An Experimental Conduction Error Calibration Procedure for Cooled Total Temperature Probes
The accurate measurement of total temperature in engine diagnostics is a challenging task which is subject to several sources of error. Conduction error is predominant among these sources since total temperature sensors are embedded into a cooled strut for measurement. This study seeks to understand the effect of conduction error on total temperature probe performance from an analytical and experimental standpoint and to provide an effective calibration procedure. The review of historical low-order models, as well as results from a developed thermal resistance model, indicates that conduction error is driven by dimensionless parameters, including the Biot, Nusselt, and Reynolds Numbers, as well as a non-dimensional temperature characterizing the flow/strut temperature difference. A conduction error calibration procedure for total temperature probes is experimentally tested in this study. Data were acquired for nominal flow total temperatures ranging from 550 °F to 850 °F with the probe Reynolds number varying from 2,000 to 12,000 for varying conduction conditions with axial temperature gradients up to 1150 °F per inch. A physics-based statistical model successfully expressed total temperature probe performance as a function of dimensionless conduction driver and probe Reynolds number. This statistical model serves as a “calibration surface” for a particular total temperature probe. Due to the scaling of the problem, this calibration is experimentally obtained in moderate temperature regimes, then implemented in higher temperature regimes. The calibration yields an overall uncertainty in total temperature measurement to be ±4% of the total temperature for flow conditions typical in engine diagnostics, with extreme uncertainties in input conditions. Conduction error is successfully shown to be independent of any temperature regime and driven by dimensionless parameters.