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## Abstract

### A specific heat ratio model for single-zone heat release models

The objective is to investigate models of the specific heat ratio for the single-zone heat release model, and find a model accurate enough to introduce a 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 approximative models of $\gamma$.

A two-zone mean temperature model, Matekunas pressure ratio management 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 specific heats for the unburned mixture is captured within 0.2 \% by a linear function, and the specific heats for the burned mixture is captured within 1 \% by a higher-order polynomial for the major operating range of a spark ignited (SI) engine.

Marcus Klein and Lars Eriksson

SAE Technical paper series SP-1830, 2004

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Last updated: 2021-11-10