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A GT-POWER Based PredictiveA GT-POWER Based Predictive Radial Turbine Model
(P t)(Progress report)
Jan Macek Oldřich Vítek Ján BuričJan Macek, Oldřich Vítek, Ján BuričCzech Technical University in Prague,
Josef Božek Research CenterJosef Božek Research Center
Overview of Presentation1. Introduction 2. Tools for 1-D Simulation of a Radial Turbine3 Application of 1 D Modules to In Turbine Flow3. Application of 1-D Modules to In-Turbine Flow
Simulation 4. Calibration of a 1-D Turbine Model5 Examples of Results5. Examples of Results6. Conclusion and Prospects
Goals: To simulate interaction between exhaust pressure waves and a turbinepressure waves and a turbine.To extrapolate a turbine map keeping physical meaning of it.
2
1. Introduction: State-of-the-Art Att t t d ib t t bi• Attempts to describe pressure waves at a turbine(or compressor) since 1960’s to present: simple, schematic models using “1D” central streamline w/o g /realistic geometry.
• “1D” central streamline steady model developed and successfully calibrated (SAE 2002 SAE 2008)and successfully calibrated (SAE 2002, SAE 2008)
• Measurements at model turbine pulsator testbeds or directly at an engine- use of results with use of results with
/ l ti ?/ l ti ?mass/energy accumulation?mass/energy accumulation?• Tools for 3-D CFD simulations – time and computer time and computer
capacitycapacity requirementrequirementss.capacity capacity requirementrequirementss.• Tools for 1-D simulations (nearly) ready for
application (SAE 2008).
3
1. Introduction: MotivationhNeed for more accurate turbine model based
IntroductionIntroductionTools for 1-D Simulation of a Radial TurbineApplication of 1-D hNeed for more accurate turbine model based
on experiments suitable for engine/TC simulation and matching and natural
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelR lt
TURBINE PARAMETERS = f(deg CA)
1 1
1.2
;
3gextrapolation of a turbine map (based on physics) to high pressure ratios (supercritical) and wide range of blade speed ratio (low
ResultsConclusion and Prospects
mm 1206
gine
BoreNumber of cylinders
0 8
0.9
1
1.1ic
ienc
y et
aT;
effic
ient
muT
;tio
x=u
/c s
]
1 5
2
2.5
tio p
i T [
1]
and wide range of blade speed ratio (low number of cylinders per a manifold branch).Diabatic turbine modelling.
r.p.m. 2000Turbocharger speed r.p.m. 90 000
deg CA 10.2Turbine stator deg CA 8.2T bi t d CA 2 1
Manifold
elay
of
pres
s.
wav
e as
sage
Eng
Engine speed
0.6
0.7
0.8
sent
ropi
c Ef
fiis
char
ge C
oeVe
loci
ty R
at [ 1
0 5
1
1.5
Pres
sure
Rat
eta T u/c shTime scales of turbine unsteadiness: large
(transient response), medium (exhaust pressure waves) small (impeller channel
Turbine rotor deg CA 2.1deg CA 33.7
Turbine revolution deg CA 8.0Turbine stator deg CA 27.1Turbine rotor deg CA 6 8
Manifold
De p w
pa
Del
ay o
f flo
w s
ingl
e pa
ssag
e0.4
0.5
90 180 270 360Crank Angle [deg from CTDC]
Is Di
0
0.5 Peta T u/c s
mu T pi T
pressure waves), small (impeller channel passage).hMedium scales should be addressed.
Turbine rotor deg CA 6.8f
Heisler Engine Technology SAE 1998
Crank Angle [deg from CTDC]
4
Medium scales should be addressed. Heisler, Engine Technology. SAE 1998
1. Introduction: MotivationhNeed for more accurate turbine model based
IntroductionIntroductionTools for 1-D Simulation of a Radial TurbineApplication of 1-D N li d V l it M f R di l T bihNeed for more accurate turbine model based
on experiments suitable for engine/TC simulation and matching and natural
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelR lt
Normalized Velocity Maps of Radial Turbine
1.0 1.1
Radial Turbine at High Pressure RatioOptimum Velocity Ratio
0.90 1.20
simulation and matching and natural extrapolation of a turbine map (based on physics) to high pressure ratios (supercritical)
ResultsConclusion and Prospects
0.8
0.9
Effi
cien
cy
1]
1.0
1.1
effi
cien
t [1
]
0 80
0.85
nd
0 80
1.00
Exit
Mac
h
p y ) g p ( p )and wide range of blade speed ratio (low number of cylinders per a manifold branch).0.6
0.7
Isen
trop
ic E
eta
nom
[
0.9
1.0
sch
arge
Coe
mu
T n
om [
0.75
0.80
ic E
ffici
ency
an
city
Rat
io [1
]
0.60
0.80
icie
nt ;
Noz
zle
umbe
r [1
]
0.4
0.5
orm
aliz
ed I
eta
T/
0.8
0.9
Rel
ativ
e D
ism
u T
/m
0.70
Isen
trop
iVe
loc
0.40
scha
rge
Coe
ffi Nu
u/cs opt
eta T max
0.2
0.3
0 600 0 800 1 000 1 200 1 400 1 600 1 800
No
0.7
0.8
R
0.60
0.65
1 5 2 0 2 5 3 0 3 5 4 00.00
0.20 Dis
mu T nom
Nozzle Mach #
5
0.600 0.800 1.000 1.200 1.400 1.600 1.800
Normalized Blade Speed Ratio x/x nom [1]
1.5 2.0 2.5 3.0 3.5 4.0
Pressure Ratio pi T [1]
1. Introduction: Motivation
hM fl ibl t bi d l f
IntroductionIntroductionTools for 1-D Simulation of a Radial TurbineApplication of 1-DhMore flexible turbine model for
different layouts with integrated boost t l EGR it bl t di
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelR lt control or EGR suitable at medium
time-scale accuracy.ResultsConclusion and Prospects
hTwin-scroll with pressure wave shift and assymetry due to scroll design, WG inlet,
hIntegrated WG chamber or outlet diffuser.
etc.
6
1. Introduction: Motivation
hM fl ibl t bi d l f
IntroductionIntroductionTools for 1-D Simulation of a Radial TurbineApplication of 1-DhMore flexible turbine model for
different layouts with integrated boost t l EGR it bl t di
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelR lt control or EGR suitable at medium
time-scale accuracy.ResultsConclusion and Prospects
hDifferent variable geometries.hOutlet diffuser with unsteady flow.
7
Introduction Tools for 1Tools for 1--D D Simulation of a Simulation of a Radial TurbineRadial TurbineApplication of 1-D M d l t I
2. Tools for 1-D Simulation of a Radial TurbineModules to In-
Turbine Flow Simulation Calibration of a 1-D Turbine ModelResults
a Radial TurbineModules and solvers for 1-D “Pipe” with variable cross/section area, source terms for enthalpy andResults
Conclusion and Prospects
cross/section area, source terms for enthalpy and momentum, external acceleration (rotating pipe) and curvature.Modules for flow momentum mixing/ splitting (“Flow splits”).Modules for orifices with variable discharge coefficient/area and sensor/signal processor/actuator h ichains.
1-D central streamline, steady flow turbine model. Definition of loss and flow separation coefficients
8Definition of loss and flow separation coefficients.
2. Tools for 1-D Simulation of a Radial Turbine
Introduction Tools for 1Tools for 1--D D Simulation of a Simulation of a Radial TurbineRadial TurbineApplication of 1-D M d l t I
Modules with external
a Radial TurbineModules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelResults Modules with external
acceleratin: splitting an impeller into parts with
ResultsConclusion and Prospects
impeller into parts with different orientation to axis of rotation
r x, w
axis of rotationrεr εa
wu
aεt
9t
2. Tools for 1-D Simulation of a Radial T bine
Introduction Tools for 1Tools for 1--D D Simulation of a Simulation of a Radial TurbineRadial TurbineApplication of 1-D M d l t I
Transformation modules must be
a Radial TurbineModules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelResults Transformation modules – must be
“programmed” separately to change total enthalpy by a source term (“heat transfer”)
ResultsConclusion and Prospects
u2
enthalpy by a source term ( heat transfer ) and velocity (pipe cross-section) maintaining all static state parameters and g pmass flow rate
I
IleakNI
m
mmm −=•
•••Δ
cu3
uNIrefI
NrN
IIrIref
wwA
mcw
222
2222
αβ
ρtantan −
=
== c3
w3
10( ) ( )IN
rIrelI
IrI
wmcwhhmH
w
22
22
222
22
000
22
22βα tantan −−=
−=−=
••Δ
Introduction Tools for 1Tools for 1--D D Simulation of a Simulation of a Radial TurbineRadial TurbineApplication of 1-D M d l t I
2. Tools for 1-D Simulation of a Radial Turbine
Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelResults
Modules and solvers for 1-D “Pipe” with variable cross/section area, source terms for enthalpy and( ) ( )wACwAm sgeomD ηρρ ==•
2222ResultsConclusion and Prospects
cross/section area, source terms for enthalpy and momentum, external acceleration (rotating pipe) and curvature.
( ) ( )whhΔhhhhhw
lostss
sgeomD
ηη
ηρρ
=−
=+−=−=2
2201201201
22
2222
22Modules for flow momentum mixing/ splitting (“Flow splits”).
Cp Pκκ
ηη
⎥⎤
⎢⎡
⎟⎞
⎜⎛
−
2
1
02
22
Modules for orifices with variable discharge coefficient/area and sensor/signal processor/actuator h i
w2
CppT= cΔh P
plost =⎥⎥⎥
⎦⎢⎢⎢
⎣⎟⎟⎠
⎞⎜⎜⎝
⎛− 2
201
0201 1
chains.1-D central streamline, steady flow turbine model. Definition of loss and flow separation coefficients
C ;C+1
1 = DP
ηη =
⎦⎣
11Definition of loss and flow separation coefficients.
C + 1 P
Introduction Tools for 1Tools for 1--D D Simulation of a Simulation of a Radial TurbineRadial TurbineApplication of 1-D M d l t I
2. Tools for 1-D Simulation of a Radial Turbine
Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelResults
Modules and solvers for 1-D “Pipe” with variable / ti t f th l d
ResultsConclusion and Prospects
cross/section area, source terms for enthalpy and momentum, external acceleration (rotating pipe) and curvature – transformation of absolute to relative;;
π II nD
wmw ==
•
2curvature – transformation of absolute to relative coordinates and back.Modules for orifices with variable discharge
;; Tu
ref
ref nw
rTpA
w == 2
2
2 60
Modules for orifices with variable discharge coefficient/area and sensor/signal processor/actuator chains.
tantan γδref
urefw
ww ±=
22 ( )tantan δγ
f
ref
w
wwcKhhq −=−
=−= 22222
22
0201 2m
12n)dissipatiokin.en.oft (assessmen
cosδref
transfww =
3. Application of 1-D Modules to In-Turbine Flow Simulationheat sink h0-h0rel
heat sink h0rel-h0CP for Borda-Carnot compensationA3 =var for outlet kinetic energy
Introduction Tools for 1-D Simulation of a Radial TurbineApplication ofApplication of
Stator –Impeller
TurbineImpeller RP 4A A / β
FlowConnection
C =K
Impeller –
StatorUnsteady Flow Pipe P1Flow
Connection
Turbine Nozzle P2Aout=Aref/cosα2
l C
FlowConnection
C 1
CP for Borda-Carnot compensationCP and A2 for incidence loss
FlowConnection
C 1
Application of Application of 11--D Modules to D Modules to InIn--Turbine Turbine Flow Flow SimulationSimulation
pP3 Aout=Aref/cosβ3
press. loss C PI
CI,=Ksep StatorP4
ImpellerLeakages
half scroll length
y pCD =1 press. loss C PN CD=1 CD=1
Existing 1-D turbine model for steady flow: Turbine
speedTurbine
transformation into unsteady 1-D scheme
speedtorque
( )δγ 22222
22
0201 2tantan −=
−±=−= refwwchhq m
13 2008-01-0295
3. Application of 1-D Modules to In-Turbine Flow Simulation
Introduction Tools for 1-D Simulation of a Radial TurbineApplication ofApplication of
Unsteady Flow Pipe P1Flow
ConnectionTurbine
Nozzle P2Flow
ConnectionTurbine
Impeller RP 4Flow
Connection
Impeller –
Stator
In Turbine Flow SimulationApplication of Application of 11--D Modules to D Modules to InIn--Turbine Turbine Flow Flow SimulationSimulation
Stator –Impeller
FlowConnection
half scroll length
y pμ=1
Connection Impeller RP 4 StatorP4
pP3
Connection
ImpellerLeakages
Turbine speedTurbine
1-D turbine model for unsteady model: transformation 1-D solvers using
speedtorque
gsensor/signal processor/actuator chains and interpolation of turbine features
14
p
3. Application of 1-D Modules to In-Turbine Flow Simulation
Introduction Tools for 1-D Simulation of a Radial TurbineApplication of Application of 11 D M d l tD M d l t11--D Modules to D Modules to InIn--Turbine Turbine Flow Flow SimulationSimulationCalibration of a 1-D Turbine
Amended modules
ModelResultsConclusion and Prospects
Sources and sinks of total enthalpy (heating, cooling) in energy conservation b d t t l d t ti t t
;;π
TI
uI
ref nD
wmw ==
•
22 60based on total and static states
measured upstream a transformation module tan
;;
γf
Tu
ref
ref
wwrTpA
±
2
2
2 60
module.Input of flow cross-section according to empirically corrected exit angles at of( )
tantan γδref
uref
wcKhh
www
−
±=
22222
22empirically corrected exit angles at of
nozzle and impeller.( )
n)dissipatiokin.en.oft(assessmen
tantan δγ
reftransf
ref
ww
wwcKhhq
=
−==−= 222220201 2
m
15
n)dissipatiokin.en.oft (assessmen cosδtransfw
3. Application of 1-D Modules to In-Turbine Flow Simulation
Introduction Tools for 1-D Simulation of a Radial TurbineApplication ofApplication of Turbine Flow SimulationApplication of Application of 11--D Modules to D Modules to InIn--Turbine Turbine Flow Flow SimulationSimulationCalibration of a 1-D Turbine
Borda Carnot pressure recovery has to becompensated at transformation pipe1-D Turbine
ModelResultsConclusion and Prospects
compensated at transformation pipeconnections (in a different way for subsonic and sonic regions)Carnot/Borda Pressure "Loss"g )Amendment of rothalpy and centrifugal acceleration terms into energy and
Carnot/Borda Pressure Loss
00 1 2 3 4 5 6
Pipe Flow Area/Nozzle Flow Area
0
momentum conservation equations.-10
-5
nt
Rel
ated
to
rgy
of w
2
-0.2
-0.1
nt
Rel
ated
to
rgy
of w
3
dze D ideal diffuser (w_3)
dze B related to w_3
25
-20
-15
oss
Coe
ffic
ien
Kin
etic
En
e
0 5
-0.4
-0.3
oss
Coe
ffic
ien
Kin
etic
En
edze B related to w_2
16-30
-25Lo
-0.6
-0.5 Lo
3. Application of 1-D Modules to In-Turbine Flow Simulation
Introduction Tools for 1-D Simulation of a Radial TurbineApplication ofApplication of Turbine Flow SimulationApplication of Application of 11--D Modules to D Modules to InIn--Turbine Turbine Flow Flow SimulationSimulationCalibration of a 1-D Turbine
Turbine torque has to be calculated from the change of angular momentum1-D Turbine
ModelResultsConclusion and Prospects
the change of angular momentum.Turbine power from the torque and speed; coupling to a compressor∫∫∫∫∫ ⎞⎛∂ →→→→→→→
input - outputaccumulationangular accelerationspeed; coupling to a compressor.Instantaneous turbine efficiency is influenced by accumulation( )
∫∫∫∫∫
⎪⎫
⎪⎧ +⎥
⎤⎢⎡ ++
=⎟⎠⎞
⎜⎝⎛ ×−×
∂∂
−=Δ
•
∂
→→→→→→
→
→
VV
bladesgasT
wrmr
dAnccrdVcrt
M
εω
ρρ
cos
.,
flow accelerationinfluenced by accumulation.( )
( )⎪⎪⎪⎪⎪
⎪⎪⎪⎪⎪
+⎥⎦⎤
⎢⎣⎡ +−
+⎥⎦⎢⎣++
⎤⎡ ⎞⎛⎤⎡ ⎞⎛∂
•
→→•→→•→→ n i
iint
wrmr
wrmr
εω
εω
cos
cosflow acceleration
( )∑
⎪⎪⎪
⎪⎬
⎪⎪⎪
⎪⎨
+⎟⎠⎞
⎜⎝⎛ −+−
⎦⎣≈⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ ×+⎥⎦
⎤⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ ×−Δ×
∂∂
−=••i
ioutiint
iout
inout mmwrr
crmcrmVcrt
εω
ρ
cos
17 ⎪⎪⎪
⎭⎪⎪⎪
⎩−− j
tjjjjj dtdw
rmdtdrm εω cos2
3. Application of 1-D Modules to In-Turbine Flow Simulation
Introduction Tools for 1-D Simulation of a Radial TurbineApplication ofApplication of Turbine Flow SimulationApplication of Application of 11--D Modules to D Modules to InIn--Turbine Turbine Flow Flow SimulationSimulationCalibration of a 1-D Turbine
Leakage flows.1-D Turbine ModelResultsConclusion and Prospects
Windage losses and mechanical efficiency prediction.Input of additional pressure losses (incidence angle, ...) as the sink term
f t d fl tiof momentum and flow separation losses.Backflo s th o gh impelle channelsBackflows through impeller channels.Twin scroll flow mixing.V l l d t diff
18Vaneless nozzle or downstream diffuser.
4. Calibration of 1-D Turbine Model
To build GT Power model:
Introduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D To build GT Power model:
Experiments at a turbine (reduced mass flow-rate & turbine efficiency at different PR and
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a Calibration of a 11--D Turbine D Turbine ModelModel rate & turbine efficiency at different PR and
BSR u/cs)Geometrical data for 1-D model
ModelModelResultsConclusion and Prospects
G t i l t f GT P d lGeometrical data for 1-D modelCalibration of steady 1-D model using optimizer for the best fit of results for sets of
Geometrical parameters for GT Power modelCalibration of GT Power model at steady flow using optimizeroptimizer for the best fit of results for sets of experiment results at similar PR and BSR ranges
flow using optimizerUse of GT Power model for unsteady simulationsgTransfer of parameters into GT Power model and unsteady simulations
simulations.
19
4. Calibration of 1-D Turbine Model
The first calibration procedure using “the
Introduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D
Calibration errors may be reduced: TheThe first calibration procedure using “the best fit model parameters” using non-linear regression published in SAE 2002-01-0337
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a Calibration of a 11--D Turbine D Turbine ModelModel
ΔμT [1] 5%
Calibration errors may be reduced: The experimental data subdivided into smaller groups in dependence on turbine speedregression published in SAE 2002 01 0337 More flexible approach based on general optimization methods (e.g., genetic
ModelModelResultsConclusion and Prospects
groups in dependence on turbine speed.
optimization methods (e.g., genetic algorithms) finding generally valid fixed parameters.
Pareto frontierΔηT [1]
5%
20
4. Calibration of 1-D Turbine Model
The first calibration procedure using “the
Introduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D The first calibration procedure using the
best fit model parameters” using non-linear regression was published in SAE 2002-01-0337 It fi d i bl lib ti
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a Calibration of a 11--D Turbine D Turbine ModelModel 0337. It finds variable ccalibartion
parameters. More suitable approach is based on general
ModelModelResultsConclusion and Prospects
More suitable approach is based on general optimization methods (e.g., genetic algorithms) finding generally valid fixedparametersparameters.
Calibration errors due to the variability of parameters may be reduced: Theparameters may be reduced: The experimental data can be subdivided into smaller groups in dependence on turbine
21
s a g oups d p d o u bspeed and/or pressure ratio.
5. Examples of ResultsIntroduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D
f fTurbine map represented by calibration parameters: examples of
l d d h ff
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l fE l f
Examples of prediction of a turbine discharge coefficient and efficiency -
d flexit angles and discharge coefficients. (“efficiencies”)
Examples of Examples of ResultsResultsConclusion and Prospects
48.0
49.0
50.0
deg.
]
Pressure Ratio 1.664.0
65.0
[deg
.]
0.9
1.0
[1]
steady flow.The unsteady 1-D model has used
41 0
42.0
43.0
44.0
45.0
46.0
47.0
Impe
ller E
xit A
ngle
[d
Pressure Ratio 1.6Pressure Ratio 2.0Pressure Ratio 2.4
61.0
62.0
63.0
Noz
zle
Rin
g E
xit A
ngle
Pressure Ratio 1.6Pressure Ratio 2.0Pressure Ratio 2.4
0.7
0.8
Isen
trop
ic E
ffici
ency
Nozzle Efficiency at Pressure Ratio 1.6Nozzle Efficiency at Pressure Ratio 2.0Nozzle Efficiency at Pressure Ratio 2.4Impeller Efficiency at Pressure Ratio 1.6Impeller Efficiency at Pressure Ratio 2.0
only simplified losses yet, i.e., no look-up tables and no correction of
40.0
41.0
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
BSR [1]
60.00.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
BSR [1]
0.60.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
BSR [1]
Impeller Efficiency at Pressure Ratio 2.4
incidence angle loss.
22BSR [1] BSR [1]
Introduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D
5. Examples of ResultsT f f 1 D t d d l i t GT
Velocity Map of a Radial Turbine
0.9Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l fE l f
Transfer of 1-D steady model into GT Power:
y Turbine map calculated from steady and 1-D0.7
0.8
0.9
y et
a T
Examples of Examples of ResultsResultsConclusion and Prospects
y Turbine map calculated from steady and 1 D unsteady models for the set of presure and blade speed ratios.
y Turbocharger test rig model used for steady0.5
0.6
0.7c
Effi
cien
cy[1
]
Isentropic Efficiency at Pressure Ratio=1 50.8
0.9
1 data based on MS ExcelEfficiencydata based on 1-D GT-PowerEfficiency
y Turbocharger test-rig model used for steady flow tests.
y Turbine used at 4 cylinder engine.0.3
0.4
Isen
trop
ic Isentropic Efficiency at Pressure Ratio=1.5Isentropic Efficiency at Pressure Ratio=2.0Isentropic Efficiency at Pressure Ratio=2.5Isentropic Efficiency at Pressure Ratio=3.0Isentropic Efficiency at Pressure Ratio=3.5Di h C ffi i t t P R ti 1 5
1
0 4
0.5
0.6
0.7
eff_
T
y Tested cases: 8Turbine map predicted by 0-D MS Excel model
interpolated by the standard GT-Power procedure
0.20.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.0
Bl d S d R ti [1]
Discharge Coefficient at Pressure Ratio=1.5Discharge Coefficient at Pressure Ratio=2.0Discharge Coefficient at Pressure Ratio=2.5Discharge Coefficient at Pressure Ratio=3.0Discharge Coefficient at Pressure Ratio=3.50.6
0.7
0.8
0.9
T
0.1
0.2
0.3
0.4
80-D MS Excel model interpolated in a look-up table
81-D unsteady model
Blade Speed Ratio [1]
0 2
0.3
0.4
0.5
mi_
T
data based on MS ExcelDischarge Coefficient
00 0.2 0.4 0.6 0.8 1 1.2 1.4
x
238Turbine map predicted by 1-D unsteady model
interpolated by the standard GT-Power procedure0
0.1
0.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
x
data based on 1-D GT-PowerDischarge Coefficient
5. Examples of ResultsIntroduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D
Test at simulated turbocharger test-rig (turbine loaded by a compressor). Turbine operation close to optimum efficiency before
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l fE l f operation close to optimum efficiency before
sonic limit is reached.Examples of Examples of ResultsResultsConclusion and Prospects
24
5. Examples of ResultsIntroduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D
fApplication of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l fE l f
Comparison of 0-D and 1-D turbine models at a 4 cylinder, single exhaust
f ldExamples of Examples of ResultsResultsConclusion and Prospects
manifold at 1200 rpm
25
5. Examples of Resultsf
Introduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D
Comparison of engine parameters using both models
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l fE l fExamples of Examples of ResultsResultsConclusion and Prospects
26
6. Conclusion and Prospectsh St d d l h b lid t d d d f
Introduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D h Steady model has been validated and prepared for
expected application. h The work on fully unsteady model in progress,
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l f application of detailed loss model will be done
soon. h Models under development:
Examples of ResultsConclusion and Conclusion and ProspectsProspects
Models under development:hTwin scroll model (momentum exchange,
backflow to the other manifold branch, assymetry of flows)assymetry of flows)hImpeller channel unsteadiness due to rotation
along scroll. Use of unsteady channel-switching model f om PWS (COMPREX®) SAE 2004 01model from PWS (COMPREX®) SAE 2004-01-1000
27
6. Conclusion and ProspectsU f i i i
Introduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D
h Use of experiments at an engine in operation with a help of “TPA” from GT Power
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l f PowerExamples of ResultsConclusion and Conclusion and ProspectsProspects
1
0.6
0.8
0
0.2
0.4
etaT
s,m
-0.4
-0.2
0
28
-180 0 180 360 540 720
Crank Angle [deg]
etaTs,m etatsmap U/Cs
6. Conclusion and ProspectsIntroduction Tools for 1-D Simulation of a Radial TurbineApplication of 1-D
f
Scroll Flow Split FS1
Turbine Nozzle N1
Turbine
Impeller Leakage 1
Turbine Nozzle N2
Scroll Flow Split FS2
Impeller Leakage 2
Scroll Flow Split FS3
Application of 1 D Modules to In-Turbine Flow Simulation Calibration of a 1-D Turbine ModelE l f
Future comprehensive model of a turbine: scroll/blades/impeller
Stator – Impeller
P1
speed
Stator – Impeller
P2
Turbine Impeller RP 1
Turbine Impeller RP 2
Impeller – Stator P1
Impeller – Stator P2 Scroll Flow Split FS1 Scroll Flow Split FS2
Examples of ResultsConclusion and Conclusion and ProspectsProspects
interactionTurbine
Nozzle N1 ImpellerLeakage 1
TurbineNozzle N2
ImpellerLeakage 2
Scroll Flow Split FS3
Turbine speed
g
Stator – Impeller
P1
Stator –Impeller
P2 Turbine
Impeller RP 2 Impeller – Stator P2
TurbineImpeller RP 1
Impeller –Stator P1
29
A GT-POWER Based Predictive Radial Turbine Model
Thank you for your attention!
Turbine Model
Thank you for your attention!
Q ?Questions?
30
Transformation StatorImpellerInputs (1...upstream, 2...downstream, 0 .. total)
)actuatedbladesofangle(
,...,,,,,,,,, = 11010101111
Ap
Acc
cTphTpv
pp κρ
)actuated ,2
wh of efficiency isentropic(
)actuatedblades,ofangle(,,2
→−= 11
22
ηC
Ap
p
ref
Δ
γ
actuated)
,Connection Flow in ncontractio flow oft coefficien(2
= KCη
sepD
statorimp ... impstator ...
actuated)
→+→−
=11
K
31
Transformation StatorImpellerVelocity and total state transformation
•
;;π
TI
u
ref
Iref n
Dw
rTpA
mw == 22
2 60
tantan γδf
urefw
KwwrT
+=
2
( )tantan δγref
ref
cwKTT
w
−+= 222
0102 2
( )tantan δγref
p
wKwhh
c
−+= 2220102
2
32 n)dissipatio kin.en. oft (assessmen cosδ
reftransf
ww =