This paper proposes an inverse method to obtain accurate measurements of the transient temperature of fluid. A method for unit step and linear rise of temperature is presented. For this purpose, the thermometer housing is modelled as a full cylindrical element (with no inner hole), divided into four control volumes. Using the control volume method, the heat balance equations can be written for each of the nodes for each of the control volumes. Thus, for a known temperature in the middle of the cylindrical element, the distribution of temperature in three nodes and heat flux at the outer surface were obtained. For a known value of the heat transfer coefficient the temperature of the fluid can be calculated using the boundary condition. Additionally, results of experimental research are presented. The research was carried out during the start-up of an experimental installation, which comprises: a steam generator unit, an installation for boiler feed water treatment, a tray-type deaerator, a blow down flashvessel for heat recovery, a steam pressure reduction station, a boiler control system and a steam header made of martensitic high alloy P91 steel. Based on temperature measurements made in the steam header using the inverse method, accurate measurements of the transient temperature of the steam were obtained. The results of the calculations are compared with the real temperature of the steam, which can be determined for a known pressure and enthalpy.
Under steady-state conditions when fluid temperature is constant, temperature measurement can be accomplished with high degree of accuracy owing to the absence of damping and time lag. However, when fluid temperature varies rapidly, for example, during start-up, appreciable differences occur between the actual and measured fluid temperature. These differences occur because it takes time for heat to transfer through the heavy thermometer pocket to the thermocouple. In this paper, a method for determinig transient fluid temperature based on the first-order thermometer model is presented. Fluid temperature is determined using a thermometer, which is suddenly immersed into boiling water. Next, the time constant is defined as a function of fluid velocity for four sheated thermocouples with different diameters. To demonstrate the applicability of the presented method to actual data where air velocity varies, the temperature of air is estimated based on measurements carried out by three thermocouples with different outer diameters. Lastly, the time constant is presented as a function of fluid velocity and outer diameter of thermocouple.