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Pomiar nieustalonej temperatury czynnika w maszynach i urządzeniach energetycznych

Jaremkiewicz M., Sobota T., Taler D.

Pomiary Automatyka Kontrola

2009

R. 55, nr 5

288-291

W stanie ustalonym, gdy temperatura jest stała oraz nie występuje zjawisko tłumienia i opóźnienia zmian temperatury czynnika przez termometr, pomiary temperatury mogą być dokonane z dużą dokładnością. Jednakże podczas rozruchu, gdy temperatura czynnika ulega gwałtownym zmianom, występują znaczne różnice pomiędzy temperaturą rzeczywistą a zmierzoną z uwagi na bezwładność masywnej osłony termoelementu. W niniejszej pracy zostały przedstawione dwa sposoby określania nieustalonej temperatury czynnika bazujące na przybliżeniu termoelementu za pomocą modelu inercyjnego I i II rzędu. Temperatura czynnika została określona na podstawie pomiarów dokonanych przez dwa termoelementy o różnych średnicach zanurzonych nagle we wrzącej wodzie.

Most books on temperature measurements concentrate on measurements of the fluid temperature under steady conditions. Estimation of the temperature measurement dynamic error is based only the thermometer unit-step response. Little attention is paid to measurements of the transient fluid temperature, despite the great practical significance of the problem. Under steady-state conditions, when the fluid temperature is constant and there is no damping as well as the time lag, temperature measurements can be made with high accuracy. However, when the fluid temperature changes rapidly, as during start-up, there occur quite significant differences between the true and measured temperature due to the time required for transferring heat to a thermocouple placed inside the heavy thermometer pocket. In this paper there are presented two methods for determining the changing in time temperature of the flowing fluid based on temperature waveforms indicated by a thermometer. In the first one the thermometer model is assumed to be first-order inertial and in the other one - second-order inertial. Local polynomial approximation based on 9 points was used for approximation of the temperature changes. It enables determining the first and second derivative from the function representing the thermometer temperature with high accuracy. Experimental investigations of an industrial thermometer at the step increase in the fluid temperature were performed. Fig. 3 shows the comparison of results when using both methods. The least square method was used to determine the time constants τ1 and τ2 in Eq. (15), and the time constant τ in Eq. (16). Both methods for measuring the fluid transient temperature presented can be used for on-line determining any fluid temperature changes as a function of time. The first method in which the thermometer is modelled with an ordinary, first-order, differential equation is appropriate for thermometers having very small time constants. In such cases the thermometer indication delay is small in reference to the fluid temperature changes. In case of industrial thermometers designed to measure temperature of fluids being under high pressure there is a significant time delay of the thermometer indication in reference to the fluid temperature actual changes. For such thermometers the second order thermometer model, allowing for modelling the signal delay, is more suitable. The techniques proposed in the paper can also be used when the time constants are a function of the fluid velocity.

Fluid temperature measurement under transient conditions

Taler J., Jaremkiewicz M., Taler D., Sobota T.

Archives of Thermodynamics

2009

Vol. 30, no. 3

75-88

Under steady-state conditions when fluid temperature is constant, there is no damping and time lag and temperature measurement can be accomplished with high degree of accuracy. However, when fluid temperature is varying rapidly as during start-up, quite appreciable differences occur between the actual fluid temperature and the measured temperature. This is due to the time required for the transfer of heat to the thermocouple placed inside a heavy thermometer pocket. In this paper, two different techniques for determining transient fluid temperature based on the first and second order thermometer model are presented. The fluid temperature was determined using the temperature indicated by the thermometer, which was suddenly immersed into boiling water. To demonstrate the applicability of the presented method to actual data, the time constant of the sheathed thermocouple placed in the air stream was estimated as a function of the air velocity.