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THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 90-GT-270345 E. 47
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Printed-in USA.
Generalized High Speed Simulation ofGas Turbine Engines
NANAHISA SUGIYAMAAero-Engine Division
National Aerospace LaboratoryChofu, Tokyo, Japan
ABSTRACTThis paper describes a real-time or
faster-than-real-time simu-lation of gas turbine engines, using an
ultra high speed, multi-processor digital computer, designated the
AD100. It is shownthat the frame time is reduced significantly
without any lossof fidelity of a simulation. The simulation program
is aimed ata high degree of flexibility to allow changes in engine
configu-ration. This makes it possible to simulate various types of
gasturbine engines, including jet engines, gas turbines for
vehiclesand power plants, in real-time. Some simulation results for
anintercooled-reheat type industrial gas turbine are shown.
INTRODUCTIONModern gas turbine engines are becoming more and
morecomplex in engine cycles and geometries, for higher
perfor-mance and multi-mission requirements. This has resulted ina
trend toward a variable geometry or a variable cycle engine,which
has numerous variable geometry features, such as vari-able nozzle
and variable stator vane, to obtain the optimumperformance over a
wide range of operating conditions. Cor-respondingly, the
requirements for engine control systems arebecoming more and more
severe due to the complexity of thestatic and dynamic behavior of
such an engine.
Real-time simulation of a gas turbine engine plays an im-portant
role in developing control systems. It is useful in de-sign,
evaluation and testing of the systems, and also is help-ful in good
technological understanding of complicated engineperformance. In
addition, since the representative simulationcan predict engine
performance, especially dynamic charac-teristics, over the whole
range of operating conditions at thedesign phase of an engine
development program, it providesan effective tool to develop an
engine itself.
All-digital simulation is generally preferred because of the
precision of computation, flexibility, repeatability and
oper-ation with a stored program. In a gas turbine simulation,the
major part of computation is the generation of nonlin-ear
multivariable functions. All digital computation is bestsuited to
this function generation task. To realize real-timesimulation using
the digital computer, the frame time of dig-ital computation must
be short enough to maintain dynamicaccuracy. Increasing complexity
of functional relations, asnoted above, causes the frame time to be
long. Conversely,increasing importance of engine dynamics at high
frequenciesrequires shorter frame times. Because of these facts,
ultra highspeed computation is needed for real-time digital
simulationof modern gas turbine engines. Due to the current
remarkableprogress in digital hardware, this short frame time
becomespossible, even for a detailed engine model.
This paper describes a hardware and software method torealize
real-time or faster-than-real-time simulation of gas tur-bine
engines, using an ultra high speed, multi-processor
digitalcomputer, designated the AD100, which is designed
specifi-cally for high-speed simulation of continuous dynamic
systems.It is shown that the frame time is reduced significantly
with-out any loss of fidelity of a simulation. The simulation
pro-gram is aimed at a high degree of flexibility to allow
changesin engine configuration. This makes it possible to
simulatevarious types of gas turbine engines, including jet
engines, gasturbines for vehicles and power plants, in real-time.
Some sim-ulation results for an intercooled-reheat industrial gas
turbineare shown.
REQUIREMENTS FOR GAS TUR-BINE SIMULATIONThere are a number of
requirements for gas turbine enginesimulation. First of all, the
simulation must represent ac-curately the static and dynamic
performance of an engine
'Presented at the Gas Turbine and Aeroengine Congress and
ExpositionJune 11-14, 1990Brussels, Belgium
Copyright 1990 by ASME
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over the whole range of operating conditions, in order toserve
as a realistic model. Thus there is a need for a wide-range,
detailed mathematical model and an accurate comput-ing method.
Highly detailed engine simulations have beendeveloped and
implemented using a large scale digital com-puter (Sellers and
Daniele, 1975, Fishbach and Caddy, 1975,Palmer and Yan, 1982,
Fishbach and Gordon, 1988) and ahybrid computer (Szuch, 1974a). The
validity of such simu-lations have been examined by comparing
results with actualengine data. However, these simulations could
not satisfy therequirement of real-time operation and were used for
detailedstudy of steady state and transient performance on an
off-linebasis.
In the case of simulations involving interaction with
actualsystems, such as the engine controller, real-time operation
isan essential requirement. This has been accomplished with
thehybrid computer for particular engines (Szuch et al.,
1974b,1975) and, currently, ultra high speed digital computers
havebecome available for this purpose. A major problem encoun-tered
in gas turbine simulation is to generate a large number ofnonlinear
multivariable functions required to describe enginecomponent
performances and properties of gas. All digitalcomputation, due to
its accuracy and reliability, is best suitedto this function
generation task and, hence, the frame timeof digital computation is
a limiting factor for real-time opera-tion. Since the frequency
range of interest in control problemis approximately 0-30 [Hz], the
frame time should be around1 [msec] for real-time operation
(Gilbert, 1966).
For realistic interaction with the real world external to
thesimulator, an interface which provides suitable signals
becomesnecessary. This can provide a facility for connection with
ac-tual system hardware as well as monitoring devices such as
agraphical display, which is helpful in gaining intuitive
insightinto complicated engine dynamics. This interface is
furnishedby A/D and D/A converters in the digital simulation.
Usually, modeling methods are more or less based on
enginecomponent performance and associated conservation equa-tions.
Component performance data can be obtained from de-sign studies or
estimates from existing engines, prior to enginehardware
availability; the data is then updated when compo-nent test and
engine test data become available. Therefore,updates in engine data
should be easily made without disturb-ing the entire simulation.
The fact that the simulation can pre-dict engine performance based
on design data or componenttest data suggests usefulness of the
simulation in developmentof the engine.
Finally, it is desirable that the simulation method be
appli-cable to a wide variety of gas turbine engines to reduce
effec-tively the man-hours for development of the simulation.
Sincemost engines consist of several common components and canbe
modeled by proper interconnection of these components,a systematic
procedure in a block diagram form is possible,where each block
corresponds to one type of engine compo-nent. Simulation of a
particular engine, then, is realized byconnecting these common
components. The purpose of thiswork is to develop the simulation
method which satisfies theabove requirements.
COMPUTATIONAL MODULES
AD100 and ADSIMFig.1 shows the basic architecture of the AD100.
Five func-
tional processors, i.e., communication and control
processor(COM), arithmetic and logic processor (ALU), multiplier
pro-cessor (MUL), storage processor (STO), and function memoryunit
-(FMU) are interfaced to the PLUSBUS, which transferdata to and
from the memory unit and the processors usinga 25 [nsec] bus cycle
time. A large number of A/D and D/Achannels are controlled by COM
processor and are used to con-nect the simulator with external
actual hardware. To accom-plish the required computational tasks,
the functional proces-sors operate in parallel and execute
instructions in a 100 [nsec]period synchronized to the bus cycle.
The high data rate onthe PLUSBUS, high speed of the processors,
parallelism andpipelining of the computation, and arithmetic
ability suited tofunction generation and numerical integration, all
contributeto high speed simulation. Especially, computational
efficiencyfor function generation is remarkable. Execution times
for 1,2, 3, and 4 variable function generation are 0.5, 0.9, 1.7
and3.6 [sec], respectively. Since 80% of computational burdenin gas
turbine simulation is multivariable function generation,this
feature is highly effective to realize real-time or
faster-than-real-time simulation.
In the AD100 system, variables and constants are repre-sented by
65-bit floating point numbers, comprised of a 12-bitexponent and a
52-bit significant fraction. Hence the computa-tional precision is
comparable to double precision arithmetic ina general purpose
digital computer. This bit length is enoughto avoid round-off
problems in summing up the derivative termin numerical integration
for a stiff system (Gilbert and Howe,1978).
ADSIM is a FORTRAN-like simulation language for theAD100 system
and its source code is very close to mathemat-ical equations. The
user can use high-speed computational,data logging and I/O
capabilities through the ADSIM lan-guage without knowledge of the
hardware. A generalized gasturbine simulation program developed
here is written by theADSIM language. In coding the many
calculations needed insimulation, the traditional approach uses a
series of additionand multiplication with minimum memory storage.
However,the function generation approach is more efficient with
avail-ability of large, low cost, high-speed memories (Gilbert
andHowe, 1977). For example, the calculation of flow function
to A/D and D/A to Host Computer
Fig.1 Architecture of the AD100
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COMP (compressor module)1. inlet temp. Ti 1. air flow rate W2.
inlet pressure Pi 2. outlet enthalpy ho3. inlet fuel/air fz 3.
outlet fuel/air fo
z 4. inlet steam/air xi 4. outlet steam/air xo5. outlet pressure
Po 5. compressor power P,6. rotor speed N7. stator angle a1. inlet
relative pressure Pr; = Grt (Ti, f;, xi)2. inlet enthalpy hi =
Ght(Ti, fi.x;)3. corrected inlet temp. 0 = TZ/T,4.corrected inlet
pressure 6 = Pi/P,
.3 5. corrected rotor speed N* = N/f
0 6. presure ratio 7r = Po/PicL, 7. outlet relative pressure Pro
= 7rPrt
8. corrected air flow rate W* = Fj c (lr, N*, a c )0 9.
adiabatic efficiency t7 = Fec (7r, N*, ac )
10. isentropic enthalpy hso = Ghr (Pro, fi, Xi)11. enthalpy rise
Oh = (h, o -12. outlet enthalpy ho = h; + Oh13. air flow rate W
=W*6/f14. compressor power PP = WOh15. outlet fuel/air ratio fo =
fi16. outlet steam/air ratio xo = xi
V a ^PiT{z
PWhjo
V fi J O`'' xt N xoP^
Fig.2(a) Compressor Module
through a nozzle;
Gwn = 7r7 (1 - it I )
(1)7-1is efficiently evaluated by considering it as a two
variable func-tion of 7r and ry, storing the appropriate table, and
using func-tion generation.
Computational Modules for Engine ComponentsAlthough there exist
various types of gas turbine engines
according to their missions, all such engines consist of a
rela-tively small number of basic components. A simulation modelof
a complete engine can be obtained by tying together sev-eral
sub-models of these basic components. Such componentsare:(1)
compressor, for compressor and fan,
(2)turbine, for high- and low-pressure turbine,(3) duct, for
connecting duct,
(4) bleed, for air bleed from compressor and turbine coolingair
bleed,
(5) combustor, for main-combustor and reheat-combustor,
(6) intercooler, for water injection intercooler,
TURB (turbine module)1. inlet temp. Tti 1. gas flow rate W2.
inlet pressure Pi 2. outlet enthalpy h03. inlet fuel/air fz 3.
outlet fuel/air fo4. inlet steam/air xi 4. outlet steam/air x0
Z3 5. outlet pressure PO 5. turbine power Pt6. rotor speed N 07.
stator angle at8. cooling air flow W19. coefficient 13cI1. inlet
relative pressure Pr; = Grt(Ti, fl, xi)2. inlet enthalpy h =
Ght(T1, fz.xti)3. corrected inlet temp. 0 = TtilT,,4. corrected
inlet pressure 6 = PP/P,5. corrected rotor speed N* = N/\/6.
presure ratio Ir = Pt/Po7. outlet relative pressure Pro =
Pri/7r
r3 8. rrrrected gas flow rate W* = Fj t (7r, N*, at )9.
adiabatic efficiency = Fet (x, N*, at )10. isentropic enthalpyP PY
h = G f x )eo hr (P roe z^ z
Q. 11. enthalpy drop Oh = (hi - h, 0 )7712. outlet enthalpy ho =
hti - Oh13. gas flow rate W = W*b/\14. turbine power Pt = Oh(W +
/31W1)15. outlet fuel/air ratio fo = fti16. outlet steam/air ratio
xo = xi
N
atPP;WTi ho{tT " XOf^ ox^ N
Pt 147c1, /'cl
Fig.2(b) Turbine Module
(7) nozzle, for main and bypass nozzle,
(8)inlet, for air inlet,(9) volume, for intercomponent volume,
and
(10) rotor, for high- and low-pressure rotor.
Mathematical models, computational procedures andschematic
diagrams for four representative components, i.e.,(1) compressor,
(2) turbine, (9) volume and (10) rotor mod-ule, are shown in
Fig.2(a)-(d). Mathematical models adoptedhere are highly detailed
models and include no simplificationsto reduce computing time and
memory storage. Descriptionsfor the rest of the components are
omitted due to limitationsof space.
Components (1) to (8) are static elements and are mod-eled as
lumped parameter systems represented by performancemaps, constant
coefficients, and thermo- and aero-dynamicrelations. Compressor and
turbine performance maps aretreated as 3-variable functions to take
into account the ef-fect of such variable geometry features as the
variable inletguide vane, variable stator vane, variable fan pitch
and vari-able turbine areas. Also nozzle area and bleed valve area
can
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VOL (volume module)1. incoming flow-1 Wit 1. temperature T2.
enthalpy-1 hil 2. pressure P3. fuel/air-1 fir 3. fuel/air ff4.
steam/air-1 xi1 ^. 4. steam/air x5. incoming flow-2 Wi2 5.
rel.humidity b6. enthalpy-2 hi27. fuel/air-2 fi28. steam/air-2 Xi2
1. temperature Tv i9. outgoing flow-1 Wo l v 2. pressure Pi10.
outgoing flow-2 W0211. outgoing flow-3 W0312. outgoing flow-4
Woo13. volume V1. incoming gas flow Wi n, = Wi i + Wi22. outgoing
gas flow Wout = Wol + W02 + Wm + W043. air/gas ratio-1 gl = 1/(1+
fil + xi1)4. air/gas ratio-2 g2 = 1/(1 + fie + xi2)5. amount of
fuel F = Wiifii9i + Wi2fi2926. amount of steam X = Wi1xii91
+Wi2xi2927. amount of air A = Wi n - F - X
2 8. fuel/air ratio f = F/A9. steam/air ratio x, = X/A10.
enthalpy h = Ght (T0 , f0 ,x)11. relative humidity c = Grx (Tv ,
P,,, x)12.gas constant R = Gr (fv ,x)13. stored mass r (minit = P=v
V/Ti v /G(0i r , 0))
m = ,l (Win - Wout ) dt14. stored energy (ut = Gut(Ti3O))
u = ( 1 /m) f(Wtithh). +Wfi2hi2 - Wosi.thv)dt15. temperature TT
= Gtu (u, f,,, x)16. pressure P = mRTv /V
Wi lif
i lT r WoiPv I_
xil fv '^Wo2I VWi2
xv' Wo3
hiefit
l v) -- - o4
xiz
Fig.2(c) Volume Module
be treated as independent variables (or constants) to makethese
controllable.
Components (9) and (10) are dynamic elements. Rotordynamics,
which is a ruling factor in transient behavior ofan engine, is
represented by the equation of conservation ofangular momentum.
Volume dynamics is represented by theequations of conservation of
mass and energy. Pressure andtemperature are assumed to be uniform
throughout each vol-ume. Volumes are introduced between successive
engine staticcomponents where a volume capacitive effect is
considered tobe important, or where it is desirable to avoid
iterative computation.
Fig.3 shows inputs and outputs for the computational mod-
ROTOR (rotor module)1. compressor power-1 PP1 1. rotor speed N2.
compressor power-2 PP23. compressor power-3 P, 3 a4. compressor
power-4 Pc45. turbine power-1 PtI6. turbine power-2 Pt2 1. rotor
speed Ni7. turbine power-3 Pt38. turbine power-4 Pt49. moment of
inertia I10. mechanical eff. s7/2
ti
1. excess power Q - (Ptl i- Pt2 1- Pt3 -f Pt4
O -- Pc 1 - 'c2 - Pc3 - Pc4) 71m
GL 2. rotational speed N = (60/2sr) 2 (1/I) (Q/N)dt
,.y Pcl Pct Pc3 Pc4 Ptl Pt2 Pt3 Pt4N
I ' Y1m
Fig.2(d) Rotor Module
ules. For gas path components, i.e., (1) to (9), the variableson
the left side of each block are variables to and from theupper
stream component, and the variables on the right sideare to and
from the down stream component. Also the vari-ables on the top of
each block are to and from rotor dynam-ics and the variables on the
bottom are control variables andconstants specific to the
component. It should be noted thatthere is a uniformity in input
and output variables throughoutthe static modules, (1) to (7), and
that the dynamic modules,(9) and (10), can be easily connected to
the static modules.'Note that each computational module assumes the
maximumpossible number of input variables to allow for the
maximumcapability of the module. If some of these inputs do not
existor are not necessary to consider, they should be set to zeroor
to a constant value. This structure of the computationalmodules can
permit a wide variety of interconnection of themodules and, hence,
can be applied to various types of engines.
Argument data required to perform necessary computa-tions in a
module consists of (i) input variables, (ii) constants,and (iii)
data tables for multivariable function generation.Computational
results from a module include not only enginevariables which are
used for input variables to other compu-tational modules, but also
variables which are useful for mon-itoring and recording of
simulation results (ref. Fig.2). Ac-cording to the mathematical
models and the computationalprocedures, each component of (1) to
(10) is coded in theADSIM language in the form of a computational
module, orsubroutine.
Execution TimeFig.4 shows the execution time for each
computational
module, measured by running the program on the AD100. Fora.
specific gas turbine engine simulation, the main program is
'Although the inlet module, (8), is static, it is connected to
the staticmodules exceptionally.
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PP N
Pi'J(1) 4P0
Xs COMP rX0xi xo
h,a,
rPi-(2 ) ^PoY
TURBx^ X"
ho
(Q, Wei) a t
Pi - (3) - Po ' (4) F',1, Puz; 1 ,,3Ti Ti
xt DUCT xo xi i5I,i:'F,l; x.
a o
W W W1, W2, W3 W1, W2,{'1'3h h,
(R
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P = 0.4769 5.5319 5.3387 1.3415 0.8867 0.8646 0.1052 0.1013
0.1003 0.4867 MPaT = 77.6 459.5 1300.0 836.8 735.0 1171.0 609.4
15.0 15.0 198.7 C
AirHP Main HP
IP Reheat LP Exhaust Intake LP LoadComp. Comb. Turb. Turb. Comb.
Turb. Duct Duct Comp. 122MW
8850 pm 3000rpmcoo-:ng_air
---"---- G = 233kg/s G = 220kg/sW fL = 4.38kg/s Wf,. =
2.95kg/s
Ww i = 10.44kg/s
Inter-Cooler
Fig.6 Configuration of Intcrcooled-Reheat Type Industrial Gas
Turbine
time does not exceed the limit needed to maintain the
desireddynamic accuracy, it is possible to simulate several engines
si-inultaneously. This capability may be useful for the study ofthe
multi-engine balancing problem, where the performance ofengines is
not identical.
SIMULATION OF INTERCOOLED-REHEAT TYPE INDUSTRIAL GASTURBINETo
illustrate the capability of the simulation program,
anintercooled-reheat type industrial gas turbine engine is
con-sidered here, because it has a very complicated
configurationand it makes full use of the capability of the program
devel-oped here. Engine component performance data and someoverall
performance data for this engine is available.
Engine ConfigurationFig.6 shows the schematical configuration
and heat balance
of intercooled-reheat type industrial gas turbine (Takeya
andOhteki, 1983 and 1984). HP compressor and HP turbine areon one
shaft, while LP compressor and IP/LP turbines are onthe other shaft
driving 120MW class electric power generator.LP compressor is a
10-stage axial compressor with variablestator vane to control air
flow rate. Intercooler is a waterinjection type cooler to cool down
the air from the LP com-pressor outlet. This contributes to reduce
the HP compressordriving power and NOx level in exhaust gas. HP
compressoris a 14-stage axial compressor with variable inlet guide
vane.For turbine cooling, rotor balancing and starting bleed,
airbleed ports are located at 6th, 8th, 11th and 14th stage of
HPcompressor. The main combustor is a cannular type combus-tor
burning LNG. Gas condition at combustor outlet reaches1573K (1300C)
and 5.5Mpa at the 120MW rated load. TheHP and IP turbines are
2-stage axial turbines with air cooledblades. The reheat combustor
is a cannular type and reheatsthe gas to 1473K (1200C). This
contributes to increasing thepower output of the 4-stage axial LP
turbine. The reheat
and intercooling processes are very effective in increasing
thethermal efficiency of the engine. The gas temperature at
theexhaust duct is 882K (609C), which is relatively high
consid-ering a bottoming cycle. The thermal efficiency of the
gasturbine obtained by experiments is 34% at 93MW load. Thethermal
efficiency of a combined cycle with a steam turbine asa bottomig
cycle is estimated at more than 50%.
ModelingSince the LP and HP compressors can be modeled by
the
compressor module, the HP, IP and LP turbines by the
turbinemodule, the main- and reheat-combustors by the
combustormodule, intercomponent volumes by the volume module,
etc.,the schematic configuration in Fig.6 can be diagrammed asshown
in Fig.7. This is accomplished by simply replacing theengine
components with the computational modules and in-troducing the
volume module between the static engine com-ponents. Note that the
HP compressor is divided into fourcompressors in order to take into
account the interstage airbleed effect. There exists eight major
control variables, con-stituting a multi-variable control system.
The total number ofusages of each module, summarized in Fig.7, is
almost twiceas many as the jet engine case in Fig.5.
Referring to Fig.7, the simulation program is easily ob-tained
by just calling computational modules sequentially fromengine
entrance to exhaust. To avoid complication of symbolsfor a large
number of variables, self-evident and systematic as-signment of
symbols is desirable. For example, the symbols areconstructed from
the letter(s) indicating some physical mean-ing and the number(s)
defining engine station numbers or en-gine components.
Component Performance Data and Gas TablesNext, the function data
for component performance map
must be set up. ADSIM accepts a rectangular grid data ta-ble
form for function generation. Usually, component per-formance data
are given in this form and, hence, the codingis straightforward.
The radial interpolation method (Szuch,1974a), or skewed grid
interpolation method, is widely usedfor function generation of
compressor performance to improve
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HP Compressor Main Combustor Reheat Combustor LP
CompressorStator Angle Fuel Flow Fuel Flow Stator Angle
Bleed Valve-1 Area Bleed Valve-2 Area Intercooler
O : Control Variables Water Flow
Computational Module No. of UsageC : Compressor 5T : Turbine 3B
Combustor 2D :Duct 3I : Intercooler 1
BL : Bleed 5R :Rotor 2V Volume 13L :Load 1
Estimated frame time = 1.1906 msec
Fig.7 Block Diagram of Intercooled-Reheat Type Industrial Gas
Turbine Simulation
accuracy with a small number of data points and to avoidthe
difficulty of interpolation in the neighborhood of a surgeline,
beyond which function values are not defined. However,this method
is not attractive using the AD100, where large,low-cost and high
speed memories are available, because moreefficient interpolation
methods are possible with such a largedata memory. Thus, to fully
exploit the speed advantage ofthe AD100, function values must be
defined at a large num-ber of arbitrarily spaced grid data points.
The data memoryrequirements are still reasonable and well within
the AD100capability.
Engine component performance data is changed frequentlyas more
realistic data becomes available. Usually the initialcomponent
performance data is obtained from design studiesin the early phase
of an engine development program. This isfollowed by several data
iterations based on experimental datain the later phase. These
iterations can be easily done withoutdisturbing the entire
simulation.
In addition to component performance data, gas propertydata is
also required. This data is available in rectangulargrid data table
form, using the gas table generation softwaredeveloped by the
author which calculate properties of a gas atan arbitrary
temperature, fuel/air ratio, steam/air ratio andH/C ratio of fuel.
It is assumed that H/C ratio for LNG fuelis 3.696. Then most gas
table data are 3-variable functions.
Function data tables required in this simulation are sum-marized
in Fig.8. Since the size of the data tables in Fig.8,or the numbers
and ranges of independent variables, influ-ence accuracy of the
simulation, they must be chosen care-fully. Roughly speaking,
larger numbers of data points resultin higher accuracy. Although
static operating ranges are ob-tained easily from steady state
analysis, it is not so easy todetermine dynamic operating ranges.
It is obvious that, if areference variable for function generation
goes out of specified
range, even if only during one calculation frame, the
simulationis invalid. Hence, wider operating ranges should be
assumedat first for variables whose dynamic operating ranges are
notcertain and then, with the observation of simulation results,the
ranges should be narrowed to improve simulation accuracy.
Size of the SimulationThe size of this simulation is summarized
in Fig.9. The
frame time of this simulation is estimated as 1.1906 [msec]
byusing equation (2) as shown in Fig.7. In this engine, com-ponent
performance of turbines and parts of compressors arerepresented by
two-variable functions, because the variable ge-ometry is not
included. After these program modifications, theframe time can be
reduced to 1.0538 [msec]. This is two timesfaster than the AD10,
the older version of the AD100, and ap-proximately 50 times faster
than a VAX8250. The simulationrequires a total of 27 function data
sets, i.e., data for 10 three-variable, 15 two-variable and 2
one-variable functions. Thesenumbers are not equal to the number of
usages of functiondata, because some function data, such as the
properties ofgas, is used several times in one cycle of
computation. Totalaccess of function data is 124 times in this
example. The to-tal number of function data is around 30,000. Since
the datamemory capacity is 2,000,000 words (64-bit) in the
functionmemory unit, FMU in Fig.1, this is not very serious. The
totalnumber of ADSIM source code lines are approximately 4,200and
man-hours for coding is approximately one month.
CONCLUSIONA generalized programming method for real-time digital
sim-ulation of gas turbine engines using the AD100 has been
de-scribed. The frame time of digital computation is reduced
sig-nificantly compared to simulation with conventional
general-
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No. of State Variables 28No. of Control Variables 8No. of
Algebraic Variables 244No. of Function Data Points 30,000No. of
Function Tables
3-variable Functions 102-variable Functions 151-variable
Functions 2
No. of Function Calls3-variable Functions 572-variable Functions
411-variable Functions 26
Frame Time [msec] 1.0538Speed Comparison
AD100 1.0AD 10 2.0
VAX8250 single precision 42.0VAX8250 double precision 54.7
ADSIM source code linesdynamic model part 1, 200component map
part ,-- 1,900gas table part -
1,100
Fig.9 Size of the Simulation
Name Size CallLP-compressor flow Ff1.(7r1c, Nlc , cat,) 33 x 33
x 4 1LP-compressor efficiency
Felc(7rtc, NNc , cq c ) 33 x 33 x 4 1HP-compressor-1 flow
Ffhcl(1nc^l, Nhcl,nhcl) 33 x 33 x 3 1HP-compressor-1 efficiency
Fehc1( 7rhcl, Nhcl, nhcl) 33 x 33 x 3 1HP-compressor-2 flow
FJhc2(1rhc2iNhc2) 33 x 33 1
n HP-compressor-2 efficiency Fehc2(lrhc2, Nhc2 ) 33 x 33
1HP-compressor-3 flow F1h03(lncC3, Nhc3) 33 x 33 1HP-compressor-3
efficiency Fehc3 ( 7ncc3, N, 3 ) 33 x 33 1HP-compressor-4 flow
Ffhc4 (?fhc4 Nh`c4) 33 x 33 1HP-compressor-4 efficiency Fehc4(
7the4, Nhr,4 ) 33 x 33 1HP-turbine flow F1ht(lrht, NNt) 24 x 6
1HP-turbine efficiency Feht ( 7rht, Nht) 24 x 6 1IP-turbine flow
Fjit (- it, Nit) 23 x 4 1IP-turbine efficiency Feit (irit, N,') 23
x 4 1
LP-turbine flow Fflt(7rjt,Njt) 26 x 4 1LP-turbine efficiency
Feit(zrjt, Nit) 26 x 4 1Enthalpy (Temp.) Ght(T, f, x) 33 x 4 x 4
20Relative press. (Temp.)
Grt(T, f, x) 33 x 4 x 4 8Enthalpy (Relative press.)
Gh, (P,., f, x) 33 x 4 x 4 8Specific heat ratio (Temp.) Gyt (T,
f, x) 33 x 4 x 4 5Temp. (Enthalpy) Gth(h, f, x) 33 x 4 x 4 5Temp.
(Internal energy)
Gtu (u, f, x) 33 x 4 x 4 7Internal energy (Temp.)
Gut (T, f) 33 x 4 7Gas constant Gr (f, x) 4x4 7Flow function
G,,,,l ( -y, 7r) 65 x 9 15
Enthalpy of water Ghtw (T.) 5 1
Saturated press. G(T) 4 4 25
Fig.8 Function Data Summary
purpose digital computers. Even allowing for the detailedmodel
and the flexible programming method, the simula-tion can be
accomplished at real-time or faster-than-real-timespeeds. For a
intercooled-reheat type industrial gas turbine,the frame time time
is 1.0538 [msec] and the engine dynamicsare considered to be valid
for frequencies up to 30 [Hz]. Theprogram is highly flexible.
Specifically, it can simulate a widevariety of gas turbines,
including future engines characterizedby numerous variable geometry
features.
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