Globe thermometer free convection error potentials

Abstract

For thermal comfort research, globe thermometers have become the de facto tool for mean radiant temperature, t_r, measurement. They provide a quick means to survey the radiant environment in a space with nearly a century of trials to reassure researchers. However, as more complexity is introduced to built environments, we must reassess the accuracy of globe measurements. In particular, corrections for globe readings taking wind into account rely on a forced convection heat transfer coefficient. In this study, we investigate potential errors introduced by buoyancy driven flow, or free convection, induced by radiant forcing of a black globe's surface to a temperature different from the air. We discovered this error in an experimental radiant cooling system with high separation of air to radiant temperature. Empirical simulations and the data collected in a radiant cooling setup together demonstrate the influence of free convection on the instrument's readings. Initial simulation and data show that t_r measurements neglecting free convection when calculating t_r from air temperatures of 2 K above t_r could introduce a mechanism for globe readings to incorrectly track air temperatures. The experimental data constructed to test this hypothesis showed the standard correction readings are 1.94 ± 0.90 °C higher than the ground truth readings for all measurements taken in the experiment. The proposed mixed convection correction is 0.51 ± 1.07 °C higher than the ground truth, and is most accurate at low air speeds, within 0.25 ± 0.60 °C. This implies a potential systematic error in millions of measurements over the past 30 years of thermal comfort research. Future work will be carried out to experimentally validate this framework in a controlled climate chamber environment, examining the tradeoffs between accuracy and precision with globe thermometer measurements.

Figure 1

Comparison between heat lost due to free and forced convection.

Figure 2

(a - left) The remapped domain calculating t_r from t_g and t_a measurements, correcting for free convection. (b-right) The remapped domain calculating t_r from t_g and t_a measurements, correcting for mixed convection for a fixed air speed of 0.3 ms⁻¹.

Figure 3

Datasets showing potential error using black globes to measure t_r. From left to right, top to bottom, datasets were taken on January 18, 28, 23, and 16 of 2019. 10 second time averaged data is shown with translucent dots, and the 5 minute time average is shown with a solid line. Air speed has the largest variability.

Figure 4

The difference in t_r measured by the globe thermometer (standard) and pyrgeometers (ground truth), plotted against air speed.

Figure 5

Datasets showing both free convection and mixed convection corrections for the data shown in Fig. 3, using n = 4 for the mixed convection Nu calculation at a 5 minute time average (Eq. 12). From left to right, top to bottom, datasets were taken on January 18, 28, 23, and 16 of 2019.

Figure 6

Correlations of t_g, t_r from the standard correction, t_r with a mixed convection correction are compared to the ground truth for all data at a 10 second time average (top) and a 5 minute time average interval (bottom).

Figure 7

(a - left) Comparison of the standard and mixed convection corrections for all experimental data during experiments at 10 second and 5 minute time averages and (b - right) data at low air speeds of less than 0.15 ms⁻¹. Red is the mean value, and the shape is the data distribution.

Figure 8

Data from less than 0.3 ms⁻¹ air speed and greater than 4 °C t_a − t_r difference when using the t_r ground truth measurement. Red is the mean value, and the shape is the data distribution.

Figure 9

(a - left) Change in %PPD for the environmental conditions measured with the standard correction, mixed correction, and ground truth. (b - right) The difference ΔQ_rad in Wm⁻² an individual would exchange with an environment measured to have t_r with a globe thermometer corrected with the standard method compared to the ground truth t_r.

Figure 10

Condensation on a globe thermometer, with a cleaned region circled, removing condensation locally.

Figure 11

Membrane-assisted radiant cooling panels avoid both condensation and convection, the ideal environment for testing potential free convection error contributions.

Figure 12

Measuring the mean radiant temperature in the Cold Tube with 6 pyrgeometers arranged orthogonally on a wooden cube alongside 4 black globes with anemometeors, air temperature and humidity sensors. The data from the top globe was used for this paper, as it was physically closest to the pyrgeometer.

Figure 13

Section and plan diagrams of the Cold Tube showing radiant cooling panels and the position of the instrumentation rig.