- Email: [email protected]
In situ response time testing of thermocouples
/
IN SRU
RESPONSE TIME / TESTING OF THERMOCOUPLES
H. K. D. M. D.
M. Hashemian M. Petersen W. Mitchell Hashemian D. Beverly
Analysis and Measurement Services Corporation
Response time information is important in most applications involving transient temperature measurements with thermocouples. Traditionally, the response time of a thermocouple is measured in a laboratory at a r e f e r ence condition. The laboratory response time information is useful for comparative evaluation of thermocouples but may have little relationship with the response time for the sensor in service. This is because of the effects of installation and process operating conditions on response time. A method has been developed and validated for response time testing of thermocouples as installed in an operating process. The de~ tails are reviewed in this paper. The method is referred to as the Loop Current Step R e sponse Test. The test involves an internal heating of the thermocouple by applying an electrical current to the thermocouple extension wires. The current is then terminated and the thermocouple output is monitored as it returns to ambient temperature. This tranISSN 0019-0578/90/04/(X)97/08/$2.50 © ISA 19~)
sient output is analyzed to identify the time constant of the thermocouple. A mathemat~ cal transformation is used to convert the internal transient data to the response of the thermocouple for an external temperature perturbation.
INTRODUCTION Frequency response and time response characterization is important for most temperature sensors. Classical testing of thermocouples often involves plunging them into a stirred water bath in a laboratory. This provides information only about the response of the thermocouple under those particular test conditions and does not provide information about the response at process operating conditions where the sensor is used. Since the response is affected by process conditions, a technique is required to perform response measurements on installed thermocouples (in situ testing). A method called the Loop Current Step Response (LCSR) Test has been developed for in situ response time testing of thermocouples and resistance thermometers li-31. The significance of this method is that it can ]SA Transactions
•
Vol. 29, No. 4
97
be used to measure the frequency response and time response of thermocouples and resistance thermometers while they remain installed in an operating process. This provides a means for measuring the sensor response for actual operating conditions and installation details. The suitability of this technique has been verified by laboratory experiments with resistance thermometers and type K, J, T, and E thermocouples as well as in-process testing in nuclear power plants for platinum resistance thermometers and in subsonic and supersonic wind tunnels for thermocouples. The LCSR method was first introduced by Warshawsky [3] while working for NASA Lewis Research Center. Carroll and Shepard [1] at the Oak Ridge National Laboratory then examined the feasibility of this method for response time testing of thermocouples in sodium-cooled nuclear breeder reactors. This method was then adapted for response time testing of resistance thermometers [4]. Several years later, the authors of this paper validated the LCSR method for testing of thermocouples in aerospace applications [5]. The resuits of this work are presented in this paper along with a review of the LCSR principles. The capability for in situ response time testing of temperature sensors has many industrial applications, especially in the aerospace and nuclear power industries, where timely temperature measurements are often crucial for control, safety, and performance testing. A sudden or significant change in temperature must be known as soon as possible (sometimes within seconds or even milliseconds) to initiate protective action. In process monitoring or control, a knowledge of the response time of temperature sensors will aid in adjusting the data to reflect the true values of signal amplitudes and to eliminate any significant phase lag.
1.0,
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0.4-
oo. m 0.2] n.0.0
98
ISA Transactions
• Vol. 29, No. 4
o:~
o'.2
o'.3
o'.4
0.5
Time (sec) Figure 1. Illustration of a Typical LCSR Transient for a Thermocouple
relates sensor output to process temperature variations has the following form: K1 Gl(s) =
(1) (1 + "rls)(1 + "r2s) . . .
where:
DESCRIPTION OF LCSR METHOD The LCSR method for thermocouples involves passing an electric current through the sensor leads, which causes the sensor to settle at a temperature several degrees above the ambient temperature. Then the heating current is stopped and the output from the sensor is monitored as it cools (Fig. 1). The output indicates the response of the sensor to changes in internal heating, but the required information is the response of the sensor to changes in the monitored temperature. Hence, an analytical method has been developed for transforming the LCSR test data into the response that would be obtained following a change in the monitored temperature. This development is summarized here. It has been shown [4] that the transfer function that
o.o
G,(s)
= gE(s)/gT(s)
gE(s)
= Laplace transform of the change in sensor output
gT(s)
= Laplace transform of the change in monitored temperature
~
= Modal time constant for mode i
K~
= A constant
It has also been shown [4] that the transfer function that relates sensor output to changes in internal heating in the sensor has the following form: K2(1 + rzs)(1 + r2s) . . . G2(s) =
(1 + "r,s)0 +)~2s)...
(2)
where: Gz(s)
= ~E(s)/~P(s)
~P(s)
= Change in power at the thermocouple measuring junction
-1/ri K2
= Zero of transfer function Sensor Output
= A constant
Power Supply
Key points are that the ~'s are the same in both transfer functions and that only the first few modes are significant in determining the sensor dynamics. This leads to the following important conclusion: A test that uses internal heating as an input provides transient data that contains information about the modal time constant (ti) and these modal time constants provide all of the information needed to determine the transfer function of interest (G1).
Thermoc•uple
The observations led to the LCSR test development. For a step change in heating power applied to the sensing element, the time response has the form: E(t) = A o + Ale-'/q
+ A2e-'/~2 + . . .
(3)
This is the time domain representation of Eq. (1). The procedure for data analysis is: (1) Fit the LCSR data to Eq. 3 to identify the modal time constants (%, "r2. . . . ) (2) Use these values in the following equation to obtain the total time constant (x): -r = ~1[1 - In (1 - "r2/~1) - In (1 - "r3/'el) . . . ] (4)
•
. : . .
•
.;-
•
, : . .
•
•
•
. . . .
•
•
.....
-
.
•
p m
i iTe.st.Medi.o:
i•
Figure 2. Simplified Schematic of LCSR Test Instrument
is shown in a simplified schematic in Fig. 2. The basic concept has been proven, but several instrumentation problems occur in LCSR testing of thermocouples. The following are some of these problems and their remedies.
where In = natural logarithm (3) Substitute "~1, T2. . . . in Eq. (1) to provide the sensor transfer function if needed. (4) Use the transfer function to determine the sensor's frequency response or the response to any other desired perturbation. The derivation of the above equations is discussed in Reference 4. It must be pointed out here that only two modal time constants can usually be identified from the LCSR data. The higher order time constants are often difficult to identify, but their contributions to the overall time constant are often insignificant.
TEST I N S T R U M E N T The setup for response time testing of thermocouples
(1) J o u l e H e a t i n g a n d P e l t i e r E f f e c t . The total heating effect, associated with electric current flow through thermocouple wires has two components: joule heating (proportional to current squared and distributed along the whole length of the wire) and the Peltier effect. Peltier heating or cooling is proportional to cjarrent and is concentrated at the measuring junction. The Peltier component can cause a problem if dc current is used, because the temperature gradient along the wire that accompanies the Peltier effect causes a temperature transient at the measuring junction that is unrelated to the radial heat transfer to the surrounding medium. To eliminate the Peltier effect, ac current may be used for thermocouple heating, but we have demonstrated that the Peltier effect is not a major problem in LCSR testing of most common ISA Transactions
• Vol. 29, No. 4
99
types and common sizes of thermocouples in typical industrial applications. (2) Magnetic Effects. Thermocouples with ferromagnetic wires experience magnetic effects that can interfere with response time measurement by the LCSR method. This problem can be resolved by using a special cutoff system for fast thermocouples with ferromagnetic wires. The magnetic effect is not a problem in thermocouples without ferromagnetic wires or thermocouples with ferromagnetic wires operating above their Curie temperatures (no magnetic effects are encountered above this temperature). In addition, thermocouples with ferromagnetic wires that have large response times will be affected less by this problem. This is because the relaxation time constant of the magnetic domains is about 50 milliseconds, which causes a small error in the results of tests for a thermocouple with a response time of several seconds. An example of a thermocouple with a ferromagnetic wire is the type K (Chromel/Alumel) thermocouple. The Alumei wire is ferromagnetic with a Curie temperature of about 60'C (320"F). (3) Resistance of Extension Wires. The electrical resistance of extension wires is usually small and is distributed along the whole length of the wire. This requires heating currents of several amperes to achieve adequate heating in the thermocouple junction. In order to minimize the current requirements and associated hazards, high quality signal conditioning equipment can be used to provide adequate signals with low current levels. However, current levels of about 1 to 3 amperes will still be needed in those cases involving extension wires of more than a few feet.
(4) Connector Effects. Connectors, terminal blocks, etc. in the thermoelectric circuit create potential thermoelectric inhomogeneities that can cause false signals in an LCSR test. The simplest solution is to eliminate all such connectors from the thermoelectric circuit. However, this is not always possible and tests should be performed to evaluate errors caused by connectors and to determine connector selections that minimize
current used for the LCSR test heats the thermocouple wires as well as the junction where the heating is actually needed for the test. The transient output of the thermocouple in the LCSR test is predominantly due to the cooling of the measuring junction. However, when the current is cut off, the thermocouple wires may cool off at a different rate than the junction and, thus, have enough heat left to be conducted toward the junction and vice versa. This will cause a transient that is not related to the response of the sensor. In particular, this phenomenon will cause the LCSR data to show drift on the otherwise steady-state portion of the LCSR transient. This problem may be dealt with during data analysis. Attempts have been made to eliminate this problem with little success, except for a successful approach found and incorporated in the analysis algorithms. These problems and others have been successfully addressed in the research reported herein, and a test instrument has been assembled to provide a capability for remote testing of response time of installed thermocouples.
LCSR VALIDATION The validity of the LCSR test has been verified in a test program [5] involving a number of different thermocouple types and sizes. These were tested in water and air at different flow rates as described in this section.
Testing in W a t e r LCSR testing of thermocouples has been performed in flowing water for two main purposes: (1) to determine whether high quality data could be obtained for several common thermocouple types (K, J, E, and T) and (2) to determine the accuracy of response time estimates obtained by LCSR testing. The facility consisted of a rotating tank with rotational speed selected to give a water velocity of approximately 1 meter/second (m/see). The facility is shown in Fig. 3. The general procedure was as follows: (1) Insert the thermocouple in the water in the rotating tank.
errors.
(5) Heat Conduction along the Wire. The electric 100
ISA Transactions • Vol. 29, No. 4
(2) Wait for the thermocouple signal to reach steady state.
(3) Turn on the heating current. The magnitude, type, and duration of the current were varied in the program depending on the type and size of the thermocouple under test. (4) Turn off the heating current and record the thermocouple emf (output voltage) as it cools to ambient temperature. The LCSR data were sampled with a digital data acquisition system until the signal reached steady state (Fig. 4). Note that Fig. 4 shows an LCSR transient that has been inverted and normalized for illustration purposes. The sampling rate and total number of points sampled were selected based on the response behavior of the thermocouple under test. Sampling times ranged from about 5 to 50 milliseconds for various thermocouples and various test conditions in this project. The
number of data points sampled ranged from 1000 to 3000. The data were stored on computer disks and subsequently analyzed. The analysis involved a mathematical fitting of the data to identify the time constant of the thermocouple tested. For validation testing, the time constant was also measured directly with the plunge test at the same water flow condition as existed during the LCSR test. The procedure was (Fig. 3): (I) Install the sensor on the pneumatic plunger above the flowing water. (2) Flow heated air around the sensor and wait for the sensor output signal to stabilize. (3) Actuate the drive mechanism in order to plunge the sensor rapidly into the flowing water.
Figure 3. Rotating Tank and Associated Hardware for LCSR Validation of Thermocouples in Water
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Table 1 LCSR Validation Results from Testing in Water
I.o r
o.el
/
TimeConstant(sec) Plunge LCSR
Thermocouple
Type
o.,I o.~[
Agreement %
K
1.3
1.4
8
J
1.3
1.4
8
E
2.0
2.1
5
Aboveresults arefromtests in roomtemperaturewaterflowingat 3 feetper second.Thethermocoupleslistedaretypicalindustrial-typesheathedthermocouples(O.D.3/16") Time (sec)
Figure 4. A Typical LCSR Test Transient for a Thermocouple in Water
(4) Record the transient on a strip chart recorder. The sensor time constant was determined by evaluating the time for the response to cover 63.2 percent of the total span. A strip chart recorder tracing of a typical data set is shown in Fig. 5. Typical LCSR validation results are shown in Table 1. Note that the LCSR results are within better than 10 percent of the standard values obtained by plunge tests. This good agreement demonstrates the validity of the LCSR method for testing of these thermocouples. Note that there will often be some differences between the results of the plunge and the LCSR tests. This is because of uncertainties in
"1%
,IIIN
'tk~
*I~L%
<15:1(~:44
,fUN
c~f~
*L3PD:
5
MM/f;
(~70(').13
M~.3/MP
the plunge test and in the LCSR data acquisition, data analysis, and departure from the assumption of the LCSR theory.
Testing in Air An air loop was assembled for LCSR validation testing at low flow rates (up to about 20 meters/sec). Testing involved the same procedure used for testing in water. The air flow rate was adjusted to approximately 6 meters/sec for the LCSR validation testing. Typical results are shown in Table 2.
Table 2 Comparison of Plunge Test Results with LCSR Test Results from Testing in Air
Thennocouple Type
TimeConstant(see) Plunge LCSR
K
15.0
17.2
J
14.8
17.4
E
15.3
18.6
T
13.0
15.0
Aboveresultsarefromtestsinairatroomtemperatureflowingat 16m/sec.All thermocouplesare3/16" industrial-typesheathedsensor.
/
/
/ /
I
/
Figure 5. A Typical Plunge Test Transient for a Thermocouple in Water 102
ISA Transactions • Vol. 29, No. 4
Tests were also performed in subsonic and super~ sonic wind tunnels at the University of Tennessee. Typical results from tests in the subsonic tunnel are shown in Table 3. The supersonic flow data taken at the University of Tennessee did not produce good resuits because the tunnel could not be operated long enough to reach temperature equilibrium. However, a supersonic air flow system capable of providing flows of up to Mach 3 was used successfully to validate the LCSR test on an exposed junction thermocouple made
of 24 gage type K wires. The air flow system used here is called VARITUNNEL Model WTM made by AMRAD International Corporation. The quality of the LCSR data and the results in the supersonic flow stream were reasonable for the thermocouple tested. A typical LCSR transient from testing of this thermocouple in supersonic flow is shown in Fig. 6. The response time of the thermocouple was found to be 0.4 second in the supersonic flow (at about Mach 2) compared with 2.8 seconds in 40 miles per hour in the air loop.
Flow = 30 MPH
Description
Time Constant (see) Plunge LCSR
Type
3/16" Dia. Probe 3116" Dia. Probe 20 Gage Wire 24 Gage Wire 30 Gage Wire
K T K K K
21 21 2.7 2.2 1.2
21 21 2.4 3.0 1.6
Flow = 60 MPH 20 Gage Wire 24 Gage Wire 30 Gage Wire
K K K
Thermocouple Type
Time Constant (see) In Water In Air
J
1.3
14.8
K
1.3
15.0
E
2.0
15.3
The test results are from plunge in water flowing at approximately I m/sec and plunge in air flowing at approximately 16 m/see.
Table 3 LCSR Validation Results from Subsonic Wind Tunnel Tests
Thermocouple
Table 4 Comparison of Time Constants of Sheathed Thermocouples in Water and Air
1.7 1.4 0,7
1.5 1.2 0.8
1.1 1.2 0.4
1.0 2.0 0.3
Table 5 Time Constant of a Thermocouple as a Function of Air Flow Rate at Ambient Temperature Flow Rate (MPH)
Time Constant (see)
30
2.7
40
1.9
60
1.7
100
1.1
Aboveresults are for a type K exposedjunction thermocouplemadeof20gage wire.
Flow = 1O0 M P H
20 Gage Wire 24 Gage Wire 30 Gage Wire
K K K
RESPONSE TIME VERSUS PROCESS CONDITIONS
I.O
ILl
o.II
0.4
o.2
I a4
I 0.I
Time
I o.8
I I.~
As mentioned earlier, the response time of a thermocouple depends on the medium in which the sensor is used. Table 4 gives typical time constant values for three thermocouples in flowing air and flowing water. Note that the time constant from water to air is different by about an order of magnitudes; this is because of the difference in heat transfer properties of air versus water. Table 5 shows the response time of a thermocouple measured in a subsonic wind tunnel as a function of air velocity. Generally, the time constant ('r) of a thermocouple may be written in terms of the properties of its environment as [2]:
(sec)
(5)
r = C~ + C t h
Figure 6. Typical LCSR Transient for a Thermocouple Tested in Air at Mach 2 Flow
where C 1 and C2 are constants and h is the surface heat transfer coefficient. The constant C~ is called the internal component of time constant because it depends only L~A T r a n s a c t i o n s
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221
thermocouple in another medium for which the heat transfer coefficient (h) can be calculated.
2.0 18
1.6-
,g
(~
"C
1.4i:
1.21.0 0
• ~
~
~
~
1'0
1'2
¢4
1;6 ' 1'8 ' 2'0
F l o w RoLe ( m / s e c )
Figure 7. Response of a Type J Thermocouple in Water as a Function of Flow Rate and Temperature
on the sensor constituents, and Cz/h is called the surface component because it is dependent on the properties of the medium in which the thermocouple is used. These properties include the temperature and velocity of the fluid. Figure 7 gives the time constant of a type J sheathed thermocouple in water as a function of flow rate and two different temperatures. These were obtained by making time constant measurements with the thermocouple at several different flow rates in water to identify the constants C~ and C 2 of Eq. (5). These constants were used with appropriate values of heat transfer coefficient for water at 20°C and 250"C (@ 2000 psi) to obtain the two curves shown in Fig. 7. It must be pointed out that, in addition to affecting the value of h, temperature can cause the internal time constant to change due to its potential effects on the thermocouple constituents. This temperature effect cannot be accounted for except by testing at the actual process temperature using the LCSR method. Equation (5) can be used to make time constant measurements with a thermocouple in a convenient test medium (such as water) to determine C a and C 2 and use the equation to estimate the time constant of the
104
ISA Transactions • Vol. 29, No. 4
CONCLUSION The validity of the Loop Current Step Response (LCSR) technique for response time testing of installed thermocouples was demonstrated. This technology is ready to be assembled into a dedicated instrument for use in aerospace, nuclear, chemical, and other industries where transient temperature measurements are important. The method provides time constant results within about 20 percent of the value obtained from plunge tests. This conclusion is based on tests performed in water at low flow rates (about 1 m/sec) and in air flow rates ranging from a few meters per second to over a hundred kilometers per hour. These tests involved common types and sizes of industrial sheathed. thermocouples as well as thermocouples made of bare wire. REFERENCES 1. Carroll, R. M.; Shepard, R. L.; and Kerlin, T. W., "In-Situ Measurement of the Response Time of Sheathed Therrnocouples," Transactions of the American Nuclear Society, Vol. 22, pp 240-241, November 1975. 2. Kerlin, T. W.; Shepard, R. L.; Hashemian, H. M.; and Petersen, K. M., "Response of Installed Temperature Sensors," Temperature Ils Measurement and Control in Science and Industry, Vol. 5, American Institute of Physics, 1982. 3. Warshawsky I., "Heat Conduction Errors and Time Lag in Cryogenic Thermometer Installations," ISA Transactions, Vol. 13, No. 4, pp 335346, 1974. . Kerlin, T. W.; Miller, L. F.; and Hashemian, H. M., "In-Situ Response Time Testing of Platinum Resistance Thermometers," ISA Transactions, Vol. 17, No. 4, 1980. 5. Hashemian, H. M., "Determination of Installed Thermocouple Response," Arnold . Engineering Developing Center, Arnold Air Force Station, Tennessee, Report No. AEDC-TR-86-46, December 1986.
IN SRU
RESPONSE TIME / TESTING OF THERMOCOUPLES
H. K. D. M. D.
M. Hashemian M. Petersen W. Mitchell Hashemian D. Beverly
Analysis and Measurement Services Corporation
Response time information is important in most applications involving transient temperature measurements with thermocouples. Traditionally, the response time of a thermocouple is measured in a laboratory at a r e f e r ence condition. The laboratory response time information is useful for comparative evaluation of thermocouples but may have little relationship with the response time for the sensor in service. This is because of the effects of installation and process operating conditions on response time. A method has been developed and validated for response time testing of thermocouples as installed in an operating process. The de~ tails are reviewed in this paper. The method is referred to as the Loop Current Step R e sponse Test. The test involves an internal heating of the thermocouple by applying an electrical current to the thermocouple extension wires. The current is then terminated and the thermocouple output is monitored as it returns to ambient temperature. This tranISSN 0019-0578/90/04/(X)97/08/$2.50 © ISA 19~)
sient output is analyzed to identify the time constant of the thermocouple. A mathemat~ cal transformation is used to convert the internal transient data to the response of the thermocouple for an external temperature perturbation.
INTRODUCTION Frequency response and time response characterization is important for most temperature sensors. Classical testing of thermocouples often involves plunging them into a stirred water bath in a laboratory. This provides information only about the response of the thermocouple under those particular test conditions and does not provide information about the response at process operating conditions where the sensor is used. Since the response is affected by process conditions, a technique is required to perform response measurements on installed thermocouples (in situ testing). A method called the Loop Current Step Response (LCSR) Test has been developed for in situ response time testing of thermocouples and resistance thermometers li-31. The significance of this method is that it can ]SA Transactions
•
Vol. 29, No. 4
97
be used to measure the frequency response and time response of thermocouples and resistance thermometers while they remain installed in an operating process. This provides a means for measuring the sensor response for actual operating conditions and installation details. The suitability of this technique has been verified by laboratory experiments with resistance thermometers and type K, J, T, and E thermocouples as well as in-process testing in nuclear power plants for platinum resistance thermometers and in subsonic and supersonic wind tunnels for thermocouples. The LCSR method was first introduced by Warshawsky [3] while working for NASA Lewis Research Center. Carroll and Shepard [1] at the Oak Ridge National Laboratory then examined the feasibility of this method for response time testing of thermocouples in sodium-cooled nuclear breeder reactors. This method was then adapted for response time testing of resistance thermometers [4]. Several years later, the authors of this paper validated the LCSR method for testing of thermocouples in aerospace applications [5]. The resuits of this work are presented in this paper along with a review of the LCSR principles. The capability for in situ response time testing of temperature sensors has many industrial applications, especially in the aerospace and nuclear power industries, where timely temperature measurements are often crucial for control, safety, and performance testing. A sudden or significant change in temperature must be known as soon as possible (sometimes within seconds or even milliseconds) to initiate protective action. In process monitoring or control, a knowledge of the response time of temperature sensors will aid in adjusting the data to reflect the true values of signal amplitudes and to eliminate any significant phase lag.
1.0,
t-
0.8.
o t..
0.6-
< ~3 O3 C
0.4-
oo. m 0.2] n.0.0
98
ISA Transactions
• Vol. 29, No. 4
o:~
o'.2
o'.3
o'.4
0.5
Time (sec) Figure 1. Illustration of a Typical LCSR Transient for a Thermocouple
relates sensor output to process temperature variations has the following form: K1 Gl(s) =
(1) (1 + "rls)(1 + "r2s) . . .
where:
DESCRIPTION OF LCSR METHOD The LCSR method for thermocouples involves passing an electric current through the sensor leads, which causes the sensor to settle at a temperature several degrees above the ambient temperature. Then the heating current is stopped and the output from the sensor is monitored as it cools (Fig. 1). The output indicates the response of the sensor to changes in internal heating, but the required information is the response of the sensor to changes in the monitored temperature. Hence, an analytical method has been developed for transforming the LCSR test data into the response that would be obtained following a change in the monitored temperature. This development is summarized here. It has been shown [4] that the transfer function that
o.o
G,(s)
= gE(s)/gT(s)
gE(s)
= Laplace transform of the change in sensor output
gT(s)
= Laplace transform of the change in monitored temperature
~
= Modal time constant for mode i
K~
= A constant
It has also been shown [4] that the transfer function that relates sensor output to changes in internal heating in the sensor has the following form: K2(1 + rzs)(1 + r2s) . . . G2(s) =
(1 + "r,s)0 +)~2s)...
(2)
where: Gz(s)
= ~E(s)/~P(s)
~P(s)
= Change in power at the thermocouple measuring junction
-1/ri K2
= Zero of transfer function Sensor Output
= A constant
Power Supply
Key points are that the ~'s are the same in both transfer functions and that only the first few modes are significant in determining the sensor dynamics. This leads to the following important conclusion: A test that uses internal heating as an input provides transient data that contains information about the modal time constant (ti) and these modal time constants provide all of the information needed to determine the transfer function of interest (G1).
Thermoc•uple
The observations led to the LCSR test development. For a step change in heating power applied to the sensing element, the time response has the form: E(t) = A o + Ale-'/q
+ A2e-'/~2 + . . .
(3)
This is the time domain representation of Eq. (1). The procedure for data analysis is: (1) Fit the LCSR data to Eq. 3 to identify the modal time constants (%, "r2. . . . ) (2) Use these values in the following equation to obtain the total time constant (x): -r = ~1[1 - In (1 - "r2/~1) - In (1 - "r3/'el) . . . ] (4)
•
. : . .
•
.;-
•
, : . .
•
•
•
. . . .
•
•
.....
-
.
•
p m
i iTe.st.Medi.o:
i•
Figure 2. Simplified Schematic of LCSR Test Instrument
is shown in a simplified schematic in Fig. 2. The basic concept has been proven, but several instrumentation problems occur in LCSR testing of thermocouples. The following are some of these problems and their remedies.
where In = natural logarithm (3) Substitute "~1, T2. . . . in Eq. (1) to provide the sensor transfer function if needed. (4) Use the transfer function to determine the sensor's frequency response or the response to any other desired perturbation. The derivation of the above equations is discussed in Reference 4. It must be pointed out here that only two modal time constants can usually be identified from the LCSR data. The higher order time constants are often difficult to identify, but their contributions to the overall time constant are often insignificant.
TEST I N S T R U M E N T The setup for response time testing of thermocouples
(1) J o u l e H e a t i n g a n d P e l t i e r E f f e c t . The total heating effect, associated with electric current flow through thermocouple wires has two components: joule heating (proportional to current squared and distributed along the whole length of the wire) and the Peltier effect. Peltier heating or cooling is proportional to cjarrent and is concentrated at the measuring junction. The Peltier component can cause a problem if dc current is used, because the temperature gradient along the wire that accompanies the Peltier effect causes a temperature transient at the measuring junction that is unrelated to the radial heat transfer to the surrounding medium. To eliminate the Peltier effect, ac current may be used for thermocouple heating, but we have demonstrated that the Peltier effect is not a major problem in LCSR testing of most common ISA Transactions
• Vol. 29, No. 4
99
types and common sizes of thermocouples in typical industrial applications. (2) Magnetic Effects. Thermocouples with ferromagnetic wires experience magnetic effects that can interfere with response time measurement by the LCSR method. This problem can be resolved by using a special cutoff system for fast thermocouples with ferromagnetic wires. The magnetic effect is not a problem in thermocouples without ferromagnetic wires or thermocouples with ferromagnetic wires operating above their Curie temperatures (no magnetic effects are encountered above this temperature). In addition, thermocouples with ferromagnetic wires that have large response times will be affected less by this problem. This is because the relaxation time constant of the magnetic domains is about 50 milliseconds, which causes a small error in the results of tests for a thermocouple with a response time of several seconds. An example of a thermocouple with a ferromagnetic wire is the type K (Chromel/Alumel) thermocouple. The Alumei wire is ferromagnetic with a Curie temperature of about 60'C (320"F). (3) Resistance of Extension Wires. The electrical resistance of extension wires is usually small and is distributed along the whole length of the wire. This requires heating currents of several amperes to achieve adequate heating in the thermocouple junction. In order to minimize the current requirements and associated hazards, high quality signal conditioning equipment can be used to provide adequate signals with low current levels. However, current levels of about 1 to 3 amperes will still be needed in those cases involving extension wires of more than a few feet.
(4) Connector Effects. Connectors, terminal blocks, etc. in the thermoelectric circuit create potential thermoelectric inhomogeneities that can cause false signals in an LCSR test. The simplest solution is to eliminate all such connectors from the thermoelectric circuit. However, this is not always possible and tests should be performed to evaluate errors caused by connectors and to determine connector selections that minimize
current used for the LCSR test heats the thermocouple wires as well as the junction where the heating is actually needed for the test. The transient output of the thermocouple in the LCSR test is predominantly due to the cooling of the measuring junction. However, when the current is cut off, the thermocouple wires may cool off at a different rate than the junction and, thus, have enough heat left to be conducted toward the junction and vice versa. This will cause a transient that is not related to the response of the sensor. In particular, this phenomenon will cause the LCSR data to show drift on the otherwise steady-state portion of the LCSR transient. This problem may be dealt with during data analysis. Attempts have been made to eliminate this problem with little success, except for a successful approach found and incorporated in the analysis algorithms. These problems and others have been successfully addressed in the research reported herein, and a test instrument has been assembled to provide a capability for remote testing of response time of installed thermocouples.
LCSR VALIDATION The validity of the LCSR test has been verified in a test program [5] involving a number of different thermocouple types and sizes. These were tested in water and air at different flow rates as described in this section.
Testing in W a t e r LCSR testing of thermocouples has been performed in flowing water for two main purposes: (1) to determine whether high quality data could be obtained for several common thermocouple types (K, J, E, and T) and (2) to determine the accuracy of response time estimates obtained by LCSR testing. The facility consisted of a rotating tank with rotational speed selected to give a water velocity of approximately 1 meter/second (m/see). The facility is shown in Fig. 3. The general procedure was as follows: (1) Insert the thermocouple in the water in the rotating tank.
errors.
(5) Heat Conduction along the Wire. The electric 100
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(2) Wait for the thermocouple signal to reach steady state.
(3) Turn on the heating current. The magnitude, type, and duration of the current were varied in the program depending on the type and size of the thermocouple under test. (4) Turn off the heating current and record the thermocouple emf (output voltage) as it cools to ambient temperature. The LCSR data were sampled with a digital data acquisition system until the signal reached steady state (Fig. 4). Note that Fig. 4 shows an LCSR transient that has been inverted and normalized for illustration purposes. The sampling rate and total number of points sampled were selected based on the response behavior of the thermocouple under test. Sampling times ranged from about 5 to 50 milliseconds for various thermocouples and various test conditions in this project. The
number of data points sampled ranged from 1000 to 3000. The data were stored on computer disks and subsequently analyzed. The analysis involved a mathematical fitting of the data to identify the time constant of the thermocouple tested. For validation testing, the time constant was also measured directly with the plunge test at the same water flow condition as existed during the LCSR test. The procedure was (Fig. 3): (I) Install the sensor on the pneumatic plunger above the flowing water. (2) Flow heated air around the sensor and wait for the sensor output signal to stabilize. (3) Actuate the drive mechanism in order to plunge the sensor rapidly into the flowing water.
Figure 3. Rotating Tank and Associated Hardware for LCSR Validation of Thermocouples in Water
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Table 1 LCSR Validation Results from Testing in Water
I.o r
o.el
/
TimeConstant(sec) Plunge LCSR
Thermocouple
Type
o.,I o.~[
Agreement %
K
1.3
1.4
8
J
1.3
1.4
8
E
2.0
2.1
5
Aboveresults arefromtests in roomtemperaturewaterflowingat 3 feetper second.Thethermocoupleslistedaretypicalindustrial-typesheathedthermocouples(O.D.3/16") Time (sec)
Figure 4. A Typical LCSR Test Transient for a Thermocouple in Water
(4) Record the transient on a strip chart recorder. The sensor time constant was determined by evaluating the time for the response to cover 63.2 percent of the total span. A strip chart recorder tracing of a typical data set is shown in Fig. 5. Typical LCSR validation results are shown in Table 1. Note that the LCSR results are within better than 10 percent of the standard values obtained by plunge tests. This good agreement demonstrates the validity of the LCSR method for testing of these thermocouples. Note that there will often be some differences between the results of the plunge and the LCSR tests. This is because of uncertainties in
"1%
,IIIN
'tk~
*I~L%
<15:1(~:44
,fUN
c~f~
*L3PD:
5
MM/f;
(~70(').13
M~.3/MP
the plunge test and in the LCSR data acquisition, data analysis, and departure from the assumption of the LCSR theory.
Testing in Air An air loop was assembled for LCSR validation testing at low flow rates (up to about 20 meters/sec). Testing involved the same procedure used for testing in water. The air flow rate was adjusted to approximately 6 meters/sec for the LCSR validation testing. Typical results are shown in Table 2.
Table 2 Comparison of Plunge Test Results with LCSR Test Results from Testing in Air
Thennocouple Type
TimeConstant(see) Plunge LCSR
K
15.0
17.2
J
14.8
17.4
E
15.3
18.6
T
13.0
15.0
Aboveresultsarefromtestsinairatroomtemperatureflowingat 16m/sec.All thermocouplesare3/16" industrial-typesheathedsensor.
/
/
/ /
I
/
Figure 5. A Typical Plunge Test Transient for a Thermocouple in Water 102
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Tests were also performed in subsonic and super~ sonic wind tunnels at the University of Tennessee. Typical results from tests in the subsonic tunnel are shown in Table 3. The supersonic flow data taken at the University of Tennessee did not produce good resuits because the tunnel could not be operated long enough to reach temperature equilibrium. However, a supersonic air flow system capable of providing flows of up to Mach 3 was used successfully to validate the LCSR test on an exposed junction thermocouple made
of 24 gage type K wires. The air flow system used here is called VARITUNNEL Model WTM made by AMRAD International Corporation. The quality of the LCSR data and the results in the supersonic flow stream were reasonable for the thermocouple tested. A typical LCSR transient from testing of this thermocouple in supersonic flow is shown in Fig. 6. The response time of the thermocouple was found to be 0.4 second in the supersonic flow (at about Mach 2) compared with 2.8 seconds in 40 miles per hour in the air loop.
Flow = 30 MPH
Description
Time Constant (see) Plunge LCSR
Type
3/16" Dia. Probe 3116" Dia. Probe 20 Gage Wire 24 Gage Wire 30 Gage Wire
K T K K K
21 21 2.7 2.2 1.2
21 21 2.4 3.0 1.6
Flow = 60 MPH 20 Gage Wire 24 Gage Wire 30 Gage Wire
K K K
Thermocouple Type
Time Constant (see) In Water In Air
J
1.3
14.8
K
1.3
15.0
E
2.0
15.3
The test results are from plunge in water flowing at approximately I m/sec and plunge in air flowing at approximately 16 m/see.
Table 3 LCSR Validation Results from Subsonic Wind Tunnel Tests
Thermocouple
Table 4 Comparison of Time Constants of Sheathed Thermocouples in Water and Air
1.7 1.4 0,7
1.5 1.2 0.8
1.1 1.2 0.4
1.0 2.0 0.3
Table 5 Time Constant of a Thermocouple as a Function of Air Flow Rate at Ambient Temperature Flow Rate (MPH)
Time Constant (see)
30
2.7
40
1.9
60
1.7
100
1.1
Aboveresults are for a type K exposedjunction thermocouplemadeof20gage wire.
Flow = 1O0 M P H
20 Gage Wire 24 Gage Wire 30 Gage Wire
K K K
RESPONSE TIME VERSUS PROCESS CONDITIONS
I.O
ILl
o.II
0.4
o.2
I a4
I 0.I
Time
I o.8
I I.~
As mentioned earlier, the response time of a thermocouple depends on the medium in which the sensor is used. Table 4 gives typical time constant values for three thermocouples in flowing air and flowing water. Note that the time constant from water to air is different by about an order of magnitudes; this is because of the difference in heat transfer properties of air versus water. Table 5 shows the response time of a thermocouple measured in a subsonic wind tunnel as a function of air velocity. Generally, the time constant ('r) of a thermocouple may be written in terms of the properties of its environment as [2]:
(sec)
(5)
r = C~ + C t h
Figure 6. Typical LCSR Transient for a Thermocouple Tested in Air at Mach 2 Flow
where C 1 and C2 are constants and h is the surface heat transfer coefficient. The constant C~ is called the internal component of time constant because it depends only L~A T r a n s a c t i o n s
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thermocouple in another medium for which the heat transfer coefficient (h) can be calculated.
2.0 18
1.6-
,g
(~
"C
1.4i:
1.21.0 0
• ~
~
~
~
1'0
1'2
¢4
1;6 ' 1'8 ' 2'0
F l o w RoLe ( m / s e c )
Figure 7. Response of a Type J Thermocouple in Water as a Function of Flow Rate and Temperature
on the sensor constituents, and Cz/h is called the surface component because it is dependent on the properties of the medium in which the thermocouple is used. These properties include the temperature and velocity of the fluid. Figure 7 gives the time constant of a type J sheathed thermocouple in water as a function of flow rate and two different temperatures. These were obtained by making time constant measurements with the thermocouple at several different flow rates in water to identify the constants C~ and C 2 of Eq. (5). These constants were used with appropriate values of heat transfer coefficient for water at 20°C and 250"C (@ 2000 psi) to obtain the two curves shown in Fig. 7. It must be pointed out that, in addition to affecting the value of h, temperature can cause the internal time constant to change due to its potential effects on the thermocouple constituents. This temperature effect cannot be accounted for except by testing at the actual process temperature using the LCSR method. Equation (5) can be used to make time constant measurements with a thermocouple in a convenient test medium (such as water) to determine C a and C 2 and use the equation to estimate the time constant of the
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CONCLUSION The validity of the Loop Current Step Response (LCSR) technique for response time testing of installed thermocouples was demonstrated. This technology is ready to be assembled into a dedicated instrument for use in aerospace, nuclear, chemical, and other industries where transient temperature measurements are important. The method provides time constant results within about 20 percent of the value obtained from plunge tests. This conclusion is based on tests performed in water at low flow rates (about 1 m/sec) and in air flow rates ranging from a few meters per second to over a hundred kilometers per hour. These tests involved common types and sizes of industrial sheathed. thermocouples as well as thermocouples made of bare wire. REFERENCES 1. Carroll, R. M.; Shepard, R. L.; and Kerlin, T. W., "In-Situ Measurement of the Response Time of Sheathed Therrnocouples," Transactions of the American Nuclear Society, Vol. 22, pp 240-241, November 1975. 2. Kerlin, T. W.; Shepard, R. L.; Hashemian, H. M.; and Petersen, K. M., "Response of Installed Temperature Sensors," Temperature Ils Measurement and Control in Science and Industry, Vol. 5, American Institute of Physics, 1982. 3. Warshawsky I., "Heat Conduction Errors and Time Lag in Cryogenic Thermometer Installations," ISA Transactions, Vol. 13, No. 4, pp 335346, 1974. . Kerlin, T. W.; Miller, L. F.; and Hashemian, H. M., "In-Situ Response Time Testing of Platinum Resistance Thermometers," ISA Transactions, Vol. 17, No. 4, 1980. 5. Hashemian, H. M., "Determination of Installed Thermocouple Response," Arnold . Engineering Developing Center, Arnold Air Force Station, Tennessee, Report No. AEDC-TR-86-46, December 1986.