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


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.


3/58

Bimetalic Example


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


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


6/58


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


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.


9/58

R1R2

R3 r1RRTD r3

RRTD R3 r1 r3


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


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


12/58

Thermistors

R R0e 1/T1/T0


13/58

Thermistors


14/58

16.5 Thermoelectric Temperature

Measurement

In this section, we will learn about perhaps the most important

temperature measuring technique--Thermocouples.

Electromotive Force


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.


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.


17/58

i i


18/58

Designations

Positive wire is listed first

Th l M


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.


20/58

Th l O


21/58

Thermocouple Output

(T)

(K)


22/58


23/58


24/58

Th l C lib ti


25/58

Thermocouple Calibration

Th l M t


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


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


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


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


30/58

Extension Leads


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


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


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


34/58

Effective Junction

dD is the spatial uncertainty

16 5 6 Th il d Th l


35/58

16.5.6 Thermopiles and Thermocouples

Connected in Parallel

16 6 Semiconductor Junction


36/58

16.6 Semiconductor-Junction

Temperature Sensors

16 10 3 T El


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


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


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


40/58


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.



41/58


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


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


43/58

16.10.4 Compensating Slow Sensors

16 11 Measurement of Heat Flux


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


45/58

Slug Type

q Mc

A

dT

dt UT

Membrane Type


46/58

Membrane Type

q 4tk

R2

T

C emf

Thin-Film Layered Type


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


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


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


50/58

16.8 Radiative Temperature

Measurements (Pyrometry)

Eb T4

Temperatures greater than 500C= 5.6710-8 W/m2K4

Two Broad Categories


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


52/58

Thermal Cameras

Radiative Temperature


53/58

Radiative Temperature

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,


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.


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


57/58

16.8.2 Total Radiation Pyrometry

16.8.3 Optical Pyrometry


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.

chap16temperature measurements

Documents