NORTHERN ILLINOIS UNIVERSITY - Department of Mechanical Engineering
MEE 390 EXPERIMENTAL METHODS IN MECHANICAL ENGINEERING
©1990-1997 M. Kostic

Objective: To measure dynamic response of a thermocouple sensor and find its time constant and 90% rising (falling) time.

Theory: The thermocouples are based on the Seebeck effect, see Thermocouple calibration, Sec.8.5-Thermoelectric Temperature measurement, Text p.343-362 or similar reference. The magnitude of the emf is in the order of few millivolts. We need a precise and accurate multimeter (MM) which can read up to microvolts to do this experiment. Otherwise, if we use less precise MM, an oscilloscope or data acquisition system, the thermocouple emf needs to be amplified (50 to 1000 times). The dynamic response of a temperature sensor will depend on its design, material properties, and the nature of the heat transfer process during the measurements (see "First-Order Systems," and Examples 3.3 and 3.4, Textbook, p.85-92). The dynamic response of a sensor is schematically presented on the Figure (left) for a step-change (increase) of the input temperature from Troom to Tbath. For a decreasing step-change input, instead of rising time, there will be the corresponding falling time. We need to take enough number of measurements (7-15) during the 90% rise time. If the latter is smaller than 15-20 seconds, we have to use an oscilloscope or data acquisition system. If we want to record measurements manually with a multimeter, we will have to modify the thermocouple sensor by putting it in a container, thus making a new sensor with larger time constant.

Procedure:

1. Check the level of water in the bath. Connect the apparatus to the Power supply.
2. Turn on the water bath by switching the main switch (1) as shown in the figure.
3. Keep the set-in switch (8) depressed and set the temperature to desired level (60 deg C for example) by turning the knob (6) and observing the display (7). Release the switch (8) after setting the temperature. In normal mode, the temperature shown on the digital display is the actual temperature of the bath (T_B) against which the thermocouple sensor is to be calibrated.
4. Connect the ends of the thermocouple to the digital multimeter (MM) and set the multimeter to read in millivolts DC.
5. Dip one junction of the thermocouple in the thermo-bath liquid and wait for few minutes for it to reach the steady state (i.e. the reading on the MM steadies down except the last digit). Be careful to hold (tape) the sensor wire away from the circulator's propeller! Record the digital MM reading in millivolts (E_MM).
6. As mentioned in the theory, the multimeter reading corresponds to the difference in temperature between the surroundings (room) and the bath. We have to take the room temperature into consideration to get the absolute value of temperature measured. Find the equivalent millivolt value for the room temperature from the corresponding Thermocouple table (E_RM) and add that millivolt value to every multimeter reading (E_MM). For example, E_RM = 0.818 mV from K-type thermocouple tables corresponding to room temperature of 20.5° C = 66.2° F.
7. Alternatively, you may connect the thermocouple sensor to a digital thermometer and read temperature directly in the last column in the Table below, instead of the steps 5 and 6 above.

The dynamic response of the thermocouple sensor while heating in bath
For heating of thermocouple sensor from room temperature to a bath temperature (60 degrees Celsius for example), the following preparation is necessary. A stopwatch is needed and a person should be ready to read the multimeter in equal time increments (every 3-5 seconds). The thermocouple should be inserted into the bath at constant temperature and stopwatch turned on at that time. Then, the multimeter readings are taken in equal time increments until the multimeter reading stabilizes (i.e. the sensor comes into an equilibrium with the bath). The process of converting the multimeter readings to degrees Centigrade or Fahrenheit should be done for every step after adding the correction for the room temperature (see above). Alternatively, you may connect the thermocouple sensor to a digital thermometer and read temperature directly in the last column in the Table below.

Plot the data with the time on X-axis and the temperature on Y-axis. Curve fit with the corresponding exponential function, and determine the time constant and the 90% rising time. Comment on the measurements and the results.

NOTE: For example, E_RM = 0.818 mV from K-type thermocouple tables corresponding to room temperature of 20.5° C = 66.2° F.

The dynamic response of the thermocouple sensor while cooling in air
For cooling of thermocouple sensor from the bath temperature (60 degrees Celsius, for example) to the room temperature, the procedure is similar to the above. However, instead of rising time, there will be the corresponding falling time. The time constant will be bigger while cooling in air (gas) than while heating in water (liquid), everything else being the same.

The thermocouple sensor in equilibrium with the bath should be taken out in the room air and stopwatch turned on at that time. Then the multimeter readings are taken in equal time increments until the multimeter reading stabilizes (i.e. the sensor comes into an equilibrium with the room, the reading should be zero volts except for the measurement errors)). The process of converting the multimeter readings to degrees Centigrade or Fahrenheit should be done for every step after adding the factor for the room temperature (see above). Alternatively, you may connect the thermocouple sensor to a digital thermometer and read temperature directly in the last column in the Table above.

Plot the data with the time on X-axis and the temperature on Y-axis. Curve fit with the corresponding exponential function, and determine the time constant and the 90% falling time. Comment on the measurements and the results.