Derivation and testing of a model to calculate electrical shunting and leakage errors in sheathed thermocouples

Abstract

A three-wire transmission line model was derived to calculate temperature measurement errors caused by electrical shunting and leakage in metal sheathed, oxide insulated, compacted thermocouple assemblies. Input parameters for the model were measured and used to verify experimentally the validity of the model on a 0.5-mm-diam stainless steel sheathed, MgO insulated, Chromel/Alumel thermocouple assembly. When a 1.27-m length of the assembly was heated to 1274 K, the errors due to shunting, calculated using the model, were 6.4% and 9.4% lower than the experimentally measured errors for theromocouple measuring junction temperatures of 273.2 and 371.5 K, respectively. With the 1.27-m length heated to 1373 K, the errors due to shunting, calculated using the model, were 12.6% and 14.9% lower than the experimentally measured errors for measuring junction temperatures of 273.2 and 371.5 K, respectively. For a 1.27-m length of the thermocouple assembly at 1274 K, the measuring junction at 273.2 K, and sheath currents of 20, 40, 60, and 80 mA, the error due to leakage, calculated using the model, was within 6% of the experimentally measured error. With the 1.27-m length heated to 1373 K and all other conditions the same, the calculated error due to leakage was within 9.1% of the measured error. This paper describes the experimental apparatus and measurements, explains the method used to infer parameters from experimental measurements, presents the model, and derives the differential equations that describe the electrical phenomena. These equations are solved exactly for a uniform line. A fortran iv coded numerical solution for nonuniform lines is described. Several illustrative examples are presented to clarify the concepts involved in electrical shunting.