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Modeling of HCCI Engine Combustion for Control Analysis
Bengtsson, Johan; Gäfvert, Magnus; Strandh, Petter
Published in:Proceedings 43rd IEEE Conference on Decision and Control
2004
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Citation for published version (APA):Bengtsson, J., Gäfvert, M., & Strandh, P. (2004). Modeling of HCCI Engine Combustion for Control Analysis. InProceedings 43rd IEEE Conference on Decision and Control (Vol. 2, pp. 1682-1687). IEEE - Institute ofElectrical and Electronics Engineers Inc..
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Modeling of HCCI Engine Combustion for Control Analysis
Johan BengtssonDepartment of Automatic Control
Lund Institute of Technology, [email protected]
Magnus GäfvertDepartment of Automatic Control
Lund Institute of Technology, [email protected]
Petter StrandhVolvo Technical Corporation
Dept. 6180, CTP,Gothenburg, Sweden
Abstract— Operation of homogeneous charge compressionignition (HCCI) engines are very sensitive to timing variationsin the combustion of the air-fuel charge mixture and requireprecise control of the ignition instant to run properly. It istherefore essential to understand the characteristics of timingvariations under various operating conditions in order tofind suitable control strategies. This paper presents a firststep towards the construction of an HCCI engine modelaimed at studies on timing control strategies. The goal isto (qualitatively) reproduce the timing effects that may beobserved on a real engine. The proposed model includesa lumped chemical kinetic model for hydrocarbon fuels topredict autoignition. Single-cycle simulations are comparedwith experimental results from a real engine to validate themodel. Comparisons are also made with a model based on theknock-integral.
I. INTRODUCTION
In homogeneous charge compression ignition (HCCI)engines the ignition timing is defined by the autoignitionproperties of the air-fuel mixture in use. Small variationsin the cylinder environment may greatly influence theignition timing. In order to control engine operation it istherefore necessary to have good models and substantialunderstanding of the ignition and combustion process. Thiswork aims at describing the major thermodynamic andchemical interactions in the course of an engine stroke andtheir influence on ignition timing. The goal is to constructa simulation model that (qualitatively) reproduces HCCIengine operation for the purpose of synthesizing, analyzing,and evaluating various ignition timing control strategies.Common strategies for timing control includes varyingthe inlet temperature and fuel composition, or to employvariable valve timing. Previous work on control of HCCIengine timing is presented in, e.g., [1], [2], [3], [4], [5].The present work is a feasibility study on requirements andchoice of complexity level for a suitable model, and is tobe regarded as a first step towards a complete model. Theproposed model structure consists of a zero-dimensionalcylinder model, combined with a reduced chemical kineticmodel to describe the ignition process. Experiments on areal engine with dual fuels and inlet air temperature controlhave been conducted to collect information on the phenom-ena to reproduce and to compare to simulated results. Theexperimental setup is described in Section II, followed bythe model description in Section III. Section IV presentsexperimental and simulated results, which are discussed inSection V. Finally, conclusions are stated in Section VI.
TABLE I
ENGINE SPECIFICATIONS.
Operated cylinders 6Displaced Volume 2000 cm3
Bore 131 mmStroke 150 mmConnecting Rod Length 260 mmNumber of Valves 4Compression Ratio 18.5:1Fuel Supply port fuel injection
II. EXPERIMENTAL SETUP
A. Research Engine
Experiments were performed on a six cylinder converteddiesel engine. The experimental setup (Fig. 1 and TableI) consisted of a heavy duty Volvo diesel engine, with adisplaced volume of 12 l. The engine was converted to portfuel injection with dual fuels. The engine was equipped with14 mm cylinder pressure transducers on all cylinders anda Variable Geometry Turbo (VGT) which made it possibleto adjust the boost pressure. It also had an intercooler andan inlet air heater for controlling inlet air temperatures. Theused dual fuels were ethanol and a fifty-fifty mixture of n-heptane and ethanol. The use of a mixture instead of puren-heptane was to improve precision of the control. The dualfuels give Research Octane Number (RON) ratings from 53up to 106.
B. Data Acquisition
The data acqusition system ran on a standard PC withGNU/Linux operating system, resulting in a flexible plat-form with good soft real-time properties. All data comingfrom various sensors around the engine were collected in themain control program (Fig. II). These data included varioustemperatures and pressures collected via a data loggersampling at low sampling rate, various temperatures andcylinder pressures collected via a Microstar DAP samplingat fast sampling rate, and exhaust emissions data fromthe emission system sampling at low sampling rate. Thecylinder pressure data acquisition was controlled by anencoder connected to the crank shaft of the engine. Asample was taken at every encoder pulse, i.e., every 0.2crank angle degree. The cylinder pressure data was sampledby a Microstar 5400A/627 data acquisition processor. Assoon as one cylinder passed exhaust valve opening, pressure
43rd IEEE Conference on Decision and ControlDecember 14-17, 2004Atlantis, Paradise Island, Bahamas
0-7803-8682-5/04/$20.00 ©2004 IEEE
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Inter cooler
Heater
Turbocharger
Air
EngineEthanol
N−Heptane
GUI
Simulink(Real−Time Workshop
generated C−code)
PCLinux
Microstar
Emission
DAP5400a/627
Logger PIC
Exhaust
Data Acquisition system
Fig. 1. Experimental set-up consisting of a 6-cylinder, 12 l, heavy dutyVolvo diesel engine, with a data acqusition system.
data were transferred from the AD card to the controlprogram. When new pressure data was available in thedata acqusition system, a simplified rate of heat releasecalculation based on pressure, [6], was performed andthereafter combustion timing was calculated. The two fuelshave different autoignition temperatures, a property that wasused to change the combustion timing. The experimentalset-up also allow for closed-loop control with controllersimplemented using Simulink and converted to C-code usingthe automatic code generation tool of Real Time Workshop.However, in this paper all experiments were carried out inopen-loop.
C. Experiments
In the experiments, the volume ratio, Rf , of the dualfuels ethanol and n-heptane, fuel energy per cycle, Qin,inlet air temperature, Tin, and the engine speed, w, werechanged according to Table II. By changing the injectedfuel energy per cycle the load is changed and Qin = 1000
TABLE II
EXPERIMENTAL CONDITIONS
Tin [◦C] 100–115 100 100 100w[rpm] 1200 1000–1500 1200 1200Qin[J ] 1400 1400 1000–1500 1400Rf [vol%] 0.93 0.93 0.93 0.892–1.0
J corresponds to a FuelMEP of 5 bar and Qin = 1500J corresponds to a FuelMEP of 7.5 bar. Only low loadexperiments in open loop were performed, when the enginetemperature was at steady state. At each operating point,data of 500 cycles were collected. Mean value of these 500cycles was thereafter used in comparison with the resultfrom the model.
III. MODEL
HCCI combustion is often achieved without a completehomogeneous mixture, but from a control-oriented pointof view it is a reasonable approximation that the mixtureis homogeneous and simultaneous ignition of the mixtureoccur. Hence, it is reasonable to use a zero-dimensional(single-zone) cylinder model. Several alternative approachesare possible for modeling the instant of autoignition forfuels. To reproduce the effects relevant for ignition-timingcontrol it is required that the autoignition model capturesthe effects on ignition delay (induction time) of varyingspecies concentrations, temperature trace, and fuel quality.Large models, e.g. [7] (PRF fuels, 857 species, 3,606reactions, CHEMKIN/LLNL), have been used to modelcomplete combustion. In addition to ignition prediction,such models are also aimed at describing intermediatespecies and end product composition. Reduced chemical ki-netics models, e.g. [8] (PRF fuels, 32 species, 55 reactions,CHEMKIN), have also been proposed, where reactionswith little influence on the combustion has been identifiedand removed. For simulation of multi-cycle scenarios itis necessary to keep the model complexity low in orderto arrive at reasonable simulation times. An attractive andwidespread alternative is to use the Shell model [9], whichis a lumped chemical kinetics model using only five repre-sentative species in eight generic reactions. This model isaimed at prediction of autoignition rather than describingthe complete combustion process. Compression ignitiondelay may also be described by empirical correlations, suchas the knock integral condition
∫ ti
t=0
dtτ
= 1, where ti isthe instant of ignition and τ is the estimated ignition time(ignition delay) at the instantaneous pressure and tempera-ture conditions at time t, often described by Arrhenius typeexpressions [10]. A drawback is that dependence on speciesconcentrations is normally not regarded. An integral condi-tion with concentration dependence was used in [11], [5]in a similar study for propane fuel, where also autoignitionmodels based on very simple reaction mechanisms wereevaluated. A final alternative is to use empirical look-uptables. This gives very little physical insight, and require
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substantial efforts to calibrate. In this work, the Shell modelwas chosen to describe the process of autoignition. A staticmodel is then used to describe the major part of the actualcombustion and corresponding heat release. The result fromthe Shell model is compared with result from an integratedArrhenius rate threshold model.
A. Cylinder Model
The cylinder gas dynamics are described by the first lawwith volume-pressure work
δQHR = (1 +cv
R)pdV +
cv
RV dp + δQHT
where p is the cylinder pressure, V the volume, Ru theuniversal gas constant, cv = cp − Ru the specific heatcapacity, and n the molar substance amount contained inthe cylinder. The time derivatives of QHR and QHT denoterates of heat released by the combustion process and heatflowing from the wall.
B. Gas Properties
The gas is described as a mixture of dry air and fuel,and the combustion products nitrogen, carbondioxide andwater. Specific heat for each species i is described by NASApolynomial approximations of JANAF data
cp,i(T ) =Ru
Mi
5∑j=1
ai,jTj−3
where Mi is the molar mass of species i and T is thecylinder temperature. The mixture specific heat is then
cp(T ) =1
n
∑i
niMicp,i(T )
where ni is the mole of species i.
C. Shell Autoignition Model
The Shell autoignition model for hydrocarbon fuels [9],CaHb, is based on a general eight step chain-branchingreaction scheme with lumped species: The hydrocarbon fuelRH , radicals R̄, intermediate species Q, and the chainbranching agent B.
RH + O2
kq
−→ 2R̄ (initiation)
R̄kp
−→ R̄ + products and heat (propagation cycle)
R̄f1kp
−→ R̄ + B (propagation forming B)
R̄ + Qf2kp
−→ R̄ + B (propagation forming B)
R̄f3kp
−→ out (linear termination)
R̄f4kp
−→ R̄ + Q (propagation forming Q)
2R̄kt−→ out (quadratic termination)
Bkb−→ 2R̄ (degenerate branching)
Autoignition is described by integrating the time variationsof species concentrations from the beginning of the com-pression stroke.
d[R̄]
dt= 2
{kq[RH ][O2] + kb[B] − kt[R̄]
2}− f3kp[R̄]
d[B]
dt= f1kp[R̄] + f2kp[Q][R̄] − kb[B]
d[Q]
dt= f4kp[R̄] − f2kp[Q][R̄]
d[O2]
dt= −gkp[R̄]
The species R̄, Q, and B are not considered in thermody-namic computations for the gas mixture. The stoichiometryis approximated by assuming a constant CO/CO2 ratio,γ, for the complete combustion process, with oxygen con-sumption g = 2[a(1−γ)+ b/4]/b mole per cycle. The heatrelease from combustion is given by
dQHR
dt= kpqV [R̄]
where q is the exothermicity per cycle for the regarded fuel.The propagation rate coefficient is described as
k−1p =
1
kp,1[O2]+
1
kp,2
+1
kp,1[RH ]
To capture dependence of induction periods on fuel and airconcentrations the terms f1, f3, and f4 are expressed as
fi = f◦
i [O2]xi [RH ]
yi
Rate coefficients and rate parameters ki and f◦
i are thendescribed by Arrhenius rate coefficients
ki = Ai exp
[Ei
RuT
], f◦
i = Ai exp
[Ei
RuT
]
Calibrated parameters for a number of fuels, including aset of Primary Reference Fuels (PRF), are found in theliterature [9]. PRFx is a mixture of n-heptane and iso-octane, where the octane number x is defined as the volumepercentage of iso-octane. Parameters for PRF90 was usedin the simulations. Autoignition was defined as the crankangle where the explosive phase of combustion starts.
D. Integrated Arrhenius Rate Threshold
The Arrhenius form can be used to determine the ratecoefficient describing a single-step reaction between twomolecules [12]. The single-step rate integral condition isbased on the knock integral with
Kth =
∫ θ
θIVC
1/τ dθ/w
1/τ = A exp(Ea/(RuT ))[Fuel]a[O2]b
where θ is the crank angle and θIVC is the cank angleof the inlet valve closure. The integral condition describesa generalized reaction of fuel and oxygen and this is anextreme simplification of the large number of reactions that
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TABLE III
SIMULATION CONDITIONS
Tin [◦C] 100–115 100 100 100w[rpm] 1200 1000–1500 1200 1200Qin[J ] 1400 1400 1000–1500 1400
take place during combustion. The empirical parameters A,Ea, a, b and Kth are determined from experiments. Valuesfor n-heptane and iso-octane from [12] was used in thecomparison below. Autoignition was defined as the crankangle where integral condition has reached the thresholdKth.
E. Combustion
When autoignition is detected by the Shell model orthe Integrated Arrhenius Rate Threshold, the completion ofcombustion is described by a Vibe function [13].
xb(θ) = 1 − exp
[−a(
θ − θ0
∆θ)m+1
]
where xb denotes the mass fraction burnt, θ is the crankangle, θ0 start of combustion, ∆θ is the total duration, anda and m adjustable parameters that fix the shape of thecurve. The heat release is computed from the rate of xb
and the higher heating value of the fuel.
F. Heat Transfer
Heat is transfered by convection and radiation betweenin-cylinder gases and cylinder head, valves, cylinder walls,and piston during the engine cycle. In this case the radiationis neglected. This problem is very complex, but a standardsolution is to use a Newton’s law for external heat transfer
dQW
dt= hcAW (T − TW )
where QW is the heat transfer by conduction, AW is thewall area, TW is the wall temperature, and the heat-transfercoefficient, hc, is given by the Nusselt-Reynold’s relationby Woschni [14].
hc = 3.26B−0.2p0.8T−0.55(2.28Sp)0.8
where Sp is the mean piston speed and B is the bore.
G. Simulations
The described models were implemented and simulatedin MatlabTM for single engine cycles with given initialgas mixtures and states. Cylinder specifications were setaccording to Table I and simulation conditions according toTable III.
−150 −100 −50 0 50 100 15010
−20
10−15
10−10
10−5
100
−150 −100 −50 0 50 100 15010
−20
10−15
10−10
10−5
100
nRH
nR
nB
nQ
nAir
nCO2
nH2O
nN2
n[m
ol]
n[m
ol]
θ [deg]
θ [deg]
Fig. 4. Concentrations of gas species from Shell model ignition dynamicsfor nominal conditions, Tin = 373 K, Qin = 1400 J, w = 1200 rpmfor PRF90 fuel.
IV. RESULTS
Experiments were carried out to investigate the influenceon ignition timing from inlet temperature, engine speed, fuelenergy, and fuel ratio. There are several alternatives howto calculate the combustion timing and in this paper thecombustion timing is calculated as the crank angle where50% of the energy has been release, α50, [6]. The timingeffects on α50 were studied by varying the correspondingvariables from a nominal operating condition of Tin = 373K, Qin = 1400 J, w = 1200 rpm, and Rf = 0.93 vol% asdescribed in Table II. The acquired pressure, reconstructedtemperature traces, and reconstructed heat release [15] forthe nominal condition are shown in Fig. 2.
Fig. 3 shows pressure trace, temperature trace, and heatrelease for a simulation of a nominal operating point ofTin = 373 K, Qin = 1400 J, w = 1200 rpm for PRF90fuel. The dynamics of the ignition model is illustratedby the species concentrations in Fig. 4. Note that theconcentrations of R̄, Q, and B are frozen as the Shellmodel is switched for the Vibe combustion model. As earlierdescribed the autoignition was defined as the crank anglewhere the explosive phase of the combustion phase andit can be observed that approximately 10% of the fuel hasbeen burned at this crank angle. This is some few percentageabove what was measured burned fuel in the experiment atthe point where the ignition started. Timing effects on α50
from variations of inlet temperature, fuel energy and enginespeed according to Tables II and III are summarized inFig. 5. It can be noted that the Shell model gives quiteaccurate estimation of the timing for the temperature andthe engine speed sweep. The model is slightly less accuratewhen changing the load, but still gives the correct trend.
Results from simulations using the integrated Arrheniusmodel are also shown in Figure 5. This method gives goodresults for load variations. The results for speed variationsare less accurate at higher speeds. However, the model fails
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−80 −60 −40 −20 0 20 40 60 800
1
2
3
4
5
6
7x 10
6
CAD [deg]
P[P
a]
−80 −60 −40 −20 0 20 40 60 80200
400
600
800
1000
1200
1400
1600
1800
CAD [deg]
T[K
]
−80 −60 −40 −20 0 20 40 60 80−200
0
200
400
600
800
1000
1200
1400
1600
CAD [deg]
Q[J
]
Fig. 2. Pressure trace (left), temperature trace (middle), and heat release (right) from experiment at Tin = 373 K, Qin = 1400 J, w = 1200 rpm(solid) and w = 1500 rpm (dashed).
−80 −60 −40 −20 0 20 40 60 800
1
2
3
4
5
6
7
x 106
CAD [deg]
P[P
a]
−80 −60 −40 −20 0 20 40 60 80200
400
600
800
1000
1200
1400
1600
CAD [deg]
T[K
]
−80 −60 −40 −20 0 20 40 60 80
0
200
400
600
800
1000
1200
1400
CAD [deg]
Q[J
]Fig. 3. Pressure trace (left), temperature trace (middle), and heat release (right) of simulation at nominal conditions, Tin = 373 K, Qin = 1400 J,w = 1200 rpm for PRF90 fuel.
100 105 110 1150
2
4
6
8
10
1000 1100 1200 1300 1400 15000
5
10
15
20
1000 1100 1200 1300 1400 15004
6
8
10
12
14
16
18
α50
[deg
]
α50
[deg
]
α50
[deg
]
Tin [deg Celsius] w [rpm]
Qin [J]
Fig. 5. Effects on ignition timing of variations from nominal conditions,Tin = 373 K, Qin = 1400 J, w = 1200 rpm. The experimental resultsare marked as ’*’, the Shell model results with ’o’, the Arrhenius RateIntegral results with ’+’, and the Planet mechanism with ’♦’.
at variations of the inlet temperature.In order to compare the ignition prediction accuracy of
these low complexity models with more refined ones, resultsfrom homogeneous calculations using detailed chemicalkinetics are included in Figure 5. Here, detailed chemistryfor an ethanol/n-heptane mixture was obtained through the
Planet mechanism for PRF fuels. For more details on thephysical and chemical modeling, see references [16], [17].From Figure 5 it can be observed that the Shell model givessimilar result of prediction of α50 as the Planet mechanismfor inlet temperature variations. This observation is also truefor the speed variations. But in the case of load variationthe Planet mechanism gives significant better result.
V. DISCUSSION
The results indicate that the proposed model may be usedfor studies on feedback strategies for ignition control. Qual-itative timing behavior is correctly reproduced at variationsin inlet temperature, engine speed, and load.
The simulation model was only crudely calibrated. Fur-ther work will address calibration issues, and the quantita-tive results are then expected to improve. The Shell-modelparameters of [9] are from experiments on a rapid compres-sion machine. Preliminary attempts with manual tuning ofthe parameters have shown to yield better agreement withthe ignition process in a heavy-duty engine.
The proposed model performed better than the integratedArrhenius model in the comparisons. It should be noted thatthe results were obtained with nominal PRF90 parametersfrom the literature. The latter model has an advantage ofhaving few parameters and engine specific calibration islikely to be easier. As in [12] the integral expression can
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also include explicit temperature dependence, which alsowas included in [5]. It may then be possible to improve theresults for temperature variations. The Shell model gavein the prediction of α50 almost similar behavior as thedetailed chemistry Planet mechanism, indicating that lowcomplexity models can be used on feedback strategies forignition control.
Presently, the model contains single-cylinder behavior forsingle-cycle simulations. It is of interest to study transienteffects over multiple cycles. This requires the inclusion ofgas-exchange models, wall heat dynamics, etc.
The Shell autoignition model is only applicable forsingle-component fuels. Therefore, no simulation results arepresented to show the timing effects of varying the fuelratio. A possible extension of the model is to include multi-component fuels. Parameters for a number of PRF fuels areavailable in the literature. These may be used to describefuel quality variations, with restrictions to a limited set offuel ratios. However, ignition control using dual fuels is aless practical approach, as it requires new infrastructure andthe consumer need to refuel to fuels. The current trend is toinstead use variable valve timing, for which the proposedmodel is straightforwardly applicable in its current form.
The experiments were performed in open-loop at low loadconditions. The applicability of a model calibrated from lowload experiments at high load conditions need to be furtherinvestigated. For high load experiments it is necessary toapply closed-loop control of ignition timing.
VI. CONCLUSIONS
The presented results indicates that a fairly simple au-toignition model may be used to predict timing behaviourof HCCI engines at low load. It is therefore reasonableto extend this model to multi-cycle simulations includingeffects of heat dynamics and gas exchange.
ACKNOWLEDGMENTS
This work was supported by the Vinnova Green Carproject. The authors gratefully acknowledges Dr. Per Am-néus at Department of physics, Division of combustionphysics, Lund Institute of Technology, for providing simula-tion result of the Planet mechanism. Dr. Per Tunestål at theDepartment of Heat and Transfer, Division of Combustion,Lund Institute of Technology, for valuable help and dis-cussions. Prof. Rolf Johansson at Department of AutomaticControl, Lund Insititute of Technology, has provided withvaluable comments on the manuscript.
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