Steady-state simulation is an important method to investigate thermodynamic processes. This is especially true for innovative micro gas turbine (MGT)-based cycles as the complexity of such systems grows. Therefore, steady-state simulation tools are required that ensure large flexibility and computation robustness. As the increased system complexity result often in more extensive parameter studies also a fast computation speed is required. While a number of steady-state simulation tools for MGT-based systems are described and applied in literature, the solving process of such tools is rarely explained. However, this solving process is crucial to achieve a robust and fast computation within a physically meaningful range. Therefore, a new solver routine for a steady-state simulation tool developed at the DLR Institute of Combustion Technology is presented in detail in this paper. The solver routine is based on Broyden's method. It considers boundaries during the solving process to maintain a physically and technically meaningful solution process. Supplementary methods are implemented and described which improve the computation robustness and speed. Furthermore, some features of the resulting steady-state simulation tool are presented. Exemplary applications of a hybrid power plant (HyPP), an inverted Brayton cycle (IBC), and an aircraft auxiliary power unit (APU) show the capabilities of the presented solver routine and the steady-state simulation tool. It is shown that the new solver routine is superior to the standard Simulink algebraic solver in terms of system evaluation and robustness for the given applications.

References

1.
Henke
,
M.
,
Monz
,
T.
, and
Aigner
,
M.
,
2013
, “
Inverted Brayton Cycle With Exhaust Gas Recirculation—A Numerical Investigation
,”
ASME J. Eng. Gas Turbines Power
,
135
(
9
), p.
091203
.
2.
Agelidou
,
E.
,
Henke
,
M.
,
Monz
,
T.
, and
Aigner
,
M.
,
2018
, “
Numerical Investigation of an Inverted Brayton Cycle Micro Gas Turbine for CHP Application Based on Experimental Data
,”
ASME
Paper No. GT2018-76377
.
3.
Panne
,
T.
,
Widenhorn
,
A.
,
Boyde
,
J.
,
Matha
,
D.
,
Abel
,
V.
, and
Aigner
,
M.
,
2007
, “
Thermodynamic Process Analyses of SOFC/GT Hybrid Systems
,”
AIAA
Paper No. AIAA 2007-4833
.
4.
Calise
,
F.
,
Palombo
,
A.
, and
Vanoli
,
L.
,
2006
, “
Design and Partial Load Exergy Analysis of Hybrid SOFC–GT Power Plant
,”
J. Power Sources
,
158
(
1
), pp.
225
244
.
5.
Steilen
,
M.
,
Salettia
,
C.
,
Heddrich
,
M. P.
, and
Friedrich
,
K. A.
,
2018
, “
Analysis of the in Influence of Heat Transfer on the Stationary Operation and Performance of a Solid Oxide Fuel Cell/Gas Turbine Hybrid Power Plant
,”
Appl. Energy
,
211
, pp.
479
491
.
6.
Traverso
,
A.
,
2005
, “
Transeo Code for the Dynamic Performance Simulation of Micro Gas Turbine Cycles
,”
ASME
Paper No. GT2005-68101
.
7.
Traverso
,
A.
,
Massardo
,
A. F.
, and
Scarpellini
,
R.
,
2006
, “
Externally Fired Micro-Gas Turbine: Modelling and Experimental Performance
,”
Appl. Therm. Eng.
,
26
(
16
), pp.
1935
1941
.
8.
Visser
,
W.
,
2015
, “
Generic Analysis Methods for Gas Turbine Engine Performance: The Development of the Gas Turbine Simulation Program GSP
,”
Ph.D. thesis
, TU Delft, Delft, The Netherlands.https://repository.tudelft.nl/islandora/object/uuid%3Af95da308-e7ef-47de-abf2-aedbfa30cf63
9.
Schefflan
,
R.
,
2011
,
Teach Yourself the Basics of Aspen Plus
,
Wiley
,
Hoboken, NJ
.
10.
Klein
,
S.
,
2009
,
EES—Engineering Equation Solver for Microsoft Windows Operating Systems
,
Manual. F-Chart Software
,
Madison, WI
.
11.
Martínez
,
J. M.
,
2000
, “
Practical Quasi-Newton Methods for Solving Nonlinear Systems
,”
J. Comput. Appl. Math.
,
124
(
1–2
), pp.
97
121
.
12.
Barnes
,
J. G. P.
,
1965
, “
An Algorithm for Solving Non-Linear Equations Based on the Secant Method
,”
Comput. J.
,
8
(
1
), pp.
66
72
.
13.
Kosmol
,
P.
,
1993
,
Methoden Zur Numerischen Behandlung Nichtlinearer Gleichungen Und Optimierungsaufgaben
,
B. G. Teubner
,
Stuttgart, Germany
.
14.
Broyden
,
C. G.
,
1965
, “
A Class of Methods for Solving Nonlinear Simultaneous Equations
,”
Math. Computation
,
19
(
92
), pp.
577
593
.
15.
Nocedal
,
J.
, and
Wright
,
S. J.
,
2006
,
Numerical Optimization
, 2nd ed.,
Springer
,
New York
.
16.
Brent
,
R. P.
,
1973
,
Algorithms for Minimization Without Derivatives
,
Prentice Hall
,
Englewood Cliffs, NJ
.
17.
Henke
,
M.
,
Klempp
,
N.
,
Hohloch
,
M.
,
Monz
,
T.
, and
Aigner
,
M.
,
2015
, “
Validation of a T100 Micro Gas Turbine Steady-State Simulation Tool
,”
ASME
Paper No. GT2015-42090
.
18.
Goos
,
E.
,
Burcat
,
A.
, and
Ruscic
,
B.
,
2010
, “
Extended Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion With Updates From Active Thermochemical Tables
,” German Aerospace Center, Institute of Combustion Technology, Stuttgart, Germany, accessed Aug. 2, 2018, https://www.dlr.de/vt/en/desktopdefault.aspx/tabid-7603/12862_read-32379/
19.
Kleiber
,
M.
,
Joh
,
R.
, and
Span
,
R.
, 2013, “
Properties of Pure Fluid Substances
,”
VDI Heat Atlas
, Springer, Berlin, pp.
301
418
.
20.
Stephan
,
P.
,
Kabelac
,
S.
,
Kind
,
M.
,
Martin
,
H.
,
Mewes
,
D.
, and
Schaber
,
K.
, eds.,
2010
,
VDI Heat Atlas
,
Springer
,
Berlin
.
21.
Gnielinski
,
V.
, 2010, “
Heat Transfer in Pipe Flow
,”
VDI Heat Atlas
, Springer, Berlin, pp.
691
700
.
22.
The MathWorks,
2017
, “
Algebraic Loops—How the Algebraic Loop Solver Works
,” The MathWorks, Natick, MA, accessed Jan. 26, 2018, https://mathworks.com/help/simulink/ug/algebraic-loops.html#bsn46y8-2
23.
Moré
,
J. J.
, and
Garbow
,
B. S.
, and
Hillstrom
,
K. E.
,
1980
, “
User Guide for Minpack-1
,” Argonne National Laboratory, Lemont, IL, Report No. ANL-80-74.
24.
Powell
,
M. J. D.
, 1970, “
A Hybrid Method for Nonlinear Equations
,”
Numerical Methods for Nonlinear Algebraic Equations: A Conference Held at the University of Essex on January 6 and 7, 1969
, Gordon & Breach, London, pp.
87
114
.
25.
Powell
,
M. J. D.
, 1970, “
A Fortran Subroutine Solving Systems of Nonlinear Algebraic Equations
,”
Numerical Methods for Nonlinear Algebraic Equations: A Conference Held at the University of Essex on January 6 and 7, 1969
, Gordon & Breach, London, pp.
115
161
.
26.
Rabinowitz
,
P
., ed.,
1970
,
Numerical Methods for Nonlinear Algebraic Equations: A Conference Held at the University of Essex on January 6 and 7, 1969
, Gordon & Breach, London.
27.
The MathWorks,
2017
, “
Bench—Matlab Benchmark
,” The MathWorks, Natick, MA, accessed Aug. 3, 2018, https://mathworks.com/help/matlab/ref/bench.html
28.
Agelidou
,
E.
,
Monz
,
T.
,
Huber
,
A.
, and
Aigner
,
M.
,
2017
, “
Experimental Investigation of an Inverted Brayton Cycle Micro Gas Turbine for CHP Application
,”
ASME
Paper No. GT2017-64490
.
29.
Zanger
,
J.
,
Krummrein
,
T.
,
Siebel
,
T.
, and
Roth
,
J.
,
2018
, “
Characterization of an Aircraft Auxiliary Power Unit Test Rig for Cycle Optimization Studies
,”
ASME
Paper No. GT2018-76377
.
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