This section describes the procedures used in calibrating all sensors installed on the test rig including the microchannel test section and the calibration results obtained. The sensors calibrated include all thermocouples, the Coriolis mass flowmeter, a reference pressure transducer used to measure the fluid pressure at six locations along the microchannel test section. All sensors were calibrated with their outputs connected to a National Instruments data acquisition system interfaced to a desktop computer running LabView software for measurement, data logging and storage. By calibrating each sensor together with the data acquisition system as used in the experiments, systematic error associated with the sensor and the data acquisition system are accounted for in the resulting calibration. Any error introduced by a standard used in the calibration process, however, will still be present. Calibration equations were implemented in the LabView data acquisition programs developed for this work.
3.9.6.1. Thermocouple calibration
Mineral insulated, stainless steel sheathed, type K thermocouples are used to measure the fluid temperatures at the microchannel inlet and outlet, the wall temperatures at six equi-spaced locations along the microchannel, the ambient temperature and the temperature of the enclosure housing local pressure transducers. The length and diameter of all the thermocouple probes were 150 mm and 0.5 mm respectively. Cold junction compensation is provided by built-in thermistors in the data acquisition (DAQ) system.
The thermocouples were calibrated against an ASL F250 MKII PrecisionThermometer coupled with a platinum resistance thermometer (Model T100-250). The specified accuracy of this instrument was ±0.025 K over the range from -50°C to 250°C. The
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thermocouples were fastened tightly to the PRT and immersed in an Omega constant- temperature circulating liquid bath. The bath was fitted with a thermoregulator (Model HCTB-3030) consisting of an immersion heater, a circulation pump and a temperature controller. The bath provides a temperature stability of ±0.005°C and has a set point accuracy of ±1°C. The liquid used in the bath was Diphyl PHT (Partially Hydrogenated Terphenyl) which has an initial boiling point of 352°C. Thermocouple calibrations were performed, for both increasing and decreasing temperature, at seven different points over the temperature range from 24 - 120°C. The ambient pressure and temperature during the calibrations were 1017 to 1018 mbar and 21-23°C respectively. Readings were taken after the liquid bath temperature became steady, as indicated by no change of the PRT reading. The temperatures measured using the thermocouples were recorded simultaneously by the LabView software. The temperature measured by the PRT, as indicated on the precision thermometer, was noted manually.
The thermocouple calibration results are presented in Appendix B, Fig. B9 in graphical form together with the linear calibration equation fitted to the data for each thermocouple. The standard deviations of the data for each calibration are listed in Table 3.6.
Table 3.6 Standard deviations of thermocouple calibration. Sensor S(K) 2S(K) Sensor S(K) 2S(K) Ti 0.07 0.14 T5 0.10 0.20 T1 0.11 0.22 T6 0.10 0.20 T2 0.10 0.20 To 0.10 0.20 T3 0.11 0.22 Tbox 0.10 0.20 T4 0.10 0.20 Ta 0.11 0.22
In Table 3.6, Ti refers to the fluid inlet temperature thermocouple, T1 to T6 the microchannel wall temperature thermocouples, To the fluid outlet temperature sensor,
Tbox the temperature thermocouple in the pressure transducer enclosure and Ta the ambient temperature thermocouple. In addition to the standard deviation (S) values, Table 3.6 lists values of 2S, the estimated random uncertainties associated with temperatures determined using the thermocouple sensors calibration lines for a 95%
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level of confidence. This can be considered a reasonable achievement, since the specified tolerance (Class 1) for Type K thermocouples over the temperature range - 40°C to 375°C is ±1.5 K. An uncertainty of 0.2 K is thus used for all thermocouple temperature measurements in this work.
3.9.6.2 Coriolis mass flowmeter calibration
The mass flow rate in the test loop is measured using a Micro Motion Coriolis mass flowmeter, comprising an Elite sensor (Model CMF010M323NB) and a transmitter (Model RFT9739E). The mass flow rate range of the flowmeter is 0 - 400 g/min. The output signal from the Coriolis meter utilizes a 4-20 mA current loop incorporating a 500 Ω resistor, thus giving a voltage output of 2-10V. The flowmeter has a low flow cut off of 3 g/min, below which the output defaults to the zero flow level of 2V. The calibration supplied by the manufacturer is a linear equation expressed as: Y = 50X - 100, where Y is in g/min and X in volts. The accuracy of the mass flow rate quoted by the manufacturer is 0.1% for mass flow rates above 40 g/min, but gradually rises to about 1.1% at 3 g/min.
Calibration of the flowmeter was performed using a collection and weighing method. A Sartorius electronic balance with a resolution of 0.1 mg was used to determine the mass of fluid collected. Calibrations were carried out for both increasing and decreasing flow rates. The time duration for each collection was measured using a Lonsdale stop watch with a resolution of 0.01 s. The calibration was performed using deionized water at a temperature of approximately 20°C. The results of the calibration are presented in the appendices. The flowmeter calibration line given by the manufacturer is also plotted for comparison. The best straight line fits obtained for increasing flow rates and decreasing flow rates fall slightly below the manufacturer’s calibration line, see Appendix B, Fig. B7. The line derived using the combined data results in a standard deviation of 0.6 g/min in the terms of a 95% confidence level. The slope value of 49.92 g/min per volt is 0.16% less than the 50 g/min per volt value for the manufacturer’s calibration line. The intercept value of -102.1 g/min obtained represents a difference of 2.1% from the manufacturer’s value of -100 g/min.
103 3.9.6.3 Druck pressure transducer calibration
A silicon diaphragm differential pressure transducer (Druck, Model PDCR4170-3400) was connected to the test loop to measure the liquid pressure against atmospheric pressure. This transducer was also used as a secondary standard in the calibration of the local differential pressure transducers fitted to the test section. The transducer measurement range is 0 - 5 bar and its specified accuracy is 0.08% of full scale. The transducer required an energisation voltage of 10 V and produces an output voltage ranging from 0 - 100 mV, corresponding to the 0 - 5 bar range, or 20 mV/bar.
Calibration of the transducer was performed at an ambient pressure and temperature of 1010 mbar and 19.5°C respectively. It was calibrated against a deadweight tester with a resolution of 1 lbf/in² (6.895 kPa) over the range of 10 – 70 lbf/in² (68.95 – 483 kPa). Readings were recorded for both increasing and decreasing applied pressures. A linear calibration was obtained with small scatter of data around the best straight line. The standard deviation of the data was found to be ±0.85 kPa for increasing pressures and ±0.89 kPa for decreasing pressures. The calibration line obtained by combining the increasing and decreasing pressure data gave a standard deviation of ±0.86 kPa. The slope of this calibration line was equivalent to 19.84 mV/bar, a difference of 0.8% from the slope of 20 mV/bar given in the manufacturer’s specification. The calibration data for the pressure transducer are presented in Appendix B, Fig. B2.
3.9.6.4 Local pressure transducer calibration
Local pressure transducers were fitted to measure the difference between local liquid pressure and atmospheric pressure at six positions along the length of the test microchannels and in the channel entry and outlet plenums. Low-cost differential pressure transducers (Honeywell PCC26) were used with a measurement range of 0 – 1 bar. The sensors used an excitation voltage of 12 V and gave an output voltage ranging from 0 – 10 V. According to the manufacturer, the transducers are temperature compensated but it was found that a consistent calibration could not be obtained if the operating temperature varied. To ensure the transducers were kept at a constant environment temperature, they were mounted in a plastic enclosure held at a steady temperature of approximately 50°C by an internal 60 W light bulb controlled by a dimmer circuit.
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The local pressure transducers were calibrated in situ on the test rig against the Druck differential pressure transducer (see Section 3.9.6.3) at high pressures and a water column manometer connected to the test loop for low pressures up to approximately 1200 mm H2O. The height difference between the Druck pressure transducer and local pressure transducers was approximately 100 mm. To compensate for this elevation difference a hydrostatic pressure correction of 0.98 kPa was subtracted from the pressures indicated by the Druck pressure transducer to refer these readings to the height of the local pressure transducers. Prior to calibration of the local pressure transducers, liquid (deionized water) was pumped through the test loop at high mass flow rate in order to flush any air from the system. Flushing of the local pressure transducer connections was achieved, one by one, by operating valves on purging pipes. After flushing, the pump was stopped to perform calibration of the transducers under zero flow conditions. Calibrations were conducted for both increasing and decreasing system pressures. The system pressure level was set by adjusting the saturation temperature at which water boils inside the mean reservoir. This was achieved by controlling the power input to the cartridge heater in the reservoir, using a West 6100 PID with a type K thermocouple immersed below the liquid surface in the reservoir as the feedback temperature sensor.
The results of the calibrations for the six local pressure transducers are given in Appendix B, Fig. B4. The standard deviations of the calibration data with respect to the calibration lines are presented in Table 3.7.
Table 3.7 Standard deviations of calibration data for the local pressure transducers.
Sensor Increasing pressure Decreasing pressure
S(kPa) 2S(kPa) S(kPa) 2S(kPa)
pi 0.09 0.18 0.09 0.18 po 0.10 0.20 0.09 0.18 p1 0.08 0.16 0.09 0.18 p2 0.09 0.18 0.09 0.18 p3 0.08 0.16 0.09 0.18 p4 0.09 0.18 0.09 0.18
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Based on the standard deviations of the calibration data shown in Table 3.7, the uncertainty for the local pressure measurements is taken to be approximately ±0.2 kPa. This value is used in the analysis propagated uncertainties in the results derived from the experimental measurements.
3.9.6.5 Digital multimeter calibration
Digital multimeters (Black Star, model 3225 MP) were used to measure the alternating current and voltage of the supply to the cartridge heater inserted in the microchannel test section. These meters have five AC voltage and six AC current measuring ranges of 200 mV to 750 V and 200 µA to 10 A respectively. In the manufacturer’s specification the stated accuracy of this meter is given as 0.25% of the reading.
One of the multimeters was calibrated against a Fluke 5500A multi-function calibrator by Optical Test and Calibration Ltd and issued with a calibration certificate. The calibration was performed at an ambient temperature of 21°C and a relative humidity of 44%. The results of calibration checks covering all AC current and AC voltage measurement range of the instrument at 60 Hz are shown in Appendix B, Fig. B8. The standard deviation values obtained from the calibrations are ±0.01 A for AC current and ±0.3 V for AC voltage. The second multimeter had also been checked and found to be accurate.