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Single-Zone Cylinder Pressure Modeling and Estimation for Heat Release Analysis of SI Engines

Abstract Cylinder pressure modeling and heat release analysis are today important and standard tools for engineers and researchers, when developing and tuning new engines. Being able to accurately model and extract information from the cylinder pressure is important for the interpretation and validity of the result. The first part of the thesis treats single-zone cylinder pressure modeling, where the specific heat ratio model constitutes a key part. This model component is therefore investigated more thoroughly. For the purpose of reference, the specific heat ratio is calculated for burned and unburned gases, assuming that the unburned mixture is frozen and that the burned mixture 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 to form the specific heat ratio, which renders a cylinder pressure modeling error in the same order as the measurement noise, and fifteen times smaller than the model originally suggested in Gatowski (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. In the second part, four methods for compression ratio estimation based on cylinder pressure traces are developed and evaluated for both simulated and experimental cycles. Three methods rely upon a model of polytropic compression for the cylinder pressure. It is shown that they give a good estimate of the compression ratio at low compression ratios, although the estimates are biased. A method based on a variable projection algorithm with a logarithmic norm of the cylinder pressure yields the smallest confidence intervals and shortest computational time for these three methods. This method is recommended when computational time is an important issue. The polytropic pressure model lacks information about heat transfer and therefore the estimation bias increases with the compression ratio. The fourth method includes heat transfer, crevice effects, and a commonly used heat release model for firing cycles. This method estimates the compression ratio more accurately in terms of bias and variance. The method is more computationally demanding and thus recommended when estimation accuracy is the most important property. In order to estimate the compression ratio as accurately as possible, motored cycles with as high initial pressure as possible should be used. The objective in part 3 is to develop an estimation tool for heat release analysis that is accurate, systematic and efficient. Two methods that incorporate prior knowledge of the parameter nominal value and uncertainty in a systematic manner are presented and evaluated. Method~1 is based on using a singular value decomposition of the estimated hessian, to reduce the number of estimated parameters one-by-one. Then the suggested number of parameters to use is found as the one minimizing the Akaike final prediction error. Method~2 uses a regularization technique to include the prior knowledge in the criterion function. Method~2 gives more accurate estimates than method~1. For method 2, prior knowledge with individually set parameter uncertainties yields more accurate and robust estimates. Once a choice of parameter uncertainty has been done, no user interaction is needed. Method~2 is then formulated for three different versions, which differ in how they determine how strong the regularization should be. The quickest version is based on ad-hoc tuning and should be used when computational time is important. Another version is more accurate and flexible to changing operating conditions, but is more computationally demanding.

Markus Klein


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Last updated: 2021-11-10