CATALOGACIÓN DEL ESPACIO

The 1.5 m3 rock bed was heated at a number of inlet temperatures ranging from 150 °C up to 530 °C. The outlet temperature is limited to ≈ 250 °C because of material constraints, so the bed could only be charged to steady state at inlet temperatures below this. Since it was not possible to charge the bed to a uniform temperature above 250 °C, all measurements are compared for the charging cycle. The shown measurements for each layer are an average of the six thermocouples. The air temperature was predicted by means of the Hughes E-NTU method (section 4.4) combined with the simplified heat transfer correlation in Eq. (91). The fluid properties were initially calculated as those of ideal air; however, at the higher temperature tests where the burner was used more extensively and the combustion gases accounted for a higher percentage of the total flow through the bed, the influence of the combustion gases on the air specific heat capacity and density was calculated based on the assumption of ideal gas properties and complete combustion (Moran and Shapiro, 1998; see Appendix G).

It was assumed that radiation heat transfer between the air – combustion gas mixture and the rock was negligible. This is reasonable, based on findings referred

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to by Adebiyi et al. (1998) for tests (0.27 – 0.44 kg/m2s) at temperatures up to 900 °C.

The heat capacity of the stainless steel container walls between the upper and lower thermocouples was included in the E-NTU calculation – it increases the effective specific heat capacity of the rock by 3 – 4 %. The rock heat capacity was calculated from Eq. (78), section 5.4.

The average temperatures for each thermocouple layer in the bed are shown in Figure 72 and Figure 73 for inlet temperatures of 150 °C and 250 °C. The rock specific heat capacity was calculated at the average between the initial and final bed temperature. The stated values of Bi, Repv and G are time-averaged for the

duration of the test. The variation in the inlet temperature in Figure 73 was caused by fan speed and burner inlet temperature alterations during the test.

Figure 72: Comparison of measured and predicted temperature for an average rock specific heat capacity at 100 °C (G ≈ 0.28 kg/m2s; Repv ≈ 605; Biv ≈ 0.31)

Figure 73: Comparison of measured and predicted temperature for an average rock specific heat capacity at 150 °C (G ≈ 0.24 kg/m2s; Repv ≈ 470; Biv ≈ 0.29)

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Figure 73 was the first of the shown tests to be conducted.

Measurements for an inlet temperature of 330 °C are shown in Figure 74. The predicted temperatures nearer the exit of the bed initially diverge from the measurements. The use of an average specific heat capacity means that at low temperatures the rock heat capacity in that region is over-estimated, which results in more energy being stored in the prediction than is actually the case. An additional calculation was performed with variable rock specific heat capacity (Figure 75) which confirms that this is the case, since the divergence is diminished. Zanganeh et al. (2012) have shown numerically that the varying specific heat capacity can significantly affect the temperature profile.

Figure 74: Comparison of measured and predicted temperature for an average rock specific heat capacity at 200 °C (G ≈ 0.26 kg/m2s; Repv ≈ 470; Biv ≈ 0.32)

Figure 75: Comparison of measured and predicted temperature for varying rock specific heat capacity

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A similar comparison is made for an inlet temperature of 450 °C in Figure 76 and Figure 77, and 530 °C in Figure 79 and Figure 80. The divergence nearer the outlet measurements is larger for constant specific heat than was the case for the 330 °C test, which is consistent with the explanation that the divergence is caused by the use of an average specific heat capacity.

Figure 76: Comparison of measured and predicted temperature for an average rock specific heat capacity at 250 °C (G ≈ 0.20 kg/m2s; Repv ≈ 360; Biv ≈ 0.28)

Figure 77: Comparison of measured and predicted temperature for varying rock specific heat capacity

The influence of the combustion gases from the diesel burner on the air specific heat capacity (increase of ≈ 2.5 %) is taken into consideration in Figure 78. It is relatively small, but slightly improves the agreement between the prediction and measurement at the bed outlet.

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Figure 78: Comparison of measured and predicted temperature for varying rock specific heat capacity and influence of combustion gas on air specific heat capacity The measured and predicted temperatures are compared for an inlet temperature up to 530 °C in Figure 79 - Figure 81 for constant heat capacity, varying heat capacity, and the influence of combustion gases, respectively.

Figure 79: Comparison of measured and predicted temperature for an average rock specific heat capacity at 290 °C (G ≈ 0.18 kg/m2s; Repv ≈ 315; Biv ≈ 0.26)

The influence of the combustion gases from the diesel burner on the air specific heat capacity (increase of ≈ 3 %) is shown in Figure 81. Again the effect is relatively small, but it does improve the agreement between the prediction and the measurement. Although no attempt was made to account for the influence of thermal radiation or conduction through the bed, the outlet temperature prediction is within 5 °C of the measured value.

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Figure 80: Comparison of measured and predicted temperature for varying rock specific heat capacity

Figure 81: Comparison of measured and predicted temperature for varying rock specific heat capacity and influence of combustion gas on air specific heat capacity To check that the combustion gases were not influencing the results, the measured temperatures from the discharge cycle of the 250 °C test are compared with the predicted temperatures in Figure 82. This was the highest temperature test where the bed could be heated to a uniform temperature prior to discharging. The agreement is similar to that obtained during charging (see Figure 73), with the exception of the top plenum.

During discharging, the cold air from the walls of the top plenum appeared to sink and form a ‗pool‘ of cooler air above the rock. This caused false low temperature readings in the top plenum in a way similar to the recirculation in the low temperature wind tunnel (section 5.1).

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Figure 82: Comparison of measured and predicted temperature for varying rock specific heat capacity (discharging; G ≈ 0.34 kg/m2s; Repv ≈ 820; Biv ≈ 0.33)

The findings of Zunft et al. (2011) bear on this problem: they constructed an 8.6 MWhth packed bed (7 x 7 x 6 m3) of alumina bricks in an internally insulated steel container. A thermal loss test was conducted on the bed by fully charging it (680 °C) and allowing it to stand stagnant for 24 hrs. The inlet pipe at the top of the bed allowed natural convection effects that resulted in the top layer of the storage suffering a temperature drop of 80 °C in 24 hours. The recommendation to avoid this is the use of valves to close the pipe.

To conclude, the Hughes E-NTU method, with the rock specific heat capacity varying as a function of temperature, predicts the air temperature at the bed outlet to within 5 °C for the charging tests at 400 – 530 °C ( ≈ 0.2 kg/m2s and 300 <Repv

< 400). This is despite the fact that no attempt was made to include the influence of radiation or axial conduction through the bed. The estimated conductivity of the bed from Eq. (61), section 4.3, is 0.3 W/mK. Including radiation, the estimated conductivity from Eq. (62) is a maximum of 1.8 W/mK at 530 °C. Based on the maximum temperature gradient between the top plenum and the next thermocouple layer in the rock (0.18 m below), this would have resulted in a maximum heat flow in that region of less than 1.5 kW. Over the same distance, at the same time, the air flow transferred heat at a rate of 28 kW. The conduction transfer amounts to 5 % or less of the heat transferred by the air flow.

It is an advantage if the Schumann equations and Hughes E-NTU method can be used at high temperatures, as this requires less computational time than more physically detailed models. This is of particular value where charge-discharge cycles must be repeated 10 – 20 times to estimate the steady state operation of the bed.

The time-averaged measured pressure drops for the high temperature tests are displayed in Table 18 and compared with predictions calculated in a similar

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manner to Zanganeh et al. (2012), using the buoyancy correction Eq.(85), and the isothermal curve fit for crushed rock in co/counter-current packing, Eq. (81) from section 6.2. Pressure drop tests under isothermal conditions showed that the two- term correlation in Eq.(81) under-predicted the measured pressure drop by 12 % or less.

The friction factors were calculated for air properties evaluated at the mean of the bed inlet and outlet temperatures, averaged between the start and completion of charging or discharging. The discharging pressure drop for the tests above 250 °C was estimated by using the final predicted charging temperature of the rock as the initial temperature for discharging.

The predicted pressure drop for these thermal tests, corrected for buoyancy, is 30 – 35 % lower than the measured pressure drop. The exception is the 250 °C test, which was the first of the listed tests to be conducted, which suggests that the packing friction factor characteristic may have altered during the thermal tests. The discrepancy does not appear to be related to the non-isothermal nature of the test, because even at a steady state temperature of 150 °C, the error is -27 %. Likewise, at the end of the charging cycle, the 250 °C prediction is 18 % lower than the measured pressure drop.

Table 18: Comparison of time-average measured and predicted pressure drop

Test Δp meas., Pa fv Δp pred., Pa Δp incl. buoyancy, Pa fv Error, % 150 °C ch 107 13.4 69 70 8.8 - 34 150 °C disch 95 9.7 69 67 6.9 - 29 250 °C ch 76 12.3 60 61 10.0 - 18 250 °C disch 93 7.6 84 81 6.7 - 13 340 °C ch 117 14.5 75 78 9.7 - 33 340 °C disch 104 9.7 75 72 6.7 - 32 450 °C ch 90 17.4 49 53 10.2 - 41 450 °C disch 77 9.0 54 50 5.9 - 35 530 °C ch 74 17.2 42 46 10.8 - 37 530 °C disch 59 8.8 46 42 6.3 - 29

An isothermal test after completion of the thermal tests confirmed that the pressure drop characteristics of the bed did change permanently during the thermal tests: Eq.(81) under-predicted the measured pressures under isothermal conditions by approximately 30 % in the same range of Reynolds numbers in which the thermal tests were conducted. This may be a consequence of rock breaking down with thermal expansion and contraction of the bed.

With buoyancy taken into account, the Ergun equation under-predicts the measured pressure drop by 50-60 % (with the exception of the 250 °C test). The isothermal correlation developed in section 6.2 is still a significant improvement.

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7 Packed bed design and cost effectiveness

Before considering the design of a packed bed, it is appropriate to consider the context in which it will be used. A brief overview of gas turbines and steam cycles is therefore given to provide an idea of the flow rates and temperatures supplied to the packed bed and demanded from it. Basic design considerations are given, after which a method for determining the mass flux and optimum particle size and bed length is presented.