Theory of Operation

7.3 Industrial sensor 7.3 Sensor 7.3 Sensor 7.3 Sensor 7.3 Sensor TheorTheorTheorTheorTheoryyyyy
Consider the sensor design shown in Figure 7.1. The heat convected to or from a fluid is propor-tional to the mass flow of that fluid.Since the constant differential temperature sensor manufacturers has 2 heater coils symmetrically spaced on thesensor tube, it is convenient to consider the upstream and downstream heat transfer modes sepa- rately.The electrical power supplied to either of the heater coils will be converted to heat, which canbe dissipated by radiation, conduction, or convection. The radiation term is negligible due to the low temperatures used by the sensor, and because the sensor construction preferentially favors the conductive and convective heat transfer modes. The thermal energy of each heater will then be dissipated by conduction down the stainless steel sensor tube, conduction to the insulating foam, plus the convection due to the mass flow of the sensed gas.Because great care is taken to wind the resistive heater coils symmetrically about the midpoint ofthe tube, it is assumed that the heat conducted along the sensor tube from the upstream heater will be equal to the heat conducted through the tube from the downstream heater. Similarly, the heat conducted from the upstream and downstream coils to the foam insulation surrounding them is assumed to be equal, based on the symmetry of the sensor construction. Since the sensor tube inlet and outlet are linked by an aluminum ambient bar, the high thermal conductivity of the bar provides a ‘thermal short’, constraining the ends of the sensor tube to be at equal surface temperature. Moreover, the tube ends and the aluminum ambient bar have intimate thermal communication with the main flow passageway prescribed by the main stainless steel flow meter body. This further constrains each end of the sensor tube to be equal to the ambient gas temperature.Further, since the length of each heater section is nearly 21 times greater than the inside tubediameter, the mean gas temperature at the tubes axial midpoint is approximately equal to the tube surface temperature at that point. Recall that the outside of the sensor tube is well insulated from the surroundings, therefore the tube surface temperature at the axial midpoint is very close to the operating temperature of the heater coils. The mean temperature of the gas stream is then approxi- mately the same as the heater temperature. Assuming the mean gas temperature is equal to the heater temperature, it can be shown that the differential pressure is : PPmCTT udpheaterambient 2 (7.1)(7.1)(7.1)(7.1)(7.1)
The value of the constant pressure specific heat of a gas is virtually constant over small changes intemperature. By maintaining both heaters at the same, constant temperature difference above the ambient gas stream temperature, the difference in heater power is a function only of the mass flow rate. Fluctuations in ambient gas temperature which cause errors in conventional mass flow detectors are avoided; The resistance of the ambient sensing coil changes proportionally with the ambient temperature fluctuations, causing the closed loop control to vary the bridge voltage such that the heater resistance changes proportionally to the ambient temperature fluctuation. Page 30