Flow bifurcation routes to chaos of thermocapillary convection for low Prandtl number fluid in shallow annular pool with surface heat dissipation

In order to understand clearly the transition characteristics of thermocapillary convection of low Prandtl number fluid in shallow annular pool with surface heat dissipation, some bifurcation routes to chaos of thermocapillary convection have been numerically investigated by using the finite volume method in this paper. The annular pool was filled with the low Prandtl (Pr) number fluid of Pr = 0.011. The range of Biot number is from 0 to 1. Results indicate that the flow bifurcation route of thermocapillary convection depends intensively on surface heat dissipation. When surface heat dissipation is smaller, with the increase of Marangoni number the flow bifurcation sequence of thermocapillary convection is two-dimensional axisymmetric steady flow → three-dimensional steady flow → coexisting hydrothermal waves and radial moving waves → radial moving waves → chaos. When surface heat dissipation is larger, the bifurcation sequence becomes simple as two-dimensional axisymmetric steady flow → hydrothermal waves → chaos. Furthermore, every bifurcation of thermocapillary convection is always accompanied by the variations of the wave number and the oscillatory frequency. Furthermore, the temperature fluctuation amplitude on the free surface increases gradually with the increase of Marangoni number.