” Ph.D. thesis, Sidney Sussex College, Department of Engineering, University of Cambridge, Cambridge, UK.
5.
Alegret
,
G.
,
Llamas
,
X.
,
Vejlgaard-Laursen
,
M.
, and
Eriksson
,
L.
,
2015
, “
Modeling of a Large Marine Two-Stroke Diesel Engine With Cylinder Bypass Valve and EGR System
,”
IFAC-PapersOnLine
,
48
(
16
), pp.
273
278
.
6.
Eriksson
,
L.
,
2007
, “
Modeling and Control of Turbocharged SI and DI Engines
,”
Oil Gas Sci. Technol.
,
62
(
4
), pp.
523
538
.
7.
Moraal
,
P.
, and
Kolmanovsky
,
I.
,
1999
, “
Turbocharger Modeling for Automotive Control Applications
,”
SAE
Technical Paper No. 1999-01-0908.
8.
Theotokatos
,
G.
,
2010
, “
On the Cycle Mean Value Modelling of a Large Two-Stroke Marine Diesel Engine
,”
Proc. Inst. Mech. Eng., Part M
,
224
(
3
), pp.
193
206
.
9.
Karlsen
,
A. T.
,
2012
, “
On Modeling of a Ship Propulsion System for Control Purposes
,”
Master's thesis
, NTNU, Trondheim, Norway.
10.
Hansen
,
J. M.
,
Zander
,
C.-G.
,
Pedersen
,
N.
,
Blanke
,
M.
, and
Vejlgaard-Laursen
,
M.
,
2013
, “
Modelling for Control of Exhaust Gas Recirculation on Large Diesel Engines
,” 9th
IFAC
Conference on Control Applications in Marine Systems
, Osaka, Japan, Sept. 17–20, pp.
380
385
.
11.
Guan
,
C.
,
Theotokatos
,
G.
,
Zhou
,
P.
, and
Chen
,
H.
,
2014
, “
Computational Investigation of a Large Containership Propulsion Engine Operation at Slow Steaming Conditions
,”
Appl. Energy
,
130
, pp.
370
383
.
12.
Tsoutsanis
,
E.
,
Meskin
,
N.
,
Benammar
,
M.
, and
Khorasani
,
K.
,
2015
, “
Transient Gas Turbine Performance Diagnostics Through Nonlinear Adaptation of Compressor and Turbine Maps
,”
ASME J. Eng. Gas Turbines Power
,
137
(
9
), p.
091201
.
13.
Watson
,
N.
, and
Janota
,
M.
,
1982
,
Turbocharging the Internal Combustion Engine
,
MacMillan
,
London
.
14.
SAE
,
1995
, “
Turbocharger Nomenclature and Terminology
,” SAE International, Warrendale, PA, Standard No.
SAE
J922_199506.
15.
Leufvén
,
O.
, and
Eriksson
,
L.
,
2016
, “
Measurement, Analysis and Modeling of Centrifugal Compressor Flow for Low Pressure Ratios
,”
Int. J. Engine Res.
,
17
(2), pp. 153–169.
16.
Leufvén
,
O.
, and
Eriksson
,
L.
,
2013
, “
A Surge and Choke Capable Compressor Flow Model—Validation and Extrapolation Capability
,”
Control Eng. Pract.
,
21
(
12
), pp.
1871
1883
.
17.
Martin
,
G.
,
Talon
,
V.
,
Higelin
,
P.
,
Charlet
,
A.
, and
Caillol
,
C.
,
2009
, “
Implementing Turbomachinery Physics Into Data Map-Based Turbocharger Models
,”
SAE Int. J. Engines
,
2
(
1
), pp.
211
229
.
18.
Sorenson
,
S. C.
,
Hendricks
,
E.
,
Magnusson
,
S.
, and
Bertelsen
,
A.
,
2005
, “
Compact and Accurate Turbocharger Modelling for Engine Control
,”
SAE
Technical Paper No. 2005-01-1942.
19.
El Hadef
,
J.
,
Colin
,
G.
,
Chamaillard
, and
Talon
,
Y. V.
,
2012
, “
Physical Based Algorithms for Interpolation and Extrapolation of Turbocharger Data Maps
,”
SAE Int. J. Engines
,
5
(
2
), pp.
363
378
.
20.
Casey
,
M.
, and
Schlegel
,
M.
,
2009
, “
Estimation of the Performance of Turbocharger Compressors at Extremely Low Pressure Ratios
,”
Proc. Inst. Mech. Eng., Part A
,
224
(
2
), pp.
239
250
.
21.
Casey
,
M.
, and
Robinson
,
C.
,
2012
, “
A Method to Estimate the Performance Map of a Centrifugal Compressor Stage
,”
ASME J. Turbomach.
,
135
(
2
), p.
021034
.
22.
Casey
,
M.
, and
Rusch
,
D.
,
2014
, “
The Matching of a Vaned Diffuser With a Radial Compressor Impeller and Its Effect on the Stage Performance
,”
ASME J. Turbomach.
,
136
(
12
), p.
121004
.
23.
Eriksson
,
L.
, and
Nielsen
,
L.
,
2014
,
Modeling and Control of Engines and Drivelines
,
Wiley
, Hoboken, NJ.
24.
Dixon
,
S. L.
, and
Hall
,
C. A.
,
2013
,
Fluid Mechanics and Thermodynamics of Turbomachinery
,
7th ed.
,
Butterworth-Heinemann
, Oxford, UK.
25.
Nocedal
,
J.
, and
Wright
,
S. J.
,
2006
,
Numerical Optimization
,
2nd ed.
,
Springer
, New York.
26.
Gander
,
W.
,
Golub
,
G. H.
, and
Strebel
,
R.
,
1994
, “
Least-Squares Fitting of Circles and Ellipses
,”
BIT
,
34
(
4
), pp.
558
578
.
27.
Ahn
,
S. J.
,
Rauh
,
W.
, and
Warnecke
,
H.-J.
,
2001
, “
Least-Squares Orthogonal Distances Fitting of Circle, Sphere, Ellipse, Hyperbola, and Parabola
,”
Pattern Recognit.
,
34
(
12
), pp.
2283
2303
.
28.
Boggs
,
P. T.
,
H-Byrd
,
R.
, and
Schnabel
,
R. B.
,
1987
, “
A Stable and Efficient Algorithm for Nonlinear Orthogonal Distance Regression
,”
SIAM J. Sci. Stat. Comput.
,
8
(
6
), pp.
1052
1078
.
You do not currently have access to this content.