### 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*

**2007**

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Senast uppdaterad: 2019-08-05