A Thermal Analysis of a Hot-Wire Probe for Icing Applications

This paper presents a steady-state thermal model of a hot-wire instrument applicable to atmospheric measurement of water content in clouds. In this application, the power required to maintain the wire at a given temperature is used to deduce the water content of the cloud. The model considers electrical resistive heating, axial conduction, convection to the flow, radiation to the surroundings, as well as energy loss due to the heating, melting, and evaporation of impinging liquid water or ice. All of these parameters can be varied axially along the wire. The model further introduces a parameter called the evaporation potential which locally estimates the maximum fraction of incoming water that evaporates. The primary outputs from the model examined in this study include the total power and axial variation of temperature, power generation, power dissipation, and evaporation potential. The model is used to examine the sensitivity of the hot-wire performance to various flow and boundary conditions including a detailed comparison of dry air and wet (i.e. cloud-on) conditions. The predicted steady-state power values are compared to experimental results from a Science Engineering Associates’ Multi-Element probe, a commonly used water-content measurement instrument. The model results show good agreement with experiment for both dry conditions and cloud-on conditions with liquid water. For ice, the experimental measurements are lower than the actual water content likely due to incomplete evaporation and splashing or bouncing. Model results, which account for incomplete evaporation but not splashing and bouncing, are still higher than experimental results where part of the discrepancy is attributed to splashing and bouncing.