Experiment model
The schematic of a copper block designed as a roof model is presented in figure 1(a), with 60 mm length, 60 mm width and 23 mm height. In this block, 3 mm measuring from the top is the model as a roof with aspect ratio 0.1 where the characteristic length is half width of the roof, 20 mm remaining is applied to heat the copper block uniformly. As shown in figure 1(b), a stand made of thermoplastic polyester (polylactide; PLA) is used to support the copper block. A proportional–integral–derivative (PID) control system comprised of a Peltier module, fins, and a cooling fan (turned off during a measurement), is placed underneath the copper block to heat and regulate its temperature during the experiment. To reduce the uncontrolled perturbation from the ventilation system in the experimental room, the cover shown in figure 1(c) is placed above the copper block and its lateral walls have two empty holes to allow the passage of the test beam (see details of PSI in [15], a similar cover was also used in [8]). For this reason, an uncontrolled disturbing flow will still come into the cover along the horizontal direction. Multiple thermocouples are also fixed above the copper block to monitor the temperature time series at geometrically symmetric locations.
Digital interferometry
A previously developed temporal phase-shifting interferometry technique was implemented here to investigate natural convection (see [15] for details). The laser beam first passes through a neutral-density (ND) filter to adjust the beam intensity while a polarising beam splitter (PBS) divides the attenuated laser beam into a test beam and a reference beam. The beam passes through a refractive-index field caused by the non-isothermal flow rising from the roof model. Then, the ‘undisturbed’ reference beam wavefront and deformed test beam wavefront are merged by a second PBS. The beams polarisation is changed from linear to circular polarisations by using a quarter-wave plate, and finally the light is filtered by a linear polariser at controlled angles before the interferogram is recorded by a CMOS camera. These interferograms represent the average temperature along the optical path. To obtain a temperature field with high spatial resolution, a three-bucket phase-shifting equation is used to obtain the phase-shifted data, which is unwrapped by an image processing program. Note that an isothermal background image (before heating) is needed [15].
To acquire the temperature field from wrapped phase-shifting images, a two boundary condition method is used [10]. First, we select the layers of the phase-shifted data in both non-isothermal (natural convection) and background phase-shifted data shown in figures 2(a) and (b), respectively. Next, these phase-shifted data are unwrapped to produce the phase maps shown in figures 2(c) and (d). Then, the isothermal unwrapped data will be subtracted with background unwrapped data to obtain the phase map in figure 2(e), which is produced by the temperature field (without major optical aberrations). Finally, we use the two boundary condition method to determine the brightest pixel as maximum temperature (heating temperature) and the darkest pixel as minimum temperature (ambient temperature) in experiment, and the actual temperature field is plotted in figure 2(f).
Experiment conditions
In the experiments, the temperature difference between the copper block and ambient air ranged from 5 K to 30 K. The flow structures on Y–Z and X–Y planes (see coordinates in figure 1(a)) are presented together with the temperature time series on three points along a Z direction. The primary nondimensional physical parameters is the Rayleigh number Ra [10], defined in equation (1) as:
![](https://myfiles.space/user_files/58854_b38fc7f3db2c487f/58854_custom_files/img1627055109.png)
the characteristic length l is half width of copper block and temperature difference ΔT is the difference between heating copper block and ambient air. When the experiment results are compared with numerical simulation results in Table 1, nondimensional temperature is used, defined in equation (2):
![](https://myfiles.space/user_files/58854_b38fc7f3db2c487f/58854_custom_files/img1627055132.png)
where Tm means the temperature monitored by thermocouples and T0 means the temperature of ambient air.