Effects of thermal buoyancy on the dynamics of a rising or falling sphere

This study investigates the effects of thermal buoyancy on the ascent or descent dynamics and path instabilities of a finite-size sphere through direct numerical simulations with the immersed boundary method. By parametrically varying the density ratio $(\rho _r)$ , Richardson number $({\textit{Ri}})$ and Galileo number $(\textit{Ga})$ , four distinct motion regimes are identified: stable vertical, zigzagging, spiralling and chaotic regimes. These regimes emerge from the competition between particle inertial, gravitational forces and fluid thermal-buoyant forces. Compared with isothermal cases, particles with positive Richardson numbers exhibit accelerated motion due to thermal buoyancy. The critical Reynolds numbers ${\textit{Re}}_{p,cr}$ for their path instability are significantly reduced by amplifying wake recirculation zones and triggering vortex shedding. This destabilization mechanism is markedly more pronounced for light particles $(\rho _r \lt 1)$ than heavy particles $(\rho _r \gt 1)$ . The present results reveal that the dynamics of heated light particles $(\rho _r=0.5, {\textit{Ri}}\gt 0)$ are governed by the codependent interplay of thermal-buoyancy intensity ( ${\textit{Ri}}$ ) and gravitational force ( ${\textit{Ga}}$ ), which collectively dictate velocity modulation and path instability patterns. Notably, thermal buoyancy elevates particle Reynolds numbers $({\textit{Re}}_p)$ while could reduce Nusselt numbers, arising from competing mechanisms between intensified convective transport and impaired conductive heat transfer – particularly pronounced for low ${\textit{Ga}}$ particles. These findings bridge the gap between fundamental fluid mechanics and thermal engineering, offering insights to optimize thermal management in particle-laden flows systems, such as industrial heat exchangers and fluidized bed reactors, where thermohydrodynamic coupling effect plays a key role in the performance.