Computational Modeling of Radiation Effects on Total Temperature Probes
The requirement for accurate total temperature measurements in gaseous flows was first recognized many years ago by engineers working on the development of superchargers and combustion diagnostics. A standard temperature sensor for high temperature applications was and remains to be the thermocouple. However, this sensor is characterized by errors due to conduction heat transfer from the sensing element, as well as errors associated with the flow over it. In particular in high temperature flows, the sensing element of the thermocouple will be much hotter than its surroundings, leading to radiation heat losses. This in turn will lead to large errors in the temperature indicated by the thermocouple. Because the design and testing of thermocouple sensors can be time consuming and costly due to the many parameters that can be varied and because of the high level of detail attainable from computational studies, the use of advanced computational simulations is ideally suited to the study of thermocouple performance.
This work sought to investigate the errors associated with the use of total temperature thermocouple probes and to assess the ability to predict the performance of such probes using coupled fluid-heat transfer simulations. This was done for a wide range of flow temperatures and subsonic velocities. Simulations were undertaken for three total temperature thermocouple probe designs. The first two probes were legacy probes developed by Glawe, Simmons, and Stickney in the 1950's and were used as a validation case since these probes were extensively documented in a National Advisory Committee for Aeronautics (NACA) technical report. The third probe studied was developed at Virginia Tech which was used to investigate conduction errors experimentally. In all cases, the results of the computational simulations were compared to the experimental results to assess their applicability. In the case of the legacy NACA probes, it was shown that the predicted radiation correction compared well with the documented values. This served as a validation of the computational method. Next the procedure was extended to the conduction error case, where the recovery factor, a metric used to relate the total temperature of the flow to the total temperature indicated by the sensor, was compared. Good agreement between the experimental results was found. The effects of radiation were quantified and shown to be small. It was also demonstrated that computational simulations can be used to obtain quantities that are not easily measured experimentally. Specifically, the heat transfer coefficients and the flow through the vented shield were investigated. The heat transfer coefficients were tabulated as Nusselt numbers and were compared to a legacy correlation. It was found that although the legacy correlation under-predicted the Nusselt number, the predicted results did follow the same trend. A new correlation of the same functional form was therefore suggested. Finally, it was found that the mounting strut had a large effect on the internal flow patterns and therefore the heat transfer to the thermocouple. Overall, this work highlights the usefulness of computational simulations in the design and analysis of total temperature thermocouple sensors.