Download - Chap16Temperature Measurements
-
7/28/2019 Chap16Temperature Measurements
1/58
Chapter 16 Temperature
Measurements
The manner in which a thermometer is calibrated needs to correspond
to how it used. Under normal circumstances, you can get accuracy
from 0.2 to 2C.
Thermometry based on thermal expansion
Liquid-in-glass thermometers
-
7/28/2019 Chap16Temperature Measurements
2/58
Bimetalic Thermometers
If you take two metals with different thermal expansion coefficients
and bond them together, they will bend in one direction if thetemperature rises above the temperature at which the boding was done
and in the other if it gets less.
-
7/28/2019 Chap16Temperature Measurements
3/58
Bimetalic Example
-
7/28/2019 Chap16Temperature Measurements
4/58
16.4 Electrical Resistance
Thermometry
This is a more useful topic to us mainly because these sensors have
an electrical output and can be interfaced to data acquisition systems.
R e l
Ac
The resistivity of most materials is temperature dependent, and
we can use this fact to sense temperature
-
7/28/2019 Chap16Temperature Measurements
5/58
Resistance Temperature Detectors
A resistance of a small wire is used to detect temperature. Other
factors that can change the resistance must be minimized. Theseinclude: Corrosion
Strain
-
7/28/2019 Chap16Temperature Measurements
6/58
-
7/28/2019 Chap16Temperature Measurements
7/58
RTDsThe relationship between the metal resistance and temperature
can be expressed as an nth order polynomial
R R0 1 A T T0 B T T0 2 ....
R R0 1 A T T0 Over a limited range,Some use instead of A
-
7/28/2019 Chap16Temperature Measurements
8/58
RTDs
If we want the high
accuracy of which RTDs
are capable, we need to
have a very accurate
resistance measurement
system anda means to
remove the effect of thelead wires from our
measurements. Even
copper lead wires have
significant resistance.
-
7/28/2019 Chap16Temperature Measurements
9/58
R1R2
R3 r1RRTD r3
RRTD R3 r1 r3
-
7/28/2019 Chap16Temperature Measurements
10/58
Examples
ux2 uu2 xu
2
uv2 xv
2
R1 = R2 = 25W1%, 0.1%
at 0C R3 = RRTD = 25W
RRTD =R0[1 + (T - T0)] = 0.003925C-1
-
7/28/2019 Chap16Temperature Measurements
11/58
Thermistors
Usually made of a semiconductor and have the following properties:
Much largerdR/dTthan RTDs, so more sensitive
Rugged
Fast Response
Inconsistent, must be calibrated individually
Can change over time
-
7/28/2019 Chap16Temperature Measurements
12/58
Thermistors
R R0e 1/T1/T0
-
7/28/2019 Chap16Temperature Measurements
13/58
Thermistors
-
7/28/2019 Chap16Temperature Measurements
14/58
16.5 Thermoelectric Temperature
Measurement
In this section, we will learn about perhaps the most important
temperature measuring technique--Thermocouples.
Electromotive Force
-
7/28/2019 Chap16Temperature Measurements
15/58
Thermoelectric Effects
Seebeck Generates voltages across two dissimilar materialswhen a temperature difference is present.
Peltier Moves heat through dissimilar materials when
current is applied.
-
7/28/2019 Chap16Temperature Measurements
16/58
Thermocouple LawsLaw of Intermediate Materials:
If you break your thermocouple
and add something of anothermaterial, it will have no effect as
long as both ends of the new
material are at the same
temperature.
Law of Intermediate Temperatures:
If you get emf1 when the two
temperatures are T1 and T2, and youget emf2 when you have T2 and T3,
you will get emf1 + emf2 when the
temperatures are T1 and T3.
-
7/28/2019 Chap16Temperature Measurements
17/58
i i
-
7/28/2019 Chap16Temperature Measurements
18/58
Designations
Positive wire is listed first
Th l M
-
7/28/2019 Chap16Temperature Measurements
19/58
Thermocouple MeasurementsThe reason we call it emf rather than voltage is that this output only
truly exists for an open circuit. We must be careful to measure the
output of the thermocouple in such a way as to not draw current, which
would load the thermocouple and effect the reading. Digital volt
meters have very high input impedance, as does our data acquisition
system. Either of these will work fine if they are sensitive enough.
The book talks of using potentiometers to measure the voltage, but thisharks back to the era prior to very high impedance measuring devices.
-
7/28/2019 Chap16Temperature Measurements
20/58
Th l O
-
7/28/2019 Chap16Temperature Measurements
21/58
Thermocouple Output
(T)
(K)
-
7/28/2019 Chap16Temperature Measurements
22/58
-
7/28/2019 Chap16Temperature Measurements
23/58
-
7/28/2019 Chap16Temperature Measurements
24/58
Th l C lib ti
-
7/28/2019 Chap16Temperature Measurements
25/58
Thermocouple Calibration
Th l M t
-
7/28/2019 Chap16Temperature Measurements
26/58
Thermocouple MeasurementsThe measurement we make with a single thermocouple is relative to the junction
temperature. The charts and polynomials tell us the temperature relative to 0C as a
function of voltage. The Law of Intermediate Temperatures allows us to convert our
datum from 0 to our measured reference temperature. WARNING: Although it lookslike it, we are not simply adding the junction temperature to the temperature indicated
by the thermocouple voltage. This works only if the thermocouple is perfectly linear,
which they are not in general.
Example 16.1
E l
-
7/28/2019 Chap16Temperature Measurements
27/58
Example
Say we hook a J type thermocouple to a volt meter and read 0.507 mV.
An independent temperature measurement at the connection to the voltmeter tells us that the temperature there is 20C. What is the
temperature at the thermocouple junction?
Table 16.6 is relative to 0C (notice that the voltage at that temperature
is zero). At 20C, the voltage from the table is 1.019 mV. So our
voltage relative to 0C is the measured voltage plus the 20 value:
1.019 + 0.507 = 1.526.
Going back to the table, this corresponds to 29.79C.
P d
-
7/28/2019 Chap16Temperature Measurements
28/58
Procedure
1) Measure the thermocouple voltage Etc
2) Measure the temperature at the location where the tc is connected tothe meter (the reference temperature, Tref)
3) Using a table or a polynomial, find the voltage generated by the
junction at the meter at Tref, call it Eref.
4) Add the two voltages E = Etc + Eref.
5) Find the temperature that corresponds to E from tables or a
polynomial.
E l
-
7/28/2019 Chap16Temperature Measurements
29/58
Example
Jethro wants to make some tc measurements, but the closest thing he
has to a thermometer is the thermostat in lab. It is set to 20 C. Heknows that the furnace kicks on at 18 and runs until it reaches 22.
He decides to assume that his reference is 20C. What bias error will
he incur?
E t i L d
-
7/28/2019 Chap16Temperature Measurements
30/58
Extension Leads
-
7/28/2019 Chap16Temperature Measurements
31/58
Thermocouples cant measure
a single temperature, but canonly tell us the difference in
temperature between two
points. If we can put one of
those points at a known
temperature, we are set.
Error in Reference Temperat re
-
7/28/2019 Chap16Temperature Measurements
32/58
Error in Reference TemperatureWe are starting to accumulate a lot of different kind of errors here. We
get a systematic error if we do not calibrate our thermocouple. If there is
an error in our reference junction temperature (and there is) this is anadditional bias error. We also need to be concerned about our voltage
measurement resolution.
Our System
-
7/28/2019 Chap16Temperature Measurements
33/58
Our System
The minimum voltage range for our system is 0.05V. Recalling that we
have a 12 bit system, and using the polynomials in Tables 16.6-7,
estimate our temperature resolution at 20C for a T type thermocouple.
Add this problem to your next lab.
Effective Junction
-
7/28/2019 Chap16Temperature Measurements
34/58
Effective Junction
dD is the spatial uncertainty
16 5 6 Th il d Th l
-
7/28/2019 Chap16Temperature Measurements
35/58
16.5.6 Thermopiles and Thermocouples
Connected in Parallel
16 6 Semiconductor Junction
-
7/28/2019 Chap16Temperature Measurements
36/58
16.6 Semiconductor-Junction
Temperature Sensors
16 10 3 T El
-
7/28/2019 Chap16Temperature Measurements
37/58
16.10.3 Temperature Element
Response
Weve already covered the first part of this in this class (step response to
first order systems) and in heat transfer. Since it is so much fun, lets do
it again. Say you have a thermocouple that is essentially a sphere with
two non-conducting wires protruding from it. You place it in a fluid
warmer than the junction. Then the first law says that Ein - Eout = Estored.No heat come in, since the bead is cooler than the fluid.
mcpdTp
dt
hAs Tg Tp
dTp
dt Tp Tg
ksds
dt F(t)
From chapter 5,
And = /k
Response to step input
-
7/28/2019 Chap16Temperature Measurements
38/58
Response to step input
We have the same equation so we will get the same response.
P P PA P et/
TTp Tg Tp 1 e t/
T Tg Tp e t/ Tp Tg TpT Tg Tg Tp e t/
In practice
-
7/28/2019 Chap16Temperature Measurements
39/58
In practice
As you are keenly aware, h is not always known or easy to compute.
Our friend Dr. Moffat suggests an empirical equation that does not
require knowledge ofh.
3500tcc tcd
1.25
TV 15.8/ T
Two Time Constant Model
-
7/28/2019 Chap16Temperature Measurements
40/58
Two Time Constant Model
Many (most) times, our temperature sensor is encased in some other
material. As a result, the first order response model may not fit well.It is relatively simple to make a richer model that can capture this
effect.
Two Time Constant Model
-
7/28/2019 Chap16Temperature Measurements
41/58
Two Time Constant Model
mjc jdTj
dt hjAj T2 T1 hpAp Tj Tp
mpcpdTp
dt hpAp Tj Tp
First law on the jacket
First law on the probe
Rewrite these:
jdTj
dt T2 T1
hpAp
hjAjTj Tp
pdTp
dt Tj Tp
This term is often insignificant. If
so, we can combine the two
equations.
jpd
2
Tj
dt2 j p dT
p
dt Tp T2
Two Time Constant Solution
-
7/28/2019 Chap16Temperature Measurements
42/58
Two Time Constant Solution
jpd2Tj
dt2 j p
dTp
dt Tp T2
T2 TpT2 T1
TTmax
1
et/p
1
1
e t/p
j
p
16 10 4 Compensating Slow Sensors
-
7/28/2019 Chap16Temperature Measurements
43/58
16.10.4 Compensating Slow Sensors
16 11 Measurement of Heat Flux
-
7/28/2019 Chap16Temperature Measurements
44/58
16.11 Measurement of Heat Flux
We seek to measure
Slug type
Foil/Membrane type
Thin Film Layers type
q kdT
dx
Slug Type
-
7/28/2019 Chap16Temperature Measurements
45/58
Slug Type
q Mc
A
dT
dt UT
Membrane Type
-
7/28/2019 Chap16Temperature Measurements
46/58
Membrane Type
q 4tk
R2
T
C emf
Thin-Film Layered Type
-
7/28/2019 Chap16Temperature Measurements
47/58
Thin-Film Layered Type
Bottom line-create a 1-D heat flow and measure temperature at two
known locations.
q kdTdx
kT
Error Sources in Temperature
-
7/28/2019 Chap16Temperature Measurements
48/58
Error Sources in Temperature
Measurements
Conduction: Your probe can conduct heat to/from the environmentto/from your desired measurement location
Analysis of Conduction Error
-
7/28/2019 Chap16Temperature Measurements
49/58
Analysis of Conduction Errorqx dx qx hPdx T(x) T
T T
q kAdT
dx
m hP
kA
d2
dx 2 m2 0
x w
coshmx
coshmL
0
w T
0
TTw T
1
coshmL
T 0 T Tw T
coshmL
L
P/A = 4/D for round
16 8 Radiative Temperature
-
7/28/2019 Chap16Temperature Measurements
50/58
16.8 Radiative Temperature
Measurements (Pyrometry)
Eb T4
Temperatures greater than 500C= 5.6710-8 W/m2K4
Two Broad Categories
-
7/28/2019 Chap16Temperature Measurements
51/58
Two Broad CategoriesSome radiative temperature measurements are made by detecting
photons emitted by the hot source. Well call these Photon
Detectors. There is essentially no difference between this and aCCD camera.
A Thermal Detector produces a rise in temperature at some detector
Thermal Cameras
-
7/28/2019 Chap16Temperature Measurements
52/58
Thermal Cameras
Radiative Temperature
-
7/28/2019 Chap16Temperature Measurements
53/58
Radiative Temperature
Measurements
-
7/28/2019 Chap16Temperature Measurements
54/58
1
The texts discussion of radiative heat transfer is somewhat dumbed
down. Since most of you are currently Heat Transfer students, I will
put this discussion at a more appropriate level. Radiative heat istransferred via photons which travel at the speed of light. When this
energy strikes a surface, it can either be absorbed, reflected, or
transmitted.
q TA4 TB
4
ET4
For a non-ideal radiator,
The radiative heat transfer between two ideal bodies A and B
If A is not ideal,
-
7/28/2019 Chap16Temperature Measurements
55/58
q AFBA TA4 TB
4In our case, the detecting element will be B, and from this we will
determine the heat flux (and thus the temperature) of A.
Calibration is required to account for unknown quantities like the
view factor and the body emissivity.
-
7/28/2019 Chap16Temperature Measurements
56/58
As the body increases in temperature, its emissive power increases,
and the peak of the spectrum shifts to higher frequencies (lower
wavelengths)
E C1
5 eC2 /T 1
16.8.2 Total Radiation Pyrometry
-
7/28/2019 Chap16Temperature Measurements
57/58
16.8.2 Total Radiation Pyrometry
16.8.3 Optical Pyrometry
-
7/28/2019 Chap16Temperature Measurements
58/58
16.8.3 Optical PyrometryOne or two wavelengths of light are selected using a series of optical
filters. For a photon detector, we can determine the temperature from
E C1
5 eC2 /T 1
If two colors (wavelengths) are examined, the influence of theunknown emissivity of the object, which may be independent of
wavelength, can be eliminated.