Time and Frequency Response of a Resistance-Wire Aircraft Atmospheric Temperature Sensor

Abstract

The heat transfer characteristics of an aircraft-mounted resistance-wire atmospheric temperature sensor are modeled to determine the time and frequency responses. The sensor element (Rosemount 102E4AL) consists of a 25-?m-diameter platinum wire wound around a cruciform mica support with approximately 143 diameters of wire between contacts with the mica. A longitudinally distributed, radially lumped capacitance model provided for the convective heat transfer to the wire and the transient heat conduction along it. Similarly, the temperature gradient across the thin dimension of the mica support was neglected, and a radially distributed model provided for the convective heat transfer to the mica and the transient conduction within it. The two solutions are coupled by the boundary conditions at the wire-mica contact. The equations were solved to produce the temperature distribution along the wire and in the mica support as a function of the frequency of a free-stream sinusoidal temperature fluctuation. The frequency response transfer function was determined and fit to a two-time-constant transfer function by regression analysis. The two-time-constant model fits the general solution very well. The small (fast response) time constant is essentially determined by the wire itself. The larger (slow response) time constant is due to conduction into and out of the mica supports. The model predicts that the effects of the mica supports are important for frequencies greater than about 0.1 Hz. The responses to five different temperature waveform inputs (sinusoid, step, pulse, ramp, and ramp level) are derived using the two-time-constant model with Laplace transform techniques for both infinite-length wire (no mica support effects) and the finite-length wire of the 102 probe. The actual temperature signals are distorted by the larger time constant of the mica supports, especially for the pulse and ramp inputs that are typical of aircraft measurements of thermals and inversions.