Two wire thermocouple: Frequency response in constant flow

Abstract

Experimental measurements are made with a novel two wire thermocouple. Signals from two wires of unequal diameters are recorded from the thermocouple suspended in constant flow with a periodic temperature fluctuation. It is demonstrated that the reconstructed signal from the two wire thermocouple requires no compensation for ω≤2ω1 where ω1 is the natural frequency of the smaller wire. A compensation factor is recommended for larger frequencies ω≳2ω1.

Application of the Deconvolution Methods for Processing of Measurement Signals in the Fast Processes

“…Among several approaches to assessing the relationship of the time constants two basic assumptions were used: (1) the time constant is a function of the size of thermocouple based on empirical equations for the heat transfer coefficient of thin wires [15]; (2) the ratio of the time constants is defined as the ratio of the temperature derivatives, which is valid at equal temperatures of both thermocouples [16,17]. The validity of such approaches in high-enthalpy flow and combustion remains uncertain, as the thermophysical properties can be changed in accordance with the conditions in the high-temperature region.…”

Difference equation approach to two-thermocouple sensor characterization in constant velocity flow environments

“…8 and was similar to that of Forney and Fralick. 5 Cold air was supplied to the rig via a pressure regulator and a needle valve. Choked flow at the needle valve ensured that the mass flow rate was approximately constant, and only small velocity variations would arise downstream due to temperature variations.…”

“…TDR algorithms may only require an a priori estimate of the time constant ratio ␣ between the two thermocouples. Frequency domain reconstruction, 5,12 on the other hand, uses the frequency component for data processing, avoiding the need to calculate unreliable derivatives from noisy temperature data. However, undesirable oscillations 4 may be introduced in the final reconstructions due to the nature of Fourier transforms and singularities due to noise.…”

“…[3][4][5][6] Therefore a first-order lag model with time constant and unity gain can represent the frequency response of a fine-wire thermocouple. [7][8][9][10] The simplified thermocouple model can be written mathematically as…”

On generalisation of dual-thermocouple sensor characterisation to RTDs

“…According to conservation of energy, the convective thermocouple heat transfer is equal to the sum of its thermal inertia plus its conductive and radiative heat transfers. For a well designed thermocouple with long fine wires, both the conductive and radiative heat transfer terms become negligible when compared to the convective heat transfer to the thermocouple from the surrounding airflow [2]- [4]. Thermocouple response can then be represented by a simplified first-order lag system [3], [5], [6] with time constant τ, as in Eq.…”