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A comparison of specific heat ratio models for cylinder pressure modeling

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 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. Based on assumptions of frozen mixture for the unburned mixture and chemical equilibrium for the burned mixture, the specific heat ratio is calculated using a full equilibrium program for an unburned and a burned air-fuel mixture, and compared to already existing and newly proposed models of $\gamma$.

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. 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.

Marcus Klein and Lars Eriksson

CCSSE, 2004

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