Correcting temperature measurement Bias in experimental data

A simple and practical method for calculating temperature correction kernels to account for sensor dynamics and correct measurements for experimental bias is given in this report. All contact sensor measurements are subject to bias error because of 1) imperfect contact between the sensor and parent material and 2) the finite volume of the sensing element which has different thermal properties from the parent material. Bias error can be mitigated through modeling of the sensor installation. Correction kernel concepts for removing sensor bias from measurements are reviewed in this study. The correction kernel calculation is generally ill-posed requiring some form of regularization. Tikhonov Regularization for stabilizing the kernel computation is introduced in this study, and a method for proper selection of the regularization coefficient is presented and demonstrated. The error correction technique is illustrated through two examples. One numerical example uses an axisymmetric model to simulate a sensor imbedded perpendicular to the heated surface. A second example develops a lumped capacitance (resistance-capacitance or RC) model of a stainless-steel sheathed thermocouple in a typical well hole installation. Experimental data from a pool boiling experiment is presented and the correction kernel is used to determine the measurement bias error. The results show that during the quasi-steady portion of the pool boiling experiment the bias errors are minimal and on the order of 1 K. However, during the transition from nucleate boiling, the bias error is on the order of 10 K.