The Betz manometer minor divisions are 2 Pa, which allows readings to an accuracy of ± 0.5 Pa. For some measurements, a Betz with divisions of 1 Pa was available. Comparison between all of the calibration curves (a time-span of more than a year) for the 0 – 2500 Pa Endress + Hauser pressure transducers, which give a voltage output sensitive to ambient temperature, shows a standard deviation of approximately 0.5 Pa at a pressure of 10 Pa increasing linearly to 6 Pa at the upper limit, 2500 Pa. The Foxboro transducer was more inaccurate, with a standard deviation of 4 Pa at 10 Pa, increasing roughly linearly to 21 Pa at 5000 Pa, the maximum pressure at which measurements were taken.
New calibration curves were obtained at regular intervals throughout the testing program, so the maximum error should be less than 1 Pa.
5.6.2 Particle and packing characteristics
The standard deviation of the test section dimension measurements varies between 0 – 3 mm for transverse dimensions, depending on whether or not a wall lining was used, and 0 – 1 mm for the flow length. The standard deviation of the cylinder and cube dimensions is less than 0.2 mm. That of the spheres is less than 0.3 mm. The value of ΣVp/ΣAp calculated from the ellipsoid approximation of the
acorns is about 3 % lower than that obtained from a sample three dimensional (3D) scan. The total rock volume from the 3D scans is on average within 3 % of that measured by volume displacement in water. The scanner is specified to measure to within 0.2 – 0.3 mm for the range in which the particles were measured. However, the post-scan processing is probably only accurate to the order of 1 mm as a consequence of trimming edges and aligning multiple scans.
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The influence of the grate at the entrance and exit of the low temperature test section was estimated by measuring the pressure drop over the empty test section. The pressure drop over the empty test section was negligible (< 0.1 – 1 %) in comparison to that measured with packing at any given mass flow.
5.6.3 Test facility measurement: overall uncertainty
The low temperature wind tunnel measurement system is capable of measuring the flow rate to within 2 % in the range for which the equations of Kröger (2004) are valid. The tunnel was checked for leaks by blocking the inlet and turning the fan on while measuring the flow rate. Leakage was negligible relative to the pressure drop and mass flow characteristics at which the tests were performed. Sample plots showing the overall uncertainty of fda (due to error propagation) are
given in Appendix E. The shown uncertainties without the use of a wall liner are ± 10 – 15 % for most of the measurements. At low flow rates and pressure drops near the limitations of the measurement capabilities, the uncertainty exceeds 20 % and in extreme cases 30 %. The calculated uncertainty for the acorns was an exception, ranging from 20 – 30 % in the high flow region and exceeding 40 % in the low flow region. This was predominantly caused by the large uncertainty of the void fraction.
The near-wall temperature at the outlet was consistently lower than the temperature nearer the centre of the duct, which indicated the presence of thermal losses. Thermocouples near the walls which were more than 2 °C lower than the average of the other thermocouples at steady state were excluded from the average outlet temperature. A minimum of fourteen thermocouples were used in calculating the average to ensure that the temperature was representative of the cross-section. Bare thermocouple junctions were used at the inlet to the bed, as the thermal inertia of 3 mm diameter probes caused them to lag the temperature by 1 – 3 minutes at the low mass flow rates at which the tests were conducted.
The high temperature facility was checked for leaks by blocking the outlet pipe and pressurizing it from the fan to the outlet valve. There was a leak through the fan axle (1 – 2 % of the total mass flow), which was measured as a function of fan outlet pressure and used to correct the flow rate. The remainder of the system had a loss of less than one percent. With the fan loss and diesel fuel combustion addition to the mass flow taken into account, the bellmouth and orifice plate mass flow rates differed during charging and discharging on average by 1 %, provided that the valve stems were sealed each time the valve settings were changed.
The difference in mass flow rate between the orifice plate and bellmouth was 2.8 % during charging for the first thermal test of those presented (250 °C – Figure 73). This difference was thought to be caused by leakage along the valve stems. For subsequent tests, the valve stems were resealed with tape each time they were used.
73 5.6.4 E-NTU numerical method
Timesteps of less than 1 s and segment lengths (Δx) of less than 20 mm were found sufficient for the convergence of the predicted temperature profiles for the charge-discharge tests.
To ensure that energy was conserved by the E-NTU method, the incremental energy transferred from/to the air stream and the particles was summed and compared with analytical values calculated by integrating the specific heat capacity curve for the rock (Eq. (78)) and air (from Incropera et al., 2007) as a function of temperature. For the highest temperature test (530 °C) the difference between the maximum and minimum of these values was less than 0.05 % (5×10 - 4) of the total energy transferred (timesteps of 1 s and Δx = 10 mm).
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6 Experimental results: pressure drop and heat
transfer
This chapter presents the isothermal friction factors calculated from pressure drop measurements over packed beds of spheres, cubes, cylinders, ellipsoids and rocks (see Allen et al., 2013a). Temperatures measured during low and high temperature thermal tests are compared with predictions using the E-NTU method and existing heat transfer correlations. Correlations to predict the friction factors and heat transfer coefficients in packed beds of crushed rock are formulated.