Ballistic missile flight test designers use thermocouples to make in-depth temperature measurements of the missile's heat shield. A cylindrical plug, fashioned of the heat-shield material, is fitted with thermocouple wires at precise depths and mounted into a complementary hole in the heat shield. The plug surface is flush with the heat-shield surface. The thermocouple wires is flush with the heat-shield surface. The thermocouple wires run some distance parallel to the surface before bending to the missile interior. A reading of the voltage difference between the two wires joined at the center of the plug is directly correlated with the temperature of the joint. The measured thermocouple temperature is generally thought to be the same as the temperature of the heat-shield material at that depth. It is shown that the thermocouple and heat-shield temperatures can be related through a time-dependent Volterra integral equation of the second kind involving a heat kernel. This equation, derived assuming constant thermal properties and infinite thermocouple conductivity, relates the local heat-shield temperature history to the thermocouple temperature history. It also quantifies the relationship between the thermocouple behavior and design parameters, enabling effective pre-mission design so that the data collected will be free of unwanted lags. For exponentially increasing heat loads, typical of atmospheric re-entry, the thermocouple lag is a fixed percentage of the change in local heatshield temperature. The lag is proportional to the thermal mass excess of the thermocouple compared to the heat shield, with the proportionality constant dependent upon the thickness of the thermocouple wire. The thinnest off-the-shelf thermocouple wires reduce lags to a few percent or less in heavy heat shields, such as silica-phenolic. Specially manufactured wires are necessary to achieve similar reductions in lags in light heat shields, such as cork. Ribbon wires of commonly used thickness have lags roughly the same as circular wires of commonly used diameter.
Thermocouple lag in transient heat-shield measurements due to thermal mass difference
Zeitliche Meßfehler infolge thermischer Massendifferenzen bei transienten Temperaturmessungen mittels Thermoelementen an Hitzeschilden
Transactions of the ASME, Journal of Heat Transfer ; 118 , 4 ; 838-841
1996
4 Seiten, 3 Bilder, 1 Tabelle, 5 Quellen
Article (Journal)
English
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