General relationships of dimensionless parameters for thermocapillary-buoyancy flow in side-heated annular pools

It is well-known that thermocapillary-buoyancy flow instability can be affected by several dimensionless control parameters. The general relationships among them are helpful for actively controlling flow instability but were not clear. This work reported some experiments in the annular pool with a radius ratio of 0.25, and proposed the general relationships among these dimensionless control parameters, especially for the critical Marangoni number of the flow destabilization and the dimensionless oscillatory frequency of pulsating pattern. Combined with previous studies, these general relationships are achieved within no more than 15% relative deviations, whose applicability is for the thermocapillary-buoyancy flow of medium Prandtl number fluids in side-heated annular pools. Based on the experimental findings, we can confirm that the flow destabilization can be suppressed by buoyancy. The steady multicellular flow appears before flow destabilization. When the flow is destabilized, the pulsating pattern first appears, and then a superimposition of the pulsating pattern and the flower-like wave.