Integrating the error in the independent variable for optimal parameter estimation. Part II: implementation to experimental estimation of the thermal dispersion coefficients in porous media with not precisely known thermocouple locations

摘要

This experimental work aims to estimate the thermal dispersion coefficients for a packed bed of glass spheres through which water is flowing. Thermocouples in the downstream neighborhood of a linear heat source measure the temperature response to a step heat input. Thermal dispersion coefficients can then be obtained by the classical estimation method of least squares. However, thermocouple locations and water velocity in the set-up are not precisely known, which leads to incorrect estimates. Only one of these two parameters can be estimated additionally by the classical method. A two terms least squares functional, as introduced in part I of this article, which takes the thermocouple positions as normal stochastic variables can simultaneously give estimates for both parameters. Experimental estimation results for the longitudinal thermal dispersion coefficient are presented for a range of Peclet numbers up to 100.