Using the method described in Section 6.2 the k-values for each curve have been calculated for each of the configurations using data collected in field. Table 6.1 shows the k-value for each night and the average across all nights for each configuration. The normalised RMSE is also displayed to show how well the average k-value explains the building behaviour.
Table 6.1 Calculated average decay constant results
Configuration 1,
174 Table 6.1 displays the expected similarity between Configuration 1 Test A and Test B, but the average decay constant for Configuration 3 is lower than Configuration 2 which is against expectations. As the uncertainty in the HTC from the co-heating test indicated, these buildings are fairly similar and the small differences in performance may not be detected.
The overlap between the decay constants for Configuration 2 and Configuration 3 may indicate a limitation on this version of the decay method, though the co-heating tests showed similar limitations when analysing these test cells.
All the decay constants estimated provided an NRMSE of less than 10%. This shows that across all nights of the tests these constants give good predictions of the building temperature profile.
Figure 6.7 shows the HTC for each configuration from Section 5.3.4 against the decay constant from Table 6.1.
Figure 6.7 HTC vs decay constant, average decay constant calculated from field data
Figure 6.7 shows good correlation between the decay constant and the HTC for each of the four configurations (R2 > 0.9). This relationship is modelled as a Power function as this fits the data very well and satisfies the logical notion of passing through the origin without
175 artificially supressing any constant. It is expected that if the decay constant is zero, then the building does not lose heat, and therefore should have a HTC of 0 W/K.
6.4.1.1 Uncertainty Analysis
The uncertainty analysis for the Experimental decay method assesses the influence of maximum or minimum temperature differences based on the uncertainty in internal and external temperatures. This follows the same approach as the Differential Sensitivity Analysis used in Section 5.4. Table 6.2 displays the actual and percentage changes in the decay constant due to the uncertainty in internal and external temperature readings.
Table 6.2 Uncertainty in calculated average decay constant
Configuration Decay constant
Change in decay constant % change in decay constant
∆T +0.65 K ∆T -0.65 K ∆T +0.65 K ∆T -0.65 K
1, Test A 0.318 -0.035 0.049 -11.01% 15.41%
1, Test B 0.304 -0.030 0.040 -9.87% 13.16%
2 0.373 -0.044 0.066 -11.80% 17.69%
3 0.368 -0.044 0.080 -11.96% 21.74%
Note: Negative values indicate a decrease in decay constant.
Changes in temperature readings cause significant variation in estimates of the decay constant. Reducing the temperature difference represents the largest risk; Table 6.2 shows an increase in the decay constant of up to 21.74% for Configuration 3. As the differences between the decay constants are small, the large influence of the uncertainty in temperature readings demonstrates a significant limitation of this analysis technique. Figure 6.8 displays the decay constants with the uncertainty represented by the error bars.
176 Figure 6.8 Calculated average decay constant
It is clear from Figure 6.8 that the uncertainty bars overlap, which reduces confidence that this method of analysing the decay constants is sophisticated enough to overcome the uncertainty in the measurements.
Simulated Decay experiments
To further test the application of the average decay constant, the array of models described in Section 4.4.5 have been analysed using this method. The models have been adjusted so that the simulation temperature has been controlled to match the observed temperatures until five minutes after the heater was turned off in the field experiments. As discussed in Section 6.2, this is to align the start times for the decay curve analysis as the blow heater was still radiating enough heat to the air to influence the decay rate. Figure 6.9 shows how the simulated results differ from the field experiments
177 Figure 6.9 HTC vs average decay constant, field and simulated results
Figure 6.9 shows there is a good match observed and simulated data. There is good correlation in the simulated datasets between the decay constant and the HTC. There is a range of HTCs for each decay constant, which is not surprising given the complexity of heat transfer through a building and the relative simplicity of the decay test. It is also not surprising as the test cell’s thermal mass is explicitly altered in the simulations, and this does not have any effect on the steady-state HTC, but does influence the dynamic response represented by the decay constant.
Predicting the HTC from Calculated Average Decay Constants
Using the simulated data as the basis for the model, regression analysis provides the function for predicting HTC from the decay constant as Equation 9
Equation 9 HTC estimate using calculated average decay constant
𝐻𝑇𝐶 = 428.37𝑘1.4637
Applying this function back to the simulated data shows a variation of between +8.06% and – 6.64% between the simulated HTC and the HTC estimated from this function.
If this function is applied to the decay constants calculated from the observed test cell data, it is shown that the variation underestimates the HTC by a maximum of 7.79%, and overestimates by up to 7.96%.
178 If the uncertainty in the decay constant calculation is accounted for, however, the uncertainty in the HTC predicted from the function increases dramatically. Table 6.3 shows the upper and lower estimates of the HTC based on the upper and lower bounds of the decay constant.
Table 6.3 HTC estimates from calculated average decay constant
Estimates from field co-heating test Estimates from decay constant
Configuration HTC HTC range HTC (%
difference)
HTC range
1, Test A 81.34 77.60 – 85.34 80.08 (-1.55%) 67.51 – 98.77 1, Test B 81.31 77.97 – 84.88 74.97 (-7.79%) 64.40 – 89.84
2 93.68 89.99 – 97.41 101.14 (7.96%) 84.17 – 128.38
3 97.91 93.81 – 102.34 99.16 (1.28%) 82.30 – 132.25
The difference on a single HTC estimate for any of the configurations is within 10% of the estimated value from the co-heating test. However, Table 6.3 shows that if the uncertainty in the decay constant is accounted for, then the uncertainty in the HTC estimate could be a range up to 50 W/K. This could underestimate the HTC by up to 20.8%, or overestimate it by up to 37.0%.
This large uncertainty range is linked to the decay constant calculation relying on just two data points: the internal temperature at the start of the decay period, and the internal temperature at the end, four hours later. The change of +/-0.65 K can dramatically change temperature differences at the end of the decay period. Uncertainties in this range are not uncommon – note that the uncertainty on the Bureau of Meteorology air temperatures is +/-0.3 degrees and is calibrated to the current international standard. This makes the method fragile under standard conditions, particularly in low performance houses where temperature differences at the end of the decay period are expected to be closer to zero.
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