Response of Compensated Thermocouples to Fluctuating Temperatures: Computer Simulation, Experimental Results and Mathematical Modelling

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Abstract
Limitations of the compensated fine-wire thermocouple technique for measurements of fluctuating gas temperature are discussed. Computer simulation has been used to analyse the thermocouple-compensator response, in the presence of noise and guidelines are suggested for regimes in which accurate compensation is possible. The analysis was for two types of scalar fluctuations that may be encountered in turbulent combustion: those corresponding to a bimodal probability density function (pdf) (expected at a high Damköhler number), and those corresponding to a Gaussian-like unimodal one (expected at a low Damköhler number). In fact, the analysis is generally applicable to any transducer with a time-lag response equation similar to that of a thermocouple, with noise contamination of the signal. The authors particular interest arises out of experimental validation of a mathematical model of turbulent combustion that employs pdfs of temperature. In the light of the simulation findings, the relationship is discussed between mathematically predicted and experimentally measured temperature pdfs in premixed, jet-stirred, turbulent combustion. Where a bimodal temperature pdf might be anticipated in the reaction zone, because of the magnitudes of practical thermocouple response times and circuit noise, it is to be expected that the recovered pdf must be unimodel and this was supported by experiment. On the other hand, when unimodal pdfs were anticipated, simulations showed thermocouples to be capable of accurately recovering them. The measured pdfs were indeed unimodal and in good agreement with those predicted by the mathematical model.