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The Analytical Modeling of the Thermometric Performance of Total Temperature Thermocouple Probes

A total temperature thermocouple probe immersed in a moving gas stream undergoes thermal energy exchange by means of forced convection between the thermocouple wires and the flowing gas stream, conduction along the thermocouple wires to the probe mount, and radiation between the thermocouple junction wires and any surrounding structure. In general, the thermocouple junction does not indicate the true (stagnation) temperature of the gas stream, thus necessitating the calibration of total temperature probes to obtain correct temperature measurements. Two models are developed to predict the temperature indicated by a total temperature probe (utilizing type K thermocouple wire) for a given set of gas stream stagnation state properties and flow conditions. MODEL 1 adheres to the traditional approach to the problem where individual temperature measurement "errors" associated with each of the three heat transfer mechanisms influencing the thermocouple junction equilibrium temperature are calculated. Improvements made to this modeling approach include a new relationship to compute the gas stream velocity flowing past the junction and the specification of "composite" velocities for the thermocouple wire base and the stagnation tube. For MODEL 2, a second-order, nonlinear, nonhomogeneous ordinary differential equation is derived for the energy exchange phenomena modeled. A solution to the resulting boundary value problem is formulated using finite difference techniques. FORTRAN programs are written for the models operating on both mainframe computer systems and the IBM PC. The models are calibrated with experimental data at standard temperature and pressure (STP) conditions and correlated at non-standard pressures. A parametric analysis reveals that the temperatures and recovery performances predicted by the two models for a hypothetical design probe diverge substantially at high temperatures in low pressure gas streams. As formulated, it appears that MODEL 2 more accurately predicts total temperature thermocouple probe temperature than MODEL 1. The models are evaluated for five criteria and a total temperature thermocouple probe design chart is presented for a range of gas stream stagnation temperatures and pressures in terms of the stagnation tube inlet-to-bleed area ratio and thermocouple wire length-to-diameter ratio. Finally, model improvements and future research needs are suggested.
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