Linköping Studies in Science and Technology Thesis No. 1104 A Specific Heat Ratio Model and Compression Ratio Estimation Marcus Klein Division of Vehicular Systems Department of Electrical Engineering Linköping University, SE–581 83 Linköping, Sweden http://www.vehicular.isy.liu.se/ Email: [email protected] Linköping 2004 A Specific Heat Ratio Model and Compression Ratio Estimation °c 2004 Marcus Klein Department of Electrical Engineering, Linköping University, SE–581 83 Linköping, Sweden. ISBN 91-7373-992-8 ISSN 0280-7971 LiU-TEK-LIC-2004:33 Printed by UniTryck, Linköping, Sweden 2004 To Sofia and Ebba Abstract Cylinder pressure modeling and heat release analysis are today important and standard tools for engineers and researchers, when developing and tuning new engines. An accurate specific heat ratio model is important for an accurate heat release analysis, since the specific heat ratio couples the systems energy to other thermodynamic quantities. The objective of the first part is therefore to investigate models of the specific heat ratio for the single-zone heat release model, and find a model accurate enough to introduce a cylinder pressure modeling error less than or in the order of the cylinder pressure measurement noise, while keeping the computational complexity at a minimum. As reference, a specific heat ratio is calculated for burned and unburned gases, assuming that the unburned mixture is frozen and that the burned is at chemical equilibrium. Use of the reference model in heat release analysis is too time consuming and therefore a set of simpler models, both existing and newly developed, are compared to the reference model. A two-zone mean temperature model and the Vibe function are used to parameterize the mass fraction burned. The mass fraction burned is used to interpolate the specific heats for the unburned and burned mixture, and then form the specific heat ratio, which renders a small enough modeling error in γ. The impact that this modeling error has on the cylinder pressure is less than that of the measurement noise, and fifteen times smaller than the model originally suggested in Gatowski et al. [1984]. The computational time is increased with 40 % compared to the original setting, but reduced by a factor 70 compared to precomputed tables from the full equilibrium program. The specific heats for the unburned mixture are captured within 0.2 % by linear functions, and the specific heats for the burned mixture are captured within 1 % by higher-order polynomials for the major operating range of a spark ignited (SI) engine. The second part is on compression ratio estimation based on measured cylin- der pressure traces. Four methods for compression ratio estimation based on both motored and fired cylinder pressure traces are described and evaluated for simulated and experimental data. The first three methods rely upon a model of polytropic compression for the cylinder pressure, and it is shown that they give a good estimate of the compression ratio for simulated cycles at low com- pression ratios, although the estimates are biased. The polytropic model lacks information about heat transfer and therefore, for high compression ratios, this model error causes the estimates to become more biased. The fourth method includes heat transfer, crevice effects, and a commonly used heat release model for firing cycles. This method is able to estimate the compression ratio more accurately at both low and high compression ratios. An investigation of how the methods perform when subjected to parameter deviations in crank angle phas- ing, cylinder pressure bias and heat transfer shows that the third and fourth method can deal with these parameter deviations. i ii Acknowledgments This work has been carried out at the department of Electrical Engineering, division of Vehicular Systems at Linköpings Universitet, Sweden. It was fi- nancially funded by the Swedish Agency for Innovation Systems (VINNOVA), through the excellence center ISIS (Information Systems for Industrial control and Supervision). SAAB Automobile AB and Mecel AB are greatfully acknowl- edged for their support during the work. There are a number of people I would like to express my gratitude to: First of all I would like to thank professor Lars Nielsen for letting me join his group of excellent people, for the interesting research discussions we have had and for introducing me to the game of Texas hold’em poker. The staff at Ve- hicular Systems for a creative and enjoyable atmosphere. This work would never have been accomplished without my supervisor Lars Eriksson, who has inspired me greatly through interesting discussions and through his indefatigable enthusiasm for engine research. Per Andersson and Erik Frisk for helping me out with numerous LaTeX-related questions and research prob- lems. The members of the vehicle propulsion group, for creative discussions. Per Andersson, Anders Fröberg, Ylva Nilsson and Johan Wahlström for proof- reading earlier versions of the material, which undoubtedly improved the quality of the thesis immensely. Carolina Jansson for making administrative stuff work smoothly. Ingemar Andersson for inspiring me to finish my thesis. To all the people who have hosted me during the last two years, among those Andrej and Maria, Dan and Tottis, Fredrik and Louise, Pontus and Emma, and especially Janne, I wish to direct my sincere gratitude for rooming me but also for making sure I had an enjoyable stay. When you come to Trollhättan, you know were to stay. My family has always supported me, and the time during which this thesis was produced, was no exception. Finally I would like to thank Sofia and Ebba, whom I love more than life itself, for all the joy you bring along. Linköping, May 2004 Marcus Klein iii iv Contents 1 Introduction 1 1.1Outlineandreader’sguide...................... 3 1.2Contributions............................. 4 1.3Publications.............................. 5 2 Heat-release models 7 2.1Modelbasisandassumptions.................... 9 2.2Rassweiler-Withrowmodel...................... 11 2.3Apparentheatreleasemodel.................... 14 2.4Matekunaspressureratio...................... 15 2.5Gatowskietal.model........................ 16 2.6Comparisonofheatreleasetraces.................. 20 2.7Summary............................... 22 3 Heat-release model components 23 3.1Pressuresensormodel........................ 23 3.1.1 Crankanglephasing..................... 25 3.2Cylindervolumemodel........................ 26 3.3Temperaturemodels......................... 28 3.3.1 Single-zone temperature model . ............. 28 3.4Crevicemodel............................. 30 3.5Combustionmodel.......................... 32 3.5.1 Vibefunction......................... 32 3.6Thermodynamicproperties..................... 34 v 3.7Heattransfer............................. 35 3.7.1 EngineHeatTransfer.................... 35 3.8Sensitivityinpressuretoparameterinitialization......... 40 3.9 Summary of single-zone heat-release models ............ 41 4 A specific heat ratio model for single-zone heat release models 45 4.1Introduction.............................. 46 4.1.1 Outline............................ 46 4.2 Existing models of γ ......................... 47 4.2.1 Linear model in T ...................... 47 4.2.2 Segmented linear model in T ................ 47 4.2.3 Polynomial model in p and T ................ 48 4.2.4 Summary of existing γ-models............... 49 4.3 Chemical equilibrium . ...................... 50 4.4Unburnedmixture.......................... 50 4.4.1 Modeling λ-dependence with fix slope, b .......... 53 4.5Burnedmixture............................ 55 4.6Partiallyburnedmixture....................... 59 4.6.1 Referencemodel....................... 60 4.6.2 Grouping of γ-models.................... 61 4.6.3 Evaluationcriteria...................... 63 4.6.4 Evaluationcoveringoneoperatingpoint.......... 64 4.6.5 Evaluationcoveringalloperatingpoints.......... 68 4.6.6 Influence of γ-modelsonheatreleaseparameters..... 72 4.6.7 Influence of air-fuel ratio λ ................. 73 4.6.8 Influence of residual gas ................... 74 4.6.9 Summaryforpartiallyburnedmixture........... 78 4.7Conclusions.............................. 79 5 Compression ratio estimation 81 5.1Introduction.............................. 81 5.2TheSVCengine........................... 82 5.2.1 SVCvolumefunction.................... 83 5.3Cylinderpressuremodeling..................... 83 5.3.1 Polytropicmodel....................... 83 5.3.2 Standardmodel........................ 84 5.4Estimationmethods......................... 84 5.4.1 Cylinderpressurereferencing................ 85 5.4.2 Method1–Sublinearapproach............... 85 5.4.3 Method2–Variableprojection...............87 5.4.4 Method3–Levenberg-Marquardt............. 88 5.4.5 Method 4 – Levenberg-Marquardt and standard model . 89 5.4.6 Summaryofmethods.................... 89 5.5Simulationresults.......................... 90 5.5.1 Enginedata.......................... 90 vi 5.5.2 Method1........................... 92 5.5.3 Methods2and3....................... 92 5.5.4 Method4........................... 94 5.5.5 Summaryofparameterestimations............. 95 5.5.6 Astudyofvaryingoperatingconditions.......... 97 5.5.7 Parametersensitivityanalysis................100 5.5.8 Conclusionsfromsimulations................100 5.6Experimentalresults.........................102 5.6.1 Enginedata..........................102 5.6.2 TDC-referencing.......................102 5.6.3 Cylinderpressurereferencing................103 5.6.4 Methods1,2and3......................105