Physical bases of freezing point measurement using ... - Boschung

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Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 282 eopt , which is rather weak, is represented in figure 7. e opt [mm] 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 Figure 7 : dependence of eopt on s. 0 10 20 30 40 s [g/m 2 ] Knowing e and Ts, the salt content can be calculated by : cT ( s) ⋅ e s = ν ( cT ( ) ) where c(Ts) is approximated by the following polynomial : s , (13) −63−42−2 cT ( ) =−6. 211⋅10 ⋅T −4. 637 ⋅10 ⋅T −1807 . ⋅10 ⋅T s s s 4.3 Accuracy of the measurement of the freezing temperature s . (14) While the accuracy of the measurement of Ts by an active probe is mostly given by the accuracy ΔT of the sensor which measures the temperature during the cooling, the one of a passive probe is dependent of the function T = T( x , x , x , K, x , K , x ) used to compute s s 1 2 3 i n the freezing temperature. In that case, the absolute error is given by : ΔT s ≅ i= 1 n Ts ∑ x ∂ ∂ i Δ x , (15) where the xi are the different variables which are measured and Δxi their absolute errors. In other words, the accuracy of a passive probe is a sum of errors depending of the different parameters themselves and their absolute error. If for instance a passive probe is able to measure the salt concentration and the thickness of the solution, it can be understood that errors on c and e (due to the measurements themselves, pollutants, etc.) will affect the i
Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 283 computation (13) of the salt content. Therefore it comes that the accuracy of active probes is better than that of passive ones. 5. CONCLUSION The physical principles of the freezing point measurement by active and passive probes have been discussed. Whatever the deicing product may be (NaCl, CaCl2, MgCl2, ethylene glycol, etc.), the active probe measures truly Ts, with a good accuracy. The measurement of this same parameter with a passive probe is less accurate. In addition, this kind of probe requires parametrizations of the software and can require the use of meteorological data. By contrast, the passive probe is cheaper than the active one. ACKNOWLEDGMENTS The author would like to thank J. Heierli for helpful discussions and P. Francey for performing the measurements of the cooling performances of the probe.
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