The effect of Rayleigh number on the temporal variation of the Nusselt number for buoyancy driven melting in a rectangular LHTES device.

Buoyancy driven melting has been studied experimentally in a rectangular LHTES device of aspect ratio 2 at Rayleigh numbers between Ra=10⁹ and Ra=10¹⁰ at Prandtl numbers 12 and 22. Based on the device geometry and operating Ra, it is hypothesized that if the flow is independent of the plate Reynolds number, three distinct regions should be present in the Nusselt number Nu as it varies with time, and should contain a local minimum and maximum. The highest Nu is expected in a region bounded by dimensionless time τ_a and τ_b. The melted liquid fraction η is expected to increase linearly with time for majority of the melting process, switching to an inverse exponential variation as it approaches unity. This is in contrast to melting at low Ra, where a monotonic decrease in Nu is expected, and the variation of η is expected to be inverse exponential throughout the process. The experimental results show that these local extrema occur at the same dimensionless time τ. The effect of plate Reynolds number on Nu is also explored to identify the minimum required Reynolds number. Time lapse images of the heat exchanger are used to calculate liquid fraction of the PCM. The identification and measurement of phases and calculation of η has been automated using unsupervised machine learning. Self-Organizing Maps (SOM) techniques show better performance than K-Means clustering due to their ability to identify number of clusters with limited user input. The SOM based analysis shows a linear variation of η with dimensionless time for majority of the melting process. The results indicate that although the LHTES device achieves the highest value of Nu between τ_a and τ_b, the rate of latent energy storage does not show such a maximum.