## Abstract |

### A specific heat ratio model and compression ratio estimation

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 Wiebe 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 $\gamma$. 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 cylinder 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 compression 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 phasing, cylinder pressure bias and heat transfer shows that the third and fourth method can deal with these parameter deviations.

*Marcus Klein*

**2004**

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Last updated: 2021-11-10