Transcript Temperature
EXM2 Experimental methods E181101 Temperature (thermocouples, thermistors) Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010 Some pictures and texts were copied from www.wikipedia.com 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 (Ek) is directly proportional to thermodynamic temperature 1 Ek kT 2 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. EXM2 Temperature measurement Thermometers 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 Seebeck effect (electrons diffuse from hot to cold end) Measured voltage is given by temperature T2-T1. Cold junction temperature T2 should be 0C. Or at least measured by different instrument (by RTD). T1 V T2 Different wire has no effect if T3 is the same at both ends T1 T3 T3 V T2 It does not matter how the connection of wires is realized (soldered, welded, mechanically connected) T1 V T2 Usual configuration – Cu wires to voltameter. Measured voltage is given by temperature T2-T1 T1 Exposed end Insulated junction T2 V Grounded junction Law of successive thermocouples (next slide) T2 T1 V2 T3 V3 Thermocouple pile EXM2 T2 T1 V 3-times greater Example of a thermocouple pile manufactured by lithography EXM2 Thermocouple types 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 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 arrangement Sensor fixed resistors V Current source (1mA) 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. 1 dR R0 dT 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 EXM2 RTD platinum thermometers RTD Platinum thermometers Pt100, Pt1000 (nominal resistance 100/1000 Ohms respectively) R R0 (1 0.0039083T 5.77 10 7 T 2 ) Therefore coefficient of relative temperature change is approximately 1 dR 0.0039 R0 dT (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 Parazitic resistances of leading wires are added to the sensor resistance V Current source (1mA) V Current source (1mA) 3-wires Parazitic resistances of leading wires are partly compensated 4-wires The most accurate arrangement Almost zero current flows in these two wires as soon as internal resistance of voltameter is high V Current source (1mA) 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 sensor Time delay of sensor follows from the enthalpy balance Enthalpy accumulation Mc p dTs S (T fluid Ts ) dt Heat from fluid to sensor [W] 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 Tfluid Mc p S Time constant is the time required by a sensor to reach 63% of a step change temperature. Ts t 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 D 2 0.4 Re Pr 0.4 fluid Re uD Pr a 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). EXM2 Example time constant of sensors EXM2 Tutorial time constant of sensors Identify the time constant of a thermocouple A/D converter PC NI-USB 6281 Labview EXM2 Tutorial science direct reading EXM2 Tutorial science direct reading Rabin, 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 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 RT 4 Lwire D 2 wire D Lwire EXM2 Example steady heat transfer (1/2) EXM2 Example steady heat transfer (2/2) 2/3 0.37 toto platí jen pro malé Re, přesnější Nu (0.4 Re 0.06 Re ) Pr EXM2 Heat transfer - tutorial Identify heat transfer coefficient (cross flow around cylinder) Pt100 Cylinder H=0.075, D=0.07 [m] cp=910, rho=2800 kg/m3 Df=0.05m T [C] Air cp=1000, rho=1 kg/m3, =0.03 W/m/K FAN (hot air) OMEGA data logger (thermocouples) T1,T2 , T3 Example: Re=8000, Pr=1 Nu (0.4 Re 0.06 Re ) Pr 2/3 Nu 0.4 Re Pr 0.37 36 Watt meter Measured 1.3.2011 1200 W 0.37 60 EXM2 Heat transfer - tutorial 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 Nu (0.4 Re 0.06 Re 80 70 60 exponential model T [C] ) Pr 0.37 82 NuD W 191 mK This is result from the heat transfer correlation More than 2times less is predicted from the time constant experiment T T0 (T T0 )(1 exp(t / )) 50 2/3 Dc p 2800 0.07 910 W 76.2 4 4 585 mK 40 30 20 Experiment 1.3.2011 =585 s Probable explanation of this discrepancy: T0=19.2, T=81 C 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) 10 0 0 5 10 15 t [min] 20 25 EXM2 Thermocouple - tutorial Record time change of temperature of air compressed in syringe. x D Thermocouple P-pressure transducer Kulite XTM 140 V p1v1 p2 v2 Example: V2/V1=0.5 p1v1 RT1 p1 v T v ( 2 ) 1 2 p2 v1 T2 v1 p2 v2 RT2 T1 v2 1 ( ) T2 v1 =cp/cv=1.4 T1=300 K T2=396 K temperature increase 96 K!!