# On the uncertainty of temperature estimation in a rapid compression machine

## TL;DR

This paper develops a Monte Carlo method to accurately estimate the uncertainty in temperature measurements within rapid compression machines, accounting for parameter correlations and non-normal distributions, improving reliability over previous methods.

## Contribution

It introduces a Monte Carlo approach for uncertainty estimation in RCM temperature calculations that considers parameter correlations and non-normal distributions, unlike prior normality assumptions.

## Key findings

- Initial pressure significantly affects temperature uncertainty.
- Uncertainty in initial temperature strongly influences overall uncertainty.
- Monte Carlo method provides more accurate uncertainty estimates than traditional methods.

## Abstract

Rapid compression machines (RCMs) have been widely used in the combustion literature to study the low-to-intermediate temperature ignition of many fuels. In a typical RCM, the pressure during and after the compression stroke is measured. However, measurement of the temperature history in the RCM reaction chamber is challenging. Thus, the temperature is generally calculated by the isentropic relations between pressure and temperature, assuming that the adiabatic core hypothesis holds. To estimate the uncertainty in the calculated temperature, an uncertainty propagation analysis must be carried out. Our previous analyses assumed that the uncertainties of the parameters in the equation to calculate the temperature were normally distributed and independent, but these assumptions do not hold for typical RCM operating procedures. In this work, a Monte Carlo method is developed to estimate the uncertainty in the calculated temperature, while taking into account the correlation between parameters and the possibility of non-normal probability distributions. In addition, the Monte Carlo method is compared to an analysis that assumes normally distributed, independent parameters. Both analysis methods show that the magnitude of the initial pressure and the uncertainty of the initial temperature have strong influences on the magnitude of the uncertainty. Finally, the uncertainty estimation methods studied here provide a reference value for the uncertainty of the reference temperature in an RCM and can be generalized to other similar facilities.