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

Abstract

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. NomenclatureA C = Cross-sectional area (m 2 ) A S = Surface area (m 2 ) = Parameter of Eq. (29) (1/K) = Heat capacity (J/kg/K) = Parameters of Eq. (29) (K/m 2 ) = Inner diameter of wire (m) = Outer diameter of wire (m) 1 = Differential length (m) = Binary diffusion coefficient of water vapor into air (m 2 /s) = Total collection efficiency (dimensionless) = Heat transfer coefficient (W/m 2 /K) = Mass transfer coefficient (m/s) = Electrical current (A) IWC = Ice water content of air parcel (g/m 3 or kg/m 3 ) = Thermal conductivity of solid wire (W/m/K) = Thermal conductivity of air (W/m/K) = Inertia parameter = where is either for water or ice = Modified inertia parameter L = Element length (m) = Latent heat of fusion (J/kg) = Latent heat of vaporization (J/kg) LWC = Liquid water content of air parcel (g/m 3 or kg/m 3 ) ̇ = Mass flow rate (kg/s) ̇ = Mass flux (kg/m 2 /s) = Mach number = Molecular weight (kg / kmol) = number of nodes along wire = Nusselt number (dimensionless) = Pressure (kPa) = Perimeter of wire (m) or power (W) = Power required to heat and evaporate water; evaluated at boiling temperature (W) = Prandtl number ̇ = Total rate of heat flow (W) ̇ = Total rate of heat flow due to conduction (W) ̇ = Total rate of heat flow due to convection (W) ̇ = Total rate of heat generation (W) ̇ = Total...

Simulation of fluid flow and collection efficiency for an SEA multi-element probe

“…Increasing the particle size in this regime does very little to change the collection efficiency because the particle paths are all relatively straight. The data from table 7 was plotted and fit to curves presented elsewhere in this conference [8].…”

“…The conditions were chosen to match available experimental results. A companion paper, at this conference [8], uses the results of this study. Results are presented for free stream velocities of 86, 100, and 135 m/s.…”

“…The first study, described in this paper, examines the flow around and through the multi-element probe via a detailed flow solution and particle trajectory study. The second study, presented in a complementary paper at this conference, examines the thermal behavior of the probe via a thermal analysis [8].…”

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“…However, while the multi-wire has been found to be a significant improvement over the Icing Blade, it is also important to recognize the sensor's limitations. Data from testing in other facilities suggests that at high liquid water contents, the multi-wire may suffer from minor effects of incomplete evaporation (pooling), and perhaps also suffer from splashing when there are ice crystals or large drops present 4,7 . It should also be noted that in some environments, the multi-wire elements can become coated due to minerals in the cloud liquid water that remain after evaporation.…”

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“…5. The SEA Multi-Element measurements were corrected 24 for collision efficiency based on the target MVD. The collision efficiency and all the measurement values used for the false response calculation are shown in Table 3.…”