Understanding the transition between conventional...

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Understanding the transition between conventional spark-ignited combustion and HCCI in a gasoline engine C. Stuart Daw, Robert M. Wagner * , K. Dean Edwards, Johney B. Green Jr. Oak Ridge National Laboratory, 2360 Cherahala Boulevard, Knoxville, TN 37932, USA Abstract We describe experimental observations of the gradual transition between conventional spark-ignited (SI) propagating flame combustion and homogeneous charge compression ignition (HCCI) in a single- cylinder, stoichiometrically fueled gasoline engine. Our objective is to better understand the transition process in terms of characteristic changes to the combustion stability as indicated by patterns of cyclic variations. The transition was experimentally achieved by incrementally adjusting the level of internal exhaust gas recirculation (EGR) using variable exhaust valve actuation. Throttle adjustments were also made to maintain a constant fueling rate. For low levels of EGR, conventional spark ignition was stable, while at the highest EGR levels, HCCI was stable. The spark was used to ignite conventional combustion and was optionally available during HCCI. The character of the cyclic combustion oscillations that occurred between the conventional and HCCI limits suggests that it can be described as a sequence of bifurcations in a low-dimensional dynamic map. Comparisons with previous studies of lean-limit cyclic variations suggest that nonlinear EGR feedback is probably a major factor in these dynamics. Published by Elsevier Inc. on behalf of The Combustion Institute. Keywords: HCCI; EGR; Nonlinear; Variability; Engine 1. Introduction Homogeneous charge compression ignition (HCCI) in internal combustion engines is of con- siderable interest because it can significantly reduce flame temperature and nitrogen oxide for- mation. In this mode of pre-mixed combustion, ignition is initiated by compression instead of a spark and the reactions occur very rapidly and uniformly throughout the combustion chamber. With HCCI there is little or no flame propagation as in conventional spark-ignited combustion. In order to initiate HCCI at the correct point in the compression stroke, it is typically necessary to preheat the fuel–air mixture to within a rela- tively narrow temperature window prior to com- pression. Furthermore, other studies have shown that the stability of HCCI operation is influenced not only by the temperature but also the composi- tion of the initial charge [1,2]. In practical engines the appropriate level of preheating and mixture composition is very difficult to achieve over the entire range of speed and load, and thus there are many operating points under which the HCCI 1540-7489/$ - see front matter Published by Elsevier Inc. on behalf of The Combustion Institute. doi:10.1016/j.proci.2006.07.133 * Corresponding author. Fax: +1 865 946 1354. E-mail address: [email protected] (R.M. Wagner). Proceedings of the Combustion Institute 31 (2007) 2887–2894 www.elsevier.com/locate/proci Proceedings of the Combustion Institute

Transcript of Understanding the transition between conventional...

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Proceedings

Proceedings of the Combustion Institute 31 (2007) 2887–2894

www.elsevier.com/locate/proci

of the

CombustionInstitute

Understanding the transition betweenconventional spark-ignited combustion

and HCCI in a gasoline engine

C. Stuart Daw, Robert M. Wagner *, K. Dean Edwards,Johney B. Green Jr.

Oak Ridge National Laboratory, 2360 Cherahala Boulevard, Knoxville, TN 37932, USA

Abstract

We describe experimental observations of the gradual transition between conventional spark-ignited(SI) propagating flame combustion and homogeneous charge compression ignition (HCCI) in a single-cylinder, stoichiometrically fueled gasoline engine. Our objective is to better understand the transitionprocess in terms of characteristic changes to the combustion stability as indicated by patterns of cyclicvariations. The transition was experimentally achieved by incrementally adjusting the level of internalexhaust gas recirculation (EGR) using variable exhaust valve actuation. Throttle adjustments were alsomade to maintain a constant fueling rate. For low levels of EGR, conventional spark ignition was stable,while at the highest EGR levels, HCCI was stable. The spark was used to ignite conventional combustionand was optionally available during HCCI. The character of the cyclic combustion oscillations thatoccurred between the conventional and HCCI limits suggests that it can be described as a sequence ofbifurcations in a low-dimensional dynamic map. Comparisons with previous studies of lean-limit cyclicvariations suggest that nonlinear EGR feedback is probably a major factor in these dynamics.Published by Elsevier Inc. on behalf of The Combustion Institute.

Keywords: HCCI; EGR; Nonlinear; Variability; Engine

1. Introduction

Homogeneous charge compression ignition(HCCI) in internal combustion engines is of con-siderable interest because it can significantlyreduce flame temperature and nitrogen oxide for-mation. In this mode of pre-mixed combustion,ignition is initiated by compression instead of aspark and the reactions occur very rapidly anduniformly throughout the combustion chamber.

1540-7489/$ - see front matter Published by Elsevier Inc. on bdoi:10.1016/j.proci.2006.07.133

* Corresponding author. Fax: +1 865 946 1354.E-mail address: [email protected] (R.M. Wagner).

With HCCI there is little or no flame propagationas in conventional spark-ignited combustion. Inorder to initiate HCCI at the correct point inthe compression stroke, it is typically necessaryto preheat the fuel–air mixture to within a rela-tively narrow temperature window prior to com-pression. Furthermore, other studies have shownthat the stability of HCCI operation is influencednot only by the temperature but also the composi-tion of the initial charge [1,2]. In practical enginesthe appropriate level of preheating and mixturecomposition is very difficult to achieve over theentire range of speed and load, and thus thereare many operating points under which the HCCI

ehalf of The Combustion Institute.

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2888 C. Stuart Daw et al. / Proceedings of the Combustion Institute 31 (2007) 2887–2894

mode is unstable. In practice it is frequently neces-sary to switch between HCCI and spark-ignited(SI) propagating flame (PF) combustion as engineconditions change. Several recent publicationsand presentations [3–6] have addressed HCCIcontrol but with few exceptions (e.g., [7]) therehas been limited exploration of the fundamentalnature of the PF–HCCI transition process.

In this paper, we describe experimental obser-vations that suggest the transition between sparkignition and HCCI combustion for our engine fol-lows a sequence of low-dimensional bifurcationsdriven by nonlinear feedback between combustionevents. High exhaust gas recirculation (EGR) isfrequently used to achieve the intake charge pre-heating needed to initiate the HCCI reactions,and this provides a potential feedback mecha-nism. For our experiments, we used internalEGR, which was varied by adjusting the timingand lift of the intake and exhaust valves so thatsome of the exhaust gas from each cycle remainstrapped in the cylinder. From a practical view-point, recognition of these EGR feedback effectscan be critical for practical utilization of HCCI.

Our main objective here is to describe the glob-al cyclic combustion behavior exhibited by ourengine during the PF–HCCI transition driven byEGR. Our perspective is influenced by similarlow-dimensional, deterministic patterns of cycliccombustion variability that we and others haveseen in spark-ignition engines operating near thelean flammability limit. While the details of lean-limit cyclic variations are clearly distinct fromwhat we see with PF–HCCI, it appears that someof the analytical approaches used for understand-ing, diagnosing, and modeling lean-limit combus-tion instability might also be useful for thePF–HCCI transition. In the next section, weprovide details for our experimental setup andmethods. We next focus on the patterns observedand how these can be characterized with nonlineartime series analysis. Finally we summarize the keyelements of our observations and suggestdirections for future research.

2. Experimental

Our experimental observations were madeusing a 0.5-L single-cylinder AVL research enginewith 11.34:1 compression ratio. The engine hastwo intake valves and one exhaust valve and isequipped with a full authority hydraulic variablevalve actuation (VVA) system. Only a singleintake valve was used in this study to promoteswirl and mixing. The fuel used in these experi-ments (indolene) was delivered by an intakemounted port fuel injector with start of injectionoccurring at top dead center (TDC) intake.Engine speed was maintained constant usingan absorbing/motoring dynamometer. Nominal

operating conditions for the results presented herecorrespond to 1600 rpm and 3.4 bar indicatedmean effective pressure (IMEP). Spark timingwas held fixed at 25� BTDC and coolant temper-ature was maintained at 90 �C. Once full HCCIoperation was achieved, the spark could be turnedoff with no impact on the combustion.

The level of internal EGR was varied with theVVA system to transition from PF into HCCIcombustion. The valve timing strategy used toachieve HCCI is commonly referred to as a nega-tive overlap strategy. In this strategy, the exhaustvalve is closed early during the exhaust stroke,resulting in the retention and recompression of alarge fraction of the exhaust mass. Intake valveopening is delayed in a nearly symmetric manner.HCCI combustion occurs when the heat of theretained exhaust charge in combination with com-pression is sufficient to initiate combustion. Inter-nal EGR levels for these experiments weretypically as high as 60% for achieving HCCI com-bustion. Experiments characterizing the transitionfrom conventional spark ignition to HCCI com-bustion were performed by increasing the internalEGR level while maintaining fixed spark timingand stoichiometric air–fuel ratio. Fueling ratewas maintained constant and an intake throttlewas used to preserve the proper air–fuel ratio.Typically, intake air flow was throttle for conven-tional SI operation and wide open for HCCIoperation.

In-cylinder pressure measurements wererecorded at 0.5 crank angle degree of resolutionfor each internal EGR level. To minimize non-combustion artifacts, all engine feedback control-lers were shut off, and the engine was operated inopen-loop mode except for the dynamometerspeed controller and coolant temperature control-ler. Measurements at each specific EGR level typ-ically included 2800 consecutive engine cycles. Aswe have seen before in the lean-limit studies, thislarge number of cycles is important for resolvingthe detailed statistics of the cyclic variability pat-terns. Standard automotive gas instrumentationwas used to provide a basic knowledge of theexhaust chemistry including steady-state measure-ments of CO, CO2, HC, NOx, and O2 concentra-tions in the raw engine-out exhaust.

After each EGR adjustment, the engine wasoperated several minutes to allow it to come toa steady-state condition (for oscillatory combus-tion states, this meant that the behavior becamestatistically consistent over time). Data acquisi-tion then occurred after this transient runout peri-od. Although the discussion here focuses on oneparticular speed, load, and spark timing condi-tion, numerous additional experiments were per-formed to investigate the effects of theseparameters on the transition patterns. Althoughthe detailed patterns at any particular EGR levelwere affected by these other parameters, the

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general trends with EGR were similar. In addi-tion, transient experiments were performed toobserve the combustion behavior for more rapidmode transitions between SI and HCCI opera-tion. These parametric and transient experimentswill be discussed in future papers.

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3. Results and discussion

3.1. General trends

The general trend in combustion stability withinternal EGR level is illustrated in Fig. 1 in termsof the coefficient of variation (COV) in the IMEPand the time average total NOx in the exhaust.The engine operating condition was held fixed at1600 rpm, 3.4 bar average IMEP, spark timingat 25� BTDC, and stoichiometric fueling. Theangle of exhaust valve closing, which is the exper-imentally controlled parameter, is plotted on thelower scale of the horizontal axis. Note that anearlier exhaust valve closing (smaller angleATDC) corresponds to higher EGR in this figure.Approximate internal EGR levels estimated fromsimulations for this engine are also indicated onthe upper scale of the horizontal axis. Four char-acteristic regions of global combustion wereapparent in the COV and NOx and are indicatedin the figure. On the far left, Region 1 representsmore conventional SI (PF) combustion wherethe COV in IMEP is relatively low and NOx emis-sions high. Region 2 reflects a transition regionwhere combustion becomes very unstable butNOx emissions remain low. A definite loss of com-bustion efficiency is also present in this modebecause of the occurrence of complete misfires.Region 3 exhibits more stable combustion withHCCI-like characteristics and low NOx emissionsas long as the spark is used. Shutting off the spark

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at this point results in increased COV and moreNOx. Region 4 corresponds to stable HCCI com-bustion with no spark necessary to maintainsteady combustion and low NOx.

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Figure 2 illustrates more details about the com-bustion process for stable PF, transition, andHCCI combustion as discerned from the0.5-crank-angle-degree pressure measurements.Here, the combustion characteristics for 2800cycles are indicated in terms of the magnitude ofthe peak pressure rise versus its crank angle loca-tion (i.e., one point is plotted per cycle). Weobserve that as the transition from PF to HCCIproceeds, combustion occurs later and the maxi-mum combustion rate increases. It appears thatat very low or no EGR, ignition typically occursvery shortly after the spark and proceeds to com-pletion in the normal manner of a propagatingflame. As internal EGR is increased to a very highlevel, the charge becomes sufficiently diluted thatspark ignition cannot occur and homogeneouscompression ignition occurs later in the cycle. Atintermediate levels of EGR, both of these limitingmodes can occur to some extent but are unstable.As a result of this instability there is a complex oscil-lation back and forth between the two processes. Insome individual cycles at intermediate EGR, itappears that both types of combustion occur. Pre-sumably in these cases there is incomplete con-sumption of the charge by the propagating flame,and thus there is sufficient remaining fuel and airfor homogeneous ignition later in the same cycle.Thus, in these cycles, the combustion event is actu-ally a hybrid between PF and HCCI.

Figure 3 illustrates an alternative view of thePF–HCCI transition, this time from the perspec-tive of the integrated net heat release. In this figurethe net heat release values for 2800 individualcycles are plotted at each of 37 distinct internalEGR levels. As in Fig. 1, the key transitionparameter is represented both in terms of theangle of exhaust valve closing and estimated inter-

Fig. 3. Experimental internal EGR bifurcation diagramfor a single-cylinder research engine.

nal EGR level. Although the heat release is anintegration of multiple features and thus obscuressome of the phase-related details, we can still seethat the PF–HCCI transition clearly evolves froma relatively stable condition (small heat releasevariations) through a series of different globalcombustion oscillation states and finally to anoth-er relatively stable condition. Many of these inter-mediate oscillation states are quite distinctive,involving a large range of heat release valuesand also ‘forbidden zones’ (i.e., intermediate val-ues of heat release that tend to be avoided). Wewere able to confirm the reproducibility of thisglobal transition pattern by repeatedly returningto specific EGR conditions on different days,and these replicate measurements have beenincluded in the figure.

One other comment about the HCCI transitionin Fig. 3 is that there appeared to be a kind of gapin the transition process over a short range ofEGR level. That is, there was a small range ofEGR for which the combustion completely extin-guished even with spark assist. Successful transi-tion to HCCI appeared to be achievableexperimentally only by ‘jumping over’ this EGRinterval. The precise location and strength of thediscontinuity also appears to be a function ofspeed and load. Additional experiments are clear-ly needed to improve our understanding of thisphenomenon.

It is apparent that, although the details are cer-tainly different, the transition process depicted inFig. 3 has some general features in common withthe lean-limit transition for SI combustion (in thepresence of significant internal EGR) that we havereported on previously [8–13]. Specifically, both ofthese combustion transitions involve two relative-ly stable limiting states and an intermediate regionwhere both limiting states can still occur but arevery unstable. (In the lean-limit transition, theend states are normal PF combustion for nearstoichiometric fueling and total misfire beyondthe lean limit). Thus it appears reasonable to con-jecture that, analogous to the lean-limit transition,the PF–HCCI transition is a type of bifurcationprocess involving destabilization of the initial PFfixed point, an evolving sequence of complex com-bustion oscillations, and ultimately a re-stabiliza-tion of the engine into a fixed point associatedwith HCCI. The overall transition process in bothcases involves an exchange of stability betweentwo characteristically different combustion states.Keeping this in mind, we now consider moredetails about the nature of the apparent bifurca-tion process.

3.2. Detailed features of the cyclic combustiondynamics

One way of observing the temporal characterof the cyclic oscillatory combustion during the

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PF–HCCI transition is the autocorrelation func-tion for the heat release time series at different lev-els of EGR. This is illustrated in Figs. 4a–c, wherewe observe that as EGR is increased from a pointof stable PF combustion, persistent anti-correlat-ed oscillations begin developing between succes-sive cycles. This oscillating combustion trendreveals a clearly deterministic ‘memory’ betweencycles, and it is qualitatively consistent with previ-ous observations for the lean-limit transition [8–13]. We conjecture that, as in the lean limit, theanti-correlation arises because small changes inthe degree of dilution of the inlet fuel–air chargeby residual gases from prior cycles tend to pro-mote either better or worse spark ignition in suc-ceeding cycles. That is, a poor burn leaves moreresidual fuel so that the next ignition is stronger,and a strong burn depletes residual fuel so thatthe next ignition is weaker. Other potential con-tributing factors are pressure fluctuations in theintake and exhaust manifolds, in the injection sys-tem, and in other yet to be determined engineparameters. Five-hundred cycles of high-speedintake and exhaust pressure data were acquiredsimultaneously for a very limited number ofengine conditions to help understand the impactof these fluctuations. We hope to discuss this datain a future manuscript.

There is a major difference between the leanlimit and PF–HCCI transitions, however, because

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in the latter we also have the possibility for HCCIignition, which is a much different function of theinitial conditions in the cylinder at the beginningof each combustion stroke. We can observe thesedifferences more clearly using first return maps forheat release. Briefly, these maps are constructedfrom time serial data by plotting pairs of succes-sive data values as points in two dimensions(e.g., the first value in every pair correspondingto the horizontal coordinate and the second valuethe vertical coordinate). Example heat releasereturn maps for conditions corresponding to fiveinternal EGR levels with spark assist are shownin Fig. 5. In Fig. 5a for SI combustion, the succes-sive heat release values are concentrated in a smallunstructured cluster of measurements around afixed point that represents the nominal PF averageheat release. Note that the measurements areslightly dispersed indicating the effects of a smallstochastic or high-dimensional component. Thisnoisy fixed-point pattern persists until EGR isincreased to a level where there are significant cyc-lic combustion oscillations (see Fig. 5b). Here weobserve that the original fixed point begins todestabilize in certain specific ways (i.e., pointsscatter primarily in certain directions on thereturn map), suggestive of unstable manifolds ina low-dimensional phase space [14–16]. InFig. 5c we see the level of destabilization is nearits maximum, while in Fig. 5d the combustion isagain becoming more stable. In Fig. 5e the transi-tion to stable HCCI is complete.

One important practical feature in the abovereturn maps is that the functional relationshipbetween successive combustion events is clearlymore complicated than can be fully representedwith simple 2D maps. In practical terms, thismeans that each combustion event is affected bymore than one previous combustion event (oralternatively, we must consider more than oneprevious combustion event when predicting afuture combustion). Although there is insufficientspace to explain in detail here, the complicatedinteraction between successive combustion eventsappears to involve hybrid combustion modeswhich combine features of both SI and HCCI.Thus we observe varying amounts of characteris-tics from both types of combustion in detailedpressure traces of individual cycles. Interestingly,in terms of integrated heat release alone, we stillfind that this multi-dimensional combustionbehavior still collapses to the simple functionalform:

HRðiÞ ¼ gðHRði� 1Þ; HRði� 2Þ; . . . ;

HRði� nÞÞ; ð1Þ

where n is the effective dimensionality of thedynamics. Without a detailed model of the kinet-ics for each ignition process, we do not know apriori the details of the mapping function g or

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Fig. 5. Experimental heat release return maps illustrating the complex dynamics encountered when transitioning from(a) stable PF to (e) HCCI operation using elevated levels of internal EGR.

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the appropriate value of n. However we can tellfrom the return maps that g is very nonlinearand n is relatively low (a high value for n wouldproduce an almost featureless blob in 2-D). Thenonlinearity of the mapping function and thepresence of the background stochastic noise makeit difficult to reconstruct the function directlyfrom the data. Nevertheless, we find that muchof the multi-cycle deterministic structure can becaptured using another nonlinear time series tech-nique referred to as symbol sequence analysis. Thereader is urged to consult other references formore details about symbol sequence analysis[17,18].

In the current context, symbol sequence analy-sis provides a way to determine joint probabilitydistributions for the observed heat releases overmultiple engine cycles. This is accomplished bydiscretizing the original heat release values into alimited number of bins, and then determiningthe relative frequency of occurrence for sequentialbin combinations involving n successive cycles.The resulting joint frequency histograms can beused to approximate the mapping function bydetermining the maximum likelihood estimatefor the next combustion heat release given theoccurrence of a specific set of past heat releases.By estimating the joint probability distributionsfor different values of n and comparing the result-ing one-cycle-ahead predictions with the observa-

tions, it is possible to determine an optimal valuefor n and a statistical approximation of g.Although there is insufficient space in this discus-sion to describe the details of our joint probabilityand optimization procedures, we provide exampleresults with the cyclic heat release data from thetransition experiments below.

3.3. Evaluation of the approximate mappingfunction

We determined through iterative analysis ofthe joint probability distributions described abovethat optimal one-step-ahead predictions of thecyclic combustion oscillations were achieved byincluding three previous cycles in Eq. (1) (i.e.,n = 3). For visualization purposes, Fig. 6 illus-trates a two-dimensional projection of the approx-imate mapping function generated from data forthe intermediate transition state correspondingto Fig. 5c. In this projection (which is one dimen-sion less than needed to fully resolve the actualfunction) g is represented approximately as a 2-D surface that relates the heat release in cycle ito the heat releases in cycles i � 1 and i � 2. Inreality, g is more complex and actually representsa 3-D hyper-surface in a 4-D space.

With an approximation of the mapping func-tion, it is then possible to simulate the predicteddynamics in the absence of the stochastic noise

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Fig. 7. Approximation of mapping function with (a) nonoise and with (b) stochastic noise.

Fig. 6. Two-dimensional projection of the approximatemapping function generated from data for the interme-diate transition state.

C. Stuart Daw et al. / Proceedings of the Combustion Institute 31 (2007) 2887–2894 2893

(i.e., only the dominant deterministic part of thedynamics that is captured by the model). To begina simulation, we simply chose an initial set ofthree heat release values (typically these can beselected at random from the experimental data).The approximate map is then repeatedly iteratedon itself to simulate a desired number of cycles.For example, HR(i + 1) is generated fromg(HR(i), HR(i �1), HR(i � 2)), then HR(i + 2)from g(HR(i + 1), HR(i), HR(i � 1)), and so on.Figure 7a illustrates the resulting first returnmap for a typical simulation of many thousandsof successive cycles using the approximate func-tion generated at the intermediate transition statecorresponding to Fig. 5c. Here we observe that thedynamics collapses onto a subset of the phasespace; that is, it collapses onto a dynamic attrac-tor. Further, we observe that the attractor retainsthe overall structure of the experimental returnmap, but without the fuzziness associated withthe stochastic background. A more detailed exam-ination of the attractor reveals that it has a char-acteristically fractal structure, implying that thedynamics here involve dissipative, deterministicchaos.

The effects of the stochastic noise can also besimulated by adding a small random componentinto the approximated map function

HRðiÞ ¼ g0ðHRði� 1Þ; HRði� 2Þ; . . . ;

HRði� nÞÞ þ eðiÞ ð2Þ

where g 0 is the approximate mapping function ande is a small random perturbation with zero mean.Figure 7b illustrates the results of specifying e tobe a Gaussian random variable with mean zeroand variance 10% to the approximation of g dis-cussed above. Note that the general appearanceof the first return plot is now quite close to theexperimental pattern in Fig. 5c. Although we havenot made any attempt here to optimize the ampli-tude and distribution assumed for e, we expectthat it should be possible to use an iterative opti-

mization process to quantitatively determine themagnitude of the stochastic component as well.

4. Conclusions

The experimental gasoline engine studied hereexhibits a repeatable region of low-dimensionaldeterministic combustion oscillations as internalEGR is increased to drive the transition betweenPF and HCCI combustion. We hypothesize thatthe oscillation behavior represents a type of non-linear map bifurcation that begins with destabili-zation of the PF fixed point and ends with thestabilization of the HCCI fixed point. The transi-tion dynamics include complex regions of multi-periodicity and deterministic chaos. The generalsimilarity of the PF–HCCI transition to thelean-limit transition suggests that both processesare driven by nonlinear feedback through recircu-lated exhaust gas.

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The types of inter-mode transition experimentsdescribed here need to be investigated using otherengines. If the same or similar patterns can be con-firmed to be general features of a range of engines, itwould seem appropriate to utilize nonlinear timeseries diagnostics and chaos control theory toexpand the practical implementation of HCCI.

Acknowledgments

This work was sponsored by Office of Free-domCAR and Vehicle Technologies, U.S. Depart-ment of Energy, with sponsorship of Kevin Storkand Gurpreet Singh. The research engine is locat-ed at AVL Powertrain in Plymouth, MI, and theexperiments were conducted under a subcontractwith Oak Ridge National Laboratory.

References

[1] G.M. Shaver, J.C. Gerdes, P. Jain, P.A. Caton,C.F. Edwards, in: Proceedings of the AmericanControl Conference (2003) 749–754.

[2] P.A. Caton, A.J. Simon, J.C. Gerdes, C.F.Edwards, International Journal of Engine Research4 (2) (2003).

[3] M. Weinrotter, SAE 2005-01-0129 (2005).

[4] T. Urushihara, K. Yamaguchi, K. Yoshizawa, T.Itoh, SAE 2005-01-0180 (2005).

[5] H. Santose, J. Mathews, W. Cheng, SAE 2005-01-0162 (2005).

[6] J. Hyvonen, B. Johansson, SAE 2005-01-0109 (2005).[7] L. Koopmans, O. Backlund, I. Denbratt, SAE

2002-01-0110 (2002).[8] C.S. Daw, C.E.A. Finney, J.B. Green Jr, M.B.

Kennel, J.F. Thomas, F.T. Connolly, SAE 962086(1996).

[9] C.S. Daw, C.E.A. Finney, M.B. Kennel, F.T. Con-nolly, Physical Review E 57 (3) (1998) 2811–2819.

[10] R.M. Wagner, J.A. Drallmeier, C.S. Daw, Proc.Combust. Inst. 27 (1998).

[11] C.S. Daw, J.B. Green Jr., R.M. Wagner, C.E.A.Finney, F.T. Connolly, Proc. Combust. Inst. 28(2000).

[12] R.M. Wagner, J.A. Drallmeier, C.S. Daw, Interna-tional Journal of Engine Research 1 (4) (2001) 301–320.

[13] K.D. Edwards, R.M. Wagner, V.K. Chakravarthy,C.S. Daw, J.B. Green Jr., SAE 2005-01-3801 (2005).

[14] H.D.I. Abarbanel, Analysis of Observed ChaoticData, Springer Publishing, 1996.

[15] S.H. Strogatz, Nonlinear Dynamics and Chaos,Addison-Wesley, Reading, MA, 1994, 353–355.

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Comments

Rainer Koch, University Karlsruhe, Germany. Youobserved cycle deviations in your engine. Do you thinkthese deviations are typical for any engine working inthe transition mode for SI to HCCI, or are the cycledeviation rather specific for the one engine investigated?

Reply. We hypothesize that engines using internal ex-haust gas recirculation to transition from SI to HCCI willexhibit similar trends in cyclic dispersion. We expect theshape of the attractor may be different but the underlyingdynamics will still be present and responsive to the samegeneral control methodologies. Data from other enginesoperating in similar modes will be necessary to confirm.

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Christian Hasse, BMW AG, Germany. How can thelimited speed of conventional cam phasers be includedin the control strategy?

Reply. The cam phasers will be used for coarsechanges in internal EGR to transition modes but willnot be used for cycle-to-cycle control. Cycle-to-cyclecontrol will most likely be accomplished with more tra-ditional systems such as ignition and injectionparameters.