Prediction of Dynamic Characteristics of Thermocouples with Thin-Wire Sensing Elements

Abstract

Thermocouples dynamic characteristicsʼ prediction is one of the relevant directions in the field of dynamic measurements of non-stationary temperatures of liquid and gaseous media. Thermocouples dynamic characteristicsʼ prediction makes it possible to provide effective continuous correction in automatic control systems for non-stationary temperatures. The purpose of this paper was to develop a theoretically justified relation linking the current or expected time constant of fine-wire thermocouples with the known time constant established at known parameters of liquid and gaseous media. A formula linking the time constant of fine-wire thermocouples with the conditions of heat exchange with the measured medium and the thermophysical characteristics of the thermocouple sensing elements has been deducted. An approximate formula is also given for calculating the internal resistance of wire sensing elements of thermocouples, which must be considered when calculating the time constant of a thermocouple. In consideration of the obtained formulas, a multi-parameter relation linking the current or expected time constant of fine-wire thermocouples with the known time constant set at the known parameters of the measured media has been formed. It is suggested to simplify the formed multi-parameter relation and make it dependent, for example, on the “expected velocity of the measured medium × expected density of the measured medium” complex (Vm2 ρm2 ). Simplified relations in the form of hyperbolic functions with constant parameters and argument in the form of Vm2 ρm2 complex were obtained for airflowat different temperatures, pressures, and velocities. On the example of airflow, it is shown that the complex multi-parametric relation linking the expected and known time constants of thermocouples can be simplified to a hyperbolic dependence, where the argument can be the Vm2 ρm2 complex. Moreover, the degree of approximation of hyperbolic dependencies to the exact values of the multi-parametric relation can reach the R-square = 0.9592 criterion. A multi-parametric relation has been proposed. That relates the known time constant of a thermocouple to the expected or current time constant of the same thermocouple at other parameters of the measured medium from the point of view of the heat exchange and thermal conduction theory. The proposed relation can be used in automatic control systems of non-stationary temperature of various liquid or gaseous media to provide continuous correction of thermocouples dynamic characteristics. Depending on the number of measured medium parameters, the suggested multi-parameter relation can be replaced by simplified relations with other complexes containing, for example, density, velocity, flow rate and pressure of the measured medium.