Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

Temperature(thermocouples, thermistors)

Experimental methods E181101 EXM2

Some pictures and texts were copied from www.wikipedia.com

EXM2 State variables- temperatureTemperature is measure of inner kinetic energy of random molecular motion. In case of solids the kinetic energy is the energy of atom vibration, in liquids and gases the kinetic energy includes vibrational, rotational and translational motion. Statistically, temperature (T) is a direct measure of the mean kinetic energy of particles (atoms, molecules). For each degree of freedom that a particle possesses (rotational and vibrational modes), the mean kinetic energy (Ek) is directly proportional to thermodynamic temperature

where k-is universal Boltzmann constant. For more details see wikipedia.

kTEk 2

1

Thermodynamic temperature is measured in Kelvins [K], that are related to different scales, degree of Celsius scale T=C+273.15, or degree of Fahrenheit F=1.8C+32.

Remark: you can say degree of Celcius, or degree of Fahrenheit, but never say degree of Kelvins - always only Kelvins.

EXM2 Temperature measurementThermometers

Glass tube (filled by mercury or organic liquid, accuracy up to 0.001 oC)

Bimetalic (deflection of bonded metallic strips having different thermal expansion coefficient)

Thermocouples (different metals electrically connected generate voltage)

RTD (Resistance Temperature Detectors – temperature dependent electrical resistance) – thermistors (semiconductors)

Infrared thermometers

Thermal luminiscence (phosphor thermometers – time decay of induced light depends upon temperature – used with optical fibres)

Irreversible/reversible sensors (labels), liquid crystals

EXM2 Temperature measurement

EXM2 Thermocouples

Leger

EXM2 Thermocouples

VT1 T2

VT1 T2T3 T3

VT1 T2

VT1

T2

Usual configuration – Cu wires to voltameter. Measured voltage is given by temperature T2-T1

It does not matter how the connection of wires is realized (soldered, welded, mechanically connected)

Different wire has no effect if T3 is the same at both ends

Measured voltage is given by temperature T2-T1. Cold junction temperature T2 should be 0C. Or at least measured by different instrument (by RTD).

Exposed end Insulated junction Grounded junction

V3

T1

T2

Law of successive thermocouples (next slide)

V2

T3

Seebeck effect (electrons diffuse from hot to cold end)

EXM2 Thermocouple pile

T1

T2

V 3-times greater

Example of a thermocouple pile manufactured by lithography

EXM2 Thermocouple types

Type K (chromel-Alumel) , sensitivity 41 µV/°C

J (iron–constantan) has a more restricted range than type K (−40 to +750 °C), but higher sensitivity 55 µV/°C

E (chromel–constantan) has a high output (68 µV/°C) which makes it well suited to cryogenic use

N (Nicrosil–Nisil) high temperatures, exceeding 1200 °C. 39 µV/°C at 900 °C slightly lower than type K.

T (copper–constantan) −200 to 350 °C range. Sensitivity of about 43 µV/°C.

Chromel= 90% nickel, 10% chromium

Alumel= 95% nickel, 2% aluminium, 2% manganese, 1% silicon

Nicrosil=Nickel-Chromium-Silicon

Constantan = 55% copper, 45% nickel

There are two basic kinds of resistivity thermometers

Thermistors (resistor is a semiconductor, or a plast) high sensitivity, nonlinear, limited temperature

RTD (metallic resistor, see next slide) stable, linear, suitable for high temperatures. R=100 .

Another classification according to sign of temperature sensitivity coef.

NTC (Negative Temp.Coef) typical for semiconductors, R=2252 is industrial standard resistance.

PTC (Positive Temp. Coef.) typical for metals, or for carbon filled plastics

EXM2 Resistivity thermometersSpecific electrical resistivity (units m) of materials depends upon temperature. Temperature can be therefore evaluated from measured electrical resistance of sensor (resistor) by using for example Wheatstone bridge arrangement

dT

dR

R0

1

Current source (1mA)V

Sensor fixed resistors

Cold Hot sample

EXM2 RTD platinum thermometersRTD Platinum thermometers Pt100, Pt1000 (nominal resistance 100/1000 Ohms respectively)

Therefore coefficient of relative temperature change is approximately

(this value slightly depends upon platinum purity, for example typical US standards =0.00392, Europian standard =0.00385).

2-wires (reading is affected by parasitic ohmic resistance of long and tiny wires (which need not be negligible in comparison with 100 of RTD). Example> compute resistance of Cu wire for specific resistivity of copper 1.7E-8 .m

3-wires

4-wires

)1077.50039083.01( 270 TTRR

0039.01

0

dT

dR

R

Current source (1mA)V

Current source (1mA)V

Current source (1mA)VAlmost zero current flows in these two wires as

soon as internal resistance of voltameter is high

Parazitic resistances of leading wires are added to the sensor resistance

Parazitic resistances of leading wires are partly compensated

The most accurate arrangement

EXM2 Systematic errors in contact measurement

Pt1000 is in fact a tiny heater (at 1 mA, sensor generates RI2=0.001 W) and the heat must be removed by a good thermal contact with measured object.

RTD-2 wires connection (resistance of leading wires are added to the measured sensor resistance). Specific resistance of copper is =1.7E-8 .m, resistance of wire is R=4L/( D2), L-length, D-diameter of wire.

Time delay due to thermal capacity of sensor (response time depends upon time constant of sensor as well as upon thermal contact between fluid and the sensor surface, see next slide)

Temperature difference between temperature of fluid and the temperature of measuring point (junction of thermocouple wires, or Pt100 spiral). This difference depends upon the thermal resistance fluid-sensor and thermal resistance sensor-wall (resistance of shield). See next slide

EXM2 Time constant of sensor

Demuth

EXM2 Time constant of sensorTime delay of sensor follows from the enthalpy balance

)( sfluids

p TTSdt

dTMc

where M-mass, cp specific heat capacity of sensor, Ts temperature of sensor, -heat transfer coefficient, S surface of sensor, Tfluid-temperature of fluid (temperature that is to be measured).

For step change of fluid temperature solution of this equation is exponential function with time constant

S

Mc p

Heat transfer coefficient depends upon fluid velocity (more specifically upon Reynolds number or Rayleigh number in case of forced and natural convection, respectively). Example: for a spherical tip of a probe and forced convection it is possible to use Whitaker’s correlation

Heat from fluid to sensor [W]

4.0PrRe4.02 fluid

DNu

uD

Rea

Pr

Nu-Nusselt number, D-diameter of sphere, thermal conductivity of fluid, u-velocity of fluid, kinematic viscosity, a-temperature diffusivity.

Conclusion: the higher is mass of sensor the greater if time constant. The higher is velocity of fluid, the better (the shorter is the time constant).

Time constant is the time required by a sensor to reach 63% of a step change temperature.

Enthalpy accumulation

t

Tfluid

Ts

EXM2 Example time constant of sensors

EXM2 Tutorial time constant of sensors

Identify the time constant of a thermocouple

A/D converter

NI-USB 6281

PC

Labview

EXM2 Tutorial science direct reading

EXM2 Tutorial science direct readingRabin, Y., Rittel, D., 1998. A model for the time response of solid-embedded thermocouples. Experimental Mechanics 39 (2), 132–136.

EXM2 Heat conduction by shield

Scheeler

EXM2 Heat conduction by shieldDistortion of measured temperature of fluid due to heat transfer through wires or shielding of detector. The error decreases with improved thermal contact (fluid-surface, see above) and reduced thermal resistance of leading wires or shield RT. For wire or a rod the thermal resistance is

wire

wireT D

LR

2

4

Lwire

D

EXM2 Example steady heat transfer (1/2)

EXM2 Example steady heat transfer (2/2)

toto platí jen pro malé Re, přesnější2/3 0.37(0.4 Re 0.06Re )PrNu

Heat transfer - tutorialEXM2

Identify heat transfer coefficient (cross flow around cylinder)

Pt100

T [C]

FAN (hot air)

OMEGA data logger (thermocouples) T1,T2 , T3

Watt meter

2/3 0.37(0.4 Re 0.06Re )Pr 60Nu Example: Re=8000, Pr=10.370.4 Re Pr 36Nu

Measured 1.3.2011 1200 W

Cylinder H=0.075, D=0.07 [m]

cp=910, rho=2800 kg/m3

Air cp=1000, rho=1 kg/m3, =0.03 W/m/K

Df=0.05m

Heat transfer - tutorialEXM2

2/3 0.37(0.4 Re 0.06Re )Pr 82Nu

Example: velocity of air calculated from the enthalpy balance is 5 m/s(Tnozzle=140 0C, mass flowrate of air 0.01 kg/s)

Corresponding Reynolds number (kinematic viscosity 2.10-5) is Re=17500

Nusselt number calculated for Pr=0.7 is therefore

191NuD W

mK

2800 0.07 91076.2

4 4 585pDc W

mK

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25

t [min]

T [

C]

experiment

exponential model

Experiment 1.3.2011 =585 s

0 0( )(1 exp( / ))T T T T t

T0=19.2, T=81 C

This is result from the heat transfer correlation

More than 2times less is predicted from the time constant

Probable explanation of this discrepancy:

Velocity of air (5m/s) was calculated at the nozzle of hair dryer. Velocity at the cylinder will be much smaller. As soon as this velocity will be reduced 5-times (1 m/s at cylinder) the heat transfer coefficient will be the same as that predicted from the time constant (76 W/m/K)

Thermocouple - tutorialEXM2

P-pressure transducer Kulite XTM 140

Record time change of temperature of air compressed in syringe.

2211 vpvp 111 RTvp

222 RTvp

V

xD

1

2

2

1

1

2

2

1 )(v

v

T

T

v

v

p

p

1

1

2

2

1 )(

v

v

T

T

Thermocouple

Example: V2/V1=0.5 =cp/cv=1.4

T1=300 K

T2=396 K temperature increase 96 K!!