Loss of axisymmetry in the mixed convection, assisting flow past a heated sphere

For flows presenting linear instabilities, the laminar regime can be delimited accurately by the onset of the first bifurcation. For an unheated sphere, the primary bifurcation is preceded by a detachment of the boundary layer and a build up of a recirculation zone. In the mixed convection, the convection tends to prevent the boundary layer of the assisting flow from detaching and from a build up a recirculation zone. In this paper, the issue of the correlation between the boundary layer detachment and the loss of axisymmetry in the assisting flow is investigated with a special focus to the Prandtl number corresponding to flows in air (Pr = 0.72). For Richardson numbers up to 0.7, the detachment of the boundary layer (not necessarily a build up of the recirculation zone) is shown to be a precursor sign of a regular primary bifurcation similarly as for the wake of an unheated sphere. At this bifurcation, the flow stays steady but looses its axisymmetry. To assess the Prandtl number effects, the separation of the axisymmetric flow is investigated also in the Pr = 7 parameter plane and for Pr varying between 0.1 and 100 at fixed Reynolds and Richardson number values. The interest of the obtained results is twofold. Firstly, in the investigated parameter sub-domain, clear limits of the physical relevance of axisymmetric computations have been found. Within these limits, accurate values of the drag coefficients and overall Nusselt numbers are given. Secondly, in axisymmetric simulations, the detachment of the boundary layer may be a useful indication of the possible loss of axisymmetry.