- Email: [email protected]
Residual Gas Model for On-Line Estimation for Inlet and Exhaust Continuous VVT Engine Configuration
Copyright © IFAC Advances in Automotive Control Salerno. Italy, 2004
ELSEVIER
IFAC PUBLICATIONS www.elsevier.comllocatelifac
RESIDUAL GAS MODEL FOR ON-LINE ESTIMATION FOR INLET AND EXHAUST CONTINUOUS VVT ENGINE CONFIGURATION
(*) DIEM, University ofBologna, Italy. (**) Magneti Marelli Powertrain, Bologna, Italy.
Abstract: In this paper a well known Residual Gas estimation model is evaluated on real data and extended to an engine configuration that involves an external Exhaust Gas Recirculation (EGR) circuit and a Variable Valve Timing (VVT) system. The model proposed by M.Mladek and C.H.Onder (Swiss Federal Institute of Technology) ha~ been modified to take into account the presence of these two systems, and has been vahdated this comparing the results to data obtained form a 6 .cyliders e~gine. The main goal work is to validate and extend to external EGR mput the given model, With the aun of designing VVT model based control strategies for combustion and pollution emission optimal performances. Copyright © 2004 IFAC
0:
Keywords: automotive, Residual Gas Fraction, Residual Gas model, VVT, model validation.
1.
quantity (some off-line ones can be found in the literature [2-8]), and the increasing complexity of intake manifold hardware configuration that has a great impact over the residual gas value, one of the most important being for example the Variable Valves Timing (VVT) system control. It is well known that a VVT system is determinant in defining the ratio between air mass flow and residual gas entering the cylinder, thus affecting both the torque production and the engine emission; it is the authors opinion that VVT control could be optirnized and correctly approached using a correct residual gas fraction estimation, by choosing as an external input of the control the gas composition in any engine point. The residual gas fraction models present in literature have been developed for engines that are not equipped with an external EGR system, while this component is part of the engine considered for the development of this work. The main goal of the paper is therefore the critical analysis of a residual gas fraction model based on incylinder pressure measurement [5], and the extension
INTRODUCTION
Residual gas fraction in Internal Combustion Engines is a critical factor in many aspects of combustion and engine performances: its influence on flame speed and combustion stability is relevant for torque production and combustion repeatability (i.e. cycle by cycle combustion variability), while its impact on incylinder gas mass temperature can be one of the prime factors over NOx production and control. For this reason it could be important for engine control purposes (e.g. dri veability, pollution emission control, engine stability at idle) to estimate with an appropriate precision the residual gas mass fraction, whose value is mainly related to two components: the gas which is drawn back from the exhaust manifold during inlet and exhaust valves overlapping phase, and the gas trapped in the cylinder when the exhaust valve closes [I]. Two main aspects have to be taken into account when approaching the problem: the complete absence of an in-line sensor to measure this
257
of the same model to engines equipped with external EGR circuit and VVT system. Such a model will then be used for VVT control strategy definition and design. 2.
Srg
S EGR Sa j,
Residual
gas
mass
fraction
inside the
cylinder EGR mass fraction inside the cylinder
Air mass fraction inside the cylinder Fuel mass fraction inside the cylinder
NOMENCLATURE
mlOI
Total mass inside the cylinder [kg]
Xc
Air Fuel Ratio Combustion efficiency
Pso
In-cylinder pressure at 50% mass burned
cv,.
Combustion
reactants
constant
volume
CV p'
specific heat [J/kg K] Combustion products
constant
volume
RN!
specific heat [J/kg K] Reactants ideal gas constant [J/kg K]
Rp,
Products ideal gas constant [J/kg K]
Hu
Fuel lower heating value [J/kg]
X rgold
Residual gas mass fraction at the beginning
X rg"....
of an iteration Residual gas mass fraction at the end of an
conditions [Pal Cylinder volume at 50% mass burned conditions [m3] Ideal gas constant for the gas mixture present at 50% mass burned condition [J/kg K] Temperature at 50% mass burned conditions [K] Intake Valve Opening Intake Valve Closing Exhaust Valve Opening Exhaust Valve Closing Top Dead Center In-cylinder pressure at lYC [Pal
lYO lYC EVO EVC TDC
iteration 3.
Cylinder volume at lYC [m3]
ENGINE MODEL
Description of the original model
Ideal gas constant for the gas mixture present at lYC [J/kg K] Temperature at lYC [K]
The approach used in this work to perform Residual Gas estimation is derived from the literature [9] , and is briefly described in Figure 1.
Mass of fresh charge entering the cylinder [kg] Residual gas mass inside the cylinder [kg]
Estimation of the in-cylinder temperature at the 50% mass burned position
Constant volume specific heat for the fresh charge [J/kg K] Constant volume specific heat for the residual gas [J/kg K] Fresh charge temperature [K] Residual gas temperature [K] Residual gas mass fraction Total internal energy at lYC [J] Total internal energy at 50% mass burned condition [J] Indicated work to the piston between lYC and 50% mass burned conditions [1] Heat developed by the combustion process up to the 50% mass burned condition [J] Heat loss between lYC and 50% mass
Qcomb
Q cooling
burned conditions [1]
qcooling
=
Q cooling / Qcomb
mEGR
EGR mass inside the cylinder [kg]
ma j ,
Air mass inside the cylinder [kg]
mf
Fuel mass inside the cylinder [kg]
X EGR
EGR mass fraction with respect to the mass entering the cylinder from the intake manifold
NO
Figure 1: Flow chart of the model
258
estimation of the in-cylinder temperature at the instant where the 50% of the mass is burned. This is possible by applying a first law energy balance between IVC and 50% mass burned positions.
It requires the measurement of the in-cylinder pressure together with the measurement of the fresh charge temperature into the intake manifold and optionally the measurement of the exhaust gas temperature or the engine speed. An estimation of the temperature inside the cylinder when the 50% of the fresh charge is burned is initially needed. This value can be chosen, for example, as a reasonable first attempt, equal to 1850 K. Applying ideal gas law to the charge inside the cylinder in the crankshaft angular position corresponding to the 50% of mass burned it is possible to obtain an estimation of the total mass:
Expliciting all the terms of Equation (6) it is possible to obtain:
(7)
(1) Equation (7) gives a new estimation of Tso , provided that an evaluation of qcocling and the measurement of the in-cylinder pressure are available. The new value of Tso is now compared to the initial value and all the procedure is repeated using the new estimation of Tso and X,g until the new value obtained at the end of the procedure equals the initial value.
where Tso has been previously chosen, Pso has been measured and Rso can be estimated considering a first attempt value of the residual gas fraction equal to 10%. The total mass inside the cylinder can be used to evaluate the temperature inside the cylinder at Intake Valve Closing (IVC) position. This can bone by applying ideal gas law, and using the knowledge of the in-cylinder pressure for that condition, and again estimating Rrvc considering an initial 10% residual gas fraction value.
Model extension The model described in the preceding section does not consider the presence of an external Exhaust Gas Recirculation (EGR) and requires particular attention when applied to an engine equipped with a Variable Valve Timing (VVT) system. Both these issues are discussed and new model equations to take EGR presence into account are introduced in this section, while the main structure of the model remains equal to the one introduced in Figure I. When an engine is equipped with an EGR system the flow entering the cylinder from the intake manifold is composed by both fresh charge and exhaust gas (EGR). Usually the amount of exhaust gas entering the cylinder is measured as a fraction of the total entering mass (air + EGR):
(2)
An energy balance at lVC allows at this point determining the residual gas fraction estimation. It can be stated in fact that, at IVC, the contribution to the total internal energy of the gas inside the cylinder is related to the internal energy of the residual gas and fresh charge before the mixture creation.
{m /ecy /e + mrgcyrg )T/Vc
=
=m/ecy/eT/e +mrgcyrgTrg
(3)
(8)
The residual gas fraction can be evaluated as the ratio between the residual gas mass and the total mass present inside the cylinder, and therefore:
The total gas mass present inside the cylinder is composed by EGR, air and fuel entering the cylinder and residual gas (or internal EGR) from the preceding combustion. The mass fractions of the in-cylinder total mass different components can be determined as:
(4)
Equation (3) can the be rewritten obtaining:
The estimation of the residual gas fraction obtained in Equation (5) can be used at this point to perform an
259
exhaust gas temperature; intake manifold temperature in a posltJon where air and EGR mass flows can be considered completely mixed VVT position in order to precisely evaluate IVC crank angular position In addition a critical sub-model has to be developed in order to evaluate the heat exchange through the cylinder walls from IVC to 50% mass burned condition.
m
Srg =~=Xrg m 101 m EGR AFR . X EGR • (1 - X rg ) SEGR = - - = ---.=..:::.::.-'-----'''-'m,o, 1 + AFR- X EGR Sa
=
(9)
mlOI
= [(AFR + 1); AFR + X EGR / (1- X EGR)]
(1- Xrg)
mf
Sf
Simplified model
= m,o, = [1+AFR(I+X EGR / (I-X EGR ))]
The model introduced in the preceding section can be used to perform Residual Gas estimation provided all the needed measurements and sub-models are available. The most critical aspect in the implementation of the model are the evaluation of the in-cylinder pressure at IVC and the evaluation of the heat exchange qcooling between IVC and 50% mass burned conditions. The first problem has been solved by applying a particular signal processing technique to the in-cylinder pressure signal, as it will be shown in a following section; the second and really critical point is instead very difficult to be solved, while its impact on model outputs behaviour is relevant.
In order to evaluate EGR, air and fuel mass fractions, additional measurements of EGR rate X EGR and Air Fuel Ratio (AFR) are required with respect to the original model. It is advantageous to define in addition the thermodynamic properties (c y and R) of the reactants (air and fuel) and products (Residual gas and EGR) of the combustion process (cYre> cvpr and R", Rpr are then considered). In this way the thermodynamic properties of a generic mixture can be determined simply by weighting the characteristic of the corresponding mass fraction. Equations (2), (3) and (5) previously defmed are still valid simply considering as fresh charge the total flow entering the cylinder from the intake manifold (composed by air, fuel and EGR) and measuring the fresh charge temperature in the intake manifold in a position where the air and EGR mass flows can be considered completely mixed. The value of Cv fe and C Yrg in Equation (5) or R IVC in Equation (2) can be determined for example by the knowledge of cYre ' cYpr ' Rre , Rpr :
Sair + Sfuel + S EGR C yrg
R/ vc
=C ypr
(10)
=RjSair + Sfuel)+ Rpr (S EGR + Srg)
Equation (7) instead needs to be slightly rearranged. In fact in this case:
and therefore:
Figure 2: Flow chart of the simplified model
(12)
For this reason a simplified version of the total model has been developed, that does not need the knowledge of heat losses through the cylinder walls between !VC and 50% mass burned condition. In this simplified model version, the air mass entering the cylinder has to be known and therefore considered as an input and not a model output anymore. The only output of the
Measurements required to obtain residual gas fraction estimation are therefore: in-cylinder pressure
260
implementation IVC does not have the meaning of the crank position where the intake valve touches its seat, but the crank position where the intake flow stops, and it can be considered equal to O. This makes the choice of IVC location even more complex, with a possible choice compatible with the valve lift trace ranging from 230 to 270 degrees after TDC. To solve this problem in-cylinder pressure signal has been used once again. In particular it has been observed that a polythropic behaviour with exponent 1.32 during the compression phase can be assumed only if the gas inside the cylinder can be considered isolated (or the cylinder can be considered as a closed system). Therefore when the in-cylinder pressure signal deviates from this behaviour, the gas inside the cylinder cannot be considered isolated anymore, and therefore a mass flow is entering or exiting the cylinder.
simplified model is therefore the residual gas fraction estimation The flow-chart of the new model implementation is described in Figure 2. The simplified model requires to be implemented Equations (2), (5) and (10) together with the simple consideration that:
Measurements required are: in-cylinder pressure; exhaust gas temperature; intake manifold temperature in a poslt1on where air and EGR mass flows can be considered well mixed; VVT position in order to precisely evaluate IVC crank angular position; Air mass entering the cylinder. It has to be stressed that no other information is required to obtain the desired residual gas fraction estimation.
i:'
cost
0.6
CII
Polythropic behavior
~--'' --'---4-/---+--
-1
5.
0.5 t 0.4 , ~ 0.3 ...---.~-...
.
,
-.---+.--.-..--~-.--.
~ 0.2 bC:::::·~ , -~-:t:=-L-L_~J CJ
c!: 0.1 -
i--.;........-.'---~--+---+--.
0.0 L-_'--_"--_"--_"'-_"'-_-'----.J
180 200 220 240 260 280 300 320 Crankshaft angle [0] Figure 3: In-cylinder pressure around IVC position
The described procedure has been applied to determine the IVC position on the considered engine at approximately 240 0 crank angle position after TDC. Results are shown on Figure 3. Algorithm convergence problems
Both the complete and simplified version of the analysed algorithm allow obtaining a residual gas mass fraction estimation as result of an iterative solution process. Sometimes the iterative process did not converge to a stable solution, as in the example presented in Figure 4a, where the value of Xrg is reported as function of iterations number.
(14)
the value of the constant cost that best fits (in the Least Mean Square sense) the measured in-cylinder pressure waveform during compression phase. This identification allows determining finally:
p{VC :;: VI.32
~
- .
In-cylinder pressure sensors are usually well suited to give a good precision while measuring high range part of the in-cylinder pressure signal. For this reason accuracy in the low pressure part of the signal is usually poor [10-15]. Therefore PlVC measurement could be affected by poor accuracy, thus negatively influencing the whole estimation process to obtain the residual gas fraction value. In order to minimize this effect the value of the pressure at IVC position has been evaluated using the in-cylinder pressure signal acquired during the compression phase. Modelling the compression phase as a polythropic compression process with exponent 1.32 [1], it is possible to identify from the general equation of a polythropic transformation
=cost
0.8
~ 0.7 ~-=::::;:=:::;::=====~h-~ . . =
In-cylinder pressure at IVC
p · V"
- - Measured
~
,Q
(IS)
{Vc
The value of PIVC determined in this way, should be less sensitive to sensor accuracy, since it derives from measurements performed in the high pressure part of the signal. Another issue that needs to be solved is the right determination of the IVC position. From figure 5 it is possible to observe that the valve lift trace is very flat when the valve starts opening or in the closing phase. It has to be underlined that for the model
261
5oo.----.,.----,....---,....----,
air entering the cylinder per cycle and then in term of fuel distribution. Finally, the engine and inlet exhaust configuration forces a particular exhaust line sensor setup, so composed:
~ 400 ~----------- ... ----.---- .. -- --- .. ---·------ ii---, .... --.
§ ::CJ ~
300~------~----~~~·R_-A-4It_~H 200~----~-r_+~~t-++-H~+-~
~
• • • • • •
'" lOO
= ~
0
';
= -lOO
-+
~
.~ -200 ~-------'------._f_+---lJ__i_-t--4___l Cl:::
.3~L-.--5"'----1...i.0--......... 15----120
while the main intake line characteristics involve the runners with double lengths (variable geometry on / oft) and the Tumble valves. For experimental and study purposes, the engine was equipped with additional sensors, mainly one pressure sensor in each cylinder, temperature and pressure sensors in the exhaust line and in the catalyst main body.
Iterations Figure 4a: Residual gas fraction evaluation using a simple iteration process
__
~
100~-----~,--~,--~
§
80 70 ~ 60 '" 50 ~
~
~
_ --L___ _
90 I - - - - -_____ --L_
r------. ---L----.-~- --.-----.,--- --- ---.-r--..-.-.-----.-t--------.----.. -----·.. ·-·--·--~- --- .. ·----····----·i
The variable valve timing system mounted on this engine can perform continuous intake and exhaust valves actuation: the intake valves opening (IVO) can be advanced and the exhaust valve closing (EVC) can be delayed from their 'mechanical' uncontrolled position. The intake and exhaust valve proftles of the engine here considered are shown in Figure 2, where it can be seen the valve overlap in the deactivated state (0 crank-angle) with respect to the applied maximum valve overlap corresponding to a 40 crank-angle degrees IVO advance and EVe delay. In Figure 2 it is also possible to observe that the intake valve flight proftle is particularly flat in the initial and [mal phases and it is therefore difficult to precisely detect the angular position of valve closing and opening.
: , .
--------L----~-
30
~ 20 - . .
.-
~ 10 r '
o
VVT system description
-----....--;.---.--.----.. ----..
I--.--__ ~------+------i-------I
40Ft o
5
.'
-- . -
•
•
10
15
20
Iterations Figure 4b: Residual gas fraction evaluation using a modified iteration process
This problem has been solved by considering as the new approximation starting value a combination of the initial and [mal result of the last algorithm iteration. As an example, if Xrg old is the first estimation value and Xrg new is the new value computed after the ftrst algorithm iteration, the new approximation value for the second iteration has to be set equal to :
x
+ .... old
x .... n.... -x 2
.... old
Test description
The pressure measurements are performed with a degree crank angle resolution using respectively:
( 16)
• •
Using this approach the convergence problem has been solved, as it can be seen in Figure 4b, where the same test as in Figure 4a has been considered.
4.
2 UEGO controlling the two different bench; 2 precat (one for each bench); 2 lambda on / off (one for each bench) 2 temperature sensors 2 Nox trap I N ox sensor
•
an un-cooled sensor for in-cylinder pressure measurement; a sensor designed for research purposes, settled in the intake runner; a water-cooled sensor in each exhaust line.
The air mass measurements are obtained from the fuel flow and the lambda measurements. The value of lambda is measured using a gas analysis system. Tests were performed throughout the engine operating range from 1000 to 4000 rpm and inlet manifold pressure equal to 300, 600 and 900 mbar. Operatively, for any engine operating point, acquisitions were made at stoichiometric conditions for different combinations of intake and exhaust valve timings, while varying EGR flow. The main experimental data over which the model is based are:
EXPERIMENTAL SETUP
Engine description
The test engine used in this study is a 3.2-liters 6 cylinders GDI engine, with four valves per cylinder. The engine is characterized by narrow-angle (15°) V6 displacement, to save space and for on car housing reasons. The particular engine design has forced an asymmetric configuration on inlet and exhaust runners and manifold structure, which in turn can lead to a different behaviour of the two benches in term of
262
• • • • •
0.15 r---;::=:r:::==-r-:----r---, = 0.141-----1- --i---'-------1 o -
engine speed cylinder pressure inlet manifold pressure and temperature exhaust temperature precise crank-angle position of intake valve closing (IYC) while varying the valves timing.
-EVO O" EVO 10· EV0 20·
~ 0.13, ~~::::::=:::j~~~~g~::'-!.:: 0.12~ ; 0.11
-_-~f-=:-::-:f'""::::-_-:;_..._~-~-;
~
7i 0.10 ~ 0.09
~
10
-
e
.§.
9
8
0.08 . . . ', . 0.07 --.-----~-.-!--+__ .•- - . 0.06
7 c:= 6 5 ~ 4 -; 3 ;> 2 1
0
5
10
15
20
25
30
35
40
IVO advance [0]
:s
Figure 6: Residual gas fraction variation as a function of the IVO advance for tests conducted at 2000 rpm and 600 mbar 0.15 0.14
-250
-150
-50 0 50
150
= 0.13
250
-
.~
Crank Angle [0 = TDC]
rvoo o !Vo 10· I----i---+-
.::
IV020·
+----'--.;- - - I
~g~: f--~--+--+----"--f-Z~
Cj
Figure 5: Valve lift
0.12
'"= 0.11 ~
7i 5.
-
-'" =
O~~--~~~~----~~~
:I
MODEL RESULTS
"Q
.~
Q,j
er::
This section reports the results obtained using the different versions of the model and a brief discussion on their possible use to define and optimise a VVT system control strategy. The results obtained using the complete model are greatly affected by the Qcooling evaluation accuracy. For example the error in evaluating the air mass flow entering the cylinder can be as high as 10 to 20% . For this reason the results obtained with this model have not been considered. the results obtained using the simplified model are reported in Figures 6, 7 and
0.10 0.09 0.08 0.07 0.06
0
5
10
15
20
25
30
35
40
EVO delay [0) Figure 7: Residual gas fraction variation as a function of the EVO delay for tests conducted at 2000 rpm and 600 mbar
As it can be seen the IVO-EVO combination that guarantees the minimum Residual Gas fraction is not the one characterised by the minimum overlap, but if the overlap is very high (as in the case of IYO advanced 40 deg and EVO delayed 40 deg) the amount of residual gas fraction increases. Considering all the IVO-EVO configurations that give the same overlap angle (for example IVO=O° EV0=40°, IYO=IO° EVO=30°, IVO=20° EYO=20°, and so on), it is possible to observe that the one that guarantees the minimum Residual Gas Fraction is the one with early EYO and IVO.
8.
Figures 6 and 7 report the value of x,-g for a given engine operating condition (2000 rpm and 600 mbar) as a function of exhaust and intake valve positions. Figure 8 reports for each VVT configuration (characterized by IVO advance and EVC delay) a map of Xrg over the engine operating range considered (in tenns of engine speed and intake manifold pressure). It can be observed that Xrg values are greatly influenced by the exhaust valve position, while less affected by the intake valve opening angle.
263
· ~~~ .-:
!..
Figure 8: Residual gas estimation for different VVT configurations
264
EXTENDED INTERNAL EGR HINT TO POSSIBLE USES [5]. The availability of a complete and validated residual internal gas model, extended to the contribution of a Variable Valve Timing system and an External residual gas component, allows defining innovative strategies such as: • Design an optimization algorithm to choose the best IVO and EVO target value (depending on engine speed and charge), in order to optimize engine consumption and pollutant emissions; • In any engine point, the appropriate internal and external EGR mass mixture can be obtained in the cylinder, so regulating the gas temperature for combustion stability and emission constraints; • The complete off-line described model can generate static points then used to identify, validate and implement in the Electronic Control Unit a simpler model, which doesn't need any information about the incylinder pressure, like the model described in [2]; • Complete and improve a combustion model for an Hardware in the Loop validation of the combustion control and management software. 7.
[6].
[7].
[8].
[9].
[10].
[11].
(12].
CONCLUSIONS
The paper presents an original review of an existing model for Residual Gas mass fraction evaluation. The model has been critically analyzed and extended to take into account the presence of an external EGR system. In addition a simplified version of the model has been presented that enables residual gas fraction evaluation without requiring a model for the heat exchange between the gas inside the cylinder and the cylinder walls. The new model has been applied to experimental data obtained from a 6 cylinder engine. The results obtained are the first step in the design of a VVT control strategy for combustion and emission optimal performances.
[13].
[14].
[15].
REFERENCES [I].
[2].
[3].
[4].
Heywood: "Internal Combustion Engine Fundamentals," McGraw Hill International Editions, 1988. Heywood, M. (1993). A model for predicting residual gas Fraction in Spark Ignition Engines. SAE Paper 931025. Ford, R (1999). Measurement of Residual Gas Fraction using a Fast Response NO Sensor. SAE Paper 1999-01-0208. Quader, Ather. A. (1999). Cycle-By-Cycle Mixture Strenght and Residual-Gas
265
Measurements During Cold Starting. SAE Paper 1999-01-1107. Miller R., Russ S., Weaver c., Kaiser E., Newmann C., Davis G., Lavole G. (1998). of Analytically and Comparison Experimentally Obtained Residual Fractions and NOx Emissions in Spark-Ignited Engines. SAE Paper 982562. Hjinze P.C., Miles P.C. (1999), Quantitative Measurements of Residual and Fresh Charge Mixing in a Modem SI Engine Using Spontaneous Raman Scattering, SAE Paper 1999-01-1106. Hall MJ., Zuzek P. (2000), Fiber Optic Sensor for Time-Resolved Measurements of Exhaust Gas Recirculation in Engines, SAE Paper 2000-01-2865. Johansson B., Neij H., Juhlin G., AIden M. (1995), Residual Gas Visualization with Laser Induced Fluorescence, SAE Paper 952463. Mladek, M. (2000). A Model for the Estimation of Inducted Air Mass and the Residual Gas Fraction using Cylinder Pressure Measurements. SAE Paper 2000-01-0958 Randolph A, Methods of processing cylinderpressure transducer signals to maximize data accuracy, SAE Paper 900170. Bumt M., Lucas G., The effect of crankangle resolution on cylinder pressure analysis, SAE Paper 910041 . Kuratle R., Marki B., Influencing parameters and error sources during indication on internal combustion engines, SAE Paper 920233. puzinauskas P., Eves J., Tillman N., Measuring absolute-cylinder pressure and pressure drop across intake valves of firing engines, SAE Paper 941881. Randolph A., Cylinder-pressure-based combustion analysis in race engines, SAE Paper 942487. Bumt M., Pond C., Evaluation of techniques for absolute cylinder pressure correction, SAE Paper 970036.
ELSEVIER
IFAC PUBLICATIONS www.elsevier.comllocatelifac
RESIDUAL GAS MODEL FOR ON-LINE ESTIMATION FOR INLET AND EXHAUST CONTINUOUS VVT ENGINE CONFIGURATION
(*) DIEM, University ofBologna, Italy. (**) Magneti Marelli Powertrain, Bologna, Italy.
Abstract: In this paper a well known Residual Gas estimation model is evaluated on real data and extended to an engine configuration that involves an external Exhaust Gas Recirculation (EGR) circuit and a Variable Valve Timing (VVT) system. The model proposed by M.Mladek and C.H.Onder (Swiss Federal Institute of Technology) ha~ been modified to take into account the presence of these two systems, and has been vahdated this comparing the results to data obtained form a 6 .cyliders e~gine. The main goal work is to validate and extend to external EGR mput the given model, With the aun of designing VVT model based control strategies for combustion and pollution emission optimal performances. Copyright © 2004 IFAC
0:
Keywords: automotive, Residual Gas Fraction, Residual Gas model, VVT, model validation.
1.
quantity (some off-line ones can be found in the literature [2-8]), and the increasing complexity of intake manifold hardware configuration that has a great impact over the residual gas value, one of the most important being for example the Variable Valves Timing (VVT) system control. It is well known that a VVT system is determinant in defining the ratio between air mass flow and residual gas entering the cylinder, thus affecting both the torque production and the engine emission; it is the authors opinion that VVT control could be optirnized and correctly approached using a correct residual gas fraction estimation, by choosing as an external input of the control the gas composition in any engine point. The residual gas fraction models present in literature have been developed for engines that are not equipped with an external EGR system, while this component is part of the engine considered for the development of this work. The main goal of the paper is therefore the critical analysis of a residual gas fraction model based on incylinder pressure measurement [5], and the extension
INTRODUCTION
Residual gas fraction in Internal Combustion Engines is a critical factor in many aspects of combustion and engine performances: its influence on flame speed and combustion stability is relevant for torque production and combustion repeatability (i.e. cycle by cycle combustion variability), while its impact on incylinder gas mass temperature can be one of the prime factors over NOx production and control. For this reason it could be important for engine control purposes (e.g. dri veability, pollution emission control, engine stability at idle) to estimate with an appropriate precision the residual gas mass fraction, whose value is mainly related to two components: the gas which is drawn back from the exhaust manifold during inlet and exhaust valves overlapping phase, and the gas trapped in the cylinder when the exhaust valve closes [I]. Two main aspects have to be taken into account when approaching the problem: the complete absence of an in-line sensor to measure this
257
of the same model to engines equipped with external EGR circuit and VVT system. Such a model will then be used for VVT control strategy definition and design. 2.
Srg
S EGR Sa j,
Residual
gas
mass
fraction
inside the
cylinder EGR mass fraction inside the cylinder
Air mass fraction inside the cylinder Fuel mass fraction inside the cylinder
NOMENCLATURE
mlOI
Total mass inside the cylinder [kg]
Xc
Air Fuel Ratio Combustion efficiency
Pso
In-cylinder pressure at 50% mass burned
cv,.
Combustion
reactants
constant
volume
CV p'
specific heat [J/kg K] Combustion products
constant
volume
RN!
specific heat [J/kg K] Reactants ideal gas constant [J/kg K]
Rp,
Products ideal gas constant [J/kg K]
Hu
Fuel lower heating value [J/kg]
X rgold
Residual gas mass fraction at the beginning
X rg"....
of an iteration Residual gas mass fraction at the end of an
conditions [Pal Cylinder volume at 50% mass burned conditions [m3] Ideal gas constant for the gas mixture present at 50% mass burned condition [J/kg K] Temperature at 50% mass burned conditions [K] Intake Valve Opening Intake Valve Closing Exhaust Valve Opening Exhaust Valve Closing Top Dead Center In-cylinder pressure at lYC [Pal
lYO lYC EVO EVC TDC
iteration 3.
Cylinder volume at lYC [m3]
ENGINE MODEL
Description of the original model
Ideal gas constant for the gas mixture present at lYC [J/kg K] Temperature at lYC [K]
The approach used in this work to perform Residual Gas estimation is derived from the literature [9] , and is briefly described in Figure 1.
Mass of fresh charge entering the cylinder [kg] Residual gas mass inside the cylinder [kg]
Estimation of the in-cylinder temperature at the 50% mass burned position
Constant volume specific heat for the fresh charge [J/kg K] Constant volume specific heat for the residual gas [J/kg K] Fresh charge temperature [K] Residual gas temperature [K] Residual gas mass fraction Total internal energy at lYC [J] Total internal energy at 50% mass burned condition [J] Indicated work to the piston between lYC and 50% mass burned conditions [1] Heat developed by the combustion process up to the 50% mass burned condition [J] Heat loss between lYC and 50% mass
Qcomb
Q cooling
burned conditions [1]
qcooling
=
Q cooling / Qcomb
mEGR
EGR mass inside the cylinder [kg]
ma j ,
Air mass inside the cylinder [kg]
mf
Fuel mass inside the cylinder [kg]
X EGR
EGR mass fraction with respect to the mass entering the cylinder from the intake manifold
NO
Figure 1: Flow chart of the model
258
estimation of the in-cylinder temperature at the instant where the 50% of the mass is burned. This is possible by applying a first law energy balance between IVC and 50% mass burned positions.
It requires the measurement of the in-cylinder pressure together with the measurement of the fresh charge temperature into the intake manifold and optionally the measurement of the exhaust gas temperature or the engine speed. An estimation of the temperature inside the cylinder when the 50% of the fresh charge is burned is initially needed. This value can be chosen, for example, as a reasonable first attempt, equal to 1850 K. Applying ideal gas law to the charge inside the cylinder in the crankshaft angular position corresponding to the 50% of mass burned it is possible to obtain an estimation of the total mass:
Expliciting all the terms of Equation (6) it is possible to obtain:
(7)
(1) Equation (7) gives a new estimation of Tso , provided that an evaluation of qcocling and the measurement of the in-cylinder pressure are available. The new value of Tso is now compared to the initial value and all the procedure is repeated using the new estimation of Tso and X,g until the new value obtained at the end of the procedure equals the initial value.
where Tso has been previously chosen, Pso has been measured and Rso can be estimated considering a first attempt value of the residual gas fraction equal to 10%. The total mass inside the cylinder can be used to evaluate the temperature inside the cylinder at Intake Valve Closing (IVC) position. This can bone by applying ideal gas law, and using the knowledge of the in-cylinder pressure for that condition, and again estimating Rrvc considering an initial 10% residual gas fraction value.
Model extension The model described in the preceding section does not consider the presence of an external Exhaust Gas Recirculation (EGR) and requires particular attention when applied to an engine equipped with a Variable Valve Timing (VVT) system. Both these issues are discussed and new model equations to take EGR presence into account are introduced in this section, while the main structure of the model remains equal to the one introduced in Figure I. When an engine is equipped with an EGR system the flow entering the cylinder from the intake manifold is composed by both fresh charge and exhaust gas (EGR). Usually the amount of exhaust gas entering the cylinder is measured as a fraction of the total entering mass (air + EGR):
(2)
An energy balance at lVC allows at this point determining the residual gas fraction estimation. It can be stated in fact that, at IVC, the contribution to the total internal energy of the gas inside the cylinder is related to the internal energy of the residual gas and fresh charge before the mixture creation.
{m /ecy /e + mrgcyrg )T/Vc
=
=m/ecy/eT/e +mrgcyrgTrg
(3)
(8)
The residual gas fraction can be evaluated as the ratio between the residual gas mass and the total mass present inside the cylinder, and therefore:
The total gas mass present inside the cylinder is composed by EGR, air and fuel entering the cylinder and residual gas (or internal EGR) from the preceding combustion. The mass fractions of the in-cylinder total mass different components can be determined as:
(4)
Equation (3) can the be rewritten obtaining:
The estimation of the residual gas fraction obtained in Equation (5) can be used at this point to perform an
259
exhaust gas temperature; intake manifold temperature in a posltJon where air and EGR mass flows can be considered completely mixed VVT position in order to precisely evaluate IVC crank angular position In addition a critical sub-model has to be developed in order to evaluate the heat exchange through the cylinder walls from IVC to 50% mass burned condition.
m
Srg =~=Xrg m 101 m EGR AFR . X EGR • (1 - X rg ) SEGR = - - = ---.=..:::.::.-'-----'''-'m,o, 1 + AFR- X EGR Sa
=
(9)
mlOI
= [(AFR + 1); AFR + X EGR / (1- X EGR)]
(1- Xrg)
mf
Sf
Simplified model
= m,o, = [1+AFR(I+X EGR / (I-X EGR ))]
The model introduced in the preceding section can be used to perform Residual Gas estimation provided all the needed measurements and sub-models are available. The most critical aspect in the implementation of the model are the evaluation of the in-cylinder pressure at IVC and the evaluation of the heat exchange qcooling between IVC and 50% mass burned conditions. The first problem has been solved by applying a particular signal processing technique to the in-cylinder pressure signal, as it will be shown in a following section; the second and really critical point is instead very difficult to be solved, while its impact on model outputs behaviour is relevant.
In order to evaluate EGR, air and fuel mass fractions, additional measurements of EGR rate X EGR and Air Fuel Ratio (AFR) are required with respect to the original model. It is advantageous to define in addition the thermodynamic properties (c y and R) of the reactants (air and fuel) and products (Residual gas and EGR) of the combustion process (cYre> cvpr and R", Rpr are then considered). In this way the thermodynamic properties of a generic mixture can be determined simply by weighting the characteristic of the corresponding mass fraction. Equations (2), (3) and (5) previously defmed are still valid simply considering as fresh charge the total flow entering the cylinder from the intake manifold (composed by air, fuel and EGR) and measuring the fresh charge temperature in the intake manifold in a position where the air and EGR mass flows can be considered completely mixed. The value of Cv fe and C Yrg in Equation (5) or R IVC in Equation (2) can be determined for example by the knowledge of cYre ' cYpr ' Rre , Rpr :
Sair + Sfuel + S EGR C yrg
R/ vc
=C ypr
(10)
=RjSair + Sfuel)+ Rpr (S EGR + Srg)
Equation (7) instead needs to be slightly rearranged. In fact in this case:
and therefore:
Figure 2: Flow chart of the simplified model
(12)
For this reason a simplified version of the total model has been developed, that does not need the knowledge of heat losses through the cylinder walls between !VC and 50% mass burned condition. In this simplified model version, the air mass entering the cylinder has to be known and therefore considered as an input and not a model output anymore. The only output of the
Measurements required to obtain residual gas fraction estimation are therefore: in-cylinder pressure
260
implementation IVC does not have the meaning of the crank position where the intake valve touches its seat, but the crank position where the intake flow stops, and it can be considered equal to O. This makes the choice of IVC location even more complex, with a possible choice compatible with the valve lift trace ranging from 230 to 270 degrees after TDC. To solve this problem in-cylinder pressure signal has been used once again. In particular it has been observed that a polythropic behaviour with exponent 1.32 during the compression phase can be assumed only if the gas inside the cylinder can be considered isolated (or the cylinder can be considered as a closed system). Therefore when the in-cylinder pressure signal deviates from this behaviour, the gas inside the cylinder cannot be considered isolated anymore, and therefore a mass flow is entering or exiting the cylinder.
simplified model is therefore the residual gas fraction estimation The flow-chart of the new model implementation is described in Figure 2. The simplified model requires to be implemented Equations (2), (5) and (10) together with the simple consideration that:
Measurements required are: in-cylinder pressure; exhaust gas temperature; intake manifold temperature in a poslt1on where air and EGR mass flows can be considered well mixed; VVT position in order to precisely evaluate IVC crank angular position; Air mass entering the cylinder. It has to be stressed that no other information is required to obtain the desired residual gas fraction estimation.
i:'
cost
0.6
CII
Polythropic behavior
~--'' --'---4-/---+--
-1
5.
0.5 t 0.4 , ~ 0.3 ...---.~-...
.
,
-.---+.--.-..--~-.--.
~ 0.2 bC:::::·~ , -~-:t:=-L-L_~J CJ
c!: 0.1 -
i--.;........-.'---~--+---+--.
0.0 L-_'--_"--_"--_"'-_"'-_-'----.J
180 200 220 240 260 280 300 320 Crankshaft angle [0] Figure 3: In-cylinder pressure around IVC position
The described procedure has been applied to determine the IVC position on the considered engine at approximately 240 0 crank angle position after TDC. Results are shown on Figure 3. Algorithm convergence problems
Both the complete and simplified version of the analysed algorithm allow obtaining a residual gas mass fraction estimation as result of an iterative solution process. Sometimes the iterative process did not converge to a stable solution, as in the example presented in Figure 4a, where the value of Xrg is reported as function of iterations number.
(14)
the value of the constant cost that best fits (in the Least Mean Square sense) the measured in-cylinder pressure waveform during compression phase. This identification allows determining finally:
p{VC :;: VI.32
~
- .
In-cylinder pressure sensors are usually well suited to give a good precision while measuring high range part of the in-cylinder pressure signal. For this reason accuracy in the low pressure part of the signal is usually poor [10-15]. Therefore PlVC measurement could be affected by poor accuracy, thus negatively influencing the whole estimation process to obtain the residual gas fraction value. In order to minimize this effect the value of the pressure at IVC position has been evaluated using the in-cylinder pressure signal acquired during the compression phase. Modelling the compression phase as a polythropic compression process with exponent 1.32 [1], it is possible to identify from the general equation of a polythropic transformation
=cost
0.8
~ 0.7 ~-=::::;:=:::;::=====~h-~ . . =
In-cylinder pressure at IVC
p · V"
- - Measured
~
,Q
(IS)
{Vc
The value of PIVC determined in this way, should be less sensitive to sensor accuracy, since it derives from measurements performed in the high pressure part of the signal. Another issue that needs to be solved is the right determination of the IVC position. From figure 5 it is possible to observe that the valve lift trace is very flat when the valve starts opening or in the closing phase. It has to be underlined that for the model
261
5oo.----.,.----,....---,....----,
air entering the cylinder per cycle and then in term of fuel distribution. Finally, the engine and inlet exhaust configuration forces a particular exhaust line sensor setup, so composed:
~ 400 ~----------- ... ----.---- .. -- --- .. ---·------ ii---, .... --.
§ ::CJ ~
300~------~----~~~·R_-A-4It_~H 200~----~-r_+~~t-++-H~+-~
~
• • • • • •
'" lOO
= ~
0
';
= -lOO
-+
~
.~ -200 ~-------'------._f_+---lJ__i_-t--4___l Cl:::
.3~L-.--5"'----1...i.0--......... 15----120
while the main intake line characteristics involve the runners with double lengths (variable geometry on / oft) and the Tumble valves. For experimental and study purposes, the engine was equipped with additional sensors, mainly one pressure sensor in each cylinder, temperature and pressure sensors in the exhaust line and in the catalyst main body.
Iterations Figure 4a: Residual gas fraction evaluation using a simple iteration process
__
~
100~-----~,--~,--~
§
80 70 ~ 60 '" 50 ~
~
~
_ --L___ _
90 I - - - - -_____ --L_
r------. ---L----.-~- --.-----.,--- --- ---.-r--..-.-.-----.-t--------.----.. -----·.. ·-·--·--~- --- .. ·----····----·i
The variable valve timing system mounted on this engine can perform continuous intake and exhaust valves actuation: the intake valves opening (IVO) can be advanced and the exhaust valve closing (EVC) can be delayed from their 'mechanical' uncontrolled position. The intake and exhaust valve proftles of the engine here considered are shown in Figure 2, where it can be seen the valve overlap in the deactivated state (0 crank-angle) with respect to the applied maximum valve overlap corresponding to a 40 crank-angle degrees IVO advance and EVe delay. In Figure 2 it is also possible to observe that the intake valve flight proftle is particularly flat in the initial and [mal phases and it is therefore difficult to precisely detect the angular position of valve closing and opening.
: , .
--------L----~-
30
~ 20 - . .
.-
~ 10 r '
o
VVT system description
-----....--;.---.--.----.. ----..
I--.--__ ~------+------i-------I
40Ft o
5
.'
-- . -
•
•
10
15
20
Iterations Figure 4b: Residual gas fraction evaluation using a modified iteration process
This problem has been solved by considering as the new approximation starting value a combination of the initial and [mal result of the last algorithm iteration. As an example, if Xrg old is the first estimation value and Xrg new is the new value computed after the ftrst algorithm iteration, the new approximation value for the second iteration has to be set equal to :
x
+ .... old
x .... n.... -x 2
.... old
Test description
The pressure measurements are performed with a degree crank angle resolution using respectively:
( 16)
• •
Using this approach the convergence problem has been solved, as it can be seen in Figure 4b, where the same test as in Figure 4a has been considered.
4.
2 UEGO controlling the two different bench; 2 precat (one for each bench); 2 lambda on / off (one for each bench) 2 temperature sensors 2 Nox trap I N ox sensor
•
an un-cooled sensor for in-cylinder pressure measurement; a sensor designed for research purposes, settled in the intake runner; a water-cooled sensor in each exhaust line.
The air mass measurements are obtained from the fuel flow and the lambda measurements. The value of lambda is measured using a gas analysis system. Tests were performed throughout the engine operating range from 1000 to 4000 rpm and inlet manifold pressure equal to 300, 600 and 900 mbar. Operatively, for any engine operating point, acquisitions were made at stoichiometric conditions for different combinations of intake and exhaust valve timings, while varying EGR flow. The main experimental data over which the model is based are:
EXPERIMENTAL SETUP
Engine description
The test engine used in this study is a 3.2-liters 6 cylinders GDI engine, with four valves per cylinder. The engine is characterized by narrow-angle (15°) V6 displacement, to save space and for on car housing reasons. The particular engine design has forced an asymmetric configuration on inlet and exhaust runners and manifold structure, which in turn can lead to a different behaviour of the two benches in term of
262
• • • • •
0.15 r---;::=:r:::==-r-:----r---, = 0.141-----1- --i---'-------1 o -
engine speed cylinder pressure inlet manifold pressure and temperature exhaust temperature precise crank-angle position of intake valve closing (IYC) while varying the valves timing.
-EVO O" EVO 10· EV0 20·
~ 0.13, ~~::::::=:::j~~~~g~::'-!.:: 0.12~ ; 0.11
-_-~f-=:-::-:f'""::::-_-:;_..._~-~-;
~
7i 0.10 ~ 0.09
~
10
-
e
.§.
9
8
0.08 . . . ', . 0.07 --.-----~-.-!--+__ .•- - . 0.06
7 c:= 6 5 ~ 4 -; 3 ;> 2 1
0
5
10
15
20
25
30
35
40
IVO advance [0]
:s
Figure 6: Residual gas fraction variation as a function of the IVO advance for tests conducted at 2000 rpm and 600 mbar 0.15 0.14
-250
-150
-50 0 50
150
= 0.13
250
-
.~
Crank Angle [0 = TDC]
rvoo o !Vo 10· I----i---+-
.::
IV020·
+----'--.;- - - I
~g~: f--~--+--+----"--f-Z~
Cj
Figure 5: Valve lift
0.12
'"= 0.11 ~
7i 5.
-
-'" =
O~~--~~~~----~~~
:I
MODEL RESULTS
"Q
.~
Q,j
er::
This section reports the results obtained using the different versions of the model and a brief discussion on their possible use to define and optimise a VVT system control strategy. The results obtained using the complete model are greatly affected by the Qcooling evaluation accuracy. For example the error in evaluating the air mass flow entering the cylinder can be as high as 10 to 20% . For this reason the results obtained with this model have not been considered. the results obtained using the simplified model are reported in Figures 6, 7 and
0.10 0.09 0.08 0.07 0.06
0
5
10
15
20
25
30
35
40
EVO delay [0) Figure 7: Residual gas fraction variation as a function of the EVO delay for tests conducted at 2000 rpm and 600 mbar
As it can be seen the IVO-EVO combination that guarantees the minimum Residual Gas fraction is not the one characterised by the minimum overlap, but if the overlap is very high (as in the case of IYO advanced 40 deg and EVO delayed 40 deg) the amount of residual gas fraction increases. Considering all the IVO-EVO configurations that give the same overlap angle (for example IVO=O° EV0=40°, IYO=IO° EVO=30°, IVO=20° EYO=20°, and so on), it is possible to observe that the one that guarantees the minimum Residual Gas Fraction is the one with early EYO and IVO.
8.
Figures 6 and 7 report the value of x,-g for a given engine operating condition (2000 rpm and 600 mbar) as a function of exhaust and intake valve positions. Figure 8 reports for each VVT configuration (characterized by IVO advance and EVC delay) a map of Xrg over the engine operating range considered (in tenns of engine speed and intake manifold pressure). It can be observed that Xrg values are greatly influenced by the exhaust valve position, while less affected by the intake valve opening angle.
263
· ~~~ .-:
!..
Figure 8: Residual gas estimation for different VVT configurations
264
EXTENDED INTERNAL EGR HINT TO POSSIBLE USES [5]. The availability of a complete and validated residual internal gas model, extended to the contribution of a Variable Valve Timing system and an External residual gas component, allows defining innovative strategies such as: • Design an optimization algorithm to choose the best IVO and EVO target value (depending on engine speed and charge), in order to optimize engine consumption and pollutant emissions; • In any engine point, the appropriate internal and external EGR mass mixture can be obtained in the cylinder, so regulating the gas temperature for combustion stability and emission constraints; • The complete off-line described model can generate static points then used to identify, validate and implement in the Electronic Control Unit a simpler model, which doesn't need any information about the incylinder pressure, like the model described in [2]; • Complete and improve a combustion model for an Hardware in the Loop validation of the combustion control and management software. 7.
[6].
[7].
[8].
[9].
[10].
[11].
(12].
CONCLUSIONS
The paper presents an original review of an existing model for Residual Gas mass fraction evaluation. The model has been critically analyzed and extended to take into account the presence of an external EGR system. In addition a simplified version of the model has been presented that enables residual gas fraction evaluation without requiring a model for the heat exchange between the gas inside the cylinder and the cylinder walls. The new model has been applied to experimental data obtained from a 6 cylinder engine. The results obtained are the first step in the design of a VVT control strategy for combustion and emission optimal performances.
[13].
[14].
[15].
REFERENCES [I].
[2].
[3].
[4].
Heywood: "Internal Combustion Engine Fundamentals," McGraw Hill International Editions, 1988. Heywood, M. (1993). A model for predicting residual gas Fraction in Spark Ignition Engines. SAE Paper 931025. Ford, R (1999). Measurement of Residual Gas Fraction using a Fast Response NO Sensor. SAE Paper 1999-01-0208. Quader, Ather. A. (1999). Cycle-By-Cycle Mixture Strenght and Residual-Gas
265
Measurements During Cold Starting. SAE Paper 1999-01-1107. Miller R., Russ S., Weaver c., Kaiser E., Newmann C., Davis G., Lavole G. (1998). of Analytically and Comparison Experimentally Obtained Residual Fractions and NOx Emissions in Spark-Ignited Engines. SAE Paper 982562. Hjinze P.C., Miles P.C. (1999), Quantitative Measurements of Residual and Fresh Charge Mixing in a Modem SI Engine Using Spontaneous Raman Scattering, SAE Paper 1999-01-1106. Hall MJ., Zuzek P. (2000), Fiber Optic Sensor for Time-Resolved Measurements of Exhaust Gas Recirculation in Engines, SAE Paper 2000-01-2865. Johansson B., Neij H., Juhlin G., AIden M. (1995), Residual Gas Visualization with Laser Induced Fluorescence, SAE Paper 952463. Mladek, M. (2000). A Model for the Estimation of Inducted Air Mass and the Residual Gas Fraction using Cylinder Pressure Measurements. SAE Paper 2000-01-0958 Randolph A, Methods of processing cylinderpressure transducer signals to maximize data accuracy, SAE Paper 900170. Bumt M., Lucas G., The effect of crankangle resolution on cylinder pressure analysis, SAE Paper 910041 . Kuratle R., Marki B., Influencing parameters and error sources during indication on internal combustion engines, SAE Paper 920233. puzinauskas P., Eves J., Tillman N., Measuring absolute-cylinder pressure and pressure drop across intake valves of firing engines, SAE Paper 941881. Randolph A., Cylinder-pressure-based combustion analysis in race engines, SAE Paper 942487. Bumt M., Pond C., Evaluation of techniques for absolute cylinder pressure correction, SAE Paper 970036.