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Modeling and Estimation of Unmeasured Variables in a Wastegate
Operated
Turbocharger
Article in Journal of Engineering for Gas
Turbines and Power · May 2014
DOI: 10.1115/1.4025498
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Modelling and Estimation of unmeasuredVariables in a Wastegate
Operated Turbocharger
Rasoul Salehi
School of Mechanical EngineeringSharif University of
Technology
Azadi Ave., Tehran,1458889694,IranEmail: r
[email protected]
Gholamreza Vossoughi∗Professor
School of Mechanical EngineeringSharif University of
Technology
Azadi Ave., Tehran,1458889694,IranEmail: [email protected]
Aria AlastyProfessor
School of Mechanical EngineeringSharif University of
Technology
Azadi Ave., Tehran,1458889694,IranEmail: [email protected]
AbstractABSTRACT
Estimation of relevant turbocharger variables is crucial for
proper operation and monitoring of turbocharged(TC) engines which
are important in improving fuel economy of vehicles. This paper
presents mean-value modelsdeveloped for estimating gas flow over
the turbine and the wastegate (WG), the wastegate position and the
com-pressor speed in a TC gasoline engine. The turbine is modelled
by an isentropic nozzle with a constant area andan effective
pressure ratio calculated from the turbine upstream and downstream
pressures. Another physicallysensible model is developed for
estimating either the WG flow or position. Provided the WG position
is available,the WG flow is estimated using the orifice model for
compressible fluids. The WG position is predicted consideringforces
from the WG passing flow and actuator. Moreover, a model for
estimating the compressor speed in low andmedium compressor
pressure ratios is proposed, using the compressor head and
efficiency modified by the turbineeffective pressure ratio. The
estimates of the turbocharger variables match well with the
experimentally measureddata. The three proposed models are simple
in structure, accurate enough to be utilized for engine modelling,
andsuitable to be validated and calibrated on an internal
combustion engine in a test cell.
NomenclatureA Area (m2)Cd Discharge coefficient (−)Cp Specific
heat at constant pressure (kJ/kg.K)d Diameter (m)F Force (N)K
Spring stiffness (N/m)ṁ Mass flow (kg/s)P Pressure (kPa)Pr
Pressure ratio (−)R Gas constant (kJ/kg.K)T Temperature (K)
∗Address all correspondence to this author.
-
U Speed (m/s)X Displacement (m)γ Ratio of specific heats (−)ρ
Density (kg/m3)ω Rotational speed (rad/s)
Subscritsa airamb ambientb boostc compressorcorr correctedcyl
cylinderds downstreamem exhaust manifoldeff effectiveeng enginef
fuelK kineticP pressureref referencesp springt turbineWG
wastegateus upstream
1 IntroductionEngine downsizing using turbochargers in gasoline
engines is a common solution to reducing vehicles’ fuel
consumption
and emissions for automotive manufacturers [1]. In fact,
displacement reduced turbocharged engines regenerate thermalpower
from exhaust gas either by a wastegate controlled or a variable
geometry turbine. The turbochargers controlled by thewastegate (WG)
benefit from low cost and high durability in the harsh thermal
environment of the exhaust manifold in thecurrent automotive market
[2].
When a turbocharger is added to a naturally aspirated engine,
different strategies should be included in the engine controlunit
(ECU). These strategies are either to control the turbocharger [3,
4] or to monitor its performance for proper and safeoperation of
both the engine and turbocharger [5, 6]. Among the strategies, gas
flow estimation is imperative for the ECUto control the gasoline
engine torque and emission. The ECU requires either measuring or
estimating the air mass flowas it enters the intake path from the
air filter and continues monitoring the flow streamline until it
exits from the tailpipe.However, measuring the turbine and the WG
flows is not possible due to harsh exhaust environment. Moreover,
measuringthe compressor variables such as its rotational speed and
efficiency requires additional sensors to be implemented in
theengine which raises cost concerns.
The compressor speed and efficiency can be predicted using its
characteristic map [7]. But this introduces large errorsdue to
linear interpolation and extrapolation [8,9]. Another problem
associated with using maps provided by the compressorsupplier is
limited information at low compressor pressure ratios [9]. On the
other side of the engine, there exist challengeswith estimation of
gas flow over the turbine and the WG when the WG is not closed. The
mean-value modelling (MVM),termed also as Zero-Dimensional (0-D)
modelling in some literatures, is the main approach to get reliable
estimation ofthe turbocharger variables in the ECU. Simple
structure of MVM is shown to be accurate enough even for transient
enginecontrol applications [10, 11]. The turbine flow is estimated
using MVM techniques such as empirical modelling [12, 13] orsemi
physical modelling [14]. In semi physical modelling the main idea
is using a model of an adiabatic flow through onenozzle with a
variable area or two successive nozzles with constant areas [15].
For the WG, the gas flow is estimated utilizingan orifice model
with a variable discharge area [16, 17].
This paper presents MVM formulations to estimate the wastegate
and turbine flows along with the compressor speed andefficiency.
The turbine flow is estimated from an isentropic compressible
orifice flow model with a constant discharge areaand an effective
pressure ratio calculated from the turbine’s actual upstream and
downstream pressures. Then, the turbineflow model is used to
estimate parameters required to develop a physically sensible model
for the wastegate position andflow. As a new method, the coupling
between the compressor and the turbine is used to predict the
compressor speed andefficiency which can be easily calibrated on an
engine test bench. The compressor speed model can replace existing
models
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Table 1. Engine specifications
Description Value Unit
Displacement Volume 1.7 Litre
Compression ratio 9.9 -
No. of cylinders 4 -
Bore × Stroke 78.6 × 85 mm
Max. torque 215@2200-4800RPM N.m
Max. power 110@5500RPM kW
Max. WG Disp. 12 mm
to improve accuracy of estimation algorithms presented in [7,
18]. The proposed models for the turbocharger main variablesare
easy to be calibrated on a new engine for possible control and
monitoring applications.
After the introduction, the experimental setup used for
validation in this paper is described in section 2. Section
3addresses modelling of the turbine gas flow. The WG model to
estimate its flow and position over different engine
operatingpoints is explained in section 4. Finally, the model for
detection of the compressor variables is outlined in section 5.
2 Experimental setupA 4-cylinder port fuel injected gasoline
turbocharged engine is used for validation of all models in this
work. As shown
in Fig. 1, the engine is equipped with a turbocharger with a
radial turbine and a centrifugal compressor. The turbine
iscontrolled by a wastegate which allows bypassing the exhaust gas
from the turbine. Opening the WG reduces exhaust backpressure
(which improves the fuel economy) in operation points where the
engine does not require high boost pressure.The WG position is
controlled by a pneumatic actuator. Conventionally, the ECU
regulates the pressure inside the actuatorcylinder (Pcyl) by
controlling an electronic solenoid valve (solenoid valve1 in Fig.
1) fed by pressures from downstream andupstream of the compressor.
To additionally make it possible to adjust the WG position
independent of the ECU command,a general control unit (GCU) is set
up and used in this work. The GCU regulates the pressure inside the
WG actuator bycontrolling solenoid valve2 (Fig. 1). Therefore,
using the setup shown in Fig. 1, two modes are available to control
the WGactuator:
Control mode-I: ECU-controlled operation. In this mode the ECU
regulates Pcyl (via the dashed line from solenoidvalve1 to the WG
actuator) utilizing solenoid valve1.
Control mode-II: GCU-controlled operation. In this mode the
solenoid valve1 is disconnected from the WG actuatorand Pcyl is
regulated using solenoid valve2 controlled by the GCU. Connected to
a pressure reservoir, solenoid valve2 canincrease or decrease the
WG opening compared to control mode-I.
In Fig. 1, Pcyl is measured using two pressure sensors PS1 and
PS2 in the two control modes and PS3 and PS4 areused to measure the
upstream and downstream turbine pressures. Figure 1 also
illustrates the engine instrumentation. Aproximity sensor is used
to measure the compressor speed with ±500(rpm) resolution.
Temperatures are measured usingK-type thermocouples with an
accuracy of ±2◦C and pressures are measured using piezoresistive
pressure transmitters with±0.1kPa accuracy. The fuel mass flow is
measured using a temperature-controlled fuel mass flow meter with a
measurementaccuracy of 0.12% and maximal measuring frequency of
20HZ. The measured fuel in the test cell is used along with
themeasured engine airflow to compute the exhaust gas flow. A
hall-effect sensor with −40 to +150◦C working temperature
isintegrated with the engine setup for measuring the WG
displacement. The hall sensor is connected to the WG actuator
usinga thermal isolating pad. Further engine characteristics are
presented in Table. 1.
3 Turbine flow modellingTurbomachine performance characteristics
such as mass flow and efficiency are specified in terms of pressure
ratio and
rotating speed. For these machines, the effect of inlet
conditions are cancelled by defining corrected mass flow and
correctedspeed. Therefore, for a machine of a specified size which
handles a single gas, the dimensional analysis for
compressiblefluids suggests the following [19]:
-
Fig. 1. Schematic of the engine test bed and the GCU to adjust
the WG position independent of the engine operation
ṁcorr = f(Pr, ωcorr) (1)
where ωcorr = ω/√Tus is the corrected rotating speed of the
machine shaft and the corrected mass flow is defined as
ṁcorr = ṁ√Tus/Pus for a turbine and ṁcorr = ṁ
√Tus/Tref/(Pus/Pref ) for a compressor. The pressure ratio, Pr,
is
either the upstream to downstream turbomachine pressure ratio or
the reverse.Radial turbines have rather weak dependencyupon the
corrected speed [19], and the pressure ratio is the most
significant variable in Eqn. 1. Figure 2 compares themeasured
corrected flow over the radial turbine with that of a conventional
nozzle. The test procedure for measuring thepresented data includes
a large region of the TC engine map. The flow over the turbine is
measured by closing the wastegatecompletely thus the entire engine
flow passes through the turbine. As plotted in Fig. 2, the turbine
flow resembles a nozzlemodel but it does not reach the choking
point at a pressure ratio about 0.53 as the nozzle model predicts
[15, 20]. Therefore,in this work the turbine flow is estimated
using a single nozzle model with a constant area but with an
”effective” pressureratio (Fig. 3) to avoid early choking
prediction. The effective pressure ratio is calculated from the
turbine actual pressureratio using; Prt,eff = (Pds,t/Pus,t)α , thus
the turbine flow is estimated by the following:
ṁt =Pus,t√RemTus,t
At,eff
√2γemγem−1 (Pr
∗t
2γem − Pr∗t
(γem+1)γem )
Pr∗t = max(Prt,eff ,2
γem+1
γem/(γem−1))
Prt,eff =Pds,tPus,eff
= (Pds,tPus,t
)α
(2)
where Aeff,t is the effective area of the turbine, α is a
constant to include the turbine effective pressure ratio in
theturbine flow model instead of its real pressure ratio, Tus,t is
the turbine upstream temperature, Rem is the gas constant forthe
exhaust manifold and, Pus,t and Pds,t are the turbine’s upstream
and downstream pressures . More details on how tooptimally estimate
α and to calculate Aeff,t are presented in [21].
The turbine flow modelled by Eqn.( 2) with α = 0.39 and At,eff =
2.85 × 10−4 (m2) is compared to the measuredengine flow in Fig. 4.
As shown, predicted flow for the turbine agrees well with measured
gas flow. The estimation error ofthe results in Fig. 4 has an
average of 1.4% with a standard deviation, σ, of 1.5%.
-
Fig. 2. Comparison between the turbine corrected flow and a
conventional orifice corrected flow
Fig. 3. The turbine schematic and 0-D model
4 WG flow and displacement modellingThe WG is an orifice with a
variable area. Therefore the flow over the wastegate is modeled
using the orifice isentropic
flow equation,
ṁWG = ACdPus,t√RemTus,t
f(Pds,tPus,t
) (3)
where the discharge factor is a function of the WG actuator
position, ACd = g(XWG) . The WG flow in Eqn. (3) can alsobe
calculated from the difference between the engine flow and the
turbine flow,
ṁWG = (ṁeng + ṁf )− ṁt (4)
-
Fig. 4. Modeled turbine flow compared to measured exhaust flow
with closed WG
where ṁeng is the engine air mass flow, ṁf is the injected
fuel mass flow and ṁt is the turbine mass flow from Eqn. (2).When
the WG flow is known from Eqn. (4), the discharge factor can be
computed using Eqn. (3). Fig. 5 shows ACdat different measured WG
positions. As shown, the discharge factor has a linear relation to
the WG displacement for adisplacement range of [0,5] (mm). The
linear relation between the WG displacement and the discharge
factor makes it easyto estimate the WG flow using Eqn. (3).
However, the WG position is not always measured in production TC
engines and itneeds to be estimated.
Fig. 5. WG discharge factor at different WG positions
The WG position is predicted based on forces applied to its
actuator and the WG flapper. Fig. 6 shows the schematic ofthe
wastegate and its force diagram. As illustrated, there are three
main sources of force which affect the WG position. Thefirst force
is from the pressure difference across the actuator cylinder (Fcyl)
which opens the WG. This pressure difference(Pcyl−Pamb) is
controlled by the WG electronic solenoid valve which incorporates
pressures from downstream and upstreamthe compressor. The second
source of the force is the WG spring force (Fsp) preloaded by an
initial displacement, X0. Thespring is to close the WG allowing
more flow over the turbine. The third force is applied by the
exhaust gas flow inside the
-
Fig. 6. Wastegate schematic and its force diagram
exhaust manifold, Fflow. Therefore, when the WG is open, XWG is
estimated using the torque balance at point A, shown inFig. 6,
as:
[Fsp − Fcyl].r2.cos(θ)− Fflow.r1 =[Ksp(XWG +X0)− (Pcyl −
Pamb).Acyl].
r2.cos(θ)− Fflow.r1 = 0(5)
in which, Acyl is the area of the piston fitted inside the WG
actuator cylinder, r1 and r2 are the length of the connecting
rods,Pamb and Pcyl are the ambient and the WG cylinder pressures,
and Ksp is the spring stiffness. Table 2 in the Appendix liststhe
measured values of parameters used in Eqn. (5).
When the exhaust flow hits the WG flapper, a force is applied to
the flapper due to change in the flow momentum. Thisforce is
calculated by applying the conservation of momentum for a control
volume bounded by a surface S around the WGflapper (Fig. 6) as:
Fflow +∫∫S
FsurfdS +∫∫∫∫CV
βρemdv =∫∫S
U(ρemUdS) +∂∂t
∫∫∫∫CV
U(ρemdv)(6)
where Fsurf is the force acting on the control surface S inN/m2,
β is the body force inN/kg, v is the volume of an elementinside the
control volume in m3 , ρem is the exhaust gas density in kg/m3 and
U is the fluid velocity at the control surfaceS in m/sec. The
following are assumptions used to calculate Fflow from Eqn.
(6):
1. Assumption I: Since we present models to predict steady-state
flow, the time dependency term is eliminated as follows.
∂
∂t
∫∫∫∫CV
U(ρemdv) = 0. (7)
2. Assumption II: The effect of body forces exerted by the
surroundings are ignored (β = 0). The body force is mainlyexerted
by the gravity and the weight of elements inside the control volume
is negligible.
3. Assumption III: The pressure in front of the flapper surface
is Pus,t and in the back is Pds,t when the WG opens. Theassumption
is considered for small displacement of the WG, where XWG affects
ṁWG noticeably. Therefore,∫∫
S
FsurfdS = (−Pus,t + Pds,t)Aflap. (8)
-
4. Assumption IV: The gas flow hitting the flapper surface
leaves it parallel to the surface. This results the following:
∫∫S
U(ρemUdS) = ṁWGUflow. (9)
(a)
(b)
Fig. 7. a) Schematic of the geometry used for the WG 3-D
numerical simulation; b) Normalized pressure difference across the
WG flapperarea at different radial positions.
A closer look into Assumption III is made by a 3-D numerical
simulation of the pressure distribution on the flappersurface in
different WG positions. The simulation is done by numerical
calculation of the fluid dynamics through a simplifiedgeometry
which resembles the WG in the exhaust path (Fig. 7-a). The
simulated pressure difference across the WG flapperis shown in Fig.
7-b. As plotted, in 1(mm) WG displacement, the normalized pressure
difference on most of the WG flappersurface is one. Moreover, when
the WG displacement increases to 5(mm), the normalized pressure
difference is still closeto unity in most area of the flapper
surface. The normalized pressure difference in Fig. 7-b is
calculated from the following:
Norm. ∆PWG =Pflapper − Pds,tPus,t − Pds,t
(10)
where Pflapper is the pressure on the flapper surface. Using the
4 assumptions above, the flow force from Eqn. (6) is:
Fflow = [ṁWGUflow + (Pus,t − Pds,t)Aflap] =[Rus,tTus,tṁ
2WG
Pus,tAWG+ (Pus,t − Pds,t)Aflap]cos(θ)
(11)
in which Aflap and AWG are the areas of the flapper and the WG
hole respectively (Fig. 6). In Eqn. (11), ṁWGUflow iscalled the
force from the gas kinetic energy (Fflow,K) and (Pus,t−Pds,t)Aflap
is called the force from the exhaust pressure,
-
(Fflow,P ). Plugging Eqn. (11) into Eqn. (5), the WG
displacement from its equilibrium point is estimated as the
following:
XWG =Tt
ksp.r2−X0 if Tt > Fs,0.r2
XWG = 0 if Tt < Fs,0.r2(12)
where Tt = Fcyl.r2 + Fflow.r1 and Fs,0 is the WG initial load
from the spring. As Eqn. (12) proposes, the WG actuatorand the flow
forces should be large enough to cancel the WG spring force
otherwise the WG stays in its initial position(XWG = 0). Figure 8
depicts results of the WG modelling. In Fig. 8-a, the modelled WG
flow from Eqn. (3) with aknown XWG is compared to the WG flow
computed from Eqn. (4). In Fig. 8-b, the WG position calculated
from Eqn. (12)is compared to the measured WG position. Results of
both the WG flow and displacement models reveal good
agreementbetween measured and estimated data.
(a)
(b)
Fig. 8. Results of the wastegate model; a) wastegate flow; b)
wastegate displacement.
Each force term in Eqn. (5) has a different contribution to the
final WG displacement. To check the contribution of theforces in
the total displacement of the WG, the contribution factor is
defined as:
Contribution factor =Fx
Fcyl + Fflow,K + Fflow,P∗ 100 (13)
-
where Fx is either Fcyl, Fflow,K or Fflow,P . Figure 9 shows how
much each force in Eqn. (5) has contributed to openthe WG. As
expected the cylinder force has the most significant and the
kinetic force has the least effect on the wastegateposition. The
pressure force, Fflow,P , is also considerable especially when the
downstream and upstream turbine pressuredifference increases. This
happens when the WG area is small and most of the exhaust flow
passes over the turbine.
Fig. 9. Contribution factor of forces applied to the WG
actuator.
5 Compressor rotational speed estimationThe rotational speed of
a centrifugal compressor can be predicted using its characteristic
map once the compressor
pressure ratio and corrected airflow, ṁc,corr , are known.
Figure10-a shows the compressor map used in this work alongwith the
compressor operating points in three engine tests; a) full load
test, b) a test with the WG kept closed and, c) atest with the WG
left open (i.e. the WG operates normally in the control mode-I as
described in section 2). As shown, thecharacteristic map represents
the compressor flow and pressure ratio at specific compressor
rotational speeds. Therefore,at a speed not included in the map,
the compressor speed can be predicted by interpolating the map.
However, linearinterpolation in the characteristic map introduces
large errors in speed prediction [8]. Moreover, the map is not
suitable foranalytical works like stability investigation for an
estimation algorithm such as presented in [18]. Dimensional
analysis isapplied, to the compressor map for estimating the
compressor speed, reducing the interpolation error. Two
non-dimensionalvariables known as the head parameter, Ψ and the
normalized compressor flow rate, Φ are defined as follow [22]:
Ψ = [Cp,aTus,c((Pds,c/Pus,c)(γa−1)/γa − 1)]/0.5U2c
Uc = π/60.dc.ωcΦ = ṁc/(ρus,c.d
3c .ωc)
(14)
where dc is the compressor impeller diameter, Uc is the impeller
tip velocity, ρus,c is the air density upstream the compressor,ωc
is the compressor rotor speed and, Pds,c and Pus,c are the
compressor upstream and downstream pressures. Results ofthis
transformation is shown in Fig. 10-b. As observed, the wide and
scattered operating points in a compressor characteristicmap are
transformed into a band by the Φ−Ψ transformation. The band is
represented by a curve fitted to the transformationresults (Fig.
10-b). This curve can be used to estimate the compressor
variables.
To investigate application of the non-dimensional variables, Φ −
Ψ, for estimating the compressor performance inlow and medium
pressure ratios, two extremely conditioned tests are discussed. In
the first extreme test, the turbochargerWG is closed completely.
The WG-closed test shows the maxima of operation variables (speed
and pressure ratio) for thecompressor when operating on an engine.
Compared to an engine full load test in Fig. 10-a, it shows that
from low to mediumcompressor pressure ratios, the WG-closed
condition also occurs during the engine full load operation. In the
second test, asanother possible extreme condition for the
turbocharger on an engine, the WG is opened as much as possible by
the engineboost pressure. In this case the entire boost pressure is
applied to the WG actuator and the WG operates based on its
appliedforces. The WG-open test shows the minima of operating
points for the compressor operating on an engine. The
compressor
-
(a)
(b)
Fig. 10. a) The compressor characteristic map and its trajectory
during the engine test points. b) Transformation results from the
compressormap and the engine test points.
trajectories for the WG-open and WG-closed tests are plotted in
Fig. 10-a. As shown, in both tests the compressor has thesame
trajectories for pressure ratios below that of point “A”, but the
two tests can be distinguished at higher pressure ratios.The reason
is the fact that the boost pressure is not high enough to open the
WG until reaching the point ”A”.
Transformation results of the two extreme tests are shown in
Fig. 10-b. As observed, when the compressor is coupledto the
engine, the Φ − Ψ relation, observable from transforming the whole
map of the compressor, is confined to a specificregion with weak
dependency of Φ on Ψ. The weak dependency of Φ on Ψ and the width
of transformed compressor mapare two sources of error when the
fitted curve is used for the compressor flow estimation.
In a turbocharged engine, the coupling between the compressor
and the turbine created by the engine limits the rangeof the
compressor operation in its characteristic map (Fig. 10-a). To use
the effect of this coupling for estimation of thecompressor
operation point, the compressor speed coefficient, CFc, is proposed
as:
CFc =ηc
Ψ.P r2t,eff(15)
-
where ηc is the compressor isentropic efficiency from the
following:
ηc =Tds,c|s−Tus,cTds,c|a−Tus,c =
Tus,c((Pds,c/Pus,c)(γa−1)/γa−1)
Tds,c|a−Tus,c(16)
in which Tus,c is the compressor upstream temperature and,
Tds,c|s and Tds,c|a are the isentropic and actual
compressordownstream temperatures. As Eqn. (15) suggests, the CFc
uses the exhaust manifold information from either the estimated[5]
or measured turbine effective pressure ratio. To explore more
conditions possible for the turbocharged engine, two newtests are
designed that resemble compressor operation under some deviations
of the engine from the normal operation. Thefirst test is with a WG
that is stuck open and cannot be closed. This test extends the
compressor trajectory to lower pointsthan those of the WG-open
test. The test is carried out using the GCU which controls the WG
position utilizing an externalpressure source (Fig. 1). The second
test is a test with a gas leakage in the exhaust manifold.
The compressor corrected speed (ωc/√Tus,c) during the four
described tests is shown in Fig. 11-a. As plotted, there is
no unique dependence of the compressor speed with its mass flow
in the four tests. If one plots ηc/Ψ at different compressormass
flow rates for the four tests, on the other hand, the test points
are merged towards a curve with higher correlation factoras shown
in Fig. 11-b . Although ηc/Ψ is correlated to ṁc,corr, but this
correlation reduces as ṁc,corr increases. Thiscreates an
estimation error if the fitted curve is used to estimate ηc/Ψ,
specifically at high compressor mass flow rates. Byusing CFc as
defined in Eqn. (15), correlation with the compressor corrected
mass flow is further improved as shown inFig. 11-c (compare the
correlation coefficientR2 in Figs. 11-b and c). Moreover, as Fig.
12 shows, CFc has better sensitivityto ṁc,corr since the fitted
curve in Fig. 11-c has higher slops (i.e. higher gradients)
compared with the curve in Fig. 11-bspecifically at high compressor
flow rates.
5.1 Modelling the compressor downstream temperatureThe proposed
strategy to estimate the compressor rotational speed in Eqn. (15)
requires the compressor isentropic
efficiency, ηc, to be known a priori. From Eqn. (16) ηc is a
function of the compressor pressure ratio, Prc, Tus,c andTds,c. The
compressor pressure ratio can be estimated using the conventionally
measured boost pressure, Pb; compensatingthe pressure drop due to
the airflow through the engine intercooler. However, Tds,c is not
usually measured in productionengines. To reduce the cost of
integrating an additional temperature sensor downstream of the
compressor, the temperatureis estimated using Prc, Tus,t, Tus,c and
ṁc . The idea of using the turbine upstream temperature is due to
the effect ofthe exhaust temperature on the compressor downstream
temperature and isentropic efficiency particularly at low
compressorspeeds and flows [23]. Moreover, Tus,t is already
required in this work to estimate the WG and turbine flows.
The compressor downstream temperature is modelled using a simple
structured neural network, NN. A two-layer feed-forward network
with 9 sigmoid neurons in the hidden layer and a linear output
neuron is trained to estimate Tds,c (Fig. 13).The error back
propagation with steepest descent is used as the training
algorithm. For training the NN network, 60% ran-domly selected data
from all the four tests in Fig. 11 are used to train the NN
network. The NN performance is demonstratedin Fig. 14. As shown,
the NN can effectively estimate Tds,c for all the four engine test
conditions described in section 5.
5.2 Results of the compressor speed estimationFinally, the
compressor speed is estimated using the following algorithm:
1. Estimate CFc at each compressor corrected flow using a curve
fitted to the results of Fig. 11-c.2. Estimate the compressor
downstream temperature utilizing the developed NN, and then use it
to compute ηc.3. Compute Ψ from Eqn. (15), and then invert it to
get ωc using Eqn. (14).
The above algorithm is schemed in Fig. 13. Results of the
estimated compressor speed are shown in Fig. 15. As shownthere is
good agreement between the estimated and measured compressor speed
for the four test conditions. The averageestimation error is ē =
430(RPM) with a standard deviation of σ = 2100(RPM). This proves
the suitability of theproposed model to estimate the compressor
speed at low and medium pressure ratios and airflows.
6 ConclusionSteady state models suitable for mean-value
computations in an engine control unit are presented to estimate a
tur-
bocharger working conditions. The turbine flow is estimated
using the model of an isentropic nozzle with an effectivepressure
ratio. The use of the effective pressure ratio circumvents wrong
prediction of early choking for the turbine. TheWG flow is
estimated using the orifice model for compressible fluids, if the
WG position is measured. For engines that theWG position is not
measured, its position is estimated using a physically sensible
model of the WG and its applied forces.Experimentally validated WG
displacement model takes into account forces from the WG passing
flow, cylinder pressure,and spring. It is shown that about 85% of
the WG displacement is due to the WG cylinder force and 15% is from
the flow
-
(a)
(b)
(c)
Fig. 11. a,b) The compressor corrected speed and ηc/Ψ at
different compressor corrected flows. c) Alignment of the test
points to a singlecurve using the defined speed coefficient.
-
Fig. 12. Sensitivity (∂/∂ṁc,corr) of CFc and ηc/Ψ to the
compressor corrected flow
Fig. 13. Overall structure of the compressor speed model.
force which comprises the force from the flow kinetic energy and
the exhaust manifold pressure. Another model for esti-mation of the
compressor rotational speed is proposed, which utilizes the
coupling between the compressor and the turbine.The new compressor
model uses the turbine effective pressure ratio to modify the
compressor head parameter utilized tocalculate the compressor
speed. The estimated compressor speed by the new model matches well
with the experimentallymeasured speed in an engine test cell.
References[1] Knecht, W., 2008. “Diesel engine development in
view of reduced emission standards”. Energy, 33(2), pp. 264–271.[2]
Capobianco, M., and Marelli, S., 2011. “Experimental analysis of
unsteady flow performance in an automotive tur-
bocharger turbine fitted with a fitted waste-gate valve”.
Proceedings of the Institution of Mechanical Engineers, PartD:
Journal of Automobile Engineering, 225, pp. 1087–1097.
[3] Muller, M. “Estimation and control of turbocharged engines”.
SAE Technical Paper(2008-01-1013).[4] Rajamani, R., 2005. “Control
of a variable-geometry turbocharged and wastegated diesel engine”.
Proceedings of the
Institution of Mechanical Engineers, Part D: Journal of
Automobile Engineering, 219, pp. 1361–1368.[5] Wang, Y. Y., and
Haskara, I., 2012. “Exhaust pressure estimation and its application
to detection and isolation of
turbocharger system faults for internal combustion engines”.
Journal of Dynamic Systems, Measurement, and Control,
-
20 40 60 80 100 120 14020
40
60
80
100
120
140
Mod
eled
T ds,
c (o C
)
Measured Tds,c
(oC)
WG−closedWG−openWG−offsetExhaust leak
ē = 0.2 oCσ = 1.5 oC
Fig. 14. Results of modelling the compressor downstream
temperature.
Fig. 15. Estimation results for the compressor rotational speed,
ωc
134(2), p. 021002.[6] Hountalas, D. T., and Kouremenos, D. A.,
2004. “A diagnostic method for heavy-duty diesel engines used in
stationary
applications”. Journal of Engineering for Gas Turbines and
Power, 126, pp. 886–898.[7] Eriksson, L., 2007. “Modeling and
control of turbocharged SI and DI engines”. Oil and Gas Science and
Technology,
62(4), pp. 523–538.[8] Moraal, P., and Kolmanovsky, I., 1999.
“Turbocharger modeling for automotive control applications”. SAE
Technical
Paper(1999-01-0908).[9] Casey, M. V., and Schlegel, M., 2010.
“Estimation of the performance of turbocharger compressors at
extremely low
pressure ratios”. Proceedings of the Institution of Mechanical
Engineers, Part A: Journal of Power and Energy, 224,pp.
239–250.
[10] Hevalier, A., Muller, M., and Hendricks, E., 2000. “On the
validity of mean value engine models during transientoperation”.
SAE Technical Paper(2000-01-1261).
[11] Guzzella, L., and Onder, C., 2010. Introduction to modeling
and control of internal combustion engine systems.Springer,
Germany.
[12] Fang, X., Dai, Q., Yin, Y., and Xu, Y., 2010. “A compact
and accurate empirical model for turbine mass flow
charac-teristics”. Energy, 35(12), pp. 4819–4823.
[13] Kong, C., Kho, S., and Ki, J., 2006. “Component map
generation of a gas turbine using genetic algorithms”. Journalof
Engineering for Gas Turbines and Power, 128, pp. 92–96.
-
[14] Serrano, J., Arnau, F., Dolz, V., Tiseira, A., and
Cervello, C., 2008. “A model of turbocharger radial turbines
appropriateto be used in zero- and one-dimensional gas dynamics
codes for internal combustion engines modeling”. EnergyConversion
and Management, 49(12), pp. 3729–3745.
[15] Payri, F., Benajes, J., and Reyes, M., 1996. “Modeling of
supercharger turbines in internal-combustion engines”.International
Journal of Mechanical Sciences, 38(8-9), pp. 853–869.
[16] Thomasson, A., Eriksson, L., Leufven, O., and Andersson,
P., 2009. “Wastegate actuator modeling and model-basedboost
pressure control”. In Proceedings of IFAC World Congress, pp.
87–94.
[17] Galindo, J., Climent, H., Guardiola, C., and Domenech, J.,
2009. “Modeling the vacuum circuit of a pneumatic valvesystem”.
Journal of Dynamic Systems, Measurement, and Control, 131(3), p.
031011.
[18] Salehi, R., Shahbakhti, M., Alasty, A., and Vossoughi, G.,
2013. “Nonlinear observer design for turbocharger in a siengine”.
In Proceedings of American Control Conference, pp. 5231–5236.
[19] Dixon, S., and Hall, C., 2010. Fluid mechanics and
thermodynamics of turbomachinery. Butterworth-Heinemann,Oxford,
UK.
[20] Tancreza, M., Galindo, J., Guardiola, C., Fajardo, P., and
Varnier, O., 2011. “Turbine adapted maps for turbochargerengine
matching”. Experimental Thermal and Fluid Science, 35(1), pp.
146–153.
[21] Salehi, R., Shahbakhti, M., Alasty, A., and Vossoughi, G.,
2013. “Control oriented modeling of a radial turbine for
aturbocharged gasoline engine”. In Proceedings of American Control
Conference, pp. 5207–5212.
[22] Sorenson, S., Hendricks, E., Magnusson, S., and Bertelsen,
A., 2005. “Compact and accurate turbocharger modelingfor engine
control”. SAE Technical Paper(2005-01-1942).
[23] Sidorow, A., Isermann, R., Cianflone, F., and Landsmann,
G., 2011. “Comparison of a turbocharger model based onisentropic
efficiency maps with a parametric approach based on Euler’s
turbo-machinery equation”. In Proceedings ofIFAC World Congress,
pp. 10627–10632.
Appendix : Turbocharger parametersThis appendix lists values for
the constant parameters used in modelling the turbocharger.
Table 2. Turbocharger parameters
Par. Value Unit Par. Value Unit
Acyl 5.9× 10−4 m2 r1 19× 10−3 m
Aflap 5.3× 10−4 m2 r2 30× 10−3 m
AWG 2.8× 10−4 m2 Ksp 12.4 kN/m
X0 4.9× 10−3 m dc 8× 10−2 m
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