ME3122-1 TEMPERATURE MEASUREMENT
2014/2015
Department of Mechanical Engineering National University of Singapore
AS A SAFETY MEASURE, WEARING OF SHOES DURING EXPERIMENTS IS MANDATORY
TABLE OF CONTENTS
LIST OF FIGURES
(ii)
LIST OF TABLES
(ii)
NOMENCLATURE
(iii)
INTRODUCTION
1
THEORY
2
DESCRIPTION OF EXPERIMENTAL SETUP
7
EXPERIMENTAL PROCEDURE
8
CALCULATIONS AND DISCUSSION
10
LIST OF FIGURES
Figure 1
A metal conductor with its ends exposed to two different temperatures
Figure 2
Two metal conductors made of different materials (A & C)
2
joined to form a junction
3
Figure 3
Two thermocouples connected to form hot and cold junctions
3
Figure 4 Figure 5
RTD construction details Thermistor construction details
5 6
Figure 6
Thermistor bridge circuit
9
Figure 7
Photograph of the temperature sensor calibration unit
12
Figure 8
Schematic of the temperature sensor calibration unit
12
Figure 9
Schematic of the perspex rod showing the embedded and
13
surface mounted sensors Figure 10
Mounting details of the temperature sensors
13
Figure 11
Temperature-resistance response of typical thermistor material compared with RTD material (platinum)
14
LIST OF TABLES Table 1
Relative sensitivities of different temperature sensors
Table 2
Calibration data
Table 3
7 11
Transient readings for temperature along perspex rod
ii
11
NOMENCLATURE
Symbol
Description
Units (SI)
ao, a1 ..... an
Arbitrary constants
Dimensionless
R
Resistance of temperature sensor
T
Temperature
K
T
Temperature difference
K
V
Voltage
V
Seebeck coefficient for thermocouples
V K-1
Temperature
coefficient
of
resistance
resistance thermocouples/ thermistor
iii
for K
INTRODUCTION PURPOSE There are different ways of measuring the temperature at a point for heat transfer analysis in experiments. The use of thermocouples, resistance thermometers or resistance temperature detectors (RTD), and thermistors is the commonest. In this manual, the basic theory behind the working principles of the three temperature sensors and a brief description of an experimental set-up for their calibration are presented. An experimental methodology for the use of the calibrated sensors to measure the temperature profile of a perspex rod is also presented. SCOPE (i)
Calibration of three types of temperature sensors (Thermocouples, RTD and Thermistors)
(ii)
Measurement of temperature profile along a perspex rod
(iii)
Measurement of surface temperature
1
THEORY (a)
Thermocouples (i)
Thermo-electric E.M.F.
TB B
TA A
Figure 1 A metal conductor with its ends exposed to two different temperatures
A temperature gradient in a continuous metal conductor causes development of a potential difference between any two points along the conductor. This phenomenon is referred to as “Seebeck Effect”. The voltage developed is directly proportional to the temperature difference:
dV dT Where, the constant of proportionality, dependent on the conductor material.
(1)
is called the Seebeck coefficient which is
The voltage developed in the conductor can be expressed as:
VB VA T dT TB
(2)
A
Consider a case where two wires of different metal conductors are joined together at one end to form a “junction” as shown in Figure 2.
2
TB
TA
TC A
C
Figure 2 Two metal conductors made of different materials (A & C) joined to form a junction
The potential difference between the points A and C can be expressed as:
VA VC VA VB VB VC TA
TB
TB
TC
1 dT 2 dT
TB
TA
(3)
if TA TC
2 1 dT
TB
21 dT TA
The coefficient 2-1 is a function of the temperature difference TA TB and is tabulated for various combinations of wire materials at the junction. Thus, the voltage developed across the conductors, VA VC becomes a function of the temperature difference TA TB . A sensor created through this arrangement where, two wires of different materials are joined at one point is called a “thermocouple”. With the aid of a voltage-temperature curve (calibration curve) and a reference temperature (generally ice point) a thermocouple can be used to measure temperature at a point where the thermocouple junction is placed. (ii)
Measurement of temperature with respect to a reference temperature
TB
Hot Junction B
TD
α1
α2
α2
α1
C
TA
Cold Junction D Reference Temperature
A E
TE
Figure 3 Two thermocouples connected to form hot and cold junctions 3
Consider the arrangement with two thermocouples connected together in a manner shown in Figure 3. TB is the temperature to be measured and TD is the reference value. Using the arguments in (i), the voltage developed across A and E can be expressed in the form,
VA VE VA VB VB VD VD VE
(4)
(Note: There is no potential difference across point C because the wires BC and CD are of the same material). TA
TB
TD
TB
TC
TE
VA VE 1 dT 2 dT 1 dT
TB
TD
if
2 1 dT
TA TE
(5)
Thus, VA - VE is a unique function of temperature TB, provided TD is a fixed reference temperature. The reference temperature TD can be of any fixed value. However, the reference is usually taken to be the melting temperature of ice (0°C) which is universally accepted.
2 1 a o a1T a 2T a 3T3 where a o , a1 , a 2 , a 3 constants. If T = (TB – TD) is not very large, 2 1 can be taken to be a constant. Note:
Generally
Therefore, V
A
V constant x T T E B D
are
(6)
Equation (6) is a linear function.
(b)
Resistance Thermometers (RTD)
The resistance thermometer is a temperature sensor which operates on the principle: a change in temperature causes a corresponding change in electrical resistance. The resistance variation of RTD with temperature is expressed as:
R=R 0 1 (T-T0 )
(7)
Where, is the temperature coefficient of resistance of the wire material and Ro is the resistance of the wire at a reference temperature To. Using RTD, temperature measurement is carried out by sending a continuous direct current through the resistance element and observing the changes in voltage that occur as a result of electrical resistance variation resulting from a change in temperature. A calibrated RTD can be used to measure temperature without the need of “cold junction” compensation. Being a noble metal, platinum has the most stable resistance-temperature relationship over the largest temperature range. It has a linear resistance-temperature relationship. Therefore, platinum commonly meets the requirements of resistance thermometry and are commonly used in RTDs. Also, platinum’s temperature drift and error with age and use is negligible 4
compared to other sensors and it has very high contamination resistance. The construction details of a typical RTD are shown in Figure 4 below.
Platinum windings, fixed at intervals
Ceramic cylinder with holes for winding
RTD construction details
Figure 4 RTD construction details
(c)
Thermistor
A thermistor is a type of resistor whose resistance varies significantly with temperature compared to that of standard resistors. Thermistors differ from resistance temperature detectors (RTD) in that the material used in a thermistor is generally a ceramic or polymer, whereas, RTDs use pure metals. When externally heated they convert changes in ambient or contact temperatures directly to corresponding changes in voltage or current. Hence, the principle of operation is very similar to a resistance thermometer.
The temperature coefficient of resistance of a thermistor can be expressed as:
1 Ro
Ro T
(8)
where, Ro is the change in resistance with a change in temperature T and Ro is the initial resistance corresponding to a reference temperature To. Unlike most materials, the value of for a thermistor is very large and is negative. This makes the thermistor an effective sensor for temperature measurement and control where high accuracy and resolution are important. The construction details of a thermistor are shown in Figure 5 below. A comparison of resistance change with temperature of a thermistor and platinum resistance thermometer is given in Figure 11.
5
R2 = 7599Ω
Semiconductor
Glass bead thermistor
R0
ΔV
Thermistor
E0
R3 = 7599Ω
R1 = 37.3kΩ
Wires
Glass shell
THERMISTOR construction details
Figure 5 Thermistor construction details
COMPARISON OF MERITS OF TEMPERATURE SENSORS (a)
Type of measurement
Resistance-temperature devices such as thermistors and resistance thermometers give a direct indication of absolute temperature. Whereas, thermocouples measure a relative temperature differential of two junctions formed by two dissimilar metal conductors. For direct temperature indication, one of the thermocouple junctions must be accurately maintained at a known reference temperature. (b)
Temperature range
Thermistors are available for measuring temperatures from a few degrees above “absolute zero” to about 300C. However, they can be used at higher temperatures but tend to decrease in stability (repeatability) above 300C. Platinum resistance thermometers normally have a temperature range of -180C to about 1000C, while iridium units can be used up to 2000C. The non-linearity of resistance change, however, increases at temperature extremes. Thermocouples are available for use up to more than 3000C.
(c)
Sensitivity
The sensitivity of a temperature sensor is S
dV dT
(9)
For a thermocouple, S = , the Seebeck coefficient. The sensitivity of resistance-temperature sensors (RTD and thermistors) is a function of the change in resistance resulting from a unit change in temperature. A typical platinum resistance bulb will exhibit a change of less than 0.2 /0C at room temperature. Thermistors, on the other hand, provide changes from 20 to 2 x 105 /0C under the same conditions (Between -100C and 400C the resistance of a thermistor may change by ten million to one, compared with a change of about four to one in the resistance of platinum over the same temperature range). Table 1 below shows relative sensitivities of thermocouples, RTD and thermistors.
6
Table 1 Relative sensitivities of different temperature sensors V/C Sensor
25C
300C
104 to 106
2 x 103
Platinum resistance bulb 30
300
200
Copper/Constantan
40
60
Chromel/Alumel
40
40
Iron/Constantan
50
55
Thermistor
(d)
Accuracy
In general, thermistors and resistance thermometers provide relatively high absolute accuracies. Ordinary commercial grade thermocouples are normally with specified accuracy of 1C or less over their measurement range. Both thermistors and resistance bulbs will provide accuracies of less than or equal to 0.01C. Repeatability of thermistor measurements is such that variations in repeated readings are smaller than the overall accuracy of the measuring circuit. (e)
Response
How fast a temperature sensor responds to temperature fluctuations is an important consideration in selecting a sensing device for transient temperature measurements. Generally, thermocouples have extremely high response compared to RTD and thermistors. However, due to the relatively large mass of the sensor, RTDs have poor temperature response and the response of thermistors is moderate.
DESCRIPTION OF EXPERIMENTAL SETUP Temperature sensor calibration (Figures 7 and 8) This part of the experimental setup consists of a thermostat-controlled heater immersed in a water bath, a motor-driven stirrer, an electrical signal box and a midi data LOGGER. The water bath can be maintained at a constant temperature ( 0.1°C) which is determined by thermostat setting of the unit. The mercury-in-glass thermometer ( 0.1°C) and the temperature sensors to be calibrated are immersed in the water bath. The temperature and voltage readings from the thermometer and the midi LOGGER, respectively, are recorded simultaneously to plot the calibration curves. The temperature of water in the bath is varied by changing the thermostat setting of the heater which controls the heat supply to the water bath. Temperature profile measurement (Figures 9 and 10) In this part of the experimental setup, a perspex rod is attached to one side of the water bathheater-stirrer assembly and is well insulated on the outside. There are six thermocouples attached to the perspex rod – 4 embedded in the rod to measure the axial temperature profile along the perspex rod and 2 partially embedded at the surface to measure the interface temperature of the two circular ends of the rod. There are another 3 temperature sensors 7
(thermocouple, RTD and thermistor, one each) attached to the exposed face of the rod in order for the surface temperature to be measured by different techniques.
The types of temperature sensors used in the apparatus for surface temperature measurements are: (i) A thermocouple glued to the surface (not embedded) (ii) A resistance thermometer (film or stud) (iii) A thermistor (stud) The specifications of the temperature profile measurement unit are as follows: Diameter of Perspex rod Length of Perspex rod Pitch of thermocouples embedded in Perspex rod Thermocouple wire material Maximum permissible water bath temperature
48 mm 50 mm 10 mm copper-constantan Gauge 30 90°C
Instrumentation The output voltage readings from the thermal sensors are directly read from the midi data LOGGER. Channels 8 to 11 of the data LOGGER are used for the calibration experiments and channels 1 to 9 for the temperature profile experiments. As the emf of a thermocouple only corresponds to the temperature difference between the hot and cold junctions, the voltage corresponding to the hot junction temperature depends on the temperature of the cold junction. In the calibration part of the experiment, two thermocouples are used. One with the cold junction at room temperature and the other with the cold junction effectively set at 0C (ice point) using an electronic compensator. A constant current source of i = 2.1 mA is supplied to the resistance element (Ro = 100) of the resistance thermometer. The expression for temperature coefficient of resistance-sensitivity S is:
1 dRo Ro dT
1 dV iRo dT
S iRo
(10)
The thermistor connected as part of a bridge circuit is shown in Figure 6 below.
8
R1= 37.3 kΩ
R0
Thermistor
E0 A
B ΔV
R2= 7599 Ω
R3= 7599 Ω
Figure 6 Thermistor bridge circuit
Changes in the resistance Rt of the thermistor causes changes in the voltage V between nodes A and B. From first principles, it can be shown that:
1 dRt Rt dT
( Rt R3 ) 2 V Eo Rt R3 T
( Rt R3 ) 2 S Eo Rt R3
(11)
Where, Eo = 1.5 V, R2 = R3 = 7599 , Rt = 30 k at room temperature and R1 is a variable resistance. Just before the commencement of the experiments, the value of R1 is adjusted until the channel 9 voltage reading is zero. In practice, due to the very high sensitivity of the thermistor, it is very difficult to adjust the voltage reading to be exactly zero. However, an attempt should be made for this value to be as close to zero as possible.
EXPERIMENTAL PROCEDURE (a) Calibration of Temperature Sensors 1. Set the voltage V of the thermistor bridge circuit to zero or as close to zero as possible by adjusting the variable resistance R1. 2. Record the temperature of the reference mercury-in-glass thermometer. Record the voltages across the RTD (channel 8), thermistor (channel 9) and the two thermocouples (without ice point channel 10 and with ice point channel 11). Note: (i) A blank form will be provided during the laboratory session for you to record your readings. (ii) If Channel 10 (thermocouple without ice point) reading is a negative value, take the reading as zero. Otherwise, take the actual reading. 9
3. Switch on the water bath heater and set the bath temperature to 40C and allow the bath temperature to reach the set temperature. Repeat Step 2. 4. Repeat Step 3 for water bath temperatures of 50C, 60C, 70C and 80C.
Measurement of Temperature Profiles of Perspex rod Before proceeding with the measurement of temperature profile of the Perspex rod, request the technician in-charge to connect the thermistor and RTD sensors attached to the exposed end of the perspex rod to the electrical signal box. 1. Record the output voltages of the thermocouples embedded in the perspex rod (channels 1 to 6 of the LOGGER) 2. Record the output voltages of the four temperature sensors mounted at the exposed end of the perspex rod (channels 7 to 9 of the LOGGER) 3. Repeat Steps 1 and 2 after 15 minutes.
CALCULATIONS AND DISCUSSION (a) Obtain calibration curves for the 4 temperature sensors (2 thermocouples, RTD and thermistor) by plotting the output voltages against the temperature of the reference mercury-in-glass thermometer. The calibration curves for the 2 thermocouples may be plotted on the same graph, but those for the RTD and the thermistor should be plotted on separate graphs. Determine the sensitivities of the 4 temperature sensors from the graphs. Calculate the temperature coefficient of resistance of the thermistor and the RTD and compare their magnitudes. (b) Using the calibration curves obtained, determine the temperature profile along the perspex rod at the two different times and plot them on a single graph. Comment on your findings. (c) In order to measure correctly the temperature at a point on a surface, one must ensure that the temperature sensor experiences the true temperature at the point. However, the temperature experienced by a temperature sensor is the result of thermal equilibrium with the surroundings. The temperature measured by the embedded thermocouple may be taken to be the true temperature of the surface of the exposed end of the perspex rod. Hence, determine the relative percentage error of the temperatures measured by the 3 surface-mounted sensors. Comment on your findings. (d) You will be given one or more questions on a separate sheet of paper. Please answer the question(s) directly on the paper and submit your answers together with your brief laboratory report before the end of the laboratory session.
PLEASE NOTE THAT YOU ARE REQUIRED TO COMPLETE YOUR EXPERIMENTS AND SUBMIT YOUR BRIEF LABORATORY REPORT BY THE END OF THE LABORATORY SESSION.
10
Date:
Experiment Set No:
Table 2 Calibration data Temp
Vout(RTD) (C)
Vout(Thermistor)
Ch 8 (mV)
Thermocouple w/o ice-pt
Thermocouple with ice-pt
Ch 10 (mV)
Ch 11 (mV)
Ch 9 (mV)
Table 3 Transient readings for temperature along perspex rod Clock Time
0 min mV
Channel 1 at 0 mm apart from the hot end Channel 2 at 10 mm apart from the hot end Channel 3 at 20 mm apart from the hot end Channel 4 at 30 mm apart from the hot end Channel 5 at 40 mm apart from the hot end Channel 6 at 50 mm apart from the hot end (Embedded thermocouple wire) Channel 7 for surface thermocouple wire Channel 8 for surface RTD Channel 9 for surface thermistor 11
15 min o
C
mV
30 min
o
C
mV
o
C
Figure 7 Photograph of the temperature sensor calibration unit
+ _
Figure 8 Schematic of the temperature sensor calibration unit
12
T7 T8
T1
T2
T3
T4
T5 T6 T 9
Temperature, oC
+ _
Te3 30 min Te2 15 min Te1 0 min 0
10
20 30 40 Distance, mm
50
Figure 9 Schematic of the perspex rod showing the embedded and surface mounted sensors
Embedded (TC)
Surface mounted (TC)
Surface mounted thermistor
Surface mounted RTD
Figure 10 Mounting details of the temperature sensors 13
108
106
Specific Resistance Ω.cm
104
Thermistor material 102
100
10-2
RTD material (platinum)
10-4
10-6 -100
0
100
200
300
400
Temperature oC Figure 11 Temperature-resistance response of typical thermistor material compared with RTD material (platinum)
14
