Effect of Temperature

Temperature is a potential noise source in capacitance measurement and its effect must therefore be studied. Similar, to the humidity effects, temperature fluctuations can cause drift o f the baseline signal (zero flow), i.e. Cp^j^. This phenomenon is particularly important in the case of on-line transducers that have to operate for long periods without re-calibration at higher than ambient temperatures. In the particular application o f the exhaust particulate monitor, international standards suggest that the test gas at the instant of measurement should be between 52 -120 °C. Within this temperature range, all the water present is in vapour form and all other uncondensed non-solid particles (i.e. uncondensed/unbumed fuel or lubricating oil) are assumed to be insignificant in normal exhaust smoke (ISO 3173, 1974; BS 8178-2, 1997; ISO/DIS 11614, 1994).

Capacitance/temperature experiments were conducted using transducer, T| (see table 6.2) with two different inter-electrode separation distances, 0.72 cm (T^g) and 0.87 cm (Tjc). An air blower equipped with an 1.3 kW heating coil was located at one end of a 15 cm long stainless steel pipe (i.d. = 3.25 cm, o.d. = 3.27 cm) with the other end connected to the capacitance transducer. The blower supplied air at a flow rate of 500 1/min, regulated at two fixed temperature levels of 15 °C or 100 °C.

Chapter 6 Results and Discussion

It should be noted that the transducer’s capacitance may change both due to the temperature dependence of the dielectric constant of air as well as the thermal expansion o f the transducer itself. In order to elucidate the relative contributions of each factor, capacitance/temperature experiments both during heating and cooling cycles were conducted. To ascertain the uncertainties associated with the measurements o f electrode temperatures by attaching temperature probes to their surfaces, measurements were obtained with the capacitance transducer and the adjoining pipe thermally insulated. The results were then compared against those in the absence o f insulation. Also, data during both heating up and cooling down cycles were recorded in order to investigate the possibility o f hysterisis.

Finally the results are used to determine a ‘capacitance temperature coefficient’ which may in turn be used as a temperature correction factor.

The capacitance probe was thermally insulated by wrapping the outer electrode and the adjoining pipe with approximately 10 mm thick layer of flexible foamed polyethylene. All temperatures were recorded using standard BS 1843 type K (NiCr/NiAl) thermocouples. These were glued to the electrode surfaces (at approximately half way along their lengths) using small quantities o f (<0.1 g) of super-glue.

Figure 6.32 shows the variation o f the mean surface temperature, Omean of the inner and outer cylindrical electrodes plotted against heating time, for both transducers T^g and Tj^. The mean surface temperature is defined as :

(6.12)

where Oj„ and Oo^t are the surface temperatures o f the inner and outer electrodes respectively.

Chapter 6 Results and Discussion

insulation. The data were obtained using air at 100 °C flowing at approximately 500 1/min through the capacitance probe.

Figure 6.33 on the other hand shows the corresponding variation o f the baseline capacitance, Cp^ir, with time. This variation is expressed as:

^^Pair~ I^Pair(t) ” ^Pair(t=0) I (6.13) where :

Cpair(t=o) = baseline capacitance at time, t = 0 at the reference mean electrode reference temperature, 0^= 26±1 °C.

Cpair(t) = capacitance at time, t at the measured mean electrode temperature 0.

A comparison o f figures 6.32 and 6.33 shows that, the variation o f capacitance with time follows similar trends to that o f temperature/time profiles.

Figure 6.34 shows the variation of, ACp^i, against the mean electrode temperature, 0mean- The data have been extracted from figures 6.32 and 6.33. The gradient, Tq for the fitting line which is equal to 0.0019 pF/°C represents the rate o f increase in, ACp^j, with respect to mean electrode temperature.

Figure 6.35 shows the mean electrode surface temperature profiles vs time for transducers T^g and Tjc with and without external insulation during a cooling cycle. In this case, measurements were recorded upon the switching off o f hot air flowing through the capacitance probes. Figure 6.36 shows the corresponding variation o f the baseline capacitance, ACp^jr (with reference mean electrode surface temperature 0^ = 26±1 °C) with time. Finally, in figure 6.37, ACp^j^ is plotted against, 0^^^^ by extracting the data from figures 6.35 and 6.36. It is clear that, the decrease in the baseline capacitance is linearly proportional to decrease in the transducer mean temperature. It is noteworthy that the rate o f change in, ACpair with respect to temperature during the cooling cycle is equal to that for the heating tests (0.0019 pF/°C).

Chapter 6 Results and Discussion 100 u o i i 2 E <x> é s 2 a S u c2 ■ A □ B AC AD 8 12 0 2 4 6 10 Time (min)

Figure 6.32. The variation of electrode mean surface temperature, ©mean with elapsed time during heating cycle for two different inter-electrode separation distances. De with and without thermal insulation . Curve A; De = 0.72 cm (insulated) ; Curve B: De = 0.72 cm (non-insulated); Curve C: De = 0.875 cm (insulated) ; Curve D: De = 0.875 cm (non-insulated).

Transducer T,; Air Relative Humidity : 9%; Flow air temperature: 100 °C; Voltage: 1 Volt; Frequency: 100 kHz.

Chapter 6 Results and Discussion 0.16 I a u I ■ AA 0.08 -- a U II ■A □ B AC A D 8 0 2 4 6 T im e (m in )

F ig u re 6.33. The variation o f the ACpair w ith elapsed time during heating cycle for tw o different inter-electrode separation distances. De w ith and w ithout therm al insulation . Curve A: De = 0.72 cm (insulated); C urve B: D e= 0.72 cm (non-insulated); C urve C: De = 0.875 cm (insulated); C urve D: De = 0.875 cm (non-insulated).

Transducer T ,; Air Relative H um idity : 9% ; Flow air tem perature: 100 °C ; V oltage: 1 V olt; Frequency: 100 kHz.