Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

1. Experimental methods E181101 EXM2 Temperature(thermocouples, thermistors) Some pictures and texts were copied from www.wikipedia.com Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

2. State variables- temperature EXM2 Temperature 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. 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.

3. Temperature measurement EXM2 • Thermometers • Glass tube (filled by mercury or organic liquid, accuracy up to 0.001oC) • 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

4. Temperature measurement EXM2

5. Thermocouples EXM2 Leger

6. Thermocouples V V V V3 V T1 T2 T1 T2 T3 T3 T1 T2 T1 T2 V2 EXM2 Measured voltage is given by temperature T2-T1. Cold junction temperature T2 should be 0C. Or at least measured by different instrument (by RTD). Seebeck effect (electrons diffuse from hot to cold end) Different wire has no effect if T3 is the same at both ends It does not matter how the connection of wires is realized (soldered, welded, mechanically connected) Usual configuration – Cu wires to voltameter. Measured voltage is given by temperature T2-T1 Exposed end Insulated junction Grounded junction Law of successive thermocouples (next slide) T2 T3 T1

7. Thermocouple pile EXM2 T2 T1 V 3-times greater Example of a thermocouple pile manufactured by lithography

8. Thermocouple types EXM2 Chromel= 90% nickel, 10% chromium Alumel= 95% nickel, 2% aluminium, 2% manganese, 1% silicon Nicrosil=Nickel-Chromium-Silicon Constantan = 55% copper, 45% nickel 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 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. E (chromel–constantan) has a high output (68 µV/°C) which makes it well suited to cryogenic use

9. Resistivity thermometers Current source (1mA) V Sensor fixed resistors EXM2 Specific 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 • 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 Cold Hot sample

10. RTD platinum thermometers Current source (1mA) V Current source (1mA) V Current source (1mA) V EXM2 RTD 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 Parazitic resistances of leading wires are added to the sensor resistance Parazitic resistances of leading wires are partly compensated The most accurate arrangement Almost zero current flows in these two wires as soon as internal resistance of voltameter is high

11. Systematicerrors in contact measurement EXM2 • 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=4L/( 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

12. Time constant of sensor EXM2 Demuth

13. Time constant of sensor Tfluid Ts  t EXM2 Time delay of sensor follows from the enthalpy balance Heat from fluid to sensor [W] Enthalpy accumulation 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  Time constant is the time required by a sensor to reach 63% of a step change temperature. 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 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).

14. Example time constant of sensors EXM2

15. Tutorial time constant of sensors EXM2 Identify the time constant of a thermocouple PC Labview A/D converter NI-USB 6281

16. Tutorial science direct reading EXM2

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

18. Heat conduction by shield EXM2 Scheeler

19. Heat conduction by shield D Lwire EXM2 Distortion 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

20. Example steady heat transfer (1/2) EXM2

21. Example steady heat transfer (2/2) EXM2 toto platí jen pro malé Re, přesnější

22. Heat transfer - tutorial EXM2 Identify heat transfer coefficient (cross flow around cylinder) Pt100 T [C] Cylinder H=0.075, D=0.07 [m] cp=910, rho=2800 kg/m3 Df=0.05m Air cp=1000, rho=1 kg/m3, =0.03 W/m/K FAN (hot air) OMEGA data logger (thermocouples) T1,T2 , T3 Watt meter Measured 1.3.2011 1200 W Example: Re=8000, Pr=1

23. Experiment 1.3.2011 =585 s T0=19.2, T=81 C Heat transfer - tutorial EXM2 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 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)

24. x D V Thermocouple - tutorial EXM2 Record time change of temperature of air compressed in syringe. Thermocouple P-pressure transducer Kulite XTM 140 Example: V2/V1=0.5 =cp/cv=1.4 T1=300 K T2=396 K temperature increase 96 K!!