EM375 MECHANICAL ENGINEERING EXPERIMENTATION THERMOCOUPLE LABORATORY

Transcription

1 EM375 MECHANICAL ENGINEERING EXPERIMENTATION THERMOCOUPLE LABORATORY PURPOSE The objective of this laboratory is to introduce the student to the manufacture and use of thermocouples. Thermocouples will be modeled as a first order system, and students will explore the transient response characteristics of their thermocouples. Particular attention will be focused on the concept of the time constant. BACKGROUND In 1821 Thomas Seebeck discovered that when two wires of different metals were joined together at each end and the junction at one end was heated, a small, continuous electrical current flowed in the circuit. The current is very small, and rather than measuring current we now connect the wires to a high input impedance meter and measure the resulting voltage. The magnitude of this Seebeck effect increases as the temperature difference between the junctions increases and we can use the measured voltage to determine the temperature difference. The phenomenon, though, is not linear. The most rudimentary thermocouple circuit we can use to measure temperature consists of two dissimilar metals joined at a junction at one end (marked hot in the illustration below) and to a high impedance meter at the other. The main problem with this arrangement is that the meter reading (Seebeck effect) depends upon the temperature difference between the hot junction and the wiring connectors at the meter. Without reference junction temperature compensation this device will measure the difference between the hot temperature and the temperature of the meter. Many thermocouple meters have reference junction temperature compensation which may use internal thermistors to measure the temperature of the wiring block, or alternatively compensating IC. These types of meter or DAQ system make it seem that we only need a single junction to make a working thermocouple. A better wiring arrangement that can give more accurate temperature measurements is shown below. This circuit has two active junctions (HOT and REFERENCE) and two parasitic junctions where the Metal B connects to the wiring block at the meter. The reference junction is maintained at a fixed temperature (e.g., by using an ice bath). The temperature difference between the two junctions can now be used to determine the temperature of the hot junction.

2 There are many different wiring configurations for thermocouples. However they all rely on the Seebeck effect increasing as the temperature difference between junctions also increases. Discussion of those many other approaches is beyond the scope of this course. THEORY You will be making K-type thermocouples which use the metals chromel and alumel 1 for the two wires in each junction. You will then verify the thermocouples are working. This is not a calibration, rather more a field check. You do this by testing your thermocouples at 0 C (melting Ice Cubes in a water bath) and at 100 C (steam). You will also check the zero-point by inserting your thermocouples into a calibrator, which is maintained very accurately at 0 C. RECORD ALL THREE FIELD-CHECK RECORDINGS. Time constant, ττ After you have verified your thermocouples work, you will test one of them to determine its time constant in air. The time constant depends upon several different parameters that include the thermocouple itself (size and materials), and the environment in which it is being used. The theoretical time constant can be estimated from the equation: ττ = ρρcc vvvv haa 1 Chromel and Alumel are trademarks of the Hoskins Manufacturing Company. Chromel is approximately 90%nickel and 10% chromium. Alumel is approximately 95% nickel, 2% manganese, 2% aluminum and 1% silicon.

3 Where ρρ is the density of the thermocouple bead (average of the two metal densities), CC vv is the thermal capacitance, VV is the volume of the bead, AA is the surface area of the bead, and h is the convective heat transfer coefficient between the thermocouple and its surroundings. Your experiment is to subject a thermocouple to a step change in temperature and measure the resulting temperature versus time data. The thermocouple is a first order system. One of the mathematical formulations for the transient response of a first order system subject to a step input is: TT(tt) = TT (TT TT 0 )ee (tt tt 0 )/ττ In this equation, TT 0 is the initial temperature of the thermocouple at time t0, TT is the actual temperature after the step input (the measurand in this case) and TT(tt) is the temperature recorded by the thermocouple system as a function of time. You will be required to process your temperature vs. time data to determine the time constant for the thermocouple and also to determine the temperature of a hot aluminum block. This is a nonlinear regression which can be achieved using a similar method to the one you used for the elastomer lab. PROCEDURE Each group will make two K-type thermocouples; a twisted wire thermocouple and a welded thermocouple. Both thermocouples will be tested to verify they are working. The twisted wire thermocouple will then be inserted in a protection tube (shroud) and brought to room temperature. Shrouds are commonly used for thermocouples; they provide mechanical protection and also change the time constant. After the thermocouple has reached thermal equilibrium you will subject it to a step change in temperature by inserting it into a hot aluminum block. From the measured temperature versus time data, you will determine the time constant for your thermocouple, and also the actual temperature of the calibrator. The detailed procedure will be given in class, and is summarized below: 1. The twisted wire thermocouple is made by stripping about half-inch of the insulation from the ends of the thermocouple wire and twisting the bare ends together. 2. The welded thermocouple is made by stripping the insulation from the ends of the thermocouple wire and joining them using a Helicarc welder. 3. Both thermocouples are verified with field checks with the thermocouples attached to a thermocouple voltmeter. How accurate was your thermocouple when it was placed in the calibrator? How accurate was your thermocouple when it was placed in melting ice? How accurate was your thermocouple when it was placed in steam? 4. Allow the thermocouple to come to room temperature. Make sure it is dry. 5. Insert one of the thermocouples into the shroud. Observe the temperature and ensure it is reasonably stable (not changing) and is close to room temperature. 6. Activate the digital recorder and record a few seconds of ambient temperature data.

4 7. While still recording, quickly lower the measuring junction into the hot aluminum block. Continue to record the temperature as a function of time for about 3 minutes. ANALYSIS and REPORT REQUIREMENTS The data collection, reduction, and report writing will be done in groups. Your report should ONLY include the transient temperature test. DO NOT include manufacturing details, but do report the field check temperatures for all the thermocouples your team manufactured. Your Matlab code should, as a minimum: 1. Plot the entire measured temperature vs. time data set. 2. Select a start point where the transient response is clean and use this to define the start of a reduced data set. Also look at the end of the data set to identify whether any of the trailing recordings need to be eliminated (for example, if you continued to record as you pulled the thermocouple out of the aluminum block). 3. Look at the raw data and estimate an initial estimate for the time constant ττ. Include this value in your report and explain how you obtained it. 4. Conduct a least squares nonlinear regression and determine the initial temperature TT 0, thermocouple time constant ττ and the actual temperature of the aluminum block, TT You will need to write a Matlab function that takes parameters of initial temperature, final temperature and time constant. It should also accept a vector of time values. It will return the temperatures calculated using the parameters and time values. You will then need to program the use of Matlab functions nlinfit and nlparci. You may want to refer back to the code you wrote for the elastomers lab. t0 will be the time of the first point in your reduced data set Use the temperature at this time as your initial guess for TT 0 Use the last temperature in your retained data set as your initial guess for TT What should you use as your initial guess for the time constant? 5. Plot the measured (full data set with all recorded values) temperature data. Overlay the theoretical transient response using your regressed parameters. Only plot the overlay for the time covered by your reduced data set. See the end of this handout for a sample plot. Note that the plot of measured data includes the initial part at ambient temperature. Those values need to be excluded for the analysis, but must be plotted for comparison. The main body of your report should include as a minimum: 1. A statement that gives the calculated time constant and its uncertainty.

5 2. A statement that gives the final temperature time TT and its uncertainty. 3. The plot from Matlab (4) above 4. A discussion about the possible accuracies and errors in the experiment. 5. A discussion about how you could change the time constant of your thermocouple, and why you might want to change it (i.e., make it smaller or larger). 6. Calculations for the following scenario: The thermocouple/shroud you made is initially at room temperature (20 C) and then is plunged into a source at 180 C. What will the thermocouple read after 1 minute? Measured Curve Fit Temperature (deg C) Time (s) Sample plot for a thermocouple tested in a source close to 0 C