Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010 Temperature (thermocouples, thermistors) Experimental methods E EXM2 Some pictures and texts were copied from

EXM2 State variables- temperature 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 (E k ) is directly proportional to thermodynamic temperature where k-is universal Boltzmann constant. For more details see wikipedia.wikipedia Thermodynamic temperature is measured in Kelvins [K], that are related to different scales, degree of Celsius scale T=C , 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 measurement Thermometers  Glass tube (filled by mercury or organic liquid, accuracy up to o C)0.001  Bimetalic (deflection of bonded metallic strips having different thermal expansion coefficient)  Thermocouples (different metals electrically connected generate voltage) Thermocouples  RTD (Resistance Temperature Detectors – temperature dependent electrical resistance) – thermistors (semiconductors) RTD  Infrared thermometers Infrared thermometers  Thermal luminiscence (phosphor thermometers – time decay of induced light depends upon temperature – used with optical fibres)phosphor thermometers  Irreversible/reversible sensors (labels), liquid crystalslabels

EXM2 Temperature measurement

EXM2 Thermocouples Leger

EXM2 Thermocouples V T1T1 T2T2 V T1T1 T2T2 T3T3 T3T3 V T1T1 T2T2 V T1T1 T2T2 Usual configuration – Cu wires to voltameter. Measured voltage is given by temperature T 2 -T 1 It does not matter how the connection of wires is realized (soldered, welded, mechanically connected) Different wire has no effect if T 3 is the same at both ends Measured voltage is given by temperature T 2 -T 1. Cold junction temperature T 2 should be 0 C. Or at least measured by different instrument (by RTD). Exposed end Insulated junction Grounded junction V3V3 T1T1 T2T2 Law of successive thermocouples (next slide) V2V2 T3T3 Seebeck effect Seebeck effect (electrons diffuse from hot to cold end)

EXM2 Thermocouple pile T1T1 T2T2 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 thermometers 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 arrangementWheatstone bridge Current source (1mA) V Sensor fixed resistors Cold Hot sample

EXM2 RTD platinum thermometers 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  = , Europian standard  = ). 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 Current source (1mA) V V V Almost 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 S ystematic errors in contact measurement  Pt1000 is in fact a tiny heater (at 1 mA, sensor generates RI 2 =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/(  D 2 ), 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 sensor Time delay of sensor follows from the enthalpy balance where M-mass, c p specific heat capacity of sensor, T s temperature of sensor,  -heat transfer coefficient, S surface of sensor, T fluid -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  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 correlationWhitaker’s correlation Heat from fluid to sensor [W] Nu-Nusselt numberNu-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 T fluid TsTs 

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 reading Rabin, Y., Rittel, D., 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 shield 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 L wire D

EXM2 Example steady heat transfer (1/2)

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

Heat transfer - tutorial EXM2 Identify heat transfer coefficient (cross flow around cylinder) Pt100 T [C] FAN (hot air) OMEGA data logger (thermocouples) T 1,T 2, T 3 Watt meter Example: Re=8000, Pr=1 Measured W Cylinder H=0.075, D=0.07 [m] c p =910, rho=2800 kg/m 3 Air c p =1000, rho=1 kg/m 3, =0.03 W/m/K D f =0.05m

Heat transfer - tutorial EXM2 Example: velocity of air calculated from the enthalpy balance is 5 m/s (T nozzle =140 0 C, mass flowrate of air 0.01 kg/s) Corresponding Reynolds number (kinematic viscosity ) is Re=17500 Nusselt number calculated for Pr=0.7 is therefore Experiment  =585 s T 0 =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 - tutorial EXM2 P-pressure transducer Kulite XTM 140 Record time change of temperature of air compressed in syringe. V x D Thermocouple Example: V 2 /V 1 =0.5  =c p /c v =1.4 T 1 =300 K T 2 =396 K temperature increase 96 K!!