A numerical study of the measurement error introduced by TCi theoretical assumptions

Abstract

Thermal conductivity is the key thermal property of materials that are used in thermal protection of aircraft and energy conservation field, and its accurate test is of great significance in such fields. TCi method is a transient method of measuring thermal conductivity and effusivity, which was developed from the transient plane source method in the last decade. TCi technique has been widely used to measure the thermal conductivity of various materials due to its advantages of simple, rapid and single-side in-situ measurement. But the nominal accuracy is lack of sufficient verification within the full test ranges. Studies have found that the results of thermal conductivity measured by different methods for the same material may be different. Even if the same method and instrument are used to measure the same material, the results by using different test modes may vary significantly. The uncertainty of a dynamic test mainly comes from two aspects, theoretical assumptions of test theory and errors of determining input/output parameters. The latter one can be improved by adopting test facilities with higher precision and resolution, and the error usually can be estimated using the error transfer function. However, the uncertainty introduced by theoretical assumptions is difficult to determine and may lead to an incorrect result when the practical measurement deviates from the theoretical assumptions. For TCi method, except for the errors of determining input/output parameters, the theoretical assumptions in deducing the theory, the calibration curves and the contact resistance will affect the test accuracy. In this study, the influence of the above factors on the accuracy of thermal conductivity and effusivity determined by TCi technique are revealed quantitatively using numerical simulation. Firstly, the practical transient test process of TCi method is reproduced in the simulation with all thermophysical properties given. Secondly, the heat transfer processes of measuring foams, ceramics and metals by TCi method are simulated, and the calibration curves of thermal conductivity and effusivity of each type materials are obtained according to the corresponding temperature increase curve and the theoretical basis of TCi method. The influence of calibration curves on the test uncertainty is analyzed by comparing the calculated values of different calibration curves with the given values in the simulation. Finally, the influence of contact resistance on the test accuracy of different materials is analyzed by setting a thin layer of air between the sensor and the sample. The results show that TCi method could measure the effusivity of different materials accurately, and the different calibration curves have little influence on it. However, the results obtained by different thermal conductivity calibration curves are quite different, especially for the foam materials. The contact resistance between the sensor and the sample will decrease the test results of the high thermal conductivity material, while the effect can be ignored for foam materials. And the influence of contact resistance can be significantly reduced by adding contact agent. Due to the calibration curve and contact resistance in theoretical assumptions of TCi method will affect the test accuracy, the errors introduced by theoretical assumptions should be analyzed when adopting TCi method.